Spatial Scale Dependence of Tropical Cyclone Damage Function: Evidence From the Mainland of China

Tropical cyclone (TC) damage function (DF) is widely used to model TC‐event level damage and thus assess the TC risk for a country or region. The scalability of these DFs at more localized scales, such as the province scale, has not been systematically explored. We use a unique Chinese data set to examine the damage at the TC‐event scale and province scale. Our results show that the parameters and performance of TC DF are spatially dependent. For a sigmoidal DF, the parameter dependence is manifested by a flatter curve calibrated on the TC‐event scale compared to the province scale. In the case of a power‐law DF, the dependence of its parameters is evident in the statistically more significant coefficients of the explanatory variables that are aggregated to the TC‐event scale, compared to the province scale. Performance comparison results further reveal that the scale dependence of performance is related to the type of DF. Integrating hazard, exposure, and vulnerability, the power‐law DF complements the typical sigmoidal DF, producing more accurate estimates of direct economic loss and annual average damage at both the TC‐event and province scales. However, its performance, compared to that of the sigmoidal DF, is more influenced by the scale at which it is calibrated. Our findings elucidate scale‐related research questions in TC risk assessment, offer insights into the selection of DFs, and inspire the future prospect of using multiple DFs to reduce the functional uncertainty. Plain Language Summary A damage function (DF) is a tool used to estimate the amount of damage caused by natural disasters such as tropical cyclones, which are also known as typhoons in China. The DF can help governments and organizations better prepare for future tropical cyclones and minimize the damage they cause. These functions are often used to estimate losses across an entire country, but there is a need to investigate whether they can be applied to smaller areas, such as provinces. This study summarized two types of DFs based on existing research and used a unique Chinese data set to explore them. The main findings are, first, that both DFs can be challenging to apply at the province scale. Second, each of the two functions has its own advantages and characteristics. One works better on smaller scales but tends to overestimate, while the other excels at estimation accuracy but underestimate. By utilizing these two types of loss functions, experts can more precisely evaluate t