## Abstract

Many of the world's largest coastal cities are becoming increasingly vulnerable to extreme events due to their growing populations and infrastructure, the changing climate, and subsidence. This paper assessed the economic impacts of extreme climatic events including sea-level rise and storm surge risk and the benefits of the adaptation strategies in the Pearl River Delta, a lowing-lying area located in southern China. An economic benefit–cost model was established for the estimation of the impacts and benefits. The damage of the extreme events was calculated using the damage rate modeled from the historic disaster database, and then the difference between the damage and the cost of heightening dikes was investigated under different scenarios. The results showed that the damage rate and storm surge level were positively related. The adaptation strategies benefited when the dike was heightened by 1.43–12.67 m, with the optimum reached at 5.15 m, and the dike did not exceed 12.67 m. The maximum benefits were obtained when the dike was designed to defend a 20-year return period storm surge in 2100, and the minimum when the dike is heightened to defend a 100-year return period storm surge in 2100.

## INTRODUCTION

(5)
where Y (US$million km m−1) is the cost of heightening one kilometre of dike by 1 m height, and x is the increased height (m). ### Optimal benefit strategies Under present conditions, that is, no adaptation is adopted and dike heights are maintained but not raised, the risk and damage increases with time as relative sea level rises. The benefit–cost model for beneficial analysis on dike construction can be established from Equations (1), (4), and (5), as shown in Figure 4. Two intersection points (respectively, points A and B), when the increased height (x) is 1.43 m and 12.67 m, respectively, were found on the damage curve and the cost curve. When x < 1.43, the cost curve is above the damage curve; when x = 1.43, the two curves intersect; and when x > 1.43, the damage curve is above the cost curve until x = 12.67; after that the cost curve is always above the damage curve. That is, when the elevation of the dike is less than 1.43 m, although there is coastal protection, the frequency of storm surges around this height is so high that the dike fails to meet the protection needs, and the damage still happens. At this stage, the cost of the dike construction is higher than the damage, and additional investment should be made to heighten the dikes. While the dikes were heightened beyond 1.43 m, the cost and the damage reversed. The property the dike protects is of a higher value than the cost of construction. According to Equation (1), at this stage, the net benefit of heightening the dike is positive. When the dike elevation reaches 5.15 m, the net benefits reach the maximum (i.e., point C in Figure 4), after which the net benefits diminish. The height at point C is the optimal level for the dike heightening under present conditions. When the height is higher than 12.67 m, the cost and damage reach a balance again. As the height of the dike continues to increase, the probabilities of storm surge at this water level would be smaller, and the investment will be much larger than the losses that may be incurred if no protection is adopted. Then the economic effects of heightening the dike will be negative. In summary, under present conditions, the construction of the dike had two balance points. When the increased height ranges from 1.43 m to 12.67 m, the net benefit is positive, and the maximum occurred when it reaches 5.15 m. The height of the dike should not be more than 12.67 m. Figure 4 The benefit–cost model for dike heightening (the benefit of dike construction is the difference between the damage curve of extreme events (dotted line) and the cost curve of dike heightening (solid line). Figure 4 The benefit–cost model for dike heightening (the benefit of dike construction is the difference between the damage curve of extreme events (dotted line) and the cost curve of dike heightening (solid line). ### Impacts under future scenario The direct economic loss with no protection, the cost and the benefit of dike construction with protection under future scenarios can be calculated from the benefit–cost model (Table 3). Table 3 Losses without adaptation and cost and net benefit with adaptations for different scenarios (US$ million)

Return period 2030

2050

2100

Losses Cost Net benefit Losses Cost Net benefit Losses Cost Net benefit
10-year 4,308.91 2,569.27 1,739.64 4,368.35 2,616.46 1,751.90 4,512.39 2,734.43 1,777.96
20-year 4,856.90 3,038.63 1,818.27 4,907.23 3,085.82 1,821.41 5,029.77 3,203.80 1,825.97
50-year 5,447.74 3,641.20 1,806.54 5,489.79 3,688.39 1,801.41 5,592.62 3,806.37 1,786.26
100-year 5,828.58 4,091.54 1,737.04 5,866.03 4,138.73 1,727.31 5,957.83 4,256.70 1,701.13
Return period 2030

2050

2100

Losses Cost Net benefit Losses Cost Net benefit Losses Cost Net benefit
10-year 4,308.91 2,569.27 1,739.64 4,368.35 2,616.46 1,751.90 4,512.39 2,734.43 1,777.96
20-year 4,856.90 3,038.63 1,818.27 4,907.23 3,085.82 1,821.41 5,029.77 3,203.80 1,825.97
50-year 5,447.74 3,641.20 1,806.54 5,489.79 3,688.39 1,801.41 5,592.62 3,806.37 1,786.26
100-year 5,828.58 4,091.54 1,737.04 5,866.03 4,138.73 1,727.31 5,957.83 4,256.70 1,701.13

As can be inferred from Table 3, the costs for constructing dikes to resist the extreme events are much lower than the losses due to not taking measures in all scenarios, suggesting that remarkable benefits can be obtained as the result of constructing dikes. Therefore, in view of the current status, the protection strategy of heightening the dikes should be adopted in response to future sea level changes and storm surge events. The largest loss happens in 2100 in a 100-year return period storm surge if no adaptation is adopted. As the height of dikes increases, the defensive capability strengthens, but the cost increases, too. In terms of the economic impacts, the optimal strategy is to heighten the dikes to meet the needs against surges with a return period of 20 years in 2100, and the minimum net benefit occurs when heightening the dikes for protection against the 100-year return period storm surge in 2100. Taking into account the depreciation expense, and large investment of human and material resources for the maintenance of the dike, it is not sensible to heighten the dike to a relatively high level, such as for protection against low probability storm surge events in 2100. The loss data used in this study is direct economic loss, and if the indirect economic losses during the disaster were considered, the net benefit from heightening the dike should be higher than in Table 3.

### Sources of uncertainty

There are three main sources of uncertainty in this study. First, due to the complexity and difficult acquisition of the indirect losses caused by the storm surge, the direct economics losses from departmental statistics were used as the losses. Second, we focused on the extreme climatic events in this study, and the risk of non-climatic events such as tsunamis was not considered. These may result in the assessment of the impacts of the extreme events being small, which means the net benefit of the dike heightening might be underestimated. Finally, the benefit of the strategies in 2030, 2050, and 2100 was estimated based on the current protection level of the dike. As the economy develops and property accumulates in the future, according to Equations (2)–(4), even in the case of constant disaster rate, the economic losses caused by extreme events would increase, and the benefits of dike heightening would increase accordingly.

## CONCLUSIONS

In this study, the benefit–cost model of storm surges was constructed based on the historical disaster data to investigate the economic impacts of sea-level rise and storm surges, and the adaptation strategy of heightening the dike in future scenarios in the PRD. The results showed that no significant correlation was found between the direct economic loss due to the storm surge and the water level, GDP, population or administrative area in the affected areas. However, the damage rate was positively correlated with the water level of the storm surge.

According to the benefit–cost model, the net benefit of dike construction is positive when the increased height ranges from 1.43 m to 12.67 m under present conditions in the PRD. And the optimal height is 5.15 m. The height of the dike should be no more than 12.67 m.

Under the scenarios of sea-level rise in the future, the present standard of dike defense in the PRD is relatively lower. In all scenarios, the protection strategies are beneficial. The heightening of the dike in the PRD is necessary in response to future sea-level rise and storm surge events. The maximum benefit occurs when the dike is heightened for defense against the 1:20 year storm surge in 2100, and the minimum happens when the height is increased for defense against the 100-year return period storm surge in 2100.

A storm surge disaster involves many industries and sectors, and the estimation includes complex types of disaster-bearing bodies, while usually little historical and economic loss data is available. The benefit–cost model established by using the damage rate and the storm surge level is scientific and feasible and would provide comprehensive analysis for storm surge estimation. It can provide a reference for research on extreme events study in other similar regions.

## ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (NO. 41571041 and 41871026) and Youth Innovation Promotion Association (2018417).

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