Future river-ood damage increases under aggressive adaptations

The risk of river ooding is expected to rise with climate change and socioeconomic development 1-6 , and therefore additional protection measures are required to reduce increased ood damage. Previous studies have investigated the effectiveness of adaptation measures to reduce ood risks 7,8 ; however, there has been no evaluation of residual ood damage (RFD), which reects the unavoidable increase in damage even under an aggressive adaptation strategy. Here, we evaluated RFD under several adaptation objectives. We found that China, India, Russia and countries in central Africa and Latin America can achieve a higher level of ood protection that will reduce RFD even under extreme scenarios. However, high RFD exceeding 0.1% of GDP remains, especially in eastern China, northern India, eastern Europe and central Africa. The high RFD are inevitable assuming the average construction period required for hard infrastructure (30 years), implying the need for immediate adaptation measures as well as soft adaptation.


Introductory Paragraph
The risk of river ooding is expected to rise with climate change and socioeconomic development [1][2][3][4][5][6] , and therefore additional protection measures are required to reduce increased ood damage. Previous studies have investigated the effectiveness of adaptation measures to reduce ood risks 7,8 ; however, there has been no evaluation of residual ood damage (RFD), which re ects the unavoidable increase in damage even under an aggressive adaptation strategy. Here, we evaluated RFD under several adaptation objectives. We found that China, India, Russia and countries in central Africa and Latin America can achieve a higher level of ood protection that will reduce RFD even under extreme scenarios. However, high RFD exceeding 0.1% of GDP remains, especially in eastern China, northern India, eastern Europe and central Africa. The high RFD are inevitable assuming the average construction period required for hard infrastructure (30 years), implying the need for immediate adaptation measures as well as soft adaptation.

Main Text
River oods are major natural disasters, causing serious economic losses and damage worldwide. Economic damage due to river ooding is projected to increase worldwide in the future, and more threatening conditions can be anticipated with the increasing global population and socioeconomic development [1][2][3][4][5][6] . Immediate effective adaptation measures should therefore be made for mitigating future damage.
Conducting effective adaptation measures at the global scale requires information about residual ood damage (RFD), which refers to unavoidable ood damage above the current protection level, even under an adaptation strategy based on feasible adaptation costs. To clarify local differences in the magnitude of RFD, estimations of the affordable adaptation level, which re ect local economic conditions and local costs of adaptation measures, are required to determine the feasibility of the adaptation measures.
Adaptation costs at the global scale have been quanti ed in a few previous studies. For example, Jongman et al. 9 demonstrated that adaptation cost of approximately €1.75 billion for increasing the ood protection level in all river basins in the EU could decrease the €7 billion total expected annual ood losses by 2050. Winsemius et al. 3 and Ward et al. 7 showed that global adaptation costs for levees could produce a much higher bene t (reduced damage through additional adaptation) in most combinations of climate and socioeconomic scenarios.
Here, we estimated global RFD under the feasible maximum adaptation level, i.e. the maximum future ood protection level that is both attainable and economically bene cial. This produced the highest net bene t (i.e. the cost of additional adaptation subtracted from the bene ts) and was referred to as the 'optimized adaptation objective'. The reduced damage was estimated by considering damage with and without additional adaptation measures (see "Estimation of RFD and bene ts" in the methods). We set a maximum limit of the adaptation level as a 1000-year return period of maximum ood magnitude in the past climate based on the current distribution of ood protection standards 10 , which was derived from the FLOod PROtection Standards (FLOPROS) database. The local adaptation level under the adaptation objective was calculated for each subnational administrative unit. It should be noted that RFD is not the total damage due to ooding, but the increase in future damage over that under the current protection level.  Interestingly, the RFD was still very high under the low emission scenario (16.7 billion USD per year, RCP2.6/SSP1), which was due to the high level of economic development in the inundation areas exposed to ooding. Because the estimated adaptation costs were similar among the scenarios (8.7-

billion USD per year)
, the ood protection level reached the level required to obtain the maximum net bene t (i.e. reduced ood damage minus the adaptation cost) (see "Estimation of RFD and bene ts" in the Methods section). On the other hand, ood protection levels remained low in countries where the adaptation costs were higher than the bene ts of adaptation (i.e. the amount of damage reduction), which was observed in many regions of Africa, Bolivia and Paraguay. The estimated RFD under the assumption of an economic limitation identi ed regions or countries where aid funding agencies or international cooperative frameworks should support adaptation to the effects of climate change in terms of ood risk. To assess the economic limitation on future ood protection levels, we conducted a similar analysis under the maximum adaptation objective, which minimized future ood damage (maximized bene ts) without considering the local economic limitation. The maximum adaptation objective would reduce future ood damage by 73.6 billion USD per year. However, a signi cant RFD still remained in regions, such as China, north-eastern Australia, southern and northern India, Siberia, eastern Europe, Nigeria, Alaska and northern Argentina. The main reason for the signi cant RFD was ood damage that occurred during construction (i.e. 2020-2050) (Supplementary Figure S4). Hardware adaptation measures require a long time to become effective; therefore, early decisions and other soft measures are also needed to reduce the increased ood damage under a warming climate 8 .
The RFD was high in areas of Asia, central Africa and Latin America that have experienced strong socioeconomic development, where the magnitude and frequency of ooding are projected to increase in the future 2 . In these regions, the ood protection standard required a high return period ( Figure 1). On the other hand, the RFD in Europe and North America exceeded 0.01% of the GDP for the optimized adaptation objective. In these regions, adaptation costs would be greater than the bene ts. This is because the high level of ood protection already exist (>50-year return period, Supplementary Figure S1), and because the frequency of large oods in the future (e.g. 100-year ood) would decrease 2 . The maintenance of current ood protection levels was the best economic option under the optimized adaptation objectives. This trend did not change with the lower or higher adaptation unit costs (Supplementary Figure S5).
The regions of eastern Asia, Siberia, western China, southern India, western and central Africa, northeastern Latin America, southern Canada and Alaska had large RFD values (Figure 3a). Among the different parameter-scenario combinations implemented in this study (e.g. SSPs, RCPs, discount rate, unit cost, operation and maintenance (O&M) costs, and protection area), more than 50% produced a signi cant RFD in these regions for the optimized adaptation objective. However, most regions had a much lower RFD for the maximum adaptation objective (Figure 3b), implying the potential needs for an international nancial mechanism to increase the resilience of these regions to future increases in ooding.
We found a signi cant RFD under the optimized and maximum adaptation objectives for most parts of the world, indicating a limit to adaptation. In this study, the limit to adaptation was caused mainly by the economic costs in subnational administrative units and assumed construction period, indicating that early decisions and international funding support are key factors for conducting effective adaptation measures at the global scale. Furthermore, the enhancement of autonomous adaptation via social adaptation activities is important for increasing the limit to adaptation because vulnerability was decreased by autonomous adaptation 6,11,12 . Future studies are needed to clarify the relationship between autonomous adaptation and ood protection measures.

Method Summary
The overall modelling framework consisted of the following steps: (1) global river ood simulation, (2) downscaling ood inundation, (3) damage calculation, (4) estimation of adaptation costs by adaptation level and (5) estimation of RFD and bene ts of the two adaptation objectives.
Global river ood simulation. The return period of river ooding under various climate scenarios was calculated from the daily total water storage derived from the global river ood simulation. We used the Catchment-based Macro-scale Floodplain (CaMa-Flood) model 13 to conduct a simulation forced by the daily runoff at a 0.5° × 0.5° resolution and output daily total storage at a 0.25° × 0.25° horizontal resolution. For future river ood simulation, we used ve general circulation models (GCMs) (GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM and NorESM1-M) and four RCPs (2.6, 4.5, 6.0 and 8.5 Wm −2 ). The cumulative distribution function-based downscaling method (i.e. a nonparametric bias-correction method) using percentiles of empirical cumulative distribution functions removed the biases of climatic variables in the GCMs 14 . A global ood inundation simulation was conducted for the period 1961-2005 for historical climate conditions and for the period 2006-2100 for future climate conditions, except for HadGEM2-ES (2006-2098). We did not consider the effects of ood protection levels, human modi cation of river discharge, or channel bifurcation in the global river ood simulation. This resulted in uncertainty regarding the inundation areas in mega delta regions (see SI6) 15,16 , and caused over-and underestimations of RFD, especially in downstream regions.
Downscaling ood inundation. The simulated over ow oodwater volume at a 0.25° × 0.25° resolution was downscaled to obtain the inundation area at a 30′′ × 30′′ resolution. First, the over ow oodwater volume was calculated from the annual maximum total water storage when the return period of the annual maximum ood water exceeded the local protection levels. The return period and corresponding river water storage were estimated based on the Gumbel distribution using the L-moment method 17 and were calculated from the annual maximum total water storage for the period 1961-2005 derived from the river ood reanalysis (see SI1). The current local protection levels were obtained from the model layer of FLOPROS 10 (Supplementary Figure S1). Finally, the over ow oodwater volume was downscaled to a 30′′ × 30′′ horizontal resolution using a high-resolution digital elevation model. The ooded area fraction was calculated at the same resolution.
Damage calculation. The RFD was calculated as the increase in ood damage over the present level  that would still occur despite the implementation of additional adaptation measures. To quantify RFD, the damage (Risk) was calculated based on the following equation:

Risk = Hazards × Exposure × Vulnerability
where Hazards is the magnitude of the ood, Exposure is the value of assets potentially affected by ooding, and Vulnerability is the susceptibility to harm or lack of the socioeconomic capacity to cope with ood risk. Hazards were derived from the over ow ood water depth from the downscaling ood inundation. Exposure was derived from the asset map, which was constructed from a gridded GDP map (see SI2). Exposure was targeted on the assets in the ooded areas, and therefore we used an asset map multiplying by the over ow ooded area fraction derived from the downscaling ood inundation. We used the global damage-depth function derived from Huizinga et al. 18 as a Vulnerability index, which was based on a literature survey, and this index covered each region (Asia, Africa, Europe, Oceania, North America and Central and South America). The damage-depth function was derived from the mean value for commercial buildings, industrial buildings, transport and infrastructure (roads) sectors. It was noted that ood protection levels were considered as Vulnerability in previous studies 7, 19,20 ; however, we did not explicitly consider ood protection levels in the damage calculation, because we already included ood protection levels in the downscaling ood inundation.
The modelled damage forced by the river ood reanalysis (see SI1) captured not only the global uctuations of ood damage (Supplementary Figure S6), but also the event-scale damage (Supplementary Figure S7). We compared the modelled damage forced by the historical simulation with the values calculated by other studies. Our estimation was within the range of other estimates (Supplementary Table S1), indicating that it was likely valid.
Estimation of adaptation costs by adaptation level. The adaptation costs of hardware measures were considered in this study. They were composed mainly of the costs of construction and O&M. The construction costs were calculated as the dimensions of the required ood protection levels multiplied by their unit costs. The unit cost was set as 2.404 [million USD/km/log 2 ( ood protection level)], which was derived from the original unit cost database of hardware measures (see SI3). The dimensions of the required protection measures were composed of their construction length and future ood protection levels. The construction length of a ood protection structure was calculated as the river length in a unit catchment (corresponding to a 0.25° × 0.25° horizontal resolution), derived from CaMa-Flood boundary data overlaid on the mask of the protection area. We assumed that the unit catchment was protected when the urban population density derived from the spatially explicit population scenarios in 2050 21 was higher than 400 persons km −2 . This value corresponded to the de nition of urban in Canada. The total length of the ood protection structure was calculated for subnational administrative units. The future protection levels were determined by adaptation levels for subnational administrative units. Because there were no future scenarios for ood protection levels, we de ned the relationship between future ood protection level (FPL) and adaptation level by the following equation: where FPL Future and FPL Current are the future and current ood protection levels described by return periods [year], respectively, and L is the adaptation level. In this study, L ranged from 0.0 to 10.0 at 0.25 intervals. FPL Future and FPL Current ranged from 0 to 1000 years. If FPL Current was 0.0, FPL Future was set to 2 years when L = 1.0. We assumed that the costs of workers, materials and land acquisition were included in the construction costs. We assumed the construction period was from 2020 to 2050. The O&M costs that were equal to 1% of the construction costs occurred during the period 2051-2100. Finally, we calculated the adaptation costs as the total cost of construction and O&M, with a 5% discount rate.
Estimation of RFD and bene ts of the two adaptation objectives. The RFD and bene ts were determined under consideration of the adaptation objectives. This analysis was conducted with a discount rate of 5% for subnational administrative units and for the evaluation period 2020-2100. The two adaptation objectives were the 'optimize adaptation objective' and 'maximum adaptation objective'. The optimize adaptation objective maximized the difference between bene ts and adaptation costs (i.e. net present value). The adaptation objectives reduced RFD if there were adaptation limitations (i.e. a future protection level within a 1000-year return period). On the other hand, the maximum adaptation objective is an ideal adaptation objective that minimizes RFD as much as possible. The RFD under the optimize adaptation objective was the most affordable option under the speci c socioeconomic conditions, while the maximum adaptation objective indicates a limit to adaptation. The RFD was estimated as the difference between future damage with additional adaptation and the relative damage equivalent to the present level .