ground penetrating radar for the parameterisation of
TRANSCRIPT
Ground Penetrating Radar for the parameterisation of
subsurface hydrological properties
By
Andrew Howe
A thesis submitted to the University of London for the
degree of Doctor of Philosophy
Department of Geography
King’s College London
September 2000
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Plynlimon, Wales.
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Acknowledgements
I would like to thank all those who have contributed towards this thesis. In
particular my supervisor, Dr. Mark Mulligan, who has helped me through all
stages of this project.
Without dedicated field workers this project would not have been completed.
Key members of the team were Rebecca Chadwick, Matthew Charlton and
David Hewitt. Staff at the Institute of Hydrology, Plynlimon, in particular Jim
Hudson, provided invaluable data and expertise. Thanks also to my colleagues
at King’s College London, Elias Symeonakis, Benito Meza Diaz, Jim Griffiths,
Sophia Burke, Sotirios Koukoulas, Mauricio Rinc n-Romero and Matthew
Charlton for numerous ideas and discussions.
Funding for this research was provided by the Natural Environment Research
Council and Sensors & Software Inc., Ontario (NERC CASE studentship
GT4/96/175/EO).
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Abstract
The subsurface plays a fundamental role in catchment hydrological response to
rainfall events, but is often a highly simplified component of hydrological
models due to the lack of high resolution spatial subsurface data required for
model parameterisation and validation. This study uses ground penetrating radar
(GPR) in order to quantify soil thickness and soil moisture in a fully distributed
manner for one of the Plynlimon catchments in Wales, UK. Soil thickness is a
hydrologically important parameter since it exerts a strong control on total
profile moisture storage capacity and soil response to precipitation events, yet
distributed models often apply a single mean depth value to a catchment (Boer
et al., 1993). Similarly the soil moisture of the upper soil layers is crucial in
determining rates of infiltration and plays a critical role in the partitioning of
precipitation into runoff or subsurface flow (Orlandini et al., 1996). Both soil
thickness and soil moisture are known to be highly spatially variable so it is
inappropriate to handle them in a lumped manner for a distributed model.
Soil thickness has been sampled at 32 sites using a PulseEKKO 1000 system
(Sensors & Software Inc.). Results show GPR depth estimates to bedrock
accurate to 0.12m (RMS) compared with auger readings, once the appropriate
interface has been identified using auguring techniques. Analysis of velocity
data from multiple frequency common midpoint surveys (CMP’s) of these same
sites can provide a non-destructive estimate of near surface soil moisture
through use of an empirical equation relating propagation velocity and moisture
content (Topp et al., 1980). GPR is able to measure soil moisture with a RMS
error of 0.04m3/m3 compared with Theta probe and gravimetric techniques for
the same soil space. Using a Geographic Information System (GIS) based
dynamic hydrological model, a 25m grid size digital elevation model and spatial
maps of GPR derived soil thickness, catchment response to precipitation events
is modelled. Validation is carried out at the plot scale using an 18 month time
series of hourly rainfall, overland flow, throughflow and soil moisture and at the
catchment scale using hourly flow data provided by the Institute of Hydrology.
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Evaluation of model output at the catchment scale shows that scenarios which
use distributed soil thickness, derived from GPR, provide an improved
prediction of the catchment hydrograph (RMS error 0.34m3/s), compared to
scenarios in which a lumped parameter for soil thickness is assumed (RMS error
0.29-0.40m3/s).
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Table of Contents
Chapter 1: Overview1.1 Introduction 16
1.2 Current issues in subsurface hydrology 17
1.3 Research objectives 24
Chapter 2: Ground Penetrating Radar2.1 Introduction 26
2.2 GPR theory 28
2.3 GPR survey types 37
2.4 Relation between dielectric constant and hydrologic parameters 40
2.5 Contemporary soil and hydrological research using GPR 43
2.6 Conclusion 48
Chapter 3: Hydrological Modelling and Model Development3.1 Introduction 49
3.2 Hydrological models 51
3.2.1 Empirical models 51
3.2.2 Physically based models 52
3.2.3 Lumped vs. distributed models 52
3.2.4 Hydrological modelling and GIS 54
3.2.5 Why another hydrological model? 55
3.3 PCRaster 57
3.4 Building an integrated hydrological – GIS model 58
3.4.1 Precipitation 60
3.4.2 Evaporation 61
3.4.3 Infiltration 63
3.4.4 Soil moisture 69
3.4.5 Subsurface flow 72
3.4.6 Surface runoff 79
3.5 Conclusion 82
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Chapter 4: Fieldwork4.1 Introduction 83
4.2 The Plynlimon catchments 84
4.2.1 Climate 86
4.2.2 Hydrology 87
4.2.3 Geomorphology and soils 87
4.2.4 Vegetation 89
4.3 Data collection of hydrological parameters 90
4.3.1 Plot-scale collection of hydrological parameters 90
4.3.2 Catchment-scale collection of hydrological parameters 93
4.4 Topography 94
4.4.1 The catchment DEM 95
4.4.2 The hillslope DEM 98
4.5 Site selection using terrain attributes 101
4.5.1 Locating sample sites using topographic indices 105
4.5.2 Site location in the field 106
4.6 GPR survey methodology 107
4.6.1 Reflection survey design 108
4.6.2 Time window 111
4.6.3 Station spacing 111
4.6.4 Sampling interval 113
4.6.5 CMP survey design 114
4.6.6 Stacking 114
4.7 Validation of GPR subsurface data 115
4.7.1 Soil thickness 115
4.7.2 Soil moisture 116
4.7.3 Soil physical properties 117
4.8 Errors 119
4.9 Conclusion 120
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Chapter 5: Soil Thickness Data Analysis5.1 Introduction 121
5.2 Analysis methodology 121
5.2.1 Initial GPR profile display 123
5.2.2 Derivation of subsurface velocities 126
5.2.3 From time domain to depth domain 128
5.2.4 Direct wave masking of shallow reflectors 134
5.2.5 GPR depth measurement errors 135
5.2.6 Theoretical resolution of reflectors 137
5.3 Analysis of individual GPR traces for depth extraction 138
5.3.1 Reflector identification 138
5.3.2 Picking horizon position within a GPR trace 140
5.3.3 Peat soils (Class 1) 140
5.3.4 Simple hillslope soils (Class 2) 147
5.3.5 Complex hillslope soils (Class 3) 151
5.4 Soil thickness measurement using GPR 155
5.5 The spatial variation of soil thickness 161
5.5.1 Plan Curvature 164
5.5.2 Profile Curvature 165
5.5.3 Slope Angle 166
5.5.4 Elevation 168
5.5.5 Upslope Area 169
5.5.6 Wetness Index 170
5.6 Conclusion 176
Chapter 6: Soil Moisture Data Analysis6.1 Introduction 178
6.2 Analysis methodology 178
6.3 Comparing GPR VMC with conventional VMC measurement
techniques 182
6.4 Soil moisture from GPR surveys 186
6.5 Conclusion 191
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Chapter 7: Hydrological Modelling Results7.1 Introduction 192
7.2 The catchment model 192
7.3 Reminder: The effect of soil thickness on modelled discharge 193
7.4 Catchment model results 195
7.4.1 High flows 198
7.4.2 Intermediate and low flows 200
7.4.3 Catchment discharge frequency distributions 202
7.5 The spatial distribution of runoff 207
7.6 Field plot data and model results 213
7.6.1 Overland flow 217
7.6.2 Subsurface flow 224
7.6.3 Plot soil moisture dynamics 229
7.7 Catchment soil moisture dynamics and GPR 233
7.8 Sensitivity Analysis 236
7.9 Conclusion 237
Chapter 8: Conclusions 239
Bibliography 242
Appendix I 251
Appendix II 259
Appendix III 270
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List of symbols
c velocity of light (m/s)f frequency (MHz)ft transition frequency (MHz)K dielectric constantσ material electrical conductivityR reflection coefficientλ wavelength (m)z depth (m)v velocity (m/s)vrms root mean square velocity (m/s)t time (s)θ Volumetric soil moisture content (m3/m3)θsat Saturated volumetric soil moisture content (m3/m3)φ Porosity (m/m)Sw Saturation (m/m)M Cementation indexKsat Soil saturated hydraulic conductivity (m/s)Epot Potential evaporation (mm/hr)E Actual evaporation (mm/hr)RN Net radiation (W/m2)π piγ latent heat of vaporisation (J)ρb bulk density (g/cm3)ρd particle density (g/cm3)b pore interaction termσg geometric standard deviation of particle diameterd g geometric mean of particle diameterQ discharge (m3/s)A Area (m2)H Hydraulic head (m)x length (m)y width (m)β slope angle (degrees)a upslope area (m2)V Voltage (V)a0 theta probe coefficient 1a1 theta probe coefficient 2D total GPR pulse duration (ns)W Wetness index valued Soil thickness (m)
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List of figures
Figure 2.1. Theoretical EM pathways between transmitter and receiver
antennae.
27
Figure 2.2. a) Random orientation of electric dipoles due to thermal motion, b)
Polarization in an electric field, thermal motion active.
30
Figure 2.3. GPR footprint dimensions. 33Figure 2.4. Maximum theoretical resolution for the frequency range 100 – 1200
MHz for 2 dielectric values (plot derived using equation 2.12).
36
Figure 2.5. Reflection Survey - constant offset. 37Figure 2.6. Common midpoint survey (CMP) - variable offset. 38Figure 2.7. Transillumination survey. 39Figure 3.1. Precipitation module.
Figure 3.2. Evaporation module.
6062
Figure 3.3. Theoretical depth – porosity relationship. 65Figure 3.4. Saturated hydraulic conductivity with varying depth of wetting front.
Figure 3.5. Infiltration module.
Figure 3.6. Soil moisture module.
666871
Figure 3.7. Possible drainage paths from a grid cell using the D8 flow algorithm. 73Figure 3.8. Cross-section of two adjacent grid cells with different elevation, soil
thickness and water table depth.
75
Figure 3.9. Subsurface flow module. 78
Figure 3.10. Surface runoff module 81Figure 4.1. Cyff catchment aerial photograph with watershed and stream
network superimposed.
85
Figure 4.2. Total monthly rainfall recorded by the field plot TBR. 86Figure 4.3. A Cyff soil profile at ~500m above sea level. 88Figure 4.4. Runoff - subsurface flow field plot. 92Figure 4.5. 25m grid resolution DEM of the Cyff catchment, overlain with a map
of the logarithm of upslope drainage area for each cell.
97
Figure 4.6. Elevation map with survey points marked in red and location of the
field plot marked in blue.
99
Figure 4.7. 5m grid DEM of the hillslope overlain with LN(upslope area) map and
local drainage direction network (white lines indicate cell drainage paths).
100
Figure 4.8. Frequency distribution of pixel values for the three topographic
indices used to locate potential GPR survey sites.
104
Figure 4.9. Soil texture data from thirty samples. 108Figure 4.10. The impact of reducing profile length on interpreting subsurface
features.
109
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Figure 4.11. The change in coefficient of variation with an increasing number of
auger samples.
110
Figure 4.12. Long-axis footprint size for variable dielectric constant. 112Figure 4.13. Depth – mean porosity relationship derived for the Cyff catchment 118Figure 5.1. Deriving soil thickness from GPR surveys 122Figure 5.2. 900MHz GPR profile (site 20) showing the difference in detail
displayed using a constant gain compared to a SEC gain.
124
Figure 5.3. CMP surveys for site 56 and site 50 using 900MHz antennae. 127Figure 5.4. Initial 10 traces from site 50 plotted using Picker software. Airwave
arrival time marked by red, ground wave arrival by green and first picked reflector
by blue lines.
127
Figure 5.5. Theoretical wave travel path for offset antennae. 130Figure 5.6. Comparison between linear and non-linear depth calculation.
(900MHz, v=0.06m/ns, x=0.17m)
132
Figure 5.7. Application of a constant gain of 2 (a) and a power gain of 2 (b) for
site 40, 0m.
139
Figure 5.8. Dry bulk density measured at 18 sites within the Cyff catchment,
depth measured using a steel ruler.
141
Figure 5.9. GPR traces: - Peat soils. a) 2m GPR profile site 33, b) Raw
amplitude extracted from trace at position 1.00m, c) Amplitude squared at
trace position 1.00m
142
Figure 5.10. Site 37 profile using 450MHz and 900MHz antennae. 145Figure 5.11. Trace amplitude comparison for site 37 bedrock boundary (O/C
horizon) for 900 MHz and 450 MHz GPR trace at the same location.
146
Figure 5.12. GPR profile: - Class 2 hillslope soils. (Site 8, 900MHz antennae,
constant gain 10).
149
Figure 5.13. GPR trace amplitude characteristics for site 8, 900MHz GPR
survey.
150
Figure 5.14. GPR profile: - Class 3 hillslope soils. (Site 54). 152Figure 5.15. Stone fragments located at 0.5 - 0.6m depth. 153Figure 5.16. Radar traces corresponding to the location of four auger points 154Figure 5.17. Soil auger measurements plotted against GPR derived soil
thickness to the B-horizon.
157
Figure 5.18. Soil auger measurements plotted against GPR derived soil
thickness to the C-horizon.
157
Figure 5.19. Average soil auger depth for each site plotted against GPR average
site soil thickness to the B-horizon and C-horizon.
158
Figure 5.20. The variation between physically measured and GPR derived soil
thickness, where physical measurements are considered to be true depth.
159
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Figure 5.21. Plan curvature. 164Figure 5.22. Profile curvature 165Figure 5.23. Slope angle 166
Figure 5.24. The distribution of slope angle less than 10o in the catchment 167
Figure 5.25. Elevation. 168Figure 5.26. Natural logarithm (LN) of Upslope Area. 169Figure 5.27. Wetness Index 170Figure 5.28. Cell soil thickness (m) predicted from the distribution of wetness
index.
172
Figure 5.29. Grid cells ≥ 445,000m2 upslope area 174
Figure 5.30. Cell soil thickness (m) predicted from the distribution of wetness
index with stream network cells assigned a value of 0.01m soil thickness.
175
Figure 6.1. Soil moisture data analysis using CMP data. 179Figure 6.2. VMC – depth relationship with trend lines for site 54. 184Figure 6.3. Soil thickness - VMC relationship for site 48 with strong soil horizon
control on VMC.
185
Figure 6.4. GPR measured moisture and gravimetric moisture. 187Figure 6.5. GPR measured moisture and theta probe moisture. 187Figure 6.6. Frequency distribution of the error between GPR water depth and a)
theta probe measurements, b) gravimetric soil samples.
188
Figure 7.1. Modelled and recorded minimum and maximum catchment
discharge, from table 7.1.
196
Figure 7.2. Outflow hydrograph of measured discharge and GPR variable soil
thickness modelled discharge.
197
Figure 7.3. A period of high flow from 27th February 1999 to 3rd March 1999. 198Figure 7.4. Low flow hydrograph. 201
Figure 7.5. Total catchment discharge (m3/s) histograms (measured and
modelled).
203
Figure 7.6. The spatial distribution of total overland flow for model scenarios of
0.2m and 1.6m soil thickness.
207
Figure 7.7. The spatial distribution of total overland flow and subsurface flow
from the GPR variable soil thickness scenario.
208
Figure 7.8. GPR variable soil thickness model: - cell water depth vs. cell soil
thickness.
211
Figure 7.9. Rainfall, overland flow and throughflow measured at the field plot. 214Figure 7.10. Output variable change (totals) in response to changing plot cell soil
thickness.
216
Figure 7.11. Modelled plot cell overland flow (25m DEM). 217
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Figure 7.12. The changing pattern of the local drainage direction (LDD) network
after decreasing cell size from 25m to 5m.
219
Figure 7.13. Model output values for 5m-grid size. 220Figure 7.14. Modelled plot overland flow data for 5m grid resolution. 221
Figure 7.15. Frequency distributions of plot overland flow (m3/hr). 223
Figure 7.16. Modelled plot cell subsurface flow for three soil depth scenarios. 224Figure 7.17. Mean and maximum subsurface flow for all soil depth scenarios and
measured data.
225
Figure 7.18. Frequency distributions of plot throughflow (m3/hr). 226Figure 7.19. Field plot measured and modelled VMC for distributed soil
thickness scenario.
230
Figure 7.20. GPR measured VMC and variable depth scenario VMC for 29 sites
across the Cyff. The trend line is fitted to a 1:1 relationship, not through data
points.
234
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List of tables
Table 2.1. Typical values of dielectric constant (K), velocity, attenuation and
conductivity for earth materials in the GPR frequency range.
32
Table 2. 2. Ideal resolution (from equation 2.12) and footprint dimensions (from
equation 2.10 & 2.11) at 1m depth for selected operating frequencies.
35
Table 2.3. Potential methods for the collection of soil thickness and soil
moisture data using GPR.
47
Table 4.1. Field plot data record. 91Table 4.2. Data collected by Institute of Hydrology hydrometric network. 93Table 4.3. Terrain attributes of the plot cell for variable DEM grid size. 98Table 4.4. GPS and DEM feature co-ordinates. 106Table 4.5. Soil thickness variation at the field plot. 109Table 4.6. Theta probe calibration values. 116Table 5.1. Reflector depth using linear/non-linear methods of calculation. 131Table 5.2. Calculation of minimum resolution depth using an average velocity
of 0.06m/ns, derived from 29 CMP ground wave velocities.
135
Table 5.3. Positioning error effects on calculated velocities. 136Table 5.4. Soil thickness measurements for site 8 using an auger and 900MHz
GPR survey.
148
Table 5.5. Summary soil thickness data for all sample sites 156Table 5.6. Correlation coefficients of soil thickness variation with respect to
DEM derived terrain attributes.
163
Table 6.1. Site Vrms and VMC values calculated for the first subsurface reflector
after groundwave arrival. Only those sites with validation data are included.
181
Table 6.2. The difference between GPR measured water and water depth
measured using gravimetric and theta probe methods.
186
Table 6.3. Signed-rank test results. 189Table 6.4. CMP measured VMC for sites without validation data. 190Table 7.1. Catchment outflow summary data for all modelled scenarios (1501-
15469 hours)
195
Table 7.2. High flow statistics for event 27th February 1999 to 3rd March 1999. 199Table 7.3. Low and intermediate discharge statistics from 17th May 1999 to
3rdJune 1999.
200
Table 7.4 Kruskal-Wallis results for catchment discharge. 206Table 7.5. Kruskal-Wallis results for field plot runoff. 222Table 7.6. Kruskal-Wallis results for field plot subsurface flow. 228Table 7.7. Modelled and measured VMC summary statistics for the field plot. 232
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Chapter 1: Overview
1.1 Introduction
Soils form an interface between the atmosphere and lithosphere. Soil is notable
for high spatial variability over scales which range from millimetres to
kilometres, a reflection of the variable processes involved in soil formation. Soil
properties have been recognised as one factor in controlling the degree of
surface and subsurface flow which occurs at a point (Mulligan & Thornes, In
Press), although catchment morphometry and the duration and intensity of
precipitation are also important influences.
This thesis is concerned with the measurement of those subsurface soil
properties that have often been a highly simplified component of the analysis of
hydrological response to precipitation. Historically this has been due both to the
lack of detailed subsurface data required for model parameterisation and
validation of results and the complexity of simulating water movement across
three dimensions. Complex models of hydrological response have been
developed, but the lack of high-resolution subsurface data remains a very
current problem. The lack of data concerned with the subsurface extends into
both the temporal and spatial domains. The problem is accentuated by the
complexity of modelling non-linear processes at a range of scales in an
environment characterised by heterogeneity and anisotropy. Quantifying the
response of a hillslope to precipitation events and post-event readjustment is
essential if the physical processes acting at the hillslope scale are to be
modelled. The importance of identifying the contributions of different
hydrological pathways to water status within a catchment has long been
recognised, but an achievable means to sample and validate subsurface
hydrological parameters over a wide area at a grid scale has been lacking.
Ground penetrating radar (GPR) potentially provides a solution as a surface
based non-intrusive tool for sampling subsurface properties.
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1.2 Current issues in subsurface hydrology
The project aims to improve the understanding of subsurface water dynamics,
using GPR to rapidly quantify soil thickness and soil moisture variability across
a hillslope and ultimately an entire catchment. A better understanding of
hydrological response is a necessary requirement for improved flood
forecasting, pollutant movement, soil erosion estimation and water management
purposes. Globally, water is an intensively managed and sensitive resource,
essential to industry, agriculture, domestic users, and to the natural
environment. In the UK the 1990’s have seen an increased interest in water
quality issues, water supply, flood defence and the environmental impact of
over-abstraction from rivers and groundwater. Many of these issues require an
improved understanding of the patterns of water movement and storage in
catchment systems.
Water flow through a river basin is a non-linear process following a complex
three-dimensional geometry (Beven, 1994). In modelling scenarios some
simplification of this geometry is necessary so that in the case of the Systeme
Hydrologique Europeen (SHE) model (Binley & Beven, 1993), subsurface flow
paths are assumed to follow surface elevations and tend to be represented by
one-dimensional vertical unsaturated and two-dimensional saturated flow
components. Alternatively the Institute of Hydrology’s distributed model
(IHDM) uses a coupled two-dimensional saturated-unsaturated component for
simplicity (Beven, 1985). TOPMODEL (Beven et al., 1984) uses a topographic
index to reflect the tendency of water to accumulate at points within the
catchment. Subsurface flow is represented by different water table positions and
the downslope flow rate is exponentially related to local water table position
(Chappell et al., 1993). Without detailed subsurface data hydrological modellers
necessarily make assumptions regarding subsurface storage and hydrological
fluxes. Two common assumptions are that subsurface flow pathways are
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controlled by surface topography and flow rates are proportional to the
hydraulic gradient, derived from local slope (Quinn et al., 1993a).
Hydrological models can be described as either lumped or distributed depending
on the area over which parameters are determined. Lumped models use spatially
averaged parameters usually at the catchment scale in which vegetation type,
soils, topography and precipitation are considered constant over the entire area.
Distributed type models account for catchment heterogeneity by subdividing a
catchment into regular (grid based) or irregular zones (triangulated irregular
networks), each of which possesses a set of parameters reflecting the values
within each cell. Simulation and validation of distributed models requires that
the parameter set for each cell is known. Often these data are unavailable,
particularly for subsurface attributes. Soil thickness exerts a strong control over
moisture storage and soil response to precipitation yet distributed models often
apply a single ‘mean’ value for an entire catchment (Boer et al., 1996). The lack
of data for other fundamental hydrological parameters e.g. hydraulic
conductivity, porosity, depth, texture and bulk density, is largely due to the
prohibitive task of collecting enough samples to adequately characterise
catchment soil characteristics. Sample collection and analysis is a time and
labour intensive process.
The requirement for more data from the vadose zone stems from hydrological
model parameterisation and validation requirements, as well as the need for an
improved conceptual understanding of subsurface water fluxes. The large
number of parameters contained within distributed models can produce the
same output from a number of different model scenarios (Beven, 1993b). Model
evaluation becomes complex in these situations since validation must take place
at the subcatchment scale. If data sets exist for comparison between modelled
and actual results they are often of poor spatial resolution and typically point
measures which require interpolation to produce estimates of properties for an
area or volume of space (Blöschl & Sivapalan, 1995). Blöschl & Sivapalan
identify spatial data as a key requirement that is presently lacking from
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distributed model validation. They suggest that monitoring the spatial patterns
of state variables could be used to evaluate model performance, the most
hydrologically useful pattern being that of soil moisture distribution to depths of
several decimetres. This requires an accurate, non-invasive technique capable of
quick data collection before appreciable changes in variable state occur. GPR is
a possible tool; a surface based remote sensing technique that offers a rapid and
non-destructive method for subsurface data collection, dependent upon a low
level of soil electrical conductivity. Soil and rock conductivity of less than
1mS/m allows penetration in ideal environments to maximum depths of up to
50m with low frequency systems (Davis & Annan, 1989). In pedological and
hydrological applications the depth of interest is often less than a tenth of this
amount, potentially allowing use of higher frequency systems with the benefits
of improved spatial resolution. Shih & Doolitle (1984), Truman et al., (1988),
and Collins et al., (1989) have successfully measured soil thickness using GPR.
A number of papers have recently appeared in the literature concerning the use
of GPR as a tool for soil water content estimation including those by Chanzy et
al., (1996), Greaves et al., (1996), van Overmeeren et al., (1997) and Gilson et
al., (1996). None however are working within a hydrological modelling
framework where detailed moisture data is required for model validation and
calibration.
A detailed overview of GPR techniques relevant to hydrology is given in
Chapter 2. The following section identifies a selection of subsurface
hydrological parameters of interest and reviews some current data collection
methods.
Soil structure is of primary importance to hydrological modelling since structure
exerts strong control over the water retention and transmission characteristics of
a soil. The transmission of water through a profile is controlled by a soil’s
hydraulic conductivity, largely determined by total porosity, pore size
distribution and pore connectivity. It is a non-linear function of volumetric
water content (Rawis et al., 1992) and determines whether infiltration-excess
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flow is generated (Anderson & Burt, 1990). Soil water retention is controlled by
soil texture. The maximum amount of water held in a soil depends on the total
porosity of the soil profile. Alternatively for two identical soils of equally
decreasing porosity with depth and equal initial soil moisture it is the thickness
of soil that controls the maximum amount of water storage. A thinner soil will
saturate first during storm events and becomes a source area for saturation
excess overland flow. Soil thickness and the spatial variation of soil thickness
across the drainage basin can therefore be seen as an important parameter in
hydrological modelling.
The water balance of the upper soil layer is the most dynamic since it forms the
boundary between atmosphere and subsurface. The soil moisture of the upper
layers is critical in determining rates of infiltration and plays a crucial role in the
partitioning of precipitation into either runoff or subsurface flow (Orlandini et
al., 1996). An understanding of subsurface water dynamics is required for
catchment response to be modelled (O’Loughlin, 1990). Anderson and Burt
(1990) note that,
‘soil moisture is a key variable in the hydrological cycle and flow overand within the soil has a strong and direct influence on the timing andmagnitude of the basin hydrograph’.
As yet no hydrological model uses fully distributed soil thickness and moisture
values within its structure. This has been recognised, but the problem remains of
finding effective techniques for measuring these parameters in the field. Soil
moisture is particularly variable owing to the range of processes acting to
redistribute over scales ranging from centimetres to kilometres. Western et al.,
(1999) identify the spatial variability in precipitation and evapotranspiration
along with topography, soils, geology and vegetation as important controls on
moisture patterns.
Measurement of subsurface properties is problematic because accurate
measurement of soil characteristics such as depth, texture and porosity are
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currently only possible through the excavation of trial pits or auguring. Soil
moisture can be measured through direct or indirect methods (Rawis et al.,
1992). Direct measurement of water content is achieved using gravimetric
methods. Indirect measurement requires that a measurable soil property can be
related to moisture content. This approach includes electrical conductance and
resistivity methods, time-domain reflectometry (TDR), radiological methods
(neutron thermalization or gamma attenuation), and remote sensing. The
indirect methods of moisture measurement explored by Rawis et al., (1992) are
termed indirect because soil water is a function of a surrogate variable such as
soil resistivity. Many of these methods of soil moisture derivation require
excavation for access to different profile depths, resulting in the alteration of
subsurface properties. The exception are remote sensing methods which
includes satellite, aerial and surface-based techniques (e.g. GPR).
Soil moisture measurement using remote sensing offers the potential to
repeatedly sample large areas. In the last five years the measurement of soil
moisture using satellite and airborne systems has concentrated on active and
passive microwave methods, although the reflected visible and thermal infrared
wavelengths are areas of on-going research (Pietroniro & Leconte, 2000).
Active microwave methods provide spatial resolutions of tens of metres,
compared with tens of kilometres for passive methods, but the extraction of soil
moisture from radar images is complicated by the equally important effects of
surface roughness and vegetation properties on radar backscatter (Verhoest et
al., 1998).
Due to limitations in sensor spatial resolution, the extraction of soil moisture
data for hillslope scale hydrology would seem to preclude the use of passive
sensors, while active instruments require improved parameterisation of
vegetation and surface roughness effects (Engman & Chauhan, 1995). The issue
of scale is a key factor in the ability of remote sensing to provide soil moisture
data of use to the hydrologist. Van Oevelen (1998) concludes that averaged
estimates of moisture content from remote sensing can be very different from
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field measurements made at the same location due to the presence of
geomorphological features undetected by the sensor. Although active
microwave methods have been applied to extract near-surface soil moisture
data, the sampled depth is typically only 0-5cm (Pietroniro & Leconte, 2000).
Point sampling of soil properties is destructive and samples only a small volume
of any catchment. An alternative methodology uses landscape position and
digital elevation models (DEM’s) to derive terrain attributes (Brubaker et al.,
1994; Moore et al., 1993b respectively). Boer et al (1996) use this method to
map soil thickness classes over three distinct geological types in south-east
Spain, generating accurate results over 40% - 78% of the area. This is only a
viable methodology if a strong identifiable correlation exists between slope
position and soil attributes, which is not always the case. While this method
may be useful for large-scale generalisations of soil classes it is of less use to
the detailed study of hydrological processes. This approach still requires
widespread validation, a problem that cannot easily be overcome without either
an expensive and manually intensive program of data collection or a faster non-
intrusive survey technique capable of collecting the parameters required.
The requirements for, and problems associated with, the current methods of
subsurface data collection have been outlined. Geophysical techniques are one
method of obtaining information about the subterranean environment. These
techniques have the advantage of being non-invasive, but are surface-based
rather than airborne/space platform-based. As a result the power available for
signal transmission into the subsurface (and detection of a reflected signal) is
substantially increased, allowing greater depths of investigation than alternative
remote sensing techniques. The volume sampled by surface based geophysical
instruments falls in intermediate scale between the point measurements typical
of a hydrological investigation and the large areas sampled by aerial platforms.
Advances in computer capabilities and technology have led to the development
of ground penetrating radar systems capable of high-resolution data collection
obtained by interpreting the velocity and attenuation changes in an
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electromagnetic pulse passing through a material. Inversion of velocity and
attenuation changes can be used to produce maps of electrical conductivity and
dielectric permittivity. These values can then be transformed given that valid
relationships exist between hydrogeology and dielectric properties (Knoll &
Knight, 1994).
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1.3 Research Objectives
The aims of this study are to use distributed soil thickness measurements from
GPR as a key parameter to the subsurface component of a distributed
hydrological model. This model will then be validated using GPR derived soil
moisture measurements collected from a sample of field sites. The initial stage
is then to evaluate the capability of GPR to measure these two parameters using
conventional intrusive measurement techniques for validation.
A simple hydrological model has subsequently been designed which uses
spatially distributed soil thickness as one input and grid cell soil moisture as an
output, along with total catchment discharge. Model validation will therefore be
carried out at two scales; the grid scale and the catchment scale. Validation will
be achieved at the catchment scale using a lumped approach, comparing
predicted model discharge with actual recorded discharge over the same time
period. Unlike the current group of physically-based distributed hydrological
models the aim is also to perform an internal state validation at the grid scale by
comparing model predicted soil moisture distribution with field moisture
patterns measured using GPR, conventional moisture measurements and a field
runoff – throughflow plot. In this way it may be possible to confirm or refute
the hypothesis that a model producing a realistic hydrograph response at the
catchment scale may not adequately simulate processes at the scale of the
individual grid cell.
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Specific objectives of this study are:
I. To quantify the variation in soil thickness across the study catchment at
the grid scale using data from GPR field measurements.
II. To use GPR, gravimetric and theta probe (Delta T Instruments,
Cambridge) field measurements to quantify spatial changes in soil
moisture at the grid scale.
III. To develop a simple distributed GIS based hydrological model which
uses soil thickness data obtained from GPR field surveys as an input
parameter to the model.
IV. To validate the predicted spatial pattern of soil moisture generated as
model output using GPR, theta probe (Delta T Instruments, Cambridge)
and field plot measurements of moisture content for sample sites located
across the catchment.
V. To compare measured catchment discharge and field plot measurements
with predicted discharge (catchment scale) and field plot runoff and
subsurface flow (grid scale) for different scenarios of cell soil thickness
over the catchment. Specifically to assess whether variable soil thickness
derived using GPR provides improved model results over model
scenarios in which soil thickness is a lumped parameter.
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Chapter 2: Ground Penetrating Radar
2.1 Introduction
Ground Penetrating Radar (GPR) is a technique of subsurface sampling using
electromagnetic (EM) radiation to construct an image of soil and geological
spatial variation. GPR transmits high frequency pulses (10-1000MHz) into the
ground and records the subsequent reflections. Reflected energy is caused by an
abrupt change in the dielectric properties of a material, and within soils this may
be associated with a change in texture, moisture or conductivity. Reviews of
GPR operation theory and methodology are presented in Annan & Davis
(1977), Daniels et al., (1988), and Davis & Annan (1989).
Subsurface mapping through the reflection of EM waves from dielectric
boundaries was first used to locate ore deposits and water table depth by
Leimbach and Lowy in 1910 (Daniels et al., 1988). Advances in electrical
engineering, GPR system design and an increased understanding of material
properties have improved the range, resolution and performance of radar
systems to the present.
GPR uses the principle of detecting reflections from layers or objects below the
ground to create a subsurface image. The first return is a direct airwave
followed by a ground wave and thereafter returns from subsurface objects
(figure 2.1). The time taken for an emitted signal to travel to and return from the
target provides an estimation of target depth. The magnitude of the reflected
signal gives an indication of target characteristics and the velocity of wave
propagation is dependent on the characteristics of the medium through which
the electromagnetic wave has passed.
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Figure 2.1. Theoretical EM pathways between transmitter and receiver antennae.
The potential advantage of GPR over conventional mapping of the subsurface is
its non-invasive nature; there is no requirement for borehole drilling or soil
augering. These invasive techniques are costly, time consuming and
fundamentally alter the structure of the sampled and adjacent area. GPR surveys
are non-destructive and in theory faster, more economical and provide a better
spatial resolution than conventional methods (Doolittle & Collins, 1995).
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2.2 GPR Theory
The basis of GPR operation is the measurement of reflected electromagnetic
waves from material boundaries. The propagation of electromagnetic waves
through a medium depends on the material properties at a specific frequency.
Wave propagation is dependent on the conductivity, dielectric constant and
magnetic permeability of a material as a response to an applied electric field.
When an electric field is applied, for example an electromagnetic pulse radiated
into a medium as a sine wave function, the electron cloud around each atom
within becomes similarly orientated by the field, forming a dipole. This is
polarization. Non conducting materials which are polarized by applying an
electric field are called dielectrics (Alonso & Finn, 1992). Polarization is a
vector quantity (P) proportional to the strength of the applied electric field
where
(2.1)
P = ε0 χe δ
χe is a measure of atomic response to an electric field, termed material
susceptibility and is dependent on the molecular properties of the material. εO is
the vacuum permittivity (8.85 × 10-12 farads/metre). In fact it is more common
to talk about material properties in terms of their relative permittivity (εR) which
is dimensionless, where
(2.2)
εR = ε / ε0 = 1 + χe
Relative permittivity is also known as dielectric constant (K). This is the
terminology that will be used throughout the remainder of this thesis. Dielectric
constants for selected earth materials at radar frequencies of 50 - 1000 MHz are
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shown in table 2.1.
When an electromagnetic wave propagates through a medium the electric field
generated causes electric charges to move. Two categories of movement exist,
these being conduction and displacement currents. Conduction currents arise
when an electric field causes free charges i.e. electrons, to move within the
material. Moving charges collide with stationary molecules, dissipating energy
as heat into the medium. The electrical conductivity of most minerals is very
low although there are exceptions to this rule e.g. magnetite, carbon, and pyrite.
In the majority of soils however conductivity is controlled by porosity, moisture
content, the concentration of electrolytes, water temperature and the amount and
composition of colloids (McNeill, 1980), rather than mineral type. Materials in
which conduction currents dominate are poor environments for GPR surveys
since electromagnetic fields will disperse (Annan, 1996). Soils with high
conductivity include those with high clay contents and soils with high pore
water conductivity due to high levels of total dissolved solids (TDS). The actual
degree of dissipation depends on the conductivity of the sample.
Displacement currents (polarization) occur when a charge may only move a
constrained distance. Four polarization mechanisms exist (Powers, 1997). These
are electronic polarization, which occurs when circular electron clouds become
elliptical, molecular polarization where charged molecules distort, orientational
polarization, where dipole molecules rotate in the presence of a electronic field,
and interfacial polarization which involves the accumulation of ions at material
interfaces. Applying an electric field causes charges to move to a new stable
equilibrium storing energy in the process. Once the electric field is removed the
charges return to their original equilibrium configuration releasing energy
(Annan, 1997). Water molecules are dipolar and respond by aligning to an
electric field, producing a high dielectric constant at radar frequencies.
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Figure 2.2. a) Random orientation of electric dipoles due to thermal motion, b)Polarization in an electric field, thermal motion active. (Alonso & Finn, 1992).
In a material of constant electrical conductivity (σ) the dominant current
mechanism is determined by signal frequency. As frequency increases
displacement frequencies become the dominant processes over conduction
(Annan, 1997). The point at which the two are equal is termed the transition
frequency (ft) and is calculated by
(2.3)
ft = σ / 2π × K × 8.85×10-12
where K is the material dielectric constant.
The ratio of conduction (Jc) to displacement (Jd) currents at a frequency (f) is
given by the loss tangent
(2.4)
tan δ = Jc/Jd = σ / (2πf × K × 8.85×10-12)
The dielectric constant (K) of any material is a complex number of the form
K = KR + j Ki (2.5)
a) b)
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The real part (KR) describes the propagation of the wave in a medium, the
imaginary component (KI) describes the attenuation losses due to conduction
processes. For non-zero conductivity, which always occurs in field situations,
both components are frequency dependent (Schmugge 1980, Power 1997).
Between 10 - 1000 MHz however a window exists for optimal GPR
performance where the velocity and attenuation of an electromagnetic wave are
relatively independent of frequency (Davis & Annan, 1989, Annan, 1996). At
frequencies below ~10 MHz losses are dispersive. Above approximately 1000
MHz the value of KI increases rapidly as the rotational relaxation of water is
approached at 10 GHz. This relaxation effect is of great importance since
almost all earth materials contain some water. Scattering losses also increase as
wavelengths approach similar magnitudes to particle sizes.
For low loss materials tan δ << 1 and attenuation (α) approximates to
α = 1.69×103 σ / ( KR)1/2 (2.6)
Similarly when tan δ << 1 the velocity of electromagnetic waves can be
approximated by equation 2.7, where c is the plane wave propagation velocity
of electromagnetic radiation in free space (3×108 m/s).
(2.7)
This equation allows conversion from wave velocity to dielectric constants.
In terms of depth (z) to a reflector
(2.8)zv t
=.2
21
R )K(
c=v
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where t is two way travel time.
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Table 2.1. Typical values of dielectric constant (K), velocity, attenuation andconductivity for earth materials in the GPR frequency range. (From: Davis &Annan, 1989).
Material K Velocity (m/ns) Attenuation α (dB/m) Conductivity σ
(mS/m)
Air 1 0.30 0 0
Distilled Water 80 0.033 0.002 0.01
Fresh Water 80 0.033 0.1 0.5
Sea Water 80 0.01 1000 300000
Granite 4-6 0.13 0.01-1 0.01-1
Ice 3-4 0.16 0.01 0.01
Limestone 4-8 0.12 0.4-1 0.5-2
Shales 5-15 0.09 1-100 1-100
Dry Salt 5-6 0.13 0.01-1 0.01-1
Silts 5-30 0.07 1-100 1-100
Clays 5-40 0.06 1-300 2-1000
Dry Sand 3-5 0.15 0.01 0.01
Saturated Sand 20-30 0.06 0.03-0.3 0.1-1
Reflection of an electromagnetic wave occurs at any interface between two
materials with different dielectric values. The reflection coefficient (R) is a
function of the difference in electrical properties between the two materials and
is calculated as
(2.9)
Reflection also depends on the thickness of the layer and on the frequency (and
hence wavelength) of the incident signal. The sign of R depends upon the values
of K1 and K2 with R being negative if the wave travels from a low K to a high K
and positive in the reverse case. This raises the possibility of material
RK KK K
=−
+1 2
1 2
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characterisation from examining the returned signal for coefficient sign. The
power reflection coefficient is R2.
Due to spherical spreading of the electromagnetic wave, signals are returned
from an area beneath the radar rather than a discrete point. The size of this area
or footprint depends on the operating wavelength (λ), depth to reflector (z) and
the dielectric constant of the material (K) through which the signal passes.
Increased survey depth leads to increased footprint size (figure 2.3) since the
wave spreads as an elliptic based cone from the source.
Figure 2.3. GPR footprint dimensions.
Transmitter
xy
z
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Increasing the dielectric constant reduces spread; a water-saturated soil has a
smaller footprint than does the same soil when dry (at equivalent depths).
Higher frequencies also reduce footprint dimensions. The equation for
determining footprint dimensions is given by Annan, (1997) as:
(2.10)
(2.11)
The volume of soil (V) sampled can subsequently be calculated using the
standard mathematical equation for the volume of an elliptical cone,
(2.12)
Antenna frequency and the dielectric properties of the ground determine the
achievable spatial resolution. Resolution in this case is the ability of a system to
distinguish between two signals separated by a small time interval (Davis &
Annan, 1989). For the frequencies used in standard GPR systems (10 – 1000
MHz) this is of the order of centimetres to metres. In all ground radar
applications a trade off exists between penetration depth and resolution. High
frequency, short wavelength antennae have improved resolution but suffer from
increased signal attenuation resulting in shallower investigation depths.
Scattering losses also increase as frequency approaches a similar magnitude to
particle size. For GPR systems the maximum theoretical resolution (z) is one
quarter pulse wavelength (Reynolds, 1997)
xz
K
yx
= +−
=
λ4 1
2
xyzV π31
=
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(2.12)
Where v equals medium velocity and f is the frequency of operation (Hz). Table
2.2 summarises the theoretical resolution and change in footprint dimensions at
three frequencies for a dry (K=4) and saturated sand (K=25).
Table 2. 2. Ideal resolution (from equation 2.12) and footprint dimensions (fromequation 2.10 & 2.11) at 1m depth for selected operating frequencies.
Frequency
(MHz)
Maximum
Resolution
(m) K=4
Maximum
Resolution
(m) K=25
Footprint (m)
Dry Sand (K=4)
x y
Footprint (m) Wet
Sand (K=25)
x y
225 0.17 0.07 0.91 0.45 0.53 0.27450 0.08 0.03 0.75 0.37 0.37 0.19900 0.04 0.02 0.66 0.33 0.28 0.14
For all frequencies in this range that the effect of increasing the water content of
the medium is one of reducing footprint dimensions. The volume returning the
transmitted signal is a dynamic property of the dielectric value of the material.
Increasing soil moisture results in a reduction in the volume of soil contributing
to the returning signal, in effect a ‘tightening’ of the radar beam. Increasing the
dielectric constant of a material also results in a theoretical increase in
resolution.
zvf
=4
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Figure 2.4. Maximum theoretical resolution for the frequency range 100 – 1200MHz for 2 dielectric values (plot derived using equation 2.12).
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
100
200
300
400
500
600
700
800
900
1000
1100
1200
Frequency (MHz)
Max
imum
Res
olut
ion
(m) Res (m) K=4
Res (m) K=25
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2.3 GPR Survey Types
The three standard survey configurations are described. Most commonly used is
the ‘reflection survey’ in which the transmitter and receiver antennae are
located on the ground surface and maintained at a constant offset (figure 2.5).
Variation in dielectric value causes partial reflection of the transmitted pulse
which is subsequently detected and recorded. Moving the system across the
ground to the next survey point delineates the spatial variation in subsurface
features. Reflection surveys enable rapid collection of data and displayed as a
two-dimensional profile from which it is possible to pick out linear and point
reflectors. In reality as discussed previously the zone of response is a volume of
soil, not a single point and therefore targets off centre of the system will
contribute to the returned signal. It is this characteristic of GPR operation that
produces the hyperbolic pattern and allows point reflectors i.e. stones and pipe
cross-sections to be identified. The concept of what constitutes a point reflector
is somewhat arbitrary since it is dependent on the frequency at which the survey
is undertaken.
Figure 2.5. Reflection Survey - constant offset.
Tx Rx
1 2 3 4
GPR surveys describe the variation in soil characteristics with respect to the
time of travel between transmitter and receiver antennae. The depth at which
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reflectors are located is determined by measuring the velocity of the EM pulse
through the material. Two methods of velocity measurement are the ‘common
midpoint survey’ (CMP) and ‘transillumination survey’.
For a CMP survey (figure 2.6) the antennae are initially placed on the ground
surface separated by one stepsize. Each antenna is then moved outwards in
increments of one half the stepsize defined for the survey. Increasing separation
(x) between antennae results in longer travel times (t) and by comparing the
change in antenna separation with the time taken for the pulse to return from
reflectors an estimate of the velocity for each layer can be calculated. The
gradient of reflection events plotted as x2 against t2 provides a measure of wave
velocity. A major assumption of CMP’s is that linear reflecting horizons must
underlie the survey area. If reflectors are inclined significantly from the radar
horizontal plane the time for reflections is not only a function of antenna
spacing but also of the varying depth to the reflector.
Figure 2.6. Common midpoint survey (CMP) - variable offset.
Tx Rx
Transillumination survey schematics are shown in figure 2.7. In this case the
transmitter and receiver antennae are separated by a constant horizontal distance
and moved vertically parallel to one another. Two data collection methods are
possible. A zero offset gather (ZOG) ensures no vertical difference between
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each antenna. Alternatively a multiple offset gather (MOG) requires that one
antenna be fixed while the second moves, producing a more detailed picture
using multiple raypaths. Transillumination has been used for internal imaging of
solid structures e.g. concrete blocks, and near-surface deposits using boreholes
(cross-hole tomography) (Gilson et al., 1996. Eppstein & Dougherty, 1998).
Variations in the propagation velocity between antennae indicates changing
dielectric values which in may indicate related changes in hydrogeological
parameters.
Figure 2.7. Transillumination survey.
Tx
TxRx
Rx
ZOG MOG
Both CMP and tomographic surveys use travel time over a known distance to
provide velocity estimates of the electromagnetic wave. Using equation 2.7
these velocities can be converted to values of dielectric constant. Variations in
velocity and hence dielectric value imply variations in material properties.
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2.4 Relation between dielectric constant and hydrologicparameters
Using GPR to collect soil information requires calculation of dielectric values
which can be related to soil properties, a process known as inversion.
Laboratory investigations have suggested that the most important parameters
controlling the dielectric response of geologic materials are water content,
porosity, clay content and measurement frequency (Knoll & Knight, 1994).
Topp et al (1980) demonstrated that soil water content is the primary control
over soil dielectric value. This is due to the unique atomic structure of water
which results in its high dielectric constant of 80 compared to dielectrics of 3-20
for most minerals. Other factors that have been found to affect dielectric values
include soil salinity and temperature. Salinity has an effect since increasing
water content leads to an increase in the dissolved ions within the water. The
effects of salinity are low at frequencies around 1000 MHz and above, but
increase with decreasing frequency, rising sharply below 25 MHz (Wensink,
1993). Over the range of 1 - 1000 MHz Topp et al (1980) found that the
temperature of liquid water did not exert a significant control on recorded
results, but upon freezing the dielectric constant of water drops from
approximately 80 to 3.
Soil water content is itself a function of available pore space and hence bulk
density. Porosity controls the maximum amount of water held in a soil and is a
factor in determining soil drainage. Schmugge (1980) has shown that textural
composition is also an important consideration, since the velocity and therefore
frequency of the electromagnetic wave is largely controlled by free moisture
held within pores. Below a transition value, water molecules are adsorbed to
soil particles. Response to the electromagnetic wave is limited until molecules
are less strongly held. The amount of water held as adsorbed water is directly
related to particle surface area meaning that clay soils are able to hold a larger
amount of water in this state than sands. The dielectric response of soil is
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therefore not a straightforward measure of total water content, but could provide
a figure of available water content, of use for hydrological modelling and
agricultural purposes.
Investigation into the relation between soil dielectric value and soil properties
has predominantly been carried out using time domain reflectometry (TDR).
This technique involves the insertion of metal transmission lines into the target
environment. The propagation time of an electromagnetic pulse through a
transmission line of known length can be used to calculate velocity and related
to dielectric value using equation 2.7. Two decades of research has identified a
positive relationship between volumetric soil moisture and soil dielectric
constant (Topp et al., 1980; Topp & Davis, 1985; Roth et al., 1992; Whalley,
1993; Weiler et al., 1998).
Determination of soil moisture from dielectric constant has been attempted
using both empirical and theoretical approaches. Topp et al., (1980) derived a
third order polynomial (2.13) using regression analysis based on 18 experiments
using four mineral soils. 93% of the data was within ± 0.025 of measured
volumetric moisture content. Therefore by calculating the velocity of a wave
through a soil layer a corresponding value of K can be derived. This value can
then be substituted into equation 2.13 to provide an estimate of volumetric
moisture content (θ) where
(2.13)
θ = -0.053 + 0.0292K – 0.00055K2 + 0.0000043K3
A more physically based theoretical methodology has been developed using a
mixture modelling approach. Given that soil is a three phase mixture consisting
of mineral grains, air and water, each with very different dielectric values, the
volume fractions of these constituents are important in determining the effective
dielectric constant of a soil unit. Knoll (1996) reviews a selection including the
semi-empirical complex refractive index method (CRIM) and the effective
medium approach of the Bruggeman-Hanai-Sen (BHS) model. Both the CRIM
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and BHS are two or three phase mixing formulae and can therefore be used to
represent the volumes of air, water and soil components with their associated
dielectric values. The BHS model also includes a micro geometry power term to
account for grain shape (Greaves et al., 1996).
CRIM (three phase)
(2.14)
At high frequencies where tan δ << 1 the BHS (two phase) model results in the
implicit expression (equation 2.15), which can only be solved explicitly by
assuming that the sample is totally saturated (Greaves et al., 1996).
(2.15)
Where Ks, Kw, Kg, Ka are the dielectric constants of the sample, water, mineral
grains and air respectively, Sw is sample saturation (0-1) and φ is sample
porosity. m (equation 2.15) is a cementation index ranging from 1.5 for
spherically grained unconsolidated sands to 2.0 for consolidated sandstones
with oblate grains (Greaves et al., 1996).
Three phase versions of CRIM and BHS require that the two unknowns,
saturation and porosity of a sample are solved from a value of K. There is
however no unique mathematical solution to this problem. The two-phase
variants assume total sample saturation i.e. Sw equals unity, allowing an
estimation of porosity below the water table. Extrapolating this value of
porosity to unconsolidated heterogeneous sediments which form the soil mantle
is likely to produce erroneous estimates of water content. Therefore despite the
K = S K K S Ks w w g w a φ φ φ+ − + −( ) ( )1 1
K K
KKKK
g
w
g
s
s wm
m
=−
−
φ1
1
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disadvantages, the Topp equation remains the simplest method for estimating
soil water content from velocity changes derived from GPR data.
2.5 Contemporary soil and hydrological research using GPR
Shallow sub-surface investigations suffer from a number of complicating
factors. The near surface environment is the most complex in electromagnetic
terms and exhibits great heterogeneity over short distances. The shallow depths
common to soil investigation result in short travel times between reflections
causing problems in the resolution of different layers. At short time windows
the direct wave dominates the received image. The small separation transmitter-
receiver offset geometry commonly used for reflection surveys can cause air
and ground wave interference. Soils are an electrically lossy environment and
the presence of conductive clays limits the use of radar as a survey tool.
Despite these difficulties the potential application of GPR as an aid to soil
survey has been recognised. Its main advantages over conventional survey
techniques are an increase in sampling rate and the ability to produce
continuous real time profiles rather than point observations. High quality data
can be collected over a large area without the need for excavation. Excavation is
time consuming, labour intensive and infeasible over large areas. It destroys the
subsurface at the site and will result in changes in hydrological flow pathways
as a result of changing soil bulk density. To date field investigations have been
concerned with investigating depth to bedrock (Collins et al., 1989) and the
thickness of soil horizons (Shih & Doolittle, 1984). Truman et al., (1988)
successfully used GPR to image depth and lateral extent of argillic horizons and
depth to water table in a course textured coastal soil. Collins et al., (1989)
working in an upland area of New England found that 120 MHz radar profiles
gave a better estimation of soil overburden than auguring. Test pits dug for
validation found that 87% of radar derived depths were within 10cm of actual
depth compared to which only 7% of auger data was within 15cm. Collins
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proposed that the auger failed to penetrate fully due to the coarse texture and
varying size distribution of the underlying till deposits.
Characterisation of subsurface heterogeneity using GPR has been attempted by
Rea & Knight (1998) using radar profiles and geostatistical analysis of a
digitized photograph of a cliff face. The cliff consisted of two alternating
lithologies, coarse sands interlaced with silts and fine clay. Visual comparison
between the GPR profile and the photograph showed good agreement in
bedding structure. Geostatistical analysis of wave amplitude after correction for
spreading losses to create a semivariogram for radar data compared well with
the semivariogram produced for the photograph. They concluded that GPR was
able to image the spatial distribution of these lithologies.
From a hydrological viewpoint GPR has primarily been used as an experimental
tool for water table detection and subsurface contaminant mapping and
monitoring. The latter has concentrated on detection of dense non-aqueous
phase liquids (DNAPL’s) and light non-aqueous phase liquids (LNAPL’s).
DNAPL’s are solvents and degreasers, which form a major source of subsurface
contaminants in the industrial world. DNAPL’s are highly mobile being low
viscosity, high density liquids which are not affected by groundwater movement
(Annan et al., 1991b, Brewster et al., 1992). LNAPL’s include all hydrocarbons
and are a second widespread contaminant type. Being less dense than water
LNAPL’s accumulate at the water table surface and impermeable horizons,
releasing toxins into the water supply (Redman et al., 1994).
Many hydrological studies have been undertaken from a theoretical viewpoint.
One approach is to create a model of a potential target or interface response.
Often this is of primary importance prior to field application to see if radar is an
applicable detection method. Assessment of the viability of radar use depends
on the frequency used, target dimensions, depth to target and the dielectric
properties of both target and host material. The general model for assessing
radar suitability is described by the radar range equation (Annan & Davis,
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1977). Theoretical assessment of radar for water table detection is outlined in
Annan et al., (1991a) while theoretical detection of preferential flow pathways
within sands is presented by Kung & Lu (1993). Beres and Haeni (1991) use
GPR to investigate depth to the water table and delineate shallow drift deposits.
More recently, studies using GPR to quantify soil moisture in the vadose zone
have been undertaken.
Soil water content measurement using geophysical techniques depends on
finding a measurable parameter that accurately represents the amount of
moisture within a soil profile. Du and Rummel (1994) and Greaves et al.,
(1996) use the Topp equation to transform dielectric constants calculated from
velocity measurements into estimates of subsurface water content. Neither of
these studies validated their results with gravimetric or TDR measurements and
therefore only succeeded in producing profiles of relative soil water contents.
As discussed a common non-invasive method of deriving wave velocity is via a
common midpoint survey (CMP). Greaves et al., (1996) used multi-offset
CMP’s to construct an image of subsurface velocity variations that was then
converted to a profile of moisture distribution. Du and Rummel (1994) use wide
angle reflection and refraction to initially identify the ground wave and set the
optimum antenna separation. The ground wave is the signal that travels from
transmitter to receiver through the ground without reflecting. At small antennae
offsets the air wave and ground wave arrive within a time interval which can be
below the spatial resolution of the system which results in interference patterns
between wave fronts. This precludes the use of the direct wave amplitude as a
measure of moisture content since it is dominated by antenna-ground coupling
effects. Increasing the antenna separation allows separate discrimination of both
return signals since the speed of an electromagnetic wave in air is 0.3m/ns
compared to a typical soil velocity of 0.06-0.15m/ns depending on material
dielectric value.
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Van Overmeeren et al., (1997) use conventional CMP’s and an alternative
method of deriving wave velocities. In this case the two way travel time of a
wave to reflector is correlated with physical measurements of depth taken by
soil cores and piezometric detection of the water table surface. Van Overmeeren
looked at two sites in the Netherlands with sandy soils over a period of 13
months and compared soil water content in the vadose zone with capacitance
probe measurements taken at the same times in access tubes at each site. Lateral
and seasonal variations in moisture content included in the paper as graphs gave
similar results for both methods although no statistical comparison between data
sets is included.
A comparison between TDR and GPR measurements of soil moisture was
carried out by Weiler et al., (1998). 52 soil samples with corresponding TDR
dielectric values were used to derive a site-specific calibration for soil moisture
and TDR readings. Subsequently the relationship was found to be in good
agreement with equation 2.13, with a maximum difference of 0.03m3/m3 VMC
for a moisture content of 0.4m3/m3. Divergence between VMC is most likely
because Weiler et al. use a linear regression based equation whereas equation
2.13 is a third-order polynomial. GPR measured water content was found to
consistently under predict by on average 0.05m3/m3 compared with that
measured using TDR. Possible reasons for this include the difference in
frequency range between the two methods, zero time shift of GPR and,
mentioned briefly, the increased sample volume of GPR.
A mixture modelling approach to define intrinsic permeability and saturation
characteristics has been used by Hubbard et al., (1997) for estimation of these
parameters for two facies. Cross well tomography was used to build up a picture
of subsurface dielectric constant values. For each stratigraphy each dielectric
constant value produced two possible values of permeability and saturation.
Maximum likelihood technique was used to select the most probable value for
each location..
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An alternative method for deriving dielectric constant from GPR data is
described by Chanzy et al., (1996). They use ground wave amplitude and
reflection coefficient rather than velocity changes to calculate soil moisture in
ground and airborne modes. However while the results look promising the exact
effect of antenna - ground coupling, wave pattern interference, antenna
orientation and site characteristics on ground wave amplitude is poorly
understood. Data gathered in the air are also a function of look angle, surface
roughness and vegetation interaction. This theme requires considerably more
research and is beyond the scope of this project.
Table 2.3. Potential methods for the collection of soil thickness and soil moisturedata using GPR.
Parameter Method Authors ofprevious
work
Advantages Dis-advantages
Assumptions
Depth tobedrock
1.ReflectionSurvey
Shih &Doolittle,(1984),Truman et al.,(1988), Collins et al.,(1989)
Non intrusive,fast method ofdata collection.
How canreflections bepositivelyidentified asbedrock?
Low loss media,reliant on theaccuratederivation ofsubsurfacevelocities.
Soilmoisture
1. Velocityfrom Trans-illumination
2. Velocityfrom CMPsurvey
3.Amplitudeanalysisfromreflectionsurvey/CMP survey
Hubbard etal., (1998), Eppstein etal., (1998)
Du & Rummel(1994)Greaves et al.,(1996), VanOvermeerenet al., (1997), Weiler et al.,(1998).
Chanzy et al.,(1996)
Detailed,multiple raypathProven K – vrelationship.
Non intrusive,fast.CMP requiredfor reflectionsurvey anyway.Proven K – vrelationship.
Easy to extractamplitude datafrom reflectionsurveys.
Intrusive,requires 2adjacentboreholes.
Low loss media.
Near horizontalreflectors.
Uniquerelationship existsbetween K andamplitude.
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2.6 Conclusion
This chapter defines fundamental concepts of GPR, introduces methods of
deriving subsurface hydrological parameters from dielectric values, and
provides a review of current research relevant to this thesis, in particular
contemporary GPR methods for measurement of soil thickness and soil
moisture.
Analysis of the current literature shows that reflection profiling is the standard
technique used to derive the depth of soil overlying bedrock. Soil moisture
estimation is most feasible using CMP data, while transillumination is an
intrusive technique in the field scenario, requiring borehole construction. The
use of signal amplitude data for moisture estimation is at an early stage of
investigation and optimally researched in a controlled environment. Therefore
reflection surveys and CMP surveys will be used in this thesis to define soil
thickness and moisture respectively.
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Chapter 3: Hydrological Modelling and Model Development
3.1 Introduction
Hydrological models are required both as decision making tools for applied
water resource problems and as tools to improve our understanding of the
interaction between different components of the hydrological cycle.
Hydrological models can be broadly grouped into predictive or investigative
types (Blöschl & Sivapalan, 1995). The latter tend to have greater data
requirements and a more complex structure but provide some insight into
interactions between subsystems. Predictive models are generally concerned
with the answers to specific questions rather than specific system
characteristics. In reality some degree of overlap between these types exists in
the majority of hydrological models. Ultimately investigative models should be
able to make some predictions within appropriate error margins concerning
specific system response to input for a range of system states. Increasingly
hydrological models are required to predict both total outputs and the internal
spatial distribution of variables such as soil moisture, water quality, pollutant
mapping and erosion (Quinn et al., 1993; Chappell & Ternan, 1993.
The trend in hydrological modelling has been one of increasing complexity both
in terms of the equations used to describe hydrological processes and the
number of processes considered to be acting across a catchment. At present the
primary aims of catchment modelling can be summarised as; 1) Prediction of
streamflow response to storm events. 2) Determination of the nature of the
processes creating surface and subsurface flow in the catchment and the spatial
distribution of these processes (Quinn et al., 1995, Orlandini et al., 1996).
Advances in computer power and availability in recent decades has resulted in a
marked increase in both the number of hydrological models and the complexity
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of the numerical methods used to simulate hydrological processes. Simulation
of coupled saturated and unsaturated three-dimensional flow is now possible
using approximate numerical solutions by computer, which can solve for
millions of nodes over millions of timesteps. Numerous models are now
available which simulate water movement over and through the landscape at a
variety of spatio-temporal scales and at various levels of complexity.
Unfortunately, creating increasingly sophisticated mathematical models is no
guarantee of improved model performance. Many authors have suggested that
while the development of complex mathematical models has been beneficial
from a theoretical viewpoint, the collection of field data to validate these
models has been lacking (Anderson & Burt, 1990; Blöschl & Sivapalan, 1995).
Without validation data the usefulness of these models to applied hydrology is
limited.
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3.2 Hydrological Models
Current hydrological models can be classified on the basis of how the model
simulates hydrological processes. The relationship between precipitation and
the catchment outflow hydrograph can be described either as a simple empirical
function or as a series of physically based equations that aim to simulate the
actual processes taking place within the catchment using physically meaningful
parameters. Between these two extremes are a wide range of models which
incorporate interaction between different hydrological processes, but use both
empirical and physically based relationships to model these processes. A
conceptual model is commonly displayed as a flow diagram showing the basic
theories of hydrological interaction, and frequently form the underlying basis of
mathematical models (Blöschl & Sivapalan, 1995).
3.2.1 Empirical Models
Empirical models take the form of input, function, output, and are typically
based upon identification of statistical relationships between recorded inputs
and outputs. Regression analysis and extreme frequency analysis are commonly
used to derive the form of the transfer function. Empirical models do not
explain why events occur and therefore do not increase our understanding of
system behaviour. Extrapolating beyond the range of observed data is error
prone, particularly for extreme events (Anderson & Burt, 1990). Since the
influence of different hydrological processes is highly spatially dependent,
using this model type for ungauged catchments can produce highly inaccurate
results. Nevertheless for catchments with an observed hydrograph this is a
popular method being mathematically simple and requiring few parameters.
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3.2.2 Physically Based Models
Physically based models represent the process of water movement from
precipitation to channel outflow via a series of stores and fluxes described by
elemental physical equations. Typically these would include mathematical
equations to simulate rainfall interception by vegetation, evaporation, surface
runoff, soil moisture storage and groundwater storage. Examples include the
Institute of Hydrology lumped model (Blackie & Eeles, 1985), TOPMODEL
(Beven et al., 1984) and SHE (Abbott et al., 1986). Each component of the
system is described by equations using meaningful physical parameters derived
from field data.
3.2.3 Lumped vs. Distributed Models
Model classification is also possible by considering how hydrological
parameters are represented across the study area. Catchments are characterised
by their extreme heterogeneity (e.g. soil properties) and great variability in
fluxes (e.g. runoff) and state variables (e.g. soil moisture). ‘Lumped’ models
consider a catchment to be spatially homogenous with respect to the inputs and
parameters used (Wood, 1995). Heterogeneity and variability within the
catchment are described using a single ‘effective’ parameter set. The parameters
are ‘effective’ rather than ‘real’ since they are not directly measurable in the
field, instead being derived from model calibration with actual data. Lumped
models provide insight into overall catchment response to events but no insight
into processes internal to the system.
Distributed models attempt to better represent the variability within a system by
dividing a catchment into sub-units. A catchment can therefore consist of sub-
catchments, hillslopes, hydrological response units or regular grid elements.
Parameter sets are, in theory, derived for each sub-unit and therefore units are
considered to be homogenous and sub unit variability is neglected. Aggregation
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of each unit response over time using flow routing provides a spatio-temporal
model of catchment behaviour. Distributed models therefore require a large
number of parameters to describe the hydrological characteristics of each sub-
unit. In reality many supposedly distributed models lump subsurface parameters
at the catchment scale resulting in uncertain subsurface flow predictions
(Chappell & Ternan, 1993). An example is the treatment of saturated hydraulic
conductivity (Ksat) within a catchment. Ksat is almost exclusively assigned a
single parameter value per catchment or per soil type, a somewhat unrealistic
scenario since specific soil horizons can show variations in Ksat of several
orders of magnitude. Ksat between soil types in a heterogeneous catchment can
vary to an even greater extent (Chappell & Ternan, 1993).
The requirement for distributed models stems from a need for improved
predictions of erosion, chemical and nutrient transport, sedimentation and
understanding of changing land-use strategies within catchments (Abbott et al.,
1986; Quinn et al., 1993). A further advantage of distributed models is their
potential for validation at the grid cell scale as opposed to the validation
methods for lumped models, which consist of comparing the modelled
hydrograph with the observed hydrograph. Validation at the grid cell scale, also
known as internal state validation, is perceived as the next major goal of
hydrological modelling (Quinn et al., 1995).
Beven (1989) has questioned the extent to which the current set of physically
based distributed models accurately represent reality. Distributed models have
been criticised because of their large data requirements, high computational cost
and the fact that they are often as highly parameterised as lumped models
(Kalma et al., 1995). These problems are a result of trying to adequately
represent inter-cell variation and sub-grid variability in heterogeneous
catchments (Blöschl & Sivapalan, 1995). A comparison between physically
based and conceptual type models has shown that the results achieved are
comparable (Refsgaard & Knudsen, 1996). Distributed type models typically
consist of a large number of parameters, often too many to collect truly
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distributed measurements for. As a result some parameters are necessarily
treated as lumped values. This is often the case for subsurface values such as
hydraulic conductivity (Binley & Beven, 1991). The large number of
parameters involved makes subsequent model evaluation difficult. Beven &
Binley (1992) and Beven (1993b) question the assumption that an optimum
parameter set exists for each modelled catchment. Instead the concept of
equifinality has been suggested, the idea that different model structures or
parameter sets can produce the same model predictions. If this is the case, it is
important that validation occurs at a grid rather than catchment scale so the
internal dynamics of throughflow, runoff and soil moisture distribution can be
identified and validated against field data. It is increasingly important that as
noted by Klemes, (1986), models must produce not only the right results, but
also the right results for the right reasons.
3.2.4 Hydrological modelling and GIS
The use of GIS for hydrological modelling has become more commonplace
over the past decade. GIS is defined as a computing system for management and
analysis of spatial data (Drayton et al., 1993) and is therefore well placed to aid
in distributed modelling due to the capacity for storage and analysis of large
quantities of spatially distributed information. GIS also provides a graphical
interface with model results generally displayed as a series of maps showing the
spatial variation of selected model outputs. Interaction between GIS and
hydrological models can be on a number of levels ranging from simple
hydrologic assessment to fully integrated distributed models (Maidment, 1993).
Increasingly GIS and hydrological models are approaching this latter phase and
becoming embedded such that dynamic modelling of a river basin is possible
within the GIS. This level of integration removes the need for separate GIS and
modelling programmes with the associated problems of data transfer between
packages. In dynamic packages the results from the previous time step can be
used as inputs at the next time step. This thesis uses an integrated GIS -
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hydrological software package called PCRaster for development of a distributed
hydrological model.
3.2.5 Why another hydrological model?
The requirements for another hydrological model are summarised below:
1. The primary aims of this thesis are concerned with using GPR to provide
spatially distributed soil thickness data as a model input and GPR data as a
validation tool for the spatial pattern of soil moisture for selected grid cells.
To the authors knowledge no hydrological models exist which use
distributed soil thickness measurements as a key input, so a new, simple
model structure is needed to incorporate this extra data. All model
components will use standard physically based equations to simulate the
hydrological processes occurring at the catchment scale.
2. Truly integrated GIS – hydrological models are still in the very early stages
of development and therefore using an existing hydrological model would
require rewriting of model code within the GIS software. This process may
be as time consuming as developing a new model code using existing
physically based relationships between parameters.
3. The advantage of running an integrated GIS model is the spatially
distributed nature of the input and output data. Existing models that were
not developed in this system do not take full advantage of this benefit.
A widely held view is that the current set of spatially distributed models has
delivered disappointing results when compared with far simpler lumped
conceptual models (De Roo, 1998a). Given that the uncertainty in estimating the
value of the numerous input variables is one possible reason for this failure, this
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model will concentrate on modelling the dominant hydrological processes using
the minimum number of parameters possible.
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3.3 PCRaster
PCRaster is a GIS with the capability for dynamic modelling of spatial
processes. This is possible through use of a high-level spatial modelling
language designed specifically for environmental applications (Van Deursen,
1995; Wesseling et al., 1996; De Roo et al., 1998b). The PCRaster modelling
language consists of some 50 mathematical functions, both general algebraic
and logical operators, and functions specific to hydrological and environmental
modelling. Standard GIS operators are also included for the spatial analysis of
data, although the main emphasis of the software is on the dynamic modelling
of environmental processes. As yet PCRaster is unable to solve directly ordinary
or partial differential equations, nor implement vector field operations required
to simulate diffusion or advection (Wesseling et al., 1996).
PCRaster is a grid based GIS. Both point operations and global operations are
included in the package using mathematical operators. Flow routing within
PCRaster is controlled using an intrinsic operator which creates a map of the
catchment drainage network based on a DEM. The flow routing algorithm is a
deterministic 8-node (D8) type, which routes all cell outflow to one of eight
possible adjacent cells, depending on which cell has the lowest elevation. Each
cell is assigned one of eight possible flow directions or flagged as a sink area
when all surrounding cells have higher elevations. The resulting map is known
as a local drainage direction (ldd) map. The D8 algorithm tends to produce
parallel flow lines and is unable to account for flow dispersion (Moore, 1996).
Quinn et al. (1993a) found the inability to model multiple flow directions from a
single grid cell increases errors at coarse grid resolutions, but for grid cells
smaller than 50m this effect is lessened. A grid size of less than 50m was also
found to produce improved results in an analysis of the sensitivity of
TOPMODEL to time and space resolution (Bruneau et al., 1994). A reduction
in errors is to be expected with increasing grid resolution since the averaged
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area within grid cells is less resulting in effective parameter values derived from
smaller areas in which parameter variation may also be smaller.
3.4 Building an integrated GIS – Hydrological Model
The core modules used here are precipitation, evapo-transpiration, infiltration,
surface runoff, lateral subsurface flow and soil moisture storage. The
development of each module will be covered in detail in subsequent sections of
this chapter. This model is not designed to include all possible processes acting
in the catchment, nor does it use the most complicated and mathematically
intensive equations possible. The number of parameters used is kept to a
minimum and, where possible, these parameters are physically meaningful and
derivable from field data. The emphasis is on designing a simple hydrological
model with a distributed subsurface input parameter (soil thickness) which can
be used to determine the spatial variation in soil moisture for each time-step.
The model is designed to simulate the hydrological fluxes of a catchment using
regular grid cells. Cell length can be changed to any value bearing in mind the
findings of Bruneau et al., (1994). For this thesis a cell length of 25m was
chosen as the principle spacing, a similar size to many studies of hydrological
model performance. Varying the cell length is likely to have a small impact on
model results but is beyond the scope of this study.
Solutions to each equation are calculated on a cell by cell basis for each
timestep. The order of equation solution is important owing to the
interdependence of solution variables between sub-models. Solutions for all
sub-models are obtained using an iteration technique whereby the final solution
set for each cell at the current time are used as the initial state values at the next
timestep.
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GPR surveys of selected zones across the catchment have been used to measure
soil thickness. Survey sites were identified which covered the range of
hydrological areas present in the catchment on the basis of topographic indices.
A detailed explanation of the methodology used for GPR site selection can be
found in Chapter Five. Within this model soil thickness is an important
hydrological parameter, since depth multiplied by total profile porosity
determines the total volume of water that can be stored within each cell.
Shallow soils have a lower storage capacity and are therefore possible zones of
runoff generation (Burt & Butcher, 1985). Soil thickness is therefore an
important factor, along with precipitation input and soil conductivity, in the
control of soil moisture status. The available moisture content of the upper soil
controls the actual evaporation rate. Runoff occurs when direct precipitation and
flow from upstream exceed the local infiltration rate (infiltration excess type) or
is generated by return flow from the subsurface. Infiltration is partially a
function of cell moisture content. Lateral saturated subsurface flow between
cells is controlled by the differences in hydraulic gradient between them.
The following sections describe the component processes modelled. Where
appropriate examples of PCRaster modelling code are included as examples of
the method used to obtain solutions. PCRaster commands are printed in bold
uppercase. The full model code is listed in Appendix I. The standard units of
length are metres and the unit of time is hours.
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3.4.1 Precipitation
Rainfall data is available on an hourly time step as input data to the model.
Rainfall may be spatially distributed across the catchment or treated as a lumped
parameter. For this thesis rainfall was treated as lumped with an hourly
resolution collected by a tipping bucket raingauge located in the catchment.
While distributed information would potentially improve model accuracy, the
small catchment area of 3km2 should ensure that significant variation in rainfall
amount is limited.
Figure 3.1. Precipitation module
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3.4.2 Evaporation
The conversion of water to vapour is termed evaporation. The rate of
evaporation is determined by the amount of energy available and the availability
of water to evaporate. Following an approach outlined by Shuttleworth (1992),
the maximum evaporation rate (Epot) can be derived from net radiation input
(RN) to a grid cell per time step and the latent heat of vaporisation (γ). Hourly
net radiation data is available from an automatic weather station (AWS) located
in the headwaters of the catchment.
(3.1)
Epot is the rate of evaporation given an unlimited supply of water from a soil
column (Wood, 1995). Actual evaporation (E) is controlled both by the
potential rate and by the availability of local soil water (θ) for that time step. As
a result actual evaporation approaches zero when soils near wilting point and
attains the maximum (Epot) for saturated soils (θsat). This approach has been
successfully used by Beven et al., (1984) and Quinn & Beven, (1993) within
TOPMODEL. Local evaporation can be calculated as:
(3.2)
In common with the rainfall module, net radiation and hence potential
evaporation is a lumped parameter with the hourly-recorded value from the
AWS applied to all cells across the entire catchment. However maximum soil
moisture and actual cell soil moisture are spatially variable resulting in different
=
SatpotEE
θθ
γN
potR
E =
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actual evaporation rates between cells. Derivation of these parameters is
discussed in the soil moisture module.
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3.4.3 Infiltration
Infiltration is the process by which water enters the soil. The rate of infiltration
is determined by antecedent soil moisture, soil porosity, the moisture dependent
hydraulic conductivity and the rate of rainfall.
The time variant infiltration rate has been simulated by empirical equations i.e.
Horton (1933), approximate theory based models i.e. Green-Ampt (1911),
Philip (1957), and by rigorous, physically based methods i.e. the Richards
equation (Rawis et al., 1992). The latter two classes of model require a large
number of parameters to calculate infiltration and the Richards equation also
needs appropriate boundary conditions to be specified. A more suitable
approach for a conceptual type model is via an equation limited to a few
physically measurable parameters, ideally derived from field measurements.
Mulligan and Thornes (In press) propose that infiltration rates are primarily
controlled by changes in porosity and saturated hydraulic conductivity (Ksat)
with depth and developed the following model of infiltration under such
conditions.
Neglecting macropore flow, water entering the soil from the surface moves
down the profile with a defined wetting front. The sharp boundary between wet
and dry areas is produced as a result of the low hydraulic conductivity of the
drier soil beneath (Campbell, 1985). The transmission zone, a zone of constant
water content, extends from the wetting front to the surface while precipitation
equals or exceeds the movement of water through the profile. The rate of water
movement through the profile is controlled by the rate of advance of the wetting
front, which therefore controls the maximum rate of surface infiltration.
Campbell (1985) demonstrated that saturated hydraulic conductivity could be
calculated as a function of bulk density and soil texture. Texture refers to the
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sand, silt and clay fractions of a soil and is the simplest method for deriving soil
moisture retention properties (Rawis et al., 1992).
(3.3)
where mfc and mfs are the mass fraction of clay and sand respectively, ρb is bulk
density (g/cm3) and b is a pore interaction term calculated using σg, the
geometric standard deviation of particle diameter and dg, the geometric mean
particle diameter. Typical b values range from 2 to 24 (Campbell, 1985).
(3.4)
For homogenous soils with uniform texture and particle size, saturated
hydraulic conductivity is a function of bulk density. For a homogenous soil,
bulk density increases linearly with depth due to compaction by overburden,
resulting in a non-linear decrease in porespace. Decreasing porespace means
that a unit volume of water will saturate an increasing volume of soil as the
water body moves downwards.
The relationship between porosity (φ) and bulk density (ρb) is given by equation
3.5, where particle density (ρd) is taken from the literature to have a value of
2.65g/cm3 (Ellis et al., 1995).
(3.5)
[ ]3.7mfs-6.9mfc-3.1
3 e3.1104b
bsatK
×= −
ρ
51 g
gdb
σ+=
d
b
ρρ
1−=φ
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The measured relationship between average sample porosity and soil thickness
from field measurements is presented in Chapter 4. A theoretical example of the
expected reduction in porosity with increasing overburden thickness is shown in
figure 3.3.
Figure 3.3. Theoretical depth-porosity relationship
Increasing bulk density also leads to a reduction in average pore volume,
resulting in reduced hydraulic conductivity values. As the wetting front
progresses downward and bulk density increases, saturated hydraulic
conductivity decreases. Correspondingly the surface infiltration rate is reduced.
Figure 3.4 shows the expected reduction in saturated hydraulic conductivity
with increasing soil thickness, derived using equation 3.3.
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Figure 3.4. Saturated hydraulic conductivity with varying depth of wetting front.
Infiltration rate is considered to be equal to the rate of advance of the wetting
front (Ksat). The depth of the wetting front (WFdepth) within the soil column
therefore controls infiltration rate. Given an initial wetting front depth and
known water input the proportion of infiltration and surface runoff (localXS)
each timestep (t) can be calculated using equations 3.3 and 3.5, and assuming
that water is preferentially infiltrated. Subsequent to infiltration the new wetting
front depth is calculated on the basis that the depth of soil needed to hold the
corresponding amount of water can be derived from the depth (x) – porosity (φ)
relationship (equation 3.6)
The total depth of soil needed to store a known amount of water between two
depths x1 and x2 is equivalent to the integral of equation of the line in figure 3.3
between the limits x1 and x2.
(3.6)
dxex
x
x∫ −= 1
2
φ
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In the case of infiltration, φ = infiltrated water this timestep, and x1 = wetting
front depth from the previous timestep. Solving equation 3.6 and rearranging to
make x2 the subject gives the new wetting front depth for the current timestep.
To maintain model simplicity, multiple wetting fronts within a soil profile were
not considered. Rainfall is added to the same wetting front for as long as the
timestep rainfall amount exceeds zero. Once rainfall ceases the wetting front is
considered to break up and disperse, resulting in a new wetting front depth of
zero until the next storm event.
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3.4.4 Soil Moisture
Soil moisture status has long been recognised as an important factor influencing
the hydrological response of catchments to storm events, for example in the
evaporation module actual evaporation is partially determined by available
moisture. In this module the store of soil moisture by the model and the impact
of soil moisture status on subsurface flow and surface runoff generation will be
explained.
The maximum water content of a soil is controlled by the amount of porespace
available. Highly porous soils hold a greater amount of water than do those with
low porosity. Equally, for soils of constant porosity the thicker the soil the
greater the amount of water required for saturation to occur (assuming rainfall
does not exceed the infiltration rate). In reality porosity is found to decrease
with increasing soil thickness. The exact form of the relationship obtained from
55 field measurements is presented in Chapter 4.
The maximum amount of water which can be stored in a cell can be calculated
using knowledge of each cell’s soil thickness from GPR measurements, and the
relationship between porosity and depth obtained from field measurements (fig
3.3). Since all cells have equal areas and as all model inputs are in metres,
(rainfall and evaporation rates) rather than areas or volumes, the model
calculations are kept as units of length. The total porosity of any depth of soil
can be calculated using the relationship between soil thickness and the
cumulative porosity to that point. Integration of the depth – porosity curve
(equation 3.6) between the limits of zero and total soil thickness is equal to the
total porespace per depth of soil.
The ratio of water filled pores (soil moisture) to maximum pore space
(maximum moisture) is the cell saturation percentage. Assuming water
preferentially reaches the bedrock boundary and subsequent water inputs build
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up towards the surface, the depth of water table for each cell can be calculated.
Saturation excess overland flow is generated once cell saturation reaches one
hundred percent, i.e. soil moisture equals maximum cell moisture. The
calculation of water table position is similar to calculation of the position of the
downward moving wetting front discussed in the previous infiltration module.
In this model profile saturation can arise from three scenarios. Saturation could
occur via the wetting front reaching the bottom of the profile (top-down type).
Alternatively total saturation can occur if lateral water input from neighbouring
cells exceeds outflow causing the water table to rise to the soil surface (bottom-
up type). The third case occurs when a downward moving wetting front reaches
the water table resulting in profile saturation.
For every grid cell soil thickness, the maximum moisture and actual moisture
content are known. Using the theoretical depth-porosity relationship of equation
3.6, the position of the water table can be calculated by integration between
maximum soil thickness (xmax) and new unknown water table depth (x) for a
known amount of water. The new water table depth (x) is referenced to the soil
surface, e.g. when actual moisture is equal to the maximum moisture value,
water table depth equals zero. Likewise when soil moisture equals zero the
water table depth is equivalent to the maximum cell soil thickness. The
cumulative porosity between the maximum depth (xmax) and an unknown depth
(x) can be calculated as the integral of equation 3.8 between xmax and x.
(3.8)
solving equation 3.8 to make x the subject allows calculation of the new water
table depth each timestep.
dxex
x
x∫ −=max
φ
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3.4.5 Subsurface Flow
Flow under unsaturated conditions is driven by gravitational and matric
potentials (Campbell, 1985). In these situations a soils hydraulic conductivity is
dependent on the volumetric soil moisture content (Rawis et al., 1992). The
model simulates flow between cells which may be partially or fully saturated.
The approach used is similar to that of Xiao et al., (1996) who used a GIS to
develop a raster based surface-subsurface hydrological model for a 2511km2
catchment in Alaska. Although the Cyff catchment has an area of only 3km2, the
subsurface flow module used by Xiao et al., (1996) is applicable at this scale
since it is physically based and only requires three parameters for each cell;
surface elevation, soil thickness and the saturated hydraulic conductivity (Ksat).
While Xiao et al., only considered lateral subsurface flow to occur when a cell
was 100% saturated i.e. the water table was at the surface, in this model flow
will be modelled for soils which are less than fully saturated. In this case the
amount of water contributing to subsurface flow is proportional to water table
height above bedrock rather than total cell depth. Calculation of water table
height each time-step as a function of total soil thickness and the depth –
porosity relationship has been explained within the soil moisture section.
The rate of saturated flow is directly proportional to the difference in hydraulic
head (H) between two points and inversely proportional to the flow length (x)
between them. This constitutes Darcy’s Law, where the constant of
proportionality is described as the saturated hydraulic conductivity (Ksat).
(3.9)
xHAKQ sat
∆∆
−=
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The hydraulic head gradient depends on the change in elevation of the water
table over a horizontal distance. In terms of lateral saturated flow from cell i to
an adjacent grid cell i +1 Darcy’s law can be written as
(3.10)
For the grid structure used by PCRaster, x equals the distance to the next
downstream cell. For flow directions cardinal to the source cell this distance is
equal to cell length. The downstream distance for flow diagonal to a cell is
calculated using Pythagorean theorem (figure 3.7). PCRaster uses the
DOWNSTREAMDIST command to automate this process.
Figure 3.7. Possible drainage paths from a grid cell using the D8 flow algorithm.
−−
−=+
+
1
1
ii
iisat xx
hhAKQ
( )2length cell 2 RED
length cell BLACK
×=
=
x
x
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The change in head (H) between cells can be calculated from water table depth
and cell elevation. This is shown in figure 3.8 and expressed as
(3.11)
Hydraulic gradient is therefore
(3.12)
Typically subsurface flow is routed using surface topography. However while
hydraulic gradient is largely controlled by cell elevation, considered to be
constant for model runs (i.e. no significant erosion or deposition takes place),
water table depth is also an important factor. Water table position reflects the
soil moisture status of each cell and is a dynamic feature. Changes in water
table depth between cells may lead to a different pattern of subsurface flow
direction than that predicted solely on the basis of topography. The effect is
likely to be greatest in valley bottom areas with low slope angle and deeper soils
where differences in elevation between cells are minimal. In order to model this
effect a local drainage direction network based on water table height and cell
elevation is calculated for each timestep and this network used for the routing of
subsurface flow.
xhhhh
xH )()( 1324 −−−
=∆∆
le) water tab thedepth to -elevation (Celldownstream and
le) water tab thedepth to-elevation Cell( where
)()(
13
24
1324
=−
=−
−−−=
hh
hh
hhhhH
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Figure 3.8. Cross-section of two adjacent grid cells with different elevation, soilthickness and water table depth.
For those cells which are not fully saturated the lateral hydraulic conductivity
was calculated using a method outlined by Campbell (1974, 1985). In this case
hydraulic conductivity (K) is determined by the ratio of cell soil moisture to
maximum soil moisture, a pore interaction term (equation 3.4), and saturated
hydraulic conductivity, calculated by:
(3.13)
The potential amount of water available to move from a cell to a downstream
cell is a function of the hydraulic gradient (Hgrad) and the hydraulic
conductivity of the soil (K). The limiting factor is the amount of water available
h3
h4
Zero level
h2
h1Water table depth
Soil depth
Cell elevation
Bedrock
d1
d2
Bedrock
)32(
satθθ
+
=
b
satKK
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to move from a cell in the time period (soilmoist). Subsurface output from a cell
(as metres of water) can therefore be expressed as:
Cell output = IF (soilmoist > Hgrad × K THEN Hgrad × K ELSE soilmoist)
Input from upstream cells is calculated using the PCRaster UPSTREAM
command which sums the output from all cells immediately upstream of the
input cell using the local drainage direction (LDD) network.
Cell input = Σ (upstream cell output)
Considering only adjacent upstream cells to be contributors to subsurface flow
can be justified by the slow rates of lateral flow, typically of the order of one to
ten centimetres per hour. This is small compared to cell widths of 10 – 25m
which the model is designed for.
A balance equation is then used to check that the maximum moisture capacity
(maxmoist) of a cell has not been exceeded. If the maximum storage capacity of
the cell is exceeded in any timestep the excess water is considered to be return
flow (ROF) and added to the localXS total, where it is routed downslope using
the surface runoff module.
The local elevation of the water table is equal to cell elevation minus water table
depth. A equals the average flow area between adjacent cells and is calculated as
the product of cell width (y) and the difference between mean water table depth
(h1, h2) and mean soil thickness (d1, d2).
(3.14)
yhhddA
+
−+
=22
1212
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Therefore cell subsurface discharge (Q) for each timestep is calculated as:
(3.15)
yhhddx
hhhhKQ
+
−+
−−−
=22
)()( 12121324
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3.4.6 Surface Runoff
Ponded surface water that cannot be infiltrated during a timestep becomes
runoff. Runoff is routed to the next downstream cell via the surface local
drainage direction network calculated from the catchment DEM. Runoff takes
the form of infiltration excess, saturation excess or return overland flow type.
Runoff in PCRaster can be modelled using a number of approaches. PCRaster
includes ‘ACCU…’, a group of functions designed to route inputs (water,
sediment etc) through and out of the catchment each timestep. These are useful
operators when the material transported is not considered to contribute to any
other model processes. It is of less use when the infiltration of surface runoff
downslope of the source cell is considered or for any processes where the
material travel time through the catchment is more than the model timestep. In
this case a more sophisticated routing algorithm is required. One example is to
use the manning equation to route runoff, another to use the kinematic wave
approximation.
The kinematic wave approximation for flow routing has been successfully
implemented in PCRaster by De Roo et al., (1998b). The algorithm is
implemented using the KINEMATIC command and requires the following
parameters
• Timestep (seconds)
• Cell length (m)
• Beta, equals 0.6 for sheet flow
• Q, side flow input, equals zero
• mannings n value
• Surface water height (m)
• Local slope gradient map (m/m)
• Local drainage direction map
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The dominant vegetation types found in the Cyff are grass species, often
cropped as a result of sheep grazing. These vegetation types correspond to a
mannings n value of 0.1-0.2 (Stephenson & Meadows, 1986). For the purposes
of this thesis a value of 0.15 for mannings n was used in all model simulations.
A height of surface water (localXS) for any cell within the catchment can be
generated by three mechanisms:
1. Direct precipitation to a cell for the timestep failing to infiltrate during that
timestep. This situation may occur either because rainfall intensity exceeds
the infiltration rate, or as a result of soil saturation at a cell.
2. Surface water (localXS) routed downslope as runoff from the previous
timestep, and that is not able to infiltrate.
3. Return overland flow (ROF) from cells that exceed the maximum moisture
capacity due to subsurface flow from upslope cells.
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3.5 Conclusion
PCRaster provides a modelling framework embedded within a GIS for the
development of dynamic, spatially distributed models. The benefit of using an
integrated GIS-model is the capability for storage and display of dynamic,
spatially heterogeneous data, using the raster architecture of the software to
overlay different data maps. The overall structure and requirements of the
model have been explained. Where possible all modules are based on standard
routines used by other hydrological models in order that the emphasis is on
using GPR data for hydrological modelling, not on developing an entirely new
model. The potential of using GPR to derive distributed soil thickness has
however resulted in this model using depth as a key parameter, for example as a
control on the maximum moisture content of each cell.
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Chapter 4: Fieldwork
4.1 Introduction
This chapter describes the methodology used to collect the hydrological data
required for model input, parameterisation and validation. An initial outline of
previous catchment studies at Plynlimon and a justification for using this area is
presented, followed by a brief description of the climatic and geomorphological
background of the region. Subsequent sections explain which hydrological
parameters were collected and the methods used. The final part of this chapter
deals with creation of the catchment and hillslope digital elevation models
(DEM’s).
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4.2 The Plynlimon Catchments
The Plynlimon catchments are located in an upland region of Central Wales.
Two adjacent ‘paired’ catchments, the Wye and the Severn, have formed the
basis for an experimental programme set up under the encouragement of the
International Hydrological Decade, 1965-1974. The primary reason for
establishing Plynlimon was to investigate the differences in annual water budget
between grassland and forested catchments, in particular to test the hypothesis
that for UK conditions, evaporative losses were greater from coniferous forests
than pasture (Hudson, 1988).
In order to answer this question a network of weather stations, rain gauges and
flumes were established throughout the two catchments and maintained by the
Institute of Hydrology. The network now provides comprehensive spatial
coverage of precipitation, channel discharge and other climatic parameters
recorded by weather stations at daily and better temporal resolutions and
stretching back 30 years. The high spatial and temporal resolution of data has
resulted in Plynlimon becoming the focus for numerous hydrological studies.
These have included channel studies (Newson et al., 1978), soil piping studies
(Gilman & Newson, 1980), the impact of soil moisture storage to upland
catchment water balances (Hudson, 1988) and catchment scale model
simulations (Beven et al., 1984), (Quinn et al., 1993).
Plynlimon was chosen as the site for this study because of the availability of
hydrometric data for model input and validation, and because of the knowledge
available from previous studies of the soils and hydrological processes active in
the catchments. The study area for this thesis is a sub-catchment of the Wye
watershed, the Cyff. The Cyff was selected because of the location of a channel
flume measuring hourly discharge at the catchment outflow and two automatic
weather stations (AWS), one in the headwaters of the catchment and one
located 500m downstream of the outflow. The area of the Cyff is approximately
3.1km2 (derived from the catchment DEM) and a 1:5000 topographic map
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(Hunting Survey Ltd) of the area was available to use as source for the
catchment DEM, as well as aerial photographs from 9th July 1995. In terms of
the suitability for GPR use the Cyff is accessible by farm tracks and there are no
forestry plantations therefore radar profiles can be taken anywhere within the
catchment. Textural analysis of 29 soil samples from the catchment showed clay
content ranged from 0–39 % (by mass), generally increasing with depth, but
preliminary site investigation with GPR indicated that signal penetration depths
of 1-2m were possible using GPR frequencies of 225-900MHz.
Figure 4.1. Cyff catchment aerial photograph with watershed and stream networksuperimposed (NERC 1995).
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4.2.1 Climate
Plynlimon is one of the wetter regions of the UK due to the high elevation (320
to 740m) and the proximity of the Atlantic Ocean. The 1961-1990 average
annual rainfall for the Cyff catchment is 2416mm. (NERC, 1999). The amount
of received precipitation in the Plynlimon catchments has been shown to
increase with altitude, but no statistical relationship was found to exist between
precipitation and either slope angle or aspect (Clarke et al., 1973).
For the purposes of this study a calibrated tipping bucket raingauge (TBR) was
installed in the Cyff catchment at the field plot, located at an altitude of 454m A
total precipitation of 2559.6mm was recorded for the 1998 calendar year.
Monthly totals from October 1997 to June 1999, the TBR operational period,
are shown in figure 4.2.
Figure 4.2. Total monthly rainfall recorded by the field plot TBR.
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4.2.2 Hydrology
A network of ephemeral and perennial open channels, ephemeral soil pipes and
perennial flushes provides drainage within the Wye and Severn catchments.
Afforestation of the Severn required excavation of drainage ditches to a depth of
1.5m; in the Cyff no afforestation was undertaken but a network of open drains
of approximately 1m cross-section were excavated in the valley bottom bog.
These were excavated to improve pasture, but were not maintained (Newson &
Harrison, 1978). In 1999 there is little evidence of these artificial drainage
channels remaining.
4.2.3 Geomorphology and soils
The adjacent catchments of the upper Wye and upper Severn exhibit similar
morphologies with total areas of 10.55 km2 and 8.70 km2 respectively, similar
aspects, mean altitudes of 450m and similar drainage densities of 2.04 km/km2
and 2.40 km/km2. 91% of the Cyff lies between 340 - 539m above sea level,
median slope angle is 10.6o while the dominant drainage direction along the
central valley is to the south east (Newson, 1976). Significant differences in
landuse do exist between the catchments. The Wye is primarily used as rough
pasture for stock grazing while the Severn was 68.3% forested (Hudson, 1988).
At the present time many forest stands have reached maturity and as a result the
Severn is undergoing extensive deforestation. The stability of landuse in the
Wye is an added advantage for this study.
The soils of Plynlimon have been extensively documented by Rudeforth (1970),
Newson (1976) and Chappell & Ternan (1993) amongst others. The soils
present in the Cyff have evolved through the interaction between bedrock,
glacial and periglacial deposits of the tertiary and climate. The parent material
consists of mudstones and shales and is dominated by illite, quartz and iron rich
chlorite. Three major soil types have been recognised in this area. Ferric
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podzols are found on the mid-slopes and characterised by depositions of
aluminium/iron (Al/Fe) from the Ea horizon over a 5-10cm depth of the Bs
horizon. Placic podzols are found both upslope and downslope of the ferric
podzols on slopes with lower gradients. In these soils the Al/Fe is precipitated
and forms an ironpan, the Es horizon becomes gleyed and the organic layer
above the Es horizon forms a peat. The Bs horizon below the pan remains
relatively permeable compared with the Bs horizon of the ferric podzol (Adams,
1974). Moving towards the crest-slope and toe-slopes peat depth increases and
the Bs horizon becomes gleyed resulting hydraulic conductivities several orders
of magnitude lower than those of the peat layer (Chappell et al., 1993). The
soils described belong to the Hiraethog series, and in this area are underlain by a
C horizon of solid rock (shale), unconsolidated scree or compact drift
(Rudeforth, 1970).
Figure 4.3. A Cyff soil profile at ~500m above sea level. Note the dark organichorizon ~20cm deep, overlying a yellow/brown horizon and a C-horizonconsisting of coarse, angular shale.
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4.2.4 Vegetation
Acid grassland communities characterised by the grasses Nardus spp.
(matgrass) and Festuca spp. (fescue) dominate on placic podzol slope systems.
Mesotrophic mires are widespread in the valley bottoms and extend upslope via
‘rush flushes’. These mire areas are dominated by Juncus spp. (rush),
Eriophorum spp. (cotton grass) and Mollinia spp. (purple moor grass), all of
which thrive in saturated soils and are tolerant of submergence common during
the winter/spring months. While plant species can be taken as an indicator of
moisture status, vegetation distribution is also affected by nutrient status and
human interference. In the case of the Cyff this has taken the form of improved
pastures using surface treatments (Newson, 1976).
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4.3 Data collection of hydrological parameters
Field measurements of hydrological parameters are required as inputs to the
model and to enable model validation. As discussed in the modelling chapter,
the hydrological inputs comprise rainfall and potential evaporation data. Model
validation will be carried out in two ways. Firstly a lumped approach involving
a comparison between predicted surface and subsurface discharge and recorded
data obtained from a field plot within the catchment. This will provide an
internal state validation for one grid cell within the catchment as proposed by
Quinn et al., (1995). At the catchment scale a lumped validation will be
achieved by comparing the model hydrograph to the actual hydrograph over the
same time period. Secondly it is planned to carry out internal state validation of
the model, validating generated soil moisture levels per cell with field data
collected using GPR. Field data is also required for the parameterisation of the
hydrological model (e.g. the infiltration equation) and as a validation of radar
derived measurements of soil thickness and volumetric water content for the
catchment.
4.3.1 Plot-scale collection of hydrological parameters
A field site was established in April 1997 in the Cyff. The plot is south facing
and approximately 454m above sea level. The underlying soil is a ferric podzol
with a well defined organic and Bs boundary. A site within the catchment was
needed to measure the hydrological variables required as model input (rainfall)
and for the internal validation of the catchment model (runoff, subsurface flow
and soil moisture). Construction of a throughflow/runoff plot required
excavation of a 2.5m long trench approximately 40cm deep and perpendicular
to the line of steepest slope. Two plastic gutters 2m long were placed at depths
of 2cm and 30cm for the interception of runoff and throughflow respectively.
The guttering was sealed at one end and slightly inclined to allow water flow
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via funnels into the respective tipping buckets located in a covered pit to one
side of the plot. Sheet aluminium was used to provide two lips over which water
from overland flow and throughflow could drain into each gutter from the soil
face. Two aluminium covers were placed over the open top of each gutter to
prevent direct input by precipitation and sediment. The trench was back-filled in
an attempt to limit the impact of the excavation on hydraulic flow pathways.
The rain gauge was installed 2m downslope and to the right of the trench in a pit
to reduce the effect of wind turbulence on rain catch. The plot area after
installation of the runoff/throughflow measurement structure is shown in figure
4.4.
Between 29th September 1997 and 7th July 1999 the field site recorded surface
runoff, subsurface flow and rainfall via three tipping bucket gauges connected
to a datalogger. Soil moisture at three depths was also monitored between 28th
September 1998 and 7th July 1999. Prior to 29th September 1997 field data were
poor due to technical problems and these data are not considered in this thesis.
The data coverage provided by field plot instruments is summarised in table 4.1
Table 4.1. Field plot data record.
MeasuredVariable
From To TemporalResolution
Required for
Rainfall* 29/09/97 07/07/99 Hourly Model input
Runoff* 29/09/97 07/07/99 Hourly Internal model validation
Subsurface
flow*
29/09/97 07/07/99 Hourly Internal model validation
Soil moisture*
at depths of:
0.08m
0.23m
0.38m
28/09/98 07/07/99 Hourly Internal model validation
*No data for periods between 27th September 1998 - 29th September 1998 and 12th April 1999 -
20th April 1999.
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Figure 4.4. Runoff - subsurface flow field plot.
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4.3.2 Catchment-scale collection of hydrological parameters
Two parameters were needed at the catchment scale. Hourly potential
evaporation figures for input into the evaporation module were calculated using
hourly weather station data. Hourly river discharge from the basin outflow
provides the means for comparison between the measured and modelled
hydrograph. Both the channel flow gauge and AWS form part of the monitoring
network maintained by the Institute of Hydrology. The period for which
discharge and AWS data are available is summarised in table 4.2
Table 4.2. Data collected by Institute of Hydrology hydrometric network.
MeasuredVariable
From To TemporalResolution
Required for
Discharge 29/09/97 31/03/99 Hourly Model validation
Net Radiation 01/01/97 14/03/99 Hourly Model input
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4.4 Topography
Topography is a critical factor in the hydrological response of a catchment. Not
only is topography a major control on surface and subsurface flow pathways
(Quinn et al., 1994), it is also an important factor in the downslope
redistribution of soil moisture during interstorm periods (Wood, 1995). For
many distributed models topography is the only truly spatially distributed
parameter available and as a result it is often used as a covariate to model the
spatial distribution of other variables (Blöschl et al., 1995).
Topography has been recognised as one factor important to the short-term
catchment hydrological response and the long-term evolution of hillslope form.
Over longer time scales topography can be considered to influence soil
development. The local influence of topography includes slope gradient which
controls rates of water movement over and through soils, and also the rates and
process of soil movement downslope (Selby, 1993). Gravity driven transport
processes typically result in thin soils on topographic ridges and those areas
adjacent to the watershed, while accumulation zones are located in valley
bottoms (Heimsath et al., 1999). As a result of the importance of topography to
hydrology, and the widespread availability of detailed topographic maps, digital
elevation models (DEM’s) are extensively used in distributed hydrological
modelling. This thesis uses a 1:5000 map of the Cyff catchment to produce a
catchment DEM. This forms the basis for modelling the internal dynamics of
hydrological response to precipitation events through routing and moisture
distribution. The area bounding and upslope of the hydrological monitoring
station was surveyed to produce a finer resolution DEM of local topography.
This was carried out to quantify the area contributing to surface runoff and also
potentially the source area of contributing to subsurface flow.
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4.4.1 The catchment DEM
Conversion from the 1:5000 contour map of the Cyff catchment to a raster
DEM was achieved by scanning the map and digitising the contour lines using
ARC/INFO. The vector file containing contours, stream network location and
spot heights was converted to a raster map using ARC/INFO-TOPOGRID and
exported to PCRaster. The catchment drainage network was derived in
PCRaster using the local drainage direction algorithm discussed previously. A
25m grid size catchment DEM is shown in figure 4.5.
An intrinsic part of DEM creation is the choice of grid size. Grid size is
important because the description of processes logically requires grid
resolutions of similar or finer scale. Coarse grids are unable to represent
detailed catchment features, for example gully features that exert control on
surface flow routing. Secondly internal validation of distributed models using
point data cannot be achieved with coarse resolutions. There seems to be no
optimum grid size for hydrological studies, rather the choice of grid resolution
depends on the output required by the modeller. The production of hydrographs
from coarse scale DEM’s is possible, but if internal state validation is required
grid resolutions finer than 50m are needed (Quinn et al., 1995).
Grid size not only determines the resolution of topographic features but also
affects the values of terrain attributes derived from DEM analysis. The impact
of changing grid size on terrain attributes and hydrology was explored by
Bruneau at al., (1994) who found that catchment area decreases as grid
resolution is increased and consequently simulated discharge is also reduced.
The topographic index was found to be sensitive to changing grid size, with grid
cells greater than 50m primarily controlled by local slope and finer grids
showing increased sensitivity to cumulative upslope area. Quinn et al., (1994)
downscaled from a 12.5m to a 50m grid to analyse the impact on topographic
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index values. They found an increased percentage of higher index values, due to
the increase in minimum cell area.
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Figure 4.5. 25m grid resolution DEM of the Cyff catchment, overlain with a map ofthe logarithm of upslope drainage area for each cell.
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4.4.2 The hillslope DEM
In order to quantify the upstream area contributing to the plot, and thereby
enable comparison between plot measured surface/subsurface flow and model
predictions, a higher resolution DEM of the immediate area was required. 277
points were surveyed over the hillslope adjacent and upslope of the plot, and
used to derive surface topography using kriging (figure 4.6 and figure 4.7).
Visually the plot is located on the toe-slope of a topographic ridge with a
pronounced gully system to one side. The drainage area upslope of the plot is
likely to be relatively small and this is confirmed by measurement of the cell
drainage area from the hillslope DEM, in this case 200m2. The effect of changes
in DEM grid resolution on topographic attribute values is summarised in table
4.3.
Table 4.3. Terrain attributes of the plot cell for variable DEM grid size.
Source DEM GridSize (m)
Slope Angle(degrees)
Area
m2
Area asnumber of
cells
WetnessIndex
LN(a/tanβ)
Catchment DEM 25 15.1 625 1 7.751
Catchment DEM 10 15.8 400 4 7.252
Slope DEM 5 15.9 200 8 6.556
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Figure 4.6. Elevation map with survey points marked in red and location of thefield plot marked in blue.
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Figure 4.7. 5m grid DEM of the hillslope overlain with LN(upslope area) map andlocal drainage direction network (white lines indicate cell drainage paths).
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4.5. Site selection using terrain attributes
DEMs provide a method to derive maps of terrain attributes potentially of use to
hydrological studies. This is because of the relationship that exists between
topography and hydrological fluxes. The first order derivatives of topographic
surfaces are slope and aspect; second order derivatives include plan and profile
curvature (Burrough & McDonnell, 1998). Terrain attributes or topographic
indices have been used as surrogate indicators to describe the spatial
distribution of variables, for example soil moisture. They are therefore useful
for designing sampling schemes when little prior knowledge of the spatial
variation in parameters is known. In this study topographic indices were used
initially to identify potential sites for subsurface investigation using GPR.
Kirkby & Chorley (1967) investigated the significance of topography in
defining zones of water accumulation and hence the likelihood of contributing
to subsurface runoff and saturation excess flow. Hillslope hollows and low
gradient slopes were found to contribute to this mechanism of flow initiation.
Both of these zones are identifiable through analysis of a DEM which can be
used to derive maps of the spatial distribution of plan curvature, upslope
drainage area and local slope. Burt et al., (1985) explored the use of topographic
indices for predicting soil moisture status for a UK catchment, and found that an
index based on upslope drainage area provided the greatest correlation with
observed soil moisture, particularly during wetter conditions.
The importance of topography has led to the development of a number of
topographic indices that predict the local state of moisture flux. One such
topographic index, also referred to as a wetness index, is calculated on the basis
of local slope angle (β) and cumulative upslope area (a) and reflects the
tendency for water to accumulate at any point. The value of accumulated
upslope area is considered proportional to the volume of water moving through
a cell, and local slope angle is a measure of the capability of a cell to transport
water (Quinn et al., 1993). On shallow gradient slopes subsurface flow is
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limited by reduced hydraulic gradients and saturation of soils is more likely
(Burt et al., 1985). The wetness index is therefore a possible indicator of soil
moisture status, which is seen as an important factor in the generation of
saturation excess flow. The exact form of the equation is given by
(4.1)
Other topographic indices include a/β and plan curvature. Plan curvature
provides an indication of flow convergence or divergence, identifying
topographic hollows that concentrate flow and are therefore potential zones of
saturation. These and combinations of topographic attributes have been used to
investigate the changing distribution of soil moisture, runoff, erosion and
deposition, and catenary development through time and space.
The concept of using topography as a covariate for soil moisture status has been
extended to include prediction of other soil attributes, including soil thickness.
Jenny (1941) summarised the key factors in soil development as climate, parent
material, topography and biotic activity. For a small catchment area, such as the
one used for this study, climate, parent material and biotic activity can be
considered to act uniformly across the basin. Topographic indices therefore
have the potential to partially explain the spatial variability of soil attributes,
including soil thickness, for many environments. One hypothesis considered is
that for landscapes experiencing dominantly fluvial processes the soil catena
develops in response to water movement (Moore et al., 1993). Heimsath et al.,
(1999) consider the dominant transport processes in upland environments to be
mass wasting and overland flow, resulting in shallow soils adjacent to
catchment divides and on steep slopes, and the accumulation of soils in valley
bottoms. Upland Wales is one such landscape.
Boer et al., (1996) and Moore et al., (1993) used terrain attributes derived from
DEM’s to estimate soil thickness variability in Southeast Spain and Colorado
respectively. Both studies used local slope angle, aspect, profile curvature and
=
βtan ln aIndexWetness
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wetness index as covariates for the prediction of soil thickness. Moore et al.,
(1993) found that up to 50% of soil thickness variability could be explained
with slope and wetness indices. Boer et al., (1996) found that these indices
provided an accuracy of 40-81% in terms of predicted and measured soil
thickness, highly dependent on lithology.
In this study topographic indices were initially used to develop a sampling
strategy for GPR site selection. The size of the catchment precluded a survey of
the entire area. Instead the catchment DEM was used to derive maps of the
spatial variation in slope gradient, upslope drainage area and wetness index.
Given that these topographic indices have been shown to explain a certain
amount of soil moisture and soil thickness variability, one hypothesis would be
that sampling areas which cover the range of index values would result in
adequate spatial coverage of the variables of interest. The indices chosen as
guides for initial site selection were slope, upslope drainage area and wetness
index.
For each index a histogram distribution function of pixel values was produced.
Figure 4.8 shows the distribution functions for slope, log(upslope area) and
log(wetness) for the 25m-grid cell DEM. The histogram for each index was
used to identify the range of pixel values present in the catchment. The number
of cells sampled for each index range was determined by the frequency of cells
in each index range. A large frequency of cells with a particular value resulted
in the allocation of a larger number of sample sites than for lower frequency
values.
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Figure 4.8. Frequency distribution of pixel values for the three topographicindices used to locate potential GPR survey sites.
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4.5.1 Locating sample sites using topographic indices
Given the large number of potential sites associated with each index value a
method of displaying only those cells within a specific index range was
required. Using boolean operators within PCRaster a series of maps were
created which identified the location of cells which met the search criteria. For
each of the three indices, cells were found with index values within their
respective histogram bin using greater than and less than operators. The
resulting map allocated a true value to all cells that met the criteria and a false
value to those that did not. Using this method a series of simple maps was
created showing the location of all possible sample sites for a particular index
range. Maps of slope, wetness and upslope area were overlain and combinations
of these index values used to display pixels that met the search criteria. In total
60 sites were identified as potential survey areas and 32 were actually sampled
during subsequent fieldwork. Due to the physical weight of the GPR system and
the lack of off-road transport it was necessary to choose sample sites which
were within approximately one kilometre of vehicle tracks. As a result the
majority of field sites are located on the south facing slopes of the Cyff, where
access is provided by a track running south-east to north-west (appendix II,
figure II.1.). The co-ordinates of the centre of each cell chosen for sampling
were recorded for subsequent use with a GPS system for cell location in the
field. The co-ordinates and key terrain indices for each sample site are listed in
appendix II, table II.1.
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4.5.2 Site location in the field
A GARMIN differential GPS system was used to locate sites in the field. The
GARMIN unit is a handheld system and in this case used two satellite receivers
for differential positioning. In differential mode the accuracy of the unit is 1-
5m. Sites were located on September 29th and 30th 1998 and marked with
wooden stakes and identification numbers. Given the 25m DEM grid size even
a worst case scenario with a GPS error of 5m would still position the site
marker within the correct grid square. Whilst in the field the GPS positions of
the catchment outflow and a road cross were recorded to allow comparison
between GPS and map co-ordinate values. The results are shown in table 4.4.
Table 4.4. GPS and DEM feature co-ordinates.
Feature GPS x(m)
GPS y(m)
DEM x(m)
DEM y(m)
x Error(m)
y Error(m)
Catchment
–outlet.
282374 284634 282374 284627 0 7
Road cross. 281514 285706 281524 285702 10 4
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4.6 GPR survey methodology
Initial site investigation took place during the Spring and Summer of 1997. A
key requirement was field testing the radar, as GPR is limited as a survey tool in
electrically conductive environments. Initial investigations to assess the
suitability of using GPR at Plynlimon concentrated on a 20m2 hillslope area,
subsequently used as the site for the hydrological monitoring station. All
available antennae frequencies (225, 450 and 900 MHz) were used to collect
subsurface data from four 20m survey lines in both reflection and CMP modes
of operation. GPR data was complemented by augur holes every metre and two
trial pits. 30 soil samples were collected for textural analysis in order to quantify
clay content at differing depths. The results shown in figure 4.9 detail a general
increase in silt with depth, and a peak in soil clay content between 0.1m - 0.2m
depth of sample. The percentage of gravel particles (>2mm) increases with
increasing sample depth. Soil textural classification used the British Standards
system (Ellis et al., 1995).
The conclusions drawn from the preliminary investigations were:
1. GPR was a viable survey tool in this area due to the relatively low clay
content of the soils (0-32%).
2. Higher frequency antennae (900MHz) with associated higher resolution
provided the optimum method for locating the soil-bedrock interface across
much of the catchment. Excavation and augur measurements showed that
the local soils were relatively thin, with an organic horizon typically less
than 0.2m thick and bedrock located within 1m of the surface.
3. Areas of peat bog in the valley floor and to an extent, drainage channels,
proved the exception to the above. In these areas of the catchment the
deeper soils required 450MHz antennae be used since the lower frequency
provided improved penetration to the bedrock boundary.
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Figure 4.9. Soil texture data from thirty samples.
4.6.1 Reflection survey design
GPR reflection surveys were carried out in order to image the subsurface, and
with the specific aim of locating the soil-bedrock boundary and measuring soil
thickness. To achieve this radar profiles were taken along a 2m-survey line at
each site. The choice of line length was based on the following reasoning. The
standard use of GPR is one of subsurface feature identification, for example
pipe location or bedrock structure. In these and for the case of bedrock
boundary identification, interpretation of subsurface structure is achieved by
examining the spatial pattern of subsurface response. Closely spaced radar
returns allow an image of the soil to be built up and the nature of features to be
resolved. It is only through the accumulation of adjacent radar traces that a
reflector can be identified as a linear, dipping or point feature, or as noise. The
actual number of adjacent traces required to identify a feature is dependent on
the survey aim and spatial variability of the target. Ultimately human input is
required to judge the precise nature of a reflector. Using the GPR profiles
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collected during the preliminary survey stage a survey line length of 2m was
found visually to be useful in interpreting linear reflectors which corresponded
to soil horizons. Figure 4.10 shows the effect of reducing survey line length on
feature identification.
Figure 4.10. The impact of reducing profile length on interpreting subsurfacefeatures. The profile, from a 225MHz survey, is displayed with DEWOW and aconstant gain of 20.
A statistical approach for the determination of an optimum GPR survey length
considered the variation in soil thickness along each profile. Using auger data
collected at one-metre intervals along the four 20m survey lines, upslope of the
field plot, the variation in depth was analysed using simple statistics and
presented in table 4.5.
Table 4.5. Soil thickness variation at the field plot.
Survey line Line1 Line2 Line3 Line4
Minimum depth 0.65 0.52 0.4 0.37
Maximum depth 0.28 0.21 0.25 0.12
Range 0.37 0.31 0.15 0.25
Mean depth 0.39 0.34 0.33 0.27
Standard deviation 0.095 0.078 0.046 0.069
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Individual depth measurements within each profile are subject to high
variability. Averaging two or more adjacent depth measurements reduces this
variability and leads to a decline in the value of standard deviation. A
dimensionless measure of variability is provided by the coefficient of variation,
which is equal to standard deviation divided by the sample mean. Figure 4.11
shows the effect of increasing the number of adjacent points used to calculate
average depth.
Figure 4.11. The change in coefficient of variation with an increasing number ofauger samples.
Initially the coefficient of variation is high, but decreases as the number of
auger measurements used to calculate the depth at any point are increased. The
rate of decrease is initially high, but the rate of change decreases after the
number of observations reaches 3-4. After this point the coefficient of variation
still declines, but at a lesser rate. For these data sets a useful auger profile length
for soil thickness measurement is 3-4 observations when the spacing between
measurement points is one metre. This is equivalent to a GPR profile length of
2-3m. Using this information it was decided to sample each site using a two-
metre survey line, orientated parallel to the maximum slope.
0 .000
0 .050
0 .100
0 .150
0 .200
0 .250
0 .300
0 1 2 3 4 5 6 7 8 9 10 11
N u m ber o f o bservation s used to averag e
coef
ficie
nt o
f var
iatio
n
L ine1L ine2L ine3L ine4
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4.6.2 Time Window
The time window refers to the length of time the GPR system records a
returning signal. Signals that take longer in time to return to the receiver have,
in general, travelled a greater distance through the subsurface. Selection of an
appropriate time window is an important component of GPR survey design
since it determines the limits of imaging depth. Augering carried out at 1m
intervals along the initial four 20m profiles showed that soil thickness ranged
between 0.12 – 0.65m over the area investigated. Analysis of four CMP’s
carried out in the adjacent area produced velocity estimates ranging from 0.06 –
0.08m/ns. These low velocity values reflect the wet soil conditions prevalent in
upland Wales and provided an initial basis for the choice of time window.
Combining the greatest depth with the slowest estimate of wave velocity
produced a minimum two-way time window of 22ns. During actual GPR
surveys the time window was set at between 60 - 100ns, given the likelihood of
soils exceeding 0.65m depth and the possibility of slower electromagnetic wave
velocities. Assuming a velocity of 0.06m/ns throughout the subsurface these
time window values are equivalent to an imaging depth of 1.8 – 3.0m.
4.6.3 Station Spacing
Station spacing refers to the horizontal interval between adjacent radar traces
along a survey line and is a key factor in the definition of subsurface features.
As the distance between sample points is increased the likelihood of
inadequately sampling the spatial variation of steeply dipping reflectors also
increases and results in the spatial aliasing of subsurface images. In this context
spatial aliasing refers to radar profiles in which the spatial variation in reflectors
is poorly defined due to station spacing of a greater interval than the variability
of the reflector. Flat or shallow dipping reflectors exhibit little variation in depth
over short distances, whereas steeply dipping reflectors are characterised by
sharp variation in depth over similar survey lengths. While the bedrock
boundary in this scenario does not dip greatly over a distance of two metres,
optimum station spacing is still required in order that profiles are visually
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interpretable.
Optimum station spacing is a function of antennae frequency and the dielectric
value of the host environment (Annan, 1997). The actual volume of subsurface
sampled at each point is a function of these parameters, and the depth of the
reflector, since the radar footprint can be thought of as a cone with an elliptical
base expanding from the radar system. The dimensions of the conical base are
given by equation 2.12. and tend to increase with depth and decrease with
increased dielectric values. (Annan and Cosway, 1992). In the standard radar
transmitter – receiver configuration the long axis of the cone is orientated
parallel to the survey line, and this is the configuration used for all data
collection in this thesis. A degree of overlap in sample volume between
successive sample points is required to reduce spatial aliasing. Figure 4.12
shows the theoretical dimensions of the long axis radar footprint for 900 MHz
and 450 MHz antennae for the range of dielectric values (K) likely to be
encountered in the field. Two reflectors are considered, located at depths of
0.2m and 1.0m respectively.
Figure 4.12. Long-axis footprint size for variable dielectric constant
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For a station spacing of 0.05m, overlap between adjacent traces occurs at 0.02m
depth for K equals 4 and 0.14m depth for K equals 20. These are very shallow
depths for the GPR system and subsequent analysis of profile data has shown
that the airwave and groundwave mask reflectors at these depths. Therefore a
station spacing of 0.05m was used for all 900MHz surveys. 450MHz surveys
were used in scenarios where it was considered likely that soil thickness
exceeded one metre and 900MHz surveys would be unable to penetrate. These
sites were located in the valley bottoms. At these sites 450MHz reflection
surveys were carried out with a station spacing of 0.1m.
4.6.4 Sampling Interval
A returning GPR trace consists of a continuous waveform. Sampling of this
waveform must be carried out at the appropriate temporal resolution in order
that the waveform can be reconstructed. Under-sampling results in a loss of data
and over-sampling leads to the collection of unnecessary data, slowing survey
time and increasing file size. The maximum sampling interval is described by
the Nyquist frequency and is one-half the period of the highest frequency. In
GPR systems the highest frequency is approximately 1.5 times the centre
frequency, therefore following the Nyquist theorem results in a sample rate
twice this, or three times the centre frequency. Annan (1997) suggests doubling
this sample rate to ensure that no GPR signal is under-sampled. Following this
guideline results in a maximum sampling interval of 0.185ns for a 900MHz
survey and 0.370ns for a 450MHz survey. For all GPR surveys carried out as
part of this thesis the sampling interval was 0.05ns, well above the minimum
Nyquist frequency.
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4.6.5 Common Midpoint survey design
A common midpoint survey was carried out at 29 of the 32 sampled sites.
CMP’s were required to measure the subsurface velocity of the electromagnetic
waves and thereby enable the calculation of reflector depth from travel time
data collected by GPR reflection surveys. In conjunction with gravimetric and
theta probe measurements of subsurface moisture, CMP’s were also used to
investigate the relationship between velocity and moisture content in a field
environment.
At each site, one CMP survey was collected along the same 2m line used for the
reflection survey. The antennae were arranged around the one metre centre
point and moved stepwise away from the centre. A Step size of 0.05m and
0.10m was chosen for surveys using the 900MHz and 450MHz antenna
respectively in order that the moveout be comparable with that used for the
reflection profiles. Each CMP was continued until either the transmitted signal
was not visible to the receiver for several traces, or antenna offset reached 2m.
4.6.6 Stacking
Stacking is the term used to define the number of times a single point
measurement is averaged to produce a final GPR trace. In electrically noisy
environments high stacking values reduce the effects of spurious background
interference since the averaging process smoothes the final output trace.
Increasing stacking to 128 measurements (the maximum allowed using the
PulseEKKO software) increases the time needed to measure at each point and
therefore slows the rate of data collection. For this study, stacking was set to 32
measurements as a compromise to ensure good data quality without appreciably
lengthening the time required to measure at each sample site.
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4.7 Validation of GPR subsurface data
Subsurface data is required for the validation of GPR derived soil thickness and
moisture, and needed for parameterisation of the subsurface component of the
hydrological model. There have been a number of studies which have used GPR
to measure soil thickness e.g. Shih et al., (1984), Collins et al., (1987), Truman
et al., (1988), Collins et al., (1989), and soil moisture e.g. Greaves et al.,
(1996), Hubbard et al., (1997) and van Overmeeren et al., (1997). The
techniques are however a current research issue. Physical data collection is
required to validate the results obtained by GPR and to assess the reliability and
accuracy of GPR for measurement of these parameters.
4.7.1 Soil thickness
Soil thickness was measured in the field using a combination of augering and
trial pits. The aim of physically sampling the subsurface at each site was to
identify any correlation between specific soil horizons and reflectors evident in
radar profiles. In order that soil horizons could be associated with specific
reflectors an auger was used to extract soil cores and provide a measurement of
total depth to bedrock. Auger samples were taken at each end of a two-metre
survey line and at the centre point if no trial pit was excavated. Trial pits were
excavated to allow more detailed examination of soil horizons over a greater
area, and were used to sample soil moisture, bulk density and soil texture.
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4.7.2 Soil Moisture
A Delta T theta probe was used to sample soil moisture at the surface and
subsurface for GPR sites. Measurements of subsurface moisture were carried
out for those sites with an excavated trial pit. Readings were taken at intervals
of 0.05m or 0.1m until insertion of the theta probe was impossible due to high
stone content or the bedrock surface was reached. In conjunction with theta
probe measurements, soil samples of a known volume were collected from the
same points for laboratory analysis of volumetric moisture content and
calibration of theta probe measurements.
Theta probes measure the soil dielectric constant and relate this to volumetric
soil moisture using a polynomial relationship (Theta probe User Manual, 1998).
Eight soil samples from four different profile depths were used to perform a soil
specific calibration for the theta probe. Table 4.6 summarises the measured
values of a0 and a1, required for derivation of volumetric soil moisture (θ) from
measured voltage (V) (equation 4.2).
Table 4.6. Theta probe calibration values.
Depth Number of soil samples a0 a1
0-10cm 2 1.32 8.5910-20cm 2 1.37 9.1320-30cm 2 1.41 8.6530-40cm 2 1.47 6.68Mean 1.39 8.26
(4.2)
( )1
032 7.44.64.607.1
aaVVV −+−+
=θ
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4.7.3 Soil physical properties
The two soil properties required as hydrological model parameters are bulk
density and texture. The variation in bulk density with depth is used by the
model to calculate soil porosity at any soil thickness, and subsequently to
calculate wetting front depth (equation 3.7) and water table depth (equation 3.9)
for each timestep. Soil texture (mass fraction sand and clay) is required as input
to the infiltration module (equation 3.3). The soil samples collected for analysis
of moisture content were also used for bulk density measurement and textural
analysis. A total of 55 bulk density measurements and 30 texture samples were
collected from trial pits excavated at sites within the catchment.
Analysis of field data shows an exponential decline in porosity with increasing
soil thickness, derived from 55 bulk density samples for 17 sites and at varying
depths across the catchment. Figure 4.13 shows the relationship between
average sample porosity and soil overburden thickness derived from field
measurements. The relationship between depth (x) and porosity (φ) from 55
field soil samples is
(4.2)
8286.0 848.0 2757.0 == − re xφ
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Figure 4.13. Depth – mean porosity relationship derived for the Cyff catchment
The total depth of soil needed to store a known amount of water between two
depths x1 and x2 is equivalent to the integral of equation 4.3 between the limits
x1 and x2.
(4.3)
In the case of infiltration from rainfall or upslope runoff, φ = infiltrated water
this timestep, and x1 = wetting front depth from the previous timestep. Solving
equation 4.3 and rearranging to make x2 the subject gives the new wetting front
depth for the current timestep.
dxex
x
x∫ −= 1
2
848.0 757.0φ
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4.8 Errors
Soil depth measurement used a steel tape to record the thickness of each soil
horizon core contained within the auger. A steel tape is unaffected by any
stretch which could occur if a plastic measuring tape were used. The tape used
was marked at millimetre intervals, allowing measurement of depth to ± 2mm.
Theta probe measurement error was minimised using the soil specific
calibration technique described in the Theta Probe User Manual (1998). Using
this method, soil moisture measurements are accurate to ± 0.02 m3/m3 over a
temperature range of 0-40oC (Theta Probe User Manual, 1998).
Measurement of wet and dry soil weight for the gravimetric method of soil
moisture content were carried out in the laboratory using a balance sensitive to
one hundredth of a gram. Using the mean of all eighty dry and wet sample
weights (Appendix III, table III.1), the effect of a measurement error of ± 0.01g
applied to wet and dry soil samples represents a soil moisture error of ± 0.001
m3/m3. More general problems associated with the gravimetric method concern
the oxidation of organic material during the drying process and the potential for
underestimating water contents, especially in clay soils where adsorbed water is
not fully evaporated during oven heating at 105oC (Ward & Robinson, 2000).
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4.9 Conclusion
A background to Plynlimon has been presented along with a justification for
choosing the Cyff as a study catchment. The hydrological parameters required
for model input and validation and the methodology used to collect the data at
scales appropriate to modelling requirements has been discussed. Topography is
an important factor in any hydrological study given that it is a control on
hydrological flow rates and pathways, and determines some of the spatial
variation of variables including soil moisture. Recreating an elevation surface as
a grid structure is problematic since the choice of cell resolution effects the
resulting terrain attribute values derived from the DEM.
The influence of topography on catchment hydrology and soils required the use
of slope, upslope area and wetness topographic indices for selection of sample
sites for subsurface investigation using GPR and physical sampling. Preliminary
investigation using frequencies of 225, 450 and 900MHz showed that GPR was
a viable survey tool for the subsurface in this area. Subsequent detailed
investigation of soil thickness and soil moisture spatial variation was undertaken
using 900MHz and 450MHz antennae for high resolution of subsurface
reflectors. Physical sampling of soil thickness, moisture, texture and bulk
density was carried out at sites to validate GPR measurements of site specific
depth and moisture, and to provide parameter values for the hydrological model.
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Chapter 5: Soil Thickness Data Analysis
5.1 Introduction
This chapter examines the methods used to derive soil thickness using radar.
The results obtained are compared with those measured by physical excavation
at each site using a soil auger and trial pits. Using the catchment DEM the
spatial variation in soil thickness is compared with a number of spatial
variables, notably local slope gradient, upslope drainage area and the
topographic wetness index. These variables are subsequently used to extrapolate
from individual site soil thickness to a catchment wide distributed map of soil
thickness variation, required as an input to the subsurface module of the
hydrological model.
5.2 Analysis Methodology
Figure 5.1 shows the processing methodology followed to analyse collected
GPR data for soil thickness measurement at each survey site. An initial radar
profile is visually displayed and simple display parameters are manipulated to
aid in identification of subsurface features, in this case the identification of soil
horizons and total soil thickness to bedrock. Visual examination of a profile is
helpful in subsequent analysis of individual radar trace characteristics. CMP
analysis is a key component of the processing stream given that accurate
derivation of the depth to a reflector relies on a detailed knowledge of the
pattern of subsurface velocities. Extraction of individual traces corresponding to
the location of physical samples and the application of the local velocity
distribution in a spreadsheet package enables a quantitative approach to
reflector characterisation. An observed correlation between reflections in a
series of individual traces and physical sampling of the soil enables a
measurement of the average depth to a reflector in a profile.
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Figure 5.1. Deriving soil thickness from GPR surveys.
GPR reflection profile
Visual display of original profile &hardcopy printout
ID potential reflectors of interestusing visual interpretation
Apply DEWOW/DCSHIFT &simple filters/gains
Data conversion(PE to ASCII)
CMP survey
Extract individual trace amplitudedata corresponding to sample
points
Import trace data tospreadsheet and apply
velocity field
Identify key reflectors in atrace which correspond to
soil features
Apply PE velocityanalysis module
Measure gradient ofgroundwave/reflectors to
derive depth-velocitystructure of the subsurface
Visual display of original CMP &hardcopy printout
Reconstruct travel time-velocitystructure of the subsurface
Apply to entire GPRprofile
Compare GPR resultswith auger measurements
of soil depth
Derive mean site soilthickness
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5.2.1 Initial GPR profile display
Visual display of each site profile was undertaken using the PulseEKKO
software. The software enables limited processing of a profile, without altering
the original amplitude data file. Initial data processing was confined to the
permanent dewowing of all GPR profiles. Wow is the term applied to a low
frequency component of the initial transmit pulse which decays slowly over
time. It is present to an extent in all GPR data and depends on ground conditions
and antennae separation. This low frequency component obscures the return
signal from reflectors but can be removed effectively by a high pass filter.
Historically this is known as dewowing (Sensors & Software Inc., 1993). The
high pass filter does, however, create a system artefact of one half-period cycle,
located before time-zero.
The second stage in display is gain recovery. Gains may take the form of a
constant multiplier to all raw amplitude data or a time-variant function. Time-
variant gains compensate for the increased spreading and attenuation of an
emitted pulse with increased travel time. As a result of these effects those
reflectors at longer travel times are of lower amplitude compared with those of
shorter travel times (Fisher et al., 1996). Two time variant functions available in
the PulseEKKO software are spreading and exponential compensation (SEC)
and automatic gain control (AGC). As an initial step all profiles were displayed
with a low constant gain of 5-10 in order to pick the highest amplitude reflectors
present in a profile. In many instances application of a constant gain clearly
showed linear reflectors within 0-30ns of the surface. In other cases a constant
gain points to zones of potential interest within a profile, usually at greater
travel times. Subsequent use of SEC or AGC gain to offset spreading and
attenuation effects yields an improved image of deeper subsurface structure.
Figure 5.2 shows the differing effect caused by the application of a constant
gain and a SEC gain to the same radar profile, site 20. The upper boundary
position of the B-horizon and C-horizon are marked in red and blue
respectively, physically identified by auger measurements.
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Figure 5.2. 900MHz GPR profile (site 20) showing the difference in detaildisplayed using a constant gain compared to a SEC gain. The depth axis valueassumes a single velocity value (0.06m/ns) applies to the entire profile.
Further improvements in image display are provided through trace averaging.
Two averaging tools were used to smooth profile images, acting between
adjacent traces (spatial) and down traces (temporal). All averaging acted on the
displayed image rather than the raw data and in the majority of cases averaging
was avoided. Spatial (trace to trace) averaging acts to smooth the spatial
variation in linear reflectors by averaging adjacent traces within a user defined
window. Temporal (down trace) averaging results in a smoothing of amplitude
data where the number of points included in the averaging operation is user
specified. Temporal averaging can lead to a reduction in high frequency noise,
which is a common feature in data from longer travel times. Image quality is
degraded by high frequency amplitude variation caused by signal degradation.
Application of a gain to data, for example application of an AGC gain to
equalise arrivals from all depths tend to show increased noise. In all instances
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where averaging was used the maximum number of adjacent traces/points used
were set to two.
Examination of each site profile is an essential first step in GPR data
processing, particularly for the identification of linear features which in this
study were potential soil horizon boundaries. Display of radar images is a
highly subjective method of interpretation as is the application of gains and
averaging operators, which can result in the creation of image artefacts. To
reduce this potential all gains have been kept as simple and as limited as was
possible to reduce the probability of artefact creation. Investigation of the
response of individual trace amplitude to varying soil horizons is the next stage
of a quantitative method to soil thickness measurement using GPR.
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5.2.2 Derivation of subsurface velocities
Given knowledge of the nature of subsurface velocity variation, travel time can
be recalculated as reflector depth. The following outlines the method used to
derive soil thickness from travel time data. Derivation of depth from any GPR
profile relies on the accurate estimation of the propagation velocity of the layer
which the EM wave passes through. The Common Midpoint (CMP) survey is
the standard method for deriving velocity profiles and therefore forms a key
requirement for depth estimation. The velocity analysis program is based on the
assumption that signal travel time from reflectors varies hyperbolically as the
separation between transmitter and receiver increases. A CMP survey was
carried out at each of 29 sites and analysed using Picker (Sensors & Software
Inc.). CMP surveys were imported into Picker, a software package that enabled
the increase in travel time (t) with increasing antennae separation (x) to be
measured and used to calculate velocity. The process was based on the normal
moveout procedure, in which a plot of increasing t against x shows a linear
change in airwave and groundwave arrival, while reflectors from subsurface
layers exhibit a hyperbolic shift in arrival time (figure 5.3). The inverse
gradients of reflectors plotted as t2 against x2 are equal to an average velocity
value from zero time (ground surface) to the reflector, termed a root mean
square velocity (vrms) (Reynolds, 1997) and calculated by
(5.1)
Figures 5.3 and 5.4 show the increase in airwave, groundwave and reflector
travel time with increasing travel time, both as a PulseEKKO CMP profile and
displayed within the Picker software enabling measurement of the change in
travel time with antennae moveout. All CMP derived velocities for sample sites
are listed in table II.4, Appendix II.
21
21
22
21
22
−−
=ttxxvrms
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Figure 5.3. CMP surveys for site 56 and site 50 using 900MHz antennae.
Figure 5.4. Initial 10 traces from site 50 plotted using Picker software. Airwavearrival time marked by red, ground wave arrival by green and first pickedreflector by blue lines.
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Actual layer velocity (Vint) can be estimated using the Dix equation (5.2), (Dix,
1955) which should provide a more accurate value for soil thickness and
potentially water content (Chapter 6). The Dix equation was applied to the CMP
velocities to produce a corresponding interval velocity. The interval velocity
was then used in all subsequent time to depth conversions of profiles.
(5.2)
Where Tn and Tn-1 are two way travel times to the nth and n-1 reflectors
respectively.
5.2.3 From time domain to depth domain
The derivation of accurate estimates of reflector depth from GPR requires that
two way travel time (T) is transformed to a value of depth using a velocity for
the layer(s) above the reflector in question. In most cases this conversion is
simply T halved and multiplied by the velocity v to give reflector depth d
(equation 5.3), which gives an adequate depth value for most GPR applications.
(5.3)
However due to the finite distance between the transmitter and receiver the path
taken by an emitted EM pulse is not vertical but forms an isosceles triangle with
the lowest vertex located on the reflector midway between the transmitter (Tx)
vTd ×
=
2
( ) ( )( )
21
1
12
1.2
.int
−−
=−
−−
nn
nnRMSnnRMS
TTTVTVV
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and receiver (Rx) (figure 5.5). Actual depth to a reflector (d) is therefore
somewhat less than half two-way travel time. As depth increases T tends to 2d
and the approximation of reflector depth equalling one way travel time is a valid
one. At shallow depths however this is not the case since T >> 2d. In this case
equation 5.3 produces apparent depths in excess of actual depth. In order to
compensate for this effect the PE1000 software module displays an initial non-
linear depth axis compared to the time axis.
This study of the use of GPR as a tool for evaluating subsurface soil structure
and hydrology requires manipulation and evaluation of data in a manner not
covered by the PulseEKKO software module. The majority of interpretation is
carried out in a spreadsheet package and one component requires the validation
of GPR derived soil thickness with soil auger depths. The auger data collected
from the Cyff fieldsites suggests that soil thickness falls in the range of 0.1 -
2.0m and therefore inclusion of a non linear time - depth conversion within the
spreadsheet is essential for the accurate positioning of GPR reflector depths and
for validation of these shallow reflectors with auger data.
Without an initial non-linear time-depth conversion shallow reflectors will
appear to be located at greater depths below the ground surface than they are in
reality. A good example is the ground wave itself, which travels directly
between Tx-Rx and therefore arrives at a time of antenna separation divided by
ground velocity. Plotted on a depth axis which increases linearly from time zero
places this reflector at a non-zero depth.
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Figure 5.5. Theoretical wave travel path for offset antennae.
The relationship between actual reflector depth (d), antennae separation (x), two
way travel time (T) and the layer velocity (v) is shown in figure 5.5. One way
travel time forms the hypotenuse of a right-angled triangle allowing the true
depth to reflector to be calculated as
(5.4)
Implementation of equation 5.4 in a spreadsheet is straightforward when
applying a single average velocity to all layers, as is the case for the
PulseEKKO software. For each increase in one way travel time the equation is
applied to calculate the depth. However if incremental depth values are
calculated from the start, the time increments are always small compared to
antenna offset distance, resulting in very small values for d or error values
caused by negative square root calculations.
21
22
22
−
×=
xvTd
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To solve this problem equation 5.4 was implemented for the first velocity layer
only while for deeper reflectors depth was calculated in increments using the
standard assumption that depth is equivalent to one way travel time (equation
5.3). This method can be justified by the decrease in importance of antenna
offset as depth increases. Neglecting the antennae offset effect results in the
largest errors in actual depth for shallow reflectors. Given that in the case of the
Cyff the initial velocity layer has a mean two way travel time of 12ns (T) for
900 MHz this method seems valid. Values of T in excess of 12ns produce little
difference in calculated reflector depth value between the two methods of
calculation (equation 5.3 & 5.4). The difference in reflector depth between
equations 5.3 and 5.4 is 0.08m. Table 5.1 shows comparisons between depth
estimates for the 900MHz (offset 0.17m) and assuming an initial layer velocity
of 0.06m/ns (the average for the data set). Figure 5.6 shows the predicted depths
calculated using standard depth estimates (equation 5.3) and incorporating
antennae offset (equation 5.4).
Table 5.1. Reflector depth using linear/non-linear methods of calculation.
FrequencyMHz
Two WayTime (ns)
Depth = Equation 5.4 (m) Depth = Equation 5.3 (m)
900 1.0 0.030 0.000
900 2.5 0.075 0.000
900 5.0 0.150 0.124
900 10.0 0.300 0.290
900 15.0 0.450 0.442
900 20.0 0.600 0.594
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Figure 5.6. Comparison between linear and non-linear depth calculation.(900MHz, v=0.06m/ns, x=0.17m)
A second concern is the calculation of total travel time. Within the PE software,
time zero is taken as the time at which the airwave arrives at the receiver and all
subsequent arrival times are zeroed from this point. Ground zero is taken as the
time taken for a direct wave to travel from Tx - Rx minus airwave travel time.
However due to the finite offset of Tx Rx the airwave does not arrive
instantaneously at Rx but takes a short period of time to travel between the two
antennae. This is calculated as
(5.5)
Where x is antenna separation and vAIR is airwave velocity (0.3m/ns).
This is the time at which the initial pulse was transmitted and should therefore
be added to all time values to give a travel time from pulse transmission rather
than from when the airwave arrives. Again when considering reflectors at
depths greater than 0.2 - 0.3m this extra time is insignificant considering the
unknown accuracy of velocity estimates for the subsurface, but at very early
times (and shallow reflectors) this can be a significant time period.
AIRvxt =
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Accurate depth measurements from GPR traces require that ground zero is
located in the correct position. Theoretically a PulseEKKO wavelet is 1.5
cycles. The first signal arrival is the airwave followed by the ground wave and it
is possible to pick these individual arrivals when antennae offsets are large as is
the case during CMP surveys. In reality at small antennae offsets these two
arrivals overlap causing interference patterns which causes problems when
attempting to visually pick ground zero with any accuracy. In this case
knowledge of ground surface velocity (vg) and antenna separation (x) could be
used to calculate theoretical ground zero. Ground-zero can be calculated as
(5.6)
This is the time from initial signal transmission, but it is more common to fix
zero time as the time at which the airwave arrives rather than actual signal
transmission. In these terms the time of ground wave arrival (t) after time-zero
(airwave arrival) is given by
(5.7)
Since time-zero can be identified from a graph of signal response as the first
zero crossing, ground-zero can now be located assuming that the ground
velocity value is correct. Within a spreadsheet model this allows the position of
the ground surface to be located and subsequent calculations for successive
reflector depths calculated using equations 5.3 and 5.4.
ggzero v
xt =
0ttt gzero −=
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5.2.4 Direct wave masking of shallow reflectors
The direct wave, a combination of the air and ground wave, acts to mask very
shallow reflections from the subsurface. This effect is termed transmitter
blanking (Annan, 1997) and results from the requirement for two events to be a
minimum of one half of the envelope width of the electromagnetic pulse in
order for these events to be resolved as separate reflectors. In terms of the
minimum path length that can be resolved this can be calculated using
knowledge of antennae frequency and direct wave travel time. The minimum
depth at which a reflector can be distinguished from the direct wave is
important in this instance because of the shallow depths of organic horizons
across the catchment.
For a 900MHz survey with antennae separation (x) of 0.17m and a ground
velocity (v) of 0.06m/ns the theoretical direct wave travel time is 2.833ns from
transmitter to receiver. GPR systems are designed such that the centre frequency
is inversely proportional to the pulse period (Reynolds, 1997), therefore a
900MHz antennae has a pulse period of 1.11ns. The output pulse envelope from
a PE1000 system is 1.5 cycle waveform and therefore in this scenario total pulse
duration (D) is a determined by pulse period and pulse envelope length. Annan
(1997) states that two events can only be distinguished as separate reflectors if
they are separated in time by a difference of half the envelope width, in which
case the minimum travel time (tmin) at which an event can be resolved is given
by equation 5.8.
(5.8)
tmin = Direct wave travel time + Pulse envelope + One half pulse envelope
DDvxt
43
23 min ++=
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Minimum travel time is more useful when converted to a minimum depth
estimate. Substituting tmin as T into equation 5.8 calculates the minimum vertical
depth to a reflector. Reflectors occurring at depths less than this value will be
indistinguishable from the direct wave return. Table 5.2 summarises the
minimum reflector depths calculated for 900 and 450MHz surveys.
Table 5.2. Calculation of minimum resolution depth using an average velocity of0.06m/ns, derived from 29 CMP ground wave velocities.
900MHz 450MHz
Antennae separation (m) 0.17 0.25
Pulse period (n/s) 1.11 2.22
Direct wave travel time (n/s) 2.83 4.17
tmin 5.33 9.17
Minimum depth (m) 0.14 0.24
5.2.5 GPR depth measurement errors
Error in GPR depth measurement is a result of a) error in the measurement of
subsurface velocities, and b) error in the measurement of signal travel time. The
magnitude of these errors is calculated using standard error methods which
enable the combination of errors in velocity (m/ns) and travel time (ns)
measurement to produce a single reflector depth error.
In order to quantify errors from measurements with different units, the precision
(Py) of each measurement (y) is calculated, where ∆y is the error associated with
the measurement (equation 5.9).
(5.9)y
ypy∆
=100
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Combination of the precision (Px) of different measurements is found by
(5.10)
Using this final precision and reflection depth (d) in metres, the total error (A)
can be calculated as
(5.11)
Error in velocity measurement can be caused by a) incorrect measurement of
travel time to the reflector with increasing antennae separation, and b) errors in
the positioning of GPR antennae along the CMP line. Positioning error is a
result of the inaccurate placement of GPR antennae along the CMP line. For this
study each CMP was carried out along a two-metre line on uneven ground using
a plastic tape with half-centimetre interval markings. The error between antenna
location for each measurement is estimated to be ±0.02m
Sources of error associated with measurement of the change in travel time to a
reflector include error in picking reflections, with Picker software able to
resolve to 0.01ns. However a greater limiting factor is the GPR sampling
interval which was set at 0.05ns for all surveys in this study. The exact point of
time zero for each trace, identified using Picker, is conservatively estimated as
accurate to 0.5ns. No filters and only constant gains were applied within the
Picker software to ensure reflector travel times were not shifted.
Using the above values of error in time and distance in equations 5.9 and 5.10
the error in velocity measurement was calculated, using a survey line length of
1m and an average velocity of 0.06m/ns, calculated from all non-air wave
velocities (table II.4, appendix II ). The calculated precision is 4.4% which
equates to a velocity error of 0.003m/ns.
22zyx ppP +=
100xPdA ×
=
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The same method was used to calculate the error in GPR depth measurement,
using the previously calculated velocity precision and combining with the
calculated error in travel time measurement with a travel time of 60ns used in
equation 5.10. Using these error values for velocity and travel time results in a
precision of 4.5%. Table 5.3 shows the absolute error calculated using equation
5.11 for reflectors at varying depths.
Table 5.3. Error associated with increasing depth to a reflection, assuming aconstant velocity of 0.06m/ns and two-way travel time of 60ns.
Reflector depth (m) Absolute error (m)
0.20 0.009
0.50 0.022
0.75 0.034
1.00
1.50
0.045
0.067
5.2.6 Theoretical resolution of reflectors
For GPR systems the maximum theoretical resolution r is one quarter pulse
wavelength (Reynolds, 1997).
(5.12)
The average of velocities calculated from analysis of site CMP’s is 0.06m/ns.
Using this value for v in equation 5.12 predicts a maximum resolution of 0.02m
for 900MHz antennae and 0.03m for 450MHz antennae.
fvr
4=
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5.3 Analysis of individual GPR traces for depth extraction
Application of the velocity data derived from a site specific CMP and
incorporation of the initial non-linear time to depth conversion enables the
response of signal amplitude with changing depth to be derived for any trace. In
the Cyff catchment the observed, visually well defined, changes in soil horizon
and associated changes in soil properties (e.g. bulk density, porosity, texture and
stone content) were thought to result in the formation of a soil profile with
defined dielectric boundaries. The presence of dielectric boundaries is evident
from standard GPR profile data by the large number of reflectors typically
shown on these profiles. However the hypothesised correlation between specific
soil horizon boundaries and zones of high/low amplitude signal requires a more
detailed analysis of the profile data. To achieve this, GPR traces along each
radar profile corresponding to soil auger and trial pit points were used to
examine the correlation of minimum and maximum amplitude values with the
physical measurement of soil horizon thickness.
5.3.1 Reflector identification
The PulseEKKO transmit pulse takes the form of 1.5 cycle waveform.
Subsequent reflections retain this waveform and therefore the location of
subsurface reflectors are identifiable by the presence of this shape within a
trace. The situation is complicated by factors including: 1) closely spaced
reflectors compared with signal wavelengths which create multiple returns
which cannot be individually recognised as specific reflectors. 2) amplitude
decay due to spreading and attenuation losses which leads to problems
identifying deeper reflectors against background noise of a similar amplitude
level. Applying a time variant SEC or AGC gain can compensate for this second
problem to an extent, but both require a knowledge of ground attenuation
characteristics and an arbitrary choice of maximum and minimum gain levels.
Applying a constant gain to trace amplitude data multiplies all data values by a
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defined amount and therefore acts indiscriminately on actual reflectors and
background noise. An alternative approach used by this study applies a power
gain to amplitude data, whereby each raw data value is raised to a user-defined
power, resulting in the suppression of low amplitude values and enhancement of
higher amplitudes. This approach assumes that low amplitudes are generally
noise and that the suppression of these parts of the trace enables easier visual
identification of potential reflectors. The difference between application of a
constant and power gain is shown in figure 5.7 using a GPR trace from site 40.
Figure 5.7. Application of a constant gain of 2 (a) and a power gain of 2 (b) forsite 40, 0m.
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5.3.2 Picking horizon position within a GPR trace
For individual trace data the position of a horizon boundary within a profile was
recorded as the first zero crossing preceding a positive peak of magnitude
greater than the preceding maximum. In general at each site, two auger samples
and one excavated pit at a spacing of one metre were compared with three GPR
traces at equivalent positions. For a number of sites located on peat deposits the
horizontal sample frequency was increased to an auger sample every 0.5m
primarily because the low bulk density of the subsurface at these sites enabled
the auger to be inserted to bedrock by hand.
The process of picking reflectors for each trace emphasised the differences
between the hillslope soils, and the peat soils of the valley bottom and ‘rush
flushes’. Rudeforth (1970) also makes a distinction between soils of the
Hiraethog series and undifferentiated peat complexes on the basis of soil
horizon properties. From the results of this study both categories exhibit
physical differences in vegetation types, soil physical characteristics and GPR
properties. Hillslope soils were further subdivided into those that were ‘simple’
and those that were ‘complex’ environments in terms of GPR profile
interpretation. These three subsurface classes are explained below.
5.3.3 Peat soils (Class 1)
The toe slopes of the Cyff are dominated by raw peats (histosols) which grade
into humic gleysols on the crest-slope shoulders and areas immediately above
the toe-slopes (Chappell & Ternan, 1993). These peat deposits were also found
to extend upslope in side valleys, features known as ‘rush flushes’ that act as
drainage routes for the adjacent hillslopes. Seven out of a total of thirty GPR
sites have been classified as belonging to class 1 subsurface environments on
the basis of GPR profile and trace characteristics discussed below. Physical
sampling of the soils at 18 of these sites show the differences in bulk density
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(figure 5.8) between peat sites and those sites classified as hillslope soils (Class
2 & Class 3). Assuming a constant soil particle density, bulk density was used
to derive soil porosity. Given the importance of water on the dielectric
properties of materials and the propagation velocity of an electromagnetic wave
through a medium, soil porosity is of interest when conducting GPR site
investigation.
Figure 5.8. Dry bulk density measured at 18 sites within the Cyff catchment,depth measured using a steel ruler.
In terms of GPR profile interpretation, peat soils provided an excellent medium
for the use of radar as a method for deriving soil thickness to bedrock. This is
due to the absence of multiple GPR reflectors within the soil profiles, rather, the
highest amplitude after the direct wave arrival correlates well with the measured
bedrock depth using a soil auger. An example radar profile from site 33 and a
single trace extracted from the 1m along line position is shown in figure 5.9.
The profile exhibits characteristics common to all GPR profiles collected from
peat sites in the catchment.
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Figure 5.9. GPR traces: - Peat soils. a) 2m GPR profile site 33, b) Raw amplitudeextracted from trace at position 1.00m, c) Amplitude squared at trace position1.00m.
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GPR profile and trace features characteristic of the peat soils found in the Cyff
are listed:
1. GPR profiles of peat soils show shallow depth horizontal banding,
effectively blanking any returns from reflectors up to 15-20ns deep (two
way travel time). This phenomenon is a result of the arrival of the high
amplitude direct air and ground waves during this time interval.
2. Subsequent high amplitude signals are predominantly caused by the
reflection of the electromagnetic wave from the boundary between the
organic peat deposits and the C-horizon. Auger samples confirmed that the
underlying material at this boundary was either solid rock or rock fragments,
given the underlying geology noted by previous soil surveys (Rudeforth,
1970) and field observation of bedrock outcrops, this material is slate and/or
shales.
3. Analysis of extracted GPR traces found that after omission of the direct
wave from each trace, the zero crossing that precedes the greatest or second
greatest peak amplitude correlates well with the measured auger depth to the
C-horizon. Often the greatest and second greatest amplitude after the direct
wave form the same PulseEKKO waveform, but no set pattern is identifiable
from these data sets as to which amplitude arrives first. This rule is
applicable when traces have had no gain or a constant gain applied to the
profile.
4. GPR profiles of peat soils were collected using both 450MHz and 900MHz
antennae. In terms of radar profiles, the lower frequency generally provided
a visually clearer indication of the soil - bedrock interface (figure 5.10.).
Examination of individual traces taken using both frequencies at the same
location (figure 5.11.) confirms that, for each frequency, the highest or
second highest positive amplitude value after the direct wave corresponds to
the bedrock boundary position. In addition the absolute values associated
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with the maximum amplitude in each trace are dependent on the frequency
used. In this example the 450MHz trace has a peak positive amplitude of
4087 compared with a positive peak value of 668 for 900MHz. This trend is
continued throughout the profile and for other sites located on peat soils. In
general peak positive amplitudes recorded using 450MHz antennae are 5-12
times larger than peak amplitudes recorded for the same position using
900MHz antennae (raw amplitude data). The resulting effect is one of
increased magnitude reflectors that are visually evident within a
profile/trace. This effect is likely to be a direct result of the increased
attenuation of electromagnetic waves at higher frequencies thereby resulting
in a reduction in the recorded amplitude at dielectric boundaries.
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Figure 5.10. Site 37 profile using 450MHz and 900MHz antennae.
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Figure 5.11. Trace amplitude comparison for site 37 bedrock boundary (O/Chorizon) for 900 MHz and 450 MHz GPR trace at the same location.
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5.3.4 Simple hillslope soils (Class 2)
57% of sites investigated (17 of 30) were classified as simple hillslope soils.
Excavation of the subsurface at these sites showed the existence of well-defined
soil horizons, generally consisting of a 0.1-0.2m thick dark brown/black organic
(O) horizon, a grey/white Ea horizon overlaying a yellow-red-brown B horizon
of high stone content. The middle and upper-slope positions which these sites
occupy are typically underlain by several metres of soliflucted regolith (Watson,
1967), and bedrock consisting of shales and mudstones (Rudeforth, 1970).
GPR profiles of these sites exhibit a more intricate subsurface image with a
greater number of reflectors than are present in the class 1 peat soils. The
presence of defined horizons within the soil profile should result in
corresponding dielectric boundaries being evident in GPR data. The assumption
is that the observed variation in soil physical properties, most importantly
moisture content, but also texture, results in a response at the frequencies used
by GPR for this thesis. Given that three distinct horizons are evident from
excavated soil profiles these three horizon boundaries should be distinguishable
within GPR data. Actual GPR profiles taken at these class 2 sites have been
found to contain a greater number of reflectors, reflecting the complexity of the
subsurface and the influence of stones within the soil profile on radar traces.
Analysis of soil thickness data for class 2, simple hillslope sites, showed that the
B and C-horizon boundary depths derived from GPR traces correspond well
with auger and trial pit measurements. However the majority of sites exhibit
shallow depth organic horizons (Organic <0.20m for 88% of class 2 sites)
resulting in no possible measurement of O horizon depth using GPR due to the
interference of the direct wave arrival at these time windows.
Figure 5.12 shows a profile from site 8, a class 2 site with a mean depth to C-
horizon of 0.43m from GPR and 0.47m from auger measurements. Figure 5.13
details traces at zero, one and two metres along the transect line which
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correspond to auger sample points. At site 8, the C-horizon boundary defined by
auger data corresponded with the zero-crossing point prior to the greatest
positive amplitude after a depth of 0.30m. Likewise the A-B soil horizon
boundary corresponded with the zero-crossing point prior to the peak positive
amplitude value and occurring after the direct wave, in a depth window between
0.25 and 0.35m. The actual points picked as GPR depth estimates are marked by
blue (B-C boundary) and red (A-B boundary) vertical lines. Table 5.4
summarises the difference in measured depth between GPR and auger data. This
analysis was carried out for each of the 30 sites investigated.
Table 5.4. Soil thickness measurements for site 8 using an auger and 900MHzGPR survey.
Position A-B auger(m)
A-B GPR(m)
Difference(m)
B-C auger(m)
B-C GPR(m)
Difference(m)
0m 0.30 0.30 0.00 0.45 0.39 -0.06
1m 0.30 0.28 -0.02 0.50 0.43 -0.07
2m 0.26 0.33 0.07 0.46 0.47 0.01
Site Mean 0.29 0.30 0.47 0.43
GPR depth error was calculated using equations 5.9 –5.11 and the site mean depths to each horizon. The
resultant errors are 0.013m for the A-B horizon and 0.021m for the B-C horizon, assuming a constant velocity
of 0.06m/ns.
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Figure 5.12. GPR profile: - Class 2 hillslope soils. (Site 8, 900MHz antennae,constant gain 10).
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Figure 5.13. GPR trace amplitude characteristics for site 8, 900MHz GPR survey.
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5.3.5 Complex hillslope soils (Class 3)
Class 3 sites composed six out of the total of thirty sites investigated (20%).
Complex hillslope soil sites were found to commonly lack coherent linear
reflectors within the GPR profile, or contained individual traces that correlated
poorly with auger observations of soil horizon position or total soil thickness.
Site 54 is an example of the latter scenario, in which four auger measurements
along the 2m-survey line varied in soil thickness to bedrock from 0.35m to
0.84m. A GPR profile obtained along the same line showed a linear boundary at
a depth of approximately 0.5-0.6m throughout the profile (figure 5.14). The site
was subsequently excavated to a depth of 0.6m along the 2m-survey line. At
this depth the B-horizon graded into a deposit of angular rock fragments
forming the upper C-horizon. The non-cohesive and brittle nature of the
underlying rock fragments had allowed auger penetration into the C-horizon
materials to a depth of 0.3m at points along the survey line, until encountering
larger rock fragments. Figure 5.15 shows the range of fragment sizes removed
from between 0.5-0.6m depth.
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Figure 5.14. GPR profile: - Class 3 hillslope soils. (Site 54).
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Figure 5.15. Stone fragments located at 0.5 - 0.6m depth.
Post processing of radar traces (DEWOW) and extraction of raw data for
amplitude – depth investigation provided an improved picture of subsurface
structure. The four trace amplitude signatures corresponding to auger samples
taken at 0, 0.5, 0.75 and 2 metres along the survey line are shown in figure 5.16.
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Figure 5.16. Radar traces corresponding to the location of four auger points
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In summary, GPR trace information from class 3 sites can be used to derive
depth to horizon measurements, but these sites generally require more extensive
physical excavation in order to positively identify the nature of specific
reflectors with a degree of certainty.
5.4 Soil thickness measurement using GPR
From the 30 sites investigated using GPR and augering, 111 physical
measurements of the depth to C-horizon and 46 measurements of B-horizon
depth were compared with GPR traces at the corresponding point. Table 5.5
summarises the mean GPR and auger measurements of B and C-horizon depth
on a site by site basis. The full table of individual auger and GPR measurements
is detailed in Appendix II, table II.5. Figures 5.17 – 5.19 show the relationship
between the depth to a specific horizon for individual measurements and as a
function of the mean horizon depth at each site.
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Table 5.5. Summary soil thickness data for all sample sites
Mean site depth (m) to B-horizon Mean site depth (m) to C-horizonSite ID Class Auger GPR Difference Auger GPR Difference
5 2 0.25 0.26 -0.01 0.5 0.43 0.076 2 0.17 0.18 -0.01 0.26 0.27 -0.018 2 0.29 0.3 -0.01 0.47 0.43 0.049 1 0.94 0.97 -0.0317 3 0.16 0.17 -0.01 0.93 0.85 0.0818 2 0.47 0.45 0.02 0.71 0.67 0.0419 2 0.26 0.23 0.03 0.42 0.42 0.0020 2 0.19 0.2 -0.01 0.47 0.44 0.0321 3 0.46 0.45 0.01 0.78 0.75 0.0322 2 0.23 0.23 0.00 0.66 0.62 0.0427 2 0.36 0.43 -0.0732 2 0.18 0.21 -0.03 0.3 0.34 -0.0437 1 0.85 0.85 0.0039 1 0.82 0.94 -0.1241 1 0.83 0.89 -0.0649 2 0.27 0.25 0.0250 2 0.29 0.34 -0.0552 2 0.22 0.26 -0.0454 3 0.24 0.25 -0.01 0.56 0.44 0.1260 2 no data 0.2913 3 0.25 0.25 0.00 0.71 0.62 0.0914 3 0.25 0.24 0.01 0.68 0.44 0.2415 2 0.14 0.2 -0.06 0.71 0.73 -0.0216 2 0.43 0.44 -0.01 0.48 0.44 0.0423 2 0.30 0.29 0.0124 2 0.37 0.29 0.0833 1 0.64 0.61 0.0340 1 no data 1.4448 3 0.59 0.52 0.07 0.85 0.7 0.1553 2 0.31 0.36 -0.05 0.62 0.5 0.1256 1 1.00 1.04 -0.04
The individual measurements of soil thickness by auger and GPR methods
(appendix II, table II.5) were used to calculate the RMS of the difference
between the two methods of depth measurement to the B and C soil horizon.
The results show a RMS of 0.04m to the B horizon and 0.12m to the C horizon.
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Figure 5.17. Soil auger measurements plotted against GPR derived soil thicknessto the B-horizon.
Figure 5.18. Soil auger measurements plotted against GPR derived soil thicknessto the C-horizon.
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Figure 5.19. Average soil auger depth for each site plotted against GPR averagesite soil thickness to the B-horizon and C-horizon.
Inspection of figures 5.17 – 5.19 shows no evidence of a trend away from the
1:1 line, indicating that soil auger and GPR measured depths offer equivalent
measurement results. The GPR method of depth measurement does however
require at least one physical measurement of depth at each site to ensure that the
reflector picked corresponds to the correct soil horizon. Once identified, GPR
can then be used to rapidly quantify the spatial variation of soil horizon depth.
Physical measurements of depth to soil horizons were taken in the field to
enable comparison between radar derived depth and actual depth. Derivation of
reflector depth required the application of subsurface velocities to radar data,
with velocities calculated from a site CMP survey. Because CMP velocities
were used to calculate radar reflector depth, physical measurements can be used
as an independent check on soil horizon depth. The assumption of independence
is valid since although auger measurements were used to identify specific
horizons in a GPR trace, the radar depth axis were not altered, being defined by
the velocity values measured and evaluated from the site CMP.
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Using a single auger core at each survey line, a GPR reflector within a single
trace was identified and flagged as corresponding to a soil horizon interface.
Following this reflector through the GPR profile of the survey line allowed the
variation in reflector depth to be quantified and compared with other physical
measurements of depth along the survey section. The results of the measured
variation in GPR and auger depths at the same point are shown in figure 5.20. A
regression line has been added to show that no systematic trend was found in
the variation of GPR measurements compared to physical measurements of
horizon depth. In this study GPR measured depth was as likely to under record
as over record soil depth at any location.
Figure 5.20. The variation between physically measured and GPR derived soilthickness, where physical measurements are considered to be true depth.
Using the data from all sites displayed in figure 5.20 the root mean square
between auger and GPR measurement of the C-horizon depth was 0.12m and
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0.04m for depth to B-horizon. The increase in GPR measurement variability
with increasing depth of measurement is potentially a result of two factors (a)
the use of higher frequency antennae for shallow depth measurement and
therefore an improved resolution of reflector position and (b) the application of
an incorrect subsurface velocity having a cumulative effect on reflector depth,
increasing the error in position as travel time (depth) increases.
Three outlying residuals are evident in figure 5.20. with values of 0.43, 0.35 and
−0.48m The two positive values are associated with two separate type 1 sites
(peat soils). In each case the remaining nine error values at each site are less
than 49% of the maximum residual value, indicating that the waveform
identified as the bedrock boundary is incorrect for that position only. The
benefit of a survey technique which samples a volume of subsurface rather than
a single point measurement is evident. The error of -0.48m is associated with a
type 3 site (complex hillslope soil). The remaining two auger-GPR comparison
measurements for this site give values of 0.01m and -0.25m. Overall the mean
absolute error between auger and GPR depth is 0.24m, the largest error value of
the 30 sites investigated.
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5.5 The spatial variation of soil thickness
An objective of this study is to investigate the use of GPR to parameterise and
validate a fully distributed hydrological model of which the subsurface is a key
component. Parameterisation has concentrated on the use of GPR to gather soil
thickness measurements from a sample of locations within the catchment with
different topographic and therefore hydrological and pedological characteristics.
Hillslope sediments have a degree of order associated with their spatial
distribution, for example the progressive increase in soil thickness with position
downslope (Daniels & Hammer, 1992). The relationship between topography,
hydrology and soil characteristics is useful since it enables a relationship
between sampled locations and topographic attributes to predict the spatial
variability of a soil characteristic for an entire catchment, over which it is
infeasible to undertake a GPR survey. The method discussed in chapter 5
proposed that topography is an important controlling factor on soil development
and as a result topographic attributes derived from the catchment DEM could be
used as surrogate indicators for soil thickness. The key topographic attributes
considered in this study are slope, upslope area and wetness index (figure 5.21 –
5.27). A number of other topographic attributes are obtainable from the
catchment DEM and have also been compared with the variation in soil
thickness over the catchment, namely altitude, aspect, plan curvature and profile
curvature. Plan curvature provides an indication of converging/diverging flow,
profile curvature a measure of the rate of change of slope and therefore
indication of flow acceleration and the likelihood of deposition/ erosion
(Burrough & McDonnell, 1998). Both plan and profile curvatures are therefore
expected to influence soil development over long time periods and water
movement over much shorter time-scales. A relationship between one of these
variables and GPR derived soil thickness would allow the prediction of soil
thickness for each cell within the catchment.
In order to compare cell topographic attributes with soil thickness it is necessary
to first obtain an average depth from each profile. Two methods of trace
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averaging were considered. The first, averaging within the radar software and
producing an averaged trace for each profile is computationally simple to
implement and produces a single trace which can then be exported to a
spreadsheet package and subsequently reflector depths picked. However while
this method may work well in sites with well-defined linear reflectors it does
less well in noisy complex environments as are characteristic of this area. If
reflectors are coherent i.e. they appear at the same depth then this method will
work well, but a shift in reflector depth or the addition of other reflectors leads
to destructive interference patterns and degradation in trace quality. In particular
the pulse and a half wave pattern that characterises a reflector is often lost
during this process, making interpretation of specific horizon depths very
difficult. This method creates an effective depth value that may not relate to any
actual observed depths. The second approach and the one used for this study
uses individual trace analysis, in this case traces which corresponded to augur
sample points, to identify reflector depth. Depths derived using this method
were then averaged to give a mean profile value. The advantage of this method
is the clarity of single rather than averaged reflection wavelets and use of augur
data to verify horizon position. Soil thickness derived using GPR and calculated
using the latter method were compared against values of slope, upslope area,
wetness, plan curvature and profile curvature for each sample site. The
relationship between these attributes and soil thickness is summarised in table
5.6.
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Table 5.6. Correlation coefficients of soil thickness variation with respect to DEMderived terrain attributes.
25m DEMderived
Terrain Attribute
Correlation coefficient (r) with GPR measured depth
A/B Horizon B/C Horizon
Number of samples 15 31
Plan Curvature 0.303 0.454
Profile Curvature -0.411 -0.190
Elevation -0.554 -0.324
Aspect -0.166 -0.229
Slope 0.156 -0.306
LN (Upslope Area) 0.392 0.831
Wetness Index 0.330 0.855
As a result of the poor correlation between depth to B-horizon and terrain
indices the subsequent use of these indices as a predictor for catchment wide B-
horizon thickness was not attempted. The lack of a good correlation may be a
result of the scarcity of collected data, and reflects the complex nature and
inherent heterogeneity of B-horizon depth in the Cyff. What can be concluded
from these data sets is that for this catchment the B-horizon is an intermittent
feature, absent in class 1 peat sites. The subsequent discussion of results deals
only with total soil thickness, defined as the depth measured from the ground
surface to the boundary of the C-horizon with bedrock.
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5.5.1 Plan Curvature
Total soil thickness to C-horizon shows a positive correlation with plan
curvature. 11 sites have a negative plan curvature value (indicative of possible
flow divergence) with a soil thickness range between 0.27m and 0.73m. Sites
with positive plan curvature (convergent zones) exhibit a soil thickness range of
0.26m to 1.44m. The relationship between erosion and deposition acting on
those sites located in convergent grid cells may explain the high degree of
variability in soil thickness with calculated plan curvature. However the impact
of local slope angle and upslope contributing area is also likely to have a strong
influence on soil thickness distribution.
Figure 5.21. Plan curvature.
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5.5.2 Profile Curvature
Concave sites (negative curvature, 21 sites) exhibit soil thickness ranging from
0.26m to 1.44m. Convex sites (positive curvature; 10 sites) exhibit a reduced
soil thickness, ranging from 0.25m to 0.97m. The overall trend is a slightly
negative, but the degree of scatter evident in the plot and corresponding low
correlation coefficient of –0.190 suggests that profile curvature is a poor
indicator of soil thickness distribution for the data sets.
Figure 5.22. Profile curvature.
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5.5.3 Slope Angle
Figure 5.23 shows that soil thickness to C-horizon generally decreases with
increased slope angle for the catchment, however shallow soil thickness occur
across the entire range of slope angles. Soil thickness could reasonably be
expected to decrease with steeper slope angles given the likelihood of increased
instability and potential for erosion of soils on steeper hillslopes.
Figure 5.23. Slope angle.
The greatest range of measured soil thickness was found on slopes of 0 – 10o
with depth ranging between 0.26 – 1.44m. Examination of the 10 sites with
slope angles less than 10o show that these are often associated with areas of the
catchment adjacent to the catchment divide or in areas adjacent to the river
course, figure 5.24 shows the spatial distribution of these slope angles over the
catchment. Those sample sites located adjacent to the catchment divide also
exhibit soil thickness typically less than 0.5-0.6m, compared with depths
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ranging from 0.85 to 1.44m for sites located adjacent to the river. The upslope
drainage area provides a method of distinguishing between sites of similar slope
angle but with a wide range of soil thickness. Due to the occurrence of similar
slope angles at very different locations in the catchment it is unlikely that slope
alone is a good predictor of soil thickness. However when linked with another
terrain attribute such as upslope drainage area, slope angle is an important
descriptor of soil thickness distribution within this catchment.
Figure 5.24. The distribution of slope angle less than 10o in the catchment.
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5.5.4 Elevation
Soil thickness shows a high degree of variability with elevation. Using this
information no strong relationship can be identified between soil thickness and
cell elevation.
Figure 5.25. Elevation.
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5.5.5 Upslope Area
The plot shows a general trend of increasing soil thickness with increasing area
upslope of a grid cell. Of the terrain attributes examined so far this relationship
is statistically the best with a correlation coefficient of 0.831. Given the range of
upslope area values (625m2 – 40,000m2) generated for all 31 sites a logarithmic
scale provided a more satisfactory plot of the variation of soil thickness with
area (figure 5.26).
Figure 5.26. Natural logarithm (LN) of Upslope Area.
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5.5.6 Wetness Index
Wetness index combines upslope area with local slope (equation 4.1). Figure
5.27 shows the observed relationship between wetness index and soil thickness
at each site. Given the relationship observed between depth and upslope area,
and the potential for upslope area to explain the observed distribution of soil
thickness at varying slope angles, wetness index could be expected to provide a
good relationship to explain depth distribution between sample sites. This is
found to be the case, with wetness index providing the highest correlation (r =
0.855) with measured soil thickness at sample sites.
Figure 5.27. Wetness Index.
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The upslope area and wetness indices provide the clearest statistical relationship
between soil thickness and terrain attributes. Prior to applying the relationship
to predict soil thickness for each grid cell across the catchment the physical
basis to using wetness index as a predictor of depth is examined. In particular
are the processes causing soil accumulation and removal similar over the
drainage basin? In this case the catchment concerned is relatively small ~ 3.1
km2 and although located in an upland region of the UK the climate is temperate
and altitude ranges from 355m to 698m (Cyff DEM). In terms of the
environmental factors governing soil creation the limited size of this catchment
and the small altitude range suggests that the climate and therefore also
weathering processes and organisms responsible for soil formation would be
expected to be constant over the entire catchment. Likewise parent material is
uniform throughout this area. Changes in soil thickness must be a result of
transport processes redistributing particulate matter according to local slope and
the capacity of the transport mechanism to move material, in this case by water.
In the long term soil thickness at a point depends on the upstream inputs and
accumulation of biomass in situ. The effect of variable rates of biomass
accumulation across the catchment from peat bogs to grazed pasture is
accounted for within the data by the fact that a cross-section of sites with a
range of upslope areas and vegetation types has been sampled. The difference in
vegetation type and hence biomass input into the soil between bog and pasture
zones may explain why the increase in soil thickness with increasing upslope
area is more complicated than a simple linear increase.
Figure 5.28 shows the spatial distribution of soil thickness after applying the
calculated relationship between wetness index (W) and soil thickness (d) below,
(5.13)
7308.0r 1376.1173.0 2 =−= Wd
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Figure 5.28. Cell soil thickness (m) predicted from the distribution of wetnessindex.
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Two features of the predicted spatial pattern of depths are evident. The impact
of the local drainage direction network (LDDN) upon predicted soil thickness is
large and the thickest soils, not unexpectedly, occur in drainage channels. The
LDDN is calculated using elevation data in which the drainage direction out of
a cell is determined by the lowest surrounding cell. The shortcomings of
different routing methods are well-documented (Moore et al. 1996, Burrough &
McDonnell, 1998) and the D8 algorithm implemented in PCRaster cannot
model flow dispersion, resulting in predicted flow networks defined as parallel
lines. For this catchment adjacent cells may have very different upslope
drainage areas, therefore resulting in abrupt changes in predicted soil thickness
between cells.
The result of using an equation to predict soil thickness that is partly a function
of drainage area is that the deepest soils occur in grid cells occupied by the
permanent stream channel. Field observation of the Cyff stream network
however shows that the lower reaches of the channel have a bedrock or boulder
bed structure and therefore soil thickness assumes a minimum value at these
locations. Within the model a permanent stream channel requires a soil
thickness of zero in order that all water entering a channel cell is treated as
overland flow. This is necessary for subsequent modelling of catchment water
flux in response to precipitation events since the catchment outflow hydrograph
is required as one method of model validation. In order to allocate zero depth
values to stream channel cells the permanent stream network was overlain by
enforcing zero depth dependent on the upslope drainage area into a cell. A
threshold of 445,000m2 was chosen, such that cells equal to or exceeding this
value were classified as stream cells (figure 5.29). This threshold value was
selected as providing the best visual fit with work carried out by Newson &
Harrison (1978) into channel characteristics in the Plynlimon catchments. The
authors present a channel classification and map for Plynlimon that classifies
the drainage network into bedrock, boulder or alluvial reaches and also specifies
the location of flushes, gullies and drains. Figure 5.30 details the spatial
variability of soil thickness with stream cells incorporated.
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Figure 5.29. Grid cells ≥ 445,000m2 upslope area
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Figure 5.30. Cell soil thickness (m) predicted from the distribution of wetnessindex with stream network cells assigned a value of 0.01m soil thickness.
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5.6 Conclusion
• Three site classifications have been developed using GPR profile and trace
amplitude and reflector characteristics. Class 1 sites are located in areas of
high moisture content and are characterised by peat deposits > 0.5m
overlying bedrock. These sites are dominated by high amplitude reflectors
which are associated with the peat/bedrock boundary. Class 2 and class 3
sites are both located on hillslope soils, but are differentiated by the extent
of lateral horizon definition evident within GPR profiles, and the degree of
correlation between GPR trace data and physical sampling of soil horizon
depth. Class 2 soils compare well with observed horizon position and allow
the extrapolation of point measurements of horizon type to an entire GPR
profile. Class 3 sites are more problematic and are treated as radar complex
environments. Intensive subsurface investigation is essential to quantify
total soil thickness. Both class 2 and 3 sites exhibit multiple reflectors over
the survey depth and require at least one physical soil sample in order to
relate GPR reflectors to specific soil horizon boundaries.
• GPR for soil thickness measurement has been used successfully in
conjunction with excavation and augering to identify soil horizon position
within a soil profile. In this catchment soil thickness has been measured
using GPR at 900 and 450 MHz. Using root mean square to calculate the
difference between radar and physically recorded depths shows that GPR is
accurate to 0.12 m of auger readings to the B/C-horizon boundary. The
accuracy of GPR improves when measuring the A/B horizon interface with
an absolute error of 0.04m compared with auger measurements. However at
least one physical measurement using a soil auger was required to check
reflector – horizon type and confirm that calculated depth for GPR profiles
corresponded with actual physical depth to horizons. The depth of organic
horizon was not generally measurable with GPR due to the shallow nature
of this reflector, with organic horizons in this catchment ranging between
0.1 and 0.2m below the surface.
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• From the 30 sites investigated for soil thickness, the spatial distribution of
soil thickness to the upper boundary of the C-horizon is strongly correlated
(r = 0.855) with wetness index derived from the 25m grid cell DEM. No
statistical relationship was identified between a terrain index and depth to
the upper boundary of the B-horizon. The observed relationship between
depth to the C-horizon and wetness index was subsequently used to
calculate distributed soil thickness to bedrock for the entire 3.1km2
catchment.
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Chapter 6: Soil Moisture Data Analysis
6.1 Introduction
The following chapter presents the analysis methods and results obtained using
GPR for measurement of shallow subsurface soil volumetric water content
(VMC) at 18 sites across the study catchment. VMC derived for different depths
using GPR are compared against VMC measurements obtained at the same
location and depths using gravimetric and theta probe methods for sampling soil
moisture. The measured value of soil moisture at each site is a potential method
for internal hydrological model validation at the scale of the individual grid cell.
6.2 Analysis methodology
Figure 6.1 outlines the data analysis process followed to derive soil moisture
from CMP surveys. Initial processing required that site CMP surveys were
displayed and subsurface velocity derived by measuring the gradient of
reflectors as the horizontal distance between the transmitter and receiver
separation was progressively increased about a common mid-point.
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Figure 6.1. Soil moisture analysis using CMP data.
Values of shallow subsurface velocities and subsequently VMC can be obtained
through measurement of groundwave velocity from a CMP survey. Using this
method with a 100MHz GPR system, Lesmes et al. (1999) found that GPR
measured VMC followed the general trend in the variation in soil moisture
derived from soil samples taken from the top 30cm of soil. A mean discrepancy
of 0.1m3/m3 was found to exist between GPR and gravimetric VMC
measurements which the authors attributed to the unknown depth of soil
sampled by the groundwave. In order to avoid the problem of an unknown soil
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volume sampled by the groundwave, this study instead used the velocity
calculated for the first reflector following the groundwave return as input to
calculate soil dielectric values and subsequently VMC. The depth to this
reflector was calculated as the one-way travel time at zero antennae offset,
therefore quantifying the depth over which subsurface velocity is measured. In
this study the depth to the first reflector at survey sites was of a similar value to
maximum depths sampled by theta probe and gravimetric soil cores for
validation of VMC (table 6.1) thereby allowing validation of GPR soil water
measurement. Using equation 5.1, vrms values calculated from each site CMP survey were used
to quantify volumetric soil moisture changes with depth using the established
relationship between velocity and dielectric value (K) (equation 2.13). Values of
K were substituted into the Topp equation (equation 2.13) to calculate the VMC
of a volume of soil. Table 6.1 summarises the calculated VMC from the soil
surface to the specified depth to reflector using GPR at each site. These
estimates of VMC were then compared with two standard and intrusive methods
of VMC sampling: theta probe measurements and soil cores.
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Table 6.1. Site Vrms and VMC values calculated for the first subsurface reflectorafter groundwave arrival. Only those sites with validation data are included.
Site Maximum depth ofvalidation data (m)
GPR CMP Reflector depth
(m)
GPRVrms
(m/ns)
Dielectricconstant
K
VMC fromGPR (m3/m3)
13 0.34 0.35 0.056 29.0 0.44
14 0.43 0.33 0.046 43.1 0.53
16 0.55 0.53 0.051 35.0 0.48
17 0.15 0.41 0.048 38.9 0.50
18 0.30 0.42 0.055 30.3 0.45
19 0.25 0.46 0.061 24.2 0.39
20 0.05 0.31 0.052 32.9 0.47
22 0.25 0.39 0.053 29.6 0.44
23 0.20 0.34 0.052 33.5 0.47
24 0.20 0.33 0.054 30.8 0.45
27 0.20 0.57 0.058 27.2 0.42
32 0.20 0.32 0.062 23.2 0.38
33 0.55 0.59 0.041 52.6 0.59
48 0.65 0.30 0.052 32.7 0.46
49 0.10 0.25 0.063 22.9 0.38
53 0.45 0.43 0.062 23.5 0.39
54 0.40 0.26 0.047 40.1 0.51
56 0.70 0.25 0.043 48.7 0.56
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6.3 Comparing GPR VMC with conventional VMC measurementtechniques
Validation of GPR derived measurements of VMC with conventional methods
is required in order to check the accuracy of this technique. Direct comparison
between VMC measured using GPR and VMC measured using a theta probe
and soil core is not immediately possible due to the different volume of soil
sampled by each technique. The theta probe samples a volume of 30cm3 (Theta
probe User Manual, 1998) and soil cores a volume of 44cm3. The measurements
derived from GPR are of an average VMC sampled from the ground surface to
the depth of the reflector providing the return signal. The sample volume is
therefore a function of reflector depth and the GPR footprint area returning the
signal (equations 2.10, 2.11 and 2.12). The geometry of an electromagnetic
wave propagating through the soil is treated in a theoretical manner and is a
current topic for research. In this study the GPR signal is assumed to propagate
as an expanding cone from a point source (the transmitter). Therefore the total
soil volume sampled by GPR can be calculated as the volume of a cone with an
elliptical base equal to the radar footprint area (figure 2.3) and a vertical height
equal to the reflector depth. For a reflector located at a depth of 0.2m and an
average velocity of 0.06m/ns this equates to a volume of 252cm3, compared
with a volume of 4420cm3 for a reflector occurring at 0.6m depth. Compared to
GPR measurements, those obtained using a theta probe or soil core are point
measures of VMC, and have been found in this study to provide similar VMC
results when comparing VMC measurements taken at the same depth positions
at a site. Closely spaced measurements were taken using these two methods,
with a depth interval of between 0.05 – 0.2m, dependant on visual examination
of the variation in subsurface soil structure at a site. Samples were taken until
subsurface stone content made insertion of a theta probe or soil core rings
impossible.
The variation in site VMC with increasing depth from the ground surface was
calculated from theta probe and soil core measurements by fitting trend lines to
the recorded data points for each of these methods. Depending on the trend of
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data points and goodness of fit, a linear or polynomial trend line was fitted to
theta and/or soil sample VMC data points over the range of depths sampled.
This assumes that the trend line adequately described the behaviour of VMC
between closely spaced sample points. The VMC at any depth can then be
calculated by substituting depth into the trend line equation. Extrapolation
beyond the sampled depth assumes that soil moisture does not change from that
predicted by the trend line, however given the observed effect of soil horizon
changes on VMC (figure 6.3) this activity was minimised.
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Figure 6.2. VMC – depth relationship with trend lines for site 54.
Trend lines do not directly provide an average value for VMC, but do enable the
calculation of point VMC for a depth. Average moisture between two depths
can be calculated as the area bounded by the trend line and the depth axis using
a method of integration. Given that VMC is a ratio, the area beneath each trend
line is equivalent to a depth of water per depth of soil over which integration is
calculated.
At all but one site (site 48, figure 6.3), integration of the trend line between the
soil surface and depth n was used to calculate the depth of water present in a
given depth n of soil at each site. Depth n was always chosen as the depth at
which a CMP reflection was present with a corresponding value of VMC for the
overlying soil to the surface. Given that GPR VMC is calculated using vrms and
vrms is an average of the velocity between the ground surface to the reflector,
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integration was between the limits of soil surface to the depth of reflector.
Wherever possible a CMP reflector depth was used which was located at a
similar depth to which theta probe and/or soil cores had been collected in order
to minimise extrapolation of VMC values beyond the range of measured data.
Figure 6.3. Soil thickness - VMC relationship for site 48 with strong soil horizoncontrol on VMC. The sharp increase in VMC between 0.25m and 0.30m depthcorresponds to the position of the O/A boundary. Manual calculation of the areabeneath the observations was used in this one case where a trend line wasunable to simulate the variation in VMC with depth.
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6.4 Soil moisture from GPR surveys
Figure 6.4 and figure 6.5 present the results of the calculation of total moisture
depth measured using GPR and theta probe, and GPR and gravimetric soil
moisture data. Raw data for soil moisture depth for each site using the three
techniques are presented in tabular format in appendix II, table II.2.
The calculated root-mean-square (RMS) error between GPR and theta probe
measured moisture is 0.03m3/m3 and 0.05m3/m3 between GPR and gravimetric
measured moisture, an average error between techniques of 0.04m3/m3.
Solving the fitted best-fit line for each graph show that for a given depth of soil
water, measured using either gravimetric or theta probe techniques, the GPR
over measures the amount of water at low water contents (depths) and under
measures the water content at higher water contents (depths). These data are
summarised in table 6.2.
Table 6.2. The difference between GPR measured water and water depthmeasured using gravimetric and theta probe methods.
Gravimetric GPR % difference Theta probe GPR % difference
0.05 0.058 +0.16 0.05 0.061 +0.22
0.15 0.141 -0.06 0.15 0.152 +0.01
0.35 0.308 -0.12 0.35 0.334 -0.05
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Figure 6.4. GPR measured moisture and gravimetric moisture.
Figure 6.5. GPR measured moisture and theta probe moisture.
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The frequency histograms of residuals (figure 6.6) for the both techniques show
very different distributions. A normal distribution is associated with the theta
probe – GPR moisture measurement technique, whilst the gravimetric – GPR
technique shows an increased frequency of higher magnitude residuals. There is
also a degree of positive skewness associated with the gravimetric technique
with GPR tending to measure less water than found in soil samples.
Figure 6.6. Frequency distribution of the error between GPR water depth and a)theta probe measurements, b) gravimetric soil samples.
The signed-rank test was applied to test the significance of the relationship
between GPR measured soil moisture and theta probe and gravimetric estimates
of moisture over the same depth of subsurface. The signed-rank test is a non-
parametric statistical test allowing comparison between pairs of observations
and examination of the difference between data pairs (Hirsch et al., 1993). In
this case the value of GPR water depth calculated for each site is paired with the
associated theta probe and gravimetric integrated value. A non-parametric test
was chosen given the non-normal distribution assumed by the residuals of GPR-
gravimetric samples. The null hypothesis (H0) for the signed-rank test states
that both data series come from the same population. The alternative hypothesis
(H1) states that a statistically significant difference between series exists.
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Assigning confidence limits of 0.95, the critical test value (ZCRIT) is 1.96.
Table 6.3 shows the calculated Z value for GPR-theta probe and GPR-
gravimetric paired water depth measurements.
Table 6.3. Signed-rank test results.
GPR-theta probe GPR-gravimetric
Number ofobservations
18 12
Z -0.305 -1.608
Action H0 accepted, no difference
exists between samples.
H0 accepted, no difference exists
between samples.
The overall correlation values between GPR and theta probe and soil sampled
VMC are equivalent (r2 equals 0.80 for each), despite the distribution of
residuals differing. The signed-rank test calculates a figure closer to zero for
GPR-theta probe observations although both data samples exhibit a Z value less
than the critical value and therefore the null hypothesis, that no statistically
significant difference exists between populations, can be retained. In this case
GPR measurements of shallow subsurface moisture content is statistically
comparable to the integrated value of moisture over the same depth derived
from a trend line fitted through a series of point measurements.
Given the relationship found between GPR and standard measurements of
VMC, CMP first reflector velocities were calculated for the remaining 11 sites
at which CMP surveys had been carried out but no validation data were
collected. The results are presented in table 6.4.
0Reject HZZ CRIT ⇒>
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Table 6.4. CMP measured VMC for sites without validation data.
Site CMP Reflector depth(m)
Vrms (m/ns) Dielectricconstant
GPR VMC(m3/m3)
5 0.56 0.051 35.2 0.48
6 0.38 0.047 40.3 0.51
8 0.35 0.054 31.3 0.45
9 0.46 0.059 25.9 0.41
21 0.50 0.044 47.5 0.55
37 0.55 0.040 57.5 0.61
39 0.93 0.041 53.2 0.59
40 0.90 0.041 52.2 0.58
41 0.75 0.040 55.9 0.61
50 0.38 0.050 36.5 0.48
60 0.59 0.080 14.2 0.26
The VMC data measured using GPR forms a set of observations of site soil
moisture for 29 sites across the catchment. These data sets provide a method of
comparing the spatial pattern of soil moisture dynamics predicted in the
catchment using the hydrological model with distributed soil thickness.
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6.5 Conclusion
Soil moisture derived using GPR CMP surveys is statistically comparable to the
depth of water predicted to be present in a depth of soil sampled by theta probe
and soil sample measurements. In order to compare GPR derived moisture with
physical soil moisture measurements there is a requirement to scale up from
point samples to the volumes sampled by GPR. The method used in this study
compares the two techniques by integration of measured soil sample and theta
probe VMC to estimate the depth of moisture per depth of soil. The two key
assumptions to this process are that soil moisture variation with depth at each
site can be described by the fitting of a trend line to observed data, and that an
expanding cone centred on the transmitter adequately describes the GPR
subsurface sample volume. The similarity in results between methods suggests
that these assumptions are valid in this case.
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Chapter 7: Hydrological Modelling Results
7.1 Introduction
This chapter presents the results obtained using the hydrological model run on a
25m-grid resolution to simulate the effect of varying soil thickness distribution
on the catchment and cell hydrological response to precipitation. Differing
scenarios of catchment soil thickness were investigated, with soil thickness
assumed to be either constant or variable over the entire catchment. The overall
response of changing soil thickness distribution on hydrological behaviour was
examined using a) total catchment discharge characteristics for each scenario,
and b) the predicted status of overland flow, subsurface flow and soil moisture
simulated for the field plot. Comparison between modelled and recorded data at
both these scales is used to examine the impact of varying soil thickness on
these hydrological variables.
7.2 The catchment model
Nine soil thickness scenarios were used to examine the hydrological response to
varying soil thickness. These consisted of eight scenarios in which the
catchment soil was a constant depth value, ranging from a minimum depth of
0.2m and increasing to a maximum depth of 1.6m in increments of 0.2m each
modelled scenario. This range of depth was chosen as being similar to the range
of depth sampled through field investigation (0.2m - 1.5m). A single model
scenario in which soil thickness was considered variable was also investigated.
The distributed pattern of catchment soil thickness used the GPR soil thickness
and soil wetness index relationship detailed in chapters six and seven, using a
25m-grid cell size. Each of the nine simulations was run at an hourly time step
for the period 1st October 1997 to 7th July 1999. This spanned a period of 15,469
hours, for which hourly rainfall and potential evaporation were available for
model input and catchment outflow discharge values for model validation at the
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catchment scale. Field plot overland flow and subsurface flow were available
over the same time period, and volumetric soil moisture monitored by hourly
theta probe readings from 28th September 1998 to 7th July 1999.
All model parameter values, input maps and initial values were kept constant
for each model run except for cell soil thickness. Model parameters and initial
values are listed in Appendix I. In all analysis of model catchment hydrograph
compared with the recorded hydrograph the first 1500 hours of data are rejected
to allow the model to reach a state of equilibrium with catchment conditions.
7.3 Reminder: The effect of soil thickness on modelleddischarge
Soil thickness is an important input parameter to this model and can be
considered either as a uniform value for the entire catchment or spatially
distributed for each grid cell contained within the catchment. The depth of soil
present in any cell controls the maximum moisture storage capacity of that cell.
The relationship between soil thickness and maximum moisture (equation 3.6)
was derived from 55 field measurements of soil bulk density at 19 sites, for a
range of depths between 0.03m and 0.50m.
Actual water input to a cell is via a combination of rainfall, and for those cells
with upslope drainage sources, subsurface throughflow. Cell soil thickness, by
controlling the maximum moisture capacity, also controls the partition of
overland flow/throughflow generation for each cell. When actual cell moisture
equals the maximum cell moisture, subsequent rainfall and subsurface
throughflow inputs are considered to be surface runoff for that cell, although re-
infiltration can occur in downstream cells. This model routine simulates
saturated overland flow.
The model also simulates the process of infiltration excess overland flow when
rainfall intensities exceed the maximum rate of infiltration. Infiltration (equation
3.3, Campbell, 1985) is a function of soil texture and bulk density. Water
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infiltrating into the soil is considered to form a defined boundary between non-
saturated soil (below the wetting front and above the water table) and saturated
soil (above the wetting front, extending to the surface). Using equation 3.6, the
rate of advance of the wetting front and therefore infiltration rates are controlled
by the depth of the wetting front within the soil profile, since soil bulk density is
a function of depth.
The volume of subsurface throughflow is controlled by the position of the water
table in each cell and the lateral hydraulic conductivity. The vertical difference
in water table elevation between a cell and its downstream neighbour is used to
calculate the hydraulic gradient for throughflow. Based on a model developed
by Xiao et al. (1996), the average soil thickness contributing to flow between
cells is the average of the sum of cell soil thickness. In this model throughflow
occurs between cells which are not fully saturated, instead using water table
position within both cells to calculate the average depth of saturated flow.
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7.4 Catchment model results
The effects of varying soil thickness model scenarios on catchment flow
response to precipitation and evaporation are summarised in table 7.1. The
outflow hydrograph generated from each model run is used to examine the
impact of soil thickness variability on catchment outflow for the same time
period. It should be noted that while a high r2 value indicates that a scenario
hydrograph has a similar pattern to the measured hydrograph, the root mean
square (RMS) error indicates the difference in magnitude between modelled and
observed hourly discharge.
Table 7.1. Catchment outflow summary data for all modelled scenarios (1501-15469 hours).
Modelled soilthicknessscenario
MeanQ
(m3/s)
Max Q (m3/s)
Min Q (m3/s)
Totaldischarge
(×106 m3)
Linear trendline R2
value: measured vs.modelled hourly
discharge
RMSError
Constant, 0.2m 0.185 5.476 0.000 9.31 0.741 0.287
Constant, 0.4m 0.186 4.000 0.002 9.33 0.578 0.334
Constant, 0.6m 0.186 3.227 0.005 9.37 0.447 0.357
Constant, 0.8m 0.187 2.812 0.007 9.39 0.334 0.371
Constant, 1.0m 0.186 2.584 0.009 9.37 0.242 0.380
Constant, 1.2m 0.185 2.439 0.010 9.31 0.170 0.387
Constant, 1.4m 0.183 2.329 0.011 9.22 0.116 0.392
Constant, 1.6m 0.181 2.249 0.012 9.13 0.076 0.396
Variable, GPR
measured
depth.
0.186 3.960 0.006 9.36 0.530 0.343
Discharge
values recorded
at gauging
station.
0.265 6.110 0.019 13.30 N/A N/A
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Figure 7.1. Modelled and recorded minimum and maximum catchment discharge,from table 7.1.
Figure 7.1 shows two key trends; decreasing maximum river discharge as soil
thickness increases and a decrease in the minimum modelled discharge as
catchment soil thickness is reduced. The variable soil thickness model shows
characteristics of both, with lower peak discharge than the shallow depth
scenarios but a larger minimum flow during drier periods. For those model
scenarios considering a catchment constant soil thickness, the rate of change in
minimum and maximum discharge is reduced as depth increases. Soils deeper
than 0.8-1.0m show increased hydrological stability, increasingly damped
against the minimum and maximum extreme flow values which are
characteristic of shallower depth soil scenarios.
The pattern of modelled maximum and minimum discharge is detailed by the
scenario hydrograph. Figure 7.2 shows the recorded hydrograph and the
simulated hydrograph for the GPR measured soil thickness scenario.
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Figure 7.2. Outflow hydrograph of measured discharge and GPR variable soilthickness modelled discharge.
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7.4.1 High Flows
One high flow period is used as an example of model behaviour (figure 7.3).
Three soil thickness scenarios are considered: - 0.2m catchment soil thickness
and 1.6m soil thickness which are the lowest and highest values of soil
thickness used, and the variable soil thickness scenario. These three scenarios
enable a comparison to be made between a lumped and distributed catchment
soil thickness simulation and actual flow measurements. The period examined
extends from 27th February 1999 to 3rd March 1999 (100 hours) during which
time a total of 127.2mm rainfall was recorded.
Figure 7.3. A period of high flow from 27th February 1999 to 3rd March 1999.
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Table 7.2. High flow statistics for event 27th February 1999 to 3rd March 1999.
Model
scenario
Mean
absolute
error (m3/s)
Maximum
flow (m3/s)
Minimum
flow (m3/s)
Linear trendline R2
value of measured
vs. modelled
hourly discharge
RMS
Error
Measured
flow
N/A 5.822
(100%)
0.151
(100%)
N/A N/A
0.2m depth
flow
0.664 3.990
(69%)
0.141
(93%)
0.813 1.147
1.6m depth
flow
0.995 1.861
(32%)
0.189
(125%)
0.589 1.682
GPR
variable
depth flow
0.771 3.132
(54%)
0.176
(117%)
0.677 1.367
While the shape of the storm hydrograph for all scenarios is similar to the
hydrograph recorded by the Institute of Hydrology flume, no model scenario is
able to recreate the magnitude of recorded peak flows. Those model scenarios
with constant shallow soil thickness provide the highest discharges and lowest
RMS error (1.147m3/s), constant deep soils the lowest discharge and highest
RMS error (1.682m3/s). The distributed soil thickness model performs more
closely to the shallow constant model particularly for the third hydrograph peak
shown in the above example. The inability of any model scenario to generate
equivalent flows to those recorded may be due to the lack of a model
component enabling macropore flow through the subsurface.
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7.4.2 Intermediate and low flows
350 hours of low flow occurred between 17th May 1999 and 1st June 1999.
During this time period 21.4mm of rainfall was recorded and the hydrograph is
dominated by base flow. Model output is presented in figure 7.4 and table 7.3
for soil thickness scenarios of 0.2m, 1.6m and GPR derived soil thickness.
Table 7.3. Low and intermediate discharge statistics from 17th May 1999 to 3rd
June 1999.
Model
scenario
Mean
absolute
error
(m3/s)
Mean
flow
(m3/s)
Maximum
flow
(m3/s)
Minimum
flow
(m3/s)
Linear trendline
R2 value of
measured vs.
modelled hourly
discharge
RMS
Error
Measured
flow
N/A 0.042
(100%)
0.073
(100%)
0.030
(100%)
N/A N/A
0.2m
depth flow
0.020 0.022
(52%)
0.046
(63%)
0.004
(13%)
0.615 0.020
1.6m
depth flow
0.009 0.049
(117%)
0.088
(121%)
0.022
(73%)
0.224 0.012
GPR
variable
depth flow
0.007 0.037
(88%)
0.068
(93%)
0.014
(47%)
0.529 0.009
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Figure 7.4. Low flow hydrograph
Throughout this period the 0.2m soil thickness scenario predicts mean discharge
values 48% less than the mean observed discharge. This characteristic is due to
the reduced amount of total soil pore volume compared with deeper soils and
therefore a reduction in the amount of subsurface water stored in each grid cell.
During periods of reduced or no precipitation shallow soil models are unable to
simulate catchment discharge due to the lack of soil water available for release
into the river channel.
The 1.6m soil thickness scenario maintains discharge values approximately
double those of the 0.2m depth model. This increase is the result of the greater
water storage capacity of deeper soils with greater pore volume per cell. The
distributed soil thickness scenario provides the closest simulation of actual flow
with the smallest RMS error, 0.009m3/s, between modelled and observed
discharge during this period.
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7.4.3. Catchment discharge frequency distributions
Analysis of the differences in discharge between varying scenarios of soil
thickness can also be achieved by examining the frequency distribution of
discharge for each scenario and recorded data. Flow results for each model
scenario and measured river flow are shown as frequency distributions in figure
7.5, where the x-axis shows the discharge interval and the y-axis the percentage
of all hourly flows falling within each interval.
The Kruskal-Wallis statistical test was used to examine for differences between
modelled scenarios and the observed catchment outflow frequency distribution.
Kruskal-Wallis is a one-way analysis of variance (ANOVA) by ranks test,
which tests for the difference between the medians of two or more samples. The
Kruskal-Wallis test is a non-parametric version of the F-test, and therefore does
not assume a normal distribution or homoscedasticity (Rogerson, 2001).
In this case the test was applied to frequency distributions of catchment
discharge by pairing measured discharge against each model scenario discharge
in turn. The null and alternative hypothesis for this test were specified
respectively as:
H0 = no statistical difference exists between observed and the modelled flow
frequency distribution.
H1 = the modelled flow frequency distribution is statistically different from
observed flow.
The results of comparison between model scenarios of soil depth and measured
flow are presented in table 7.4.
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Figure 7.5. Total catchment discharge (m3/s) histograms (measured andmodelled).
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The frequency distribution of measured catchment discharge is positively
skewed, with 95% of hourly flow values occurring between 0.03m3/s and
1.00m3/s. The distribution is typical of many catchment flow regimes, in which
high magnitude flows are low frequency events. The frequency distributions of
modelled soil thickness show that none are able to fully simulate the distribution
of observed discharges.
Increasing catchment soil thickness leads to a reduction in the range of
discharges observed, achieved through a reduction in the frequency of high flow
and low flow values. The effect of a reduction in the range of discharges
modelled is to increase the contribution of ‘medium’ flows to the hydrograph.
This is seen in the frequency distribution as an increase in the maximum
percentages of discharge, for example discharges in the range 0.12m3/s to
0.25m3/s contribute 52% of discharge for the 1.6m soil thickness scenario
compared with 31% for the 0.2m scenario. As soil thickness increases,
catchment discharge is shown to decrease in variability, with a reduction in both
the highest and lowest values, a damping of discharge in response to
hydrological input, also highlighted by figure 7.1.
Shallow, constant depth soils perform well in comparison to deeper, constant
depth soils when simulating high discharges. The 0.2m depth frequency
distribution shows that 2.1% of flows occurring are greater than 1.0m3/s,
compared with 0.6% for the 1.6m depth and 4.4% measured in the field. The
reverse is true for low flows. Shallow soil model scenarios over-predict the
frequency of low flow occurrence. The 0.2m depth scenario has 5.1% of
discharge in the range 0-0.01m3/s. Neither the 1.6m depth scenario nor the
measured hydrograph recorded discharges below 0.01m3/s.
The GPR, variable depth frequency distribution exhibits characteristics of both
shallow and deep soils, unsurprising given that cell soil thickness in this
scenario range from 0.22m to 1.70m, with an average soil thickness of 0.51m.
The variable depth histogram is not, however, an average of the frequency
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distributions produced for 0.4m and 0.6m constant soil thickness scenarios.
Maximum discharge frequencies (1.4% between 3.7-4.0m3/s) are equivalent to
those simulated by the 0.4m scenario, while the frequency of discharges
between 0-0.01m3/s is 0.3%, compared with 0.4% and 2.4% for scenarios of
0.6m and 0.4m constant soil thickness.
For this model, soil thickness is one control on both the range of catchment
discharge and the distribution of discharges. The effect of increasing soil
thickness is to de-sensitize the model to periods of extreme hydrological
behaviour. Peak flows are lower than those simulated by shallow soils, while
discharge during periods of low flow are greater. Using the frequency
distributions of scenario discharge, it can be seen that scenarios with deeper,
uniform soils produce a smaller range of flows, with the greatest reduction
occurring for the high values of discharge. The reduction of hydrological
response to periods of intense and zero precipitation is due to the increased
moisture storage capacity of deeper soils. These soils are able to store greater
volumes of water prior to saturation, thereby reducing the amount of overland
flow generated by a rainfall event. During inter-storm periods this water is
released into the river network, maintaining discharges above zero.
Shallow soils exhibit a range of discharges similar to those recorded at the
gauging station. However the frequency distributions shows that for shallow
soil scenarios during interstorm periods, discharge volumes are underestimated.
The volume of water contributing to catchment outflow is limited during these
periods because of the limited soil moisture capacity of each cell.
The variable soil thickness scenario improved simulation of the catchment
hydrograph, primarily for periods of low and intermediate flow. The frequency
distribution for this scenario showed that the frequency of discharge less than
0.01m/s was less than for scenarios of similar uniform depth, but that the
distribution of high discharge values was similar to that achieved by the
uniform, shallow depth model runs.
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Table 7.4 Kruskal-Wallis results for catchment discharge frequency distributions.
Modelled soildepth scenario
Kruskal-Wallis test value 1
p - value H0
Variable depth 3.08 0.079 Accept
0.2m depth 1.27 0.259 Accept
0.4m depth 2.61 0.106 Accept
0.6m depth 3.63 0.057 Accept
0.8m depth 4.53 0.033 Reject
1.0m depth 5.37 0.021 Reject
1.2m depth 5.90 0.015 Reject
1.4m depth 6.17 0.013 Reject
1.6m depth 6.68 0.010 Reject
1 Critical test statistic value 3.841 (p = 0.05) using chi square distribution for 1 degree
of freedom (Rogerson, 2001).
Table 7.4 shows that the null hypothesis (H0) is rejected for all soil depth
scenarios between 0.8m and 1.6m deep. The frequency distributions for these
scenarios are statistically different to the observed distribution of catchment
discharge. The results are significant, since the p-values for each of these 5
distributions are below the alpha value of 0.05, such that the probability of
making a type I error (rejecting the null hypothesis when it is in fact true) is less
than 5% in all cases.
Variable soil depth and scenarios of constant depths of 0.2m, 0.4m and 0.6m
calculated test values less than the critical value, and therefore the null
hypothesis was not rejected. In each of these scenarios the modelled distribution
of flows was not statistically different from that observed. Again the p-values
for these 4 scenarios confirm this finding.
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7.5 The spatial distribution of catchment runoff
Figure 7.6 shows the variation in source area for total overland flow exceeding
an arbitrary threshold, in this case 0.1m depth, generated over the model
simulation period. The percentage catchment area contributing to overland flow
using this threshold is 64% for the 0.2m depth scenario compared with 36% for
the 1.6m soil scenario. The spatial pattern of overland flow occurrence on
deeper soils shows a well-defined network, with overland flow concentrated
along lines of flow equivalent to stream channels. In contrast the shallow soil
simulation shows less defined linearity, with an increasing number of cells
adjacent to the drainage divide contributing to overland flow.
Figure 7.6. The spatial distribution of total overland flow for model scenarios of0.2m and 1.6m soil thickness.
GPR soil thickness scenario results (figure 7.7) show the spatial distribution of
total overland flow and throughflow after removal of cells that contained the
permanent stream channel within them. Stream channel cells were assigned a
constant soil thickness of 0.01m to simulate the bedrock form of these channels
at Plynlimon.
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Figure 7.7. The spatial distribution of total overland flow and subsurface flowfrom the GPR variable soil thickness scenario.
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Total overland flow shows greater network linearity than patterns of subsurface
flow. This is due to the influence of upslope flow area and the local drainage
network on the distribution of surface flow. Despite the model clearly defining
stream networks, every catchment cell records an amount of overland flow for
at least one timestep of the model simulation extending to cells adjacent to the
catchment divide. Figure 7.8. a) shows that soil thickness has a large control on
total overland flow, because of the influence of upslope contributing area on
both routed overland flow and, in this model, soil thickness through the use of
the wetness index as a covariate for cell soil thickness.
Cell subsurface flow totals show a less defined channel network and a more
smoothed spatial distribution of total flow. This is a result of subsurface flow
being partially controlled by cell soil thickness, along with subsurface drainage
direction. Adjacent cells are likely to have similar magnitude soil thickness
because of the likelihood that adjacent cells have similar wetness index values
and hence soil depths.
The range of total subsurface flow is of a similar magnitude to overland flow
totals for the modelled period. The variation in total flow depth is responsive to
soil thickness variability, given that soil thickness controls the soil water storage
capacity of each cell within the model. Graphs of modelled overland and
throughflow cell totals plotted against cell soil thickness show a trend of
increasing depths of water for deeper soils (figure 7.8). All cells within the
catchment produce both types of flow at some point within the simulated
period, but total runoff depths follow a pattern similar to throughflow. This is
due to the high values of throughflow compared with overland flow depths for
the same time period.
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The increase in throughflow for deeper soils is a result of two factors:
(a) In this model, deeper soils have a larger moisture capacity than shallow
soils, and therefore a larger depth of water to potentially transmit to
downstream cells.
(b) Deeper soils exhibit increased maximum cross-sectional area available to
transmit water to a downstream cell.
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Figure 7.8. GPR variable soil thickness model: - cell water depth vs. cell soilthickness.
(a) Overland flow.
(b) Subsurface throughflow.
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(c) Total cell runoff.
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7.6 Field plot data and model results
The instrumented field plot provided an event record of subsurface flow,
overland flow and soil moisture. In order to compare logged data with the
hourly values produced by the model, event records were processed to provide
hourly totals for each parameter (figure 7.9). These records provided validation
for the modelled hydrological state at the plot location within the model,
allowing internal state validation for part of a single cell in addition to the
aggregated catchment validation outlined above.
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Figure 7.9. Rainfall, overland flow and throughflow measured at the field plot.
Plot m e as ure d ove r land flow
0
0.005
0.01
0.015
0.02
0.025
0.03
1-Oct-97
1-Nov-97
1-Dec-97
1-Jan-98
1-Feb-98
1-Mar-98
1-Apr-98
1-May-98
1-Jun-98
1-Jul-98
1-Aug-98
1-Sep-98
1-Oct-98
1-Nov-98
1-Dec-98
1-Jan-99
1-Feb-99
1-Mar-99
1-Apr-99
1-May-99
1-Jun-99
1-Jul-99
Tim e
Flo
w (
m3/
hr)
Plot m e as ure d throughflow
0
0.005
0.01
1-Oct-97
1-Nov-97
1-Dec-97
1-Jan-98
1-Feb-98
1-Mar-98
1-Apr-98
1-May-98
1-Jun-98
1-Jul-98
1-Aug-98
1-Sep-98
1-Oct-98
1-Nov-98
1-Dec-98
1-Jan-99
1-Feb-99
1-Mar-99
1-Apr-99
1-May-99
1-Jun-99
1-Jul-99
Tim e
Flo
w (
m3/
hr)
Hour ly rainfall (m m )
0
2
4
6
8
10
12
14
16
1-Oct-97
1-Nov-97
1-Dec-97
1-Jan-98
1-Feb-98
1-Mar-98
1-Apr-98
1-May-98
1-Jun-98
1-Jul-98
1-Aug-98
1-Sep-98
1-Oct-98
1-Nov-98
1-Dec-98
1-Jan-99
1-Feb-99
1-Mar-99
1-Apr-99
1-May-99
1-Jun-99
1-Jul-99
Tim e
Ho
url
y ra
infa
ll (m
m)
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Because of the scale difference between the 25m-model grid size and the 2m-
field plot cross-section three assumptions were made regarding volumes
contributing flow compared to the volume of the grid cell.
1. In order to directly compare between recorded data for the grid cell and
model results, modelled subsurface flow and overland flow measurements
were reduced to simulate a 50m2 contributing area. A 25m model grid cell
resolution has an area of 625m2, therefore model values of overland flow
and subsurface flow were reduced to 8% of the cell value each hour to allow
direct comparison with hourly recorded plot measurements.
2. Overland flow and subsurface flow were measured as the amount of water
entering two lengths of two-metre length of pipe located perpendicular to
the line of steepest slope gradient. Surveying of the immediate area
(approximately 100m2, from which the hillslope 5m grid cell DEM was
derived) calculated that an upslope area of 50m2 contributed overland flow
to the plot. The same area was also assumed to contribute to subsurface
flow.
3. Soil moisture measured by three theta probes at depths of 0.08m, 0.23m and
0.37m was assumed to be representative of soil water over the entire 25m
square grid cell.
To examine the differences between the variable depth scenario and constant
depth scenarios for key model output variables all results are expressed as a
fraction of the variable soil thickness output values. Therefore the output from
the variable depth scenario is assigned a value of unity, and all other scenario
results are expressed as a fraction of this value. This enables the magnitude and
direction of all output variables for all scenarios to be compared in a single
graph (figure 7.10). The soil thickness (x-axis) for each scenario is expressed as
the fraction of the variable soil thickness for the field plot cell. The output
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variable (y-axis) is calculated as the fraction of the value of the variable soil
thickness model.
Figure 7.10. Output variable change (totals) in response to changing plot cell soilthickness.
Increasing plot soil thickness results in a decline in simulated overland flow to
zero, but an increase in the amounts of subsurface flow and, not unexpectedly,
increased total soil moisture within the cell. Actual evapo-transpiration values
are relatively insensitive to an increase in cell soil thickness, indicating that, as
expected for a temperate climate with relatively high annual rainfall, evapo-
transpiration is limited by net radiation rather than the available soil moisture.
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7.6.1 Overland flow
The model predicts that overland flow at the field plot cell is only initiated for
model scenarios of 0.2m-catchment soil thickness and distributed soil thickness.
Scenarios with deeper soils fail to generate any overland flow at the field plot
cell for the period simulated. Modelled data for those two model runs that do
generate overland flow compares poorly with the frequency and magnitude of
measured flow. Figure 7.11 shows the model simulation of overland flow events
between 1st October 1997 and 7th July 1999 for the plot cell.
Figure 7.11. Modelled plot cell overland flow (25m DEM)
One explanation for the poor reproduction of overland flow events by the model
is grid scale. Overland flow that was observed on hillslopes in the catchment
was highly spatially variable. Flow on the slopes adjacent to the plot was
concentrated in narrow channels generally less than one metre wide and moved
downslope in response to micro topography. While the overall modelled flow
direction may be correct, within any cell actual flow is concentrated into areas
far smaller than the 625m2 cell area can resolve.
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To examine the impact of changing the grid resolution on modelled overland
flow occurring at the plot cell, the model was run for the hillslope immediately
upslope and containing the plot cell for a 5m-cell size. The hillslope DEM was
derived from surveying measurements of the area, not interpolation of the 25m
grid DEM. Figure 7.12 details the change in the local drainage direction (LDD)
when using a 25m and a 5m DEM of the same hillslope. In the case of the 25m
DEM, the plot is contained within a cell with no drainage from upslope cells.
Due to the improved resolution of the 5m DEM the plot cell is shown located
with a maximum of 6 cells upslope possibly contributing to flow.
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Figure 7.12. The changing pattern of the local drainage direction (LDD) networkafter decreasing cell size from 25m to 5m.
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Soil thickness for the upslope area and plot was measured using a 30m GPR
profile extending from 2m downslope of the plot, upslope to the sub-catchment
drainage divide. All other model parameters retained the values assigned for the
catchment simulation. As was the case for the catchment model, soil thickness
of 0.2m to 1.6m in increments of 0.2m were used to examine model output
using lumped soil thickness scenarios. The mean values of model output derived
from this second simulation run on a 5m grid are shown in figure 7.13.
Figure 7.13. Model output values for 5m-grid size.
The effect of the reduction in grid size on modelled overland flow generation is
striking. Compared with the 25m grid in which only the GPR and 0.2m depth
scenario produced overland flow, all scenarios generated overland flow. The
trend is similar to the 25m model, with shallow soils generating a larger volume
of overland flow than deeper soils. This is due to the saturation of shallow soils
for longer time periods than deeper soils with their greater soil moisture storage
capacity.
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In common with model results at the 25m scale, volumes of throughflow are
linearly related to an increase in soil thickness because the model calculates cell
subsurface outflow as a function of Ksat, hydraulic gradient and the amount of
water stored in each cell. Evaporation is least affected by changing soil
thickness, only slightly increasing with increased depth (and therefore stored
moisture).
Soil moisture storage is a non-linear function of depth because the controlling
equation on soil moisture uses field sampled porosity data to reconstruct the
measured decrease in pore volume with increasing sample depth. In this case
the relationship between depth and porosity (bulk density) was found to be
exponential (equation 3.6).
The frequency and magnitude of plot equivalent modelled overland flow after
compensation for the 5m-cell size used is shown in figure 7.14. The reduction in
grid size and the creation of cells upslope which contribute to plot overland
flow leads to an increased frequency of events and greater predicted discharge.
Figure 7.14. Modelled plot overland flow data for 5m grid resolution.
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Frequency distributions of simulated overland flow for all nine soil thickness
scenarios are shown in figure 7.15. Compared with the distribution of observed
overland flow, the model over predicts the frequency of high volumes of surface
flow and does not recreate overland flow of similar magnitude to that measured
by the field plot. However the effect of increasing model catchment soil
thickness is to reduce the total volume of flow occurring and reduce the overall
frequency of these events for the modelled period.
The Kruskal-Wallis 1-way ANOVA was again applied to compare each
modelled distribution of flow with that observed at the field plot. The results are
presented in table 7.5.
Table 7.5. Kruskal-Wallis results applied to frequency distributions of field plotrunoff.
Modelled soildepth scenario
Kruskal-Wallis test value 1
p - value H0
Variable depth 0.40 0.525 Accept
0.2m depth 1.56 0.212 Accept
0.4m depth 0.32 0.571 Accept
0.6m depth 0.01 0.958 Accept
0.8m depth 0.37 0.543 Accept
1.0m depth 0.94 0.332 Accept
1.2m depth 1.58 0.209 Accept
1.4m depth 2.25 0.134 Accept
1.6m depth 4.24 0.039 Reject
1 Critical test statistic value 3.841 (p = 0.05) using chi square distribution for 1 degree
of freedom (Rogerson, 2001).
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Figure 7.15. Frequency distributions of plot overland flow (m3/hr).
M e as ure d plot runoff
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7.6.2 Subsurface flow
Modelled subsurface flow (figure 7.16) follows a similar pattern to the
catchment hydrograph and shows continuous flow occurring. Measured
subsurface flow (figure 7.9) is instead event based, with discrete time periods
during which no flow is recorded for up to several weeks. Within the measured
record, a period of zero flow is recorded between 26th March 1998 and 21st July
1998, following a large rainfall event. A subsequent site visit found that the
equipment funnel was blocked, resulting in any subsurface flow bypassing the
tipping bucket. This period of data is therefore suspect and given the frequency
of subsurface flow occurring throughout the remaining record, is not used in
subsequent analysis.
Figure 7.16. Modelled plot cell subsurface flow for three soil depth scenarios.
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Figure 7.17 shows the trend in subsurface flow for all model scenarios and
recorded data. Compared with the modelled overland flow results, modelled
subsurface flow values are of a similar magnitude to those measured. Reducing
cell soil thickness results in a linear reduction in average flow from the cell
while the maximum simulated flow within the record is approximately
0.005m3/hr for depths ranging from 1.6m to 0.4m.
Figure 7.17. Mean and maximum subsurface flow for all soil depth scenarios andmeasured data.
The probability distribution functions for recorded and modelled plot cell
throughflow are shown in figure 7.18. The results show that the effect of
increasing model soil thickness is to increase the total volume of cell
throughflow but to reduce the minimum flow value simulated over the time
period. The frequency distribution of measured flow is skewed to the lower
range of hourly flow totals, with the greatest frequency of observed throughflow
occurring between 0 and 0.00005m3/hr which corresponds to the range in which
a single bucket tip (0.000047m3/hr) is located.
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Figure 7.18. Frequency distributions of plot throughflow (m3/hr).
M e as ure d plot throughflow
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The mean of the distributed GPR measured soil thickness of the plot cell is
0.20m. This is equivalent to the value of 0.2m depth for the lumped scenario
and it would therefore seem logical that the two scenarios would produce
equivalent results, given that no upslope cells drain into the plot cell. This is not
observed in model subsurface flow results however, where the mean flow
generated by the variable depth model is double that of the lumped 0.2m depth
scenario. Since the plot cell soil thickness are equal in both scenarios and no
cells are located upslope of the plot cell this response must be due to
downstream grid cells.
The influence of downstream cells on subsurface flow is controlled by the
model routine calculating hydraulic gradient. As explained in chapter 3, the
movement of subsurface water between cells is calculated using D’Arcy’s law
(equation 3.9) such that flow is a function of soil hydraulic conductivity and the
hydraulic gradient between cells. In this model hydraulic conductivity is based
on Campbell’s 1974 formula (equation 3.3) which requires soil texture and bulk
density as input parameters. Texture and bulk density values were based on the
measurement of 68 soil samples taken from 19 sites across the catchment and is
assigned as a lumped model parameter. Model hydraulic gradient is calculated
as the difference in water table elevation above sea level between a cell and its
downstream neighbour in the subsurface drainage network. It is a distributed
parameter based on cell soil moisture and soil thickness. Cell water table depth
is calculated by the model for each time step based on the amount of soil water
in the profile and the depth – porosity relationship derived from field samples.
When a cell and the downstream cell are fully saturated, i.e. water table depth
equals zero, hydraulic gradient is the difference in cell elevation divided by the
horizontal distance between cells. The depth of soil in a cell controls the
maximum soil water table depth and is one important control on hydraulic
gradient, along with surface elevation differences between cells. Soil thickness
therefore affects the potential rate of subsurface flow generation within cells,
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although actual flow to the downstream cell is also controlled by the hydraulic
conductivity of the soil.
The Kruskal-Wallis 1-way ANOVA was again applied to compare each
modelled distribution of throughflow with that observed at the field plot. The
results are presented in table 7.6.
Table 7.6. Kruskal-Wallis results applied to frequency distributions of field plotsubsurface flow.
Modelled soildepth scenario
Kruskal-Wallis test value 1
p - value H0
Variable depth 2.89 0.089 Accept
0.2m depth 0.00 0.977 Accept
0.4m depth 2.85 0.091 Accept
0.6m depth 8.90 0.003 Reject
0.8m depth 10.78 0.001 Reject
1.0m depth 7.07 0.008 Reject
1.2m depth 5.52 0.019 Reject
1.4m depth 4.35 0.037 Reject
1.6m depth 4.35 0.037 Reject
1 Critical test statistic value 3.841 (p = 0.05) using chi square distribution for 1 degree
of freedom (Rogerson, 2001).
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7.6.3 Plot soil moisture dynamics
Theta probe voltage measurements were used to derive VMC at the field plot by
solving equation 4.2. The hydrological model, in its current format, simulates
the depth of water, not the VMC of each cell. The model is designed in this
manner because the actual depth of water is, for this model, a more useful value
for the calculation of model water table depth, subsurface flow and infiltration
rate each timestep. VMC can however be easily calculated from model
generated cell soil moisture using the following relationship,
(7.1)
Applying this transformation to modelled moisture data allows direct
comparison between theta probe and model simulated VMC. In this section the
temporal variation in model plot cell VMC is contrasted with that obtained by
the three theta probes installed at the same location. The model scenario used is
one of variable soil thickness. The results obtained are shown in figure 7.19.
CELL
CELLCELL soildepth
erdepthofwatVMC =
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Figure 7.19. Field plot measured and modelled VMC for distributed soil thicknessscenario.
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The theta probe located at 0.08m below the ground surface maintains a
relatively constant VMC of 0.55 – 0.56 m3/m3 from record start on 28th
September 1998 to 14th March 1999. Subsequently near-surface VMC exhibits a
greater range of VMC values as precipitation is reduced and evapo-transpiration
increases in the summer months, until the record end on 7th July 1999.
Theta probes located at 0.23m and 0.37m below ground level follow a pattern of
year round fluctuation and do not exhibit the plateau characteristic of the
shallow probe during the winter months. Both however show an increased
frequency of wetting events during the first 3000 hours of records compared
with the more pronounced periods of soil drying evident in the latter 4000 hours
of records as precipitation decreases and evapo-transpiration increases during
the spring and summer period.
Modelled field plot VMC is an integrated value of moisture across the entire
soil profile from bedrock to soil surface. Table 7.7 summarises the key changes
in VMC with different soil thickness scenarios. As depth is increased the
average value of VMC for the cell is reduced and the range of values within the
record also lessens. The model predicts that deeper soils result in a less
responsive VMC trace and an overall reduction in VMC due to the dispersal of
water over a deeper soil profile. It is however the variable soil thickness and
0.2m depth model scenarios which predict mean values closest to the mean
theta probe VMC for the duration of the record. The range of VMC measured
over the period is less well simulated, with the model predicting VMC greater
than that recorded during wetting cycles whilst the reverse occurs during
periods of drying. In this case the modelled response of VMC for the variable
depth scenario follows a pattern similar in frequency to that of the two deeper
probes than the shallower probe. The soil drying curve is less well simulated
because the model initially reduces VMC at a rate less than that recorded, but
continues to reduce VMC below the level at which observed VMC stabilised,
approximately 0.45 m3/m3. The effect is of a modelled soil hydrograph with a
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greater range of VMC values, but the correct pattern of response to
precipitation.
Thresholds could be implemented within the model to prevent modelled VMC
from exceeding the limits of VMC observed in the field. The problem may be
linked to the simplistic depth – porosity relationship derived from soil samples
taken from sites across the catchment, not only from the field plot.
Implementation of an upper VMC value for this model would result in reduced
maximum soil water storage as pore volume in the soil profile becomes less.
The frequency and magnitude of overland flow would increase as cells fully
saturate for lower amounts of rainfall. Application of a lower VMC threshold
would limit cell subsurface drainage during periods of low rainfall, resulting in
an event rather than continuous subsurface flow record. However the
implementation of thresholds would be based on observational data rather than
the physical basis of soil water behaviour and has not been attempted in this
thesis.
Table 7.7. Modelled and measured VMC summary statistics for the field plot.
Modelled Values Mean VMC (m3/m
3) VMC range (m
3/m
3)
0.2m soil thickness 0.507 0.440
0.4m soil thickness 0.479 0.323
0.6m soil thickness 0.449 0.256
0.8m soil thickness 0.421 0.214
1.0m soil thickness 0.395 0.184
1.2m soil thickness 0.372 0.162
1.4m soil thickness 0.349 0.145
1.6m soil thickness 0.329 0.131
Variable soil thickness 0.490 0.438
Measured Values Mean VMC (m3/m
3) VMC range (m
3/m
3)
Probe at 0.37m depth 0.494 0.210
Probe at 0.23m depth 0.478 0.123
Probe at 0.08m depth 0.541 0.096
Average theta probe VMC 0.504 0.143
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7.7 Catchment soil moisture dynamics and GPR
The spatio-temporal dynamics of soil moisture are an intrinsic component of
this hydrological model. Soil moisture partially determines the magnitude of
evaporation (equation 3.2), overland flow generation and subsurface flow,
through the relationship between soil moisture and hydraulic conductivity
(equation 3.13). GPR offers a relatively fast and non-invasive method for the
internal validation of modelled soil moisture using GPR measured values.
From analysis of CMP results (chapter 5), 29 GPR derived VMC measurements
were available for 29 individual sites within the catchment. The data was
collected during two periods of fieldwork during October 1998 and June/July
1999. The VMC calculated by the variable soil thickness model was used to
compare the VMC measured by GPR at the corresponding site in the catchment.
In order to compare between GPR and model VMC for each sampled grid cell
the model soil moisture result closest to the time at which the GPR
measurement were taken was used as the source of VMC data. Figure 7.20.
shows the resulting plot of GPR VMC against model VMC, site details and
results are listed in table II.3, appendix II.
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Figure 7.20. GPR measured VMC and variable depth scenario VMC for 29 sitesacross the Cyff. The trend line is fitted to a 1:1 relationship, not through datapoints.
Figure 7.20 shows that an increase in GPR measured VMC are linearly related
to the VMC for the associated model grid cell. The largest deviation from the
1:1 line (site 60) recorded an RMS velocity of 0.08m/ns, the highest value of the
data set, and is probably an erroneous figure resulting from the complexity of
CMP – velocity processing.
Those points with the greatest deviation from the ordinate are located above the
line. Data points that plot above the line indicate that modelled VMC for the
cell is greater than the VMC measured in a subsection of the grid cell using
GPR. Assuming that GPR VMC measured over a 2m-survey line is
representative of VMC over the 25m-grid cell this indicates that specific cells
with the model are storing greater volumes of soil moisture than is physically
measured. Neglecting site 60, the six data points with residuals greater than
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0.1m3/m3 from the ordinate were measured in the field between 6th – 16th
October 1998. This period coincides with a rapid rise in VMC recorded by field
plot theta probes (figure 7.19) and VMC simulated at the plot cell. The
overestimation of VMC by the model for these six sites indicates that the depth
– porosity relationship, and/or subsurface flow, is poorly modelled at these
locations. The remaining 12 sites at which VMC data was measured over the
same time period have soil VMC values varying between -0.02 to +0.09m3/m3
from the ordinate. The fact that GPR and model VMC correspond for some sites
and not others for the same time period is an indication that the model simulates
some areas of the catchment less well than others.
Although VMC data using GPR was only available for two periods throughout
the model simulation, the results show the potential of GPR to quantify soil
VMC for selected cells in a distributed hydrological model. Divergence of
modelled cell VMC from measured values could indicate areas within the
catchment that required further investigation. Although this analysis has
concentrated on the spatial variability of soil moisture, the quantification of soil
moisture variation for the same grid cells over time is also possible. Divergence
between observed and modelled data would provide information on model
performance at the grid scale for different types of events, such as model
response to storm events or to prolonged periods of drought.
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7.8 Sensitivity Analysis
Sensitivity analysis is used in modelling to assess the effect of uncertainty in
model parameters and variables on model outputs. The complex nature of many
environmental models requires a mathematical approach since the interactions
between model parameters and their relative effects on model response cannot
be easily understood. The relative importance of different parameters on model
response can be defined using sensitivity analysis (Campolongo & Braddock,
1999; Cryer & Havens, 1999).
In this thesis, model sensitivity analysis has not been formally carried out.
However the model was designed to examine the impact of varying soil depth
on catchment and hillslope scale discharge, and the effect of changes to this
parameter on model output have been clearly shown.
A full sensitivity analysis would (a) throw light upon the manner in which soil
thickness affects at-a-point and spatially integrated hydrological responses
through the various hydrological processes and (b) help understand the
magnitude of soil thickness sensitivity compared with the sensitivity to other
parameters, thereby indicating the significance of soil thickness sensitivity.
This would be an appropriate activity for further work in this research area.
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7.9 Conclusion
a) No model scenario could simulate peak discharge during storm events and
this is likely to be due to the lack of a macropore subsurface flow
mechanism within the model. Analysis of the recorded hydrograph with all
model scenario discharge shows that shallow soil models are best able to
simulate maximum flows. RMS errors of 0.29m3/s, 0.34m3/s and 0.40m3/s
are associated with soil thickness scenarios of 0.2m, variable and 1.6m.
Shallow soil scenarios perform poorly during periods of low flow, when
predicted discharge approaches zero (RMS error = 0.020m3/s). Deeper soil
scenarios maintain baseflow throughout periods of low rainfall (RMS error
= 0.012m3/s), but are unable to simulate the peak flows generated during
precipitation events. The variable soil thickness model has a range of soil
thickness distributed over the catchment and behaves similarly to shallow
soil models during high flows whilst simulating well intermediate and low
flows, with an RMS error of 0.009m3/s for the event studied.
b) The model is unable to simulate plot overland flow when implemented at a
25m-grid size probably because hillslope overland flow occurs at sub-grid
scales. Large scale grids poorly define the area contributing to flow, but
smaller grids have an improved capacity to model the flow paths and
network of contributing areas. A reduction from a 25m to a 5m-grid size
resulted in a greater frequency and magnitude of modelled overland flow
events. A finer grid also resulted in the creation of upslope cells and is
approaching the scales at which observed overland flow occurred.
Increasing soil thickness at this scale resulted in a decline in cell overland
flow.
c) In this model subsurface flow is affected not only by the soil thickness of
the cell examined but also by downstream cells. This is in response to the
calculation of hydraulic gradient, which drives flow and depends both on
cell elevation and cell water table depth from the soil surface. With all other
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parameters constant, similar depths of soil at the plot cell produce different
subsurface flow because of the difference in soil thickness of the
downstream cell.
d) Modelled subsurface flow occurs continuously in all depth scenarios at the
25m-grid size. Actual subsurface flow is event based, but of a similar
magnitude to modelled results. Soil moisture modelled using the variable
depth model has a similar wetting frequency and mean VMC, but the range
of observed values is smaller than those modelled. Both the range of VMC
and the frequency of subsurface flow could be curtailed using upper and
lower thresholds for flow and VMC, these thresholds would be without
physical basis and may reflect the need for an improved, distributed soil
thickness – porosity relationship. This is currently a lumped parameter
within the model.
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Chapter 8: Conclusions
This thesis has used GPR as a tool for the measurement of two hydrological
parameters across a catchment; soil thickness and soil moisture. However it is
recognised that because of the complex nature of GPR output, some form of
physical measurement of depth and water content is required to calibrate and
validate GPR data.
GPR was successfully applied to the Cyff catchment to measure the variation of
soil thickness at 30 sites, and soil moisture at 29 sites. Using a simple, GIS,
physically-based model with an emphasis on subsurface hydrology, GPR was
used along with physical measurements to parameterise the model for
distributed soil depth and subsequently to perform an internal state validation of
individual cell soil moisture for two periods over the model simulation period.
The results show an improved method for soil thickness and moisture
measurement, with GPR used in conjunction with other techniques to
interpolate between extractive measurements. Correlation of the variability
between GPR and physical measurements of soil thickness showed that the
GPR method was not biased to either over or under recording soil thickness,
although the magnitude of variation between the two methods increased as
measurement depth increased.
The RMS of the difference between auger and GPR measured soil thickness
was calculated as 0.04m to the A-B horizon boundary and 0.12m to the soil-
bedrock B-C boundary. The increase in thickness variation with greater depths
of sampling probably results from the cumulative effects of errors in the
calculation of GPR velocity values, and because the soil-bedrock interface is a
gradual, rather than abrupt boundary.
The observed relationship between GPR soil thickness and TOPMODEL
wetness index, derived from a 25m-grid cell DEM, enabled the prediction of
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soil thickness over the entire catchment. Spatially distributed soil thickness in
conjunction with 55 soil bulk density measurements allowed quantification of
the maximum soil moisture storage capacity for each cell within the catchment.
Soil moisture was derived from CMP radar surveys. Subsurface velocities were
converted to dielectric values and subsequently volumetric moisture content
using standard methods. Validation of GPR measured soil moisture was
provided by theta probe and gravimetric measurements. Because the volume
sampled by GPR in this study is of the order of 0.1-5.0m3, compared to <0.1m3
for point samples, comparison between data sets required scaling up. This was
achieved using a method of integration to sum total soil moisture over a known
depth given the relationship between sample depth and theta probe and
gravimetric moisture. Results show a high degree of correlation between theta
probe and GPR measured VMC (r2 = 0.80, RMS error = 0.03m3/m3) and
gravimetric and GPR measured VMC (r2 = 0.80, RMS error = 0.05m3/m3).
The results of multiple model simulations run using 18-months of hydrological
data show that soil thickness is an important control both on total catchment
discharge and cell overland/subsurface flow frequency and magnitude. Initially,
when considering soil thickness to be lumped at the catchment scale, shallow
soils reproduce hydrograph peaks more accurately than deeper soil scenarios.
The reverse is true during periods of reduced precipitation, when deeper soil
scenarios simulate the decline in river flow more accurately. This behaviour
results from the impact of soil thickness on the different amounts of soil
moisture that can be stored during each simulation.
The distributed GPR derived model of catchment soil thickness contains,
unsurprisingly, an element of both shallow and deep soil models. This enables
the model to simulate low flows and to an extent the peak flows recorded. One
reason for the limited success in simulating peak flows may be the lack of a
model component to simulate subsurface macropore flow, which would rapidly
contribute soil water to the stream network.
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A comparison between GPR measured and the distributed soil thickness model
scenario VMC shows the ability of GPR to perform an internal state validation
of soil moisture. Site GPR VMC were plotted against model VMC for the same
location and time to compare results. Divergence from the expected pattern
indicates potential areas and time periods within the catchment that are poorly
simulated, requiring more detailed investigation and improved parameterisation.
Future work could also include verification of modelled soil thickness at other
locations within the catchment not measured as part of this study.
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Bibliography
Abbott, M.B. Bathurst, J.C. Cunge, J.A. O’Connell, P.E. Rasmussen, J. 1986.An introduction to the European Hydrological System – SystèmeHydrologique Europèen, SHE, 2: structure of a physically-based, distributedmodelling system. Journal of Hydrology 87: 61-77.
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Appendix I. PCRaster model code and parameter values.
Variable GPR soil thickness. 25m grid# Version id = msd02. # Soil moisture model with evaporation, infiltration, runoff & throughflow modules# Non-linear porosity term included in subsurface calculation# Ksat is a function of bulk density (Campbell, 1985)# Depth = variable (sd02.map)# Drainage LDD calculated each timestep on the basis of hydraulic gradient# Surface routing uses kinematic flow# Model assumes one soil layer of variable depth derived from GPR measurements# Water calculated/input must be as depth NOT area or volume
#-----------------------------------------------------------------------------------------------------------------binding RainTimeSeries=Rain4.txt; # rainfall input timeseries PotEvapTime=PE4.txt; # Potential evapotranspiration time series
InitMoist=imc.map; # initial moisture content, m water /m soil thickness,set as 0.9 maxmoist
soildepth=sd02.map; # soil thickness from GPR - Upslope area results.Forced depth of 0.01m in river network
Ldd=Ldd25.map; # catchment drainage network dem=dtm25.map; # digital elevation model Slope=slope25.map; # slope angle (degrees), must be scalar
timestep=scalar(3600); # timestep in seconds cellwidth=scalar(25); # cell width (m)
beta=scalar(0.6); # kinematic wave parameter, 0.6 = sheet flow q=scalar(0.0); # kinematic wave parameter, side flow, not used MN=scalar(0.15); # mannings n value
sites=allsites.map; # Location of GPR sample sites Outflow=pit25.map; # catchment outflow cell location plot=plot.map; # location of field plot
b=scalar(2.4); # b value from Campbell (1985) mfc=scalar(0.150); # mass fraction of clay mfs=scalar(0.282); # mass fraction of sand
areamap bool25.map; # catchment mask map
timer 1 9999 1; # 9999 step simulation. Hourly. Start 0100 1 Oct 1997 reportdefault = 1+50..endtime; # selective storage of maps on harddisk (every fiftieth
stored) #-------------------------------------------------------------------------------------------------------------initial soilmoist=InitMoist; # Initial soil moisture infilwater=scalar(0); # cell surface water for infiltration equals zero
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localXS=scalar(0); # cell surface water height is zero (m)
WFdepth=scalar(0); # wetting front depth (m) grad=scalar(tan(slope25.map)); # DEM slope gradient (m/m) ROF=scalar(0); # return overland flow initially zero (m) WTdepth=scalar(0); # water table depth initially zero (m)
# soildepth=scalar(1.6); # Use for soil constant depth scenarios (m) # soil depth = 1.6m maxmoist=(((-0.848/0.757)*exp(-0.757*soildepth))-((-0.848/0.757)*exp(-0.757*0)));# new porosity profile from all bulk density samples (except bog samples)
# maximum total moisture in profile, f(changing porosity with depth)# integral maxmoist gives area under depth-porosity curve per cell (m porosity / m soil)# Non-linear porosity decrease with depth derived from Cyff soil samples.
sat_pc = (soilmoist/maxmoist*100); # Percentage saturation of cell soil
#----------------------------------------------------------------------------------------------------------------dynamic
Rain=timeinputscalar(RainTimeSeries,1); # Rainfall (mm) Raincell=Rain/1000 # Rainfall (m)
Epot=timeinputscalar(PotEvapTime,1); # Potential evaporation (m)
E=Epot/1000*(soilmoist/maxmoist); # Actual evaporation (m)
# Surface water infiltration module
Check0=Raincell+localXS; # Sum inputs this timestep
WFdepth = if(Raincell eq 0, 0, WFdepth); # If no rainfall in previous time step wetting front depth assumed to be zero
# WFdepth = if(WFdepth + (soildepth-WTdepth) ge soildepth,soildepth,WFdepth); # If wetting front plus water table height above bedrock >= soildepth, entire soil profileis saturated
# Calculate porosity at wetting front depth from previous timestep P = 0.848*exp(-0.757*WFdepth);
# Convert porosity to bulk density for input into Campbell (1985) equation BD = (1-P)*2.65;
Ksat=0.004*((1.3/BD)**(1.3*b))*exp(-6.9*mfc-3.7*mfs); # Campbell (1985) equation for Ksat
infilwater=min((Raincell+localXS),Ksat); # infiltration amount this timestep localXS=max((Raincell+localXS)-Ksat,0); # infiltration rate determines localXS Check1=Check0 - (localXS+infilwater); # Check previous inputs equal new
partition of water
Check2=(infilwater+soilmoist) gt maxmoist; # Boolean map of cells where maxmoist is exceeded. Should not occur.
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localXS=localXS+(max(infilwater+soilmoist-maxmoist,0));
soilmoist=min(infilwater+soilmoist,maxmoist);# if infilwater and current moisture > maxmoist the excess is added to localXS # Calculate new wetting front depth for the next timestep # i.e. real depth of soil taken by infiltrated water WFdepth = infilwater+(-0.848/0.757*exp(-0.757*WFdepth)); WFdepth = WFdepth/(-0.848/0.757); WFdepth = (ln(WFdepth))/-0.757; #-------------------------------------------------------------------------------------------------------- # Create ldd for subsurface flow # dynamic, responds to changes in water table position each timestep
# Initially calculates depth of water table (m) given: # 1. Water input (soilmoist) # 2. Total profile depth # 3. Knowledge of non-linear porosity decrease with depth
WTdepth = soilmoist - ((-0.848/0.757)*exp(-0.757*soildepth)); WTdepth = WTdepth/(0.848/0.757); WTdepth = (ln(WTdepth))/(-0.757);
# this value is with reference to the DEM surface # ie when soilmoist = maxmoist, WTdepth = 0 # and when soilmoist = 0, WTdepth = soildepth
Check3 = WTdepth gt soildepth; # check water table < soil depth
WTldd = lddcreate((dem-WTdepth),1e31,1e31,1e31,1e31);# ldd for soil moisture uses height of water table to calculate drainage net eachtimestep
distance = if(downstreamdist(WTldd) gt 0,downstreamdist(WTldd),cellwidth);# horizontal distance between cells use downstreamdist command except for pit cellswhich must be cellwidth
Hgrad = ((dem-WTdepth)-(downstream(WTldd,dem)-downstream(WTldd,WTdepth)))/distance; # Hydraulic gradient between cells# This gradient includes amount of soil depth contributing to flow so soils do not needto be fully saturated for flow to occur
#------------------------------------------------------------------------------------------------------------ # Subsurface throughflow module # Actual flow out of a cell depends on: # a) amount of potential water available to move, the soil moisture # b) hydraulic gradient between a cell and its downstream neighbour # c) cell K
K=Ksat*((soilmoist/maxmoist)**(2*b+3)); # Percolation rate, Campbell (1985)
out = min((K*Hgrad),soilmoist); # water output from a cell cannot exceed the water available to transport (m/timestep)
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in = upstream(WTldd,out); # water input from upstream cells
balance = soilmoist + in - out;
soilmoist = if(balance gt maxmoist,maxmoist,balance); ROF = max(balance-maxmoist,0); # if the new balance exceeds cell capacity the excess becomes return overland flow soilmoist=if(soilmoist gt E,soilmoist-E,0); # final soil moisture includes evaporation losses
sat_pc=(soilmoist/maxmoist*100); # percentage saturation of soil in a cell
soilm = soilmoist; # renamed to allow storage of results
#----------------------------------------------------------------------------------------------------------# Runoff module. Uses kinematic flow routing. From De Roo et al.,. (1998)
localXS=localXS+ROF; # New localXS includes any return flow from saturated cells
alpha=((MN*(cellwidth+2*localXS)**(2/3))/(sqrt(grad)))**beta;# alpha is a roughness parameter Q1=if(alpha gt 0.0, ((cellwidth*localXS)/alpha)**(1/beta), 0.0); Q2=kinematic(Ldd,Q1,q,alpha,beta,timestep,cellwidth);# overland flow discharge (m
3/s)
localXS=alpha*(Q2**beta)/cellwidth; # first approximation using old alpha alpha=((MN*(cellwidth+2*localXS)**(2/3))/(sqrt(grad)))**beta; # new alpha localXS=alpha*(Q2**beta)/cellwidth; # second approximation for localXS using new alpha Runoff=localXS gt 0; # Boolean map, true value shows runoff is occurring in a cell
#--------------------------------------------------------------------------------------------------------------- # Subsurface discharge calculation # Based on Xiao 1996 for saturated flow between cells
x = ((dem-WTdepth)+downstream(WTldd,(dem-WTdepth))/2)-((dem-soildepth)+(downstream(WTldd,dem)-downstream(WTldd,soildepth))/2); # mean depth of saturated soil contributing to subsurface flow between cells (m)
A = x*cellwidth; # Cross sectional area contributing to subsurface flow (m2)
ssQ = A*out; # subsurface discharge (cell/timestep)
#-------------------------------------------------------------- --------------------------------------------------# Storage of output as maps
report stack1_ = soilm; # soil moisture report stack2_ = WTldd; # subsurface flow LDD report stack3_ = sat_pc; # percentage cell saturation report stack4_ = ROF; # return overland flow
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report stack5_ = Hgrad; # hydraulic gradient report stack6_ = Q2; # overland flow report stack7_ = ssQ; # subsurface throughflow report stack8_ = WTdepth; # water table depth report stack9_ = WFdepth; # wetting front depth # TimeSeries output
report Q2ts=timeoutput(Outflow,Q2); # Q from kinematic routing report ssQts=timeoutput(Outflow,ssQ); # subsurface Q report XSts=timeoutput(Outflow,localXS); # water height of outflow cell report plotrun=timeoutput(plot,Q2); # plot runoff report plotsub=timeoutput(plot,ssQ); # plot subsurface flow report Evap=timeoutput(plot,E); # Evaporation report Kval=timeoutput(plot,K); # Hydraulic conductivity report smoist=timeoutput(plot,soilm); # Plot soil moisture status report infil=timeoutput(plot,infilwater); # Infiltration value report sat=timeoutput(plot,sat_pc); # Percentage cell soil saturation
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Model inputs and parameters
Table I.1 Model parameters and initial data requirements.
Name Description Value Required for Spatialdistribution
Temporalstatus
Unit
RainTimeSeries
Hourlyrainfall data
Variable Model input Lumped Dynamic mm
InitMoist Initial soilmoisturestatus
0.9 ×maxmoist
Initialisation Distributed N/A m
PotEvapTime
Hourlypotentialevaporation
Variable Model input Lumped Dynamic m
NetRadiation
Hourly netradiation
Variable Calculation ofpotentialevaporation
Lumped Dynamic W/m2
Lamda Latent heatofvaporisation
2.5 Calculation ofpotentialevaporation
Lumped Constant J/kg
soildepth Map of soildepth (fromGPR depthandtopographicrelationship)
Variable Maximum soilmoisturestoragecapacity
Distributed Constant m
DEM Catchmentelevation
Variable Ldd networkand slope
Distributed Constant m
Ldd Localdrainagedirectionnetworkfrom DEM
Variable Routing ofsurface runoff
Distributed Constant N/A
Slope Local slopeangle fromDEM
Variable Input forsurface runoff
Distributed Constant degs
Timestep Modeltimestep
3600 Kinematicequation
N/A N/A s
Cellwidth
Cell width 25 Kinematicequation
N/A N/A m
Outflow Catchmentmap withoutflow cellselected
TRUE Catchmenthydrograph
1 cell Constant N/A
Plot Catchmentmap withfield plotcell flagged
TRUE Recording thetemporal statusof plotoverland flow,throughflowand soilmoisture
1 cell Constant N/A
Bool25 Booleanmap of theentirecatchment
TRUE Definecatchmentextent duringmodel
N/A Constant N/A
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area simulation
Name Description Value Required for Spatialdistribution
Temporalstatus
Units
sites Map of allsitessampledusing GPR
TRUE Analysis ofcell soilmoisturedynamics
Distributed Constant N/A
beta Kinematicwaveparameter,sheet flow(De Roo etal, 1998b)
0.6 Kinematicequation
Lumped Constant N/A
q Kinematicwaveparameter,side flow(De Roo etal, 1998b)
0.0 Kinematicequation
Lumped Constant N/A
b Poreinteractionterm fromCampbell(1985)
2.4 Calculation ofKsat
Lumped Constant N/A
MN Manning’s nvalue forcroppedgrassland(Meadows&Stephenson,1985)
0.1 Kinematicequation
Lumped Constant N/A
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Table I.2 Model internal variables.
Name Description Value Required for Spatialdistribution
Temporalstatus
Unit
soilmoist Cell soilmoisture
Variable Infiltration,evaporation,runoff andsubsurfaceflow
Distributed Dynamic m
localXS Ponded surfacewater in a cell
Variable Surface runoff Distributed Dynamic m
infilwater Amount of waterinfiltrating eachtimestep
Variable Infiltration Distributed Dynamic m
WFdepth Wetting frontdepth
Variable Infiltration Distributed Dynamic m
WTdepth Water tabledepth
Variable Subsurfaceflow andWTlddcalculation
Distributed Dynamic m
WTldd Ldd calculatedfrom water tableheight and cellelevation
Variable Routing ofsubsurfaceflow
Distributed Dynamic
Hgrad Hydraulicgradient betweena cell and thedownstream cell
Variable Subsurfaceflow
Distributed Dynamic m/m
ROF Return overlandflow. From cellswhen subsurfaceflow exceedsmaxmoist
Variable Surface runoff Distributed Dynamic m
Sat_pc Cell saturationpercentage
Variable Cell soilmoistureanalysis
Distributed Dynamic %
A Average depthcontributing tosubsurface flowbetween cells
Variable Subsurfaceflow
Distributed Dynamic m
Runoff Cell surfacewater discharge
Variable Catchment andplothydrograph
Distributed Dynamic m3/s
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Appendix II. GPR sample site information.
Figure II.1. Location of GPR sample sites within the Cyff. See table II.1 for site co-ordinates, terrain attributes and average GPR derived soil thickness.
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Table II.1 Site attributes and GPR measured soil thickness to horizons.
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Table II.2. Summary data of trend line r2 value, the number of samples used to fitthe trend line, total soil thickness to the CMP reflector, and the depth of watercalculated within the soil column using GPR, theta probe and gravimetricanalysis methods.
Theta probe
measurements
Gravimetric
samples
Site r2 No. of
readingsr2 No. of
samples
Soil thickness
to reflector (m)
GPR water
depth (m)
Theta probe
water depth
(m)
Gravimetric
water depth
(m)
13 0.774 8 0.481 3 0.349 0.152 0.166 0.179
14 0.863 8 0.971 3 0.330 0.175 0.166 0.141
16 0.622 11 0.879 5 0.525 0.251 0.298 0.290
17 0.904 4 n/a 0 0.410 0.207 0.167 -
18 0.969 4 n/a 0 0.423 0.189 0.147 -
19 0.989 4 0.988 4 0.461 0.181 0.197 0.172
20 1.000 2 n/a 0 0.314 0.146 0.162 -
22 0.548 6 0.459 5 0.511 0.244 0.224 0.308
23 0.576 5 n/a 0 0.336 0.158 0.143 -
24 0.786 5 n/a 0 0.330 0.149 0.122 -
27 0.095 3 0.081 3 0.565 0.238 0.249 0.201
32 0.961 4 1.000 2 0.322 0.123 0.151 0.164
33 0.156 12 0.942 6 0.591 0.347 0.375 0.416
48 Manual 14 Manual 5 0.297 0.138 0.130 0.111
49 0.744 3 n/a 1 0.372 0.145 0.085 -
53 0.879 10 0.972 3 0.425 0.164 0.226 0.210
54 0.992 5 0.824 4 0.260 0.133 0.124 0.107
56 0.486 14 4E-06 3 0.253 0.142 0.164 0.212
RMS error 0.031 0.045
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Table II.3. Variable soil thickness model scenario and GPR VMC for 29 sites inthe Cyff catchment.
Site Date Time Cell soilmoisture (m)
Cell soilthickness (m)
VMC cell GPR VMC
13 29/06/99 13:00 0.25 0.53 0.46 0.4414 29/06/99 11:00 0.30 0.58 0.51 0.5316 29/06/99 16:00 0.26 0.53 0.49 0.4823 01/07/99 12:00 0.15 0.33 0.45 0.4724 01/07/99 14:00 0.11 0.25 0.42 0.4533 08/07/99 12:00 0.35 0.66 0.53 0.5940 08/07/99 13:00 0.62 1.09 0.57 0.6048 30/06/99 13:00 0.34 0.70 0.49 0.4653 30/06/99 17:00 0.23 0.52 0.45 0.3956 30/06/99 11:00 0.38 0.75 0.50 0.565 16/10/98 17:00 0.26 0.41 0.64 0.486 07/10/98 10:00 0.19 0.40 0.49 0.518 06/10/98 11:00 0.19 0.38 0.51 0.459 14/10/98 15:00 0.58 0.97 0.60 0.4117 15/10/98 13:00 0.33 0.54 0.63 0.5018 09/10/98 15:00 0.31 0.57 0.54 0.4519 09/10/98 11:00 0.30 0.55 0.55 0.3920 14/10/98 16:00 0.31 0.62 0.50 0.4721 07/10/98 15:00 0.49 0.77 0.63 0.5522 15/10/98 11:00 0.46 0.72 0.64 0.4827 08/10/98 13:00 0.08 0.19 0.40 0.4232 08/10/98 12:00 0.14 0.32 0.44 0.3837 15/10/98 15:00 0.59 0.99 0.60 0.6339 15/10/00 16:00 0.60 1.00 0.59 0.5941 08/10/98 16:00 0.61 1.041 0.59 0.6149 06/10/98 14:00 0.23 0.45 0.52 0.3950 06/10/98 16:00 0.15 0.31 0.47 0.4954 07/10/98 14:00 0.29 0.52 0.56 0.5160 16/10/98 11:00 0.21 0.32 0.64 0.26
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Table II.4. Variable soil thickness model scenario and GPR VMC for 29 sites inthe Cyff catchment.
Site GPR survey Layer 2-way Interval Calculated Layer Total K VMCfrequency ID travel
time(time) Velocity depth depth rms
MHz ns ns m/ns m m m3/m3
5 900 1 0.0 0.281 0.00 0.00 1.12 22.0 22.0 0.051 0.56 0.56 34.4 0.483 26.0 4.0 0.055 0.11 0.67 29.6 0.444 31.0 5.0 0.068 0.17 0.84 19.6 0.34
6 900 1 0.0 0.291 0.00 0.00 1.12 16.0 16.0 0.047 0.38 0.38 40.5 0.514 22.0 6.0 0.068 0.20 0.58 19.6 0.34
20 900 1 0.0 0.277 0.00 0.00 1.22 5.5 5.5 0.050 0.14 0.14 35.8 0.483 12.5 7.0 0.052 0.18 0.32 33.1 0.474 20.5 8.0 0.065 0.26 0.58 21.2 0.36
21 450 1 0.0 0.325 0.00 0.00 0.82 12.5 12.5 0.048 0.30 0.30 39.6 0.513 22.5 22.5 0.044 0.50 0.50 46.2 0.554 26.5 14.0 0.055 0.39 0.68 29.6 0.445 35.0 8.5 0.068 0.29 0.97 19.6 0.34
22 900 1 0.0 0.319 0.00 0.00 0.92 9.0 9.0 0.050 0.23 0.23 35.8 0.483 15.0 6.0 0.055 0.17 0.39 29.6 0.444 22.5 7.5 0.063 0.23 0.62 22.9 0.38
27 900 1 0.0 0.313 0.00 0.00 0.92 10.0 10.0 0.050 0.25 0.25 35.8 0.483 21.2 11.2 0.058 0.32 0.57 27.0 0.42
9 450 1 0.0 0.294 0.00 0.00 1.02 4.5 4.5 0.055 0.12 0.12 29.6 0.443 19.5 15.0 0.070 0.53 0.65 18.2 0.324 44.0 24.5 0.055 0.67 1.32 29.6 0.44
9 900 1 0.0 0.313 0.00 0.00 0.92 4.0 4.0 0.045 0.09 0.09 44.1 0.533 16.6 12.6 0.059 0.37 0.46 25.7 0.414 45.0 28.4 0.055 0.78 1.24 29.6 0.44
49 450 1 0.0 0.284 0.00 0.00 1.12 8.0 8.0 0.065 0.26 0.26 21.2 0.363 16.5 8.5 0.085 0.36 0.62 12.4 0.234 45.0 28.5 0.100 1.43 2.05 8.9 0.17
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Site GPR survey Layer 2-way Interval Calculated Layer Total K VMCfrequency ID travel
time(time) Velocity depth depth rms
MHz ns ns m/ns m m m3/m3
49 900 1 0.0 0.279 0.00 0.00 1.12 8.0 8.0 0.063 0.25 0.25 22.9 0.383 18.0 10.0 0.080 0.40 0.65 14.0 0.26
8 450 1 0.0 0.287 0.00 0.00 1.12 15.0 15.0 0.050 0.38 0.38 35.8 0.483 23.0 8.0 0.070 0.28 0.66 18.2 0.324 40.0 17.0 0.068 0.57 1.23 19.6 0.34
8 900 1 0.0 0.310 0.00 0.00 0.92 13.0 13.0 0.054 0.35 0.35 30.7 0.453 25.0 12.0 0.065 0.39 0.74 21.2 0.36
17 450 1 0.0 0.297 0.00 0.00 1.02 7.5 7.5 0.058 0.22 0.22 27.0 0.423 15.5 8.0 0.048 0.19 0.41 38.8 0.504 29.5 14.0 0.068 0.47 0.88 19.6 0.34
17 900 1 0.0 0.293 0.00 0.00 1.02 10.0 10.0 0.060 0.30 0.30 24.8 0.403 17.5 7.5 0.058 0.22 0.52 27.0 0.424 32.5 15.0 0.068 0.51 1.02 19.6 0.34
18 450 1 0.0 0.300 0.00 0.00 1.02 10.0 10.0 0.060 0.30 0.30 24.8 0.403 14.5 4.5 0.055 0.12 0.42 29.6 0.444 40.0 25.5 0.075 0.96 1.38 15.9 0.29
18 900 1 0.0 0.287 0.00 0.00 1.12 7.5 7.5 0.055 0.21 0.21 29.6 0.443 20.0 12.5 0.063 0.39 0.60 22.9 0.384 35.0 15.0 0.075 0.56 1.16 15.9 0.29
19 900 1 0.0 0.285 0.00 0.00 1.12 5.5 5.5 0.040 0.11 0.11 55.9 0.613 17.0 11.5 0.061 0.35 0.46 24.0 0.394 22.5 5.5 0.068 0.19 0.65 19.6 0.345 30.0 7.5 0.075 0.28 0.93 15.9 0.29
41 450 1 0.0 0.289 0.00 0.00 1.12 5.5 5.5 0.040 0.11 0.11 55.9 0.613 37.5 32.0 0.040 0.64 0.75 55.9 0.614 50.0 12.5 0.053 0.33 1.08 32.4 0.46
41 900 1 0.0 0.333 0.00 0.00 0.82 5.5 5.5 0.058 0.16 0.16 27.0 0.423 42.0 36.5 0.045 0.82 0.98 44.1 0.534 47.5 5.5 0.050 0.14 1.12 35.8 0.48
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Site GPR survey Layer 2-way Interval Calculated Layer Total K VMCfrequency ID travel
time(time) Velocity depth depth rms
MHz ns ns m/ns m m m3/m3
37 450 1 0.0 0.268 0.00 0.00 1.22 5.5 5.5 0.045 0.12 0.12 44.1 0.533 21.5 21.5 0.040 0.43 0.55 55.9 0.614 40.0 34.5 0.055 0.95 1.07 29.6 0.445 60.0 20.0 0.060 0.60 1.67 24.8 0.40
39 450 1 0.0 0.278 0.00 0.00 1.22 4.5 4.5 0.043 0.10 0.10 49.5 0.573 45.0 40.5 0.041 0.83 0.93 53.2 0.594 55.0 10.0 0.060 0.30 1.23 24.8 0.40
50 900 1 0.0 0.328 0.00 0.00 0.82 10.0 10.0 0.055 0.28 0.28 29.6 0.443 14.0 4.0 0.050 0.10 0.38 35.8 0.484 22.0 8.0 0.075 0.30 0.68 15.9 0.29
54 900 1 0.0 0.258 0.00 0.00 1.32 5.0 5.0 0.050 0.13 0.13 35.8 0.483 10.8 5.8 0.047 0.14 0.26 40.5 0.51
60 900 1 0.0 0.294 0.00 0.00 1.02 7.5 7.5 0.043 0.16 0.16 49.5 0.573 18.2 10.7 0.080 0.43 0.59 14.0 0.26
13 900 1 0.0 0.325 0.00 0.00 0.82 3.4 3.4 0.050 0.09 0.09 35.8 0.483 12.5 12.5 0.056 0.35 0.44 28.5 0.43
15 900 1 0.0 0.306 0.00 0.00 1.02 3.2 3.2 0.053 0.09 0.09 31.8 0.463 17.6 17.6 0.063 0.56 0.64 22.5 0.37
16 900 1 0.0 0.308 0 0.00 0.92 4.0 4.0 0.042 0.09 0.09 50.7 0.573 20.6 20.6 0.051 0.53 0.61 34.4 0.48
23 900 1 0.0 0.274 0 0.00 1.22 3.4 3.4 0.050 0.09 0.09 35.8 0.483 12.9 12.9 0.052 0.34 0.42 33.1 0.474 20.2 20.2 0.065 0.65 1.08 21.2 0.36
24 900 1 0.0 0.292 0 0.00 1.02 3.3 3.3 0.052 0.08 0.08 33.1 0.473 12.2 12.2 0.054 0.33 0.41 30.7 0.45
33 900 1 0.0 0.260 0 0.00 1.32 3.1 3.1 0.055 0.09 0.09 29.6 0.443 6.0 6.0 0.050 0.15 0.24 35.8 0.484 21.5 21.5 0.041 0.44 0.68 53.2 0.59
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Site GPR survey Layer 2-way Interval Calculated Layer Total K VMCfrequency ID travel
time(time) Velocity depth depth rms
MHz ns ns m/ns m m m3/m3
40 450 1 0.0 0.272 0 0.00 1.22 1.4 1.4 0.118 0.09 0.09 6.4 0.113 45 43.6 0.041 0.90 0.99 52.2 0.585 60.0 15.0 0.111 0.83 1.82 7.3 0.13
48 900 1 0.0 0.298 0 0.00 1.02 2.4 2.4 0.071 0.08 0.08 17.7 0.323 11.3 11.3 0.052 0.29 0.38 33.1 0.474 20.7 9.3 0.088 0.41 0.79 11.5 0.22
53 900 1 0.0 0.270 0 0.00 1.22 3.0 3.0 0.057 0.08 0.08 27.5 0.423 13.7 13.7 0.062 0.43 0.51 23.3 0.38
56 900 1 0.0 0.313 0 0.00 0.92 4.1 4.1 0.041 0.08 0.08 53.2 0.593 11.8 11.8 0.043 0.25 0.34 48.4 0.564 37.1 25.3 0.069 0.87 1.21 18.8 0.33
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Table II.5. Soil thickness measurements (m) to B and C horizons using auger andGPR methods.
site ID f (MHz) A-B auger A-B gpr Difference B-C auger B-C gpr Difference5 900 0.25 0.26 0.01 0.5 0.43 -0.076 900 0.25 0.21 -0.04
0.3 0.3 0.29 -0.010.17 0.18 0.01 0.25 0.26 0.01
no data 0.22 0.21 -0.01no data 0.29 0.33 0.04no data 0.25 0.29 0.04
8 900 0.3 0.3 0.00 0.45 0.39 -0.060.3 0.28 -0.02 0.5 0.43 -0.07
0.26 0.33 0.07 0.46 0.47 0.019 450 no data 0.94 0.93 -0.01
no data 1.0 1.01 0.01no data 0.87 no pick
9 900 no data 0.94 no pickno data 1.0 no pickno data 0.87 no pick
17 450 0.16 no pick 0.84 0.78 -0.060.175 no pick 0.95 0.84 -0.11
0.15 no pick 1.0 0.92 -0.0817 900 0.16 0.16 0.00 0.84 no pick
0.175 0.18 0.005 0.95 no pick0.15 0.18 0.03 1.0 no pick
18 900 0.42 0.45 0.03 0.77 0.61 -0.160.485 0.45 -0.035 0.66 0.63 -0.03
0.49 0.46 -0.03 0.70 0.77 0.0719 900 0.21 0.2 -0.01 0.40 0.34 -0.06
0.265 0.25 -0.015 0.35 0.55 0.200.35 0.24 -0.11 0.63 0.46 -0.17
Pit 0.21 0.22 0.01 0.30 0.33 0.0320 900 0.18 0.23 0.05 0.35 0.40 0.05
0.22 0.21 -0.01 0.34 0.46 0.120.23 0.18 -0.05 0.65 0.55 -0.10
0.155 0.18 0.025 0.56 0.33 -0.230.17 0.18 0.01 0.46 0.48 0.02
21 450 no data 0.47 0.73 0.67 -0.06no data 0.36 0.72 0.71 -0.01
0.375 0.36 -0.015 0.89 0.79 -0.100.54 0.47 -0.07 0.77 0.97 0.20
900 no data 0.46 0.73 0.7 -0.03no data 0.50 0.72 0.76 0.04
0.375 0.36 -0.015 0.89 0.68 -0.210.54 0.52 -0.02 0.77 0.68 -0.09
22 450 0.16 0.66 0.65 -0.010.25 0.78 0.85 0.070.31 0.89 0.88 -0.01
900 0.16 0.21 0.05 0.66 0.67 0.010.25 0.23 -0.02 0.78 0.65 -0.13
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0.31 0.27 -0.04 0.89 0.63 -0.26Pit 0.2 0.21 0.01 0.31 0.53 0.22
27 900 No B horizon present 0.15 0.39 0.24No B horizon present 0.48 0.55 0.07
Pit No B horizon present 0.3 0.29 -0.01No B horizon present 0.39 0.36 -0.03No B horizon present 0.5 0.54 0.04
32 900 0.21 0.24 0.03 0.29 0.35 0.060.15 0.18 0.03 0.29 0.35 0.060.18 0.22 0.04 0.31 0.33 0.02
37 450 0.90 0.88 -0.020.90 0.92 0.020.73 0.70 -0.030.60 0.95 0.351.00 0.94 -0.061.00 0.97 -0.030.55 0.5 -0.050.85 0.85 0.000.92 0.85 -0.071.00 0.91 -0.09
39 450 0.95 1.12 0.170.78 0.85 0.070.84 0.88 0.041.00 1.07 0.070.85 0.81 -0.040.9 1.12 0.22
0.72 1.15 0.430.76 0.93 0.170.7 0.82 0.12
0.65 0.68 0.0341 450 No data 0.88 0.98 0.10
No data 0.87 0.84 -0.03No data 0.74 0.85 0.11
49 900 No A horizon present 0.26 0.23 -0.03No A horizon present 0.3 0.26 -0.04No A horizon present 0.31 0.26 -0.05
Pit No A horizon present 0.2 0.26 0.0650 900 0.29 0.29 0.34 0.0552 900 No data 0.2 0.3 0.1
0.19 0.245 0.25 0.0050.1 0.25 0.27 0.02
No data 0.21 0.21 0.00No data 0.26 0.26 0.00Organic to C horizon 0.17 0.24 0.07
54 900 No data 0.35 0.31 -0.040.3 0.25 0.05 0.36 0.35 -0.01
No data 0.67 0.47 -0.200.15 0.84 0.64 -0.20
Pit 0.26 0.25 0.01 0.3+ See 2nd position forthis site
13 900 0.25 No match 0.7 No matchPit 0.28 0.27 -0.01 0.34+ 0.65
0.23 0.23 0.00 0.72 0.59 -0.13
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14 900 0.26 0.26 0.00 0.86 0.61 -0.250.23 0.28 0.05 0.37 0.38 0.010.25 0.19 -0.06 0.82 0.34 -0.48
15 900 0.1 Too shallow 0.8 0.69 -0.11Pit 0.12 0.15 0.03 0.17+ 0.68
0.20 0.25 0.05 0.62 0.81 0.1916 900 0.41 0.39 -0.02 0.41 0.39 -0.02
Pit 0.45 0.48 0.03 0.55 0.48 -0.0748 900 0.52 0.4 -0.12 0.79 0.73 -0.06
Pit 0.66 0.64 -0.02 0.66+ 0.640.64+ No match 0.9 0.73 -0.17
53 Pit 0.38 0.42 0.04 0.78 No match900 0.3 0.3 0.00 0.5 0.5 0.00
0.24 No match 0.57 0.49 -0.0856 900 No A or B horizon present 1.00 1.06 0.06
Pit No A or B horizon present 0.7+ 1.02No A or B horizon present 1.00 1.03 0.03
23 900 No A horizon present 0.32 0.32 0.00Pit No A horizon present 0.3 0.31 0.01
No A horizon present 0.29 0.23 -0.0624 900 no data 0.49 0.32 -0.17
Pit No A horizon present 0.32 0.29 -0.03No A horizon present 0.3 0.27 -0.03
33 450 No A horizon present 0.69 0.64 -0.05Pit No A horizon present 0.56 0.55 -0.01
No A horizon present 0.66 0.65 -0.0140 No A horizon present 1.04+ 1.27
No A horizon present 1.05+ 1.51No A horizon present 0.97+ 1.55
B Horizon C HorizonRMS ofdifference (m)
0.04 RMS ofdifference (m)
0.12
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Appendix III. Soil sample data.
Table III.1 Soil sample wet and dry weights.
Site ID Depth (m)from
groundsurface
Wetweight
(g)
Dryweight
(g)
VMC %(gravimetric)
BulkDensity(g/cm
3)
%Porosity
6 0.1 43.29 16.90 60.57 0.39 0.856 0.2 56.72 39.77 38.91 0.91 0.6632 0.1 44.06 18.95 57.64 0.43 0.8432 0.2 51.86 31.45 46.85 0.72 0.7319 0.1 44.23 18.01 60.18 0.41 0.8419 0.2 59.67 40.09 44.94 0.92 0.6519 0.15 50.63 27.44 53.23 0.63 0.7619 0.29 39.32 28.49 24.86 0.65 0.7527 0.04 36.34 15.39 48.09 0.35 0.8727 0.1 38.84 24.58 32.73 0.56 0.7927 0.18 53.16 34.66 42.46 0.80 0.7049 0.1 49.24 31.06 41.73 0.71 0.738 0.1 47.27 20.98 60.35 0.48 0.828 0.2 49.77 30.83 43.47 0.71 0.738 0.3 73.48 54.57 43.41 1.25 0.5350 0.1 49.38 26.55 52.40 0.61 0.7750 0.2 53.06 34.07 43.59 0.78 0.7054 0.04 47.60 23.64 55.00 0.54 0.8054 0.1 53.56 35.59 41.25 0.82 0.6954 0.2 55.27 43.01 28.14 0.99 0.6354 0.3 51.43 39.06 28.39 0.90 0.6622 0.05 32.97 9.73 53.34 0.22 0.9222 0.1 41.95 15.45 60.83 0.35 0.8722 0.15 66.16 46.76 44.53 1.07 0.5922 0.2 59.30 36.63 52.04 0.84 0.6822 0.25 44.16 26.25 41.11 0.60 0.7733 0.1 71.36 7.75 73.00 0.09 0.9733 0.15 73.40 8.28 74.74 0.10 0.9633 0.25 75.93 9.44 76.31 0.11 0.9633 0.35 77.82 8.17 79.94 0.09 0.9633 0.45 95.84 37.32 67.16 0.43 0.8433 0.55 60.70 36.51 55.52 0.42 0.8448 0.05 82.36 38.17 50.72 0.44 0.8348 0.2 103.52 89.57 16.01 1.03 0.6148 0.3 45.99 22.67 53.53 0.52 0.8048 0.4 52.91 30.07 52.43 0.69 0.7448 0.5 66.68 47.61 43.77 1.09 0.5916 0.05 87.10 28.23 67.56 0.32 0.8816 0.2 60.96 37.75 53.28 0.87 0.6716 0.3 55.84 32.04 54.63 0.74 0.7216 0.4 63.66 41.32 51.28 0.95 0.6416 0.5 67.78 49.17 42.72 1.13 0.57
Andrew Howe
272
15 0.05 77.20 22.86 62.37 0.26 0.9015 0.1 51.14 26.87 55.71 0.62 0.7715 0.15 53.37 43.80 21.97 1.01 0.6214 0.05 85.45 40.60 51.47 0.47 0.8214 0.15 60.62 40.73 45.65 0.93 0.6514 0.25 58.05 42.85 34.89 0.98 0.6313 0.05 84.25 37.11 54.10 0.43 0.8413 0.15 108.69 58.38 57.74 0.67 0.7513 0.25 60.81 41.21 44.99 0.95 0.6453 0.15 41.84 17.79 55.20 0.41 0.8553 0.25 54.58 32.74 50.13 0.75 0.7253 0.35 64.54 46.75 40.83 1.07 0.6056 0.1 88.52 13.08 86.58 0.15 0.9456 0.3 80.58 11.40 79.40 0.13 0.9556 0.7 86.87 12.67 85.16 0.15 0.95
Field plot 0.03 43.61 17.62 59.66 0.40 0.85Field plot 0.1 49.94 22.19 63.70 0.51 0.81Field plot 0.19 64.72 46.75 41.25 1.07 0.60Field plot 0.2 67.97 47.90 46.07 1.10 0.59Field plot 0.3 48.42 34.19 32.66 0.78 0.70Field plot 0.05 42.69 18.45 55.65 0.42 0.84Field plot 0.1 61.13 40.84 46.57 0.94 0.65Field plot 0.15 50.40 30.08 46.64 0.69 0.74Field plot 0.2 49.75 27.49 51.09 0.63 0.76Field plot 0.25 57.14 39.94 39.48 0.92 0.65Field plot 0.33 64.56 35.65 66.36 0.82 0.69
37 0.2 40.59 8.88 72.79 0.20 0.9237 0.3 45.10 8.72 83.51 0.20 0.9237 0.4 42.40 7.06 81.12 0.16 0.9437 0.1 37.02 4.49 74.67 0.10 0.9637 0.5 41.85 5.79 82.77 0.13 0.9537 0.7 65.28 34.95 69.62 0.80 0.7037 0.7 53.73 20.85 75.47 0.48 0.8237 0.2 40.61 6.96 77.24 0.16 0.9437 0.3 38.70 6.76 73.31 0.16 0.9437 0.6 44.78 6.88 86.99 0.16 0.9437 0.4 41.45 5.54 82.43 0.13 0.9537 0.5 43.26 5.49 86.70 0.13 0.95
Mean 57.83 28.33 67.71