Storm Surge Risk Assessment for Non-Life Insurance

2.1 Study on stochastic storm surge evaluation

As a storm surge hazard study, Suzuki [13] conducted flood simulation over the whole of Japan, estimated the loss along the coast from the results, and developed loss function which is the relationship between water level at the representative point and the economic loss in the coastal area. The characteristics of this study are that the target area is wide and that large-scale storm surges due to climate change are also incorporated. However, since flood calculation is performed by a simple flood model, there is a issue in the accuracy of flood analysis, and no probabilistic discussion has been made in this study. Examples of publication on probabilistic storm surge damage estimation are following. Tsujita et al. [14] probabilistically calculated storm surge loss in the three major bays in Japan by using stochastic typhoon model. The stochastic typhoon model used in this study statistically processes past typhoon information and calculates the assumed typhoon that will occur in one year for 1000 patterns, so it does not consider future climate. The random variables are typhoon parameters (central pressure, location of typhoon, moving speed). This approach is common to the calculation of insurance purposes, which analyzes natural disaster risk in the coming year in many patterns and uses it for risk management and insurance premium setting. Exceedance probability used for risk management in non-life insurance companies is low. If the calculation period set long, the number of evaluation typhoons will increase and the calculation results will be stable and the uncertainty will decrease. The issue is that there is no discussion about the calculation period that was carried out. In addition, this study did not incorporate levees explicitly in the storm surge simulation, and no discussion on astronomical tide level setting. Similarly, Jiang et al. [15] probabilistically evaluated the current and future climate storm surge losses in the inner part of Ise Bay and showed the relationship between the annual exceedance probability and the storm surge loss. As for the present and future climates, a virtual typhoon for 25 ensembles of 200 years is used to evaluate the loss.

In the previous research mentioned above, it is common that firstly storm surge flood is calculated and secondly the loss is calculated from the inundation depth and the damage function which convert inundation depth into damage rate of the targeted assets. On the other hand, there is not enough discussion about uncertainty. In the process of calculating the storm surge loss, there are many parameters such as astronomical tide level, wind velocity/pressure distribution formula, maximum wind velocity radius, damage function, etc., and it is important to evaluate their effect on the estimated loss. Another issue is that there is no discussion about whether the calculation period is sufficient for the important return period.

A representative example of storm surge risk assessment efforts is the HUZUS-MH (Hazards U.S. Multi-Hazard) [16] developed by the Federal Emergency Management Agency (FEMA). This is software that estimates the damage caused by earthquakes, hurricanes, and floods in the United States, and displays damage of buildings and infrastructure due to past hazards. In addition, for the flood insurance program in the United States, FEMA has created a storm surge risk map with annual exceedance probability of 10, 2, 1, 0.2% in the United States, and has evaluated storm surge risk by various methods [17]. As a method, extreme value analysis, EST (Empirical Simulation Technique), and JPM (Joint Probability Method) have been studied. EST is a method of estimating the occurrence probability of the water level based on the observed tide level at a certain point by Probability distribution and constructing an artificial event set by the bootstrap method. JPM captures characteristics of hurricanes from observation information, constructs possible hurricanes from probability distributions of central pressure, moving speed and so on, and performs storm surge numerical calculation for all of them. While EST depends on limited observation data, JPM can comprehensively consider hurricanes etc. that may occur, and in recent years, JPM approach has been recognized as suitable for stochastic evaluation [17].

Similarly, in the natural disaster model of the insurance industry and probabilistic storm surge risk assessment in academic research, the method of calculating storm surges using assumed typhoons that capture past typhoon characteristics like JPM for a long term such as 1 year × 10,000 patterns has become common (eg AIRWORLDWIDE [18], Risk Management Solutions [19], Tsujita et al. [14]). That is, for example, when analyzing typhoons stochastically in Japan, it is assumed that a total of about 30,000 typhoons will land for 10,000 years because about 3 typhoons land in one year in average. However, it has been pointed out that the issue is that the computational cost is high because JPM calculates storm surges for all possible typhoons [17].

In order to reduce the calculation load of storm surge simulation, Jiang et al. [15] limited the typhoons that numerically calculate storm surge under the following three conditions.

• Typhoons that pass within 100 km of the bay

• Typhoons with a minimum central pressure of 950 hPa or less

• Typhoons with a typhoon speed of 20 km/h or more when landing

Through this process, typhoons that can flood are extracted. However, when considering variations in astronomical tide levels, it is not sufficient to evaluate storm surge risk because storm surge risk also depends on astronomical tide level, and it is necessary to use the total water level considering tides. In addition, the discussion on how much small and medium-scale storm surge damage can be extracted and uncertainty of annual expected loss of storm surge are insufficient in this paper.

In the US, FEMA has developed and is currently using JPM-OS (Joint Probability Method – Optimal Sampling), which is a method that reduces the calculation load of JPM (Johnson et al. [20]). Here, JPM-OS is briefly described. First, JPM-OS performs storm surge inundation analysis only on representative events selected from the numerous typhoon events. Then, the results are interpolated to estimate the inundation depth of the event for which no flood analysis has been performed. Although it is possible to reduce the calculation load by one digit compared to JPM [17], the problem is that uncertainty arises during interpolation. In order to reduce the uncertainty, research is underway on JPM-OS interpolation methods (eg Yang et al. [21]). Yang et al. compared the calculation results of the inundation depth for different JPM-OS interpolation method for each return period in Florida, USA. The RMSE of each method was 0.16 to 0.82 m when the inundation depth at each point was compared with the calculation result by JPM for each interpolation method for the return period of 50, 100, and 500 years. It was shown that an error occurs between the interpolated result and the numerical calculation result regardless of whether the return period is long or short.

As another approach, Hisamatsu et al. [5] selected a typhoon that can be inundated by a simple formula for typhoons of the stochastic typhoon model, and calculated the storm surge inundation only for the selected typhoon using a numerical model. Procedure by Hisamatsu et al. is described in Figure 2. This method aims at both reduction of calculation load and preservation of calculation accuracy by extracting floodable typhoons. Additionally, fluctuation of astronomical tide can be considered. The brief results of applying this procedure to the Tokyo Bay, Japan are shown in Section 3.

2.2 Study on hazard modeling

There are various storm surge models all over the world, but here some of them are introduced.

As a method for numerical analysis of storm surge hazards, a lot of studies have shown that considering wave set-up improves reproducibility. Kim et al. [22] developed a SuWAT (Surge-Wave-Tide coupled model), which is a model that considers wave set-up. SuWAT is a two-way coupled model that considers the interaction between tidal, storm surge and wave. The SuWAT model, composed of depth-integrated nonlinear shallow water equations and a simulated-waves near-shore (SWAN) model, can simultaneously run an arbitrary number of nested domains by using the message passing interface (MPI). Mase et al. [23] simulated typhoon Vera 1959 using SuWAT, and showed that the reproducibility of the storm surge is greatly improved if wave set-up is incorporated explicitly. Since SuWAT has been used by a lot of research especially in Japan and other Asian regions (eg Hisamatsu et al. [5]), this model has been adopted to natural disaster model of the insurance industry as numerical simulation model for storm surge [24].

In flood calculation, models that improve the calculation speed have been used. For example, Ramirez et al. [25] used LISFLOOD-FP [26] for flood calculation, which is dynamic and has a small calculation load. Inundation calculation load of storm surge was further reduced by using the flood model with the results of the storm surge model as boundary conditions (eg. Tsujita et al. [14]).

2.3 Study on vulnerability modeling

Some existing research on the damage function, which estimates the damage of assets from the inundation depth, are presented.

Regarding the relationship between tsunami inundation depth and its damage, as a representative of the tsunami damage caused by the 2011 Great East Japan Earthquake, the fragility curves expressing the probability of occurrence for each degree of damage have been published (eg Suppasri et al. [27], Aránguiz et al. [28]). These fragility curves are functions that calculate the occurrence probability P_iof each damage level i(minor, moderate, major, complete) using the inundation depth ηas an explanatory variable as shown in the following equation (Eq. (1)).

However, since this fragility curve does not show the damage ratio of assets, it is not possible to directly calculate the loss from the hazard intensity of the tsunami. Dias et al. [29] presented a method of converting the fragility curves into damage function. In other words, the tsunami fragility curves that have been accumulated so far can be converted into a tsunami damage function that can directly calculate the asset damage ratio Rusing the inundation depth as an explanatory variable, as shown in the following equation (Eq. (2)).

The storm surge damage function of HAZUS in the United States is frequently used to estimate the storm surge damage amount, which converts the storm surge inundation depth into asset damage rate (eg, Johnson et al. [20], Lin et al. [30]). The damage function installed in HAZUS was developed by US Army Corps of Engineers through post-flood research and interviews with experts [31, 32]. In addition, Kar and Hodgson [33] theoretically constructed a storm surge damage function.

In Japan, damage functions in Manual of Economic Survey for Water Management published by Ministry of Land, Infrastructure, Transport and Tourism (MLIT), Japan is widely used (eg Hisamatsu et al. [5], Tsujita et al. [14], Jiang et al. [15]). The reason is that there is no other storm surge damage function for Japanese assets. This was constructed based on the survey conducted in 1993 to 1996, and the issue is that the information of the material and equipment of the house, etc. surveyed deviates from present. Therefore, some study described relationships between inundation depth and damage ratio based on survey and simulation as following. Suzuki et al. developed flood damage function by hearing-based survey [34]. And Hisamatsu et al. developed flood damage function using the result of flood simulation and insurance data [35]. Unfortunately, small number of studies on damage functions is conducted. However, it is possible to accumulate storm surge damage functions based on the approach described above for actual events.

The shape of the damage function is roughly divided into two types, a step function and a continuous function. Kar and Hodgson [33] and the MLIT are the former, while US Army Corps of Engineers [32], Suzuki et al. [34] and Hisamatsu et al. [35] are the latter. In other cases, such as Tsujita et al. [14], the step function of the MLIT is regressed and converted into a continuous function and is used for damage estimation. In the case of the step function, since the damage function is constructed by setting the damage of modeled building according to the inundation depth, the function that the damage increases when the water level reaches the floor or ceiling of the modeled building. However, the structures of buildings that are actually damaged vary, damage ratio at the same inundation depth differs depending on the building. Therefore, the damage functions of US Army Corps of Engineers [32] and Suzuki et al. [34], which were constructed based on the disaster survey, is a continuous damage function because it covers buildings with various structures.