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Analysis of a Distributed Hydrological Model Response
by Using Spatial Input Data with Variable Resolution
F. Soria
1
, S. Kazama
2
, M. Sawamoto
1
1 Graduate School of Engineering, Tohoku University, Japan;2 Graduate School of Environmental Sciences, Tohoku University, Japan
1. Introduction
The Stanford Watershed Model was in the 1960s one of the first programs
developed to predict streamflow through simplifications and idealizations towards
understanding the components of the hydrological cycle, the physical
environment, and all interactive and complex interactions that link them together.
From the engineering point of view, the interest may be focused in the temporal
variation and spatial distribution of water quantity, water quality and sedimentload, because of its importance in water management policies development and
currently increasing concerns about climate and land use changes and its effects in
water resources availability. Distributed hydrological models can be considered as
a useful tool to analyze and quantify catchments response because its capacity to
account spatial variability of watershed processes, inputs, boundary conditions and
physical characteristics, only if spatial input data demand is adequately fulfilled.
Such issues become difficult to accomplish in poorly and ungauged basins
specially in developing countries, where measurement networks density have
decreased in the last decades mainly because the high cost of maintenance and
monitoring, and where geographical, geological and physical information is also
scarce to accomplish certain modeling resolution requirements. In such frame,
some initiatives such as the PUB (prediction of ungauged basins) of theInternational Association of Hydrological Sciences have been considering
situations to better represent the catchment response in poor data situations.
Heterogeneity of the land surface condition, soil structure, vegetation, land use,
etc, and the spacetime variability of climatic inputs occurring over a wide range
of space and time scales, and which never seems to disappear at whatever scale we
observe (Sivapalan, 2003) could be seen as the main problem for hydrologic
predictions. Its representation in distributed models is difficult to overcome and
the best suited modeling scale should theoretically follow the definition of Singh
(1995) about the term scale itself as the size of a unit or a subwatershed within
which the hydrological response can be treated as homogeneous . Many papers
analyze the effects of such heterogeneity by introducing variation in the scale of
input data. Kalin et al. (2003) uses the Kinematic Runoff and Erosion Model
KINEROS (Woolhiser et al., 1990) to show that as the geomorphologic resolution
decreases the peak runoff also decrease for all simulated runoff hydrographs;
moreover, the author shows that time to peak does not change appreciably with
increasing resolution, except for the pure overland flow case where time to peak is
larger than expected.. Since it is clear that heterogeneity becomes more evident as
smaller the scale considered, resolution issues need more attention for smaller
basins (Shresta et al., 2006). Grid size effects can also be evaluated on catchment
parameters. Yin and Whang (1999) estimate some drainage basin parameters for
20 basins for the US Geological Survey (USGS) 1:24 000 (30m) Digital Elevation
Models DEMs and the USGS 1:250 000 (approximately 92m) DEMs. They found
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that for the coarser resolution considered parameters as the mean maximum basin
elevation, the total stream length and main stream length, the drainage density and
in general slope parameters were underestimated; the opposite was observed for
the mean minimum basin elevation and the relief ratio. Jetten et al. (2003) analyzethe effect of 5m, 10m, 20m and 50m grid size in simulated discharge by the
application of the Limburg soil erosion model LISEM. There it is shown that
increasing grid size has indirect relationship to both peak discharge and runoff
volume which decrease. The author points to the change in slope as the main
responsible for lower water depth and velocity values obtained. LISEM model is
also studied by Hessel (2005), who analyzes modeling results for grid cells
ranging from 5 to 100 for a single time step, and for time steps ranging from 2 to
120 s with single grid size. Simulated discharge results show similar behavior in
peak discharge as cited from previous researchers; besides, the author establishes
that the numerical errors effect in the kinematic wave solution might be an
additional cause for flood dispersion and infiltration time increasing.
Predictions of hydrological response as river discharge are linked to issues cited
above. Seems clear that higher data resolution would represent better watersheds
heterogeneity than the opposite one, although is also clear that such high-quality
data may not be always available. This paper aims to evaluate the variations that
could be observed in runoff simulation as a way to contribute in the analysis of
modeling uncertainty in various scenarios. A distributed hydrological model is
applied for different spatial input data resolutions. Then, observed and simulated
hydrographs are analyzed through visual and statistical comparison. No
considerations have been focused on analyzing climatic input data resolution or
time step calculation interval, which are maintained invariable. Final conclusions
and recommendations are based on such frame.
2. Model description
The model is developed under the structure suggested by Tsuchida et.al (2003). It
aims to describe spatial variability of hydrological processes in three reservoirs, as
a way to estimate river discharge in a watershed.
Snowmelt contribution to total discharge is calculated using the degree day
method, where the relation snowmelt - temperature is
)( bif TTMM = (1)
whereMis the depth of meltwater in a period of time, Ti and Tb are the index and
base air temperature respectively, and Mf is the melt factor. Commonly used
values forTi and Tb are the mean daily temperature and 0C respectively. Mf is
determined empirically by Totsuka (2003); such values are taken in this study.
To describe overland flow routing of runoff is used the classical kinematic wave
equation. It is derived from the continuity equation (equation 2), considering
lateral inflow or outflow per lineal distance along the watercourse q as
precipitation and snowmelt, besides water loss as evaporation. Then, the equation
can be expressed in terms of finite-differences as follows
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0=
+
q
x
Q
t
A (2)
BESrx
Q
t
hB
m
)( =
+
(3)
where A is the flow cross-sectional area with constant surface width of flow B,
depth of flow h, time t, discharge Q, rainfall rate r, snowmelt rate Sm,
evapotranspiration rate E, and x as the distance along the longitudinal axis of the
watercourse.
Infiltration estimation simply considers constant parameters estimated assuming a
homogeneous soil structure for the entire basin. Infiltration capacity varies with a
soil saturation rate controlled with the number of days with rain.
The volume of storage Sat any time in each cell of the watershed is related to a
representative discharge q in the element at the same time as in equation 1.
Moreover, Yoshikawa (1966) suggests empirical values of 40.3 for kand 0.5 for
m. Then, storage depth is estimated with a storage function method (Yoshikawa,
1966):mkqS= (4)
where kis a dimensional parameter and m a dimensionless.
qrdt
dSo= (5)
where So is the storage depth, and q the discharge rate.
Dynamic wave model is used for channel flow routing. The method employs
St. Venant equations describing the laws of mass conservation (equation 2) and
momentum conservation (equation 6). Later, the numerical solutions for both are
written in equations 7 and 8.
02
11
34
22
=+
+
+
h
vvn
x
H
x
v
gt
A
g (6)
qB
tv
hhv
hh
x
thh
ij
ijij
ij
ijij
ijij
+
+
=
++
+ 1121
1
211
1122
(7)
3/4
2
1
2
21
2
213/4
2
1
1
21
)()(4
)2
1(
h
tvgn
HHx
tgvv
x
t
h
tvgnv
vij
ijijijij
ij
ij
ij
+
=
++
+
(8)
where g is acceleration due to gravity, H water level, v flow velocity, and n
Mannings friction factor. Besides, in the x-tplane, i refers to x spatial axis and j
refers to time axis.
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3. Studied watershed and input data
The study is developed in the Natori River basin, center of Miyagi Prefecture,
northeastern Japan (Fig. 1). The contributing area is 1015km 2, somehow bigger
than the 970km2 showed in other studies since it is considered a major proportion
of plain land. The main stream length is 55km (Natori River). Two large-scale
dams (Kamafusa Dam and Ookura Dam) are located upstream Goishi River and
Ookura River respectively. The basin is approximately 72% a mountainous region
and 26% plain-land, with elevations that vary from 0MSL to 1470MSL. The
average river slope is 40% in the mountainous region.
Meteorological data is available hourly for three stations: Kawasaki, Nikkawa and
Sendai, from the Automated Meteorological Data Acquisition System (AMeDAS)
database. Inverse distance method is used to estimate spatial distribution ofprecipitation and temperature. Discharge records in daily frequency are available
at the outlet of Kamafusa Dam, Ookura Dam and Yokata gauging station.
Input grid data consists of elevation, river network, flow direction for north-south
and west-east directions, flow accumulation, land use and mean monthly
evapotranspiration raster maps. Land use is characterized by the Geographical
Survey Institute and considers mainly urban areas, forests and crop fields.
Evapotranspiration grid map is calculated indirectly from the Normalized
Difference Vegetation Index NDVI, estimated from the National Oceanic and
Atmospheric Administration-Advanced Very High Resolution Radiometer
NOAA-AVHRR sensor (Nourbaeva et al, 2003). The 250m grid size input data isused to derive the correspondent 500m and 1000m inputs. Elevation data, land use
and evapotranspiration data are derived from the correspondent 250m grid by
bilinear interpolation, and then manually corrected for non-sense values. Flow
direction grid is derived from the correspondent corrected elevation grid, and
determined by the D-8 method finding the steepest direction of each cell and its
eight neighbors; later, flow direction grid is manually corrected to force and allow
the main elements of the original network to appear in coarser resolution maps.
Flow accumulation is derived from corrected flow direction grids. Figure 2, 3 and
4 shows variations in grid size for the elevation and river network maps.
The model is applied for 250m, 500m, and 1000m grid resolution, with
simulations carried out for the period July 1999 to June 2000, only for simplicity.Time step calculation is fixed to 10s, and time step of meteorological input data is
fixed hourly in the modeling process. Calibration is developed in the original
250m grid size based on comparisons with observed discharge at Yokata station.
Calibrated parameters of infiltration, groundwater storage function, surface flow
and snow melt are maintained invariable for the simulations of 500m and 1000m
grid resolution. Initial conditions for mean water surface velocity, surface and
groundwater water depth are estimated from results of an initial testing simulation.
The results from a second simulation are the ones considered for analysis.
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Figure 1. Location of Natori River basin Figure 2. Natori River basin system.(Shiraiwa et al., 2005) 250 m grid size
Figure 3. Elevation grid for a) 500m resolution, b)1000m resolution
4. Results and discussion
The distributed model is calibrated using the Yokata gauging station discharge
records for the period July 1999 to June 2000, assuming (later verified) that the
best model performance would be for the 250m grid size resolution and time step
calculation of 10s. The calibration considers additional runoff contribution from
discharge of Kamafusa Dam and Okura Dam to allow the model describe an
extraordinary event observed in August 1999 (Fig. 7). Other periods do not
consider such in the simulation.
Simulations for the 500m and 1000m grid size were developed with calibrated
values of the 250m grid size simulation. Model performance examination is made
for the period July 1999 to November 1999, to simplify the analysis avoiding at
this time the evaluation for winter season and the correspondent snow melt
contribution in spring.
15 km
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a Hirose River Natori Rive
0
50
100
150
200
250
300
350
0 5 10 15 20 25 30 35 40 45
Atitu
[ms
0 5 10 15 20
Table 1. Catchment and river network general characteristics for different resolutions
Contributing
Area
[km2]
Elevation[msl] Grid Slope[%] Stream
length [km]
Elevation [msl] Slope [%]
Max. Mean Max. Mean Total Max. Mean Max. Mean250 m grid size 1014.88 1470 327 79 13 82 250 41 4.0 0.3500 m grid size 984.25 1412 322 47 8 79 278 47 8.6 0.61000 m grid size 943.00 1386 324 27 5 70 300 55 8.2 1.0
Catchment characteristics River network characteristics
Figure 5. Longitudinal section profile in a) Hirose River and b) Natori River for different resolutions
Analysis of general characteristics of the catchment and main streams might be
useful to deepen the analysis of variations in discharge. The method used to create
low grid resolution inputs has direct effect in some variables as catchment area,
average and maximum elevation, and corresponding average and maximum slope
values (table 1). Expected effect in runoff response might be linked to a reduction
of total discharge as a consequence of catchment area reduction, besides a
decreasing effect in runoff velocity and for instance in peak times arrival. The
method used for deriving coarser grid maps has important effect when delineating
the stream network (Fig. 2, 3, 4), which length generally decreases. In the 1000m
grid size elevation and flow direction maps main rivers are more difficult to
Hirose river Natori river
Horizontal longitude [km]
Altitude[msl]
250mgrid500mgrid1000mgrid
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identify automatically and requires manual corrections which are applied only to
main network vicinity to avoid further deterioration of geographical features,
which cause effects shown in Figure 5. Elevation and slope values have a
tendency to increase, contrary to the effect observed by Jetten (2003) whichsupports his final conclusions. Errors related to re-location of required river
network may have influenced in the appreciations of elevation and slope values.
As stated later, slope reduction influence is not as expected, perhaps because the
grid size considered for the analysis is too big, or because an underestimation in
other streams of the network (e.g. Fig. 5, right).
0
100
200
300
400
500
600
700
1-
Aug
1-
Sep
1-
Oct
1-
Nov
DischargeQ(
m3/s)
Observed discharge Qi
Simulated discharge Pi, 250 m grid
Simulated discharge Pi, 500 m grid
Simulated discharge Pi, 1000 m grid
Aug-99 Sep-99 Oct-99 Nov-99
Figure 6. Simulated discharge at Yokata gauging station. Period: August 1999 to November 99
Table 2. Monthly average values of total discharge at the outlet of Yokata gauging station fordifferent resolutions
Jul 99-Nov 99 Jul Aug Sep Oct Nov
Total Mean To tal Mean To tal Mean To ta l Mean Total Mean To ta l Mean
Observed 5952.3 38.9 1648.6 53.2 1842.9 59.4 1347.7 44.9 686.8 22.2 426.3 14.2
Discharge [m3/s], 250 5353.9 35.0 1246.5 40.2 1363.2 44.0 1412.6 47.1 668.8 21.6 662.8 22.1
Discharge [m3/s], 500 5478.3 35.8 1175.3 37.9 1772.6 57.2 1291.8 43.1 588.5 19.0 650.1 21.7
Discharge [m3/s], 1000 2303.7 15.1 446.9 14.4 1704.6 27.9 314.9 10.5 123.3 4.0 151.7 5.1
Simulation results show a decreasing tendency of discharge estimation, except for
August 1999 where an extraordinary event occurred (Figure 2). The influence of
topographical features in model results can be supported when comparing total
and mean monthly values. Hessel (2005) works in a small catchment (3-5km 2)
with higher resolutions than those used in the current study, where effects cited are
observed; besides he establishes that the infiltration would also be beneficiated
since more time is available for the process. Although such effect is not studied in
detail here, infiltration contribution to baseflow does not seem to be important in
the 1000m grid simulation where is observed an important tendency to
underestimate total discharge.
Visual comparison between observed and simulated hydrographs can be made
(Fig. 6) together with statistical indices to further analyze time series behavior
(Table 3). The Pearson Moment Correlation coefficient PM, the Nash-Sutcliffe
Coefficient NS, the Index of Agreement IA and the Root Mean Square error
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RMSE are now considered. Values of PM, NS and IA indices close to one and/or
RMSE close to zero would mean time series coincidence.
[ ] [ ]
(4))(O
RMSE(3)][
)(-1
(2))()(-1NS(1)
)()(
))((
2
i
2
2
2
2
5.025.02
N
P
OOOP
POIA
OOPO
PPOO
PPOOPM
i
mimi
ii
mi
ii
mimi
mimi
=
+
=
=
=
where Oi is the observed value, P i the simulated value, and Om and Pm are the
average values.
Table 3. Statistical indices comparison of discharge simulated at Yokata gauging station for different
resolutions
PM NS IA PM NS IA PM NS IA PM NS IA PM NS IA
250m grid 0.675 0.334 0.669 0.967 0.548 0.752 0.936 0.848 0.951 0.948 0.783 0.915 0.780 -3.69 0.574
500m grid 0.335 0.005 0.500 0.477 0.136 0.653 0.549 0.268 0.723 0.261 -0.03 0.458 0.642 -4.87 0.527
1000m grid 0.427 -0.47 0.484 0.483 0.206 0.617 0.572 -0.39 0.481 0.278 -0.19 0.314 0.915 -4.05 0.462
Nov 99Jul 99 Aug 99 Sep 99 Oct 99
General performance of simulation for coarser grids tends to be towards
underestimating discharge. An exception is found when simulating the event of
August 1999, where the response to direct contribution from dams is more
notorious in larger grids for the peak observed. Despite such anomalies, the
simulation for the calibrated grid size has an overall description much closer than
the simulation results for coarser grids, as should have been expected.
Table 4. Maximum discharge and time to peak at Yokata gauging station for different resolutionsJul Aug Sep Oct Nov
Max.
discharge
[m3/s]
Time to
peak
[day]
Max.
discharge
[m3/s]
Time to
peak
[day]
Max.
discharge
[m3/s]
Time to
peak
[day]
Max.
discharge
[m3/s]
Time to
peak
[day]
Max.
discharge
[m3/s]
Time to
peak
[day]
Observed 183.8 12 672.2 14 178.1 15 205.9 28 28.1 no peak
250 m grid 110.0 12 224.4 14 176.3 15 130.7 28 35.8 no peak
500 m grid 106.9 13 519.5 15 162.9 16 120.2 29 39.0 no peak
1000 m grid 41.7 no peak 388.4 15 33.8 16 26.2 29 16.8 no peak
Peak discharge and time to peak follow the same direction than the ones analyzed
before. The coarsest grid simulation tends to have difficulties when describing
discharge peaks, with an exception in the case of August 1999. Both 500m and
1000m grid size simulations present delay in peak arrival. That could be explainedremembering what seen before, related mainly to the general tendency to
underestimate discharge perhaps because flow spread caused by the increasing
size of individual channels of every grid cell as grid size is increased.
5. Conclusions
Results show that the effect of grid size in distributed hydrological modeling has
the expected influence in model performance. Main characteristics observed lead
to establish that as the gird increases, discharge values decrease, and peak flow
estimations are every time more difficult to overcome. The affirmation of Shresta
(2006) respect to the need of more attention when working in smaller basins
seems to be evident.
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Jetten (2003) establishes additional factors to explain discharge decreasing
tendency as grid size resolution grows based on known practical facts referring to
the limitations of the kinematic wave theory and the kind of numerical methodapplied for its solution (Maidment, 1993). The author cites the effect that would
have the kinematic wave theory and the numerical method used for its solution in
flow routing description. Although no further analysis is shown at the time, his
affirmation should lead to further work to quantify the influence of kinematic
wave numerical solution in the simulation of total discharge values.
DEMs preparation should get special attention to overcome issues related to the
inaccurate description of catchments characteristics, as shown in the results of the
current where despite the overestimation of elevation and slopes values in the river
network discharge values remained below observed ones. Prediction in ungauged
basins may find in this point one of the main sources that leads to uncertainty in
hydrological response predictions, for which further work to overcome it isneeded. Meteorological input resolution is an additional issue where the minimum
requirements and the influence of the variations in the time step should also be
analyzed to contribute in the construction of the solution of this interesting field.
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