Assessment of climate change impacts on river flooding due to Typhoon Hagibis in 2019 using nonglobal warming experiments

In this study, a series of numerical analyses of meteorology, runoff, river flow, and inundation were performed to quantitatively evaluate the effects of historical warming on precipitation, discharge, water level, and flood inundation. This study was on the flood inundation of the Chikuma River Basin in Japan caused by Typhoon Hagibis in 2019. The historical warming impact on Typhoon Hagibis was analyzed by comparing nonglobal warming experiments (NonWs) and control experiments (CTLs) to reproduce the current situation. Calculated results showed that the ratios of the index of CTLs to that of NonWs (mean CTL to mean NonW) as indicators of the impact of historical warming were 1.08, 1.22, and 1.08–3.08 for total precipitation, peak river discharge, and peak water level (from pre‐flood level and high‐water level), respectively, and 48.1 and 595 for overflow depth and inundation volume for the Chikuma River, respectively. Results of the hydrologic‐sensitivity analysis indicated that the influence of historical warming during the last 40‐year period was already evident on overflow and flooding, whose sensitivities were higher than those of discharge and water level.


| INTRODUCTION
In Japan, large-scale heavy-rain disasters occur in various parts of the country almost every year (Udmale et al., 2019). Examples of such occurrences are the Western Japan Heavy Rain of 2018 and Typhoon Hagibis in 2019 (Cabinet Office, 2018. Typhoon Hagibis caused high-intensity precipitation over a wide area, Abbreviations: CTL, control experiment; EA, event attribution; GHG, Greenhouse Gas; HWL, high water level; IPCC AR6, Intergovernmental Panel on Climate Change Sixth Assessment Report; JMA-NHM, Japan Meteorological Agency Nonhydrostatic Model; kp, kilometer point; MLIT, Ministry of Land, Infrastructure, Transport and Tourism; NonW, nonglobal warming experiment; RRAP, radar/raingauge-analyzed precipitation; RRI, rainfall-runoff-inundation; T.P., Tokyo Peil; WL, water level; 1D, one-dimensional; 2D, two-dimensional. mainly in eastern Japan, leading to the issuance of special warnings for heavy precipitation in Tokyo and 12 other prefectures. The outcome of Typhoon Hagibis was record-breaking precipitation, including the highest 3-, 6-, 12-, and 24-h precipitation records in various parts of eastern and northern Japan. This precipitation caused river flooding in many parts of Japan, with 142 dike breaches on 71 rivers and enormous inundation damages, including 99 deaths and destruction of 96,572 houses (Ministry of Land, Infrastructure, Transport and Tourism (MLIT), 2019; Cabinet Office, 2019).
Climate change has been cited as a factor in the increasing severity and frequency of heavy rains that cause such disasters (Hirabayashi et al., 2013). According to the Intergovernmental Panel on Climate Change Sixth Assessment Report (IPCC AR6), human influence has warmed the atmosphere, ocean, and land, and human-induced climate change is already affecting weather extremes, such as heavy precipitation, in every region across the globe (IPCC, 2021). Kawase et al. (2020Kawase et al. ( , 2021 pointed out that the total precipitation (P) of the Western Japan Heavy Rain in 2018 and Typhoon Hagibis in 2019 increased by 6.7% and 10.9%, respectively, owing to climate change. An increase in the intensity and frequency of heavy rain resulting from climate change has been noted in other countries as well (Burke et al., 2016;Goswami et al., 2006;Guhathakurta et al., 2011;Ueda et al., 2006). Furthermore, in addition to the increase in precipitation due to climate change, increases in river discharge (Q) (Nakakita & Osakada, 2018;Sato et al., 2013) and flood inundation risk (Arnell & Gosling, 2016;Kaspersen et al., 2017;Ramachandran et al., 2019;Swain et al., 2020;Try et al., 2020;Veijalainen et al., 2010) were also considered. Among these studies, Swain et al. (2020) showed a mean increase in 100-year precipitation events in terms of magnitude and frequency by 20% and > 200%, respectively, in a high-warming scenario, causing an increase in population exposure by 30%-127%. Try et al. (2020) conducted a climate change assessment using the rainfall-runoffinundation model for the Mekong River Basin and found that an increase of 6.6%-14.2% in precipitation could lead to an increased extreme discharge of 13%-30%, peak inundation area (Ai) of 19%-43%, and peak inundation volume (Vi) of 24%-55% in the Lower Mekong River Basin.
Another approach to assessing the impact of climate change is storyline event attribution (EA), which reveals the extent to which climate change impacted the magnitude of a particular flood event . Shepherd et al. (2018) stated that storyline event attribution offers a powerful way of linking the physical and human aspects of climate change. Prior studies employing EA include cases focusing on temperature change (Otto et al., 2012;Stott et al., 2004), precipitation (Kawase et al., 2020;Kawase et al., 2021;Lackmann, 2015;Meredith et al., 2015;Otto et al., 2018;Pall et al., 2017;Reed et al., 2020;Takayabu et al., 2015;van der Wiel et al., 2017;van Oldenborgh et al., 2016;Wolski et al., 2014), and runoff (Kay et al., 2018;Li et al., 2018;Pall et al., 2011;Schaller et al., 2016;Sebastian et al., 2019 ;van Oldenborgh et al., 2017). For instance, Hurricane Harvey, which struck Texas in August 2017, produced heavy rain with a return period of up to 9000 years, showing that precipitation increased by 15% and runoff by 20% because of climate change (Sebastian et al., 2019;van Oldenborgh et al., 2017). Although many studies using EA have made climate change impact assessments of precipitation and Q, very few have covered river flow and flooding. Villarini et al. (2020) conducted an analysis of precipitation, runoff, and flood inundation based on EA and demonstrated that the extent of inundation increased by a factor of 1.28 due to climate change, but they did not address issues, such as low reproducibility of Q and water level (WL). To assess flood damage resulting from climate change, it is essential to examine not only the changes in precipitation and Q but also its impact on river WL, overflow, and Ai. Climate change impact assessments of river WLs and flood inundation conditions are fundamental to the design of river plans and the implementation of flood control measures that consider climate change. Therefore, EA studies that deal with climate change assessments for specific flood events are vital.
This study aims to quantitatively evaluate the impact of historical warming on precipitation, Q, WL, and inundation conditions caused by Typhoon Hagibis based on an analysis using the EA approach. In this study, meteorological and runoff analyses covering a wide area of Japan, were performed. Furthermore, river flow and inundation analyses pertaining to the Chikuma River, which was extensively inundated by Typhoon Hagibis, were conducted. The meteorological analyses of Typhoon Hagibis (Kawase et al., 2021) were based on nonglobal warming experiments (NonWs) and control experiments (CTLs). The details of CTLs and NonWs are described in Section 3. Using the Rainfall-Runoff-Inundation (RRI) model (Sayama et al., 2012;Sayama, Tatebe, Iwami, & Tanaka, 2015;, which enables wide-range and high-resolution distributed runoff analyses, was utilized for analyses of entire eastern Japan, including the Chikuma River Basin . Based on the results of these analyses, river flow analysis of the Chikuma River was performed employing a one-dimensional (1D) unsteady flow model to determine the longitudinal distribution of the river WL and Q, as well as the temporal variation of the overflow discharge. Finally, inundation depth, Ai, and Vi were calculated by performing a horizontal two-dimensional (2D) analysis for a single area where overflow inundation occurred. Runoff, river flow, and inundation analyses were performed for CTLs and NonWs, and the results were compared. Meteorological and runoff analyses conducted by Kawase et al. (2021) and Sayama et al. (2020), respectively, were utilized in this study. The present study mainly focuses on the impact of historical warming on river WLs, overflow, and inundation conditions. 2 | CHIKUMA RIVER FLOODING DURING TYPHOON HAGIBIS 2.1 | Field site Figure 1 shows an overview of the Chikuma River and its basin. The Chikuma River is a first-class river, which is mainly managed by MLIT, it begins at the 2475-mhigh Kobushi-ga-take located on the border of the Nagano, Yamanashi, and Saitama Prefectures, flows through the mountains and basins, and merges with the Sai River midstream. It is renamed the Shinano River after moving from Nagano Prefecture to Niigata Prefecture and flows into the Sea of Japan. The Shinano River has a total length of 367 km and a basin area of 11,900 km 2 , making it the longest river in Japan. The Chikuma River has a total length of 214 km and a basin area of 7163 km 2 ; and the Sai River, its largest tributary, has a total length of 157 km and a basin area of 3037 km 2 . Figure 2 shows the distribution of the riverbed height and width in the Chikuma River, which was provided by F I G U R E 1 Study area of the Chikuma River Basin. Red and blue lines indicate the river within and without the computational domain of the one-dimensional river flow analysis, respectively. The dotted yellow line shows the computational domain for two-dimensional flooding analysis. Color maps show the inundation depth due to Typhoon Hagibis, which was measured by the Geospatial Information Authority of Japan (2019).
MLIT. As the Chikuma River flows through narrow and wide basin sections, its width varies considerably. The Tategahana Narrow section is located downstream of the Nagano Basin. The river width varies greatly from 120 to 450 m in the Tategahana Narrows and from 400 to 1200 m in the Nagano Basin, making this region face flood control issues for a long time. The Nagano Basin is a flood-prone area.

| Flooding in the Chikuma River
After its formation on October 6, 2019, Typhoon Hagibis made landfall in Japan at 7 pm on October 12, traversed eastern Japan, and became an extratropical cyclone at noon on October 13. This typhoon caused intense precipitation within 24 h, resulting in extensive heavy precipitation over a relatively short period of time (Takemi & Unuma, 2020). Consequently, severe flooding and landslides have occurred in a wide area of eastern Japan, including the Chikuma River Basin. Figure 3 illustrates the hourly and cumulative precipitations and WL in the Chikuma River during this typhoon. Precipitation data were obtained from radar/ raingauge-analyzed precipitation (RRAP), which were made by radar and in situ station observations, and basin-averaged in the Chikuma River upstream of the F I G U R E 2 Longitudinal profile of riverbed height (upper) and river width (lower) in the Chikuma River. The sections of the two basins and two narrows are divided with dashed lines. In the lower figure, the two lines show the lateral distance from the center of the cross-section.
F I G U R E 3 Temporal variations of hourly and cumulative precipitation (upper) and water level (lower) in the Chikuma River. Precipitation averaged over the basin at Ikuta station (108.0 kp) was used. Water levels measured at Ikuta, Kuiseke (82.5 kp), Tategahana (51.5 kp), and Kashiohashi (25.5 kp) stations are depicted. Cumulative precipitation was defined as the cumulative value starting at 09:00 on October 11, 2019. Ikuta water-level observation station (108.0 km point (kp): the longitudinal distance from the starting point of the Chikuma River with the unit of kilometer). This shows that in the upper Chikuma River Basin, precipitation peaked at 22 mm/h at 15:00 on October 12 and stopped after 22:00. Cumulative precipitation was approximately 275 mm. This precipitation caused the WL to exceed the designed high-water level (HWL) at all four WL observation stations listed in Figure 3. Specifically, both WLs at the Tategahana and Kuiseke stations, located upstream and downstream from 57.5 kp of the Chikuma River, where the dike breach occurred, exceeded the HWL for 7-8 h.
As indicated by the color contour in Figure 1, the precipitation caused overflow inundation at many points of the mainstream of the Chikuma River from the night of October 12 to the early morning of the next day, producing widespread flooding (Natsuaki & Nagai, 2020;Tay et al., 2020). On the left bank of the Chikuma River at approximately 57.5 kp, 70 m of the dike broke, resulting in a flooded area of 9.5 km 2 . In the flooded area, the Hokuriku Shinkansen Train Base also took in water, leading to two victims (Chikuma River Embankment Investigation Committee, 2020). Meanwhile, the Sai River did not produce any inundation from overflow or dike breach. Table 1, meteorological, runoff, river flow, and inundation analyses were conducted using CTLs and NonWs. The outline of each analysis is as follows.

| Meteorological analysis with the Japan Meteorological Agency Nonhydrostatic Model
The precipitation dataset was derived from Kawase et al. (2021) who conducted CTLs and NonWs using the Japan Meteorological Agency Nonhydrostatic Model (JMA-NHM). The analysis conditions are listed in Table 1. The number of computational grids were 400 Â 400 and 50 in the horizontal and vertical directions, respectively. The area covered by this analysis was around Japan and the spatial resolution in the horizontal direction was as fine as 5 km. Initial and lateral boundary conditions of CTLs were derived from the JMA mesoscale analysis data. Four members in the CTLs were conducted using different initial dates, that is, from 09:00, 12:00, 15:00, and 18:00 on October 9, 2019 (JST). All four experiments were ended at 09:00 on October 14, 2019 (JST). In the analysis, Typhoon Hagibis was given initial and lateral boundary conditions for wind, air temperature, water vapor, and geopotential height from the JMA-NHM. In the model domain, the typhoon was recalculated by the JMA-NHM.
NonWs were conducted by using the JMA mesoscale data in which the linear trends of sea surface temperature, atmospheric temperature, and geopotential height during the 40-year period from 1980 to 2019 were removed. The year 1980 was assumed to be the base for the calculation of NonWs since the rapid warming appears from around 1980 in Japan in autumn. The linear trend from 1980 to 2019 includes not only the anthropogenic external forcings but also the natural forcings, such as volcanic and solar forcings and decadal natural atmospheric and oceanic variability. Here, the linear Outline of computational conditions for meteorological, runoff, river flow, and flooding analyses. trends were calculated by the regional-mean values around the eastern and western Japan (130 E-150 E, 25 N-40 N). Cases of ensemble calculation for NonWs were considered to estimate uncertainty from initial dates and trends of the month. For ensemble calculation in NonWs, 20 types were used: four calculation initial times (09:00, 12:00, 15:00, and 18:00 JST on October 9, 2019) multiplied by five methods for removing atmospheric and sea surface temperature trends. Three cases used the trends from 1980 to 2019 calculated by monthly averages of August, September, and October as the target months. The other two cases used the 3-month average from August to October and September to November. In this simulation, the GHG (Greenhouse Gas) concentrations are fixed, but the atmospheric temperature is controlled by initial and lateral boundary conditions of the simulation with regional models. The same model parameter, whose accuracy was verified under CTLs, was also used for NonWs. The impact of historical warming was extracted from the difference between the results of CTLs and NonWs. For details of the analysis method and accuracy, readers are encouraged to refer to Kawase et al. (2021).

| Runoff analysis with the RRI model
Runoff analysis was performed using the RRI model with precipitation data as input obtained through the meteorological analyses of the JMA-NHM. This study focused on river and inundation flows in the Chikuma River Basin and hence the model was identified by comparing the observed and simulated Q at the Kuiseke station (82.5 kp) in the Chikuma River Basin. The calculation cases were composed of 4 CTLs and 20 NonWs, and the calculation period was from 09:00 on October 11 to 09:00 on October 14, 2019 (JST) for all 24 cases (Table 1). For details on the calculation model and others, readers are encouraged to refer to Sayama et al. (2020). The calculated precipitation obtained by the JMA-NHM was compared to the observed precipitation from the RRAP. Although they agreed for the upper basin of the Chikuma River, they differ for the Sai River. Input precipitation for the RRI model was used for the calculated results from the JMA-NHM in the upstream basin of the Chikuma River, and RRAP was used in the Sai River Basin, indicating that the impact of climate change on Q should be considered only for the mainstream of the Chikuma River. However, in the Chikuma River Basin, the precipitation in the upper basin was higher than that in the Sai River Basin during this typhoon. Therefore, the setting of flow conditions for the Sai River did not have a significant impact on the results of the river flow analysis.

| River flow analysis with the unsteady 1D flow model
An unsteady 1D flow model was used for river flow analyses to calculate the longitudinal distribution of the river WL and discharge at each moment, as well as the overflow discharge if the river WL exceeded the dike height. The basic equations and boundary conditions are explained in Appendix. To include the inundation and dike breach point (57.5 kp) shown in Figure 1, the analysis covered the 31-km section of the Chikuma River between Kuiseke and Tategahana observation stations and the 9-km section of the Sai River between the Koichi observation station and the confluence point with the Chikuma River. Geomorphological data for these calculation sections were provided by the MLIT using crosssectional survey data for the river channel in 2017 and did not include any cases of dike failure. The number of cases for the river flow analysis was 4 CTLs and 20 NonWs, as in the meteorological and runoff analysis, and the calculation period was from 00:00 on October 12, 2019 to 00:00 on October 14, 2019 (JST; Table 1). The number of computational grids in the 1D river flow analysis was 310 for the Chikuma River and 90 for the Sai River, and the grid resolution was approximately 100 m in the longitudinal direction. Manning's roughness coefficient (n), the only parameter in the basic equations for river flow analysis, was given to achieve data assimilation of the peak WL observed during flooding caused by this typhoon using Equation (A5).

| Inundation analysis with the horizontal 2D flow model
For inundation flow analysis, a horizontal 2D shallowwater flow model was used to calculate the water depth and flow velocity in the inundation area by utilizing the overflow discharge obtained from the river flow analysis as input conditions. Nays2DFlood (iRIC software, 2021; Nelson et al., 2016) was used for inundation analysis. The river flow analysis showed that overflow occurred at several locations, as described below. Among these locations, an inundation area around 57.5 kp on the left bank of the Chikuma River (yellow dotted line in Figure 1), where the maximum overflow discharge was observed, was selected for inundation analysis. The computational period was from 0:00 to 12:00 on October 13, 2019 (Table 1). In this model, a general curvilinear coordinate system was used; the number of computational grids was 476 Â 136, and the average computational grid interval was approximately 16 m. Ground elevation data were provided using the Digital Elevation Model (Geospatial Information Authority of Japan, https://fgd.gsi.go.jp/ download/menu.php) with a 5-m resolution. The area in the inundation analysis was a mixture of residential areas and farmland, and n used in the inundation analysis was uniformly given as 0.1 m À1/3 s. For the boundary conditions, the time series of the overflow discharge obtained from the river flow analyses was provided. Because overflow occurred in four CTLs and two NonWs, as described below, six inundation analyses were performed in total.

| Hydrologic-sensitivity analysis
To quantitatively evaluate the historical warming using the CTLs and NonWs results obtained from the analyses mentioned above, hydrologic-sensitivity analysis, which makes a quantitative evaluation of the increased Q in relation to the increased precipitation (P) (Dooge, 1992;Sankarasubramanian et al., 2001;Schaake, 1990), was applied to the results of the analyses. Following Schaake (1990), the elasticity index (ε) for P and Q was used.
where ε is the ratio of the precipitation increase ratio, dP/P, to the discharge increase ratio, dQ/Q. The following equation was used for ε of various indices f (Sayama, Tatebe, Iwami, & Tanaka, 2015).
where ε indicates that the increase in the ratio of index f will be % for each 1% increase in the P ratio.  Figure 4a,b show the hourly and cumulative precipitation; as for the average of CTLs, the calculated precipitation increased on the morning of October 12, reached its peak value (23.7 mm) at 16:00 on the same day, the hourly precipitation dropped to less than 3 mm/h, making total precipitation P = 273.1 mm. The observed peak precipitation was 22.5 mm/h (at 15:00 on October 12), which was almost same as for the average of CTLs, and the observed P was 275.6 mm, which was almost the same as that for the average of CTLs. This confirms the validity of the results of the JMA-NHM analysis. The calculated results for NonWs varied by ensemble members. Specifically, their peak precipitations ranged from 18.1 to 25.8 mm/h (mean: 22.2 mm/h) and their peak occurrence times ranged from 15:00 to 19:00 on October 12. In addition, P varied from 235 to 262 mm (mean: 252.1 mm). This shows that both the peak hourly precipitation and P for all 20 members in NonWs were lesser than those in CTLs. As in other areas of Typhoon Hagibis (Kawase et al., 2021), an increase in precipitation was observed in the upper Chikuma River Basin due to historical warming. In the meantime, in the Sai River Basin, the observed peak hourly precipitation and P were 13.1 and 134.7 mm, respectively, which were much lesser than those in the upper Chikuma River Basin. Attention was focused on the results of runoff analyses at the Kuiseke station on the Chikuma River according to the RRI model ( Figure 4c). In the CTLs, the Q began to increase after 15:00 on October 12 and peaked at 22:00 on the same day at 6489-7558 m 3 /s (mean: 7034 m 3 /s). The observed peak times (21:00 on October 12) and discharge (7267 m 3 /s) were identical to those of the calculated values in the CTLs. These results suggested validity of the calculations of the RRI model. In the NonWs, the Q peak was 4942-6526 m 3 /s (mean: 5756 m 3 / s), less than those in the CTLs for the most members. This suggests that, in addition to the P, the Q peak of this typhoon increased under the influence of the historical warming. For the Sai River, the calculated Q peak (1787 m 3 /s) was almost identical to that of the observed value (1649 m 3 /s). The peak occurrence was at 01:00 on October 13. In addition, the Q peak at Koichi station on the Sai River was only approximately 20% of that at Kuiseke station because the precipitation was concentrated in the upper Chikuma River basin, not in the Sai River basin. River discharge and inundation analyses were conducted without NonWs conditions in the Sai River Basin, and the result showed a slightly lesser impact of historical warming on the WL and inundation conditions there. As the discharge of the Sai River is lesser than that of the upper Chikuma River basin, even if the calculated results of the NonWs for the Sai River were considered, their effects on WL and inundation conditions will not be significant. Figure 5 shows the longitudinal distributions of peak WLs and n values for the Chikuma River (left) and the Sai River (right) obtained by Equation (A5) in the precalculation using the CTL in which the peak discharge was largest among all CTLs, here called as CTL1. The results indicate that the calculated and observed values of peak WL were identical, and the root mean square error for the difference between the two was 0.0120 m, with a maximum value of 0.0361 m. The calculated n was 0.012-0.060 (mean: 0.033 ± 0.011) m À1/3 s. Similar results were obtained for the Sai River. Specifically, the differences between the calculated and observed peak WLs were low (0.014-0.038 m), whereas the n was 0.016-0.047 (mean: 0.028 ± 0.011) m À1/3 s. Thus, it can be concluded that with respect to peak WL, the river flow analyses succeeded in reproducing the observed water marks and the calculated n values were valid.

| Longitudinal variations of water level in the Chikuma River
The longitudinal distributions of the peak WL in the CTLs (four members and average values) and the NonWs (20 members and average values) are shown in Figure 6. Figure 6a indicates that the peak WL distribution based only on the general reference level (Tokyo Peil: T.P.) is not sufficient to judge whether the WL has overflowed the dike and extent to which it exceeded HWL. For this reason, the longitudinal distributions of WL based on the dike height on the right and left banks and the HWL are also indicated (Figure 6b-d). The figure based on the dike height on the right bank indicates that the peak WL in the CTLs was mostly higher than that for all 20 members in the NonWs at all points. The differences between the average of CTLs and NonWs ranged from 0.33 to 1.19 m. For the right river dike, although overflow occurred at four locations (stations R1-R4) in the CTL1 and one location (R3) in other CTLs (hereinafter CTL2, CTL3, and CTL4), no overflow occurred in any of the 20 NonWs. Similarly, for the left river dike, overflow occurred at stations L1 in the CTL1 and stations L2 in all CTLs. Then, at station L1, no overflow occurred for NonWs, but at station L2, overflow was observed in two of the 20 members of the NonWs. However, for both cases, where overflow occurred, the overflow depth on the dike was shallower than that in the CTLs. There were six overflow locations in the CTLs and only one location in the NonWs, and overflow occurred in only two of 20 NonWs, indicating that there were substantial differences between the CTLs and the NonWs in terms of flooding occurrence situations. An extent of 82.6-85.8% of the entire computational section of the Chikuma River exceeded the HWL in the CTLs, and the WL at 57.5 kp exceeded the HWL for 10.3-11.3 h, the longest duration. In contrast, in the NonWs, 59.4%-82.3% of the entire section exceeded HWL, and the duration of the exceedance ranged from 6.8 to 10.2 h, suggesting that the hazardous condition continued for a long time in the NonWs. However, the peak WL for the NonWs was lower than that for the CTLs, and both the section length and duration of HWL exceedance were lesser than those of the CTLs. Figure 7 shows the total overflow volume in the six sections to quantitatively illustrate the overflow situations that occurred in all CTLs and the two members in NonWs (hereinafter NonW1 and NonW2). The total overflow volumes on the right bank side in CTLs were 24.4, 37.1, 23.7-619.1 (mean: 260.0), and 1.9 [Â10 3 m 3 ] at stations R1, R2, R3, and R4, respectively. Meanwhile, on the left bank side, the total overflow volumes in the CTLs were 37.7 and 684.4-3070 (mean: 1754) [Â10 3 m 3 ] in stations L1 and L2, respectively, indicating that the total overflow volume at station L2 was the largest among those on the right and left banks. The total overflow volumes of the NonW1 and NonW2 at station L2 were 55.4 and 3.5 [Â10 3 m 3 ], respectively, which were by two or three orders of magnitude less than those in the CTLs. This can be explained by the fact that the overflow depth (H of ) and duration of overflow (T of ) in the NonWs decreased more than those in the CTLs because of the overall decrease in the river WL, as illustrated in Section 4.2.

| Overflow and flooding area
To express the effects of this difference in overflow volume on the inundation situation, Figure 8 presents contour maps of the maximum inundation depths (h max ) obtained from the inundation analysis at station L2. These figures show that the Ai in the CTLs became wider than that in the NonWs, and the inundation depth in the CTLs was larger. Specifically, the Ai values were 1.87-4.86 (mean: 3.05), 0.63 and 0.10 km 2 and h max values were 1.57-2.64 (mean: 2.15), 0.69, and 0.37 m for CTLs, NonW1 and NonW2, respectively. These larger Ais and depths in the CTLs were considered to reflect the difference in the total overflow volume (Figure 7). Moreover, these data suggest that Ai with depth > 0.5 m, equivalent to inundation above floor level, was widespread in the CTLs, rare in the NonW1, and nonexistent in the NonW2. If inundation above the floor level occurs, not only will house damage increase, but household goods will also be damaged (MLIT, 2005). Furthermore, a flood F I G U R E 5 Longitudinal distribution of water elevation (upper) and roughness coefficient n (lower) calculated using Equation (A5) in the pre-calculation using the control experiment 1 (CTL1) in which the peak discharge was the largest among all CTLs. The results for the Chikuma and Sai Rivers are shown in the left and right figures, respectively. The calculated water elevation was displayed with the observed water marks. The roughness coefficient n was first evaluated using data assimilation with observed water marks, and Equation (A5) and then interpolated as constant values at the points between those for observing water marks. depth of 2 m or more, at which the number of drownings due to flood inundation increased rapidly (Sato et al., 2019), was found only in the CTLs. This indicates that the differences in results between the CTLs and the NonWs can have implications for estimating of personnel and property damages.

| Summary of increases in
precipitation, river discharge, water level, overflow, and inundation due to historical warming Figure 9 summarizes the results of the analyses with respect to total precipitation (P), Q peak , river WL, overflow parameters, and inundation characteristics. The average WL increase for all sections between the peak values and the pre-flood or the HWL (ΔH bf , ΔH HWL ), the duration of the time when the WL exceeded the HWL T HWL , and the lengths of the sections where the WL exceeded the HWL L HWL were used as indicators. T HWL F I G U R E 7 Total overflow volume at each overflow section in the control experiments (CTLs) and the nonglobal warming experiments (NonWs). In the CTLs, overflow occurred at six sections. In sections R3 and L2, the overflow occurred in all members of CTLs, while in other four sections, the overflow occurred only in CTL1. In the two members of NonWs, the overflow occurred in section L2. The total overflow volume was determined by integrating the overflow discharge for each overflow section over time. The vertical axis is logarithmic because of the wide range of the total overflow volumes.
F I G U R E 6 Longitudinal distribution of peak water levels in the Chikuma River. T.P. (a), the dike height in the right bank (b) and left bank (c), and high-water level (HWL) (d) were used as the datum of the water level. The calculated water levels for the control experiments (CTLs) (4 members and the average) and the NonWs (20 members and the average) are shown. Locations of overflow at stations R1-R4 and L1-L2 are displayed with black arrows.
was measured at 57.5 kp, in which the longest value was recorded in the CTLs. Overflow depth H of and time T of on the left bank at 57.5 kp and the overflow section length L of on the left and right banks for the entire section were obtained. As inundation characteristics, maximum inundation depth h max , inundation area F I G U R E 8 Contour maps of the maximum inundation depth h max due to overflow at station L2. The calculated results for the control experiments (CTLs) (a)-(d), and the nonglobal warming experiments (NonWs) (e), (f) are shown on the maps. The computational domain for flooding analysis, river dike, and overflow sections are depicted with white, brown, and red lines, respectively.
F I G U R E 9 Historical warming impacts of total precipitation P (a), peak river discharge Q peak at the Kuiseke station in the Chikuma River (b), water-level increase before flood ΔH bf (c) and from high-water level (HWL) ΔH HWL (d), HWL excess time T HWL at 57.5 kp (e), length of HWL excess section L HWL (f), overflow depth H of at 57.5 kp (g), overflow time T of at 57.5 kp (h), length of overflow section L of (i), maximum inundation depth h max (j), inundation area A i (k) and total inundation volume V i (l).
A i and total inundation volume V i were selected. Additionally, Table 2 summarizes the minimum, average, and maximum values for the CTLs and the NonWs, as well as their ratios of average value of the CTLs to the NonWs (=CTL/NonW) for each index in Figure 9. First, for all 12 indices, the results of these parameters in the CTLs were higher than those of the 20 members in the NonWs, indicating that the historical warming markedly contributed not only to the increase in precipitation and Q, but also to the increase in river WL, overflow, and inundation. However, the increase in volume from the NonWs to the CTLs varied according to the indicators.
The P was 265-281 mm (mean: 273 mm) for the CTLs and 235-262 mm (mean: 252 mm) for the NonWs. Thus, CTL/NonW, which corresponds to the ratio of increase in P by the historical warming, was 1.083 ( Figure 9a). This means that the historical warming increased P by 8.3%. The Q peak was 6489-7558 m 3 /s (mean: 7034 m 3 /s) for the CTLs and 4942-6526 m 3 /s (mean: 5756 m 3 /s) for the NonWs, resulting in a CTL/NonW ratio of 1.22 (Figure 9b). Thus, the ratio of the increase in the Q peak was higher than that of the P.
The ΔH bf were 8.74-9.10 m (mean: 8.93 m) for the CTLs and 7.90-8.65 m (mean: 8.29 m) for the NonWs, and CTL/NonW was 1.08. This indicates that the ratio of increase in the water level from the pre-flood level was lesser than that in the Q peak . The range of the ΔH HWL of 20 members in the NonWs was from À0.10 to 0.66 m (mean: 0.30 m), suggesting that the flood could have exceeded the HWL even if the impact of historical warming from Typhoon Hagibis were removed. The ΔH HWL for the CTLs was 0.74-1.10 m (mean: 0.92 m), which means that ΔH HWL in mean CTLs was 0.62 m higher than that in mean NonWs, resulting in CTL/NonW of 3.08. ΔH HWL was higher than ΔH bf in terms of CTL/NonW because, although the peak WL was the same, the reference surface for calculating the WL was higher for the HWL than for the pre-flood level. T HWL at 57.5 kp was 6.8-10.2 and 10.3-11.3 h for the NonWs and the CTLs, respectively. Similarly, for the L HWL , the WL exceeded the HWL in a long section from 18.4 to 25.5 km in the NonWs, while it was longer, 25.6-26.6 km, in the CTLs. CTL/NonW was 1.23 for T HWL and 1.10 for L HWL , which was equal or slightly higher than the increase ratio for ΔH bf .
The H of on the left bank at 57.5 kp was 0.28-0.44 m (mean: 0.36 m) in the CTLs, while those in NonW1 and NonW2 were 0.11 and 0.04 m, respectively. The mean overflow depth in the NonWs was 0.0076 m, including 18 nonoverflow cases, and the CTL/NonW was 48.1. T of at 57.5 kp was 3.8-5.5 h (mean: 4.6 h) in the CTLs, whereas it was 0-2.3 h (mean: 0.18 h) in the NonWs, leading to CTL/NonW of 25.7. The L of on the left and right banks in all sections was 0.80-1.20 km (mean: 1.05 km) for the CTLs and 0-0.40 km (mean: 0.03 km) for the NonWs, resulting in CTL/NonW of 35.0.
The inundation analysis at station L2 showed that V i in the CTLs and the NonWs were 684 À3067 Â 10 3 and 0-55.4 Â 10 3 m 3 , respectively. The CTL/NonW for h max , A i , and V i were 40.6, 84.3, and 595, respectively. These facts suggest that this ratio for overflow and inundation situations was higher than that for Q and WL by one to two orders. Notably, these ratios for overflow and inundation situations are very sensitive to the calculated results. 4.5 | Hydrologic sensitivity of river discharge, water level, and inundation due to increased precipitation Figure 10 illustrates the correlation charts between P and, among 11 indices, Q peak , WL (ΔH HWL , T HWL , L HWL ), H of , and V i that enable obtaining df/dP in Equation (2). Table 3 summarizes the results of these linear regression equations (slopes and intercepts) and R 2 , showing that the indices of Q peak and WL have a statistically significant linear relationship with P for all data. Similarly, a linear relationship at the 1% significance level was obtained for data of H of and V i , but the R 2 of 0.53-0.59 was less than that of Q and WL because overflow and inundation occurred at the places where the P was large (CTLs: P = 265-281 mm, NonWs: P = 259-261 mm). Therefore, it was appropriate to remove P data where overflow or inundation did not occur. Then, a threshold value P th was set for P, and linear regression equations between H of , V i , and P were recalculated (Figure 10c,d). Here, the applicable data under the condition of P th = 259.0 mm (n = 10, including CTLs) were used in the calculation. Consequently, a linear relationship at the 1% significance level with higher R 2 was obtained between H of or V i and P for data with P ≥ P th . Table 3 shows that the elasticity indices ε of Q and WL were 2.20 and 0.85 to 8.15. Meanwhile, the ε for the overflow conditions (H of , T of , and L of ) and the inundation conditions (h max , A i , and V i ) were 7.18-7.72 for all data and 14.91-21.39 for data with P ≥ P th , respectively. Thus, similarly to CTL/NonW, ε varied depending on the index type. 5 | DISCUSSION 5.1 | Differences in hydrologic sensitivity among discharge, water level, overflow, and inundation A series of analyses of precipitation, runoff, river flow, and flooding inundation was conducted to quantify the impact of historical warming on precipitation, Q, river WL, overflow, and flooding inundation. Analyses results in the averaged values of the CTLs and the NonWs (=CTL/NonW) as indicators of the impact of historical warming were 1.08, 1.22, 1.08-3.08, 26-48, and 41-595 for P, Q peak , WL, overflow, and inundation parameters, respectively. As explained above, only 2 of 20 NonWs members experienced overflow and inundation, whereas the other 18 members did not experience them. In terms of average values in NonWs, CTL/NonW tends to be overestimated in the case of overflow and inundation compared to P, Q, and WL. Therefore, to evaluate the F I G U R E 1 0 Relationship between total precipitation P and peak river discharge Q peak and water-level increase from HWL ΔH HWL (a), HWL excess time T HWL at 57.5 kp and HWL excess section length L HWL (b), overflow depth H of at 57.5 kp (c), and inundation volume V i (d). Linear regression lines are shown for each index. Two linear regression lines for H of and V i were obtained for all data and data with P ≥ P th , separated by green dashed line.
impacts of historical warming quantitatively, ε in Equation (2) was obtained using hydrologic-sensitivity analysis. The increase in P ratio due to historical warming was 8.3%. Using ε listed in Table 3, the increases in the ratios were 18.2%, 7.1%, and 67.7% for Q peak , ΔH bf , and ΔH HWL , respectively. The increases in the ratios of the overflow and inundation indices were 124%-178%, with an ε for data of P ≥ P th .
First, ε for the Q peak is 2.20, which is within the general runoff elasticity range of 1.0-2.5 (Sankarasubramanian et al., 2001). The reason that the increase in the ratio of Q was greater than that of precipitation is discussed. Considering the water balance on the land surface, precipitation equals the sum of surface runoff, evapotranspiration, and subsurface infiltration. Assuming evapotranspiration does not change during rainfall (Komori et al., 2012) and subsurface infiltration volume is also constant considering the saturated state of the topsoil, as in the case of heavy rainfall, the precipitation and surface runoff volume Q can be modeled as a linear equation (P = Q + C, C: constant). In this case, because dQ/dP = 1, ε of Q is expressed as: Because the constant C is positive, Equation (3) shows that the runoff elasticity ε Q > 1, meaning that the Q peak increases at a higher rate than the P.
While ε for river WL is 0.85 based on the pre-flood level (ΔH bf ), that based on HWL ΔH HWL and the overflow depth H of are 8.15 and 16.42, respectively. Even at the same peak WL, because the reference surface for the WL increases in the order of pre-flood level < HWL < dike crest, the WL increases are described as pre-flood level > HWL > dike crest. In Equation (2), because index f is in the denominator, the magnitude relationships among the elasticity indices are ΔH bf < ΔH HWL < H of . However, the slope (df/dP) of the linear regression equation shown in Figure 10 becomes an inverse relationship as ΔH bf = ΔH HWL > H of . If overflow inundation occurs, the increase in precipitation and Q will contribute not only to the increase in WL but also to the increase in overflow volume. Consequently, the df/ dP ratio in the presence of overflow inundation would be less than that in the absence of overflow.
The elasticity of ΔH bf (0.85) was lesser than the value of the Q peak (2.20). The reason for this is discussed using the simplest Manning's mean velocity formula. For a rectangular open channel flow with width B, depth h, and energy gradient I, the discharge Q is given by The ratio of ε (ε Q /ε h ) with respect to the discharge Q and water depth h derived from Equations (2) and (4) is expressed as Equation (5) indicates that ε Q is greater than ε h . If the water depth is replaced by the increase in WL from the T A B L E 3 Slope, intercept, R 2 , and elasticity index ε for linear regression equations between the total precipitation and 11 indices obtained by hydrologic sensitivity analysis. Note: This table also lists the indices ΔH bf , T of , L of , h max , and A i , which are not shown in Figure 10. Here, the slope of the linear regression equation was plugged in for df/dP in Equation (2), while the control experiments (CTL) results were plugged in for P and f.

Items
pre-flood level ΔH bf , the ε of ΔH bf is expected to be less than that of Q peak . The ε of overflow and inundation, the most important factor in this study, ranges from 14.9 to 21.4, considerably exceeding ε for Q peak and river WL. As previously described, the increase ratio of V i and A i in response to the increase in precipitation exceeding the value for Q is consistent with existing studies (Kaspersen et al., 2017;Sayama, Tatebe, Iwami, & Tanaka, 2015;Swain et al., 2020), suggesting that the impact of historical warming is greater on overflow and inundation. Because the inundation phenomenon in this analysis is caused by overflow, the overflow volume is the starting point for inundation, making H of the most important index in Equation (A3). The reason for the large ε of H of is that f, which is included in the denominator of Equation (2) (in this case, H of ), is small. Sayama, Tatebe, Iwami, and Tanaka (2015) conducted a hydrologic-sensitivity analysis of the Chao Phraya River and showed that ε for the V i was 4.2. Regarding ε for V i in this study, because the value of ε (=21.4) is calculated only for data of P ≥ P th , ε becomes higher than that for the whole P range ( Table 3). The evaluation of ε of overflow and inundation is affected by the presence of the dike and topography of the floodplain. Because all overflow locations of the Chikuma River that were subjected to this analysis are in the sections where dikes exist, for a more general discussion on ε evaluation for overflow and inundation, it is necessary to consider various cases of river channels and floodplain topography, including the presence or absence of dikes, which is beyond the scope of this work and needs to be addressed in the future.
The river WL in the NonWs indicates that the WL exceeded HWL over the section from 18.4 to 25.5 km out of the 31 km of the Chikuma River. Therefore, this flood would have had an inundation risk even if the impact of historical warming was removed. The average peak WL in the NonWs exceeded HWL by up to 0.30 m, but overflow occurred in only 2 of 20 members, leading to the conclusion that the remaining 18 members were able to control overflow flooding at the river dike with freeboards. However, in the CTLs, the peak WL increased by 0.92 m, which is higher than that in the NonWs, increasing the overflow duration and the length of the section at which the WL exceeded the HWL. This suggests that 8.3% increase in P due to historical warming was the final cause of the overflow inundation. Thus, flooding would have exceeded the HWL but would not have caused overflow inundation or other damage when the climate was considered free from the impact of global warming and, consequently, a warmer climate in the future is likely to cause overflow inundation. In Japanese rivers, as the number of observation stations at which WL exceeds the HWL increases, the risk of overflow inundation increases due to climate change.

| Uncertainty of the historical warming impact assessment
There were some uncertainties in the impact assessment of historical warming in the above analyses. In a series of numerical analyses, same ensemble members are used for meteorological, runoff, and river flow analysis. Specifically, because the results of river flow analysis are greatly influenced by n, which is the only parameter, it is necessary to perform ensemble calculations that consider the perturbation of the parameter and the uncertainty. However, in this analysis, n is assimilated at the peak WL during the flood of this typhoon, so it is suitable as a parameter for high WL, whether there is overflow or not. We presumed that the effect of this on the results of our analysis is low. In addition, during this typhoon, levee breach occurred in the section of station L2; however, in this inundation analysis, the levee breach situation was not taken into consideration, and the inundation analysis was performed only by overflow. Therefore, the A i of the CTLs was lower than the actual A i (9.5 km 2 , MLIT, 2019). Originally, it was necessary to perform inundation analysis considering the levee breach, but it was very difficult to quantify levee breach conditions in the analysis, especially for the NonW. An inundation analysis that incorporates the levee breach scenario is an important topic for future research.
In the hydrologic-sensitivity analysis, ε was calculated under the condition of total rainfall P ≥ P th for the overflow and flooding conditions. The value of P th was set at 259 mm, which was obtained for this typhoon. Therefore, it is necessary to set different P th values for the spatiotemporal patterns of rainfall that are different from those of this typhoon. Therefore, it is necessary to change P th and perform hydrologic-sensitivity analysis when conducting a pseudo-warming experiment or considering the progress of flood defense in future research.
In the meteorological analysis, we conducted the hindcast experiments and evaluated the impacts of historical trends in atmospheric and sea surface temperatures on Typhoon Hagibis 2019. The evaluations of uncertainty are limited. To probabilistically evaluate the impacts of historical warming on heavy precipitation caused by typhoons approaching Japan, the other probabilistic method using large ensemble experiments with global climate models, which is called risk-based event attributions, would be required.

| CONCLUSIONS
In this study, considering the flood inundation of the Chikuma River Basin caused by Typhoon Hagibis in 2019, a series of numerical analyses of meteorology, runoff, river flow, and inundation was performed to quantitatively evaluate the impacts of historical warming on precipitation, Q, river WL, overflow, and flood inundation. The main results obtained are as follows: 1. The ratios of analyses results between the average of the CTLs and NonWs (CTL/NonW), which indicate historical warming impact since 1980, were 1.08, 1.22, 1.08-3.08 for total precipitation, peak river discharge, and river WL, respectively. In addition, CTL/NonW for the overflow and inundation indices was 26-48 and 41-595, respectively, which were higher by at least one order of Q and WL. Only 2 of 20 members of the NonWs had overflow. Therefore, considering the average value of NonWs, in the case of overflow and inundation, CTL/NonW tended to be overestimated compared to P, Q peak , and WL. 2. To evaluate the historical warming impact in another form, ε was introduced using hydrologic sensitivity analysis. The rate of increase in the total precipitation due to historical warming, Q peak , WL increase ΔH bf , ΔH HWL , and overflow and inundation indices were 18.2%, 7.1%, 67.7%, and 124-178%, respectively. The effects of Q and WL increase (ΔH bf ) on this increase in total precipitation are explained by the Equations (3) and (5). The most important ε for overflow and flood in this study is 14.9-21.4, which greatly exceeded the ε of Q and WL. The influence of historical warming on overflow and flooding was more pronounced. 3. The WL in the NonWs exceeded the HWL over a long duration, and there was a high risk of flooding even when the effects of historical warming were removed. The average peak WL in the NonWs exceeded HWL by a maximum of 0.66 m, and flooding occurred in only 2 out of 20 members, so overflow flooding was suppressed in the freeboard part in the remaining 18 members. In the CTLs, which accounted for the influence of historical warming, flooding also occurred at over 0.8-1.2 km, suggesting that the increase in total precipitation due to historical warming was the key factor that caused the overflow flooding. Therefore, evidently, the probability of overflow flooding will increase, owing to global warming, in floods that exceed the HWL but do not cause overflow.

APPENDIX A
A.1 | Method for river flow analysis The basic equations of the unsteady 1D flow model consist of the continuity equation (Equation (A1)) and motion equation (Equation (A2)).
In these equations, x is the main flow direction, t is time, A is cross-sectional area, Q is river discharge, q of is overflow discharge per unit length, η is water level, R is hydraulic radius, and g is acceleration of gravity. Manning's roughness coefficient (n) is the only model parameter in the equations. A finite difference method was employed for the numerical solution. Honma's overflow formula (Honma, 1940) was used to evaluate overflow discharge per unit length q of . Equation (A3) was used for complete overflow: In Equation (A3), h 1 refers to the water depth from the top level of the river dike.
The boundary conditions are the Q at the upstream end and WL at the downstream end of the computational section, respectively. The calculated Q obtained using the RRI model was given for both the CTLs and NonWs. The time series of the actual WL at the Tategahana observation station η C t ð Þ was provided in the CTLs for the WL at the downstream. In the NonWs, however, a WL of η N t ð Þ must be set in place of the observed WL used in the CTLs. Accordingly, using the peak river discharge (Q peak ) of each member of the NonWs and discharge-WL relation at Tategahana station, the peak WL of each member η N max was obtained. Using η N max , the WL in each NonW η N t ð Þ is given as where η C max is the peak WL of the CTLs and η 0 is the pre-flood WL corresponding to the initial WL, which is the same for the CTLs and NonWs. η N t ð Þ obtained with Equation (A4) is depicted in Figure 11, showing that the peak WLs in the NonWs were 0.41-1.83 m lower than that in the CTLs. Although an extension of the computational length to avoid the influence of the downstream condition is necessary, it was not implemented in this study because of the increased computational load, this issue must be considered in the future.
For n, a pre-calculation was performed to achieve data assimilation of the peak WL observed during flooding caused by this typhoon. Specifically, a nonuniform 1D flow model was used by removing the unsteady term from Equation (A2).
The n was calculated by substituting the observed peak WL into the difference equation of Equation (A5). The observed peak WLs are the peak WLs at the three points mentioned above (Kuiseke, Tategahana, and Koichi), and the observed water marks at points 56 and 14 on the Chikuma and Sai Rivers, respectively, provided by MLIT.