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J-STAGE Advance published date: November 11, 2022
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SOLA, 2022, Vol.18, 235-238, doi: 10.2151/sola.2022-040

1

Global warming effect and adaptation for a flooding event at

2

Motsukisamu River in Sapporo

3
4

Yuka Kanamori1, Masaru Inatsu2, Ryoichi Tsurumaki3, Naoki Matsuoka3,

5

Tsuyoshi Hoshino4 and Tomohito J. Yamada5

6
1

7
8

2

Sapporo Regional Headquarters, Japan Meteorological Agency, Sapporo, Japan

Faculty of Science and Center for Natural Hazards Research, Hokkaido University,
Sapporo, Japan

9
3

10
4

11
12
13

5

Hokkaido Weather Technology Center Co. Ltd., Sapporo, Japan

Civil Engineering Research Institute for Cold Region, Sapporo, Japan

Faculty of Engineering and Center for Natural Hazards Research, Hokkaido
University, Sapporo, Japan

14(Submitted to Scientific Online Letters on the Atmosphere on 10 September 202215

and in a revised form on 13 October 2022)

16
17

Corresponding author: Masaru Inatsu, Hokkaido University, N10W8, Kita-ku, Sapporo,

18

Hokkaido, Japan, 060-0810. E-mail: inaz@sci.hokudai.ac.jp1920

Kanamori et al., Global warming effect and adaptation for a flooding event

21

2

Abstract

22

A set of hydrological experiments for a flooding event on September 11, 2014 at

23

Motsukisamu River in Sapporo were performed. Dynamical downscaling to 5-km

24resolution of a large-ensemble global simulation allowed us to estimate that a 99%-tile25

hourly precipitation in Sapporo would increase by 70% in a future climate, when the26

global-mean temperature increases by 4 K compared with the present climate. After27

developing a three-tank model of which parameters were optimized on the basis of the28

in-situ observation at the Motsukisamu River during the event period, the model was

29

forced by hypothetical hyetographs of the event that would occur under the future climate.

30

The results of this experiment suggested that the peak flow rate would increase by 75%.

31

However, it was also revealed that an upstream aqueduct tunnel, just completed in autumn

32

2021, would effectively reduce the peak flow rate and mitigate the flooding risk even in

33

extreme precipitation under the future climate.

34
35

1.

Introduction

36

Many reported that extreme precipitation was intensified with the recent

37

temperature increase (Peterson et al. 2008; Westra et al. 2013; Fujibe 2013). The global

38

climate model simulation projected the increase in extreme precipitation over most of the39

mid-latitude land-masses in a warmer climate (IPCC AR5 WG1). Global flood40

projections showed flood hazards increasing over East-to-South Asia, in spite of great

41

variability at the catchment scale (Dankers et al. 2014; Hirabayashi et al. 2013). On the42

other hand, flood risk of local river basins to climate changes has been recently assessed

43

by a river model tuned individually and then forced by many possible hyetographs

44

provided by a large ensemble climate-model simulation (Hoshino and Yamada, 2018;

3

SOLA, 2022, Vol.18, 235-238, doi: 10.2151/sola.2022-040

45

Tachikawa et al. 2017). Hoshino et al. (2020) evaluated the characteristics of tropical

46

cyclones that induced heavy rainfall over the Tokachi River basins in Hokkaido, Japan.

47This technique can be applied to relatively smaller river basins in Hokkaido (Nguyen et48

al. 2021).

49

As introduced above, the assessment of flooding risk to climate change was50

established for rivers with their catchment area larger than 100,000 km2 by global models

51(Hirabayashi et al. 2021) and even for river basins > 1,000 km2 with dynamical

52

downscaling. However, it remains challenging to assess smaller river basins like urban

53

rivers. A hindrance is attributed to difficulty to accurately simulate meso-scale convective

54

systems that bring torrential rainfall such as squall lines and rainbands by atmospheric

55

models even with 1-km resolution. Although the extreme precipitation is reproduced

56

statistically with a 5-km resolution model (Sasaki et al. 2011), the model is hardly to57

reproduce the occurrence probability and short-time variability of these phenomena and58

let alone its change in a warmer climate. Another difficulty in the assessment of small-59

scale river basins is to find feasible modeling approaches amid the lack of rainfall and60

discharge observations (Grimaldi et al. 2021); Despite no assurance on its simplification,61

the tank model was widely used for its convenience to be easily fit with an event in an

62

arbitrary river. Recently, Yoshioka et al. (2020) attempted to evaluate the flood risk of an63

urban river in Tokyo, by utilizing a large-ensemble dynamically-downscaled data.

64

The purpose of this study is to evaluate the impact of climate change to a small

65

urban river. In order to mitigate the former difficulty, we proposed an idea combining

66

gauged precipitation and a change ratio from model simulations focusing a particular67

torrential rainfall event. We here assumed that, if the same event occurred under the68

global warming environment, the rainfall intensity would only depend on the content of

Kanamori et al., Global warming effect and adaptation for a flooding event

4

69

water vapor in the atmosphere. Although regional climate models cannot accurately

70

reproduce all the events, we estimated the change ratio as the difference of extreme

71

precipitation intensity between present and future climate simulations. In order to tackle

72

the latter difficulty, we targeted the Motsukisamu River, running through residential areas73

of Sapporo, Hokkaido, Japan (Figs. 1a,b). We focus on the event of the river flooding on

74

September 11, 2014, due to torrential rainfall associated with a line-shaped rainband

75(Kato 2020), elongated along the direction from southwest to northeast over central

76

Hokkaido. The rainfall amount at this event strongly depended on the location of the77

rainband, so that we also used other hyetographs observed near the site under the78

assumption that the rainband were horizontally shifted. Furthermore, this study evaluates79

the effect of an aqueduct tunnel in the upstream of the Motsukisamu river (Fig. 1c).

80

Data and Methods

81

2.

82

2.1 In-Situ Observation

83

We used the in-situ observation data of the water level and rainfall at a84

downstream point of the Motsukisamu River (43.0317°N, 141.3861°E; Fig. 1c) by85

Hokkaido Weather Technology Center. Rainfall has been observed with a tipping bucket

86

rain gauge with 0.5 mm error, and the water level has been observed with hydraulic crystal

87

water gauge with 0.1%FS error. The data were a 10-minute interval.

88

We also used the rainfall data with a 10-minute interval of Automated89

Meteorological Data Acquisition System (AMeDAS) observation sites by the Japan

90

Meteorological Agency. The nearest site is Sapporo (43.06°N, 141.33°E), but we used91

other 11 sites in Ishikari subprefecture of Shinshinotsu (43.22°N, 141.65°E), Yamaguchi

92(43.15°N, 141.22°E), Teineyama (43.08°N, 141.20°E), Koganeyu (42.96°N, 141.22°E),

5SOLA, 2022, Vol.18, 235-238, doi: 10.2151/sola.2022-040

93

Eniwa-Shimamatsu (42.93°N, 141.57°E), Shikotsukohan (42.77°N, 141.41°E), Ishikari

94(43.19°N, 141.37°E), Hamamasu (43.58°N, 141.39°E), Atsuta (43.40°N, 141.44°E),

95

Chitose (42.78°N, 141.69°E), and Ebetsu (43.11°N, 141.60°E; Fig. 1b).

96
97

2.2 Downscaling Data

98

The database for Policy Decision-Making for Future Climate Change (d4PDF)

99

dataset contained a large ensemble simulation by the Meteorological Research Institute100

Atmospheric General Circulation Model, version 3.2 (Mizuta et al. 2012) with a101horizontal resolution of 60 km and the dynamical downscaling by Non-Hydrostatic

102

Regional Climate Model (Sasaki et al. 2011; Murata et al. 2013) covering the Japanese103

territory with a horizontal resolution of 20 km. The number of ensembles is 100 for the104

historical 1950-2010 simulation and 90 for the future climate simulation, where the105

global-mean surface temperature increases by 4 K relative to the preindustrial period.

106

In this study, we used the further dynamical downscaling results to a horizontal

107

resolution of 5 km covering Hokkaido Island (Hoshino and Yamada, 2018). This was108

conducted for selected years in the d4PDF ensembles with the heaviest 72-hour

109

precipitation totals in the Tokachi River basin between 1 June and 1 December. Because

110

the probability density of hourly precipitation in the 20-km d4PDF data at Sapporo was

111

independent of the selection of years related to precipitation over the Tokachi River basin

112(Fig. 2a), we regarded this selection as random sampling. In total, 769 years from 3000

113

years of the historical simulation and 735 years from 5400 years of the future simulation

114

were downscaled from 20-km resolution d4PDF dataset. Among them, we statistically115

analyzed hourly precipitation data at the nearest grid-point to the observation site at the116

Motsukisamu River (the southwest blue point in Fig. 1c).

Kanamori et al., Global warming effect and adaptation for a flooding event

6

117
118

2.3 River Model119

We developed a three-tank model for the domain (6.61 km2), upstream to the120

monitoring site (green point in Fig. 1c), which predicted runoff and ground water flow

121

rates (Sugawara 1972, 1995). The parameters of runoff coefficients, penetration122

coefficients, and heights of tank holes (Appendix A) were optimized with differential

123

evolution (Storn and Price 1997), based on precipitation and water level observed at the124

Motsukisamu River site on September 11, 2014. The flow rate 𝑄 (m3 s−1) was converted

125

into water level 𝐻 (m) by the following formula based on observation:

126(34.80 ≦ 𝐻 ≦ 34.90)
12.50 (𝐻 − 34.80)2
2(𝐻− 34.83)(34.90 < 𝐻 ≦ 35.06)(1)
𝑄 = { 24.91
2
12.94 (𝐻 − 34.74)(35.06 < 𝐻)
We included the effect of the aqueduct tunnel in this three-tank model.

127

Considering the capability and location of the tunnel, we divided the rainfall forcing into128

the upstream basin (𝑆1 = 4.78×106 m2) from the tunnel entrance (72% of the total

129

catchment area) and the downstream (28%): 𝑅in = 0.72 𝑅rm + 0.28 𝑅ob , where 𝑅ob

130[mm (10 min)−1] is observed precipitation, and 𝑅rm [mm (10 min)−1] is the upstream-

131

oriented precipitation after drainage. The upstream water flowed out following an132

overflow formula that had been obtained by the statistical fitting based on measurement133of flow and water level in hydraulic model experiments for the design of aqueduct tunnel

134

entrance:
𝑄1 = −3.0650 × 10−4 𝑄02 + 0.94947𝑄0 − 1.7005(𝑄0 ≤ 50)−22
𝑄1 = −1.1381 × 10 min(𝑄0 , 𝑄𝑎 ) + 1.8566 min(𝑄0 , 𝑄𝑎 ) − 19.303(𝑄0 > 50)
{

135

(2)

where 𝑄0 and 𝑄1 are the inflow just before the tunnel and the outflow to the tunnel and7136

SOLA, 2022, Vol.18, 235-238, doi: 10.2151/sola.2022-040

𝑄𝑎 is 58.5 m3 s−1.

137
138

2.4 Experiments

139

We performed the historical and future experiments with the three-tank model

140

forced by precipitation in the flooding event on September 11, 2014, or its processed one.

141

The reference historical experiment was a hindcast experiment with on-site rainfall itself

142(Section 2.1). In addition, we performed “ensemble” historical experiments with possible

143

hyetographs hypothesized that the line-shaped rainband were horizontally shifted. This144

was done by the same three-tank model but forced by AMeDAS rainfall data at 12145

different sites.

146

The future experiments were also performed with possible hyetographs147

hypothesized that the flooding event occurred in future environment. The hyetograph was

148

simply created by the procedure that the rainfall amount in all the timeframes was149

multiplied by 1.70. This rate was computed by the ratio of a 99%-tile value of hourly

150

precipitation exceeding 0.1 mm threshold in June-July-August-September months at the151

nearest grid-point to the Motsukisamu observation site from 735-year future simulation

152

with 5-km resolution to that from 769-year historical simulation. We used this value as

153

the multiplying factor, because the historical simulation almost reproduced the extreme

154

statistics of hourly precipitation and the ratio was comparable for higher precipitation

155

intensity like the target event with a 99.95%-tile value at the peak (Fig. 2b). The

156“ensemble” future experiments were also done with 12 AMeDAS rainfall data multiplied157

by 1.70.

158
159

3.

Results

Kanamori et al., Global warming effect and adaptation for a flooding event

8160First, we validated the three-tank model specially tuned to the flooding event by

161

the differential evolution method with the learning data of water levels estimated by the162

H-Q relation [Eq. (1)] from 00:00 10 September to 24:00 11 September. The reference

163

historical experiment with the input precipitation observed at the Motsukisamu River site164on the date showed a reasonable variation of hydrograph, compared with the observed at165

the same site (Fig. 3a). There were two peaks in hyetograph exceeded 8 mm (10 min)−1

166

at 2:00-2:20 and 3:30-4:20 on this date (Hereafter time is in Japanese Standard time). The

167

observed and simulated hydrographs showed that the peaks were emerged almost at the168same timing but with a 10-minute delay to the precipitation peak surpassed 36.30 m, the169flood stage level 4. The torrential rainfall ceased at 8:00 there. The simulated water level

170

dropped to the baseline soon1, while the observed one was gradually declined.

171

Figure 3b displays the hyeto-hydrograph of the “ensemble” historical experiments

172

with hypothesized precipitation at 12 different AMeDAS sites in Ishikari area that would

173

occur at the Motsukisamu river basin. We here paid attention to two sites at

174

Shikotsukohan and Chitose, quite close to the line-shaped rainband. At Shikotsukohan

175

the rainfall exceeded 15 mm (10 min)−1 in two periods, the first around 5:30 and the176

second around 18:45. In the hypothesized experiment with this rainfall data given to the1

The flow rather than water level tended to show a peaky graph (not shown), sothat the fitting likely took a stronger influence from the larger flow around the peak.
Hence, we made light of an error around the weak flow, or water levels near baseline. We
guess that other possible reasons are the heavier rainfall in the upstream that we did notcope with and some leakage in the river that was not well reproduced in this simple tankmodel.

9

SOLA, 2022, Vol.18, 235-238, doi: 10.2151/sola.2022-040

177

Motsukisamu River model, the water level attained local maxima in the peak rainfall

178

period there. The first peak was 37.3 m and the second peak exceeded 37.5 m. A similar179

hyetograph was found in Chitose, with a secondary rainfall peak in 23:00. In the180

hypothesized experiment, secondary flooding would have happened at the Motsukisamu

181

River in this second rainfall peak. Because rainfall data in other sites have a similar

182

variation but with an unclear peak, the result of ensemble simulation showed the water

183

level would increase in the period during 2:00-6:00 but would not likely attain the184

flooding level.

185

The result of the future reference simulation is shown in Fig. 4a. Accompanied

186

with the heavier rainfall, the simulation showed spiky peaks of runoff almost at the same187

timing as the rainfall peaks. The peak flow rate was 1.75 times higher. Similarly, the188“ensemble” simulation showed more spiky peaks of runoff and the water level would

189

approach to the flood stage level 4 if some AMeDAS points were replaced with (Fig. 4b).

190

Finally, we assessed the effect of the aqueduct tunnel effect to the water level at

191

the Motsukisamu River. The reference historical experiment with the tunnel effect192

revealed that the peak water level would be much lower than the flood stage level 4 (Fig.

1935a). Even in the reference experiment, the tunnel effect would significantly reduce the194

peak water level (Fig. 5b). Hence it can be indicated that the aqueduct tunnel is a treatment

195

of flood risk in the present climate as well as an adaptation of the future climate.

196
197

4.

Discussion

198

The assessment of climate change effect to a small urban river has been

199

challenging, but the technique proposed here is so simple that it could be highly versatile200

for the urban rivers where the hyeto-hydro graph was available with enough a shorter

Kanamori et al., Global warming effect and adaptation for a flooding event

10

201

sampling interval compared to the rainfall-runoff timescale. We targeted a specific flood

202

event and used a lumped model to avoid hydrological uncertainty in the urban-river203

modeling. If one attempted to make a more accurate and more universal river model to204

use any flooding events with a sophisticated manner like distributed models, a stumbling205

block would be the necessity of densely distributed verification data. Moreover, an

206

accurate urban-river modeling needed complete inflow/outflow information of a city

207

drainage network. Because it seemed virtually impossible to resolve these problems in208

the present engineering level, this study is considered to be the best-effort approach to the209

flood-risk assessment of small urban rivers.

210

A caveat of our method is a rough estimate of hyetograph for the target event that211

would occur in the global warming environment. Even if a meteorological phenomenon

212

that brought extreme rainfall occurred under a warmer climate, a simple multiplication of213

rainfall amount without any other changes in the hyetograph would not be warrant. To

214relieve this problem, one possible way is to use pseudo global warming (PGW) dynamical

215

downscaling (Sato et al. 2007), in which the boundary conditions are obtained by adding216

the future-to-present difference estimated by GCM into observed data. However, even217

state-of-the-art atmospheric models cannot always well reproduce the meso-scale

218

convection system. Even though the model were capable to reproduce the system, its219

possible few-kilometer shift would be critical for the estimate of urban river input. These220

are reasons why we avoided a PGW method in this paper.

221
222

5.

Conclusions

223

We adopted an idea of simple multiplication of precipitation amount in a heavy

224

rainfall event and assessed the flooding risk at the Motsukisamu River in Sapporo under11

SOLA, 2022, Vol.18, 235-238, doi: 10.2151/sola.2022-040

225

a warmer climate. First, we checked that extreme precipitation at Sapporo increased by

226

70% in future climate where the global-mean temperature increases by 4 K, based on

227

dynamical downscaling to 5-km resolution of a large-ensemble global simulation called

228

d4PDF. Next, we validated that a three-tank model driving the observed precipitation

229

during the target period of a flood event at the Motsukisamu River. The river model forced

230

by hypothetical hyetographs of the event that would occur under the future climate as a231

manner of PGW experiment suggested that the peak flow rate would increase by 75%. It

232

was also revealed that the upstream aqueduct tunnel would effectively reduce the peak233

flow rate and mitigate the flooding risk even in extreme precipitation under the future234

climate.

235
236

Acknowledgement237

MI and TJY are supported by JSPS KAKENHI grant 19H00963, by

238

JPMXD0717935457 and JPMXD0722680734 of Ministry of Education, Sports, Culture,

239

Science and Technology (MEXT), and by Research Field of Hokkaido Weather Forecast

240

and Technology Development (endowed by Hokkaido Weather Technology Center Co.

241Ltd.). MI was also funded by the Environment Research and Technology Development

242

Fund JPMEERF20192005 of the Environmental Restoration and Conservation Agency

243

of Japan. We used d4PDF produced with the Earth Simulator of the Japan Agency for

244

Marine-Earth Science and Technology jointly by the MEXT science programs SOUSEI,

245

TOUGOU, and SI-CAT. We expressed our gratitude Mr. Yoshimichi Tachikawa and Mr.

246

Hidenori Yamahira to provide us the detailed hydrological information on the aqueduct247

tunnel and Dr. Yousuke Sato to give a technical assistance for handling meteorological248

data. Figure 1c was based on Map of Geospatial Information Authority of Japan with

Kanamori et al., Global warming effect and adaptation for a flooding event

249

12

some modifications.

250
251

Appendix A. Tank model and the parameters252

We implemented the standard three-tank model that consists of a set of253

prognostic equation of storage of first, second and third tanks, 𝑆1, 𝑆2 , and 𝑆3 , forced by254

rainfall 𝑅 as

255

𝑑𝑆1
= −𝛽1 𝑆1 − 𝑞1 (𝑡) + 𝑅,𝑑𝑡𝑑𝑆2
= −𝛽2 𝑆2 − 𝑞2 (𝑡) + 𝛽1 ,𝑑𝑡𝑑𝑆3
= −𝛽3 𝑆3 − 𝑞3 (𝑡) + 𝛽2 ,
𝑑𝑡

(A1)

𝑞1 (𝑡) = 𝛼1 (𝑆1 (𝑡) − 𝐿1 ) + 𝛼2 (𝑆1 (𝑡) − 𝐿2 ),𝑞2 (𝑡) = 𝛼3 (𝑆3 (𝑡) − 𝐿3 ),𝑞3 (𝑡) = 𝛼4 (𝑆4 (𝑡) − 𝐿4 ).

(A2)

and

256

The coefficients of outflow from the lower side hole in the first tank are 𝛼1 = 1.79476

257

hr−1 and 𝛼2 = 0.21718 hr−1, respectively; Those from the side hole in the second and258

third tanks are 𝛼3 = 1.27943 hr−1 and 𝛼4 = 1.13114 hr−1, respectively. The

259

coefficients of leakage from the bottom hole in the first, second and third tanks are 𝛽1 =260

3.32828 hr−1, 𝛽2 = 4.10502 hr−1 and 𝛽3 = 4.67506 hr−1, respectively. The heights

261

of the lower and upper side hole in the first tank are 𝐿1 =0.77872 mm and 𝐿2 =9.40112

262

mm, respectively; Those of the side hole in the second and third tanks are 𝐿3 =0.01223

263

mm and 𝐿4 =10.39208 mm, respectively.

264
265

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Figure 1: (a) Map and (b) zoom-in map and (c) pictures around the Motsukisamu River.

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Sapporo City was shaded in (a) and (b). Circles in (b) denote the location of Automated346

Meteorological Data Acquisition System (AMeDAS) observation points in Ishikari area

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described below. Black line in (c) is the Motsukisamu River basin and purple dotted line348

is the aqueduct tunnel in the upstream. The river model is constructed for the pink and349

yellow areas, and the rainfall in the yellow area partly flows out by the tunnel. Green, red,350

and blue dots show the observation point of precipitation and water level, AMeDAS

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observation point of Sapporo, and the neighbor grid-points of d4PDF surrounding the site,

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respectively.

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Figure 2: (a) The quantile-quantile (Q-Q) plot of hourly precipitation in June-July-

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August-September months at Sapporo in 20-km d4PDF historical simulation (blue) for

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years selected in the 5-km downscaling and (black) for other years and (red) in 20-km

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d4PDF 4K simulation. (b) The Q-Q plot of hourly precipitation at Sapporo (blue)359

historical and (red) 4K experiments in 5-km downscaling and (black) AMeDAS

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observation from 1991 to 2020. All the statistics were taken for hours where the361

precipitation exceeded 0.1 mm.

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Figure 3: Hyetograph and hydrograph on September 11, 2014, at the Motsukisamu River366

under historical climate. (a) (Line in the upper side) Rainfall and (black line) water level367

observed at the Motsukisamu River. Blue line shows the water level in the reference

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simulation. Gray dotted line shows the flood stage level 4. (b) Same as (a), but the results

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for “ensemble” simulation with precipitation observed in 12 sites of Ishikari area.

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Shikotsukohan and Chitose sites were emphasized by coloring as legend.

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Figure 4: Same as Fig. 3, but for +4 K climate.

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Figure 5: (a; dotted lines) The net precipitation inversely estimated considering the379

amount of the removal of water through the aqueduct tunnel and the simulated water level

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forced by the net precipitation. The hyetograph and hydrograph in the reference

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experiment were superimposed with solid lines. (b) Same as (a), but all under +4 K

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climate. Note that the hydrograph is colored red in (b). The black line is the observed

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water level as a reference.

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