京都大学防災研究所年報 第 48 号 B 平成 17 年 4 月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 48 B, 2005

Use of Disaggregated Rainfall Data for Distributed Hydrological Modeling in
Yodo River Basin

Roshan K. SHRESTHA*, Takahiro SAYAMA, Yasuto TACHIKAWA, Kaoru TAKARA*Graduate School of Urban and Environmental Engineering, Kyoto University
Synopsis
This study tested the disaggregated rainfall field as the input field for hydrologicalsimulation of various sub-catchments of the Yodo River. The multiplicative randomcascade (RC) method (based on the beta lognormal model), the multiplicative randomcascade HSA (RCHSA) method, and the space-time rainfall modeling (STRaM) method are
employed to disaggregate the rainfall field from coarse (48-km, 100-min) to fine (3-km, 10min) resolution. The Yodo River model, an OHyMoS assisted distributed hydrologicalmodel with saturated-unsaturated surface-subsurface flow mechanism, is used for
simulating the runoff at Ootori, Ieno, Kamo and Inooka having catchments areas of 156
km2, 476 km2, 1469 km2 and 1589 km2 respectively. The simulated discharge using thedisaggregated rainfall with STRaM is quite similar to the one obtained from using the radarobserved rainfall.
Keywords: downscaling, rainfall field, yodo river model, RCHSA, STRaM method

1. Introduction
A fully distributed hydrological modeling, which
includes distributed process descriptions, takes
spatially and temporally distributed input fields, andemploys fully distributed parameterization, often
finds difficulty in producing entirely satisfactory
outcome. Most of the distributed hydrological models
are reported being unable to make accuratehydrological simulation and/or prediction (Reed et al.
2004). There are multiple reasonings that cause anadvanced distributed hydrological model perform
inferior than a simple lumped parameter model.
Existence of scale gap between meteorologicalstudies and hydrological studies is often cited as thedominant cause failing the distributed hydrologicalmodeling. Most meteorological models perform wellat the scale of several hundred kilometers in spaceand monthly scale in time. But the hydrologicalanalyses require daily scale in time and few
kilometers in space or even a finer scale. Numerical
weather simulators of much finer scales in space andtime are feasible but they are suffered heavily by alarger degree of uncertainty caused by problems inparameterization and lack of knowledge of
meteorological processes at much finer scales (Bateset al., 1998; Chen et al., 1996; Giorgi and Mearns,
1991; Houze, 1997). This weakness comes to the coreof the problem area because the hydrometeorological
data are the one of key-role player in the hydrologicalstudies involving a distributed hydrological model(Shrestha et al., 2004a). Recent advances in
distributed hydrological modeling are continuously atodds with the use of inappropriate scale at various
levels of the modeling (Shrestha, 2005). There iscontinuous interest in the study of scale dependentfeatures and scale effects in hydrological modeling tounderstand the current limitations.
A poor outcome is associated with theuncertainty coming not only from the heterogeneityof the parameters, processes and input field but also
from their scale of representation (Shrestha et al.,2005). An intuitive solution to overcome the scalemismatch between the input field and the processdescription is to employing an appropriate
disaggregation of the input field. Predictably, thebasic tenet of this solution is the accuracy of thehydrological simulation involving disaggregatedrainfall field, whose original source is of a muchcoarser scale equivalent to the one we usually obtainfrom a regional scale meteorological model. While
such a claim at first glance seems unexpected, it isexamined in this study involving multiple sets ofdisaggregated rainfall in multiple catchments ofdifferent sizes. The rainfall is disaggregated into finer
resolution using three different disaggregation

methods from a coarse scale rainfall field that was
initially aggregated from radar observed rainfall fieldof fine resolution.
In order to disaggregate the rainfall field, themultiplicative random cascade methods based on betalognormal model are used. First two methods are therandom cascade method (the RC method) and therandom cascade hierarchical and statisticaladjustment method (the RCHSA method). The third
method is the space-time rainfall modeling method(STRaM method). Shrestha et al., (2004) and
Shrestha (2005) have described the methods in detail.
These methods yield the disaggregated rainfall fields
that are fed into the hydrological model. The
hydrological model used in this study is the Yodo
River model (Sayama et al., 2004).
We concentrate our efforts on testing the use of
disaggregated rainfall field irrespective of their interrelation with the variability of model parameters invarious subcatchments of the Yodo River in Japan(Figure 1). The standard set of the model parameters
are calibrated using the radar observed rainfall field.
Similarly, we validate that the disaggregated rainfall
field can produce promisingly accurate discharge
simulation if the disaggregation scheme is sufficiently
good. Thereby the meteorogical models andhydrological models can agree to accomplish the goalof making better simulation irrespective of the scalemismatch.

Hiyoshi Dam

Biwa Lake

Katsura River
Seta Weir
Ootori
Shinmachi

Uji River

Makioyama
Hirakata

Kizu River

Amagase Dam
Takayama Dam
Nunome Dam

Inooka
Kamo

Ieno
N

Dams
Discharge Obs.

Hinachi Dam
Shorenji Dam

20 km

Murou Dam

Fig. 1. Location of the study region.
The rest of this paper is organized as follows.
We motivate the need for bridging the scale gap insection 1 and 2. To surmount this quandary, wedemonstrate that while the distributed hydrologicalmodel includes all major components of catchment
complexities (section 3), the simulation results are
hardly perfect (section 4). Furthermore, to show theimportance of proper space-time structure of rainfall
field, we present the simulation results using thedisaggregated rainfall, which we use to show that an
improper disaggregation scheme yields very uncertain
runoff but a good runoff simulation is possible toobtain from the disaggregated rainfall if thedisaggregation method is accurate and robust (Section
5). And we conclude in section 6.

2. Disaggregation of rainfall field
There is a large scale difference between global
scale (climate or atmospheric) models and regional or
local hydrological models. Still these models arenecessary to be coupled in order to understand andpredict a clear scenario of local and regional impacts
on hydrological cycle due to global changes. Coarse
scale products of GCMs are an inadequate basis forassessing local / regional scale impacts as it is hardly
able to resolve many important sub-grid scale
processes (Hostetler, 1994; Wilby et al., 1999). The
need of disaggregation is pretty high to use theoutputs obtained from current GCM scale. It isnecessary to identify the sub-grid scale features for
local or regional hydrological analysis, which is notseen in a coarser scale frame.
The analysis based on hydrological simulation
are highly dependent on rainfall structure as it has
significant effect in simulation results of small tolarge-scale catchments (Shrestha et al., 2002). Many
methods have been developed to fulfill the ambitionof modeling the rainfall structure properly, forexample, Schertzer and Lovejoy (1987), Marsan et al,(1996), Gupta and Waymire (1993), Over and Gupta(1994), Tustison et al. (2002), etc. We took themethod proposed by Over and Gupta, (1994). This isa discrete form of multiplicative random cascademethod, which has ability to separate rainy and nonrainy area. This method is called the Random
Cascade method (RC method) in this paper. In
addition to the RC method, two new disaggregation
methods we developed, the RCHSA method and the
STRaM method (described in next paragraph), arealso used for disaggregating the coarse scale rainfall
field.
The RC method generates spatially uncorrelated
rainfall field. This is the major drawback of the RC
method for many practical applications as the spatial
structures of rainfall are observed to have spatial
correlation (Bell, 1987). The RC method is modified
by Shrestha et al. (2004b) and is named the Random
Cascade Heirarchical and Statistical Adjustment
method (the RCHSA method). The RCHSA method
generates a spatially correlated rainfall field bycontrolling the spatial location of the cascade
generator weights while it undergoes into
multiplicative cascade process. Both the RC method
and the RCHSA method employes the spatial
disaggregation only.
The Space Time Rainfall Modeling method (theSTRaM method) includes an improved version of the
RCHSA for the spatial disaggregation and thetemporal disaggregation based on the rainfall
translation mechanism (Shiiba et al., 1984). In thismethod, the magnitudes of random cascade generator
weights are restricted to remain within an envelopethat defines the relation of the cascade generators fora successive level of disaggregation. The temporaldisaggregation is firstly guided by a splineinterpolation to generate a dummy rainfall field. The
dummy rainfall field is updated based on thediscrepancy between the translated rainfall field andthe dummy rainfall field. The combination of the
improved RCHSA method and updated dummy fieldprovides the Space-Time disaggregation of the coarse
rainfall field.
The rainfall data is obtained from a radar locatedat Miyama Radar station in Central Japan. The data
was recorded in a typhoon event of 1991 September.
The data set is having 3-km spatial resolution and 5minute temporal resolution. This resolution setting isused to calibrate the hydrological model paramters.
Further, the data is upscaled to 48-km spatial
resolution and 100-minute temporal resolution. This
resolution setting is the coarsest resolution, which islater disaggregated to 3-km spatial resolution and 10minute temporal resolution. For the RC method and
RCHSA method, because they do not have thetemporal disaggregation component, the rainfall fieldis linearly interpolated in time to match thehydrological model’s requirement.

3. Description of the Yodo River model
The Yodo River hydrological model wasdeveloped aiming to attain high accuracy inhydrological simulation via distributed hydrologicalmodeling in the Yodo River basin in Japan. Thismodel is developed to analyze the complexhydrological variability in the Yodo River basin,
which has a large natural water storage depression,
called as the Biwa Lake, and installation of several
numbers of dams and control structures for operating
multipurpose reservoirs. This model is also developed
using OHyMOS libraries and hence simulates water
movement following automated procedures andlinking sub-basin models together to produce total
run-off. Main features of the Yodo River model
include following features in addition to that of the
MaScOD model are:a. This model defines a greater catchment as a
combination of multiple smaller sub catchments
each having approximately 150-km2 coverage.

b. Each sub catchment further includes distributedhydrological modeling which is developed basedon 250-m resolution DEM
c. This model contains current anthropogenic
controls over the river flow such as the Damrelease policies, and multi-reservoir operation
rules.
d. This model uses measured data of channel
geomorphology e.g. Channel width and depth.

Fig. 2. Schematic of the soil layer in an element of
the Yodo River model
3.1 Element model description
The element model, which is responsible to yield
runoff from the interaction of soil water storage in
multiple layers of soil and soil water storage capacity,
is based on the saturated-unsaturated flow mechanism(Tachikawa et al., 2004). This model takes into
account three types of flows: unsaturated flow in
capillary pore, saturated flow in non-capillary pore,and surface flow on soil surface. Figure 2 shows theschematic diagram of the soil layer of the model. In
which, D [m], ds [m], and dc [m] denote the soil depth,
depth of water in saturated condition, and the
maximum water content in the capillary pore
respectively. Figure 3 shows the stage-discharge
relationship of the model. This relation is defined bya non-linear runoff yield relation that is given by
β
⎧
⎛ h ⎞
⎪
vc d c ⎜⎜ ⎟⎟⎪⎝ dc ⎠⎪q=⎨
vc d c + v a (h − d c )⎪v d + v (h − d ) + α (h − d )m
a
c
s
⎪ c c
⎩⎪

0 ≤ h ≤ dc
dc < h ≤ ds

(1)

ds < hwhere, q is the discharge per unit width [m2/s]; h is
the stage [m]; vc and va are flow rates from thecapillary pore and non-capillary pore respectively.
When kc and ka be the saturated hydraulicconductivities in capillary pore and non-capillarypore, respectively, then vc = kc i and va = ka i for irepresenting intensity. The β is a non-dimensionalparameter that describes the reduction of hydraulicconductivity in capillary pore as the water content
reduced. The β equals to be ka / kc so as to keep thecontinuity of the stage-discharge relationship between
the capillary pore and non-capillary pore.

the effect of anthropogenic activity in hydrologic
system of the Yodo river basin. Since, these issues areirrelevant to this study, the DOEM is made defunctwhile building the total simulation system. Also moredetails of the DOEM are excluded here.
River Channel

River BasinRiver Channel

River Channel
River Basin

Fig. 3. Stage-discharge relationship for saturatedunsaturated layer

River Basin

3.2 Flow Route Model (FRM) and Total
simulation system
The flow route model of the Yodo river model isbased on kinematic wave routing model. Runoff yieldobtained from the element model are routed
downstream through a kinematic wave approximation,
which relates the unit discharge q [m2/s] and therunoff depth h [m]. This is given by

q = αh m

(2)

∂h ∂q
+
= r (t )
∂t ∂x

(3)

where α is a parameter ( α = i / n , i = slope[rad], n = roughness coefficient [m-1/3s]), m is aconstant (m = 5/3), and r(t) is the rainfall treated as
the lateral inflow per unit length [m/s].

Fig. 4. Schematic of the Yodo River Modelcomponents
There is also a Dam Operation Element Model(DOEM) included in the Yodo river model, which
can include the operational dam control mechanism inthe simulation system (see Figure 4). The DOEM isdeveloped and included in this model to investigate

Fig. 5. Schematic simulation system of the Yodo
River Model
The elements of the Yodo river model (Figure 5)
are combined through the DSP and DRP of the
OHyMoS system to build a total simulation system.
For this operation, the model uses the OHyMoS
library.
Thedetailsareavailableon
http://hywr.kuciv.kyoto-u.ac.jp/~shiiba/documents/unix/ohymos/.
4. Calibration of model parameters
The Yodo River hydrological model wascalibrated using the radar observed rainfall as the
input data. Because the model is configured to accept
the 3-km spatial resolution and 10-minute temporal
resolution data format, it average the 5-minutetemporal resolution of the radar rainfall into 10minute resolution. The calibration process did not
employ any automated algorithm but the initial
guesses of parametric values are referred fromprevious studies, e.g. Tachikawa et al., (2004). The
parameters for the routing models are kept same forall study basins. Only the saturated hydraulicconductivities (kc and ka), the permissible depth ofwater in soil layers (ds and dc) and the initialdischarge. These values are slightly modified (trial
method) until the simulated hydrograph comesenough closer to the observed one.
Figure 6 shows the simulation result at Inooka(1,589 km2), which is definitely not a best-matchedresult. Not only to the parametric values, thesimulation results also depends on model components
we involved in the simulation. Presence of multiple
numbers of dams upstream to Inooka, which
massively modify the downstream flow, easily
disconfirm that our model is solidly grounded inreality. Inclusion of the dam elements, as mentioned
above, may improve the modeling task.

1000

viewing the presence of three dams upstream. A
rapid growth in runoff and very effective peak-cut
control are clearly visible in the observed hydrograph.
The simulated hydrograph lacks the effect of theanthropogenic control.
Figure 9 shows the simulation result at Ootori(156 km2). This catchment is very small and also
having no dams upstrea. So the observed runoff isless affected by the anthropogenic control. The modelwith the calibrated parameter set is best-successful tosimulate the hydrograph in this catchment.

Observed
Simulated

900

Runoff (m^3/sec)

800
700
600
500
400
300
200
100
0
0

5

10

15

20
25
30
Time (hour)

35

40

45

110

50

Simulated
Observed

100

Fig. 6. Hydrograph at Inooka (1,589 km2)

90

1000

Runoff (m^3/sec)

80

Observed
Simulated

900

Runoff (m^3/sec)

800

70
60
50
40
30

700

20

600

10
500

0
0

400

5

10

15

20
25
30
Time (hour)

35

40

45

50

300

Fig. 9. Hydrograph at Ootori (476 km2)

200
100
0
0

5

10

15

20
25
30
Time (hour)

35

40

45

50

Fig. 7. Hydrograph at Kamo (1,469 km2)

450

Observed
Simulated

400

Runoff (m^3/sec)

350
300
250
200
150
100
50
0
0

5

10

15

20
25
30
Time (hour)

35

40

45

50

Fig. 8. Hydrograph at Ieno (476 km2)

Figure 7 shows the simulation result at Kamo
(1,469 km2). This is better than the previous case incatching rising and falling limb of hydrograph. The
observed hydrograph presents a clear evidence ofpeak-cut control set off by the dam-operation, which
is abscent in the simulated hydrograph.
Figure 8 shows the simulation result at Ieno (476km2). This result can be said as a satisfactory result

5. Simulation results using the disaggregatedrainfallAfter obtaining the disaggregated rainfall field
having 3-km spatial resolution and 10-minutetemporal resolution, we ran the hydrological model
replacing the radar rainfall by the disaggregatedrainfall. Tha parametric values are kept the same, andthe deviation from the earlier simulation result isobserved. For having chance of strongly stochastic
rainfall structure, the simulation is repeated several
times and obtained an ensemble of simulation resultsfor each of the different disaggregation methods. Our
simulation results seek to prove three hypotheses: (1)that hydrological simulation has significantly highsensitivity to the structure of input field particularly
the rainfall (2) that the response to the structure of
rainfall field tends to damp as the catchment size
grows (3) that the disaggregated rainfall can simulatesignificantly tiny catchments when improving thespace-time structure adequetely.
Figure 10, 11 and 12 shows the hydrographs
obtained at Inooka (1,589 km2) from the use of
rainfall disaggregated by the RC method, RCHSA
method and STRaM method respectively. The
simulation results at Kamo (1,469 km2) (see Figures
13, 14 and 15), at Ieno (476 km2) (see Figures 16, 17
and 18) and at Ootori (156 km2) (see Figures 19, 20
and 21) are similar to the results obtained at Inooka interms of the bandwidth of ensemble simulation result.

Fig. 10. Hydrographs at Inooka (1,589 km2) obtained
from the use of rainfall disaggregated by the
RC method

Fig. 13. Hydrographs at Kamo (1,469 km2) obtained
from the use of rainfall disaggregated by the
RC method

Fig. 11. Hydrographs at Inooka (1,589 km2) obtained
from the use of rainfall disaggregated by the
RCHSA method

Fig. 14. Hydrographs at Kamo (1,469 km2) obtained
from the use of rainfall disaggregated by the
RCHSA method

Fig. 12. Hydrographs at Inooka (1,589 km2) obtained
from the use of rainfall disaggregated by the
STRaM method

Fig. 15. Hydrographs at Kamo (1,469 km2) obtained
from the use of rainfall disaggregated by the
STRaM method

Fig. 16. Hydrographs at Ieno (476 km2) obtained
from the use of rainfall disaggregated by the
RC method

Fig. 19. Hydrographs at Ootori (156 km2) obtained
from the use of rainfall disaggregated by the
RC method

Fig. 17. Hydrographs at Ieno (476 km2) obtained
from the use of rainfall disaggregated by the
RCHSA method

Fig. 20. Hydrographs at Ootori (156 km2) obtained
from the use of rainfall disaggregated by the
RCHSA method

Fig. 18 . Hydrographs at Ieno (476 km2) obtained
from the use of rainfall disaggregated by the
STRaM method

Fig. 21. Hydrographs at Ootori (156 km2) obtained
from the use of rainfall disaggregated by the
STRaM method

The widespread bandwidth of ensemblehydrographs obtained from the use of rainfall
disaggregated by the RC method and RCHSA method
reveals the higher uncertainty associated with thedisaggregated rainfall field. The narrowest bandwidthof the ensemble hydrograph obtained from rainfall
disaggregated by the STRaM method proves therobust characteristics of the disaggregation method,which is plausible in a wide range of catchments sizes.
While the simulation results are better and morerobust by the use of STRaM method, a considerable
amount of bias is evident in the catchments other than
Ootori. In an ideal case, the biases measure adverse
properties of the disaggregated rainfall field to theradar rainfall. It might however explain a different
perspective as we see the rising and falling limbs ofhydrographs simulated by the disaggregated rainfall(using the STRaM method) are better matched to theobserved hydrograph than that yielded by the radar
rainfall. Recalling tremendous uncertainties in themethods of converting the radar reflectivity to therainfall rates, the bias noticed here might have an
unknown inter-relations. As we zoomed the rainfal
structure in and out through the scaling processes (theaggregation and disaggregation) of the radar rainfall
field, a significant changes might have occurred in the
disaagregated rainfall field that could have resulted
the simulated hydrographs better than the one
obtained using the radar rainfall. In this regard, thebias noticed in the hydrographs using thedisaggregated rainfall can be a positive achievement
if the bias leads the simulation results toward an
improved accuracy. This phenomenon is prominently
visible in Figure 12, 15 and 18.

6. Conclusion
Bridging the scale gap has been an attractive
research motivation in hydrology, which expects toovercome the limitations of the scale-mismatch via
scale-transformation. The results obtained from adisaggregation model becomes useful only if it canproperly describe the sub-grid scale variability.
Testing the disaggregated rainfall in hydrologicalmodeling is the best way to examine the rainfall
structure as far as the runoff simulation is concerned.
Our simulation results seek to prove threehypotheses: (1) that hydrological simulation has
significantly high sensitivity to the structure of input
field particularly the rainfall (2) that the response to
the structure of rainfall field tends to damp as thecatchment size grows (3) that the disaggregatedrainfall can simulate significantly tiny catchments
when improving the space-time structure adequetely.
In addition to that, the results have indicatedpossibility of self correcting the rainfall field, though
this requires extensive investigation to confirm.
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淀川流域を対象とした分布型流出モデルへのダウンスケール降水量データの適用

ローシャン，クマール，シュレスタ* ・佐山敬洋・立川康人・寶馨*

京都大学大学院工学研究科都市環境工学専攻
要 旨

淀川流域を対象として構築した広域分布型流出モデルを用いてダウンスケールした降水量データを検証する。
降雨データをダウンスケールする方法として，β lognormal モデルを用いたマルティプリカティブランダムカ
スケード法(RC)，階層統計的配置法(HAS, Hieratical Statistical Arrangement)を導入したランダムカスケー
ド法，ランダムかスケート法に移流モデルを導入した STRaM(space-time rainfall modeling)法の 3 種の手法を用いる。これらの手法をもちいて，それぞれ空間分解能 48km，時間分解能 100 分の降水量データを空間分解能
3km，時間分解能 10 分にダウンスケールする。生成した降水量データを分布型流出モデルへの入力データとし，
大鳥居(156 km2), 家野 (476 km2), 加茂 (1469 km2)，飯岡 (1589 km2)での計算流量を，3km，5 分分解能のレーダー雨量計を用いた場合の計算流量と比較してダウンスケールしたデータを検証する。その結果，STRaM を用いた場合の流量シミュレーション結果が，他の 2 つのダウンスケール手法に比べて極めてレーダー雨量を用いた
場合のシミュレーション結果に近いことが分かった。

キーワード: ダウンスケール，降水量データ, 分布型流出モデル, RCHSA 法, STRaM 法