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Predictions in Ungauged Basins: PUB Kick-off (Proceedings of the PUB Kick-off meeting held in Brasilia,
20–22 November 2002). IAHS Publ. 309, 2007.

Selection of scale for distributed hydrologicalmodelling in ungauged basins
ROSHAN SHRESTHA, YASUTO TACHIKAWA &KAORU TAKARA
Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japanroshan@flood.dpri.kyoto-u.ac.jp

Abstract A macro scale grid based distributed hydrological model is developed using an object oriented hydrological modelling system (OHyMoS) andapplied to the Huaihe River Basin (132 350 km2) and its sub-basins, Wangjiaba(29 844 km2) and Suiping (2093 km2), with different resolution data (10 min
to 2.5 degree) obtained from the GAME re-analysis data and Hubex-IOP
EEWB data. The model performances are evaluated by comparing simulated
discharge against observed discharge. Using the concept of IC Ratio (a ratio
between the input grid area and the catchment area), the performance
behaviour is observed. The study has found that the distributed model
performs well with finer resolution data, and good performance is obtainedwith an IC Ratio 1:10 or higher, which sets a preliminary criterion for
selecting the scale for distributed hydrological modelling in ungauged basins.
Key words distributed hydrological model; GAME re-analysis product; IC ratio;
input data resolution

INTRODUCTION
It is broadly accepted that hydrological behaviours are predictable through somemeans of modelling. The development of hydrological modelling techniques is still
progressing in a bid to achieve better accuracy and understanding. The basic principle
elements of hydrological modelling procedures generally include data collection,model development, model calibration/validation, and model application. Experiencehas shown that data collection, one of the most essential and initial elements, is themost time consuming, expensive and heterogeneous part of the job. Further, large partsof the world do not have systematic installation and measurement of important hydrological information over the time period needed, such that they would enable computation of hydrological variables to the accuracy acceptable for practical applications.
On the other hand, the necessity of hydrological modelling is rapidly growing allover the world, since it provides information of prime importance for strategicplanning of water use, disaster prevention, sustainable water management and manyother applications. In addition, hydrological modelling often becomes a part ofmultidisciplinary studies. It demands an ability to analyse series of spatially variablehydrological behaviours and impacts of natural and human activities such as massive
land-use changes, global warming effects, heavy rainfalls and droughts due to climaticfluctuations (Refsgaard & Abbott, 1996). In an effort to meet such demands, one must
adopt the distributed approach to hydrological modelling, which again needs hugevolumes of data. Thus hydrologists are having trouble meeting the demand for
accurate and efficient modelling because of the limited availability of data.
Copyright © 2007 IAHS Press

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A good strategy to deal with the problem could be using the best available data inthe modelling, leaving the option open to improve it further, and immediate ratificationof results until the availability of better data. For most basins, at least some basic
hydrological information can be obtained through various sources, for example,
General Circulation Models (GCM), remote sensing observation, global data archives
and digital elevation models, etc., which can be applied plausibly. The absence ofground-based hydrological instrumentation in a basin no longer means that it is anabsolutely ungauged basin. All basins have some data; however, their applicability
may be questioned in relation to accuracy and proper scale issues. Usually GCM
outputs are considered too coarse and not adequate for hydrological modelling(Burlando, 2002) to describe the variability in the components of hydrologicalprocesses at the basin scale. Digital elevation models are sometimes found to be
erroneous, and remote sensing data may occasionally contain illusions. The basins
having several types of hydrological information may still be referred to as ungauged
basins according to the IAHS PUB definition, as the accuracy of available data may
not be acceptable for practical application.
The modelling procedure for an ungauged basin begins with uncertainty andconfusion. Moreover, to practice distributed hydrological modelling in an ungauged
basin, there is an additional challenge to determine the scale at which spatial variability
can be neglected, with the average characteristics of a given area providing sufficient
information for accurate modelling of basin runoff generation (Molnar, 2000). The
ability to choose an adequate scale at the preliminary investigation stage will definitely
reduce the amount of painful exercises in the modelling task, and may produce resultsof higher accuracy.
This paper will illustrate the sensitivity of a distributed hydrological model’s
performance due to changing the scale of GCM-based input data. Applying amacroscale distributed hydrological model, which uses the object orientedhydrological modelling system (OHyMoS) (Takasao et al., 1996), the study was
conducted for three basins in China, namely the Huaihe River (132 350 km2),
Wangjiaba (29 844 km2) and Suiping (2093 km2) basins.

BACKGROUND
Exciting improvements in the resolution and accuracy of GCM products have reduced
the gap between the needs and availability of input data for distributed hydrologicalmodels. The available grid resolution of GCM data should resemble the needs of thehydrological model’s spatial resolution. Shrestha et al. (2002a) demonstrated that theresults of distributed hydrological models are better when the IC Ratio (the ratio
between input data resolution and the catchment’s area) is more than 1:10, suggestingthat a marginal IC Ratio could serve as a criterion to finding a suitable resolution.
Macroscale hydrological modelling is often practiced for a large river basin. An
object-oriented hydrological modelling system, OHyMoS (Takasao et al., 1996;
Ichikawa et al., 2000) has eased many tasks associated with the modelling procedure
for water movement in a grid-based analysis. For example, basin partitioning,hydrological process modelling for a sub-basin, linking sub-basin models together tomake a total runoff model, processing channel network linkages to incorporate river292

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flow routing, etc., involve a lot of substantial tasks, which have now been incorporated
into an automatic procedure (Tachikawa et al., 2000). In this system, a basin is subdivided into grid boxes, according to the grid system of a meso-scale atmosphericmodel outputs.
The model consists of a runoff process model, based on the Xinanjiang model(Zhao, 1992), and a lumped stream kinematic-wave flow routing model, combined foreach grid cell to constitute an element model. These element models areinterconnected 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 for the Shigan River basin, a
sub-basin of the Huiahe River basin, which is assumed to include the representative
geomorphology of the entire basin.

EXPERIMENTAL FORCING DATA
Using the grid precipitation and grid evapotranspiration data obtained from the
HUBEX-IOP EEWB data (termed EEWB data here after), and 5-min spatial resolution
data created at DPRI, Kyoto University (Tanaka et al., 1998), discharges are
successfully simulated (Tachikawa et al., 2000a). Using 2-dimensional forecast data of
the GAME Re-analysis (Version 1.1) with 1.25 degree resolution (termed GAME data
hereafter), produced by the Japan Meteorological Agency using the 4 DDA-system
including the GAME special observation off-line radiosonde data set, the discharges
were successfully simulated again and it was observed that the simulation result withGAME data is better than EEWB data for large basins and the opposite is true forsmaller basins (Shrestha et al., 2002a). Errors in the EEWB data are argued as themain reasons behind poorer simulation of the large basin. On the other hand, thecoarser resolution of the GAME data is argued to be the reason behind poorer
simulation of the smaller basin.
Merging the spatial pattern of the EEWB data at 10-min spatial resolution andmapping the magnitudes of GAME data into the same resolution, a test data set was
created for experimentation. The EEWB data set considers both the distance anddirection of each ground observation station to produce distributed data for precipitation fields. It uses the Simple Biosphere with Urban Canopy (SIBUC) model and thedata collected during an intense observation period to obtain the evapotranspiration
data field. Because the EEWB data is the product of the HUBEX IOP, it offers themost accurate patterns. Also, EEWB data is the finest resolution data among the
distributed data available for the experimental basin until now. Therefore this data ischosen to describe the spatial pattern in the test data. On the other hand, GAME data iscoarse resolution data produced by a numerical model. This data set has produced abetter match of the simulated discharges for larger basins, which would hardly occur if
the larger scale averages of the data field had contained a larger bias.
An arithmetic approach is used in the process of generating the experimental dataof 10-min spatial resolution. This approach simply adds or reduces the differences ineach pixel from the GAME 1.25-degree data. The differences are calculated for eachpixel by comparing the EEWB 10-min data and its average over the domain covered
up by GAME 1.25 degree data. Thus the new data set is given by:

Selection of scale for distributed hydrological modelling in ungauged basins

P4 = P1 + P2 – P3

293

(1)

where P4 is the new 10-min resolution data, P1 is GAME 1.25-degree, P2 is EEWB 10min, and P3 is the average of EEWB data over the coarse resolution.
The pixel values of P4 may sometimes be negative, which requires forcing into
zero. This may cause the accumulated value of the new data to appear slightly higher
than the original GAME data, which requires normalization to assure no-gains. We use
a multiplication factor for this purpose, which is given by taking a ratio between theaccumulated values of new and original data. After multiplying the new data and thefactor, it maintains the same total input as that of the original data. The newexperimental 10-min data is then used further to create coarser resolution data such as
20-min, 30-min and so on by passing an averaging window of (2 × 2), (3 × 3) and soon up to 150-min (2.5-degrees).
RESULTS AND DISCUSSION
Comparing the simulated discharge against the observed discharge, it is found that theexperimental data produces better results than any of the original data, either fromGAME or EEWB, for all three study basins. We use this case as the benchmark andproceed for checking the performances of the model at different scales of catchment
and at different input resolution. We are, however, limited to conduct morecomparisons at different scales of catchments because of the lack of gauged station
discharge at additional points within our model set-up domain. We check the
performance at different input resolution for the study basins. The model performances
are evaluated by using several indexes to compare the hydrographs: Pearson’s Moment
Correlation Coefficients (PMC coeff.), the Nash-Sutcliffe coefficient (NSI coeff.),
Index of Agreement (IOA), Covariance and Root mean square.
Distinct changes in the hydrographs are clearly visible for different spatial
resolution data input. These changes indicate the influence of the spatial resolution anda clear indication of worse simulation results at coarser resolution (see Fig. 1). A point
worth noting is that the coarser resolution data applied here for simulation is nothing
more than the spatially-averaged value from the same finer resolution data that has
kept the constant accumulation and same data pattern over the time series, warranting ajust smoothened spatial variability of the data while the input water budget hasremained constant.

IC-Ratio – a comparison index
It is obvious to expect different model performances from the data having different
orders of heterogeneity as a consequence of differences in forcing resolution. In
addition to that, it is expected to obtain variable model performances where the study
basins are different. The constitutive relations for different flow processes that are afunction 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 are not proper
indices to describe the effect of forcing data resolutions and scale issues. The concept

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(a) Comparison of hydrograph and water budget at Suiping with 10 minute and 2.0 degree data.

(b) Comparison of hydrograph and water budget at Wangjiaba with 10 minute and 2.5 degree data.

(c) Comparison of hydrograph and water budget at Bengbu with 10 minute and 2.5 degree data.

Fig. 1 The hydrographs with routing model: simulated vs observed.

of a ratio between the input grid resolution and the catchment’s sizes, the IC-Ratio(Shrestha et al., 2002b), is a more useful and convenient index for investigating this issue.
Recall that the finest resolution in this experiment is 10-min spatial distance (~13.5km). The input data for Suiping basin (2093 km2) varies from 10-min 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). A higher IC-Ratio corresponds to finer
resolution and a lower IC-Ratio corresponds to a coarser resolution of input, when thecatchment’s size remains constant. The IC-Ratio values for Wangjiaba basin (29 844
km2) and Bengbu basin (13 2350 km2) vary from 1:167.8 to 1:0.75 and 1:744.5 to
1:3.3, respectively, within the framework of this experiment.
The trend of change in model performance from the graphs presented (see Fig. 2)
clearly shows that the smaller basin has higher sensitivity in its response to the forcing

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Fig. 2 Model performances of Suiping, Wangjiaba, and Bengbu at different IC Ratios.
X-axis is IC Ratio, Y-axis is model performance index.

data resolutions. This indicates that the resolution issues for smaller basins need more
attention than for larger basins, which seems quite natural because, in larger basins alarger portion of the heterogeneous field may be represented as a homogeneous
segment than in smaller basins.
Improvement of the model performance due to higher resolution of forcing data
has a tendency to saturate at some point. The rate of improvement is higher when the
IC Ratio values are lower. As the IC Ratio value grows high, the rate of improvementof the model performance is not as significant as it is at the lower IC Ratio. Looking at
the trend of RMSE values, the errors are found to stay very stable after the IC Ratio
reaches 1:20 (see Fig. 3). Similar behaviour is displayed from the covariance between
the observed and simulated discharges. This shows that the rate of improvement inmodel performance starts to saturate beyond an IC Ratio of 1:20 with respect to theincreases in spatial resolution; the response appears to follow a trend of an S-shaped
curve with its point of inflection near to 1:10 (Shrestha et al., 2002b).

SELECTION OF SCALE FOR UNGAUGED BASIN
Knowing the useful range of IC Ratio values helps perform simulations at a satisfactory level. It is of note that the simulation result with an IC Ratio lower than 1:10 has
displayed the possibility of significant improvement if higher resolution input isprovided, but this is untrue when the IC Ratio values are higher, for example 1:100 or
more. We have seen that the results are always slightly better at the higher IC Ratio
side but, at the cost of high-resolution data and calculation loads. Little improvement

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Fig. 3 Model performance vs IC Ratio.

in results using higher resolution input and modelling is likely to discourage the choiceof high resolution data that maintains the IC Ratio value at 1:100 or 1:200. In fact, theperformance improvement beyond IC Ratio 1:20 are no more attractive.
In an ungauged basin, where hydrologists often need to begin work from scratch, a
lot of unknown challenges are faced before there is any success in model setting or
analysis. The need for spatially-distributed data at the required scale with a sufficientlevel of accuracy, as demanded by a distributed hydrological model, definitely hinders
the modeller from the start. Most likely, the data will either be unavailable orinadequate in ungauged basins. In both cases, it would compel a hydrologist to rely on
external sources of information such as GCM data, remotely sensed data and DEMs.
Choosing to go for a higher resolution of distributed hydrological modelling would
require substantial tasks in collecting finer scale details. There would be an additional
task load in defining the model parameters, acquiring data, and performing computations. In addition, it includes a risk of persistent error amplification. On the other hand,selection of lower resolution reduces the workload considerably, but it has a risk ofpoor results and losing the advantages of the distributed modelling approach. Distributed modelling rarely yields a nice result using coarse and rough information. In bothcases, the modelling effort may end up in failure. Therefore a trade-off is needed
between these two sides of problems.
The results obtained in this experiment have demonstrated that an IC Ratio rangeof 1:10 to 1:20 produces satisfactory results. This means a target of 10 to 20 units of
discrete block would not be a bad choice. If there are less than 10–20 units of
distributization in the basin, the distributed model may not yield good results, which ismore critical in smaller basins. Increasing the distributization has the tendency toalways yield better results, but too much distributization, may not improve the results
much. The model performance tends to level off when the numbers of blocks are
increased beyond 20. This concept is likely to be very useful for setting up model
frameworks and selecting a proper scale for distributed hydrological modelling in
ungauged basins.

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CONCLUSIONS
Better model performance is always the motto of a hydrologist. However, this depends
greatly upon the quality of modelling, which refers to the quality of techniques
employed, model parameters, and input data. The input data’s quality is associated withaccuracy and resolution issues. Among the catchments studied, the data resolution
effects in the discharge simulation results are found to be more sensitive in the 2000 km2
catchment range compared to other catchments. The catchments of the order of
132 350 km2 did not require very high resolution input data to produce fairly goodresults. The sensitivity of input data resolution across various scales of catchment isassessed via the ratio of the input data resolution and the catchment area termed the
IC-Ratio. It is argued that the IC-Ratio can serve as an index to evaluate the suitabilityof data resolution and thus guide for the selection of a proper scale for distributedhydrological modelling in ungauged basins.
Performance of distributed hydrological modelling depends very much on theforcing data resolution, which plays a significant controlling role in the selection ofscale for modelling purposes. Demanding very high-resolution data is, however, notalways a solution in view of the efforts required for processing high resolution data,
particularly for an ungauged basin. Obtaining the best simulation results from theminimum data, minimum parameter and minimum calculation load is the primary goalfor ungauged basins. The results of this study suggest that the simulation results aremost favourable when the marginal IC Ratio value is approximately 1:10–1:20 as it
trades off best with data resolution and model performance for a wide range ofcatchment scales. Thus this could be a good choice as a preliminary selection criterionof scale for distributed hydrological modelling in ungauged basins.

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