Temporal and spatial distributions of flood water storage volume of
the main river and tributaries in the Ishikari River basin
Shoji Fukuoka 1, Yutaro Ishii 22

51
Research and Development Initiative, Chuo University, Tokyo, 112-8551, Japan
Civil, Human and Environmental Engineering, Chuo University, Tokyo, 112-8551, Japan

Correspondence to: Yutaro Ishii (a.18.6xpw@g.chuo-u.ac.jp)
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 in addition
to flood control of the main river. This will be accomplished by understanding flood formation process in the10basins 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 the Ishikari
River, Hokkaido, Japan. Temporal and spatial water storage volume distributions in the Chitose River and Ishikari
River basins give a new graphical representative method to visualize that when, where, how much volume ofrainfall are stored in each basin, and make it possible to verify effects of flood control measures.

15 1 Introduction

30 rainfall distribution and topographical and geologicalcharacteristics are used to estimate runoff discharge.

In recent years, Japan experienced frequent and intense

On the latter method, Fukuoka (2004) proposed 2D flood

heavy rainfalls, resulting in serious flood disasters. To

flow analysis method to obtain flow velocity distributions

have an integrated flood control plan of the entire basin

and flood flow discharge hydrographs at any point in rives.

including the main river and tributaries is important for
20 reducing effectively flood disasters. For this purpose, it is

35 Fukuoka (2017) also estimated the temporal and spatial
distributions of water storage volume in the upstream basin,essential to estimate the flood flow dynamics in the maindams, rivers, and inundation area in the September 2015

river and tributaries. There are two analysis methods forflooding of the Kinu River basin and visualized watersuch studies: hydrological rainfall-runoff analysis andstorage volumes in the basin. Mikami et al. (2021)

hydraulic flood flow analysis.
25 The former is a method for mainly representing the runoff

40 evaluated effects of the discharge hydrographs of the
primary and secondary tributaries on the flood discharge

mechanism of rainfall and estimating the discharge. Theof the main river in the upper Tone River basin by 2D flood

storage function method (Kimura 1961; Hoshi et al.1982),

flow analysis.

tank models (Sugawara 1972; Gotoh et al. 2019), andIn this study, analysis of flood flow of the 2016 typhoon

distributed models (Tachikawa et al. 2004) considering

45 was conducted to obtain the water surface profiles over1

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

Figure 2: Basin map of the lower Ishikari River.

time for the main river and tributaries in the lower Ishikari
River basin shown in Figure 1 and Figure 2. The discharges

2 Characteristics of river basin and rainfall

from most of secondary tributaries are estimated by using
the storage function method by Hoshi et.al (1982). We first

The Ishikari River has the second largest basin in Japan

5 examined propagation characteristics of the three floodand consist of a large number of tributaries. The

flows of 2016 typhoon and the effects of the discharge

Ikusyunbetsu River, Yubari River, and Chitose River arehydrographs in the Chitose River basin on the Ishikari

15 primary tributaries and confluent in the lower Ishikari

River. Then, the temporal and spatial water storage volume

River reach between Ishikariohashi (25 km) anddistributions in each tributary and entire basin are

Iwamizawaohashi (45 km).
There are 83 rainfall observation stations in the lower

10 discussed.

Ishikari River basin as shown in Figure 1. The hyetographs
20 at the main stations in the upper Ishikari River basin and2

Figure 3: Flood surface profile of the Ishikari River

Figure 5: Flood surface profile of the Ishikari River

in Typhoon No. 7.

in Typhoon No. 11.

Figure 4: Flood surface profile of the Chitose River

Figure 6: Flood surface profile of the Chitose River

in Typhoon No. 7.

in Typhoon No. 11.

the Chitose River basin are also shown in Figure. 1.
Typhoons No. 7, 11, and 9 hit Hokkaido during August 17-

20 3.2 Calculation method of runoff discharge insecondary tributaries

23, 2016, and brought extensive disasters in the Ishikari
The three typhoons took different paths,

Flood flows of the secondary tributaries coloured by red in

5 resulting in different rainfall distributions. Typhoon No. 7

Figure 2 were analysed in the same way as the flood

brought the rain exceeding 20 mm/h in the Chitose Rivercalculation of the main and primary rivers. However, forbasin and Typhoons No. 11 and 9 did the peak rain about

25 the secondary tributaries coloured by orange in Figure 2,

River basin.

water levels were not available. Therefore, runoff volumes

25 mm/h in the upper basin of the Ishikari River basin.

from such tributaries were estimated by the storage
function method (Hoshi et al.1982).
3 Analysis method
10 3.1 Flood flow analysis in the main river and primary
tributaries

4 Analysis results

The objective rivers of this study are coloured in red in

30 Figure 3 shows the temporal variations of the water surface

Figure 2. The upstream boundary condition for the analysis

profiles of the Ishikari River floods due to Typhoon No. 7.

was given by observed water level. The 2D flood flow

Figure 4 also shows the temporal variations of the water

15 analysis was conducted to coincide with the observed

surface profiles of the Chitose River. The peak discharge

water surface profiles and then, flow velocity distributionsof Ishikari River occurs at 21:00 August 18. On the otherwere calculated at each cross-section. The discharge

35 hand, the Chitose River reaches its peak at 1:00 August 18.

hydrograph was obtained from calculated velocity

Backwaters from the Ishikari River to the Chitose River

distributions and channel area during flood.

are comparatively small at the peak time.
3

Figure 8: Discharge hydrograph of the Chitose River.

Figure 7: Discharge hydrograph of the Ishikari River.

Typhoon No. 11 brought more rainfall in the upper reach

30 determined to coincide with the observed temporal andof the Ishikari River than Typhoon No. 7. Figure 5 shows

spatial distributions of the water level of each river. The

that the peak water level of the Ishikari River of Typhoon

discharge

11 is higher than that of Typhoon No. 7. Figure-6 showsdetermined from the velocity distributions and water level

5 that the water level of the Chitose River is also rising duechange obtained from the analysis. Then, the temporal andto the influence of the backwater of the Ishikari River. In

35 spatial river water storage volume, 𝑆𝑟𝑖𝑣𝑒𝑟 , is calculatedhydrographs

at

each

particular, at 19:00 August 21, the backwater reaches up to

from Equation (1).

40 km.

𝑑𝑆𝑟𝑖𝑣𝑒𝑟 /𝑑𝑡 = 𝑄𝑖𝑛 (𝑥) − 𝑄𝑜𝑢𝑡 (𝑥 + ∆𝑥)

The discharge hydrographs of the Ishikari River are shown

compared in Figure 8. Typhoon No. 7 brought heavy(1)

𝑄𝑜𝑢𝑡 (𝑥 + ∆𝑥) (m3/s) is the discharge at the downstream
40 section x+∆x.
Then, the water storage volume of the river basin can be

rainfalls in the Chitose River basin, and the peak of floodobtained by Equation (2), storage volume equation, whichflows of the Chitose River occurred about 1 hour before ofis based on the rainfall volume in the basin, storage

15 the Ishikari River. In particular, the peak at 1:00 a.m.

volumes by dams, retarding basins, etc., and river channel

August 18 was 491 m3/s at Uranosawa.
In the second and third typhoons, the Chitose River areare

𝑄𝑖𝑛 (𝑥) (m3/s) is the discharge at the upstream section x.

10 in Figure 7. The calculated discharge hydrograph and theobserved discharge at two stations of the Chitose River arecross-section

45 storage volume calculated by Equation (1).
𝑑𝑆𝑟𝑖𝑣𝑒𝑟 /𝑑𝑡 + 𝑑𝑆𝑟𝑖𝑣𝑒𝑟 /𝑑𝑡 + 𝑑𝑆𝑟𝑖𝑣𝑒𝑟 /𝑑𝑡

strongly influenced by the backwater of the Ishikari River.
At 19:00 August 21, the peak discharge time of the Ishikari=

20 River, the discharge at 0km of the Chitose River is nearly1
3.6

𝐴 ∙ 𝑅 − 𝑄𝑜𝑢𝑡

(2)

zero. As the water level of the Ishikari River drops, theA(km2) is the basin area, R(mm/h) is the rainfall in the

discharge from the Chitose River to the Ishikari Riverbasin, 𝑆𝑑𝑎𝑚 (m3) is the volume of water storage in dams,

increases, reaching 240 m3/s at 7:00 August 22.

50 retarding basins and lakes, 𝑆𝑏𝑎𝑠𝑖𝑛 (m3) is the volume ofwater stored in the basin, and 𝑄𝑜𝑢𝑡 (m3) is the riverdischarge outgoing from the downstream end of the basin.

5 Graphical representations of the distribution of
25 temporal and spatial water storage volume in the basin

Calculated distributions of temporal and spatial water

Let us discuss the method how to obtain the temporal andstorage volume demonstrate when, where, how much rain

spatial water storage distributions of the entire basin and

55 waters are in the basin. Figure 9 shows the graphicaleach tributary basin. Temporal and spatial water storage

representation of distribution of water storage volume involumes are estimated by the 2D flood flow analysis

the Chitose River basin for three typhoons. Typhoon No. 7
4

Figure 9: Graphical representation of temporal andFigure 10: Graphical representation of temporal andspatial water storage volume distributions

spatial water storage volume distributionsin the Chitose River basin.

in the Ishikari River basin.

brought a large amount of rainfall in the basin, and the

It is an essential subject to find how the flood control inflood flow in the Ishikari River was affected by inflow

tributaries reduces severe floodings in the entire basin.

from the Chitose River flood. The storage volume in theCreating this map before and after the implementation of

Chitose River increased significantly due to the rising

30 flood control measures in the basin makes it possible to

5 water level of the Ishikari River. This is evident by theverify effect of measures to be adopted.

water storage volume distributions described in the red
area of Figure 9. This shows that the flood of the Chitose

6 Conclusion

River is markedly controlled by the water level of the
Ishikari River. Figure 10 also shows the integrated water

The flood flow analysis was conducted in the lower

10 storage volume distributions in the Ishikari River basin for

Ishikari River basin for three typhoons in 2016. Based on

three typhoons.

35 the analysis results, we investigated the flood formation

The amount of water storage volume in the basin, 𝑆𝑏𝑎𝑠𝑖𝑛 ,process of the Chitose River and its effects on the floodis estimated from the difference between the total rainfall

flow of the Ishikari River. The temporal and spatial water

volume and the summation of water volume stored into thestorage volume distributions in the Ishikari River basin and

15 dams, lakes, and rivers and water volume outgoing fromthe Chitose River basin were analysed. The graphicalthe basin. Therefore, it is a future issue to examine how,

40 representation of storage water volume distributions

where, when, how much, 𝑆𝑏𝑎𝑠𝑖𝑛 waters are stored and topresents a new way to visualize when, where, how muchinvestigate the mechanism of water movement in 𝑆𝑏𝑎𝑠𝑖𝑛 .

volume of rainfall exist in the basin.
Graphical representation of storage water volume

By analysing the main river and tributaries as a whole, it isdistributions before and after the implementation of flood

20 possible to obtain the water storage volume distributions
not only in each basin consisting of these tributaries, but

45 control measures provides important means for making a
choice of the proper flood control in the river basin.

also in the entire basin including the main river.
Figure 11 presents the graphical representation of storage
water volume distributions in each basin and the entire
25 basin. This makes it easy to understand not onlyhydrological and hydraulic characteristics of each basins.
5Figure 11: Graphical representations of temporal and spatial water storage volume distributions in each basinon the basin map.

Fukuoka, S., Watanabe, A., Hara, T. and Akiyama, M.：
Highly accurate estimation of hydrograph of flood

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