The construction of flood loss ratio function in cities lacking loss data based on dynamic proportional substitution and hierarchical Bayesian model

A reliable flood loss assessment in city is the basis of efficient flood risk management. However, it is difficult to fit empirical functions with typical case data for most of the world's arid or semi-arid cities that lack or even have no historical flood loss data. Under the background of frequent global extreme weather events and high-speed urbanization, urban flood loss assessment has become increasingly important to support urban flood risk management. At present, few researches have focused on the modeling of Flood Loss Ratio Function (FLRF) for cities lacking loss data. Therefore, based on the improved analogy principle, a Dynamic Proportional Substitution (DPS) method in this paper was proposed to transfer large sample data from multiple quoted cities into a sample matrix of loss ratios in the study city to address the lack of data. Then, according to the hierarchical data structure characteristics of the loss ratio matrix, a Hierarchical Bayesian Model (HBM) of FLRF with unknown parameters was constructed based on the prior distribution of parameters. Finally, taking the city lacking data-Zhengzhou, China as the study area, the water depth - loss ratio functions of four land types (industry, commerce, residence, and public utilities) were calculated. The results showed that: 1. The combined feature schemes achieved dynamic selectivity; 2. The parameters gradually converged after a certain number of iterations; 3. The error of FLRF solved by HBM was less than that of the least square method (LSM); 4. The DPS-HBM model had good performance in transplantation verification. This study is expected to provide a reference for the establishment of flood loss functions in cities lacking data.

Automated summary

This study proposed a DPS-HBM model to calculate the flood loss ratio function in cities lacking data, combining the improved analogy principle and Hierarchical Bayesian Model. The model showed good performance in transplantation verification and provided a new approach for establishing flood loss functions in cities with data scarcity.