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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

[email protected]

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



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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Hessel R. Effects of grid cell size and time step length on simulation results of theLimburg soil erosion model (LISEM), Hydrol. Process. 19 (2005), pp. 30373049.

Jetten V., Govers G., Hessel1 R. Erosion models: quality of spatial predictions, Hydrol.Process. 17 (2003), pp. 887-900.

Kalin, L., Govindarajua R.S. and Hantush M.M. Effect of geomorphologic resolution onmodeling of runoff hydrograph and sedimentograph over small watersheds, Journal of

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modeling. J. of Hydrology 319 (2006), 36-50.Singh, V.P.. Computer Models of Watershed Hydrology. Water Resources Publications,

USA (1995), pp. 1-12.

Sivapalan M. Prediction in ungauged basins: a grand challenge for theoretical hydrology.

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2003 Annual conference, JSHWR (2003), 230-231.Woolhiser, D.A., Smith, R.E., Goodrich, D.C. KINEROSa kinematic runoff and erosion

model: documentation and user manual. US Department of Agriculture, AgriculturalResearch Service (1990), ARS-77, 130.

Yin Z-Y, Wang X. A cross-scale comparison of drainage basin characteristics derivedfrom digital elevation models. Earth Surface Processes and Landforms 24 (1999), pp.

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