Hydrology in a Changing World: Environmental and Human Dimensions
Proceedings of FRIEND-Water 2014, Montpellier, France, October 2014 (IAHS Publ. 363, 2014).

431

Application of a hydrological model to evaluate the potential
hydro energy in a mountainous small river basin of JapanKAZUMASA FUJIMURA1, MASAHIRO MURAKAMI2, YOSHIHIKO ISERI3 &SHINJIRO KANAE3

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

Abstract The low flow from mountainous basins has long been developed to supply water to urban areas
downstream. Little attention was paid to developing hydro-electricity for the community in the hilly andmountainous regions. After the disaster of TEPCO’s Fukushima no. 1 nuclear power plant, a new energy
policy of Japan directs a decrease on the dependence on nuclear power. Feed-in tariff (FIT) of renewableenergy was enacted on 1 July 2012 to cope with the increasing small-scale distributed types of naturalenergy development, including mini-hydro-power. The aim of this study is to apply the hydrological model(Fujimura et al., 2012) with an hourly time scale coupling the Diskin–Nazimov infiltration model for themini-hydropower development. The Seto River basin (53.7 km2), which is located in the central mountainregion of Shikoku in western Japan, was selected to develop mini-hydro-electricity for the local community.
The low flow of the Seto River, which is being diverted to supply M&I water for Kochi city by tunnels witha differential head of 25 m, is not used for mini-hydropower. The optimal parameters of the storage function
equation for low flow are estimated on the basis of hydrological model analysis. The discharge duration
curve and the potential hydropower duration curve are calibrated by the hydrological model to apply 20years of hourly time-series data (1991–2010) using optimized parameters. The results of the analysis of theSeto River basin indicate that: (i) the set of two parameters in the storage function equation for the low flowin the hydrological model is identified, and (ii) the potential of the mini-hydropower is evaluated to satisfy
local power demand as well as restoring the economy of the handicapped community with the surplus
hydropower electricity.
Key words hydrological analysis; low flow; storage function equation; optimal parameters; hydropower duration curve

INTRODUCTION
The mountainous areas occupy about 70% of the land area in Japan and its climate is subject to theinfluence of the Asia monsoon which brings much rainfall and snowfall in mountainous areas inthe summer and the winter. Water resources in Japan are therefore obtained from the mountainous
areas, especially for the low flow from the basin.
Hydroelectric power in Japan began in 1888 at Miyagi Boseki Sankyozawa silk spinning plantin Sendai, Miyagi Prefecture. Since then many low head hydropower plants were developed as themain energy at the time. However, in the last half century, most of the plants disappeared becauseof the shift from hydropower to thermal power and nuclear power as the main energy sources.
Water resources in mountainous areas are used to supply water for the urban areas downstream. In
recent years little attention has been paid to economically vitalize the regional community using
the low head hydropower in the hilly and mountainous regions. After the serious disaster ofTEPCO’s Fukushima no. 1 nuclear power plant on 11 March 2011, the new energy policy of Japan
has tried to decrease the dependence on nuclear power. A feed-in tariff (FIT) for renewable energy
was started on 1 July 2012, owing to increasing the small-scale distributed type of natural energy
development, including mini-hydropower.
Reliable estimation of the available runoff water for the hydropower in mountainous basins isimportant for the local community due to vitalization. The daily hydrological model for a hilly andmountainous basin was proposed by Ando (1988), and was based on earlier studies by Ando et al.
(1983, 1984). Owing to the advances in computer and gauging technology, which have promoted
the development of new methods for analysing hydrological processes, Fujimura et al. (2012)
developed the hourly hydrological model based on the Diskin-Nazimov infiltration model (DiskinCopyright  2014 IAHS Press432

Kazumasa Fujimura et al.

& Nazimov, 1995, 1996) and the storage function method for the direct runoff for mountainousbasins, and applied the hydrological model to 16 years of data for the Sameura Dam basin locatedin Kochi Prefecture, in the mountains of Shikoku in western Japan. Although the model showssatisfactory to good performance in terms of obtaining accurate long-term hydrographs and can beused to reproduce the hydrographs for flood events, the parameters used in the model aredetermined by trial-and-error.
The aim of this study was to apply the hourly hydrological model which was developed forthe mountainous basins to the mini-hydropower development in local communities. The specificobjectives were to: perform a sensitivity analysis using the hourly hydrological model and toidentify the optimal parameters in the storage function equation for low flow; and to estimate thedischarge duration curve and the potential hydropower duration curve for 20 years hourly timeseries data (1991–2010) using optimized parameters.
MATERIALS AND METHODS
Seto River basin
The Seto River basin (Fig. 1) is located within the Sameura Dam basin, which is in the central
mountain region of Shikoku in western Japan. The basin area is 53.7 km2 for the Seto River basin
and 472 km2 for the Sameura River basin. The elevation in the Seto River basin ranges from 369 to1498 m a.s.l. and its average elevation is 911 m a.s.l. The land is completely covered with forest
and there are few houses are in the Seto River basin. The low flow of the Seto River is being
diverted to supply M&I water for Kochi City by two tunnels of the Seto River Diversion and theJizoji River Diversion. The Seto River Diversion has a head water differential of 25 m which is
not used for mini-hydropower, therefore the Seto River basin is selected to develop a minihydropower for the local community in this study.

Kochi
0100kmKochi CityFig. 1 Map of the Seto River basin and hydrological stations.

Data
To analyse the hydrological process with an hourly time step, hourly rainfall, temperature anddischarge into the tunnel at the Seto River Diversion weir are used in this study. The rainfall data
at Kuromaru station in the basin and the discharge data at the weir are measured by the Ministry ofLand, Infrastructure and Transport. The temperature data at Motoyama station obtained by theAutomated Meteorological Data Acquisition System (AMeDAS) of Japan Meteorological Agency
is used. The period of data is the 20 years from 1991 to 2010. The DEM data with 50 m resolution
were obtained from the Geospatial Information Authority of Japan. The annual rainfall during 20years varies from 2192 mm as minimum value to 6523 as maximum value, and the average andApplication of a hydrological model to evaluate the potential hydro energy

433

median annual rainfall are 3353 mm and 3234 mm. The seasonal variation of rainfall as maximum,average, median and minimum in a 10 day period for 20 years at Kuromaru station are shown inFig. 2. The maximum and minimum rainfall have a significant difference throughout the year.
Except from February to June, the average and median rainfalls are different. There are extreme
rainfalls both at the high and low values in the Seto River basin in the year.

Fig. 2 Seasonal variation of rainfall based on 10 day period in the Seto River basin; maximum, average,
median and minimum data in 20 years from 1991 to 2010.

Fig. 3 Simplified schematic of the hourly hydrological model.

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Kazumasa Fujimura et al.

Hydrological model
The schematic structure of the hourly hydrological model is shown in Fig. 3. The model iscomprised of four components: infiltration and soil moisture in surface soil, soil moisture in
unsaturated zone, groundwater storage in saturated zone, and direct runoff component as surface
water storage within the basin. The output from each reservoir element uses the linear function andthe nonlinear function. The Diskin-Nazimov model was used to calculate infiltration on surface
soil, which accounts for the variable intensity of the rainfall.
APPLICATION
Sensitivity analysis
Nonlinearity of the low flow from a basin is calculated by the storage functional equation of thegroundwater runoff in the hydrological model. The equation is expressed by:(1)

Qg = Au N ⋅ Sg N
(1-N) / N, Sg is the groundwater storage in thewhere Au is the fractional recession constant in mm
saturated zone in mm, Qg is the groundwater runoff in mm h-1, and N is the exponent value.
Since the two parameters, the fractional recession constant Au and the exponent value N, aredetermined by trial-and-error, there is a remaining uncertainty in these parameters. In order toevaluate these two parameters for the low flow, a sensitivity analysis was carried out in this study.
In the analysis the Au value ranges from 0.0002 to 0.0080 in steps of 0.0002, with a total of 40steps, and the N value ranges from 2.0 to 16.0 in steps of 0.5, with a total of 29 steps; therefore thetotal number of simulations was 1160 (40 × 29). One simulation for the 20-year period tookapprox. 1.366 minutes on an Intel® Core™ i7-975 at 3.33GHz. Each simulation and twoparameters were assessed using the average daily runoff relation error (ADRE) of the hydrologicalresult by the model:ADRE = Q − Qod
1× ∑  cd× 100 n Qod

(2)

(%)

Fractional recession constant value Au

where Qcd is the calculated mean daily total runoff, Qod it the observed mean daily total runoff, andn is the number of evaluated observations.
The results of this sensitivity analysis are shown in Fig. 4. Visualized ADRE with respect tothe relationship between the Au and the N is shown in Fig. 4 left. The lower relative error of the0.008
0.007
0.006
0.005
0.004

Au=1/{26.81N

1.172}

0.003
0.002
74.51 % (minimum) <= ADRE < 76.0%
155 plots

0.001
234 5 6 7 8 9 10Exponent value N20Fig. 4 Visualized ADRE (left) and selected ADRE values (right) with respect to the relationshipbetween the Au value and the N value in the storage functional equation for the low flow.

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435

ADRE, was around 75%, and is shown in the central region of Fig. 4 left. The selected ADRE of155 values out of 1160 results, between the minimum value of 74.51% and the value of 75.99%
are shown in Fig. 4, right. For the basin of the Seto River, the relationship between the fractional
recession value Au and the exponent value of N are formulated as the following exponent equation;
1(3)26.81⋅ N 1.172
The optimum values of the Au and the N in the storage function equation for low flow is identified
by the exponent equation in regard to the relationship of the Au and the N value.
Au =Rainfall （mm/day）

Seto River basin, 1991 - 2010 Mean daily hydrograph100200300
400Rainfall
Snowfall500

Runoff (mm/day ）Observed
Calculated
1001011991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Fig. 5 Comparison between the observed and calculated runoffs shown as log–log graph (left) andmean daily hydrograph (right) calculated by the hourly hydrological model using the optimized
parameters of the values Au = 0.0028 and N = 9.0.

Hydrological analysis
An analysis using the hourly hydrological model involving the optimal parameters in the storage
function equation for the low flow was carried out for the 20 years of hourly data between 1991
and 2010. The observed runoff data is the discharge which was measured at the entrance of thediversion tunnel of the Seto River Diversion weir. The weir is a fixed type so that the under flow at
the weir height flows to the diversion tunnel, while the overflow at the weir flows downstream tothe Sameura Dam. Therefore the maximum value of the observed runoff is 4.4 m3/sec,
7.08 mm/day and 0.295 mm/h for the basin area of 53.7 km2. Scatter plots of the hourlyhydrograph is shown as log–log graphs in Fig. 5 (left). The square of the correlation coefficient(R2) indicated as 0.666 and the relationship between the calculated runoff and the observed runoff
were roughly in agreement with the model performance. This is because the flood runoff occurs
frequently in year. When the water levels rise due to floods, it disturbs the water levelmeasurement. When the sand trap is controlled the data measurements are also disturbed. Figure 5(right) shows the observed and calculated hydrograph for 20 years. The observed hydrograph isunder 7.08 mm/day because of the diversion discharge. However, the value of the ADRE is
74.51% for the observed runoff discharge of under 7.08 mm/h, it also shows rough agreement withthe calculated hydrograph. The hydrograph greater than the value of 7.08 mm/h is simulated.
Potential hydropower duration curve
In order to estimate the potential hydropower for the Seto River basin, the simulated hydrograph isused for the discharge duration curve and the potential hydropower duration curve. Figure 6(a)shows the discharge duration curve for 20 years. The runoff height of 7.08 mm/day is themaximum discharge of the Seto River Diversion. In Fig. 6(a), the runoff height of 7.08 mm/day is
the runoff of the 1096th day of a total of 7305 days of the 20 years. It is equivalent to the 55 day
runoff in 365 days of a year. Therefore the 7.08 mm/day runoff from day 1 to day 55 is effective
for hydropower. The effective runoff of the hydropower from day 56 to day 365 is subjected to436

Kazumasa Fujimura et al.

simply the discharge duration curve. The practical hydropower output is calculated by thefollowing equation:(4)

P = 9.8 Q H ηtwhere P is the hydropower output in kW, Q is the discharge in m3 s-1, H is the differential waterhead (= 25 m) and ηt is the synthesis efficiency coefficient (assuming 0.7).
Daily hydropower generation is calculated by:(5)

Pd = 24× 9.8 Qday H ηtwhere Pd is the daily hydropower output in kWh, P is the hydropower output in kW and Qday is thedaily discharge in m3 s-1.

10010Seto River Diversion, Potential hydropowre duration curve 1991- 2010(a)
Runoff of the Maximum potential hydropower
1096day/7305day(55day/365day)
7.08mm/day
1901day/7305day(95day/365day)
4.88mm/day

3702day/7305day(185day/365day)
2.55mm/day

5503day/7305day(275day/365day)
1.50mm/day

17104day/7305day(355day/365day)
0.63mm/d

Hydropower (kWh)Daily Runoff (mm/day)

Seto River Diversion runoff (mm/day) 1991- 2010

1000000
A: Hydropower generation from day 1 to day 55.
991,749 kWh
B: Hydropower generation from day 55 to day 365.
2,112,112 kW (average of 20 years from day 1097 to day 7305)
100000
A+B: Annual potential hydropower generation
991,749 kWh +2,112,112kWh
1096day/7305day= 3,103,861kWh ≒3,100,000 kWh
10000(55day/365day) 1901day/7305day(95day/365day)

3702day/7305day(185day/365day)

5503day/7305day(275day/365day)(b)7104day/7305day(355day/365day)

1000

0.101000

2000
3000
4000
Duration of 20 years (Days)

5000

6000

7000

01000

2000
3000
4000
Duration of 20 years (Days)

5000

6000

7000

Fig. 6 (a) 20 years duration curve of the daily runoff and (b) the potential hydropower duration curve ofthe Seto River Diversion simulated by the hourly hydrological model.

Figure 6(b) shows the potential of the annual hydropower calculated by using equations (4)and (5). The potential of annual hydropower generation is evaluated to be 3 100 000 kWh
assuming the hydropower duration curve in Fig. 6(b). Annual income of the hydropower
generation is estimated to be JPY89 900 000 (USD934 061), assuming the unit price of feed intariff (FIT) of JPY29/kWh (USD0.30/kWh), for which the unit price is derived from the new feedin tariff (FIT) in July 2013, and JPY100 is converted to USD1.04. The mini-hydropower projectsatisfies the local power demand and generates the surplus economic benefit to the local
community in the mountainous small river basin.
CONCLUSION
In this study, the two parameters of the storage function equation for low flow, the recession
coefficient constant Au and the exponent value N, were identified and formulated by the exponent
equation based on a sensitivity analysis using the hourly hydrological model. As an application of
the hydrological cycle model using the optimized hydrograph, the Seto River basin was evaluatedfor the potential hydropower generation for the local community in the mountainous basin in Japan.
REFERENCES
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