doi:10.5194/piahs-364-51-2014
Evolving Water Resources Systems: Understanding, Predicting and Managing Water–Society Interactions
Proceedings of ICWRS2014, Bologna, Italy, June 2014 (IAHS Publ. 364, 2014).

51

Identification of low-flow parameters a using hydrologicalmodel in selected mountainous basins in JapanKAZUMASA FUJIMURA1, YOSHIHIKO ISERI2, SHINJIRO KANAE2 &MASAHIRO MURAKAMI3

1 School of Science and Engineering, Meisei University, 2-1-1 Hodokubo, Hino, Tokyo 191-8506, Japanfujimura@ar.meisei-u.ac.jp
2 Department of Civil Engineering, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1
Ookayama, Meguro-ku, Tokyo 152-8550, Japan
3 School of Environmental Science and Engineering, Kochi University of Technology, 185 Miyanokuchi, Tosayamada,Kami-city, Kochi 782-8502, Japan

Abstract Accurate estimation of the low-flow discharge is very important in evaluating the impact ofclimate change on water resources. This study focuses on the storage–discharge equation and the optimal
parameters of the low flow. In order to investigate the sensitivity of the two parameters in the process of thecalculation of low flow, we prepared 19 900 sets of the two parameters in the storage–discharge equationand carried out hydrological analysis using the hourly hydrological model presented by Fujimura et al.
(2012). The study basins are the Sameura Dam basin (SAME basin) located in western Japan which has
variability of rainfall, and the Shirakawa Dam basin (SIRA basin) located in a region of heavy snowfall ineastern Japan. The period of available hydrological data is 20 years for the SAME basin and 10 years for theSIRA basin. The results suggest that the optimal combination of two parameters can be identified byexponential equations. This study also estimates the annual water balance for the two basins based onhydrological analysis using the optimal parameters in the storage–discharge equation of low flow.
Key words low-flow; storage-discharge exponential function; optimal parameter; sensitivity analysis; hydrological analysis

INTRODUCTION
In Japan, about 70% of the land area is mountainous and provides water resources to the remaining
30%, where agricultural, industrial and urban activities are carried out. Projection of the impact ofclimate change on water resources at the local level would provide useful information to decision
makers formulating policies for climate change adaptation. In particular, low flow is strongly
related to the occurrence of drought, and thus the accurate estimation of low flow is very importantfor evaluating the impact of climate change on water resources.
Low flow from basins has been studied for more than 100 years because of the significant roleof water in human activities. On the basis of the review paper of low-flow studies in the early work
presented by Hall (1968), the nonlinearity of low flow in terms of storage volume in the basin was
suggested by Horton (1936) and others to satisfy the following exponential function:
Q = KSN(1)

where Q is the discharge, S is the storage, K is a constant and N is the exponential value. Thisequation is often used in developing recession analysis, estimating low flow, and modellinghydrological processes (e.g. Wittenberg 1994, Tallaksen 1995, Ress et al. 2004). However, in themathematical approach, the groundwater runoff was divided into unconfined and confined aquifers
by Ding (1965), and the groundwater runoff from unconfined aquifers is expressed as thefollowing quadratic exponential equation:
Q = K2 S 2(2)Equation (2) has been used for groundwater estimation in the daily hydrological modelling ofurban hilly, natural hilly and mountainous basins (Ando et al. 1983, 1984, Ando 1989). Fujimura
et al. (2012) developed this daily hydrological model into an hourly hydrological model based on
the Diskin-Nazimov infiltration model and the storage function method for the direct runoff for amountainous basin and applied it to the SAME basin. However, increasingly accurate estimationof reservoir inflow is required. In a recent study, Ding (2011) approximated the storage–discharge
relationship of equation (2) as the following general equation:
Copyright  2014 IAHS Press

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Kazumasa Fujimura et al.

Q = KNSN(3)Although Ding used the generalized storage–discharge relationship of equation (3) for a short-term
runoff event of less than 14 hours using the instantaneous unit hydrograph method, equation (3)was not yet used for a long-term runoff event including the low flow. Since the constant K isdefined as the fractional recession constant and symbolized as Au by Ando et al. (e.g., 1983), in
this study, we rewrite equation (3) as follows:
Qg = AuNSgN(4)

where Qg is the groundwater runoff and Sg is the groundwater storage. The purpose of this study
is to apply the storage–discharge equation of the low flow, equations (3) and (4), to the hourlyhydrological model for a long-term period, and identify the properties of the two parameters inequation (4) of the constant Au and exponent value N by sensitivity analysis. The study basins aredifferent in climatic and geological conditions.
MATERIALS AND METHODS
Study area
To examine the low-flow parameters Au and N in equation (4), we selected two mountainousbasins with very different climatic and geological conditions. One is the Sameura Dam basin(SAME basin) located in the Shikoku mountains in western Japan, and the other the Shirakawa
Dam basin (SIRA basin), located in the Iide mountains in the Tohoku region in eastern Japan. The
locations of the basins are shown in Fig. 1. The SAME basin is the upriver basin of the Yoshino
River basin and has a basin area of 472 km2. Its elevation ranges from 324 to 1880 m a.s.l. and theaverage elevation is 910 m a.s.l. Water resources for agricultural, industrial and urban use, as well
as household water supply for the four prefectures on the island of Shikoku (Kochi, Ehime,
130°E

135°E

140°E

Shirakawa Dam basin

145°E

45°N

45°N

40°N

40°N

35°N

35°N

30°N

130°E

135°E

140°E

145°E

30°N

Sameura Dam basin

Fig. 1 Maps of the Sameura Dam basin (SAME basin) in the Shikoku region and the Shirakawa Dam basin(SIRA basin) in the Tohoku region.

Sameura Dam basin

20(a)April - OctoberNovember - March

P=0.001533EL+10.319

1000Shirakawa Dam basin

1 April 1991 - 31 March 2010

P=0.0007730EL+3.287

500

Elevation（m）

1000

Mean daily precipitation（mm/day）

Mean daily precipitation（mm/day）

Identification of low-flow parameters using a hydrological model in mountainous basins in Japan
2053

1 April 1982 - 31 March 2013(b)

April - OctoberNovember - March

P=0.02048EL+1.321
P=6.069lnEL-26.97

10P=0.001633EL+4.332

00500

Elevation（m）

1000

Fig. 2 Seasonal relationship between mean daily precipitation and elevation for the SAME basin (a) andfor the SIRA basin (b).

Tokushima and Kagawa), are dependent on Sameura Dam. In particular the low flow of the Seto
River in the basin is diverted to supply municipal and industrial (M&I) water to the Kochi City via
two tunnels: the Seto River Diversion and the Jizoji River Diversion. The SIRA basin is theupstream basin of the Mogami River, which is in a region of heavy snowfall in Japan, and has abasin area of 205 km2. Its elevation ranges from 321 to 2029 m a.s.l. with the average elevation
being 697 m a.s.l. The water stored in Shirakawa Dam is mainly used in rice fields.
The rainfall data measured by the Ministry of Land, Infrastructure and Transport and theAutomated Meteorological Data Acquisition System (AMeDAS) of Japan Meteorological Agency
are used. Figure 2 shows the seasonal relationship between precipitation and elevation of the twobasins using the available AMeDAS data. The SAME basin has much precipitation in the spring /summer season (from April to October) because of typhoons rather than the autumn / winterseason (from November to March), whereas the SIRA basin has a strong relationship between
precipitation and elevation in the autumn / winter season because of heavy snowfall in the winterseason rather than the spring / summer season. These relationships between precipitation andelevation were used in the hydrological analysis. The period of available hydrological data is 20years from 1 January 1991 to 31 December 2010 for the SAME basin and 10 years from 1 October2003 to 30 September 2013 for the SIRA basin.
Hydrological model
The schematic structure of the hourly hydrological model is shown in Fig. 3. The model comprises
approximately three components: the Diskin-Nazimov rainfall infiltration model (Diskin andNazimov, 1995, 1996), groundwater recharge and groundwater runoff calculations, and a direct
runoff component that represents surface water storage within the basin. The output from eachreservoir element can be described by a linear function or a nonlinear function. The basin wasdivided into a 500 m mesh, and at each grid the rainfall was estimated by an inverse distanceweighting method using the seven rainfall gauges in the basin. Also at each grid, the infiltration
rate and then the excess rainfall were calculated. The parameters except Au and N were calibrated
and measured by Fujimura and Ando (2001) and Fujimura et al. (2012).
RESULTS
Sensitivity analysis
Since the two parameters, the fractional recession constant Au and the exponent value N, aredetermined by trial-and-error, uncertainty remains in these parameters. To evaluate these twoparameters for low flow, sensitivity analysis was carried out. In the analysis, the Au value ranges
from 0.0001 to 0.0100 in steps of 0.0001 (a total of 100 steps), and the N value ranges from 1.0 to100.0 in steps of 0.5 (a total of 199 steps). Therefore, the total number of simulations was 19 900(100 times 199) for each basin. One simulation for the 20 year period of the SAME basin and 10year period of the SIRA basin took approx. 0.82 minutes and 0.27 minutes, respectively, on a54

Kazumasa Fujimura et al.
SF；Snowfall

Ｐｒｅｃｉｐｉｔ ａｔ ｉｏｎ

Snowfall-snowmelt
Sugawara model

R； Rainfall

SW；Snowmelt
Actual infiltration
to surface soilf ；Infiltration rate
f = f０-(f0-fc)・S / Smax

Excess rainfall

f0； initial infiltration
fc；final infiltration
Smax；Maximum soil moisture

Diskin-Nazimov
infiltration model

S；Soil moisture in surface soilE；evapotranspiration
Hamon formulaPr；percolation
Pr = fc・S／Smax

Sd；Surface water stored within basin

Ms；Soil moisture in unsaturated zone
Mn；
Normal soil moisture
Gr；Groundwater recharge
Gr = α・(Ms-Mn)
α：constant

Storage function method
Sd = K・Qd P
K, P：constant

Direct runoff
calculation
Qd；Direct runoff

Sg；Groundwater storage
in saturated zone

Groundwater runoff
Qg = Au N・Sg N
Au, N：constant

Groundwater recharge
and groundwater runoff
calculation

Q；Total runoff
Q = Qg + Qd

Fig. 3 Simplified schematic of the hourly hydrological model.
Fractional recession constant Au

0.0100(a)0.00900.0080(b)

0.00700.00600.00500.00400.00300.00200.0010
10 20 30 40 50 60 70 80 90 100
Storage exponent value N
2550

75 100 125

ADRE (%)

Fig. 4 (a) Visualized ADRE of the SIRA basin and (b) lower 1% values of the ADRE and identified AuN exponential equations for the two basins.

computer with an Intel® Core™ i7-3820 processor at 3.60 GHz. Each simulation and the twoparameters were assessed using the Average Daily runoff Relative Error (ADRE) as the following:
ADRE =

 Q − Qod
1× ∑  cd
× 100 n
 Qod


(%)

(5)

Identification of low-flow parameters using a hydrological model in mountainous basins in Japan55

where Qcd is the calculated mean daily total runoff, Qod it the observed mean daily total runoff andn is the number of evaluated observations. In this study, the ADRE focused on low flow with theobserved runoff values from 0.4 to 10 mm/day.
The results of this sensitivity analysis with respect to the relationship between Au and N areshown in Fig. 4. For example, for the SIRA basin, the visualized ADRE is shown as contours in
Fig. 4(a), in which the plots of the lower values of the ADRE is shown as the central contour in thegraph. For both basins, the plots of the lower (lower 1%) values of the ADRE are shown in Fig. 4(b). The plots of the lower 1% values of the ADRE for the SAME basin overlap those for the SIRAbasin. The relationship between Au and N is formulated as the following exponential equations;1(SAME basin)
26.91 N 1.041

Au =andAu =1
34.55 N 1.060(SIRA basin)(6)

Precipitation（mm/day）

The combinations of Au and N that yield the lower values of the ADRE are identified by theexponential equations, such as equation (6). The values of the constants in each equation aresimilar, despite the different natural conditions of each basin. It is considered that when N valueshigher than 10 are input into the exponential equation and Au values obtained, hydrologicalanalysis can be performed within the satisfaction situation. Furthermore, the relationship between
groundwater storage and groundwater runoff (discharge) exhibits strong nonlinearity because theN values are considered to exceed 10. The minimum value of the ADRE is 32.196% using N =100.0 and Au = 0.0003 for the SAME basin, and 38.058% using N = 70.0 and Au = 0.0003 for theSIRA basin. The minimum ADRE values are not low; it is higher than 30% for both basins, which
seems the effect of the turbulence of the observed hydrograph. An example of the simulated mean
daily hydrograph for the SIRA basin using optimal parameters is shown in Fig. 5.
Shirakawa Dam basin 1 October 2003- 30 September 2013

Au；0.0003 N；70.0

020
40
60
80
100
120
140

RainfallSnowfall

Runoff（mm/day）

100

101

Observed
03

2004

2005

2006

Simulated
2007

2008

2009

2010

2011

2012

2013

Fig. 5 An example of simulated mean daily hydrograph for the SIRA basin using the optimized
parameters of Au = 0.0003 and N = 70.0.
(a)Fig. 6 Annual water balance for the SAME basin (a) and for the SIRA basin (b).

(b)

56

Kazumasa Fujimura et al.

Annual water balance
The annual water balances have been estimated by hydrological analysis using the optimal
parameters of low flow. The SAME basin experiences some heavy rainfall events in the summer
season, e.g. typhoons, whereas the SIRA basin is subjected to heavy snowfall in the winter season,
as indicated by the precipitation in Fig. 6(a),(b). Geologically, Mesozoic and Palaeozoic
formations are found in the SAME basin, and Quaternary, and Tertiary Quaternary volcanic rockformations are found in the SIRA basin. Low flows are classified according to the basin geology(Musiake et al. 1975); the recession curves are gentle for Quaternary/Tertiary Quaternary volcanic
rock basins and steep for Mesozoic/Palaeozoic formation basins. These are indicated in annual
water balances in Fig. 6(a),(b), where the SIRA basin has much greater groundwater runoff thanthe SAME basin.
CONCLUSIONSIn this study, the two parameters of the storage–discharge equation for low flow, that is theconstant Au and the exponent value N, were identified and formulated using the exponential
equation on the basis of the results of sensitivity analysis using the hourly hydrological model. The
optimal sets of Au and N, which yield the lowest relative error in the hydrological analysis, areexpressed in the exponent function of Au and N. The optimal value of exponent N appears as
higher than 10 in this study, which suggests low flow has high nonlinearity because low flow is
the cumulative hydrological phenomenon in a wide basin scale for a long time period.
Acknowledgements The authors wish to express their sincere gratitude to Ikeda Dam Control andManagement Office of Japan Water Agency for providing rainfall and dam inflow data. This work
was supported by the Research Program on Climate Change Adaption (the RECCA Project) of the
Ministry of Education, Culture, Sports, Science and Technology.
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