International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

IC ratio concept in distributed hydrological modelingfor optimal performance

ROSHAN K. SHRESTHA
Graduate School of Civil Engineering, Kyoto University, Japane-mail: roshan@rdp.dpri.kyoto-u.ac.jp
TACHIKAWA YASUTO
Disaster Prevention Research Institute, Kyoto University, Japan
TAKARA KAORU
Disaster Prevention Research Institute, Kyoto University, Japan

Abstract General Circulation Models (GCMs) are one of the major data source in distributedhydrological modeling for gauged and un-gauged basins. However, the available grid resolution of
GCM data should resemble to the need of hydrological model’s spatial resolution, which largely
depends on catchments size. Observing the behavior of spatial resolution in distributed hydrologic
modeling, data requirement criterion with respect to catchments size is investigated by evaluating IC
Ratio (ratio between input data resolution and catchments area), expecting massive use of GCM dataand coupled atmospheric and hydrologic model in near future. A macro scale distributed hydrologicalmodel is developed using object oriented hydrological modeling system (OHyMoS) and test
simulations are conducted for the case of Huaihe River Basin (132,350 sq. km.) in China and its two
sub-basins Wangjiaba (29,844 sq. km.) and Suiping (2,093 sq. km.). A 10-minute spatial resolution
data set is generated using the 1.25 degree GAME Reanalysis Data Version 1.1 referring the spatial
pattern of 5-minute HUBEX EEWB Data; a field measurement based distributed data set. The newly
created data has improved the modeling result. Later on, the generated 10-minute spatial data isconverted to 20-minute, 30-minute and so on. Model performances are examined by feeding thegenerated forcing data into the model with the same parameters as before. A changing behavior ofsimulation result displayed a rapid improvement on model result with finer resolution. The
improvement in model performance saturates afterward which suggests an existence of a thresholdvalue of IC Ratio. Optimal simulation results are observed while the IC Ratios are around 1:10 ~ 1:20.
Higher sensitivity in model performance due to spatial resolution is observed in smaller catchments
in both presence and absence of routing models than that of larger catchments.
Keyword

GCM data, Macro-scale distributed hydrological modeling, OHyMoS, IC Ratio, spatial
resolution

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International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

INTRODUCTION
Hydrological models are evolved to get better understanding of surface runoff generated fromcomplex watersheds. Several surface runoff models, which broadly can be classified as either
Lumped-conceptual model or Distributed physically-based model, have already been tested andapplied for this purpose. The lumped conceptual models are repeatedly proved unable to handle thespatial variability. Distributed models are developed, with a hope to obtain solution to the problemsof lumped model, to represent the variability in physical watershed characteristics.
It is noticed that for many of the problem areas the need for the distributed models reflects a demandfor predictive capability on the effects of man-induced impacts (Refsgaard & Abott, 1996) such as
massive land-use changes, global warming effects and effects caused by natural reasons such as
heavy rainfalls and droughts due to climatic fluctuations. The distributed models’ strength to assess
the effects of spatially variable impacts on hydrologic responses has made it an essential tool toanalyze the hydrologic behavior of watershed with increased accuracy.
However, to use a distributed models is complicated by the need to establish a suitable spatial scale tobe used in characterizing watershed conditions such as topography, drainage density, degree of soil
saturation and rainfall properties or in a broad sense the input information to the model. The
challenge in applying distributed models to large watersheds is to determine a scale at which spatial
variability can be neglected, with average characteristics of a given area providing sufficient
information for accurate modeling of basin runoff generation (Molnar, 2000). Probably this is one
major reason to make distributed models not so popular in practical application.
Development of hydrological simulations for gauged and un-gauged basins frequently uses
meteorological data inputs retrieved from global climatic scenario, which are provided by General
Circulation Model (GCM). Unfortunately, the structure of GCMs is such that their space resolution isoften too coarse and not adequate (Burlando, 2002) to describe variability in hydrologic processes
components at the basin scale. Large efforts to produce finer resolution GCM data with greater
accuracy have increased the possibility of extensive use of GCM data in distributed hydrologic
models.
The available grid resolution of GCM data should resemble to the need of hydrological model’s
spatial resolution. Some criteria are necessary to determine a scale at which spatial variability can beignored for a given area providing sufficient information with average characteristic of the area withrespect to catchments size for accurate modeling of surface runoff generation. Shrestha et al. (2002)
found that the results of distributed hydrological models are better while an IC Ratio (ratio between
input data resolution and catchments area) is more than 1:10, which may serve as a criterion toevaluate suitable input data resolution.
This paper will illustrate the IC Ratio concept in distributed hydrological modeling by examining themodel performance with different forcing data resolutions. Applying a macro scale distributedhydrological model, which uses the object oriented hydrological modeling system (OHyMoS)(Takasao et al., 1996), the study is conducted for three-basins in China, namely Huaihe River Basin(132,350 km2), Wangjiaba (29,844 km2) and Suiping (2,093 km2).
BACKGROUND
Macro scale hydrological modeling is often practiced for a large river basin. An object orientedhydrological modeling system - OHyMoS (Takasao et al., 1996, Ichikawa et al., 2000) has eased a lotof tasks associated with the modeling procedure of water movement in a grid based analysis. For
example, basin partitioning, hydrological process modeling for a sub-basin, linking sub-basin models
together to make a total runoff model, processing channel network linkages to incorporate river flowrouting, etc. involve a lot of heavy tasks, which now has been arranged in an automatic procedure791

International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur(Tachikawa et al., 2000). In this system a watershed basin is subdivided into grid boxes according toa grid system of a meso-scale atmospheric model outputs.
The model consists of a runoff process model based on Xinanjiang model and Lumped stream
kinematic-wave flow route model for each grid cells to constitute an element model. These element
models are interconnected by data sending ports and data receiving ports defined as per the river
network arrangement to construct the total simulation process. The model parameters are calibrated
on the basis of field observation records inside Shigan River Basin, a sub-basin inside Huiahe River
Basin, which is assumed to include the representative geomorphology of entire basin.
Using the grid precipitation and grid actual evapo-transpiration data obtained from the HUBEX-IOP
EEWB data (termed EEWB data here after), a 5 minute spatial resolution data created in DPRI,
Kyoto University (Tanaka et al 1999), discharges are successfully simulated (Tachikawa et al 2000).
Using 2-dimensional forecast data of GAME Reanalysis (Version 1.1) with 1.25 degree resolution(termed GAME data here after), produced by Japan Meteorological Agency using 4 DDA-system
including the GAME special observation off-line radio-sonde dataset, the discharges are successfully
simulated again and observed that the simulation result with GAME data is better than EEWB data
for large basin and just opposite for smaller basins (Shrestha et al., 2002). Magnitude errors in EEWB
data are assumed as one of the reasons behind the large basin simulation error. Coarser resolution of
GAME data is assumed as one of the reasons behind the smaller basin simulation error. Thus it has
demanded some additional and closer investigations.
METHODS AND DATAIn this study, a finest resolution of 10 minute data is created by preserving the spatial pattern of
EEWB data and magnitude of GAME data. EEWB data is created using interpolations of the groundobservation points by considering both distance and direction of each observation station for
precipitation field. It uses the simple bio-sphere with urban canopy (SIBUC) model to obtain theevapo-transpiration data field.
The reason behind following the spatial pattern of EEWB data is that it is created basically on thebasis of ground observations. The EEWB data, with finest resolution among the available data until
now, is therefore assumed to represent the spatial pattern better than any other data. On the other hand,
GAME data is coarse and produced by an atmospheric model, which has given better simulation
results in previous analyses, therefore its magnitude is assumed to be nearer to the actual data. The
following two approaches are tested in the process of generating the 10 minute test data.
1. Multiplicative approach:This approach generates 10-minute disaggregated grid data by multiplying a factor based on theratio between the original data and mean data. Thus the new data set is represented as:

P4 = P1 *P2
P3

Where P4 = GAME 10-minute
P1 = GAME 1.25-degree
P2 = EEWB 10-minute
P3 = average of EEWB 10-minute
The resolution of P1 and P3 are maintained same. If P3 data field is zero, the P4 value is simply
assigned P1 value of corresponding grid to avoid the chance of infinity error.
2. Arithmetic approachThis approach simply adds or reduces the value from the averaged GAME 1.25-degree data on
the basis of differences between the EEWB 10 minute data and its averaged figure. Thus the newdata set is represented as:792

International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

P4 = P1 + P2 − P3
Here P1, P2, P3 and P4 represent the values as before. Sometimes, P4 values may appear negative,
which is forced to make zero. Thus, the accumulated value frequently appears to be higher thanthe original. A factor of ratio between the new accumulated value and original value is multiplied
to all the data for maintaining the total input as same as that of the original data.
The arithmetic approach is found to yield better results for all test basins. Hence this approach isadopted to create the new experimental 10-minute data, which is used then to create 20-minute, 30minute data and so on by passing an averaging window of (2 × 2), (3 × 3) and so on up to 150minutes (2.5-degrees) respectively.
To see the effects of routing model in the simulation result, especially while the forcing data
resolution differs, the experiment is conducted with and without routing model separately.
RESULTS AND DISCUSSION
Simulation results with experimental data are found better than either of original data. They arecompared against the observed discharge. The model performances are evaluated by using several
indexes. The indexes used here to compare the hydrographs are Pearson’s Moment Correlation
Coefficients (PMC coeff.), Nash-Sutcliff’s index of efficiency (NSI coeff.), Index of Agreement(IOA), Covariance, Root mean square error (RMSE), Mean bias, Volume error (VER), Unbalance,
Peak flow error (QER), Peak time error (TER), Maximum difference at the same time (Max diff),
Average absolute error (AAE) and Average absolute error within +/- 2 hour interval (AAE +/- 2hr).
Indications about the model’s performance with these indexes often coincide with very few
exceptions. Therefore, some of the index parameters only mentioned in the discussions ahead. Some
result hydrographs and the tabulated results are presented here.
Modeling without routing model
The simulation results without routing model do not display a good match at first look in all the cases
except the result in Suiping with 10 minute-data (see fig.1). Mostly, the results are similar to thefinding of Tachikawa et al. (2002) - too bad without routing model. Distributed hydrologic modelingwithout routing model should therefore not be practiced either in larger watersheds or with coarser
resolution data. Routing model has significant influence in larger basins and with coarser data
resolution. The results are too bad, so that it is doubtful to perform the comparisons between theperformances; therefore, the attempt to evaluate the spatial resolution issues without routing model
are abandoned then.

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International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

At Suiping with 10 minute data

With 2 degree data

At Wangjiaba with 10 minute data

With 2 degree data

At Bengbu with 10 minute data

With 2 degree data

Figure1: The Hydrographs without routing model: Simulated vs. Observed.

Modeling with routing model
Inclusion of routing model yields good results in the simulation. The model performances are betterand comparable against the observed discharge. Distinct changes in hydrograph are clearly visible atdifferent spatial resolution data input. This change indicates the influence of the spatial resolution
with a clear sign of worse simulation result at coarser input data resolution. A worth noting point isthat the coarser resolution data applied here for simulation is nothing more than the spatiallyaveraged value from the same finer resolution data, which just smoothens the spatial variability at acoarser scale. The total accumulated values are kept constant in all the analysis.

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International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

Comparison of hydrograph & water budget at Suiping with 10 minute and 2.0 degree data

Comparison of hydrograph & water budget at Wanjiaba with 10 minute and 2.5 degree data

Comparison of hydrograph & water budget at Bengbu with 10 minute and 2.5 degree data
Figure 2. The Hydrographs with routing model: Simulated vs. Observed.

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International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

Slight differences in the water budget, which are not detectable in graph scale, are observed. Thisshould be due to the nonlinear soil-water interaction phenomenon of Xinanjiang model based runoff
element process.
IC-Ratio and the results:
With the coarser resolution forcing data, one obtains poor model performance in the simulation result
than that with the finer resolution. This result is obvious; in addition, it is expected to obtain variable
model performances once the test basins are different. The constitutive relations for different flow
processes that are function of the detailed geometry of flow pathways in different catchments are
difficult to compare (Beven, 2002). Some indexes for example average slope, flow lengths,
watershed relief etc. exist to represent the catchments features but they may not be compatible to test
against forcing data resolutions. The concept of ratio between the input grid resolution andcatchments size, termed as IC-Ratio (Shrestha et al 2001) may be generally useful index forinvestigating the phenomenon observed due to effects of resolution changes.
The finest resolution in this experiment is 10 minute spatial distance (approximately 13.5 km). The
input data for Suiping basin (2093 km2) varies from 10 minute to 2 degree resolution. Therefore the
IC-Ratio value ranges from 1:11.77 to 1:0.08. Model performances are consistently better at 1:11.77(called higher IC-Ratio values here) than near the ranges of 1:0.08 (lower IC-Ratio). Higher IC-Ratio
corresponds to finer resolution and lower IC-Ratio corresponds to coarser resolution of input ascatchments size remains constant.

Figure 3. The model performances of Suiping, Wangjiaba, and Bengbu at different IC Ratios

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International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

The IC-Ratio values for Wangjiaba basin (29844 km2) and Bengbu basin (132350 km2) vary from
1:167.8 to 1:0.75 and 1:744.5 to 1:3.3 respectively. Model performances are better while IC-Ratio
values are higher in both these cases also.
The trend of change in model performance from the graphs presented (see fig.3) clearly shows thatthe smaller basin has higher sensitivity in response to the forcing data resolutions. The rate of change
in performance is higher in Wanjiaba than that in Bengbu. Similarly, the rate of change inperformance is higher in Suiping than that in Wangjiaba. This indicates that the resolution issues
need more attention for the smaller basins than the larger ones. This indication seems quite natural
because, in larger basins, the larger heterogeneous parts may be represented as homogenous parts
than in smaller basins.
Table 1: A summary of model performance indexes values for all the basins
IC Ratio
(1:X)
0.08
0.10
0.12
0.15
0.18
0.24
0.33
0.47
0.74
0.75
0.86
0.99
1.17
1.31
1.39
1.68
2.07
2.62
2.94
3.31
3.43
3.80
4.41
4.66
5.17
6.15
6.71
7.44
9.19
10.49
11.63
11.77
15.19
18.65
20.68
29.78
41.97
46.53
82.72
167.87186.12744.47

S
S
S
S
S
S
S
S
S
W
W
W
W
S
W
W
W
W
S
B
W
B
B
W
B
B
W
B
B
W
B
S
B
W
B
B
W
B
B
W
B
B

PMC
coeff

NSI
coeff

IOA

Covariance

RMSE

Mean
Bias

VER

Unbal

QER

TER

Max
diff

AAE

0.62
0.62
0.61
0.61
0.67
0.68
0.65
0.70
0.68
0.84
0.86
0.86
0.87
0.70
0.87
0.86
0.86
0.87
0.71
0.74
0.88
0.74
0.74
0.88
0.75
0.77
0.88
0.77
0.77
0.88
0.76
0.72
0.76
0.88
0.76
0.77
0.88
0.76
0.76
0.88
0.77
0.76

0.37
0.36
0.34
0.33
0.44
0.43
0.40
0.46
0.43
0.65
0.66
0.68
0.70
0.47
0.72
0.70
0.71
0.72
0.48
0.49
0.70
0.47
0.47
0.72
0.50
0.51
0.70
0.50
0.50
0.70
0.50
0.49
0.42
0.70
0.43
0.47
0.70
0.46
0.45
0.69
0.47
0.44

0.74
0.75
0.75
0.75
0.80
0.80
0.78
0.82
0.81
0.91
0.92
0.92
0.93
0.82
0.93
0.92
0.92
0.93
0.83
0.86
0.93
0.86
0.86
0.93
0.87
0.87
0.93
0.87
0.87
0.93
0.87
0.84
0.86
0.93
0.87
0.87
0.93
0.87
0.87
0.93
0.87
0.87

0.31
0.32
0.33
0.34
0.38
0.40
0.36
0.42
0.41
0.20
0.21
0.21
0.21
0.42
0.20
0.19
0.19
0.21
0.44
0.06
0.22
0.05
0.06
0.21
0.06
0.06
0.22
0.06
0.06
0.22
0.06
0.45
0.06
0.22
0.06
0.06
0.22
0.06
0.06
0.22
0.06
0.06

0.28
0.28
0.28
0.28
0.26
0.26
0.27
0.25
0.26
0.11
0.11
0.11
0.10
0.25
0.10
0.10
0.10
0.10
0.25
0.08
0.10
0.08
0.08
0.10
0.08
0.08
0.10
0.08
0.08
0.10
0.08
0.25
0.08
0.10
0.08
0.08
0.10
0.08
0.08
0.11
0.08
0.08

-0.0135-0.0137-0.0143-0.0140-0.0135-0.0120-0.0138-0.0136-0.01260.0006-0.0009-0.0017-0.0019-0.0135-0.0012-0.0008
0.0000-0.0004-0.01320.0018-0.00260.00180.0017-0.00150.00130.0019-0.00200.00050.0003-0.0012-0.0002-0.0125-0.0032-0.0017-0.0032-0.0008-0.0020-0.0009-0.0011-0.0023-0.0008-0.0015-14.31-14.59-15.16-14.82-14.33-12.78-14.68-14.41-13.33
0.56
-0.92
-1.71
-1.94
-14.35
-1.21
-0.78
0.03
-0.36
-14.00
2.35
-2.60
2.33
2.22
-1.47
1.71
2.54
-2.00
0.72
0.42
-1.21
-0.24
-13.23
-4.25
-1.67
-4.25
-1.03
-2.00
-1.22
-1.46
-2.28
-1.03
-1.98

39.78
40.56
42.13
41.21
39.85
35.52
40.82
40.06
37.07
-1.65
2.69
5.03
5.71
39.89
3.57
2.30
-0.09
1.07
38.92
-5.30
7.65
-5.24
-5.01
4.32
-3.84
-5.71
5.87
-1.61
-0.94
3.56
0.55
36.78
9.58
4.90
9.57
2.32
5.87
2.74
3.30
6.71
2.32
4.46

-61.6
-54.1
-51.9
-50.6
-53.2
-46.3
-56.5
-44.6
-45.6
37.5
38.8
35.1
28.1
-45.4
21.4
22.5
28.1
30.2
-41.8
8.1
31.6
6.9
7.0
30.7
10.9
14.2
30.7
16.9
17.6
32.5
18.9
-40.7
26.2
30.6
29.9
28.8
30.7
27.7
27.6
31.0
28.8
29.5

-5
3
-5
-5
8
3
3
8
3
3
3
3
2
3
2
3
3
3
3
3
3
2
2
3
2
2
4
3
3
4
3
3
4
4
4
4
4
4
4
4
4
5

4.99
4.52
4.50
4.49
4.43
4.38
4.51
4.03
4.31
0.99
1.01
1.05
0.92
4.01
0.89
0.88
0.87
0.92
3.84
0.51
1.00
0.55
0.53
0.97
0.47
0.44
1.03
0.44
0.44
1.05
0.44
3.79
0.49
1.02
0.47
0.43
1.03
0.44
0.44
1.05
0.43
0.44

0.92
1.02
1.06
1.07
0.89
0.76
0.96
0.82
0.77
0.40
0.39
0.39
0.40
0.83
0.39
0.40
0.39
0.39
0.79
0.54
0.39
0.54
0.54
0.39
0.54
0.53
0.38
0.54
0.54
0.38
0.55
0.76
0.58
0.38
0.58
0.56
0.38
0.56
0.56
0.38
0.56
0.56

797

AAE
+/2hr
0.67
0.73
0.76
0.77
0.62
0.53
0.68
0.56
0.53
0.31
0.30
0.30
0.31
0.57
0.31
0.31
0.31
0.31
0.53
0.48
0.30
0.49
0.48
0.30
0.49
0.48
0.29
0.49
0.49
0.29
0.50
0.51
0.52
0.29
0.52
0.50
0.29
0.50
0.50
0.29
0.50
0.51

International Conference on Urban Hydrology for the 21st Century
14-16 October 2002, Kuala Lumpur

Optimal performance and IC Ratio
The obtained results unanimously argue that the model’s performance depends upon forcing data
resolution. However, demanding very high resolution data is not a solution in response to thisphenomenon. Minimum data, minimum parameter and minimum calculating load to obtain best
simulation results make the distributed hydrological model easier and popular to apply elsewhere.
Improvement rate of the model performance has a tendency to saturate at some points. The rate of
improvement is higher while the IC Ratio is lesser than 1:10. When the IC Ratio values reach higher
than the 1:20, the improvement rates of the model performances are not much significant. Thisbehavior is believed to follow the trend line of S-shape curve with its point of inflection near to 1:10
(Shrestha et al., 2002).
Looking the trend of RMSE values, the errors are found to stay stable after the IC Ratio 1: 20 or near
this value. Similar behavior is displayed from the covariance between the observed and simulated
discharges. Thus, on the basis of all these result, the optimal performance should lie within IC Ratio
1:10 ~ 1:20.

Figure 4. Model performance vs. IC Ratio
The IC Ratio figure (1:10 ~ 1:20) mentioned here in fact represents a marginal value of IC Ratio toobtain the simulation result at a satisfactory level. This mean, the simulation result with IC Ratio
lower than 1:10 ~ 1:20 may not yield nice result. With higher IC Ratio values for example 1:100, theresult will always come better but, at the cost of high resolution data and calculation. The interesting
part is that, slight improvements are expected in the results even with the decision of choosing highresolution data such as 1:100 or 1:200.
In an un-gauged basin, where hydrologists need to start work from beginning, a lot of unknowns are
expected to encounter at an attempt of distributed hydrological modeling. Heavy tasks involve in
defining the model parameters, modeling scales, data acquisitions, etc. Probably in such case, theidea of IC Ratio may be very useful to set up model framework at early stage.

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CONCLUSION
In distributed hydrological modeling, the model’s performance is believed to be better than the
lumped-conceptual type of modeling. This greatly depends upon the quality of modeling, whichrefers to the quality of modeling technique, model parameters and input data. Talking about the input
data, its quality is associated with accuracy and resolution issues. The ratio of input data resolution
and catchments area, called as IC-Ratio, can be an index to evaluate the suitability of data resolution
in distributed hydrological modeling.
In this experiment, 3 catchments, ranging from small (2,093 km2) to large (132,350 km2) size, havebeen taken to study the data resolution effects in the discharge simulation results. Smaller catchments
are found more sensitive than the larger catchments indicating that, the resolution issues need more
attention for the smaller basins than the larger one.
The simulation results deteriorate sharply when the IC Ratio is kept lower than 1:10. The
improvement rate in model performance is small after increasing the IC Ratio values higher than 1:20.
A marginal IC Ratio value of 1:10 ~ 1:20 seems to be appropriate to obtain optimum performance inthe results of distributed hydrological modeling viewing the need of efforts to process the highresolution data.

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