Journal of Hydrology 319 (2006) 36–50
www.elsevier.com/locate/jhydrol

Input data resolution analysis for distributed hydrological modeling
Roshan Shresthaa,*, Yasuto Tachikawab, Kaoru TakarabaDepartment of Urban and Environmental Engineering, Graduate School of Engineering, Kyoto University, Kyoto, Japanb
Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan
Received 13 August 2003; revised 22 April 2005; accepted 28 April 2005

Abstract
A distributed hydrological model is often needed to analyze spatially variable hydrologic behavior. Such a model can bedifficult to set up, especially for an ungauged basin, as it demands a massive amount of data. Moreover, there is an additional
challenge of selecting a proper grid resolution as the grid size selection generally leads to predictive uncertainty and also
directly determines the amount of work required. In this study, a distributed macro-scale hydrological model, named as the
MaScOD model, is applied with a 10-min spatial resolution to the Huaihe River basin, China, to simulate discharge at Bengbu(132,350 km2) and at sub-basins at Wangjiaba (29,844 km2) and at Suiping (2093 km2). A range of input data resolutions areused, from 10 min to 2.58, based on an experimental hydro-meteorological input data set abstracted from the GAME re-analysis
data and the Hubex-IOP EEWB data. Performance of the model is evaluated by comparing observed discharge against
simulated discharge for a range of IC-ratio values (the ratio between the input forcing resolution and the Catchment area).
Similar results are obtained for all three catchments, despite their different sizes. It is found that improvement in distributedmodel performance is more pronounced below the IC-ratio 1:10, whereas the rate of improvement is negligible above the ICratio 1:20. The IC-ratio range 1:10–1:20 is found to be the optimum performance range considering the data and resource
demands of distributed models. This may provide a preliminary criterion for selecting the scale for distributed hydrologicalmodeling in ungauged basins.
q 2005 Elsevier Ltd All rights reserved.
Keywords: Input data resolution; Distributed hydrological modeling; Optimal model performance; IC-ratio; MaScOD model; Ungauged basins

1. Introduction
To fulfill the heavy demand for distributed data is amajor challenge in distributed hydrological modeling,* Corresponding author. Address: Fluvial and Marine Disaster
Research Division, Disaster Prevention Research Institute, Kyoto
University, Uji Campus, Gokasho, Uji, Kyoto 611-0011, Japan.
Tel.: C81 774 38 4127; fax: C81 774 38 4130.
E-mail address: roshan@rdp.dpri.kyoto-u.ac.jp (R. Shrestha).

0022-1694/$ - see front matter q 2005 Elsevier Ltd All rights reserved.
doi:10.1016/j.jhydrol.2005.04.025

despite the superior ability of such models to analyze
spatially variable hydrologic behavior and the impactsof natural and human activities on runoff (Refsgaard
and Abott, 1996). Ungauged basins present thegreatest challenge, as most ungauged basins havebasically no hydro-meteorological data other than thatfrom regional or global data sets obtained fromreanalysis of a limited number of observations using a
General Circulation Model (GCM) or a mesoscale numerical weather prediction model. Regional

R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

hydro-meteorological data, such as GAME-IOP 1.258
reanalysis data which covers the Asian Monsoon
region (JMA, 2000), and HUBEX-IOP EEWB 5-mindata which covers the Huaihe Basin in China (Kozan
et al., 2001), can help compensate for the absence ofground-based hydrological instrumentation. However, the limitations of regional datasets may severely
limit the accuracy in the hydrological simulation.
Obtaining satisfactory results by using regional
datasets depends on the resolution of the dataset andcatchment scale because current regional datasets areoften too coarse (Burlando and Rosso, 2002), they
may not be adequate, in the case of small-scalehydrological modeling, to describe the variability inhydrologic process components at the basin scale. To
understand the hydrologic predictive uncertainty
associated with the gap between the need and theavailability of input data for distributed hydrologicalmodeling will provide guidance in setting up an
appropriate hydrological modeling framework and on
the selection of an appropriate data scale.
There is a choice to make regarding the required
resolution of hydro-meteorological input data. The
resolution of input data has a direct link with themodeling resolution in distributed hydrologicalmodeling, since the model’s resolution is often set
equal to or finer than the input data. The grid cell size
selection will generally lead to predictive uncertainty
and the challenge is to determine a scale above which
spatial variability can be neglected, with averagecharacteristics of a given area providing sufficient
information for accurate modeling of basin runoff(Sivapalan and Kalma, 1995; Blöschl and Sivapalan,
1995; Molnar and Julien, 2000). Coarser resolutionhydro-meteorological datasets, such as outputs fromcurrently available atmospheric models (which may
extend to hundreds of kilometers) do not satisfy theneed of hydrologists. Also, there are serious scaleissues within hydrological analysis (Koren et al.,1999) and within meteorological analysis (Renssen
et al., 2001), and these problems are essentiallymismatched. The scaling issue assumes an evengreater significance when developing regional or
global hydrology models (Singh and Woolhiser,
2002) or in continental scale catchment modeling.
The discrepancy in scale between meteorologicalmodels and hydrologic models will continue until
reliable criteria emerge to provide guidance on

37

the optimal scale for investigating hydrologicalprocesses.
The scale and resolution issues are raised here witha view to finding if there is a certain preferred orconsensus scale of input data at which optimal
performance may be feasible in distributed hydrologic
modeling. Several researchers have investigated scaleand resolution issues for distributed hydrologic
modeling. For example, Bathurst’s (1986) suggestion
to divide the watershed into elements no larger than
1% of the total area was a conclusion from his study
on the Wye watershed (10.55 km2) using the SHEmodel, to ensure that each grid element was more orless homogeneous. Introducing the concept of arepresentative elementary area (REA), Wood et al.
(1988) found that an REA of approximately 1 km2
existed for the hydrologic response of the Coweeta
watershed. The size of REA was more strongly
influenced by basin topography than by rainfall lengthscales (Woods et al., 1995) and its limited utility are
discussed by Fan and Bras (1995). Zhang andMontgomery (1994) proposed a 10 m grid size as acompromise between increasing spatial resolution anddata handling requirements by examining the effect ofdigital elevation model grid size on the portrayal of
the land surface and hydrological simulations.
Bruneau et al. (1995) suggested an optimum region
for modeling with a grid size of 50 m after analyzing
the effect of space and time resolutions using
TOPMODEL on the Coetdan Experimental watershed(12 km2), in France. The simple scaling and multiscaling framework (Gupta et al., 1994), the HRU(Hydrological Response Units) concept (Flügel,1995), and the basin-scale model equations (Kavvas
et al., 1998) provide understanding of scaling effects
in distributed hydrologic modeling. Other research
focusing on the effects of grid size on model
parameters and hydrologic response include Quinn
and Beven (1991), Franchini et al. (1996), Saulnier
et al. (1997), Sunada et al. (2001), Horritt and Bates(2001), and Shrestha et al. (2002). However, despite
these efforts, a suitable resolution for distributedhydrological modeling is still difficult to establish.
Selecting a higher resolution in distributed hydrological modeling brings with it heavy tasks of dataacquisition, defining the model parameter values, andcomplex calculations. These tasks increase the cost ofmodeling. In addition, higher resolution increases

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R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

the risk of insistent error amplification. On the other
hand, selecting a lower resolution greatly reduces theworkload but risks losing the advantage of the
distributed modeling approach, leading to poor results
due to lack of consideration of important spatial
features. Therefore, a choice of appropriate scale isprominently needed to attain optimum model performance. We consider that the first step in thisprocess is the selection of an appropriate input data
resolution. Knowledge of the effect of forcing input
scale is important for both hydrological and meteorological studies. Ability to choose an adequate input
resolution at the preliminary investigation stage will
result in an appropriate modeling framework, withfewer problems later and higher simulation accuracy.
In this paper, a criterion for selection of an
appropriate input data resolution is expressed interms of the IC-ratio (the ratio between the model
input spatial resolution and the area of the catchment;
Shrestha et al., 2002), based on the sensitivity of a
distributed hydrological model’s performance to thescale of an experimental hydro-meteorological input
dataset based on GAME-IOP reanalysis data and
HUBEX-IOP EEWB data. Applying the MaScOD(Macro-Scale OHyMoS assisted Distributed) hydrological model with a fixed 10-min model resolution,
the study is conducted on the Huaihe River Basin,
China, by simulating the hydrographs at Bengbu,
Wangjiaba and Suiping (having contributing areas of
132,350; 29,844 and 2093 km2, respectively) for
various spatial input data resolutions, from 10 min
to 2.58. In Section 2, the MaScOD macro-scale
distributed hydrological model is described. Section
3 deals with the hydro-meteorological input data usedin this study, and the discharge simulation results are
given in Section 4. Section 5 provides an analysis of
the results in terms of the IC-ratio. In Section 6, theselection of an appropriate input data grid resolution(in the context of a proposed IC-ratio Rule) is
discussed, and conclusions are presented in Section 7.

2. The MaScOD macro-scale distributedhydrological modelbasin partitioning, hydrological process modeling for a
sub-basin, linking sub-basin models together to make atotal runoff model, and processing channel network
linkages to incorporate river flow routing, into an
automatic procedure (Tachikawa et al., 2002) with theassistance of an object oriented hydrological modelingsystem—OHyMoS (Takasao et al., 1996; Ichikawa
et al., 2000). The “Macro-Scale OHyMoS assisted
distributed hydrological model” (referred to hereafter as
the MaScOD model) is developed accordingly, and isbriefly presented here.
The MaScOD model subdivides a watershed basin
into grid-cells according to a defined grid system that
also facilitates the direct input of hydro-meteorological data from a meso-scale atmospheric model. Thismodel considers the exact location and linkage ofriver segments within grid-cells to give better flowrouting, resulting in a better simulation of thedischarge hydrograph. An automated procedure rearranges the vector river networks (Fig. 1) by dividing
up grid cell frames into separate sub-network
elements and re-assigning new identities.
The MaScOD model consists of a MaScOD
Element Model (MEM) on every grid cell. The total
number of MEMs for the entire catchment depends on
the size of the catchment, and the grid cell resolution(which is fixed at 10-min in this study). Each MEM,
having a river segment inside the grid cell, contains arunoff process model (RPM), based on the Xinanjiang
model (Zhao, 1992), and a flow routing model (FRM)
based on the lumped stream kinematic-wave equation(Shiiba et al., 1996). The MEM can have multiple
numbers of RPM inside the same grid cell when thegrid cell contains multiple river segments. The total
number of MEM constituents (the RPM and FRM) is
determined on the basis of the river network rearrangement procedure. Each RPM receives input
from its own sub-catchment, i.e. from the fraction of
the grid cell defined as the proportion of the length of
the RPM’s river segment to the total length of riversegments inside the grid cell. The RPM yields runoff
directly from impervious area and from groundwater
storage (Fig. 2). This is given by
R Z Qi C kg S2gMacro-scale hydrological modeling is often practiced for a large river basins. It is possible to incorporate
preliminary tasks involved in the modeling, such as(1)

where R is the runoff; Qi is the discharge fromimpervious area; kg is the yield parameter; and Sg is

R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

39

Fig. 1. River networks inside the study region, Huaihe River Basin, China.

the groundwater storage. The Qi is given by
Qi Z Ai ðP K EÞ

(2)where Ai is the impervious proportion of a basin; P is
the precipitation; and E is the evapo-transpiration.
The groundwater storage Sg is continuously updated
by the discharge from the pervious portion Qp, which
occurs after the soil water storage capacity is
exceeded:
Qp Z ðP K EÞð1 K Ai Þ K Wm C W;
when im % i0 C P K E

water depth; and Wm is the maximum storage depth
over the basin expressed as
Wm Z

imð1 K Ai Þ
1 Cb

The soil water depth i is given by8 1=b 
<i
im 1 K AKA
when Ai % A% 1:0
1KAiiðAÞ Z:0when 0% A% Ai
(6)

(3)

If
im R i0 C P K E;

then Qp

Z ðP K EÞð1 K Ai Þ K Wm C W

i C P K E 1Cb
C Wm 1 K 0
im(4)

where W is the current soil water depth that
contributes to evapo-transpiration; i0 is current water
depth in the unsaturated zone;, im is the maximum soil

(5)

Fig. 2. Schematic of the runoff process model (RPM).

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R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

where A is the fraction (in the range 0–1) of a subbasin that contributes to a particular segment of theriver; and b is a model parameter that depends upon
the shape of the soil water storage capacity
distribution.
The FRM models flow routing along the river
network. This is given by
Qj ðx; tÞ Z Qj ð0; tÞ C q0 ðtÞx(7)

where Qj(x,t) is the jth segment discharge at distance x
from an upper end; Qj(0,t) is the inflow at the upper
end of the drainage segment; and q0(t) is the discharge
flux rate in space along a drainage segment, as givenby the RPM. The RPM and the FRM are connected
through a data-sending port (DSP) and a datareceiving port (DRP) (Fig. 3). The FRM computes
discharges from the MEM outlets. To reduce thecomputational burden, it assumes that the dischargevaries linearly along each river segment at each time
step instead of computing that for each computationalcross-section within the grid-cell (Shiiba et al., 1996).
The functions of the DSP and DRP are to exchange
computed data (Fig. 4) within each grid-cell andbetween the MEMs. Inside the MEM, the DRP feeds
grid-cell-mean input data (such as precipitation andevapo-transpiration averaged over each grid-cell) to
the RPM, which produces runoff from the grid-cell.
The DSP feeds that value into the FRM. The FRM
receives information through its DRP from the RPMof the same grid and the adjacent MEMs of upstream
grids in order to provide the discharge to thedownstream MEMs. The accumulated values aretransferred to the downstream MEMs only after
calculations for all upstream MEMs are completed.

Fig. 3. Schematic of the flow routing model (FRM).

Fig. 4. Structure of the MaScOD element model (MEM).

The flow path of the river network is linked to provide
a total runoff simulation model that is a combinationof MEMs (Fig. 5).
The RPM in the MaScOD model considers the soil
properties and interacts with the FRM in terms oflateral flow. The FRM considers topographic attributes such as channel slope using kinematic wave
routing. Piecewise connectivity of the flow networkand the calculation sequence from upstream todownstream help reduce bias.
The discharge simulation is conducted in HuaiheRiver Basin (270,000 km2). The Huaihe River, one of
the China’s major rivers, runs for about 1000 km
between the Yellow and Yangtze Rivers, throughHenan, Anhui, Jiangsu, and Shandong provinces.

Fig. 5. Schematic of total system.

R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

Fig. 6. Locations of discharge observation points.

This region is home to a population of about 165
million and frequently undergoes disastrous flooding.
The MaScOD model parameters were calibrated on
the basis of field observation records in the Shiguan
River Basin (6000 km2), a sub-basin of the HuaiheRiver Basin, which is assumed to be representative of
the physiographical characteristics of the entire basin.
The hydro-meteorological data obtained from 48
rainfall stations, five discharge stations and four pan
evaporation stations inside the basin were utilized tocalibrate the model. The model parameters calibrated
for the Shiguan River basin were subsequently
assigned to the entire study area, the basic assumption
being that the similar regions should have similarparameter values. Separate parameter sets were
calibrated for mountainous and flat regions. Topographic maps were used to identify similar regions
before the calibrated parameters were assigned. The
details of the calibration process are described by
Tachikawa et al. (2001).
In this study, simulation results are compared withthe observed discharges at Suiping, Wangjiaba andBengbu (Fig. 6), the corresponding contributing areas
being 2093; 29,844; and 132,350 km2, respectively.

3. Experimental hydro-meteorological input data
3.1. Input data source
Grid precipitation and grid actual evapo-transpiration data, for the period of May 1st, 1998 to August

41

31st, 1998 are the forcing input data to thehydrological model. Experimental forcing data werecreated from two data sets, namely the HUBEX-IOP
EEWB dataset and the GAME re-analysis dataset.
The HUBEX-IOP EEWB data (abbreviated from the“Huaihe River Basin Experiment—Intensive observation period—Estimation of Energy and Water
Budget” termed ‘EEWB data’ here-after) have
5-min spatial resolution and 1-h temporal resolution(Kozan et al., 2001). The precipitation field of the
EEWB data is generated from ground-based observation using a time and space interpolation technique.
The evapo-transpiration field is the output of a simple
biosphere with urban canopy (SIBUC) model(Tanaka, 1998). In an earlier study, the EEWB data
did not produce good results for discharge simulationin the Bengbu basin (Tachikawa et al., 2002), thelargest basin of this study, while the results for thesmaller sub-basins were good.
The GAME (GEWEX Asia Monsoon Experiment)
Re-analysis data (Version 1.1) with 1.25-degree
spatial and 6-h time resolutions (termed as “GAME
data” here-after) is another data set used in thisexperiment (JMA 2000). These data were produced
using a 4DDA system in a co-operative study of theJapan Meteorological Agency (JMA), and the Earth
Observation Research Center (EORC), NASDA.
Using the GAME data, the river discharges in thethree study basins were successfully simulated by
Shrestha et al. (2002), which yielded a better
simulation result than the EEWB data used by
Tachikawa et al. (2002) for the large basin but did
not yield a better simulation result for the smaller two
sub-basins.
3.2. Generation of experimental forcing data
Possible errors in the magnitude of the EEWB data,
especially in the evapo-transpiration field over the
grid-cell system, may be one of the reasons behind thesimulation error for the large basin. The coarser
resolution of the GAME data was suspected to be thedominant reason for simulation error in the two
smaller basins (this is proved true by the resultspresented in this paper). Hence, an alternate data set isneeded to investigate the effect of forcing data
resolution, one that overcomes the weaknesses ofboth of the two available data sets. To acquire an

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R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

experimental data set with a 10-min spatial resolution,
the GAME data are converted according to the spatial
pattern of the EEWB data such that the resulting
experimental 10-min data set preserves the spatial
pattern of the EEWB data and the magnitudes of the
precipitation and evapo-transpiration of the GAME
data. The reason behind adopting the spatial pattern of
the EEWB data is that the EEWB data are basicallyground-based data, which take into account both the
distance and the direction of each ground observation
station. Also, the EEWB data are the finest resolution
data among the available distributed data for the study
basin. Therefore, these data are assumed to represent
the spatial pattern better than any other data. The
reason behind adopting the magnitudes of the
precipitation and evapo-transpiration of the GAME
data is that they have produced a good fit of theobserved basin-scale discharge, showing their better
accuracy in describing the water balance (Shrestha
et al., 2002). The temporal scale (6-h time resolution)of the GAME data is adopted for the experimental
data.
Various methods may be adapted to transfer the
spatial pattern from one data set to another, in thiscase from EEWB to GAME data. The spatial patternof the precipitation and evapo-transpiration of the
EEWB data is considered in terms of a fluctuationfrom its mean value over the corresponding spatial
domain of a single grid cell of the GAME data, as
shown in Eqs. (8) and (9):

(
P4j Z

P1j C P2j K P3j

if ðP1j C P2j K P3j ÞR 00otherwise

For time j Z 1; 2; 3; .; mP
P1j
P5j Z P4j P
P4j

For time j Z 1; 2; 3; .; m

ð8Þ

(9)

Here, the P4j are intermediate newly createdexperimental 10-min data. The P1j are the GAME
1.25-degree data; the P2j are the EEWB 10 min data;
and the P3j are the average of EEWB 10-min data at
1.25-degree resolution, all of them have the same unitof intensity per unit area. Sometimes, the P4j values
may appear negative, but are forced by Eq. (8) tobecome zero. The accumulated value of the experimental data inside the catchment frequently appears
to be slightly different from the accumulated value ofthe original GAME1.25 data due to forcing thenegative P4j values to become zero. Hence, in Eq.
(9), a scaling factor of the ratio between the new
accumulated value and the accumulated value of theoriginal GAME1.25 data is applied to all the P4j data
value to ensure that the total accumulated input of P5j
values is the same as that of the original GAME1.25
data. Thus the P5j are the final experimental input data
(Fig. 7). Fig. 7 also shows a typical spatial pattern of
rainfall intensity for the 1.25-degree GAME reanalysis data. It can be seen that the rainfall intensities forthe experimental 10-min dataset are higher and more

Fig. 7. Typical example of spatial patterns of experimental data (P5j) and GAME1.25 data (P1j).

R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

43

Table 1Comparison of performance indices using different forcing data
Pearson MC coeff.

Suiping
Wangjiaba
BengbuAverage

Nash Sutcliffe coeff.

Index of agreement

E

G

Exp

E

G

Exp

E

G

Exp

0.727
0.911
0.677
0.772

0.456
0.761
0.729
0.648

0.722
0.881
0.759
0.787

0.516
0.635
K0.031
0.373

0.190
0.465
0.433
0.363

0.493
0.693
0.441
0.543

0.828
0.893
0.692
0.804

0.582
0.802
0.851
0.745

0.835
0.931
0.866
0.877

Note: E: EEWB 10-min data; G: GAME 1.25-deg data; Exp: experimental data.

localized. The hydrologic response of a small
catchment to these two rainfall fields will be different,
as demonstrated later in this paper.
The experimental 10-min data set is used further tocreate 20-min, and 30-min data sets, etc., by passing aspatially averaging window of (2!2), (3!3), etc., up
to 150-min (2.5-degrees), respectively. The total
accumulated value of the input data is kept constant.

4. Discharge simulation results
The experimental data and the EEWB data, both of
10-min spatial resolution, and the GAME 1.25-degree
were fed into the MaScOD model to simulatedischarge in all three-study basins: Suiping(2093 km2), Wangjiaba (29,844 km2) and Bengbu(132,350 km2). Four performance indices (a) the
Pearson moment correlation coefficient (PMC), (b)the Nash-Sutcliffe coefficient of efficiency (NSI)(Nash and Sutcliffe, 1970), (c) the Index of agreement(IOA) (Willmott, 1981) and (d) root mean square error(RMSE) were used to evaluate the model performances by comparing the simulated and observed
discharges. Eqs (10)–(13) describe the evaluation
criteriaPN
iZ1 ðOi K OÞðPiPÞPMC Z P
PN
0:5
N
2

 2 0:5iZ1 ðOi K OÞ
iZ1 ðPi K PÞsﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
PN2
iZ1 ðOi K Pi Þ
RMSE ZN(13)

Here, Oi represents observed value at the ith time;
Pi represents simulated value at the ith time; N is thetotal number of observations/simulations; O and P are
the mean values of Oi and Pi, respectively. The best
condition is that Eqs. (10)–(12) yield a value of unity,
and that the RMSE is zero.
In terms of the IOA values shown in Table 1, thesimulation results from the experimental (P5j) data arefound to be better than the corresponding results fromboth the original EEWB and GAME data sets for all
three basins (Tachikawa et al., 2002; Shrestha et al.,2002). The NSI and PMC results were also quitefavorable. The experimental data are then used as thebase-line data and to prepare the input data of various
resolutions.
The hydrograph of simulated discharge changes as
the input data resolution changes (Fig. 8). Coarser
resolution input data, which is just a set of spatiallyaveraged values, yielded different simulation results(10)
PNðOi K Pi Þ2
NSI Z 1:0 K PiZ1N 2iZ1 ðOi K OÞ
PN
IOA Z 1:0 K PN

iZ1 ðOi K Pi Þ

(11)
2


 2
iZ1 ðjPi K Oj C jOi K OjÞ(12)Fig. 8. Simulated hydrographs at Bengbu (132,350 km2) obtained
from various input data resolutions.

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R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

than finer resolution input data in all three basins. Thisis solely due to the effect of spatial variability.
Overlapping simulation results obtained fromvarious input data resolutions, yields a band of
simulated hydrographs. Wide bands of simulatedhydrographs (Fig. 9) show that there is high sensitivity
to input data resolution in all three study catchments.
The hydrograph obtained from the finest resolution
input data is closest to the observed hydrograph forthe smallest catchment (Fig. 9(a)); however, for thelarger catchments (Fig. 9(b) and (c)), the hydrographs
obtained from the finest resolution input data are not
the best ones.
Fig. 10 shows accumulated discharge for the threestudy catchments. The bandwidth of accumulated
discharge diverges more in the case of the smallerbasin than for the larger basins, which might be due
to a lower capacity of the smaller basin to store
soil-water within the catchment compared to that of
the larger basins. Despite the presence of significant

Fig. 9. The simulation band for hydrographs at (a) Suiping(2093 km2 ), (b) Wangjiaba (29,844 km2 ), and (c) Bengbu(132,350 km2) produced by overlapping the hydrographs obtained
from different resolutions of input data yields. It can be seen that thefinest resolution data is not necessarily the best.

Fig. 10. Cumulative runoff for various input data resolutions (a) at
Suiping (2093 km2 (b) at Bengbu (132,350 km2); the smallercatchment has the larger difference in accumulated discharge.

R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

45

mismatches between the simulated and observedhydrograph (Fig. 8), the accumulated values of thesimulated and observed discharge at Bengbu(Fig. 10(b)) match well. This indicates that themodel has preserved the basin outflow volumes. The
mismatch in hydrographs and good match inaccumulated discharge could have occurred due tochanges in the runoff processes induced by humanactivities, e.g. irrigating large paddy fields or flow
regulation at the hydraulic control structures andreservoirs that exist within the study basins.
The effects of forcing input data resolution on the
distributed hydrological modeling are shown in
Fig. 11. In which, the discharges simulated by various
resolution input data are compared with the discharge
simulation by 10-min resolution. Using coarse
resolution input data can give very different runoff
to that obtained using fine resolution input data,
especially for the smallest catchment. The hydrographpeaks are particularly affected. This shows that
resolution issues need more careful consideration inhigh flow simulation than in low flow simulation.

5. Model performance in terms of the IC-ratio

Fig. 11. Deviation of simulated discharge due to change inresolution of input data (a) at Suiping (2,093 km2), (b) at Wangjiaba(29,844 km2), (c) at Bengbu (132,350 km2).

The components of flow processes, being functionsof the detailed geometry of flow pathways in different
catchments, are difficult to compare (Beven, 2002).
Some indices, for example average slope, flow
lengths, watershed relief, etc. represent various
catchment features but they may not be suitable fortesting against forcing data resolutions and scaleissues over different catchments since these values arehighly variable from one catchment to another. A
wide range of responses may be obtained when using
these indices to investigate scale issues. Size ofcatchment is probably the only absolute statistic
providing consistent information and a sound basis forinvestigating suitable resolution for hydrologic modeling. The ratio of the input forcing resolution tocatchment size, called the IC-ratio (Shrestha et al.,2002), may therefore prove to be a useful index forinvestigating the effects of input data resolution ondischarge.
The finest spatial resolution adopted in thisexperiment is 10-min (approximately 13.5 km ineach direction at 338N, or 175 km2). The input data

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R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

for the Suiping basin (2093 km2) varies from 10-min
to 2.5-degree resolution. Therefore, the IC-ratio value
ranges from about 1:12 to 1:0.05. Model performanceis found to be consistently better at 1:12 than near
1:0.05. The convention of the ratio is to keep thenumerator equal to one, such that a higher denominator value (called a higher IC-ratio) corresponds tofiner resolution and a lower denominator value (calleda lower IC-ratio) corresponds to a coarser resolutionof input for a given catchment. The IC-ratio values for
the Wangjiaba basin (29,844 km2) and the Bengbu
basin (132,350 km2) vary from 1:168 to 1:0.75 and1:745 to 1:3.3, respectively, within the framework ofthis experiment.
Concise information on the changes in the model
performance in response to the altered resolution offorcing data can be represented, as in Fig. 12, using
the IC-ratio index. This facilitates the comparison of
the responses at various scales of catchment size. In
this figure, the Pearson moment correlation coefficient(the PMC of Eq. (3)) between the observed andsimulated hydrographs is used as the performanceindex. The figure shows that the smallest basin(Suiping) has higher sensitivity in response to theforcing data resolution, as the steepness of theperformance versus IC-ratio curve is highest for thatcase. A similar sensitivity is displayed in Fig. 11. In
the small basin, the simulation results deteriorate
faster as the input resolution becomes coarser. Model
performance improvement with finer resolution input

Fig. 13. Model performance versus IC-ratio for four indices.

data has a tendency to level off. At the higher IC-ratio
values, the improvement rates of the model performances are not very significant.
The four model performance indices are evaluatedand plotted against the IC-ratio in Fig. 13. Since the
IC-ratio is a dimensionless number, the performanceindices in Fig. 13 are not separated for different basins
but are plotted as an overall trend line for each index.
The Pearson moment correlation coefficient, the Nash
Sutcliffe coefficients and the index of agreement all
follow similar trend lines, which indicate a faster rateof performance improvement in the lower IC-ratio
range. As the IC-ratio increases, the rate of
improvement in performance gradually reduces andthe value of model performance indicator levels off toa constant value. In contrast, the trend of the RMSE
followed a converging path toward constant values atboth ends of the IC-ratio range. The results obtained inthis experiment are satisfactory while the IC-ratio
remains above 1:10. All the performance indices arefound to level off above the IC-ratio 1:20 and theperformance improvement beyond that are likewise
un-attractive. Poorer performance index values below
the IC-ratio 1:10 suggest that if there are less than 10
input grid cells over the basin, the distributed model
does not yield good results. This is more critical in thecase of smaller basins.

6. Selection of input grid resolution

Fig. 12. Model performances versus IC-ratio for the threecatchments.

Although most modelers are well aware that an
appropriate resolution of input data may differ from anappropriate resolution of model disaggregation, it isR. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

generally preferred, for convenience in the simulation
exercise, to keep the input data grid resolution thesame as that of the grid resolution of the model. In
numerical modeling, a finer-resolution model can
accept a coarser-resolution input data by splitting up
the input data in proportion to the grid size of themodel. However, a coarser-resolution model cannot
be easily devised to take a finer-resolution input data
without losing the data properties. This limitation
becomes a dictating factor in selecting the modelingframework while the needed input resolution is finer
than the resolution opted for the distributed hydrological modeling.
A finer-resolution input data is preferred for its
better description of spatial variability. It may be
impractical effort to include every details of input
field in catchment-scale modeling, especially in thecase of large and scarce-information catchments. This
leads to the option of looking for a homogenous area,
which may still preserve the representative characteristics of the larger heterogeneous input data field.
However, this introduces a confusion relating to thescaling problem because it is not easy to predict thelargest input resolution that is capable of preserving
the average hydrologic response characteristics of thelarge regional heterogeneity of the input data field.
The results obtained in this study indicate that,while the response to input resolution change is not
same in all basins, they are however quite similar thatthe size of the largest homogenous region of input
data field depends upon the catchments size. Looking
toward a higher degree of input disaggregation, there
is initially a tendency to yield better results always,
but too much disaggregation fails to improve theperformance much. With respect to a further increase
in resolution, little improvement can be achieved once
it crosses the resolution corresponding to the IC-ratio
1:20. For example, the model performance is almost
the same at ratios 1:20 and 1:200, but the later caseneeds to bear the cost of having to acquire highresolution data. The slight improvement in results
obtained by using higher resolution data is usuallysuch as to discourage choosing a high-resolution data.
The characteristic relationship between model
performance and scale is represented qualitatively
by the performance curve in Fig. 14. The relationshipbetween the cost and scale in Fig. 14 is difficult todetermine mainly because the conditions of one basin

47

Fig. 14. Trade-off between model performance and model cost withrespect to scale in terms of the IC-ratio.

differ from those of another. However, the cost is
likely to increase geometrically upon for an arithmetic
increase in resolution. The cost curve shown in Fig. 14
indicates the higher cost associated with finer
resolution scales (or higher IC-ratio). Even though aquantitative cost analysis is not conducted in thisstudy, the optimum performance range can beappreciated simply by observing the performanceversus IC-ratio curve in Fig. 13, bearing in mind thecost considerations shown in Fig. 14
In an un-gauged basin, where a hydrologist needs tostart work from a very low base-line, a lot of unknowns
are expected to be encountered in the process of setting
up the hydrological model. The needs for spatiallydistributed data with sufficient accuracy and resolution
scale, as demanded by a distributed hydrologic model,
hinders the modeler right from the start of the exercise.
Being able to select an appropriate input data
resolution, as a function of the catchment area interms of IC-ratio, may help designing the modelingwork. A useful range of IC-ratio values that provides asatisfactory simulation result is noticed to be within
1:10 to 1:20. Larger catchments may be modeled
successfully at coarser scale by representing its larger
heterogeneous input data field as homogenous units but
smaller catchments need finer scales, which the ICratio tends to quantify. Model sensitivity to thediscretization scales of input data exists up to an
upper limit of the IC-ratio with constant parametervalues for the selected hydrological/routing model
structure. This distinction is likely to be very useful insetting up a model framework for an ungauged basin.

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R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

The model resolution was kept constant at 10-min
for this study, in order to consider the effects of input
data resolution in isolation from other modelingissues. While a resolution of 10-min is required tomodel the smallest catchment considered here, theeffort required to set up a distributed model at thisresolution may not be justified for larger catchments,
particularly if an input data resolution coarser than 10min is selected based on the proposed IC-ratio rule. If
this is the case, and provided that the river networkand hydrological processes can be adequately modeled at the coarser resolution, the hydrologicalmodel’s spatial resolution could be chosen to matchthe resolution of the hydro-meteorological input data.

7. Conclusions
The performance of a macro-scale distributedhydrological model depends upon the quality of themodel, the selected model parameters, and the qualityof the input data. The quality of the input data set isassociated with accuracy and resolution issues. The
ratio of input data resolution to the catchment area,
called the IC-ratio (Shrestha et al., 2002), can serve asa useful index to evaluate the suitability of data andchoose a model resolution for distributed hydrologicalmodeling.
In this study, three catchments, ranging from small(2093 km2) to large (132,350 km2) size, were used toinvestigate the effects of data resolution on the
discharge simulation results. The two smaller catchments were found to be more sensitive to data
resolution than the larger one, indicating that
resolution issues need more attention for smallerbasins, and that model performance depends upon the
input data resolution. However, demanding very highresolution data is not a sensible or practical solution in
response to this. The minimum amount of input data,
the minimum number of parameters, and theminimum computational load which produce reasonable simulation results, make the distributed hydrological model easier to apply and more cost-effective.
We find that an IC-ratio of 1:10–1:20 gives overall
optimum performance of a macro-scale distributedhydrological model, bearing in mind the effort
required to process high resolution data for an
ungauged basin. An IC ratio in this range gives

a sensible balance of accuracy, cost, time, andcomplexity.
Our recommendation of an IC ratio in the range of
1:10–1:20 implies that the distributed modeler should
obtain hydro-meteorological input data at a scale
such that about 10–20 pixels are sufficient to cover
the catchment. We certainly would not recommend
an IC ratio of less than 1:6, i.e. using less than six
input data pixels to model a catchment. This has
implications for the minimum size of ungauged
catchment that can be successfully modeled by a
distributed model. The finest spatial resolution ofhydro-meteorological input data that was obtained
for this study was 10-min data, giving a pixel
covering approximately 175 km2 at 338N. Thisrequired a substantial amount of processing andcross-checking of the quality of the data, based on
both the 1.258 GAME-IOP reanalysis dataset thatcovers the Asian Monsoon region (JMA 2000), andthe poorer-quality 5-min HUBEX-IOP EEWB dataset that covers the Huaihe River Basin in China(Kozan et al., 2001). Thus good quality regionalhydro-meteorological datasets at resolutions of 10min or finer are difficult to obtain. This, along with
our recommended range for the IC-ratio, implies thatthe use of hydro-meteorological datasets to model
ungauged catchments may be difficult for catchments
much smaller than 1700 km2. The ease with whichappropriate data can be obtained improves as thecatchment size increases. However, future improvements in resolution and accuracy of the outputs of theatmospheric models used for regional data reanalysis
will improve this situation.
In our effort to establish a preliminary data
resolution criterion (i.e. the proposed IC-ratio Rule)for modeling an ungauged basin, which would
indicate at least an approximation of the datarequirements, and to highlight the necessity ofconsidering catchment area for setting an objective
grid resolution of re-analyzed data at the regional
scale, we focused in this study on the trade-off
between data density and the efforts needed inhydrological modeling. We appreciate that our casefor the IC-ratio Rule could be strengthened andrefined by considering more sub-basins of the HuaiheRiver basin and also that the applicability of the rule
could usefully be tested using a gauged sub-basin as

R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

a control. It is our intention to address these
considerations in a later phase of this research.
Acknowledgements
The contribution of the HUBEX-IOP EEWB data
by Dr K. Tanaka, DPRI, Kyoto University and of the
GAME Re-analysis data by the Japan Meteorological
Agency is sincerely acknowledged. We are grateful toProf. M. Shiiba and to Dr Y. Ichikawa for providing uswith the OHyMoS library source codes and to Dr
Timothy Harrold for providing helpful comments. We
also acknowledge two anonymous reviewers, whosesuggestions have improved the paper.
References
Bathurst, J.C., 1986. Physically based distributed modeling of
upland catchment using the Systeme Hydrologique Europeen.
Journal of Hydrology 87, 79–123.
Beven, K., 2002. Towards an alternative blueprint for a physically
based digitally simulated hydrologic response modeling system.
Hydrological Processes 16, 189–206.
Blöschl, G., Sivapalan, M., 1995. Scale issues in hydrologicalmodeling: a review. Hydrological Processes 9, 251–290.
Bruneau, P., Gascuel-Odoux, C., Robin, P., Merot, P., Beven, K.,
1995. Sensitivity to space and time resolution of a hydrologicalmodel using digital elevation data. Hydrological Processes 9,
69–81.
Burlando, P., Rosso, R., 2002. Effects of transient climate change on
basin hydrology. Hydrological Processes 16, 1151–1175.
Fan, Y., Bras, R.L., 1995. On the concept of a representative
elementary area in catchment runoff. Hydrological Processes 9,
821–832.
Flügel, W.A., 1995. Delineating hydrological response units bygeographical information system analyses for regional hydrological modeling using PRMS/MMS in the drainage basin of theriver BRÖL, Germany. In: Kalma, J.D., Sivapalan, M. (Eds.),
Scale Issues in Hydrological Modelling. Wiley, England,
pp. 181–194.
Franchini, M., Wendling, J., Obled, Ch., Todini, E., 1996. Physicalinterpretation and sensitivity analysis of the TOPMODEL.
Journal of Hydrology 175, 293–338.
Gupta, V.K., Mesa, O.J., Dawdy, D.R., 1994. Multiscaling theory offlood peaks: regional quantile analysis. Water Resource
Research 30, 3405–3421.
Horritt, M.S., Bates, P.D., 2001. Effects of spatial resolution on araster based model of flood flow. Journal of Hydrology 253,
239–249.
Ichikawa, Y., Shiiba, M., Tachikawa, Y., Takara, K., 2000. Object
oriented hydrological modeling system. The Fourth International Conference on HydroInformatics CD-ROM. Cedar
Rapids, Iowa.

49

Japan Meteorological Agency (JMA), 2000. GAME-IOP Reanalysis Data (Version 1.1), downloading site ftp://hydro.iis.utokyo.ac.jp/GAME/GAIN/GAME-REANL/
Kavvas, M.L., Chen, Z.Q., Tan, L., Soong, S.-T., Terakawa, A.,
Yoshitani, J., Fukami, K., 1998. A regional-scale land surface
parameterization based on areally-averaged hydrological conservation equations. Hydrological Sciences Journal 43 (4),611–631.
Koren, V.I., Finnerty, B.D., Schaake, J.C., Smith, M.B., Seo, D.-J.,
Duan, Q.-Y., 1999. Scale dependencies of hydrologic models tospatial variability of precipitation. Journal of Hydrology 217,
285–302.
Kozan, O., Tanaka, K., Ikebuchi, S., 2001. Estimation of energy andwater budget in the Huaihe River Basin, China. GAME
Publication 28, 32–35.
Molnar, D.K., Julien, P.Y., 2000. Grid-size effects on surface runoff
modeling. Journal of Hydrologic Engineering, ASCE January,
8–16.
Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting throughconceptual models. Part 1. A discussion of principles. Journal of
Hydrology 10, 282–290.
Quinn, P.F., Beven, K.J., 1991. The prediction of hillslope flow
paths for distributed hydrological modeling using digital terrain
models. Hydrological Processes 5, 59–79.
Refsgaard, J.C., Abott, M.B., 1996. The role of distributedhydrological modeling in water resources management. In:
Refsgaard, J.C., Abott, M.B. (Eds.), Distributed Hydrologic
Modeling. Kluwer, Dordrecht, The Netherlands.
Renssen, H., Isarin, R.F.B., Jacob, D., Podzun, R., Vandenberghe, J.,
2001. Simulation of the Younger Dryas climate in Europe using a
regional climate model nested in an AGCM: preliminary results.
Global and Planetary Change 30, 41–57.
Saulnier, G.M., Obled, C., Beven, K., 1997. Analytical compensation between DTM grid resolution and effective values ofsaturated hydraulic conductivity within the TOPMODEL
framework. Hydrological Processes 11 (9), 1331–1346.
Shiiba, M., Ichikawa, Y., Ikebuchi, S., Tachikawa, Y.,
Takasao, T., 1996. Scale-up of a runoff model using GIS
and an object-oriented hydrological modeling system. In:
Kovar, K., Nachtnebel, H.P. (Eds.), Proceedings of HydroGIS
96: Application of Geographic Information System inHydrology and Water Resources Management, vol. 235.
IAHS, pp. 63–70.
Shrestha, R., Tachikawa, Y., Takara, K., 2002. Effect of forcing data
resolution in river discharge simulation. Annual Journal of
Hydraulic Engineering, JSCE 46, 139–144.
Singh, V.P., Woolhiser, D.A., 2002. Mathematical modeling ofwatershed hydrology. Journal of Hydrologic Engineering,
ASCE 7 (4), 270–292.
Sivapalan, M., Kalma, J.D., 1995. Scale problems in hydrology: thecontributions of the Robertson workshop. In: Kalma, J.D.,
Sivapalan, M. (Eds.), Scale Issues in Hydrological Modeling.
Wiley, England, pp. 1–8.
Sunada, K., Aoki, K., Fujimura, T., 2001. Effects of scale ofcatchment element on runoff response of the distributed model(in Japanese). Annual Journal of Hydraulic Engineering, JSCE
45, 145–150.

50

R. Shrestha et al. / Journal of Hydrology 319 (2006) 36–50

Tachikawa, Y., Kawakami, T., Ichikawa, Y., Shiiba, M., Takara, K.,
2001. Application of a macro grid based hydrological model tothe Huaihe River Basin in China. Annual Journal of HydraulicEngineering, JSCE 45, 127–132.
Tachikawa, Y., Takara, K., Tanaka, K., Suishu, T., Ichikawa, Y.,
Shiiba, M., 2002. Simulation of River Discharge in the HuaiheRiver Basin in China. Journal of Japan Society on Hydrology
and Water Resource 15 (2), 139–151.
Takasao, T., Shiiba, M., Ichikawa, Y., 1996. A runoff simulation
with structural hydrological modeling system. Journal of
Hydroscience and Hydraulic Engineering, JSCE 14 (2), 47–55.
Tanaka, K., 1998. Activities in Huaihe River Basin (HUBEX) study
area. Asia-Pacific Network for Global Change Research, Reportof 1997–1998, 69–91.

Willmott, C.J., 1981. On the validation of models. PhysicalGeography 2, 184–194.
Wood, E.F., Sivapalan, M., Beven, K., Band, L., 1988. Effects ofspatial variability and scale with implications to hydrologic
modeling. Journal of Hydrology 102, 29–47.
Woods, R.A., Sivapalan, M., Duncan, M., 1995. Investigating
the representative elementary area concept: an approachbased on field data. Hydrological Process 6 (3/4), 291–312.
ED 830.
Zhang, W., Montgomery, D.R., 1994. Digital elevation model gridsize, landscape representation, and hydrologic simulations.
Water Resources Research 30 (4), 1019–1028.
Zhao, R.J., 1992. The Xinanjiang model applied in China. Journal of
Hydrology 135, 371–381.