Open Access

Temporal and spatial distributions of flood water storage
volume of the main river and tributaries in the Ishikari
River basin
Shoji Fukuoka1 and Yutaro Ishii2
1 Research and Development Initiative, Chuo University, Tokyo, 112-8551, Japan
2 Civil, Human and Environmental Engineering, Chuo University, Tokyo, 112-8551, Japan

Correspondence: Shoji Fukuoka (sfuku@tamacc.chuo-u.ac.jp)
Received: 21 July 2023 – Revised: 18 October 2023 – Accepted: 13 December 2023 – Published: 19 April 2024

Abstract. In recent years, Japan experienced frequent and intense heavy rainfalls, resulting in serious flood

disasters in many areas. It is also necessary to control floods in tributaries and basins of these tributaries inaddition to flood control of the main river. This will be accomplished by understanding flood formation process
in the basins of tributaries as well as the main river. Integrated flood flow analysis for the main river and tributaries
was conducted by the use of observed temporal changes in the water surface profiles of the 2016 flood in theIshikari River, Hokkaido, Japan. Temporal and spatial water storage volume distributions in the Chitose Riverand Ishikari River basins give a new graphical representative method to visualize that when, where, how muchvolume of rainfall are stored in each basin, and make it possible to verify effects of flood control measures.

1Introduction

In recent years, Japan experienced frequent and intense
heavy rainfalls, resulting in serious flood disasters. To havean integrated flood control plan of the entire basin including the main river and tributaries is important for reducing
effectively flood disasters. For this purpose, it is essential toestimate the flood flow dynamics in the main river and tributaries. There are two analysis methods for such studies: hydrological rainfall-runoff analysis and hydraulic flood flowanalysis.
The former is a method for mainly representing the runoff
mechanism of rainfall and estimating the discharge. The storage function method (Kimura, 1961; Hoshi and Yamaoka,1982), tank models (Sugawara, 1972; Gotoh et al., 2019),
and distributed models (Tachikawa et al., 2004) consideringrainfall distribution and topographical and geological characteristics are used to estimate runoff discharge.
On the latter method, Fukuoka et al. (2004) proposed 2Dflood flow analysis method to obtain flow velocity distributions and flood flow discharge hydrographs at any point inrives. Fukuoka (2017) also estimated the temporal and spatial
distributions of water storage volume in the upstream basin,

dams, rivers, and inundation area in the September 2015
flooding of the Kinu River basin and visualized water storage
volumes in the basin. Mikami et al. (2021) evaluated effectsof the discharge hydrographs of the primary and secondary
tributaries on the flood discharge of the main river in the upper Tone River basin by 2D flood flow analysis.
In this study, analysis of flood flow of the 2016 typhoon
was conducted to obtain the water surface profiles over time
for the main river and tributaries in the lower Ishikari Riverbasin shown in Figs. 1 and 2. The discharges from most of
secondary tributaries are estimated by using the storage function method by Hoshi and Yamaoka (1982). We first examined characteristics of the three flood flows of 2016 typhoonand the effects of the discharge hydrographs in the ChitoseRiver basin on the Ishikari River. Then, the temporal and spatial water storage volume distributions in each tributary andentire basin are discussed.
2Characteristics of river basin and rainfall

The Ishikari River has the second largest basin in Japanand consist of a large number of tributaries. The Ikusyunbetsu River, Yubari River, and Chitose River are primary

Published by Copernicus Publications on behalf of the International Association of Hydrological Sciences.

ICFM9 – River Basin Disaster Resilience and Sustainability by All

Proc. IAHS, 386, 47–53, 2024
https://doi.org/10.5194/piahs-386-47-2024© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.48

S. Fukuoka and Y. Ishii: Temporal and spatial distributions of flood water storage volume of the main river

Figure 1. Basin map of the Ishikari River and the Chitose River and the rainfall hyetographs at the main stations in the upper Ishikari Riverbasin and the Chitose River basin.

Figure 2. Basin map of the lower Ishikari River.

tributaries and confluent in the lower Ishikari River reach
between Ishikariohashi (25 km from the river mouth, hereinafter shown as KP25) and Iwamizawaohashi (KP45). Thereare 83 rainfall observation stations in the lower Ishikari Riverbasin as shown in Fig. 1. The hyetographs at the main stationsin the upper Ishikari River basin and the Chitose River basin
are also shown in Fig. 1. STS Chanthu, TS Kompasu, andTY Mindulle which are the names of typhoons hit Hokkaido
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during 17–23 August 2016, and brought successively extensive disasters in the Ishikari River basin. The three typhoons
took different paths, resulting in different rainfall distributions. STS Chanthu brought the rain exceeding 20 mm h−1 inthe Chitose River basin and TS Kompasu and TY Mindulle
did the peak rain about 25 mm h−1 in the upper basin of theIshikari River basin.

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S. Fukuoka and Y. Ishii: Temporal and spatial distributions of flood water storage volume of the main river

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Figure 3. Flood surface profile of the Ishikari River in STS Chanthu.

Figure 4. Flood surface profile of the Chitose River in STS Chanthu.

3
3.1

Analysis method
Flood flow analysis in the main river and primary
tributaries

Parts of red line shown in Fig. 2 are river reaches analysed inthe 2D flood flow analysis so as to match the observed water surface profiles. The upstream boundary condition for theanalysis was given by observed water level. Velocity profiles
were then calculated at each cross-section. The discharge hydrograph was obtained from calculated velocity distributions
and channel area during flood.

3.2

Calculation method of runoff discharge in secondary
tributaries

Flood flows of the secondary tributaries coloured by red inFig. 2 were analysed in the same way as the flood calculation of the main and primary rivers. However, for the secondary tributaries coloured by orange in Fig. 2, water level
data was not available because there were not water-level observation stations. Therefore, runoff volumes from such tributaries were estimated by the storage function method (Hoshiand Yamaoka, 1982) and added as lateral inflow to the 2D
flood flow analysis. The residual areas were not included in
the lateral inflow because their areas are very small.
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4Analysis results

Figure 3 shows the temporal variations of the water surface
profiles of the Ishikari River floods due to STS Chanthu. Figure 4 also shows the temporal variations of the water surface
profiles of the Chitose River. The peak discharge of Ishikari
River occurred at 21:00 JST (Japan Standard Time), 18 August. On the other hand, the Chitose River reached its peak at
01:00 JST, 18 August. Backwaters from the Ishikari River tothe Chitose River are comparatively small at the peak time.
TS Kompasu brought more rainfall in the upper reach ofthe Ishikari River than STS Chanthu. Figure 5 shows thatthe peak water level of the Ishikari River of TS Kompasu
is higher than that of STS Chanthu. Figure 6 shows that thewater level of the Chitose River is also rising due to the riseof water level of the Ishikari River (backwater). In particular,
at 19:00 JST, 21 August, the backwater reaches up to 40 km
from the confluence of the Ishikari River.
The discharge hydrographs of the Ishikari River are shownin Fig. 7. The calculated discharge hydrograph and the observed discharge at two stations of the Chitose River are compared in Fig. 8. STS Chanthu brought heavy rainfalls in theChitose River basin, and the peak of flood flows of the Chitose River occurred about 1 h before of the Ishikari River. In
particular, the peak at 01:00 JST, 18 August was 491 m3 s−1at Uranosawa.
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S. Fukuoka and Y. Ishii: Temporal and spatial distributions of flood water storage volume of the main river

Figure 5. Flood surface profile of the Ishikari River in TS Kompasu.

Figure 6. Flood surface profile of the Chitose River in TS Kompasu.

Figure 7. Discharge hydrograph of the Ishikari River.

Figure 8. Discharge hydrograph of the Chitose River.

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S. Fukuoka and Y. Ishii: Temporal and spatial distributions of flood water storage volume of the main river

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Figure 9. Graphical representation of temporal and spatial water storage volume distributions in the Chitose River basin.

Figure 10. Graphical representation of temporal and spatial water storage volume distributions in the Ishikari River basin.

In the second, the Chitose River are strongly influenced by
the backwater of the Ishikari River. At 19:00 JST, 21 August,the peak discharge time of the Ishikari River, the discharge at0 km from the confluence of the Ishikari River is nearly zero.
As the water level of the Ishikari River goes down, the discharge from the Chitose River to the Ishikari River increases,
reaching 240 m3 s−1 at 07:00 JST, 22 August.

5

Graphical representations of the distribution of
temporal and spatial water storage volume in thebasin

Let us discuss the method how to obtain the temporal andspatial water storage distributions of the entire basin andeach tributary basin. Water storage distributions and volumes
are estimated by the 2D flood flow analysis determined tocoincide with the observed water level of each river. Thedischarge hydrographs at each cross-section are determinedfrom the velocity distributions and water level change obtained from the analysis. Then, the temporal and spatial riverwater storage volume, Sriver , is calculated from Eq. (1).
dSriver /dt = Qin (x) − Qout (x + 1x)
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Qin (x) (m3 s−1 ) is the discharge at the upstream section x(m). Qout (x + 1x) (m3 s−1 ) is the discharge at the downstream section x + 1x.
Then, the water storage volume of the river basin can beobtained by Eq. (2), storage volume equation, which is basedon the rainfall volume in the basin, storage volumes by dams,retarding basins, etc., and river channel storage volume calculated by Eq. (1).
dSbasin /dt + dSdam /dt + dSriver /dt=

1
A · R − Qout
3.6(2)A (km2 ) is the basin area, R (mm h−1 ) is the rainfall in thebasin, Sdam (m3 ) is the volume of water storage in dams, retarding basins and lakes, Sbasin (m3 ) is the volume of water
stored in the basin, and Qout (m3 ) is the river discharge outgoing from the downstream end of the basin.
Calculated distributions of temporal and spatial water storage volume demonstrate when, where, how much rain waters are in the basin. In this study, the average rainfall forthe basin was calculated by the Thiessen method using theobserved rainfall data from the rainfall stations shown inFig. 1. The storage capacity of the dam is obtained from thedifference between the actual discharge and the inflow calProc. IAHS, 386, 47–53, 202452

S. Fukuoka and Y. Ishii: Temporal and spatial distributions of flood water storage volume of the main river

Figure 11. Graphical representations of temporal and spatial water storage volume distributions in each basin on the basin map.

culated from the water level change. The storage capacityof Lake Shikotsu is obtained from the product of the water level change and the surface area of Lake Shikotsu. Lake
Shikotsu stored 2.65 × 107 m3 at the peak. Izari River Dam
stored 9.00×104 m3 at the peak. Figure 9 shows the graphicalrepresentation of distribution of water storage volume in theChitose River basin for three typhoons. In the lower basinof the Chitose River, there was a station where small-scale
rainfall of 0.5 mm h−1 was measured for 1 h at 00:00 JST on
17 August, so that the figure shows the basin storage from thebeginning of the graph. STS Chanthu brought a large amountof rainfall in the basin, and the flood flow in the Ishikari River
was affected by inflow from the Chitose River flood. Thestorage volume in the Chitose River increased significantly
due to the rising water level of the Ishikari River. This is evident by the water storage volume distributions described in
the red area of Fig. 9. This shows that the flood of the Chitose River is markedly controlled by the water level of theIshikari River. Figure 10 also shows the integrated water storage volume distributions in the Ishikari River basin for threetyphoons.
In this way, the graphical representation of storage water
volume distributions can clearly illustrate the characteristicsof the basin. Therefore, as shown in Fig. 11, the characteristics of the basin can be represented according to each scaleby overlaying them on the basin map. In addition, creating
this map before and after the implementation of flood control measures in the basin makes it possible to verify effectof measures to be adopted. This is an essential task in order toknow how flood control at each basin scale affects the entire
basin.
In this study, the amount of water storage volume in thebasin, Sbasin , is not directly evacuated, but estimated from thedifference between the total rainfall volume and the summation of water volume stored into the dams, lakes, and rivers

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and water volume outgoing from the basin. In the future, theanalysis using the observation of water surface profile in thetributaries will be extended upstream to calculate properly
the amount of runoff volume from upstream small basins.
Then, we will investigate the runoff mechanism and storage
conditions by using distributed tank model so as to fit theflow discharge hydrographs obtained in the tributary.
6Conclusion

The flood flow analysis was conducted in the lower Ishikari
River basin for three typhoons in 2016. Based on the analysis results, we investigated the flood formation process of theChitose River and its effects on the flood flow of the Ishikari
River. The temporal and spatial water storage volume distributions in the Ishikari River basin and the Chitose Riverbasin were analysed. The graphical representation of storage
water volume distributions presents a new way to visualize
when, where, how much volume of rainfall exist in the basin.
Graphical representation of storage water volume distributions before and after the implementation of flood control
measures provides important means for making a choice ofthe proper flood control in the river basin.

Code availability. The program was developed by Research andDevelopment Initiative, Chuo University Fukuoka Unit. It is notopen to the public.

Data availability. The data is provided by the Hokkaido Regional

Development Bureau of the Ministry of Land, Infrastructure, Transport and Tourism. It is not open to the public.

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S. Fukuoka and Y. Ishii: Temporal and spatial distributions of flood water storage volume of the main river
Author contributions. SF: Conceptualization, Funding acquisi-tion, Methodology, Project administration, Supervision, Validation,Writing-review & editing. YI: Formal analysis, Writing-originaldraft preparation, Investigation, Software, Data curation, Visualization.

Competing interests. The contact author has declared that noneof the authors has any competing interests.

Disclaimer. Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibilitylies with the authors.

Special issue statement. This article is part of the special issue“ICFM9 – River Basin Disaster Resilience and Sustainability byAll”. It is a result of The 9th International Conference on FloodManagement, Tsukuba, Japan, 18–22 February 2023.

Acknowledgements. We would like to thank the Hokkaido Re-gional Development Bureau of the Ministry of Land, Infrastructure,
Transport and Tourism and the River and Erosion Control Divisionof the Construction Department of the Hokkaido Government providing the data of the Ishikari River Basin for us.

53

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Review statement. This paper was edited by Mohamed Rasmy

and reviewed by three anonymous referees.

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