Katholieke Universiteit Leuven
Belgium
Radar Based Rainfall Estimationfor River Catchment Modeling
Promotor:Prof. P. Willems
Advisor:T. Goormans
Master dissertation in partial fulfilmentof the requirements for the Degree of
Master of Science in Water Resources Engineering
by: Shrestha Narayan Kumar
September 2009
Radar based rainfall estimation for river catchment modelling
i
Acknowledgement
First and foremost, I would like to express my sincere gratitude to my promoter Prof. dr. ir.
Patrick Willems for valuable suggestions and guidance right from the beginning. His constant
encouragement has been the key for successful completion of this thesis.
I would also like to thank my advisor ir. Toon Goormans; with whom I had so many
interesting discussions and made me comfortable during field visits too. He read this thesis
from beginning to end and offered many valuable comments.
From a practical standpoint, the thesis would not have been possible without the collaboration
of the Royal Meteorological Institute (RMI) of Belgium who provided the radar data of the
Wideumont station and the raingauge data as well. I would also like to express gratitude to
the resource people from the RMI for their technical support and guidance, in particular Dr.
ir. Laurent Delobbe and ir. Edouard Goudenhoofdt. Also, I would like to thank the Flemish
water company Aquafin and the Flemish Environment Society for providing the raingauge
series.
Special thanks go to VLIR-UOS for providing the scholarship for this Inter-University
Program in Water Resource Engineering (IUPWARE) 2007-2009 session and Katholieke
Universiteit, Leuven and Vrije Universiteit Brussel for providing the platform.
On a more personal note, I would like to thank my wife Sabi Shrestha for her constant
support and her love as well as my family for their support for me from day one.
Finally, the author would like to thank all those in IUPWARE 2007-2009 for being like a
family, contribute to the success of the thesis to great extent.
Radar based rainfall estimation for river catchment modelling
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Table of Contents
Acknowledgement --------------------------------------------------------------------------------------- i
Table of Contents --------------------------------------------------------------------------------------- ii
List of Figures ------------------------------------------------------------------------------------------ vi
List of Tables ------------------------------------------------------------------------------------------viii
List of Acronyms -------------------------------------------------------------------------------------- ix
Abstract -------------------------------------------------------------------------------------------------- x
CHAPTER 1: INTRODUCTION ------------------------------------------------- 1
1.1 Problem definition ----------------------------------------------------------------------------- 1
1.2 Motivation of the study ------------------------------------------------------------------------ 2
1.3 Thesis aims and objectives -------------------------------------------------------------------- 3
1.4 Thesis outline ----------------------------------------------------------------------------------- 3
CHAPTER 2: LITERATURE REVIEW ---------------------------------------- 4
2.1 Rainfall ------------------------------------------------------------------------------------------ 4
2.2 Rainfall measurement -------------------------------------------------------------------------- 4
2.2.1 Rain gauges -------------------------------------------------------------------------------- 4
2.2.2 Weather radars ---------------------------------------------------------------------------- 5
2.2.2.1 The RMI weather radar at Wideumont ------------------------------------------- 6
2.2.2.2 Local Area Weather Radar (LAWR) of Leuven -------------------------------- 8
2.2.2.3 Uncertainty associated with radar estimates -----------------------------------10
2.2.2.4 Radar-gauge merging techniques ------------------------------------------------12
2.3 Hydrological modelling ----------------------------------------------------------------------13
2.3.1 The VHM Model ------------------------------------------------------------------------14
2.3.1.1 Model structure ---------------------------------------------------------------------15
2.3.1.2 Model parameters ------------------------------------------------------------------16
2.3.1.3 Model calibration ------------------------------------------------------------------17
2.3.2 The NAM model -------------------------------------------------------------------------17
Radar based rainfall estimation for river catchment modelling
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2.3.2.1 Model structure ---------------------------------------------------------------------17
2.3.2.2 Model parameters ------------------------------------------------------------------18
2.3.2.3 Model calibration ------------------------------------------------------------------19
2.4 Significance of spatial variability of rainfall and basin response ----------------------20
2.5 Similar past studies ---------------------------------------------------------------------------21
2.5.1 Radar-gauge comparison and merging -----------------------------------------------21
2.5.2 Stream flow simulation using radar data ---------------------------------------------22
CHAPTER 3: APPLICATION -------------------------------------------------- 23
3.1 Methodology -----------------------------------------------------------------------------------23
3.2 Study area --------------------------------------------------------------------------------------23
3.3 Radar-gauge comparison and merging -----------------------------------------------------25
3.3.1 The raingauge network ------------------------------------------------------------------25
3.3.2 Correcting raingauge measurements --------------------------------------------------25
3.3.3 Conversion of radar records to rainfall rates -----------------------------------------26
3.3.4 Data periods ------------------------------------------------------------------------------27
3.3.5 LAWR - gauge comparison and merging --------------------------------------------28
3.3.6 RMI Wideumont estimates and gauge comparison and merging -----------------32
3.4 Hydrological modelling ----------------------------------------------------------------------32
3.4.1 The catchment ----------------------------------------------------------------------------32
3.4.1.1 Choice of catchment ---------------------------------------------------------------32
3.4.1.2 Catchment geomorphology -------------------------------------------------------33
3.4.1.3 Input meteorological series -------------------------------------------------------34
3.4.2 Catchment modelling with VHM------------------------------------------------------35
3.4.3 Catchment modelling with NAM------------------------------------------------------36
3.4.4 Performance evaluation of the model results ----------------------------------------36
3.4.5 The significance of spatial data --------------------------------------------------------38
3.4.5.1 Quantifying rainfall variability ---------------------------------------------------38
Radar based rainfall estimation for river catchment modelling
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3.4.5.2 Basin response ----------------------------------------------------------------------39
CHAPTER 4: RESULTS AND DISCUSSION ------------------------------- 41
4.1 LAWR estimates − gauge comparison and merging -------------------------------------41
4.1.1 Using an average value of CF ----------------------------------------------------------41
4.1.2 Range dependent adjustment on CF --------------------------------------------------42
4.1.3 Statistical analysis on range dependent adjustment ---------------------------------43
4.1.4 Mean field bias adjustment -------------------------------------------------------------46
4.1.4.1 Brandes spatial adjustment -------------------------------------------------------48
4.1.4.2 Statistical analysis on the MFB and BRA adjustment ------------------------48
4.2 RMI Wideumont estimates − gauge comparison and merging -------------------------50
4.2.1 MFB adjustment -------------------------------------------------------------------------50
4.2.2 Brandes spatial adjustment -------------------------------------------------------------51
4.2.3 Statistical analysis on the MFB and BRA adjustment ------------------------------51
4.3 Comparison of LAWR-Leuven and RMI-Wideumont estimates ----------------------52
4.4 Catchment modelling -------------------------------------------------------------------------53
4.4.1 Catchment modelling with VHM------------------------------------------------------53
4.4.2 Catchment modelling with NAM------------------------------------------------------54
4.4.3 Model performance evaluation --------------------------------------------------------55
4.5 The significance of spatial data -------------------------------------------------------------60
4.5.1 Rainfall spatial variability --------------------------------------------------------------60
4.5.2 Basin response ---------------------------------------------------------------------------60
CHAPTER 5: CONCLUSIONS ------------------------------------------------- 69
5.1 Comparing and merging of radar − gauge estimates -------------------------------------69
5.2 Hydrological modelling ----------------------------------------------------------------------70
5.3 Limitation and future perspectives ----------------------------------------------------------71
CHAPTER 6: REFERENCES --------------------------------------------------- 72
CHAPTER 7: ANNEXES --------------------------------------------------------- 78
Radar based rainfall estimation for river catchment modelling
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A-1: Prior time series processing results -----------------------------------------------------------78
A-2: Model results -------------------------------------------------------------------------------------79
A-3: Rainfall series (in terms of Pref) for selected storm events --------------------------------82
A-4: Accumulated rainfall over radar pixels for selected storm events -----------------------84
A-5: LAWR-Leuven simulated results -------------------------------------------------------------86
Radar based rainfall estimation for river catchment modelling
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List of Figures
Figure 2-1: Different types of weather radars and their aspects (Einfalt et al., 2004) --------------------- 6
Figure 2-2: Simplified sketch of beam cut-off ------------------------------------------------------------------- 9
Figure 2-3: Influence of choice of Z-R relationship on rainfall rates (Einfalt et al., 2004) -------------- 11
Figure 2-4: Errors related to height of the measurement (Delobbe, 2007) --------------------------------- 11
Figure 2-5: Some typical vertical profile of reflectivity (Delobbe, 2007) ---------------------------------- 12
Figure 2-6: General lumped conceptual rainfall-runoff model structure (Willems, 2000) --------------- 14
Figure 2-7: Steps in the VHM structure identification and calibration procedure ------------------------ 15
Figure 2-8: The NAM structure ----------------------------------------------------------------------------------- 18
Figure 3-1: Belgium (light green), the RMI-Wideumont radar (black star), the LAWR-Leuven (red
star) and the catchment (dark green). Black arcs indicate the distance to the RMI-Wideumont,
with an increment of 60 km. The red circle shows 15 distance to the LAWR-Leuven ------------ 24
Figure 3-2: The study area with the location of 12 gauges (red dots: Aquafin &VMM; black triangles:
RMI), the LAWR (yellow star), catchment (dark green polygon) and part of the Walloon region
(light green polygon). Circles indicate the distance to the LAWR, with increment of 5 km ----- 24
Figure 3-3: Catchment under consideration with position of LAWR (star), radar beam blockage sector
(blue shade), rain gauges (dots-the VMM and Aquafin TBRs; triangles-the RMI non-recording
gauges), water courses (blue lines) and circles - distances of 5, 10 and 15 km from the LAWR 33
Figure 3-4: The DEM map of catchment with stream network ---------------------------------------------- 34
Figure 4-1: Evolution of RFB with range (using constant CF on the LAWR estimates) ---------------- 41
Figure 4-2: Plot of CF as a function of distance to the LAWR, each point representing a TBR
(Aquafin &VMM) -------------------------------------------------------------------------------------------- 42
Figure 4-3: Evolution of RFB with range (using range dependent CF on the LAWR-Leuven estimates)
------------------------------------------------------------------------------------------------------------------- 43
Figure 4-4: Scatter plot of daily accumulated radar-gauge valid pairs for summer storm using constant
value of CF and CF after range dependent adjustment on the LAWR-Leuven estimates --------- 45
Figure 4-5: Cumulative rainfall plot of radar and gauge records for the winter and summer periods of
the LAWR estimates after range dependent correction on CF----------------------------------------- 46
Figure 4-6: Frequency distribution of field bias of valid gauge-radar (LAWR) pairs -------------------- 47
Figure 4-7: Probability distribution of field bias of valid gauge-radar (LAWR) pairs ------------------- 47
Figure 4-8: Evolution of different statistical values with different adjustments on the LAWR-Leuven
estimates; [a]-summer period and [b]-winter period ---------------------------------------------------- 49
Figure 4-9: Scatter plot of radar-gauge daily accumulated estimates for week 1 & 2 before [a] and
after [b] MFB correction on the RMI-Wideumont estimates ------------------------------------------ 50
Figure 4-10: Scatter plot of radar-gauge daily accumulated estimates for week 3 & 4 before [a] and
after [b] MFB correction on the RMI Wideumont estimates ------------------------------------------ 51
Radar based rainfall estimation for river catchment modelling
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Figure 4-11: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for
summer weeks ------------------------------------------------------------------------------------------------- 53
Figure 4-12: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for
winter weeks --------------------------------------------------------------------------------------------------- 53
Figure 4-13: Graphical comparison of nearly independent peak flow maxima ---------------------------- 57
Figure 4-14: Graphical comparison of nearly independent slow flow minima ---------------------------- 58
Figure 4-15: Graphical comparison of peak flow empirical extreme value distributions ---------------- 58
Figure 4-16: Graphical comparison of low flow empirical extreme value distributions ----------------- 59
Figure 4-17: Graphical comparison of cumulative flow volumes ------------------------------------------- 59
Figure 4-18: NSEobs for different rainfall descriptors and for different storm events ------------------- 61
Figure 4-19: Observed and simulated flows derived from different rainfall descriptors ----------------- 65
Figure 4-20: Observed and simulated flows derived from different rainfall descriptors ----------------- 66
Figure 4-21: Plot of SDIR and NSEref for both the VHM and NAM -------------------------------------- 67
Figure A-1: Baseflow filter results ------------------------------------------------------------------------------- 78
Figure A-2: Interflow filter results -------------------------------------------------------------------------------- 78
Figure A-3: Observed and NAM simulated hydrograph for the calibration period (3/1/2006-
2/28/2009) ----------------------------------------------------------------------------------------------------- 79
Figure A-4: Cumulative observed and NAM simulated discharge for calibration period (3/1/2006-
2/28/2009) ----------------------------------------------------------------------------------------------------- 79
Figure A-5: Observed and NAM simulated hydrograph for the validation period (1/1/2004-
12/31/2005) ---------------------------------------------------------------------------------------------------- 80
Figure A-6: Observed and VHM simulated hydrograph for the calibration period (3/1/2006-
2/28/2009) ----------------------------------------------------------------------------------------------------- 80
Figure A-7: Cumulative observed and VHM simulated discharge for the calibration period (3/1/2006-
2/28/2009) ----------------------------------------------------------------------------------------------------- 81
Figure A-8: Reference rainfall evolution for storm event-1 -------------------------------------------------- 82
Figure A-9: Reference rainfall evolution for storm event-2 -------------------------------------------------- 82
Figure A-10: Reference rainfall evolution for storm event-3 ------------------------------------------------- 83
Figure A-11: Reference rainfall evolution for storm event-4 ------------------------------------------------- 83
Figure A-12: Accumulated rainfall for storm event -1 (RMI pixels), north is upward ------------------- 84
Figure A-13 : Accumulated rainfall storm event-1 (LAWR pixels), north is upward -------------------- 84
Figure A-14: Accumulated rainfall for storm event -3 (RMI pixels), north is upward ------------------- 85
Figure A-15: Accumulated rainfall storm event-3 (LAWR pixels), north is upward --------------------- 85
Figure A-16: LAWR-Leuven VHM simulated river discharge for the period of 7/2/2008 to 9/30/2008
------------------------------------------------------------------------------------------------------------------- 86
Figure A-17: LAWR-Leuven NAM simulated river discharge for the period of 12/1/2008 to
2/28/2009 ------------------------------------------------------------------------------------------------------ 86
Radar based rainfall estimation for river catchment modelling
viii
List of Tables
Table 2-1: Some characteristics of the Wideumont radar ------------------------------------------------------ 7
Table 2-2: Some characteristics of the LAWR-Leuven ------------------------------------------------------- 10
Table 3-1: Correction Factors [k] for the Aquafin and VMM raingauges ---------------------------------- 25
Table 3-2: Calibration Factor [CF] for Aquafin and VMM raingauges ------------------------------------- 26
Table 3-3: Data periods of the RMI radar of Wideumont ----------------------------------------------------- 27
Table 3-4: Data periods of the LAWR of Leuven -------------------------------------------------------------- 27
Table 3-5: Selected storm events; LT means Local Time ---------------------------------------------------- 38
Table 4-1: Some statistical parameter values before and after range dependent adjustment on the
LAWR estimates. --------------------------------------------------------------------------------------------- 44
Table 4-2: Some statistical parameter values before and after MFB and BRA adjustment on the
LAWR estimates for both summer and winter periods; RAW stands for the LAWR estimates
using constant CF values, RDA(LAWR estimates after range dependency adjustment on CF) - 48
Table 4-3: Some statistical parameter values before and after MFB adjustment on the RMI
Wideumont radar estimates, RAW stands for original RMI-Wideumont estimates --------------- 52
Table 4-4: The calibrated VHM parameters with their short description ----------------------------------- 54
Table 4-5: The calibrated NAM parameters with their short description ----------------------------------- 55
Table 4-6: Some goodness-of-fit-statistics ---------------------------------------------------------------------- 56
Table 4-7: Rainfall spatial variability measured in terms of SDIR for the different rainfall descriptors
and for selected events --------------------------------------------------------------------------------------- 60
Table 4-8: Results in terms of NSEobs for the different rainfall descriptors and for different storm
events ----------------------------------------------------------------------------------------------------------- 61
Table 4-9: Results in terms of NSEref for the different rainfall descriptors ------------------------------- 63
Radar based rainfall estimation for river catchment modelling
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List of Acronyms
AD Average Difference
BC Box-Cox Transformation
BRA Brandes spatial adjustment
CF Calibration Factor
DEM Digital Elevation Model
DHI Danish Hydrological Institute
DMI Danish Meteorological Institute
IUPWARE Inter-University Program in Water Resource Engineering
KMI Koninklijk Meteorologisch Instituut
LAWR Local Area Weather Radar
MAE Mean Absolute Error
MFB Mean Field Bias
NAM Nedbør-Afstrømnings-Model (Rainfall-Runoff Model)
NSE Nash-Sutcliff Efficiency
POT Peak Over Threshold
RFB Relative Field Bias
RMI Royal Meteorological Institute
RMSE Root Mean Square Error
SDIR Reference Spatial Deviation Index
SWAT Soil & Water Assessment Tool
VHM Veralgemeend conceptueel Hydrologisch Model (Generalized lumped
conceptual and parsimonious model structure-identification and
calibration)
VLIR Vlaamse Interuniversitaire Raad
VMM Vlaamse Milieumaatschappij (Flemish Environment Agency)
VPR Vertical profile of reflectivity
WETSPRO Water Engineering Time Series PROcessing tool
Radar based rainfall estimation for river catchment modelling
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Abstract
This paper discusses the first hydro-meteorological potential of the X-band Local Area Weather Radar
(LAWR), installed in the densely populated city centre of Leuven (Belgium). Adjustments are applied
to raw radar data using gauge readings from a raingauge network of 12 raingauges. The significance
of spatial rainfall information on hydrological responses is investigated in the 48.17 km2
Molenbeek-
Parkbeek catchment, south of Leuven. For this, two lumped conceptual models, the VHM and the
NAM, are calibrated with reference rainfall (Pref) − a rainfall representation defined by raingauges
which are inside the catchment. Three alternative rainfall descriptors are derived, namely the RG1
(single raingauge for the whole catchment taking a gauge which is approximately at the centroid of
the catchment), the LAWR estimates and the estimates from a C-band weather radar installed by the
Royal Meteorological Institute (RMI) at Wideumont (Belgium). An index, reference spatial deviation
index (SDIR) is defined based on the difference between Pref and the alternative rainfall descriptors. A
modified Nash-Sutcliff Efficiency (NSEref) is used to evaluate the performance of simulated runoff
with respect to reference simulated runoff – runoff derived by reference rainfall.
Range dependent adjustment is applied on the LAWR data combining a power and second degree
polynomial function. C-band RMI estimates tend to overestimate summer storms and strongly
underestimate winter storms. The mean field bias correction followed by Brandes spatial adjustment
improved the radar estimates to a great extent. After adjustments, the mean absolute error is found to
decrease by 47% and the mean absolute error by 45% compared to the original radar estimates. Still,
the gauge-radar residuals even after adjustments are found to be not negligible. No large differences
in streamflow simulation capability of the two types of models can be distinguished. Runoff
simulations based on the RG1 rainfall descriptor are almost as accurate as those based on Pref. Using
radar estimated rainfall for runoff simulations showed lower performance compared to both Pref as
well as RG1 indicating that the catchment is less sensitive to spatial rainfall variability and/or the
accuracy of radar based rainfall estimates is low. Runoff peaks for summer and extreme events are
underestimated due to high damping and filtering effects of the catchment or more obviously, due to
the localized summer rainfall events. More uniform storms are simulated with more or less the same
accuracy for all rainfall descriptors. An inverse correlation between SDIR and NSEref is observed. An
SDIR of more than 10% affected the hydrograph reproduction indicating that the catchment requires
more robust areal rainfall estimation.
Key words: Weather radar; Runoff; Lumped conceptual model; Spatial rainfall variability.
Radar based rainfall estimation for river catchment modelling
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CHAPTER 1: INTRODUCTION
1.1 Problem definition
Rainfall is the driving force for the hydrologic cycle, a physical phenomenon which controls
the terrestrial water supplies. Its nature and characteristics are important to conceptualize and
predict its effect on runoff, infiltration, evapotranspiration and water yield. For most of the
simulation models, it is primary input, often considered spatially uniform over the catchment
which is actually not usually the case. Rather, it is highly variable in both space and time.
During a storm, rainfall may vary by tens of millimetres per hour from minute to minute and
over distances of only a few tens of metres (Austin et al., 2002). Hence the assumption of
uniform rainfall leads to a major uncertainty in simulated events (Willems, 2001). Also, it can
be observed that hydrologists have traditionally paid much more attention to the development
of more sophisticated rainfall-runoff models or the local models to suit the local conditions
than to the development of improved techniques for the measurement and prediction of the
space-time variability of rainfall. This is to be deplored, since rainfall is the driving source of
water behind most of the inland hydrological processes (Berne et al., 2005). So, better
understanding on the rainfall input to the hydrological modelling is required to acquire more
robust and accurate hydrological simulation. Hence, it demands a dense rain gauge
observation network to cover this spatial variability, which is difficult to install and maintain,
making it an undesirable solution (Wilson and Brandes, 1979).
Weather radars, which are capable of providing continuous spatial measurements which are
immediately available, are increasingly being used as an alternative. For the showery rain at
least, the advantage of using radar derived rainfall to raingauge is expected to be obvious.
One particular storm which caused severe flooding at some location might not have passed
over the raingauges and can not be reflected in basin response through a hydrological model.
The weather radar can detect rainfall events to over one hundred kilometres from the radar
site.
Also, it is an inherent property of radar measurements that the uncertainty on measurements
increases as the rainfall intensity increases (Einfalt et al., 2004). These uncertainties should
be minimized before using them as input to simulation models by using adjustment
techniques (Wilson and Brandes, 1979). Hence, merging of both forms of rainfall estimates is
advised. There have been a range of methods to merge the radar and raingauge data for better
Radar based rainfall estimation for river catchment modelling
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estimates of rain gauges; from simple merging methods to sophisticated spatial methods.
Many researchers have carried out rigorous study on the evaluation of these merging methods
(e.g. Delobbe et al. (2008); Goudenhoofdt and Delobbe (2009)) and found that raw radar data
can be greatly enhanced. However, radar-gauge residuals, even after adjustment are not
always negligible (Borga, 2002). So, both measurement devices are complementary;
concurrent use of both can provide better estimates of rainfall (Einfalt et al., 2004).
The importance of considering the spatial distribution of rainfall for process-oriented
hydrological modelling is well-known. However, the application of rainfall radar data to
provide such detailed spatial resolution is still under debate (Tetzlaff and Uhlenbrook, 2005)
and is the subject of ongoing research. A network of rain gauges can provide more accurate
point-wise measurements but the spatial representation is limited (Goudenhoofdt and
Delobbe, 2009) but should be supported by quite a dense raingauge network.
In this study, emphasis is made to use the relatively new Local Area Weather Radar (LAWR)
of Leuven, Belgium for its first stream flow modelling. The raingauge network will serve as
ground truth data and hence serves as validation source as well as basis for correction on the
radar estimates. Data from the radar of the Royal Metrological Institute (RMI) − in Dutch:
Koninklijk Meteorologisch Instituut (KMI) − located at Wideumont is also used to check the
importance of the spatial variability of rainfall information on the catchment under
consideration. Two lumped conceptual runoff models, the VHM (Veralgemeend conceptueel
Hydrologisch Model) and the NAM (Nedbør-Afstrømnings-Model), are used for this
propose.
1.2 Motivation of the study
The hydro-meteorological potential of the weather radars has already been explored by many
researchers and interest in this subject is growing because of their capability of spatial
coverage to finer resolutions which are impossible to obtain with a raingauge network. The
C-band weather radar installed by the RMI at Wideumont has already been used for
hydrological modelling. But the LAWR-Leuven, installed by the Flemish water company
Aquafin, has rarely been used for such propose. Hence, a research has to be performed to
evaluate the performance of the LAWR- Leuven for catchment modelling. In this study, a
catchment named Molenbeek/Parkbeek, south of the Leuven is chosen for this propose. Using
Radar based rainfall estimation for river catchment modelling
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both the RMI-Wideumont and the LAWR-Leuven for stream flow simulation would lead to
assess the significance of spatial resolution of the two different weather radars.
1.3 Thesis aims and objectives
For this thesis, data are available from a raingauge network and two different types of radars,
all providing rainfall information for the Molenbeek/Parkbeek catchment, south of Leuven,
Belgium, and this leads to the following objectives:
� To compare rainfall information from three sets of data; the raingauges, the C- and X-
band weather radars and hence quantifying the accuracy of radar estimates.
� To test procedures for merging the radar-gauge estimates for better rainfall estimation.
� To investigate the significance of spatial rainfall information by using the above
stated rainfall information on hydrological modelling.
� To provide recommendations on spatial resolution requirements of rainfall
information for the particular catchment.
1.4 Thesis outline
Chapter 1 gives the general problem definition, motivation for the study, the aims and
objectives of the thesis.
Chapter 2 gives the relevant literature review including the different rainfall descriptors, the
models used for simulating the basin response and similar previous studies.
Chapter 3 describes the methodology of the thesis in general and gives a description of the
study area, the rain gauge network and the radars that are used and the data periods. Also,
different comparison as well as adjustment methodologies, modelling methodologies and
different statistical tools used for the study are explained.
Chapter 4 discusses the results.
Chapter 5 covers the conclusions and recommendations for further researchers and the
limitation of different approaches used in the study as well.
Apart from this the thesis also contains an appendix and list of references used.
Radar based rainfall estimation for river catchment modelling
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CHAPTER 2: LITERATURE REVIEW
2.1 Rainfall
Rainfall is one of the many forms of precipitation and a major component of the hydrological
cycle. It is the driving force of water for most of the terrestrial hydrological process (Berne et
al., 2005). The rainfall must satisfy the intermediate demand of evapotranspiration,
infiltration and surface storage before it results in runoff. In hydrological modelling, it is the
primary input (Segond et al., 2007; Velasco-Forero et. al., 2008).
Rainfall can be mainly divided into stratiform and convective rainfall. Stratiform rainfall
essentially results from stratiform clouds, has small drops and uniform spatial and temporal
gradients. Convective storms on other hand are generally more intense and consist of larger
drops. They are characterised by large temporal and spatial gradients.
2.2 Rainfall measurement
Rain gauges and weather radars are the two sensors that are most widely used in rainfall
measurement (Velasco-Forero et. al., 2008).
2.2.1 Rain gauges
The most common device that is being used for rainfall measurement is a rain gauge. Because
of its simple working principle, the tipping bucket rain gauges (TBRs) are widely used in
recent time though there are modern techniques coming up as well. The total amount of
rainfall over a given period is expressed as the depth of water which would cover a horizontal
area if there is no runoff, infiltration or evaporation. This depth is generally expressed in
millimetres and is the rainfall depth (FAO irrigation and Drainage Paper 27, 1998).
Rain gauge measurements, although representing only point rainfall, are very often
considered the “true” rainfall although there are some errors still associated with it. During
tipping motion of the bucket, water continues to flow through the funnel which is not taken
into consideration, resulting in an underestimation of the rainfall rate (Goormans and
Willems, 2008). Thus a dynamic calibration procedure should be applied. This procedure is
well defined by Luyckx and Berlamont (2001). Vasvari (2007) applied the same procedure on
several rain gauges in the city of Graz, Austria and found that not all of them are
underestimating. Several rain gauges had a positive relative deviation; some up to 22%, in the
Radar based rainfall estimation for river catchment modelling
5
low intensity range up to 0.5 mm/min. He ascribed this phenomenon by the retention of water
in the buckets between tips. But for higher intensities, the study showed a clear
underestimation. Another error associated with rain gauge measurement is due to wind
effects. FAO irrigation and Drainage Paper 27, Annex 2 (1998) states that wind errors are a
major error which can be very large, even more than 50%. Hence, local wind shelter
influences should also be considered. Goormans and Willems (2008) studied several
raingauges around the city of Leuven, Belgium and found that the wind effects
underestimated the long term rainfall accumulation depth by a factor as high as 1.32. These
two forms of errors that are always associated with rain gauges should be considered because
rain gauge based estimates of rainfall are generally used for validation of radar-based rainfall
quantities and will affect final radar performance.
2.2.2 Weather radars
Rain gauges are reliable instruments for which hydrologists can rely on at least for point
measurement (Moreau et al., 2009) but rainfall can vary both in space and time which is not
really captured by the rain gauges. Thus, there have been considerable interests in utilizing
the weather radar, since it provides spatially and temporally continuous measurements that
are immediately available at the radar site (Wilson and Brandes, 1979, Einfalt et al., 2004).
But the inherent feature of weather radars are that they did not measure rainfall directly but
rather the back scattered energy from precipitation particles from elevated volumes and an
algorithm should be developed and calibrated against the raingauge network.
Wilson and Brandes (1979) and Einfalt et al. (2004) describe the methodology of using
weather radars in quantitative precipitation estimates and the potential error sources. The first
study also focuses on the methodologies on radar-gauge comparisons and adjustments. The
second one gives a clear outline of requirements for weather radars, examples of good and
bad practices more in terms of online and offline applications of weather radar.
Mostly three types of weather radars are used in hydrometeorology - the S-band, the C-band
and the X-band radars. Their relative advantages and disadvantages are given in Figure 2-1.
Radar based rainfall estimation for river catchment modelling
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Figure 2-1: Different types of weather radars and their aspects (Einfalt et al., 2004)
The difference is in the wavelength of the emitted electromagnetic waves. The S-band radars
have the longest wavelength while the X-band radars have the shortest. Using a larger
wavelength for radar measurement would certainly enhance the usable range but problems
arise from radar beam interaction with ground. The shorter wave length radars, although
having fine spatial resolution, suffer from attenuation significantly (Einfalt et al. 2004).
2.2.2.1 The RMI weather radar at Wideumont
The RMI of Belgium operates C-band radar located in Wideumont, in the south of Belgium.
The radar performs a volume scan every 5 minutes with reflectivity measurements up to 240
km. A Doppler scan with radial velocity measurements up to 240 km is performed every 15
minutes (RMI, 2009). The 5 minute radar data are summed up to produce 1h and 24h
precipitation accumulation products. The radar is equipped with a linear receiver and the
reflectivity factors are converted to precipitation rates using the Marshall-Palmer (1948)
relation with ‘a’ and ‘b’ values being 200 and 1.6 respectively.
A time domain Doppler filtering is applied which removes the ground clutter. An additional
treatment is applied to the volume reflectivity file to eliminate residual permanent ground
clutter caused by surrounding hills. Reflectivity data contaminated by permanent ground
clutter are replaced by data collected at higher elevation. A Pseudo-Cappi image at 1500 m is
calculated from the volume data. An advection procedure has also been applied to correct the
effect of time sampling interval on accumulation maps (Delobbe et al. 2006).
Characteristics: Some relevant characteristics of the C-Band Doppler radar located at
Wideumont are presented in Table 2-1 (Berne et al. 2005).
Radar based rainfall estimation for river catchment modelling
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Table 2-1: Some characteristics of the Wideumont radar
Property Value
Location Wideumont , Belgium
Operational since October 2001
Type of radar Gematronik pulse Doppler
Frequency/wavelength C-band (5.64GHz/5.32 cm)
Mean transmit power 250 W
Height of tower base 535 m (above mean sea level)
Height of tower 50 m
Height of antenna 585 m (above mean sea level)
Antenna diameter 4.2 m
Radome diameter 6.7 m
Elevations 0.5°, 1.2
°, 1.9
°, 2.6
°, 3.3
°, 4.0
°, 4.9
°, 6.5
°, 9.4
°, 17.5
°
Maximum range reflectivity processing 240 km
Time interval precipitation products 5 min.
Working principle: Radars do not measure rainfall directly but rather the back scattered
energy from precipitation particles from elevated volumes. The received energy from the
precipitation particles is given by:
2
2
r
ZKCPr = (1)
With,
C = radar constant
K = imaginary dielectric constant
r = range of the target
Z = radar reflectivity
The radar reflectivity, Z (mm6/m
3), is proportional to the summation of the sixth power of
particle diameters (Di6) in a unit volume illuminated by the radar beam; and is defined as:
dDDDNDNZ ii
66)(∫∑ == (2)
Where,
Ni= number of drops per unit volume with diameter Di
N(D) = number of drops with diameters between D and D+dD in a unit volume.
Radar based rainfall estimation for river catchment modelling
8
The rainfall rate (R) can be related to N(D) by the following equation if no vertical air motion
is assumed.
∫= dDDVDDNR t )()(6
3π (3)
Where,
Vt(D)= drop terminal velocity of a drop diameter D which is also a function of D.
But the problem is that both Z and R are functions of the drop size distribution which is
unknown and hence using an empirical Z-R relationship is imminent which is usually in the
exponential form such as:
bRaZ = (4)
with a and b being constants.
It is worth noting that the Equation (4) itself can be regarded as semi-empirical as it has been
derived assuming empirical relationships for Vt(D) and N(D).
Some currently used Z-R relationships as depicted in Einfalt et al. (2004) are as follows;
� 6.1200 RZ = , suitable for stratiform events also known as the Marshall and Palmer
(1948) relationship.
� 2.1250 RZ = , suitable for tropical climates.
� 4.1300 RZ = , suitable for convective events.
Limitation of the above stated relationships should be clear due to the fact that there can not
be null vertical air motion such as the case of a thunderstorm. Also, the drop size distribution
is rarely known and it varies in space and time (Wilson and Brandes, 1979).
2.2.2.2 Local Area Weather Radar (LAWR) of Leuven
Outcome of a project ‘development of a system for short-time prediction of rainfall’, the
Danish Hydrological Institute (DHI) together with the Danish Meteorological Institute (DMI)
developed a cost effective X-band radar called LAWR (DHI Website, 2009). It is based on
X-band marine radar technology and emits only a tenth (25 kW) of the power emitted from
conventional weather radars (250 kW) and is capable to penetrate high intensity rainfall.
From this, DHI also developed a smaller version of the LAWR, the so-called City LAWR.
Important feature of the City LAWR is that it has a compact antenna (diameter of 65 cm) and
Radar based rainfall estimation for river catchment modelling
9
total weight of only 8 kg, which makes it fairly easy to install. It has a horizontal opening
angle of 3.9° making quantitative precipitation estimation possible up to a distance of 15 km
from the radar site (Goormans et al., 2008). But, the large vertical opening angle of 20° makes
it susceptible to direct ground reflection.
In an ongoing research project of the Hydraulics Laboratory of the Katholieke Universiteit
Leuven for the Flemish water company Aquafin, a City LAWR is installed in the densely
populated city centre of Leuven. Based on quite rigorous clutter tests, the city LAWR is
installed on the roof of the Provinciehuis building – the main office of the province of
Flemish Brabant. This location produced acceptable amounts of clutter, mainly due to a pit
wall which cuts off the lower part of the beam (Goormans et al., 2008). The simplified sketch
of this beam cut-off is shown in Figure 2-2. From here on, the City LAWR will be referred to
as the LAWR.
Figure 2-2: Simplified sketch of beam cut-off
Characteristics: Some relevant characteristics of X-Band LAWR located at Leuven are
presented in Table 2-2.
Working Principle: Contrary to conventional weather radars like C-band weather radars,
which are equipped with a linear receiver, the LAWR has a logarithmic receiver. This
suggests that the conventional transformation from reflectivity to rainfall rate should be
linear. A relationship between the ‘count’ (representation of back scattered energy) and the
rainfall rate recorded at ground level has to be established. According to the manufacturer
and as confirmed by some studies, (e.g. Rollenbeck and Bendix, 2006), a linear relationship
Radar based rainfall estimation for river catchment modelling
10
between ‘counts’ recorded and ground rainfall rate exists. The conversion factor which
converts radar records to rainfall rate can be termed as Calibration Factor (CF).
Table 2-2: Some characteristics of the LAWR-Leuven
Property Value
Location Leuven, Belgium
Operational since July 2008
Frequency X-band (9410±30GHz)
Peak output power 4 kW
Height of tower (Building) 48 m
Antenna type Hybrid array
Antenna diameter 55cm
Horizontal beam opening 3.9°
Vertical beam opening 20°
Rotation speed 24 rpm
Time interval precipitation products 1 min
2.2.2.3 Uncertainty associated with radar estimates
As the weather radar does not measure rainfall rates directly, it is prone to errors from
different sources. Wilson and Brandes (1979) stated three major sources of errors associated
with radar estimates. These are:
� Variations in the relationship between the backscattered energy and rainfall rates.
� Changes in precipitation forms before reaching the ground.
� Anomalous propagation of beams.
Some other researchers describe similar error sources. Delobbe (2007) mentioned mainly
three sources of errors:
� Erroneous Z-R relationship: It is the basic error source that can greatly affects the
final radar estimates. The plot of reflectivity (Z, in dbZ) and rainfall rate (mm/hr) can
be seen in Figure 2-3. It can be seen that the most important differences exist for
higher rainfall intensities and the higher intensities are of importance while dealing
with flood warnings and urban hydrology applications.
Radar based rainfall estimation for river catchment modelling
11
Figure 2-3: Influence of choice of Z-R relationship on rainfall rates (Einfalt et al., 2004)
� Errors related to the height of the measurements: The errors related to the height of
the measurement might be significant while dealing with areas located at larger
ranges. The height of the radar beam increases with the range increases leading to
following erroneous phenomena:
(1) Evaporation
(2) Growth
(3) Partial beam filling
(4) Overshooting
These four phenomena can be seen schematically in the Figure 2-4 and it is obvious
they can greatly affect the final radar performance.
Figure 2-4: Errors related to height of the measurement (Delobbe, 2007)
Radar based rainfall estimation for river catchment modelling
12
� Non-uniform vertical profile of reflectivity (VPR): Even at the lowest scan angle, the
radar beam is well above the surface at longer ranges and it has been found that the
reflectivity from all the elevations is non-uniform. It depends on the type of
precipitation as can be seen in Figure 2-5. Presence of a bright band, which leads the
maximum reflectivity, poses another problem. The bright band is a layer of enhanced
radar reflectivity resulting from the difference in the dielectric factor of ice and water
and the aggregation of ice particles as they descend and melt. Gray and Larsen (2004)
observed the need to correct the VPR effect to enhance final radar estimates.
Figure 2-5: Some typical vertical profile of reflectivity (Delobbe, 2007)
Also, radar estimates are based upon a number of working hypotheses and these hypotheses
have to be at least approximately fulfilled to have some reliable estimates on the rainfall rates
(Einfalt et al., 2004). And, because of the inherent hypotheses in radar data measurements,
there is always uncertainty in the final estimates. As far as possible, these uncertainties need
to be quantified. Continued research and use of new technologies might help to reduce these
uncertainties.
2.2.2.4 Radar-gauge merging techniques
It is evident that the strength of radar estimates, to capture spatial information, is the
weakness of gauge records and that the strength of gauge estimates, the ability to capture
rainfall amount at single location, is the radar’s weakness. Hence, merging of both forms of
rainfall information is necessary to obtain better rainfall information. Merging techniques
combine the individual strengths of the two measurement systems. Merging radar and gauge
observations has been a burning topic of research since weather radar is being used in the
early seventies. Different methods have been proposed by different researchers and
Radar based rainfall estimation for river catchment modelling
13
evaluation of these merging methods has been carried out by different researchers, for
example, Brandes (1975), Wilson and Brandes (1979), Michelson and Koistinen (2000),
Borga (2000), Delobbe et al. (2008) and Goudenhoofdt and Delobbe (2009). Results are more
or less similar. Significant improvements have been observed compared to original radar
estimates. Wilson and Brandes (1979) adjusted radar estimates calculating storm to storm
bias (R/G) and applied it uniformly through out the radar ranges and managed to reduce the
errors up to 30%. They also applied the spatial adjustment (details on Wilson and Brandes,
1979) after utilizing uniform mean field bias correction. Goudenhoofdt and Delobbe (2009)
evaluated a range of merging methods on the data from RMI C-band radar of Wideumont,
Belgium from a simple merging method like mean field bias (MFB) to geospatial merging
methods like kriging, kriging with external drift etc. They concluded that geospatial methods
are better, reducing the mean absolute errors by 40% compared to original radar estimates,
although simple method like MFB reduced the error by 25%. Spatial methods such as
Brandes Spatial Adjustment also performed well reducing the errors as close to the geospatial
methods, which are less tedious and time consuming compared to geospatial methods.
2.3 Hydrological modelling
Hydrological models are simplified, conceptual representations of (a part of) the hydrologic
cycle. They are primarily used for hydrological predictions and for understanding hydrologic
processes. The development and application of hydrological models have evolved greatly
through time. Once the rational method to determine the runoff discharge given rainfall depth
as input is introduced, several concepts to predict and understand the hydrological cycles
have been developed since the 1850’s (Maidment, 1993). The development of the de Saint-
Venant equations for unsteady open channel flow was a boon compounded by the concept of
unit hydrograph to calculate the volume of surface runoff produced by rainfall event. These
inventions led the scope of hydrological modelling to a new height.
Several hydrological models can be found in current time hydrology field as hydrologists try
to develop their new models that suit the local conditions (Berne et al., 2005), which may
operate over different spatial scales and time steps and are developed for various applications.
In literature, the hydrological models are classified in numerous types. It is worth noting that
the classifications based on spatial description (lumped and distributed) and the descriptions
of the physical process (conceptual/empirical and physical) are the most commonly used
Radar based rainfall estimation for river catchment modelling
14
ones. Spatially distributed models have the potential to represent the effect of spatially
variable inputs while lumped models treat the input in an averaged manner (Arnaud et al.,
2002). The compensation is ease of calibration with expense of detailed information because
calibrating a distributed model is not a straightforward task due to the large number of
parameters involved.
Conceptual models have been widely developed and applied for hydrological modelling because
of the ease on calibrating them. They lump, in a broad sense, the highly complex soil processes
and properties in few macro-scale processes and parameters (Willems, 2000). Most of the
conceptual models have similar structure. The rainfall input (xt) is separated into different
fractions that contribute to the different subflows namely the quick flow (xQF), the slow flow (xSF)
and flow contributing for soil storage (xu). The quick flow can be further separated in the rainfall
portions to overland flow and to interflow. The soil storage plays a role determining the actual
evapotranspiration. After certain routing mechanisms, the total runoff y(t) is sum of the three
runoff components: yOF, yIF and ySF (Willems, 2000). A typical structure of a conceptual model is
shown in Figure 2-6. This is general representation of the processes involved in a typical
conceptual model though the detailed process may vary from one model to another.
Figure 2-6: General lumped conceptual rainfall-runoff model structure (Willems, 2000)
2.3.1 The VHM Model
The VHM (Veralgemeend conceptueel Hydrologisch Model) is a Dutch abbreviation for
generalized lumped conceptual and parsimonious model structure-identification and
Radar based rainfall estimation for river catchment modelling
15
calibration. It is an approach with which a lumped conceptual rainfall runoff model can be
calibrated in a step wise way. It is developed by Prof. Patrick Willems, Hydraulics
Laboratory, Katholieke Universiteit Leuven, Belgium. The approach aims to derive
parameter values which are as much as possible unique, physical realistic and accurate. It is
data mining based and aims to derive a parsimonious model structure (Willems, 2000).
2.3.1.1 Model structure
The model structure identification and calibration is carried on four distinct ways as can be
seen in Figure 2-7.
Prior time series processing
Step 1a: Reverse river routing
observed river flow series → rainfall-runoff
Step 1b: Subflow separation
→recession constants
→series of overland flow, interflow and slowflow
Step 1c: Split in quick and slow flow events
→event based runoff volumes
Step-wise model-structure identification and calibration
Step 2: Identification and calibration of routing models
→ event-based rainfall fractions to subflows
Step 3: Identification and calibration of soil moisture storage model
→ closing water balance
Step 4: Identification and calibration rainfall fraction to quick and
slow flow events
Figure 2-7: Steps in the VHM structure identification and calibration procedure
Radar based rainfall estimation for river catchment modelling
16
The step 1 is prior time series processing where a number of prior time series processing
tasks have to be carried out:
� Transformation of the river flow series in a series of lumped rainfall-runoff discharges
(step 1a, Figure 2-7).
� Separation of the rainfall-runoff series in subflow series using a numerical digital
filter. The riverflow series can be either separated into quick flow and the slow flow
(baseflow) or the overland flow, the interflow and the baseflow (step 1b, Figure 2-7).
� Split of the rainfall-runoff series in individual nearly independent peak over threshold
(POT) values. The POTs can be extracted to that of quick flow events and slow flow
events (step 1c, Figure 2-7).
After the prior time series processing, the next step is step-wise model-structure identification and
calibration where lumped representations of different specific rainfall-runoff process equations
are identified and calibrated to related subsets of model parameters. This includes the following
sub-steps:
� Identification and calibration of the routing submodels (step 2, Figure 2-7).
� Identification and calibration of the soil moisture storage submodel where the rain
water fraction fu, the parameter umax (maximum soil moisture content) and uevap (the
threshold moisture content for evapotranspiration is identified (step 3, Figure 2-7).
� Identification and calibration of the submodels describing the rainfall fractions of
quick; fQF (overland and interflow; fOF and fIF) and slow flows; fSF (step 4, Figure 2-
7).
2.3.1.2 Model parameters
The VHM model structure identification and calibration approach deals with the following
parameters related to steps 2 to 4 of the Figure 2-7.
� Recession constant of surface runoff (overland flow): kOF
� Recession constant of interflow: kIF
� Recession constant of baseflow: kBF
� Maximum soil moisture content: umax
� Soil water content at maximum evapotranspiration: uevap
� Surface runoff separation process parameters: aOF,1
� Surface runoff separation process parameters: aOF,2
� Surface runoff separation process parameters: aOF,3
Radar based rainfall estimation for river catchment modelling
17
� Interflow separation process parameters: aIF,1
� Interflow separation process parameters: aIF,2
� Interflow separation process parameters: aIF,3
2.3.1.3 Model calibration
The model parameters are tuned manually as per the information obtained in prior time series
processing. The recession constants of subflows can be adopted as per the values obtained in
step 1b. Optimizing soil storage sub-model parameters can be done by different graphical
plots, for example the plot of fu versus u/umax. The surface and interflow runoff separation
process parameters can be tuned till a good match is observed which can visually be checked
in plots of subflows filter results (overland and interflow) versus model results. This VHM
procedure has clear advantages above an automatic or manual calibration technique, which
most often is based on overall goodness-of-fit statistics optimization. In this approach, when
doing the optimization based on the statistical properties of the model residuals errors for the
different submodels or flow components considered, statistically unbiased sub-model
structures and parameters are derived (Willems, 2000).
2.3.2 The NAM model
NAM is the abbreviation of the Danish "Nedbør-Afstrømnings-Model", meaning
precipitation-runoff-model. This model was originally developed by the Department of
Hydrodynamics and Water Resources at the Technical University of Denmark. The NAM is a
deterministic, lumped and conceptual rainfall-runoff model which simulates the rainfall-
runoff processes occurring at the catchment scale. The NAM is part of the rainfall-runoff
(RR) module of the MIKE 11 River modelling system (DHI, 2004).
2.3.2.1 Model structure
The model structure is shown in Figure 2-8 as adopted from NAM reference manual (DHI,
2004) developed by Danish Hydraulic Institute (DHI). It is an imitation of the land phase of
the hydrological cycle. NAM simulates the rainfall-runoff process by continuously
accounting for the water content in four different and mutually interrelated storages that
represent different physical elements of the catchment. These storages are:
� Snow storage
� Surface storage
� Lower or root zone storage
� Groundwater storage
Radar based rainfall estimation for river catchment modelling
18
Figure 2-8: The NAM structure
In addition NAM allows treatment of man-made interventions in the hydrological cycle such
as irrigation and groundwater pumping. Based on the meteorological input data NAM
produces catchment runoff as well as information about other elements of the land phase of
the hydrological cycle, such as the temporal variation of the evapotranspiration, soil moisture
content, groundwater recharge, and groundwater levels. The resulting catchment runoff is
split conceptually into overland flow, interflow and baseflow components (DHI, 2004).
2.3.2.2 Model parameters
There are quite a number of model parameters according to the different storage elements
listed below. Detailed information on the parameters can be found in the NAM reference
manual (DHI, 2004). The list of the parameters can be divided in following five subgroups:
Radar based rainfall estimation for river catchment modelling
19
a. Surface and root zone parameters
� Maximum water content in surface storage [mm]: Umax
� Maximum water content in root zone storage [mm]: Lmax
� Overland flow runoff coefficient [-]: CQOF
� Time constant for interflow [hr]: CKIF
� Time constant for routing interflow and overland flow [hr]: CK12
� Root zone threshold value for overland flow [-]: TOF
� Root zone threshold value for interflow [-]: TIF
b. Ground water parameters
� Baseflow time constant [hr]: CKBF
� Root zone threshold value for groundwater recharge [-]: TG
c. Extended ground water parameters
� Recharge to lower groundwater storage [-]: CQLOW
� Time constant for routing lower baseflow [hr]: CKlow
� Ratio of groundwater catchment to topographical catchment area [-]: Carea
� Maximum groundwater depth causing baseflow [m]: GWLBF0
� Specific yield [-]: SY
� Groundwater depth for unit capillary flux [m]: GWLFL1
d. Snow module parameters
� Degree-day coefficient [mm/ o
C /day]: Csnow
� Base temperature (snow/rain) [oC]: To
� Radiation coefficient [m2/W/mm/day]: Crad
� Rainfall degree-day coefficient [mm/mm/°C/day]: Crain
e. Irrigation module parameters
� Infiltration factor [mm/day]: K0,inf
� Crop coefficients and irrigation losses
2.3.2.3 Model calibration
The process of model calibration is normally done either manually or by using computer-
based automatic procedures including 9 default parameters enlisted above under the
headings; surface, root zone parameters and ground water parameters (DHI, 2004). While
applying the routine for auto-calibration, the following objectives are usually considered:
� A good agreement between the average simulated and observed catchment runoff (i.e.
a good water balance).
Radar based rainfall estimation for river catchment modelling
20
� A good overall agreement of the shape of the hydrograph.
� A good agreement of the peak flows with respect to timing, rate and volume.
� A good agreement for low flows.
Final tuning is always advised to be done manually which relies on the experience and
knowledge of the modeller, as auto-calibration routines are based on optimizing some
objective function and they are likely to end up in local optimum case rather than global
optimum.
2.4 Significance of spatial variability of rainfall and basin response
The literature on the significance of spatial rainfall for runoff estimation is complex and
sometimes contradictory. Effects can be expected to vary depending on the nature of the
rainfall, the nature of the catchment, the spatial scale of the catchment and the rainfall runoff
model used.
Basin response will obviously vary as rainfall patterns vary. Stratiform and convective
patterns have distinct characteristics on their spatial variability and drop size. In Belgium, the
summer rainfalls are more of convective nature and the winter storms are of stratiform nature.
Many researchers have studied the rainfall-runoff prediction capability of different models
with respect to the type of rainfall. Segond et al. (2007) found a better match between
simulated and observed runoff on winter storm than on summer storms. They concluded that
summer storms have more variability and are less accurate to reproduce flow at the catchment
outlet. Pechlivanidis et al. (2008) reached similar conclusions while testing different rainfall
scenarios on the Upper Lee catchment of UK.
On urbanized catchments, a high proportion of the rainfall becomes effective due to the large
amount of impervious areas. Hence, the effect of spatial rainfall on more urbanised
catchments would obviously be greater. Segond et al. (2007) found that radar estimated
rainfall data are more suitable for stream flow simulation than that from the raingauge
network consisting of one and seven raingauges indicating that the spatial variability of
rainfall is important on urbanised catchments.
Radar based rainfall estimation for river catchment modelling
21
Arnaud et al. (2002) conducted a study on catchments ranging 20 to 1500 km2 and observed
that the relative error in runoff increases with the size of the catchment while Segond et al.
(2007) showed that as the scale increases, the importance of spatial rainfall decreases because
of the fact that there is a transfer from spatial variability of rainfall to catchment response
time distribution as the dominant factor governing runoff generation which can be regarded
as a dampening effect of the spatial variability of rainfall.
The basin response is essentially dependent on the type of rainfall-runoff model used. Fully
distributed physically based models are believed to better represent the basin characteristics
than the lumped one. But it has always to do with the type of rainfall field used. Radar
rainfall fields, capable of generating more spatial variability, are likely to be more suitable for
distributed models. Shah et al. (1996) conducted a study on a relatively small catchment of
10.55 km2
where they compared the results from a physically distributed SHE (Système
Hydrologique Européen) with the results form a linear transfer function model for spatially
distributed rainfall and found a significant error by using the latter model.
2.5 Similar past studies
Numerous similar past studies can be found in literature and the findings are complex and
sometimes contradictory too.
2.5.1 Radar-gauge comparison and merging
It dates back to the 1980’s that there had already been some study on radar-gauge
comparison. Some notable are:
� Wilson and Brandes (1979) performed a rigorous study on radar-gauge comparison in
an area of over 8000 km2 and found that the R/G ratio varied from 0.41 (radar
underestimate) to 2.41 (radar overestimate). They applied a correction on these data
and managed to reduce the average difference (AD) from 63% to 24%.
� Vieux and Vieux (2005) analysed 60 event samples from Cincinnati, USA for the
purpose of using them in sewer system management and found that for those events,
the agreement between radar and gauge was expected within ± 8% based on the
median average difference between gauge and radar. They also applied a Mean Field
Bias (MFB) correction and found that 60% of the bias factors are expected to fall
between 0.94 and 1.70, where they assume the bias (G/R) would follow a normal
distribution which might not always be the case.
Radar based rainfall estimation for river catchment modelling
22
� Delobbe et al. (2008) evaluated several radar-gauge merging techniques in the
Walloon region of Belgium using the dense rain gauge network maintained by the
RMI and the RMI-Wideumont radar. The evaluated techniques ranged from simple
MFB adjustment to sophisticated spatial adjustment. They concluded that even simple
adjustment procedures like MFB already improved the original radar estimates
significantly. Results showed that the geo-statistical merging methods sucha as
merging based on kriging are the most effective ones. Similar findings were observed
by Goudenhoofdt and Delobbe (2009) using the same radar data and catchment.
2.5.2 Stream flow simulation using radar data
Accuracy of radar estimated rainfall data for stream flow simulation has been tested by many
researchers. Some notable ones are:
� Berne et al. (2005) tested the hydrological potential of the RMI-Wideumont radar on
the 1597 km2 Ourthe catchment of Belgium using the gauge calibrated HBV-model.
Mean areal average rainfall estimated from the radar was given as input and resulted
in an underestimation of discharge. They ascribed this underestimation to uncertainty
in the final radar estimates and lumped nature of the model.
� Borga (2002) used a conceptual rainfall runoff model to a catchment of 135.3 km2, the
Brue basin in South-West England. He found that model hydrograph predictions
driven by adjusted radar data had similar efficiency (NSE) than the ones obtained
from gauged based rainfall. He got NSE of 0.75 from the former case and 0.83 from
the latter one, meaning a slight underperformance while using the radar estimates.
� Segond et al. (2007) performed an elaborate research on assessing spatial information
requirements of rainfall on the 1400 km2 Lee catchment, UK and found that the gauge
calibrated semi-distributed model called ROBB (details in Laurenson and Mein,
1988) can produce a better match between observed and simulated discharge while
using radar estimated rainfall and they attributed this improvement to the spatial
coverage of rainfall information by the radar.
Radar based rainfall estimation for river catchment modelling
23
CHAPTER 3: APPLICATION
3.1 Methodology
The methodology mainly consists of two steps. First, the raw radar data of both the LAWR-
Leuven and the RMI-Wideumont are compared with rain gauge data defined by a rain gauge
network of 12 rain gauges as shown in Figure 3-2. Different merging techniques are tested to
increase the accuracy of the final radar estimates. Secondly, the corrected radar data will be
used for modelling of a catchment using two types of lumped conceptual models, namely the
NAM and the VHM. Significance of spatial representation of rainfall is also evaluated
through the basin response.
3.2 Study area
The study area is situated in the Flanders region of Belgium, near the densely populated city
of Leuven. The study area is within 15 km radius of the LAWR-Leuven. The rain gauge
network comprises of 12 rain gauges, most of them towards the north-west direction with
respect to the LAWR-Leuven and within 10 km from the LAWR-Leuven. The entire rain
gauge network lies in between 117 and 128 km from the RMI-Wideumont, in north-west
direction. The catchment is situated south/south-east of the LAWR-Leuven and north/north-
west of the RMI radar of Wideumont as can be seen in Figure 3.1. Two of the twelve
raingauges are located in the catchment. More descriptions on the raingauge network can be
found under the section of 3.3.1. For the catchment, the description is presented under the
section 3.4.1. The study area with the radar location, the catchment and the raingauge
network can be seen in Figure 3.2.
Radar based rainfall estimation for river catchment modelling
24
Figure 3-1: Belgium (light green), the RMI-Wideumont radar (black star), the LAWR-Leuven (red
star) and the catchment (dark green). Black arcs indicate the distance to the RMI-Wideumont, with
an increment of 60 km. The red circle shows 15 distance to the LAWR-Leuven
Figure 3-2: The study area with the location of 12 gauges (red dots: Aquafin &VMM; black
triangles: RMI), the LAWR (yellow star), catchment (dark green polygon) and part of the Walloon
region (light green polygon). Circles indicate the distance to the LAWR, with increment of 5 km
Radar based rainfall estimation for river catchment modelling
25
3.3 Radar-gauge comparison and merging
3.3.1 The raingauge network
Comparing radar estimated rainfall essentially requires ground “truth” data which is assumed
to be correctly represented by the raingauge network. For our purpose, the network of 12
raingauges is used; 4 of them being operated by Aquafin, 5 by the Flemish Environmental
Agency (VMM) and the other 3 by the RMI of Belgium. The Aquafin raingauges are TBRs
having a gauge resolution of 0.2 mm and a time resolution of 2 minutes. The VMM
raingauges are also TBRs having a gauge resolution of 0.2 mm and a time resolution of 10
minutes. The RMI maintains quite a dense network of non-recording raingauges giving daily
precipitation accumulations between 8 AM and 8 AM Local Time (LT). The network with
the position of the LAWR-Leuven as well as the watershed is shown in Figure 3-2.
3.3.2 Correcting raingauge measurements
As already stated, raingauge data will be used as reference and will be considered as ground
truth data. Goormans and Willems (2008) conducted full dynamic calibration on these
Aquafin and VMM raingauges for the purpose of calibrating the LAWR. Local wind shelter
influences on these TBRs were also investigated and it was found that both sets of TBRs
clearly underestimated rainfall compared to the standard non-recording RMI gauge of Herent.
Long term underestimations up to 24% (corresponding to correction factor of 1.321) were
found. To correct this systematic underestimation, the study proposed a correction factor ‘k’
based on the minimization of the sum of squared differences between cumulative daily RMI
and TBR rainfall series, as presented in Table 3-1.
Table 3-1: Correction Factors [k] for the Aquafin and VMM raingauges
Operator RG Location Correction Factor, k [-]
Aquafin
RWZI Kessel-Lo 1.321
Keulenstraat 1.121
Hoge Beekstraat 1.157
Warotstraat 1.158
VMM
Derijcklaan 1.157
Oudstrijderslaan 1.158
Eenmeilaan 1.143
Brouwersstraat 1.252
Weggevoerdenstraat 1.237
Radar based rainfall estimation for river catchment modelling
26
3.3.3 Conversion of radar records to rainfall rates
As already depicted, the C-Band radar measures reflectivity (Z) values, as representative for
rain droplets in a certain volume. This Z-value is converted to rainfall rate, R with a Z-R
relationship of the form: Z = aRb. The RMI-Wideumont radar uses values of a and b equal to
200 and 1.6 respectively. The radar is fitted with a linear receiver.
Unlike the C-Band radar, the X-band LAWR-Leuven has a logarithmic receiver and records
the number of counts (a dimensionless measure for the amount of reflected power) as
representative value of rainfall. A relationship between the count and the rainfall rate
recorded at ground level has to be established for conversion. The conversion factor can be
termed as Calibration Factor (CF). As the LAWR is relatively new giving records from July 2
2008 and onwards, and research is ongoing to have optimal CF values, the presented CF
factors in Table 3-2 can be considered as the best estimates currently available. These
calibration factors are the result of a regression analysis, based on the storm average
intensities and measured counts in the corresponding radar pixels of the period 2nd
July- 8th
October 2008 (Block-1, Table 3-4), which can be considered as a summer period. The
intensities are from calibrated raingauge data, and also corrected for the systematic bias due
to local wind effects, the ‘k’ factors as presented in Table 3-1.
Table 3-2: Calibration Factor [CF] for Aquafin and VMM raingauges
Operator RG Location Calibration Factor,
CF [(mm/hr)/(counts/min)]
Aquafin
RWZI Kessel-Lo 0.0600
Keulenstraat 0.1131
Hoge Beekstraat 0.0934
VMM
Derijcklaan 0.0421
Oudstrijderslaan 0.0615
Eenmeilaan 0.0531
Weggevoerdenstraat 0.1601
Average 0.0833
Radar based rainfall estimation for river catchment modelling
27
3.3.4 Data periods
Owing to the rainfall pattern in Belgium, the comparison study is distinguished into two
periods namely summer storm and winter storm periods. Convective rainfall is encountered
in most of the summer storm cases and stratiform rainfall in both summer and winter periods.
For the data of RMI-Wideumont, a collaboration is reached between the RMI and the
Hydraulics Division of the Katholieke Universiteit Leuven and data of some interesting storm
periods are made available. These periods are named week 1 to week 4 as presented in Table
3-3, weeks 1 and 2 being that of a summer period and weeks 3 and 4 that of a winter period.
The data is hourly accumulation rainfall (mm), the binary file 600x600 with data coded in
single precision float. Matlab algorithms are developed to read, filter and extract the data.
Table 3-3: Data periods of the RMI radar of Wideumont
Week Data Periods
1 July 2, 2008 to July 12, 2008
2 August 3, 2008 to August 13, 2008
3 January 17, 2009 to January 23, 2009
4 February 9, 2009 to February 17, 2009
The data extracted from the LAWR-Leuven are counts with time resolution of one minute in
240x240 grids each measuring 125 m by 125 m. The data can be divided on the three periods
as per the setting of signal processing parameter of the LAWR as presented in Table 3-4. For
block 3, the parameters of signal processing were set to neutral; hence these periods are not
taken into consideration. For the LAWR-gauge comparison, the summer period considered
spans from July 2 2008 to September 30 2008, and the winter period from December 1 2008
to March 31 2009. As the CF values presented on Table 3-2 are the result of analysis made on
block 1 (summer period), the work is sought to see performance of these CFs on block 2
(winter period).
Table 3-4: Data periods of the LAWR of Leuven
Block Data Periods
1 July 2, 2008 to October 8 , 2008
2 October 9 to October 31, 2008 & December 1, 2008 to till now
3 November 1, 2008 to November 30, 2008 (parameters are set to neutral)
Radar based rainfall estimation for river catchment modelling
28
3.3.5 LAWR - gauge comparison and merging
The first attempt is to use a constant CF value for all radar pixels. This procedure does not
account for the range dependency of the CF values. The results will be compared with the
case where range dependent CF-values are applied. The range dependent adjustment on CF
values is essential to some extent because of ever increasing height of measurement, beam
broadening and attenuation effect. Goudenhoofdt and Delobbe (2009) accounted for a range
dependency of the RMI-Wideumont using a second order polynomial with R/G expressed in
log scale. The same adjustment procedure will be the first trial with R/G (CF) expressed in
linear scale followed by power function as well.
After applying the range dependent CF values (to obtain rainfall rate values), the Mean Field
Bias (MFB) adjustment is applied. In MFB adjustment, it is assumed that the radar estimates
are affected by a uniform multiplicative factor. The factor is determined by gauge-radar
agreement after integration over a space-time window. Although it is a simple adjustment
technique; it can already enhance the quality of rainfall estimate significantly. Goudenhoofdt
and Delobbe (2009) found that the MFB correction reduced the error by 25% compared to
raw radar data. Similar improvements have been observed by Borga (2002). The MFB is
given by:
MFB = ∑∑
=i
ii
R
G
NN
F 1 (5)
With,
N= Number of valid radar-gauge pairs.
Gi, Ri = gauge and radar daily accumulated values associated with gauge i.
The concept of implementing MFB adjustment on the daily accumulated basis rather than
real-time fashion is to avoid additional uncertainty due to time and space mismatching of the
radar and gauge samples at shorter time intervals.
If both daily raingauge accumulation and radar accumulations are greater than 1 mm then
these were considered as “valid pairs”. This ensures that the same data set is used for
comparison. Different authors have used different threshold values for their study.
Goudenhoofdt and Delobbe (2009) used a threshold value of 1 mm; the same threshold value
was taken by Delobbe et al. (2008) on daily time scale basis. A threshold value of 0.5 mm
Radar based rainfall estimation for river catchment modelling
29
was used by Borga (2002). Germann et al. (2006) used 0.3 mm for the evaluation of radar
precipitation estimates in Swiss mountains. Wilson and Brandes (1979) stated, citing their
previous experiences, that if the gauge rainfall is light (<2 mm), it is best not used in an
adjustment procedure. By this, they advised using a threshold value no less than 2 mm on
daily accumulation. For all purposes, the average counts over 9 radar pixels surrounding the
gauge location is used so as to limit the effect of wind drift which can be very significant
(Lack and Fox, 2007). The number of valid pairs influences the index of statistical
parameters. A low threshold value would result in a significant amplification of some of the
statistical parameters, such as the MFB. For example, for gauge and radar pairs of 2 mm and
0.2 mm respectively, MFB will be 10 and this distorts the mean MFB. Applying a threshold
value will exclude such pairs and will counter the problem to some extent.
Also, arithmetic averaging of individual bias to get the MFB value, as suggested by (5),
requires these individual values to follow a normal distribution which is rather unlikely. After
all, the bias is the ratio of the gauge to radar estimates and can be considered as a product of
two stochastic variables, and this always tends to follow a lognormal distribution. Hence, the
distribution of the bias is checked by fitting theoretical distributions (normal, log-normal,
exponential etc.) over the empirical (observed) distribution. The empirical distribution can be
calculated by using one of the most used formulas, the distribution of Hazen (1930), and is
given by:
Probability of exceedance =n
r )5.0( − (6)
Cumulative probability = 1 - (Probability of exceedance) = n
rn )5.0( +− (7)
With,
r = rank number of current value in the data set.
n = total number of values in the data set.
In case the individual bias follows a lognormal distribution, equation (5) can be modified as:
MFB =
∑
∑
= i
ii
R
G
NN
F
eelog
1)log(
(8)
With,
N= Number of valid radar-gauge pairs.
Gi, Ri = gauge and radar daily accumulated values associated with gauge i.
Radar based rainfall estimation for river catchment modelling
30
It should be noted that the MFB adjustment is applied uniformly over the entire radar range
using a single factor. The MFB attempts to minimize the bias between the gauge and radar
estimates uniformly. The smoothed radar field is then subjected to an additional adjustment,
the Brandes spatial adjustment, hereafter referred to as BRA. The main idea is to use the
correction factors from rain gauge sites to each radar grid (Brandes, 1975). The rain gauges
which are closer to a grid point take higher weight and those lying further take lower weights.
The weight (wi) applied to each gauge calibrated bias (Gi/Ri) for a particular grid point is
given by:
−=
k
dwi
2
exp (9)
With,
d = distance between the gauge and the grid point in km.
k = a factor controlling the degree of smoothening and is generally given as an inverse of
mean gauge density (number of gauges divided by total area), denoted by ‘δ’. This is
calculated using a formula used by Goudenhoofdt and Delobbe (2009), and is given by:
k = (2 δ)-1
(10)
For a network consisting of ‘N’ raingauges, the Brandes spatial adjustment then can be given
by:
∑
∑
=
==N
i
i
N
i
iii
BRA
w
RGw
C
1
1
)/(
(11)
With,
CBRA = Brandes spatial adjustment factor.
In order to evaluate the improvements achieved by each adjustment procedures, comparison
on some goodness-of-fit statistics is made before and after adjustment. Several of these
parameters are found in literature. However, the Root Mean Square Error, Mean Absolute
Error, Relative Fractional Bias and Nash Criterion are used in this study.
The Root Mean Square Error (RMSE) is one of the most common parameter for verification
studies and is given by:
Radar based rainfall estimation for river catchment modelling
31
N
GR
RMSE
N
i
ii∑=
−
= 1
2)(
(12)
With,
Ri, Gi = radar and gauge valid pair values.
N = number of valid pairs.
The Mean Absolute Error (MAE) is another parameter used for goodness of fit statistics and
is given by:
N
GR
MAE
N
i
ii∑=
−
= 1
)(
(13)
With,
Ri, Gi = radar and gauge valid pair values.
N = number of valid pairs.
Similarly, the Relative Fractional Bias (RFB) accounts for the bias of radar estimated to
gauge value in a relative manner. It is similar to the term Average Difference (AD) used by
some researchers (e.g. Vieux and Vieux, (2005), Wilson and Brandes (1979) etc.) where they
used absolute values and expressed them in percentage. It is given by:
i
ii
G
GRRFB
−= (14)
With,
Ri, Gi = radar and gauge valid pair values.
However the RFB is sensitive to small values. For example, if the radar estimate for a gauge
value of 0.5 mm is 1.0 mm, then the RFB will be 100% though the absolute difference on the
pair is only 0.5 mm. Hence, the RFB is calculated with cumulative rainfall volumes.
The Nash Criterion evaluated through the Nash-Sutcliff Efficiency (NSE), is usually used to
assess the predictive power of hydrological models (Nash et al., 1970), but adapted for this
case as;
Radar based rainfall estimation for river catchment modelling
32
∑
∑
−
−
=
−
−
−=n
i
i
n
i
ii
GG
RG
E
1
2
1
2
)(
)(
1 (15)
With,
E = Nash Criterion value.
Gi, Ri = instantaneous gauge and radar values.
The rainfall events can be assumed fairly independent to each-other and hence the Nash
Criterion can be used to evaluate how well radar estimates match with gauge values.
3.3.6 RMI Wideumont estimates and gauge comparison and merging
Regarding the data of the RMI-Wideumont, rainfall volumes can be directly extracted. A
threshold value of 1 mm is taken for this case as well. Similar goodness-of-fit statistics
(Equations 12 to 15) are used to evaluate the accuracy of the radar data. The raw radar
estimates are smoothed by firstly applying the MFB and then the BRA adjustment. While
doing so, weeks 1 and 2 have been merged in to one period, as they are both summer periods,
and same for the weeks 3 and 4, both being winter periods.
3.4 Hydrological modelling
3.4.1 The catchment
3.4.1.1 Choice of catchment
Several criteria influence the selection of a suitable watershed for radar hydrology research.
The most obvious requirements are complete areal coverage of the catchment by the radar,
and the availability of stream gauge data. For this case, the choice of the catchment is limited
by the fact that the LAWR of Leuven is capable of giving quantitative estimates up to a
radius of 15 km only. Another fact associated with LAWR is that the Zaventem airport
authorities do not allow transmission in the sector indicated by the light blue sector in Figure
3-3. Due to these constraints the catchment named Molenbeek/Parkbeek, having area of
48.17 km2, has been selected. This choice is also favoured by the absence of heavy clutters as
can be seen from the study of Goormans et al. (2008). The catchment contains two rain
gauges; one is operated by the RMI (Korbeek-Lo) and the other by the VMM (Derijcklaan).
The selected catchment falls within 240 km range of RMI radar of Wideumont. The
catchment, along with raingauges, the LAWR and water courses, is shown in Figure 3-4.
Radar based rainfall estimation for river catchment modelling
33
Figure 3-3: Catchment under consideration with position of LAWR (star), radar beam blockage
sector (blue shade), rain gauges (dots-the VMM and Aquafin TBRs; triangles-the RMI non-
recording gauges), water courses (blue lines) and circles - distances of 5, 10 and 15 km from the
LAWR
3.4.1.2 Catchment geomorphology
The catchment has a temperate climate, is relatively flat, primarily composed of sandy soils
with high hydraulic conductivity, and hence intensively drained. The Digital Elevation Model
(DEM) of the catchment is shown in Figure 3-4. The elevation ranges from 22 m to 117 m
above mean sea level, with a mean elevation of 59.19 m. Almost 90% of the area has an
elevation less than 78 m. The land use of the catchment is dominated by agricultural land.
Around 53% of the area is used for agricultural activities, 33% of the area has a mixed type
of forest, 13% of the area is urbanised and less than 1% consists of water bodies. Primarily,
the soil types of the catchment can be classified into three groups, namely sand, land-dune
and clay. The sandy soil is the dominant one as it covers almost 70% of the area. Around
28% of the area is covered by land-dune and the remaining 2% by clay.
Radar based rainfall estimation for river catchment modelling
34
The catchment experiences around 800 mm of yearly precipitation, which is evenly
distributed throughout the winter and summer months. The average daily temperature ranges
from 4 degrees centigrade in winter to 22 degrees centigrade in summer. These data are based
on the data available on the HydroNet (2009) website (www.hydronet.be).
Figure 3-4: The DEM map of catchment with stream network
3.4.1.3 Input meteorological series
Both the VHM and the NAM require rainfall, temperature, potential evapotranspiration and
observed discharge series as input. The rainfall series are obtained through the raingauge
network of the VMM and RMI as one VMM rain gauges. Their weight is calculated using the
Thiessen Polygon method. As the VMM rain gauge’s time resolution is 10 minutes, the data
are aggregated to the hourly aggregation level and corrected with the ‘k’ factor as presented
in Table 3-1. The RMI rain gauge produces only daily rainfall series from 8 AM to 8 AM
local time hence this series is converted to hourly series using its nearest neighbouring station
applying a correction factor for daily accumulated rainfall volume. In doing so, the VMM
rain gauge Derijcklaan is taken as the neighbouring station and its temporal variation is
considered and corrected by a factor. The factor is obtained by dividing the daily
accumulated rainfall volume of the Korbeek-Lo to the Derijcklaan.
Radar based rainfall estimation for river catchment modelling
35
The daily maximum and minimum temperature series are obtained from HydroNet website
(www.hydronet.be) for station with station number HIS_M08_045, Heverlee/Molenbeek
having X and Y coordinates of 173868 m and 172838 m respectively. The potential
evapotranspiration (ETo) is calculated using the Penman Monteith method. This method
allows calculating ETo even if only maximum and minimum temperature data are available
(Allen et al. 1998). The hourly observed discharge series are also obtained from the
HydroNet website.
3.4.2 Catchment modelling with VHM
The VHM model parameter set for this catchment has already been derived by Prof. P.
Willems of the Hydraulics Laboratory, Katholieke Universiteit Leuven, Belgium. The same
set of parameters with minor adjustments is tested for the studied period of September 2003
to December 2009. The simulated values for the first three months are discarded in order to
eliminate the influence of erroneous initial conditions.
Prior time series processing tasks have been carried out except the step-1a (Figure 2-7) as no
detailed river hydrodynamic model for this catchment is available. Hence, the observed
discharge series is used as the rainfall-runoff series, though this assumption will lead to some
discrepancies. After all, the flow observed at the river flow gauging station is the cumulated
result of the runoff entering the river network upstream of the flow gauging station, which is
further affected by flow attenuation along the river network. By the spatial variability in the
runoff and the river network hydrodynamics, the flow observed at the river gauging station
will probably differ from the rainfall-runoff spatially averaged over the river network
upstream of the gauging station. This effect is often neglected in current rainfall-runoff
modelling. Hence, reverse routing (derivation of rainfall-runoff serries from observed
discharge) should be done (Willems, 2000). But this requires detailed hydrodynamic
modelling. It has been seen in some studies that the flow attenuation could be neglected in
low flows but above the bank-full stage, river flooding strongly affects the runoff series, for
example in the study of the Molenbeek brook subcatchment in the Dender basin in Belgium
(Willems, 2000).
The other two steps (step-1b and step-1c; Figure 2-7) of the prior time series processing tasks
are performed in Water Engineering Time Series Processing Tool (WETSPRO). The
WETSPRO software is developed by Prof. P. Willems of the Hydraulics Laboratory,
Radar based rainfall estimation for river catchment modelling
36
Katholieke Universiteit Leuven, Belgium. It is a time series processing tool that allows the
users to conduct:
� Sub-flow filtering.
� Peak flow selection and related hydrograph separation; for quick flow and slow flow
periods and related low flow selection.
� Construction of the different model evaluation plots.
The tool makes use of a continuous time series of any hydrological variable as input
(Willems, 2009) and if model performance evaluation is to be carried out, the model results
also form a part of input.
3.4.3 Catchment modelling with NAM
The calibration period is selected from January 1 2006 to February 28 2009. Validation of the
calibrated parameter is made in another independent period from September 10 2003 to
December 31 2005. Calibration is done using both manual and auto-calibration option
available in the NAM software because both the manual and auto-calibration have their own
advantages and disadvantages. Given the advantages and disadvantages of both procedures,
combined use of the two would be most beneficial (Willems, 2009). Good estimation of
routing constant values for sub-flows is made using the WETSPRO tool. Initial conditions are
set according to the guidelines in the reference manual of the NAM software. The simulated
values for the first three months are discarded in order to eliminate the influence of erroneous
initial conditions.
3.4.4 Performance evaluation of the model results
The performance evaluation of the model results is accessed using both the basic goodness-
of-fit statistics supported by graphical tools following the procedure described by Willems
(2009). The use of both goodness-of-fit statistics and graphical goodness-of-fit plots is due to
the fact that these goodness-of-fit statics summarise the performance evaluation information
only in few numbers and values which are difficult and misleading to interpret. The basic
goodness-of-fit statistics used for model performance evaluation are Mean squared error
(MSE) and Nash Sutcliffe efficeinecy (Nash and Sutcliffe., 1970) and are given as:
[ ]
n
iQiQ
MSE
n
i
om∑=
−
= 1
2)()(
(16)
Radar based rainfall estimation for river catchment modelling
37
[ ]
[ ]
−=
−
−
−=
∑
∑
=
=
2
1
2
1
2
1
)(
)()(
1
oQ
n
i
oo
n
i
om
S
MSE
QiQ
iQiQ
NSE (17)
with,
)(iQo and )(iQm = the observed and modelled river discharge, respectively.
i = the number of observations (1, n) and,
oQ and 2
oQS = the mean and variance of observed discharge series.
The performance evaluation is performed by using a number of sequential time series
processing tasks in the WETSPRO tool. Sub-flows separation, splitting the river flow series
in nearly independent quick and slow flow hydrograph periods, and the extraction of (nearly)
independent peak and low flows are performed to have a more unbiased model performance
evaluation overcoming the problem of serial dependence, which is mostly overlooked in
current rainfall-runoff calibration applications (Willems, 2009). Also, the model residuals
(difference between flow observation and model result) typically increases with higher flows
meaning that model residual variance typically increases with increasing flow, a phenomenon
called heteroscedasticity. This heteroscedasticity has to be addressed by applying any suitable
transformation. The Box-Cox (BC) transformation (Box and Cox, 1964) is very flexible since
it only one parameter. Therefore, it is used in this study. The transformation is given by:
λ
λ 1)(
−=
qqBC (18)
With,
q = the variable taken into consideration (flow series in this case)
λ = parameter of BC-transformation that needs to be calibrated to have homoscedasticity the
model residuals.
The following graphical plots are used to complement the above mentioned goodness-of-fit
statistics (Equations (16) and (17)):
� Scatter-plot for peak flow maxima.
� Scatter-plot for low flow minima.
� Comparison of cumulative volumes
� Extreme value distribution of peak flow maxima
� Extreme value distribution of low flow minima
Radar based rainfall estimation for river catchment modelling
38
3.4.5 The significance of spatial data
3.4.5.1 Quantifying rainfall variability
In this study, the rainfall derived from the rain gauge network was perceived as more robust
and hence considered as reference rainfall (Pref) to be used as input for the calibration
process. Using Thiessen-polygon method, it was found that 75.94 % of weight can be given
to the rainfall station named Korbeek-Lo and the remaining 24.06% to the rainfall station
named Derijcklaan. With these weights, a weighted average rainfall is calculated. The
following alternative rainfall inputs are tested to quantify the rainfall variability.
� Single rain gauge for the entire catchment and hence uniform rainfall over the
catchment (RG1). For this, the RMI raingauge named Korbeek-Lo is used as it is
almost in the centroid of the catchment.
� Rainfall data derived from the X-band LAWR of Leuven. Accumulated rainfall depth
over one hour is used for this purpose. Altogether 3085 LAWR pixels covered the
catchment and their weight is calculated using the Thiessen-polygon method and the
total weighted average rainfall is used.
� Rainfall data derived from the RMI-Wideumont radar. It was found that 136 RMI-
Wideumont pixels covered the whole catchment. Their weight is calculated using the
Thiessen-polygon method and the total weighted average rainfall is used.
To see the distinct effect of the significance of rainfall spatial variability, 4 storms were
selected in accordance to the available data and the total rainfall volume over the storm
periods as shown in Table 3-5.
Table 3-5: Selected storm events; LT means Local Time
Storm
Events
Start [LT] End [LT] Duration Pref
[mm/dd/yy HH:MM] [mm/dd/yy HH:MM] [h] [mm]
3-Aug-08 8/3/08 19:00 8/4/08 2:00 8 30.7
5-Dec-08 12/5/08 14:00 12/5/08 20:00 7 7.80
22-Jan-09 1/22/09 12:00 1/23/09 19:00 32 30.4
9-Feb-09 2/9/09 16:00 2/10/09 23:00 32 27.2
The Reference Spatial Deviation Index (SDIR) can now be defined for each storm. The SDIR
is an index that compares the rainfall spatial deviation between the areal estimates from the
Radar based rainfall estimation for river catchment modelling
39
tested rainfall representation to the reference areal precipitation estimates (Segond et al.,
2007) and is given by:
r
ri
P
PPSDIR
−= (19)
With,
Pi = areal precipitation from either radar or subset of the gauges in mm.
Pr = reference areal precipitation in mm.
The use of only one rain gauge located at the centroid of the catchment can be regarded as a
degradation of the spatial representation of rainfall and hence a higher SDIR value is
expected. Radar estimated rainfall improves the spatial representation and a lower SDIR is
expected, compared to the one-gauge situation. However, by definition, the SDIR evaluates
the deviation from Pref and Pref for this study case is defined by only 2 raingauges. So, Pref
itself might not represent actual areal average rainfall adequately, although it is assumed that
it is the most robust estimate of areal rainfall available. Hence, a range of SDIR values can be
expected for the radar estimated rainfall values too, especially when considering the various
errors in radar rainfall measurements. The LAWR-Leuven radar should cover better spatial
coverage as it has a finer resolution than RMI-Wideumont radar. Hence, it is expected that
the LAWR-Leuven should give lower SDIR compared to the RMI-Wideumont.
3.4.5.2 Basin response
After quantifying the rainfall variability for different storms, their basin response is analysed.
The basin response for all the above stated rainfall input is analysed using the same model
parameter sets derived from the calibration using Pref. The NSE value (defined as in Equation
(17)), denoted by NSEobs, can be calculated with reference to the observed discharge series to
see the simulating capability of different rainfall descriptors. It is expected that NSE will
degrade for RG1, and improve for the radar estimated rainfall.
The simulated flow driven by the reference rainfall (Pref) is referred to as the reference flow.
The difference between the reference flow and flow driven by an alternative rainfall
descriptor is the relative error induced due to the tested alternative rainfall keeping model
parameter uncertainty the same. A modified definition of NSE is introduced at this stage to
Radar based rainfall estimation for river catchment modelling
40
measure the performance of the simulated runoff in comparison to reference flow as used by
(Segond et al., 2007) and is given as:
∑
∑
=
=
−
−
−=N
i
i
N
i
ii
ref
RR
RC
NSE
1
2
1
2
)(
)(
1 (20)
With,
Ci, Ri = calculated and reference discharge at ith
hour
R = mean value of reference discharge
N= number of data set.
Both the NSEobs and NSEref will be defined for the NAM as well as the VHM. These
indicators will lead us to conclude and understand the importance of spatial variability of
rainfall data. The latter indicator enhances the opportunity of testing the rainfall descriptors
making the parameter uncertainty the same for each model.
Radar based rainfall estimation for river catchment modelling
41
CHAPTER 4: RESULTS AND DISCUSSION
4.1 LAWR estimates − gauge comparison and merging
4.1.1 Using an average value of CF
Using an average value of CF shows a significant fluctuation on the radar and gauge values
for cumulative rainfall volumes for summer periods. The RFB ranges form +1.25 (125%
overestimation) to -0.57 (57% underestimation) as can be depicted from Figure 4-1. A
similar trend can be observed for winter periods (+0.78 to -0.40). As can be seen, the RFB
for the RMI gauges (indicated by circles) − which were not used to derive the CF values −
are systematically under the zero RFB line (dotted horizontal line), meaning a systematic
underestimation by the LAWR which increases as the range increases. A similar trend can
also be observed for other rain gauge stations as well.
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0.0 2.5 5.0 7.5 10.0
RF
B [
-]
Range, r from LAWR [km]
SUMMER [Aquafin+VMM] WINTER [Aquafin+VMM]
SUMMER [KMI] WINTER [KMI]
Figure 4-1: Evolution of RFB with range (using constant CF on the LAWR estimates)
It is therefore easy to understand that there exists some kind of range dependency on CF
values and hence on the radar estimated rainfall values. So, a single averaged value of CF is
not sufficient to convert the “counts” to rainfall estimates. It is clear that the radar tends to
overestimate rainfall in those pixels which are closely located to the LAWR and to
underestimate rainfall in those pixels which are further away.
Radar based rainfall estimation for river catchment modelling
42
4.1.2 Range dependent adjustment on CF
A second degree polynomial fit (CF = 0.0006 r2 + 0.015r + 0.0159, R
² = 0.6891; r = range
from the LAWR in km) for the CF strongly increses with range, especially for higher ranges,
as depicted by Figure 4-2. This results in a serious overestimation of the radar estimates for
far-away pixels. For example, the RFB was +0.36 (36% overestimation) for the RMI rain
gauge located at Leefdaal (range: 9.5 km) for summer storms. But this fit showed quite a
good match for nearby pixels, with a RFB of 0.0034 (0.34%) on the RMI rain gauge station at
Korbeek-Lo. This shows that using only a second degree polynomial fit for the CF is not
appropriate for the range dependent adjustment on CF.
Hence, a power function [CF = 0.0272 r 0.8226
, R² = 0.8038] is applied which produces quite
good results reducing overall RFB to nearly 6%. The choice of the power function is well
supported by higher R2
value as well. The problem associated with using the power function
for range dependent adjustment is that when range is equal to 0 (at the pixels very close to the
LAWR), the CF will be zero which is unrealistic. But from Figure 4-2, it is clear that for
lower ranges, the second degree polynomial function and the power function are matching
very well. Therefore, the second degree polynomial function is used for ranges less than 1.5
km. Hence, a combination of both functions is used for the range dependent adjustment on
CF.
y = 0.0006x2 + 0.015x + 0.0159R² = 0.6891
y = 0.0272x0.8226
R² = 0.8038
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1 3 5 7 9 11 13 15
CF
[(m
m/ h
r) /
(co
un
ts /
min
)]
Distance from Radar , r [km]
Figure 4-2: Plot of CF as a function of distance to the LAWR, each point representing a TBR
(Aquafin &VMM)
Radar based rainfall estimation for river catchment modelling
43
The advantage of a range dependent adjustment on the radar estimates is clear. Prior to this
adjustment, the RFB showed a quite significant variation: overestimation for nearby pixels
and underestimation for far-away ones. After applying the range dependent adjustment on
CF, the fluctuation is limited as can be seen from Figure 4-3. The total RFB for the summer
periods was decreased to -0.06 (-6 %) and mean RFB for the winter storms was about +0.07
(+7%). The interesting thing to be noted is that the RFB shows no trend of either
overestimation or underestimation as the range increases.
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0.0 2.5 5.0 7.5 10.0
RF
B [
-]
Range, r from LAWR [km]
SUMMER [Aquafin+VMM] WINTER [Aquafin+VMM]
SUMMER [KMI] WINTER[KMI]
Figure 4-3: Evolution of RFB with range (using range dependent CF on the LAWR-Leuven
estimates)
4.1.3 Statistical analysis on range dependent adjustment
Some goodness-of-fit statistics are presented in Table 4-1 which validates the idea of using
range dependent adjustment on the CF. Altogether 187 valid pairs for the summer period and
240 pairs for the winter period were analyzed for the constant CF case. And, for the range
adjusted CF case, 197 and 254 valid pairs were analysed respectively for the summer and
winter period.
Using constant CF, the resulted radar estimates are not in accordance to the ground “truth” as
indicated by the low NSE value of 0.47 for the summer period. The case is even below par
Radar based rainfall estimation for river catchment modelling
44
for the winter period where the Nash Criterion is negative. After the range dependent
adjustment on CF, the statistics improved significantly. The Nash Criterion increases to 0.67
for the summer period. For the winter period, the Nash Criterion increases to 0.42, which is
of course positive compared with the constant CF case but still not promising.
Table 4-1: Some statistical parameter values before and after range dependent adjustment on the
LAWR estimates.
Statistical SUMMER WINTER
Indicators constant CF range adjusted CF constant CF range adjusted CF
Valid Pairs [-] 187 197 240 254
RMSE [mm] 4.12 3.21 5.99 3.86
MAE [mm] 2.76 2.14 3.55 2.63
Nash Criterion [-] 0.47 0.67 -0.53 0.42
Improvement on RMSE and MAE values also favours the adjustment. The RMSE for the
summer period improves from 4.12 mm to 3.21 mm and for the winter period from 5.99 mm
to 3.86 mm. For MAE, a similar trend can be observed.
All the statistics show that the LAWR has low performance in the winter period. This low
performance may be due to precipitation forms, for example snow. For snow-fall, the rain
gauge shows the record after it melts but the radar has already detected it. Hence, there exists
significant time lag for these two records. But it is also to be noted that making use of valid
pairs will solve this problem, at least partially. The low performance could also be explained
because of non-uniform vertical profiles of reflectivity (VPR). For the stratiform storms,
presence of a bright band will lead to higher reflectivity and hence a non-uniform VPR
subsequently, resulting in erroneous precipitation estimates.
Figure 4-4 presents a scatter plot of radar and gauge readings (both TBRs & RMI) for the
summer periods before and after the range dependent adjustment on CF. It can be seen that
the scatter is minimized after the correction, as indicated by the change in slope of the linear
regression lines for each case. The slope improves to from 0.85 to 0.90 after applying the
range dependent adjustment on CF.
Radar based rainfall estimation for river catchment modelling
45
y = 0.85x
y = 0.90x
0
10
20
30
40
50
60
0 10 20 30 40 50 60
LA
WR
[mm
]
Gauge [mm]
Using constant CF
Using range dependency corrected CF
1:1 Line
Figure 4-4: Scatter plot of daily accumulated radar-gauge valid pairs for summer storm using
constant value of CF and CF after range dependent adjustment on the LAWR-Leuven estimates
Although adjusting the CF with range improves the radar estimated rainfall to a great extent,
there are still some discrepancies on the overall RFB (Figure 4-3) as well as on cumulative
rainfall depths for both periods as can be seen from the Figure 4-5.
As can be seen from Figure 4-5, more scattering can be observed for the winter period than
for the summer period. In the winter period, a quite significant overestimation of the radar
estimated cumulative rainfall volume can be observed for some rain gauges as also seen in
the RFB plot, Figure 4-3. For the summer period, the points are consistently on the 1:1 line
and no serious under − or overestimations are present. The three low cumulative volume plots
for the summer period are due to the fact that three VMM rain gauge stations (Derijcklaan,
Oudstrijderslaan and Weggevoerdenstraat) were out of order for the entire month of July and
August and the cumulative volume plot is for the month of September alone. The scatter
although is expected to be minimised as subsequent merging methods have been incorporated
to the radar estimates.
Radar based rainfall estimation for river catchment modelling
46
0
50
100
150
200
250
300
0 50 100 150 200 250 300
Rad
ar E
stim
ated
[m
m]
Gauge Recorded [mm]
Summer StormWinter Storm1:1 Line
Figure 4-5: Cumulative rainfall plot of radar and gauge records for the winter and summer periods
of the LAWR estimates after range dependent correction on CF
4.1.4 Mean field bias adjustment
Figure 4-6 shows the frequency distribution of the bias for both summer and winter period.
And, as expected, a high frequency occurs around unit bias. For the summer period, highest
frequency is in between the bias class of 0.75-1, for the winter period the highest frequency is
between the bias class of 0.5-0.75 indicating slight overestimation of the radar estimates.
Overall, more than 75% is in between 0.75-1.25 which is positive as far as radar’s capability
on quantitative precipitation estimation concerns.
Figure 4-7 shows the probability distribution of the field bias calculated for all valid pairs.
The field bias based on the summer period agrees well with the expected lognormal
distribution even for higher biases. The winter period shows a small deviation from the
theoretical distribution. The bias values for the winter period are consistently below the
theoretical lognormal distribution line for low biases and above the theoretical distribution
line for some higher bias values.
The MFB for the whole summer and winter period was found to be 1.015 and 0.974
respectively and are calculated as per Equation (8) for the lognormal distribution. An upper
and lower limit for the 90%-confidence interval of the bias has been calculated for both
Radar based rainfall estimation for river catchment modelling
47
periods. It can be stated that the real MFB adjustment factor for the summer period lies in
between 0.953 to 1.076 with high probability, for the winter period the MFB factor lies
between 0.920 to 1.030.
0
0.2
0.4
0.6
0.8
1
1.2
0
10
20
30
40
50
60
70
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00
Cu
mu
lati
ve F
req
uen
cy [
-]
Fre
qu
ency
[-]
Bias, (G/R) [-]
Frequency (Summer Period)
Frequency (Winter Period)
Cumulative Frequency (Summer Period)
Cumulative Frequency (WInter Period)
Figure 4-6: Frequency distribution of field bias of valid gauge-radar (LAWR) pairs
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
Bia
s (G
/R) [
-]
Cumulative Probability [-]
Empirical Distribution (Summer)
Empirical Distribution (Winter)
Lognormal Theoretical Distribution
Figure 4-7: Probability distribution of field bias of valid gauge-radar (LAWR) pairs
Radar based rainfall estimation for river catchment modelling
48
4.1.4.1 Brandes spatial adjustment
As two (the Aquafin rain gauge located at Warotstraat and the VMM raingauge located at
Brouwersstraat) of the 12 rain gauges were in the beam blocking sector, only 10 rain gauges
were used to adjust the radar estimates applying the Brandes spatial adjustment procedure.
The threshold of 1 mm to select valid pair is used for this case as well. Brandes spatial
adjustment factors for each grid and for each valid storm event (defined by valid pairs) were
calculated and applied separately for the summer and winter storms.
4.1.4.2 Statistical analysis on the MFB and BRA adjustment
The MFB adjustment has improved the radar estimates to some. Some statistical parameters
can be seen in Table 4-2. For the summer period, the parameters did not improve
significantly. The NSE value improved from 0.67 to 0.68; the RMSE slightly improved and
no improvement has been observed for the MAE. This is obvious because of the fact that the
MFB correction factor was almost equal to 1. For the winter period, the statistics showed
significant improvement. The RMSE reduced from 3.86 mm to 3.74 mm; the MAE from 2.63
mm to 2.57 and the NSE value improved from 0.43 to 0.46.
Table 4-2: Some statistical parameter values before and after MFB and BRA adjustment on the
LAWR estimates for both summer and winter periods; RAW stands for the LAWR estimates using
constant CF values, RDA(LAWR estimates after range dependency adjustment on CF)
Statistical SUMMER WINTER
Indicators RAW RDA MFB BRA RAW RDA MFB BRA
RMSE [mm] 4.12 3.21 3.19 3.09 5.99 3.86 3.74 3.40
MAE [mm] 2.76 2.14 2.14 2.06 3.55 2.63 2.57 2.42
Nash Criterion [-] 0.47 0.67 0.68 0.70 -0.53 0.42 0.46 0.55
The advantage of using a spatial correction factor is obvious as can be seen in Table 4-2.
Goodness-of-fit-statistics is improved after the Brandes spatial adjustment is applied. For
summer storms, significant improvements can be observed in RMSE and MAE values as well
as in Nash Criterion. For winter storm, improvements are even better.
Figure 4-8 [a] & [b] show how goodness-of-fit statistical values improved when adjustment
procedures have been applied on raw LAWR estimates for the summer and winter periods
respectively. It can be seen that the adjustment procedures have greatly improved the radar
estimates for both periods especially for the winter case where the raw radar estimates had
Radar based rainfall estimation for river catchment modelling
49
negative NSE value, overcome significant improvement to 0.55. Decreasing trend of the
RMSE and MAE values and increasing trend of NSE values can be observed when the raw
radar data are subjected to subsequent adjustment procedures.
0
1
2
3
4
5
RMSE MAE NSE
RM
SE
an
d M
AE
[mm
], N
SE
[-]
Statistical Indicators
[a] Raw dataRange dependent adjustmentMean field bias adjustmentBrandes spatial adjustment
-1
0
1
2
3
4
5
6
RMSE MAE NSE
RM
SE
an
d M
AE
[mm
], N
SE
[-]
Statistical Indicators
[b] Raw data
Range dependent adjustment
Mean field bias adjustment
Brandes spatial adjustment
Figure 4-8: Evolution of different statistical values with different adjustments on the LAWR-
Leuven estimates; [a]-summer period and [b]-winter period
It appears that gauge-radar residuals even after the spatial adjustment are not negligible but
considerable improvements have been observed compared to raw LAWR estimates. It can be
observed that the RMSE values improved by 25%, the MAE by about 34% for summer
weeks. More significant improvements have been observed in the winter period than the
summer period denoted by about 43% improvement on the RMSE and 47% on the MAE
compared to the original LAWR estimates.
Radar based rainfall estimation for river catchment modelling
50
4.2 RMI Wideumont estimates − gauge comparison and merging
A threshold value of 1 mm is used to define valid pairs. The same 12 rain gauge network is
utilised. Altogether 99 valid pairs for weeks 1 and 2 and 88 valid pairs for weeks 3 and 4
were analysed.
4.2.1 MFB adjustment
The scatter plot of raw radar-gauge data for the week 1 and 2 shows a complex picture. In
overall, radar estimates tend to overestimate the daily accumulated values as in Figure 4-9
[a]. This might be caused by evaporation, where rain droplets are present on high elevation
and evaporates before reaching ground due to hot and humid conditions.
0
10
20
30
40
0 10 20 30 40
Rad
ar E
stim
ated
[m
m]
Gauge Value [mm]
[a]
Before MFB correction
1:1 Line0
10
20
30
40
0 10 20 30 40
Rad
ar E
stim
ated
[m
m]
Gauge Value [mm]
[b]
After MFB Correction
1:1 Line
Figure 4-9: Scatter plot of radar-gauge daily accumulated estimates for week 1 & 2 before [a] and
after [b] MFB correction on the RMI-Wideumont estimates
For the weeks 3 and 4 the situation is different. As can be seen in Figure 4-10[a], the radar
tends to underestimate the daily accumulated rainfall volumes. This may be because of the
fact that the weeks 3 and 4 are from a winter period and for winter periods, Belgium
experiences mostly stratiform rainfall. This rainfall originates from stratiform clouds which
are low in elevation. Also, as already depicted, the entire raingauge network lies in between
118 to 129 km from the RMI-Wideumont radar. That means the radar beam will be
sufficiently high to miss the raindrops resulting in low radar estimates. This phenomenon is
called ‘overshooting’. Clear underestimation of radar estimates might possibly caused by
another phenomenon called ‘growth’ of rainfall, as it approaches the ground surface. Smaller
droplets at higher elevation, which are measured by the radar, might grow and hence larger
raindrops may be caught by rain gauges at the ground, a process relatively possible in the
stratiform rainfall.
Radar based rainfall estimation for river catchment modelling
51
0
10
20
30
0 10 20 30
Rad
ar E
stim
ated
[mm
]
Gauge Value [mm]
[b]
After MFB correction
1:1 Line0
10
20
30
0 10 20 30
Rad
ar E
stim
ated
[mm
]
Gauge Value [mm]
[a]
Before MFB correction
1:1 Line
Figure 4-10: Scatter plot of radar-gauge daily accumulated estimates for week 3 & 4 before [a] and
after [b] MFB correction on the RMI Wideumont estimates
By looking at the scatter plots (Figures 4-9 [a] and 4-10 [a]), it is clear that radar data
requires a suitable correction before using it for rainfall-runoff modelling. The MFB is
calculated as the mean of an empirical lognormal distribution as it has already been shown
that the bias of individual valid pairs follows a lognormal distribution (Figure 4-7). The MFB
values for ‘weeks 1 and 2’ and ‘3 and 4’ were calculated as 0.732 and 2.217 respectively. The
90%-confidence limit on the bias is also calculated. The upper and lower confidence limit for
summer weeks (weeks 1 and 2) were found to be 0.808 and 0.662 respectively and we can
say there is high probability that the real MFB will lie in between the limit. For winter weeks
(weeks 3 and 4), the upper and lower limits were found to be 2.414 and 2.036 respectively.
4.2.2 Brandes spatial adjustment
The Brandes spatial adjustment is applied in a similar way as with the LAWR data. All 12
rain gauges have been used to calculate the adjustment factors for both summer and winter
weeks.
4.2.3 Statistical analysis on the MFB and BRA adjustment
The advantage of applying MFB adjustment is obvious as can be seen in Figures 4-9 [b] and
4-10 [b]. The points of radar-gauge valid pairs are somewhat oscillating around the 1:1 line.
This is followed by the Brandes spatial adjustment and some statistical parameters after the
adjustments have been calculated as presented in Table 4-3.
It is clear that the MFB adjustment improves the radar estimates to a great extent. The RMSE
value reduces from 5.70 mm to 4.93 mm for the summer periods. Better adjustment can be
observed for winter periods where RMSE value reduced greatly from 6.79 mm to 3.80 mm.
Radar based rainfall estimation for river catchment modelling
52
The MAE showed good improvement on the summer periods. The Nash Criterion (NSE)
improved from 0.31 to 0.48 for the summer periods. For the winter periods, the stastical
parameters show quite significant improvements. The NSE value improved from -0.10 to
0.66.
Although the improvements after Brandes spatial adjustment are minimal on summer weeks,
some improvements can be seen on winter weeks.
Table 4-3: Some statistical parameter values before and after MFB adjustment on the RMI
Wideumont radar estimates, RAW stands for original RMI-Wideumont estimates
Statistical SUMMER WEEKS WINTER WEEKS
Indicators RAW MFB BRA RAW MFB BRA
RMSE [mm] 5.70 4.93 4.91 6.79 3.80 3.76
MAE [mm] 4.24 3.06 3.02 5.08 4.52 4.38
NSE [-] 0.31 0.48 0.48 -0.10 0.66 0.66
Hence, it can be seen that the adjustment procedures can improve the raw radar estimates to a
great extent. For summer weeks, around 14% improvement has been observed on the RMSE
value compared to the raw RMI-Wideumont estimates. The MAE improves with about 29%.
In terms of improvement, the winter week’s estimates are better. The RMSE improved with
about 45% and the MAE with about 14%.
4.3 Comparison of LAWR-Leuven and RMI-Wideumont estimates
Figures 4-11 and 4-12 show a comparison plot of LAWR and RMI daily accumulated rainfall
estimates for the summer weeks (week 1 and 2) and the winter weeks (week 3 and 4)
respectively after MFB adjustment. It is observed that the RMI-Wideumont estimates tend to
underestimate higher rainfall accumulation depths though a fair matching can be observed for
lower intensities. This systematic underestimation for higher rainfall depth values might be
an indication of a strong MFB correction for the summer weeks (MFB = 0.732). The plot for
the winter weeks has not followed systematic underestimation or overestimation throughout
the range of rainfall depth values, although a slight underestimation can be observed for
extreme events. Trend of higher scatterings can be observed for higher intensities.
Radar based rainfall estimation for river catchment modelling
53
0
5
10
15
20
25
30
0 5 10 15 20 25 30
KM
I [m
m]
LAWR [mm]
SUMMER WEEKS
Figure 4-11: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for
summer weeks
0
5
10
15
20
25
30
0 5 10 15 20 25 30
KM
I [m
m]
LAWR [mm]
WINTER WEEKS
Figure 4-12: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for
winter weeks
4.4 Catchment modelling
4.4.1 Catchment modelling with VHM
The flow separation using the WETSPRO tool has resulted in time constants of 3500 and 50
hours for baseflow and interflow respectively. The baseflow filter result for the first 32000
Radar based rainfall estimation for river catchment modelling
54
time steps (hour) can be seen in Figure A-1 (Appendix). Similarly, the interflow filter result
for time step of 2000-4000 hours is shown in Figure A-2. Two linear reservoirs in series have
been applied for routing the overland flow each having a time constant of 5 hours. A linear
model is selected for describing the storage sub-model. Maximum soil water content of 500
mm and soil water content at maximum evapotranspiration of 200 mm is chosen. Similarly,
the surface runoff and interflow separation process parameters are tuned by heuristic
approach and with visual comparison of different sub-model results. Table 4-4 presents the
calibrated VHM parameters.
Table 4-4: The calibrated VHM parameters with their short description
Storage sub-model parameters
Umax (Maximum soil water content) 500 mm
Uevap (Soil water constant for maximum evapotranspiration) 200 mm
Overland flow model
aOF,1 (Surface runoff separation process parameter) 0.0523 -
aOF,2 (Surface runoff separation process parameter) 1.5 -
aOF,3 (Surface runoff separation process parameter) 0.3 -
Inter flow model
aIF,1 (Interflow separation process parameter) 0.0150 -
aIF,2 (Interflow separation process parameter) 2.5 -
aIF,3 (Interflow separation process parameter) 0 -
Flow routing parameters
KBF (Time constant for routing baseflow) 3500 hr
KIF(Time constant for routing interflow) 50 hr
KOF (Time constant for routing overland flow) 5 hr
4.4.2 Catchment modelling with NAM
Altogether 15 parameters have been calibrated to have a better agreement between the
simulated and observed river discharge. The WETSPRO analysis made it easy to fix the
range of the CKBF and CKIF while running the auto-calibration routine. A range of 3000-
4000 hr was fixed for CKBF and 50-150 hour for CKIF. CK1,2 value of 5.5 hours was
selected for routing the overland flow. Extended ground water parameters and a snow module
were also included. The GWLBFO value of 11 m is adopted owing to the flat and low lying
catchment. Similarly, the value of GWLFL1was fixed to 1.5 m as the predominant soil type
is sand. As CKlow is always greater than CKBF, a value of 7500 hours is taken with 0.1 as
Radar based rainfall estimation for river catchment modelling
55
portioning factor. A Csnow of 2 mm/°C/day together with a base temperature of 0°C have been
fixed for the snow module. The auto-calibration was run to match the overall water balance,
minimize overall RMSE and match low and high flows. The parameter values after auto-
calibration was further tuned manually to obtain better results. This has to be done because of
the fact that auto-calibration routines are made to optimize certain objective function and are
prone to errors due to the presence of local optima. The calibrated values can be seen in Table
4-5:
Table 4-5: The calibrated NAM parameters with their short description
Surface water parameters
Umax (Maximum contents of surface storage) 4.1 mm
Lmax (Maximum contents of root zone storage) 2000 mm
CQOF (Overland flow coefficient) 0.165 -
CKIF (Time constant for interflow) 150 hr
CK1,2 (Time constant for routing overland flow) 5.5 hr
TOF (Root zone threshold value for overland flow) 0 -
TIF (Root zone threshold value for interflow) 0.4 -
Ground water parameter
TG (Root zone threshold value for recharge) 0.24 -
CKBF (Time constant for routing baseflow) 4000 hr
Extended ground water component
GWLBFO (Threshold ground water depth for baseflow) 11 m
GWLFL1 (Capillary flux, depth for unit flux) 1.5 m
CQlow(Lower baseflow, recharge to lower reservoir) 0.1 -
CKlow (Time constant for routing lower baseflow) 7500 hr
Snow Melt Parameter
Csnow (Constant degree day coefficient) 2 mm/°C/day
T0 (Base temperature) 0 °C
The simulated hydrograph for the calibration period of January 1 2006 to December 28 2009
can be seen in Figure A-3. The comparison for cumulated volume for the same period is
shown in Figure A-4. And, the simulated hydrograph for the validation period can be seen in
Figure A-5 (Appendix).
4.4.3 Model performance evaluation
Table 4-6 along with Figures 4-13 to 4-17 show the results of the model performance
evaluation made with the WETSPRO tool. The statistics and graphical plots are the result of a
Radar based rainfall estimation for river catchment modelling
56
performance evaluation using the observed and modelled rainfall-runoff values for the period
of January 1 2004 to February 28 2009 which includes both calibration and validation periods
allocated for the NAM modelling. Altogether, 273 and 13 POTs are extracted for quick flow
and slow flow periods. The parameter − λ for BC-transformation is taken as 0.25. Statistics
indicate that the VHM simulated the rainfall-runoff more accurately than the NAM. The
VHM simulated rainfall-runoff series has lower MSE values and higher NSE values than the
corresponding NAM results both for quick and slow flow periods especially for quick flow
periods. Performance of both models in slow flow periods can not be highly distinguished.
Table 4-6: Some goodness-of-fit-statistics
Figure 4-13 shows the peak flow comparison after BC-transformation. It is clear that the
NAM simulated discharge shows a higher scatter. The mean deviation line is below the
bisector meaning that the peak flows simulated by the NAM are systematically
underestimated. This is also reflected in the peak flow extreme value plot (Figure 4-15)
where the NAM data points are systematically lower than the observed ones. Nonetheless the
comparison plot of observed and simulated discharge for the calibration period of the NAM
does not indicate that much underestimation (Figure A-3); it is due to the strongly
underestimated peak flows in the validation period (Figure A-5) and as already depicted, the
performance evaluation is made merging both periods. The underperformance in the
validation period is generally expected because of the fact that the calibrated parameters have
been tested to another independent period. Also, the performance of the model is known to be
affected by a significant change in trend of the annual average precipitation (Pipat et. al.,
2005) and the calibration of the parameters was based on a given precipitation trend and we
have a slightly varying trend in the validation period. As can be seen in Figure 4-13, the
VHM modelled peak flows show less scatter and almost no bias (slightly positive biased) as
indicated by the overlap of the bisector and the mean deviation line. Hence, the VHM can
simulate peak discharges with high accuracy. This is also confirmed in the peak flow extreme
value plot (Figure 4-15). But both models have the tendency to underestimate the peak flows
towards the upper tail of the extreme value distribution.
Flow
Periods
Number
of POTs
MSE [m3/s] NSE [-]
VHM NAM VHM NAM
Quick Flow periods 273 1.06 1.14 90% 75%
Slow Flow periods 13 1.01 1.02 92% 89%
Radar based rainfall estimation for river catchment modelling
57
Figure 4-14 shows the scatter plot for slow flow or base flows. In this regard, the VHM can
be considered as performing quite well, due to the low scatter and almost zero bias. The
NAM simulated results clearly overestimate the low flows which is also reflected in the low
flow extreme value plot (Figure 4-16) where the NAM simulated points are systematically
under the observed minima (the y-axis is plotted taking 1/ discharge). Nevertheless, both
models have a tendency to overestimate the low flows towards the upper tail of the extreme
value distribution.
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
BC
(Sim
ula
ted
Max
ima)
BC (observed Maxima)
NAM
VHM
Bisector
Mean Deviation [NAM]
Mean Deviation [VHM]
Standard Deviation [VHM]
Figure 4-13: Graphical comparison of nearly independent peak flow maxima
Radar based rainfall estimation for river catchment modelling
58
-2
-1.8
-1.6
-1.4
-1.2
-1
-2 -1.8 -1.6 -1.4 -1.2 -1
BC
(Sim
ula
ted
Min
ima)
BC (observed Minima)
NAMVHMBisectorMean Deviation [NAM]Mean Deviation [VHM]Standard Deviation [VHM]
Figure 4-14: Graphical comparison of nearly independent slow flow minima
0
1
2
3
4
5
6
0.01 0.1 1 10
Pea
k F
low
s [m
3/s
]
Return period [years]
observed
NAM
VHM
Figure 4-15: Graphical comparison of peak flow empirical extreme value distributions
Radar based rainfall estimation for river catchment modelling
59
3
4
5
6
7
8
9
0.1 1 10
1 /
Lo
w fl
ow
s [m
3/s
]
Return period [years]
observed
NAM
VHM
Figure 4-16: Graphical comparison of low flow empirical extreme value distributions
Figure 4-17 shows the graphical comparison of cumulative flow volumes. It is clear that the
VHM simulated discharge values are slightly overestimated (3.8%). The NAM gives better
results in this respect, with a slight underestimation (0.82%).
0
2000
4000
6000
8000
10000
12000
14000
0 10000 20000 30000 40000 50000
Cu
mu
lati
ve v
alu
e [m
3 /s]
Time [number of hours]
observed
NAM
VHM
Figure 4-17: Graphical comparison of cumulative flow volumes
Radar based rainfall estimation for river catchment modelling
60
4.5 The significance of spatial data
4.5.1 Rainfall spatial variability
Table 4-7 represents the total rainfall volume for each period event as well as the rainfall
characteristics and variability in terms of the SDIR. Across all events and all rainfall
descriptors, the SDIR varies from 0% to 43.2%. As expected, a large discrepancy is
introduced for the event-1, the storm of 3-Aug-08, because of its convective nature. The radar
data lead to higher SDIR-values in areal rainfall than RG1 for all events. Better agreement
has been observed between the Pref and the RG1 for all periods. The storm event-1 has the
highest SDIR even for RG1. The radar estimates have been seen to represent the areal
average rainfall in a better way for the storm event-3 (22-Jan-08), as suggested by low SDIR
values. No RMI Wideumont data was available for storm event-2.
Hence, the results indicate that for this catchment RG1 can capture areal average rainfall in
almost same accuracy as Pref. This may be because of the fact that the catchment is small and
a network of only 2 raingauges forms the Pref. On the other hand, the radar areal average
estimates are poor as compared to the Pref as indicated by higher SDIR values. This may be
due to discrepancies in the sampling mode, an inappropriate conversion equation, a non-
optimal correction/adjustment methodology. Another, more important reason and perhaps
more evident reason may be that the radars represent the true areal rainfall and that rain
gauges may have failed to capture all the spatial variability.
Table 4-7: Rainfall spatial variability measured in terms of SDIR for the different rainfall
descriptors and for selected events
Events Rainfall Record SDIR
Reference RG1 LAWR RMI RG1 LAWR RMI
[d-m-yy] [mm] [mm] [mm] [mm] [%] [%] [%]
3-Aug-08 30.67 33.07 20.11 17.43 7.8 34.4 43.2
4-Dec-08 7.75 7.65 6.95 - 1.4 10.3 -
22-Jan-09 30.36 30.37 26.87 28.86 0.0 11.5 4.9
9-Feb-09 27.22 26.47 17.07 29.95 2.8 37.3 10.0
4.5.2 Basin response
Table 4-8 shows the results in terms of the NSEobs for the different rainfall descriptors.
Across all storm events, the NSEobs for Pref varies from 0.66 to 0.90 for the VHM and from
Radar based rainfall estimation for river catchment modelling
61
0.34 to 0.93 for the NAM simulated results. The storm event of 9-Feb-09 results in the
highest NSEobs value for both models. The storm event of 3-Aug-08 results in the lowest
NSEobs value for the VHM and the storm of 5-Dec-08 for the NAM. Degradation of the
NSEobs can be observed for other alternative rainfall descriptors in most of the cases. For the
RG1, the NSEobs closely matches with the same derived with the Pref. The radar simulated
discharge results in a lower NSEobs value than that based on Pref except for the event of 5-
Dec-08 where the LAWR-Leuven data driven discharge has the highest NSEobs (0.84 for the
VHM and 0.57 for the NAM). A further mismatching is observed between the RMI-
Wideumont simulated discharge and the observed discharge where NSEobs values are as low
as 0.19. Considerable improvement can be observed in NSEobs values when using radar
estimated rainfall in winter periods rather than in summer periods. Across all events, the
performance of the VHM and NAM can not be highly distinguished except for the event of 4-
Dec-08 where the VHM simulated runoff matches more closely than the NAM simulated
runoff where runoff driven by Pref has NSEobs value of 0.78 for the VHM and 0.34 for the
NAM.
Table 4-8: Results in terms of NSEobs for the different rainfall descriptors and for different storm
events
Storm Pref RG1 LAWR KMI
VHM NAM VHM NAM VHM NAM VHM NAM
3-Aug-08 0.66 0.70 0.63 0.69 0.45 0.45 0.19 0.27
4-Dec-08 0.78 0.34 0.81 0.36 0.84 0.57 - -
22-Jan-09 0.83 0.82 0.84 0.83 0.89 0.78 0.39 0.33
9-Feb-09 0.90 0.93 0.91 0.92 0.68 0.68 0.50 0.58
0.0
0.2
0.4
0.6
0.8
1.0
3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09
NS
Eo
bs
[-]
Storm events
[NAM] Pref
RG1
LAWR
KMI
0.0
0.2
0.4
0.6
0.8
1.0
3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09
NS
Eo
bs
[-]
Storm events
[VHM]
Figure 4-18: NSEobs for different rainfall descriptors and for different storm events
Radar based rainfall estimation for river catchment modelling
62
Figure 4-18 is a graphical representation of the Table 4-8 where the evolution of NSEobs for
alternative rainfall descriptors for both models can be seen. It is clear that NSEobs values are
degrading for alternative rainfall descriptors especially for the radar estimates.
As observed, the Pref and RG1 derived response can not be highly distinguished for all events.
The radar estimates showed low performance compared to that derived from Pref. The
performance was further degraded for RMI-Wideumont derived rainfall. This might be
because of courser spatial resolution of the RMI-Wideumont radar than that of the LAWR-
Leuven. The low performance of radar data against the raingauge data may be due to the fact
that the model has been calibrated against the rain gauge data. Better agreement might be
observed when calibrating it against the radar estimated rainfall. This was not possible in this
study because too few radar data from both the LAWR-Leuven and the RMI-Wideumont
radars was available for calibration.
Results indicate that lower NSEobs values are expected for summer events than for winter
events. This may be due to the rainfall spatial variability in summer events. Summer events
are of highly convective nature and the raingauge may have missed the rainfall information.
On the other hand, the winter events have less spatial gradients and the rain gauge network
can represent them quite well. This fact is reflected in the SDIR values as well as in the
coefficient of variance (CV, defined as standard deviation normalized by mean) which is
calculated by taking storm accumulated rainfall depth over the pixels covering the catchment
as variable. The storm event-1 (3-Aug-08) shows the highest CV of 18% for RMI-
Wideumont data while it is significantly lower for the winter events, for example: 11 % for
event-3 (22-Jan-09) and 8% for event-4 (9-Feb-09). This can also be seen in Figures A-12 to
A-15 where the pixel to pixel distribution of the accumulated rainfall depths for storm event-1
and storm event-3 for both the RMI-Wideumont as well as the LAWR-Leuven pixels are
presented. It is clear that the storm event-1 (3-Aug-08, Figure A-12) shows a higher pixel to
pixel variability where the accumulated rainfall depth varies from 11 to 28 mm across the
RMI-Wideumont pixels covering the catchment. The storm event-3 (22-Jan-09, Figure A-14)
shows less variability as compared to event-1 as the accumulated rainfall depth varies from
23 to 28 mm across all the RMI-Wideumont pixels. The LAWR data show a complex picture
(Storm-1, Figure A-13 and storm-3, Figure A-15). Some pixel values even show total
accumulated rainfall depths equal to zero which is highly unrealistic. This is because of the
Radar based rainfall estimation for river catchment modelling
63
algorithms set on the LAWR-control to remove permanent clutter where even a maximum
count (255) is subtracted from the reflected counts making those pixels reading always zero.
Also, the difference in simulating capacity of VHM and NAM is not that pronounced. Across
all events, the VHM produced more consistent results which were also indicated by the
model performance evaluation (section 4.4.3). This might indicate a more robust model
structure or at least it might favour the step-wise calibration procedure of the VHM.
Simulated runoff with the different rainfall descriptors is compared to the observed series as
shown in Figure 4-19 and Figure 4-20. The results in terms of NSEref can be found in Table
4-9 and express the errors in reproducing the reference flow introduced by the alternative
rainfall representations, keeping the parameter uncertainty the same.
Table 4-9: Results in terms of NSEref for the different rainfall descriptors
Strom RG1 LAWR RMI
VHM NAM VHM NAM VHM NAM
3-Aug-08 0.98 0.98 0.72 0.72 0.42 0.51
4-Dec-08 1.00 1.00 0.97 0.94 - -
22-Jan-09 1.00 1.00 0.89 0.97 0.80 0.84
9-Feb-09 1.00 1.00 0.74 0.79 0.83 0.82
For all events, the average NSEref values for RG1, LAWR and RMI estimated rainfall driven
flows from the VHM are 0.99, 0.83 and 0.69 and from the NAM 0.99, 0.86 and 0.73
respectively. Looking to the corresponding values of NSEobs, values of 0.79, 0.72 and 0.36
for the VHM could be found, and 0.70, 0.62 and 0.36 for the NAM. The average NSEobs for
the reference rainfall driven flow is 0.79 for the VHM and 0.70 for the NAM (the difference
from 1 can be regarded as model error). Hence the deviation can be considered as the error
introduced by using the other rainfall descriptor. For all events, the value of NSEref for RG1
is close to 1 meaning that RG1 closely matches with Pref as far as basin response concerns.
For radar estimated rainfall driven flows, NSEref decreased to 0.83 (for the VHM) and 0.86
(for the NAM) for the LAWR-Leuven; and 0.69 (for the VHM) and 0.73 (for the NAM) for
the RMI-Wideumont radar estimates, indicating better performance of the LAWR-Leuven
estimates. The better performance of the LAWR-Leuven estimated rainfall could be
attributed to its high resolution (125x125 m) compared to the RMI-Wideumont radar
Radar based rainfall estimation for river catchment modelling
64
(600x600 m). Results (NSEref for RG1 ≈ 1) indicate that only one raingauge can sufficiently
reproduce the flows with some accuracy as far as this catchment concerns. Also, better
performance can be seen for storm events of winter periods than summer periods, clearly
indicated by the rather low NSEref as well as NSEobs values for summer storm of 3-Aug-08.
Looking at the hydrographs produced by different rainfall descriptors (Figure 4-19 and
Figure 4-20), it is clear that the LAWR-Leuven and the RMI-Wideumont estimated rainfall
tend to give lower peaks especially for extreme and summer events. It might be due to the
dampening effect because of the fact that the weighted average of 3085 LAWR-Leuven
pixels and 136 RMI-Wideumont pixels were used to calculate areal average rainfall. This
trend is clearly seen for the storm event-1 (3-Aug-2008, Figure 4-19 [upper]) both from the
VHM simulated and the NAM simulated. This also has to do with the lumped nature of the
models used because both the VHM and the NAM uses catchment average rainfall meaning
that localized summer events are dampened. The mismatching of hydrograph trend for the
same storm event is possibly due to flood influence (having flatter recession limb) or due to
man made influences or regulation when the discharge is greater than certain threshold. Less
severe trends are observed for uniform winter events where peaks are quite nicely matched
for all rainfall descriptors except for the event-4 (9-Feb-09; Figure 4-20 [lower]), where the
LAWR estimated rainfall driven flow is characterized by slightly earlier responding lower
peaks. On other hand, for the winter storms, the RMI-Wideumont driven flows are
characterised by high peaks with early response (Figure 4-20 [both]) for both the VHM as
well as the NAM. This might be due to the strong MFB in the winter periods (MFB = 2.217)
based on the data period of few weeks although the Brandes spatial adjustment is applied
after the MFB adjustment. Also, higher peaks and quick response might also be attributed to
the lumped nature of the models used. As can be seen in Figure A-13, the pixels having
higher rainfall accumulation are on the very upstream side of the catchment. If a fully
distributed model could have been used, the response from the pixels having higher rainfall
depth would have been sufficiently lagged to have less severe peaks and the response would
have been in time due to routing of the flow along the river.
Figure 4-21 shows a plot of SDIR versus NSEref for both models. As can be depicted from
the figure, a correlation between increase in SDIR and decrease in NSEref is observed. Up to
an SDIR value of around 10%, the NSEref remains close to 1 and then tends to decrease as
SDIR increases. These trends are almost similar for both models.
Radar based rainfall estimation for river catchment modelling
65
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 12 24 36 48
Dis
char
ge
[m3/s
]
Hours
[VHM] Qobs
Pref
RG 1
LAWR
KMI
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 12 24 36 48
Dis
char
ge
[m3/s
]
Hours
[VHM] Qobs
Pref
RG1
LAWR
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 12 24 36 48
Dis
char
ge
[m3/s
]
Hours
[NAM] Qobs
Pref
RG 1
LAWR
KMI
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 12 24 36 48
Dis
char
ge
[m3/s
]
Hours
[NAM] Qobs
Pref
RG1
LAWR
Figure 4-19: Observed and simulated flows derived from different rainfall descriptors
for storm-1 [upper] and storm-2 [lower]
Radar based rainfall estimation for river catchment modelling
66
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0 12 24 36 48 60 72 84 96
Dis
char
ge
[m3/s
]
Hours
[VHM] Qobs
Pref
RG 1
LAWR
KMI
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 12 24 36 48 60 72 84 96 108 120
Dis
char
ge
[m3/s
]
Hours
[VHM] Qobs
Pref
RG 1
LAWR
KMI
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0 12 24 36 48 60 72 84 96
Dis
char
ge
[m3/s
]
Hours
[NAM] Qobs
Pref
RG 1
LAWR
KMI
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 12 24 36 48 60 72 84 96 108 120
Dis
char
ge
[m3/s
]
Hours
[NAM] Qobs
Pref
RG 1
LAWR
KMI
Figure 4-20: Observed and simulated flows derived from different rainfall descriptors
for storm-3 [upper] and storm-4 [lower]
Radar based rainfall estimation for river catchment modelling
67
0.0
0.2
0.4
0.6
0.8
1.0
0 10 20 30 40 50
NS
Ere
f [-
]
SDIR [%]
VHM
NAM
Figure 4-21: Plot of SDIR and NSEref for both the VHM and NAM
Hence from the results, contrary to expectation, the radar estimated rainfall driven flows
underperformed compared to the RG1. The RG1 on the other hand, which was presumed as
the degradation of spatial rainfall representation over the catchment, can reproduce the flow
with an accuracy as good as Pref. The underperformance of radar estimated rainfall is related
to the calibration strategy used, where both the models were calibrated against Pref. It is also
related to the nature of the models used. Both are lumped rainfall runoff models, using
averaged areal rainfall rather than using spatially variable input. Hence, for extreme and
summer events where the spatial variability of rainfall is high, the radar estimates are always
dampened due to averaging effects of large number of pixels covering the catchment.
Analyzing the significance of spatial representation of rainfall through stream flow
simulation revealed that a single raingauge can reproduce the flow with some accuracy for a
small catchment of size around 50 km2. The radar though has better spatial coverage of
rainfall, the spatial resolution of LAWR-Leuven being as fine as 125 m, has resulted lower
NSEobs as well as NSEref values. By this fact, it can be worthwhile to note that the importance
of spatial rainfall depends on how variable the rainfall is and whether there is enough
variability to overcome the damping and filtering effect of the basins because fast responding
catchments are more sensitive to spatial rainfall variability. As the studied catchment is flat
and characterised by predominant sandy soils, hence quite a large portion of rainfall
Radar based rainfall estimation for river catchment modelling
68
infiltrates and local variation of the rainfall input is smoothed and delayed within the soil.
Hence, rainfall variations are dampened by integrating response of the catchment. As a result,
for this catchment, more precise areal rainfall estimates are required than spatially variable
rainfall information. Similar results have been observed by Smith et al. (2004) where they
tested rainfall spatial variability in two catchments having high and low level of basin
filtering and found that precise estimates of catchment average rainfall are requited rather
than having spatially more variable rainfall information. Also, a deviation of 10% on areal
average rainfall in terms of SDIR merely affects the simulated stream flow but deviations of
more than 10% proved to cause larger variations, because of the small scale of the catchment.
After all, it has to be noted that the effect of rainfall spatial variability is accessed indirectly,
via lumped conceptual models.
Radar based rainfall estimation for river catchment modelling
69
CHAPTER 5: CONCLUSIONS
In conclusion, this thesis addressed two themes related to the hydrological community. First,
a comparison study is made which allowed validating and merging the gauge and radar
estimates from two different types of radars, namely the X-band and C-band radars. Second,
the significance of spatial representation of rainfall is assessed using two lumped conceptual
models, namely the VHM and the NAM.
5.1 Comparing and merging of radar − gauge estimates
The goal of radar-gauge comparison was to quantify the accuracy of radar precipitation
estimates. For this, a rain gauge network consisting of 12 rain gauges having different time
resolutions was used. Merging of radar-gauge estimates which involved rainfall information
from the X-band LAWR-Leuven and the C-Band RMI-Wideumont radar was done to have
robust final radar estimates. The study period was sub-divided into summer and winter
periods according to data availability. A threshold value of 1 mm for daily rainfall
accumulation was used to define valid pairs.
For the LAWR-Leuven estimates, using constant CF value to convert the “counts” to rainfall
rates was found to be inappropriate as the radar estimates were heavily overestimated in
nearby pixels and heavily underestimates in far-away pixels. A power function (CF = 0.0272
r 0.8226
, r ≥ 1.5 km) and a second degree polynomial function (CF = 0.0006 r2 + 0.015r +
0.0159, r < 1.5 km) were combined to apply a range dependent adjustment on the CF values.
Then, a MFB adjustment was applied to adjust these radar estimates. It was observed that the
individual bias (G/R) followed a lognormal distribution both for summer and winter periods.
The MFB was found to be 1.015 and 0.974 for summer and winter periods respectively. The
90% upper and lower confidence limit for the MFB was found to be 1.076 and 0.95
respectively, for summer periods. For winter periods, the limits were 1.030 to 0.920
respectively. After the MFB adjustment, a Brandes spatial adjustment was applied. Radar
estimates after adjustments improved quite significantly. It was observed that the mean
absolute error as much as high as 47% compared to raw radar estimates.
For the RMI-Wideumont estimates, it was observed that the raw radar data were
overestimated in summer period and underestimated in winter periods. Taking that the
individual bias (G/R) followed a lognormal distribution, the MFB for summer and winter
Radar based rainfall estimation for river catchment modelling
70
periods was found to be 0.732 and 2.217 respectively. The 90% upper and lower confidence
limit for the MFB was found to be 0.808 and 0.662 respectively, for summer periods. For
winter periods, the limits were 2.414 and 2.036 respectively. The advantage of using the
Brandes spatial adjustment on radar estimates has been shown quite well. It was observed
that the root mean square error decreased as much as high as 45% with respect to the original
radar estimates.
5.2 Hydrological modelling
Significance of spatial rainfall information was tested using two lumped conceptual models,
the VHM and the NAM. Calibration of the models was done using rain gauges situated in the
catchment. The calibrated parameter set thus derived was tested to alternative rainfall
descriptors namely RG1 (using one rain gauge station located approximately at the centroid),
the LAWR-Leuven estimates and the RMI-Wideumont estimates after applying adjustment
procedures. Four storm events were selected to investigate the effects.
In terms of runoff simulations, the performance of both models could not be highly
distinguished. Contrary to expectation, RG1, which was presumed as rainfall with a
degradation of rainfall representation, was found to reproduce hydrographs with almost the
same accuracy those based on by Pref. Radar estimated rainfall driven flows were less
accurate than those simulated with RG1. The radar estimates from the LAWR-Leuven were
better than the estimates from the RMI-Wideumont for simulating the runoff. Extreme and
summer events could not be well simulated by radar estimates although the winter events
have been simulated with higher accuracy. A trend between increase in SDIR and decrease in
NSEref was observed. It was observed that SDIR values greater than 10% proved to cause
large variations in on hydrograph reproduction for both the models.
Hence, for the studied catchment, a central rain gauge alone can be used to simulate the flows
with good accuracy. This is because of the fact Pref is based on a network consisting of only 2
rain gauges. Lower performance of the radar estimates on stream flow simulation can be
attributed to the dampening and filtering effect of the catchment and/or to non-optimal radar-
gauge adjustments. The flat catchment with predominant sandy soil allows a larger portion of
water to infiltrate and hence the local variation of the rainfall input is smoothed and delayed
within the soil. It is observed that a robust method to estimate the catchment averaged rainfall
Radar based rainfall estimation for river catchment modelling
71
(SDIR ≈ 10%) is required. These findings are also in accordance to some studies that have
been carried out by some researchers (Chaubey et al., 1999; Smith et al., 2004; Segond et al.,
2007 etc.).
5.3 Limitation and future perspectives
Radar data handling and processing tasks are very time consuming since both spatial and
temporal aspects are taken into consideration. Also, a quite dense network of raingauges is
required to validate the radar estimates. Radar gauge merging techniques also demand many
data. The main limitation of the study is the availability of data. The LAWR-Leuven is
relatively new producing radar estimates from July 2, 2008. Also, data of only a few weeks of
RMI-Wideumont radar could be made available. The availability of a dense rain gauge
situated in another direction of the study area is also a limitation as most rain gauges are
along the north-west side of the LAWR and only a limited number of raingauges is available
in the southern part. Part of the LAWR radar beam blockage towards the Zaventem airport
led to a limitation on choosing the catchment for hydrological modelling. Also, use of lumped
conceptual models might be a limitation to investigate significance of the spatial rainfall
variability. Model parameters resulted by calibrating the models using rain gauge data is a
limitation too because the parameter set might not necessarily be the same if the model would
have been calibrated against the radar data.
Hence, merging the radar – gauge rainfall estimates should be carried out using longer data
period series. Separate analysis on different storm periods (summer and winter) is
recommended because of the difference in drop size distributions as well as spatial rainfall
patterns. Use of a model which can use full spatial information of rainfall is recommended.
Such models might reproduce better hydrographs while using adjusted radar estimated
rainfall. Or, a comparison study between lumped conceptual and fully distributed models
might be interesting. Testing the rainfall spatial information on more urbanized catchments
which are characterised by high imperviousness is recommended as they are fast responding.
It is presumed that these catchments have low filtering and local rainfall variations should be
reflected more clearly in stream flow simulation.
Radar based rainfall estimation for river catchment modelling
72
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CHAPTER 7: ANNEXES
A-1: Prior time series processing results
0.1
1
10
0 4000 8000 12000 16000 20000 24000 28000 32000
Dis
char
ge
[m3/s
], lo
g s
cale
Number of time steps [hours]
Time seriesFiltered baseflowSlope recession constant baseflow
Figure A-1: Baseflow filter results
0
0.5
1
1.5
2
2.5
2000 2400 2800 3200 3600 4000
Dis
char
ge
[m3/s
]
Number of time steps [hours]
Time seriesFiltered overland flowFiltered interflowFiltered baseflow
Figure A-2: Interflow filter results
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A-2: Model results
Figure A-3: Observed and NAM simulated hydrograph for the calibration period (3/1/2006-
2/28/2009)
Figure A-4: Cumulative observed and NAM simulated discharge for calibration period (3/1/2006-
2/28/2009)
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Figure A-5: Observed and NAM simulated hydrograph for the validation period (1/1/2004-
12/31/2005)
Figure A-6: Observed and VHM simulated hydrograph for the calibration period (3/1/2006-
2/28/2009)
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Figure A-7: Cumulative observed and VHM simulated discharge for the calibration period
(3/1/2006-2/28/2009)
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A-3: Rainfall series (in terms of Pref) for selected storm events
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
1 2 3 4 5 6 7 8
Rai
nfa
ll [m
m]
Storm duration [hr]
Pref [3-Aug-08]
Figure A-8: Reference rainfall evolution for storm event-1
0.0
0.5
1.0
1.5
2.0
2.5
1 2 3 4 5 6 7
Rai
nfa
ll [m
m]
Storm duration [hr]
Pref [5-Dec-08]
Figure A-9: Reference rainfall evolution for storm event-2
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Rai
nfa
ll [m
m]
Storm duration [hr]
Pref [22-Jan-09]
Figure A-10: Reference rainfall evolution for storm event-3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Rai
nfa
ll [m
m]
Storm duration [hr]
Pref [9-Feb-09]
Figure A-11: Reference rainfall evolution for storm event-4
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A-4: Accumulated rainfall over radar pixels for selected storm events
Figure A-12: Accumulated rainfall for storm event -1 (RMI pixels), north is upward
Figure A-13 : Accumulated rainfall storm event-1 (LAWR pixels), north is upward
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Figure A-14: Accumulated rainfall for storm event -3 (RMI pixels), north is upward
Figure A-15: Accumulated rainfall storm event-3 (LAWR pixels), north is upward
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A-5: LAWR-Leuven simulated results
0
0.4
0.8
1.2
1.6
2
2.4
2.8
7/2/2008 7/17/2008 8/1/2008 8/16/2008 8/31/2008 9/15/2008 9/30/2008
Dis
char
ge
[m3/s
]
Date [mm/dd/YYYY]
Observed
VHM Simulated
Figure A-16: LAWR-Leuven VHM simulated river discharge for the period of 7/2/2008 to
9/30/2008
0
0.4
0.8
1.2
1.6
12/1/2008 12/16/2008 12/31/2008 1/15/2009 1/30/2009 2/14/2009 3/1/2009
Dis
char
ge
[m3/s
]
Date [mm/dd/YYYY]
Observed
NAM Simulalted
Figure A-17: LAWR-Leuven NAM simulated river discharge for the period of 12/1/2008 to
2/28/2009