Joint probability analysis of tropical cyclone wind and precipitation with the Archimedean copula function
YE Yanting1,2, GONG Junqiang1, ZHANG Haixia2, LI Jian3
1. Jinhua Meteorology Bureau of Zhejiang Province, Jinhua 321000, China; 2. Institute of Disaster Risk Science, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China; 3. Institute of Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing 100084, China
Abstract：[Objective] Tropical cyclone (TC) is one of the biggest threats to life and assets in coastal areas. TC is a stochastic event characterized by various hazards, such as strong wind, heavy rain, storm surge, and flooding, which can cause significant impacts individually or in combination. Exploring the relationship between the multiple attributes of TC can help estimate the severity of TC and aid in the emergency response and risk management. Strong wind and heavy rain are the two most severe hazards of TC disasters. Generally, TC weakens rapidly after landfall due to the mountainous terrains in coastal areas, and its intensity (wind) decays within a very short period. The maximum wind speed (MWS) of the TC at landfall reflects the threats posed by the strong winds of the cyclone. MWS also contributes to the rise in water levels caused by storm surges. Total precipitation (TP) can indicate the intensity of TC rainfall as well as the potential impact of inland floods and water logging. However, the relationship between MWS and TP is complex and nonlinear, and there is a lack of a clear formula to express this relationship. Copula is an effective probability method to model the dependence between two or more variables with uniform cumulative distribution functions (CDFs).[Methods] Therefore, in this study, a bivariate copula function was used to construct the joint probability of MWS and TP. Four marginal distribution models (Gamma, Gumbel, Weibull, and generalized extreme value (GEV)) were first fitted based on 553 MWSs at landfall and TPs over land in China (1951-2015). Three two-dimensional Archimedean copula functions (Clayton, Frank, and Gumbel) were then used to construct the joint probability of MWS and TP. The Kolmogorov-Smirov (K-S) test at a 5% significance level and the ordinary least squares (OLS) values were used to determine the best marginal and copula models. The characteristics of marginal CDFs and joint probability were also discussed. The conditional probability of TP was also calculated and discussed since TC intensity (wind) is easier to achieve than precipitation.[Results] The results of this study are as follows: (1) Weibull and Gamma are the best marginal CDFs for MWS and TP, respectively, and the Gumbel copula is the best copula function. Fitted Gumbel copula PDF values in the upper and lower tail are relatively high, indicating the probability of TCs with MWS and TP simultaneously being strong or weak is higher than TCs with either MWS or TP being severe. (2) The maxima of conditional probability increases with MWS, indicating that the most probable TP is also strong when MWS is strong. (3) Here, TP∈[1000, 2000]×108 m3 is defined as strong TP. When MWS ≤60 m/s, the conditional probability of strong TP increases with MWS; but when MWS >60 m/s, the conditional probability of strong TP increases with MWS before the threshold and decreases with MWS after the threshold. Each TP is associated with an MWS threshold, which increases with the concerned TP.[Conclusions] Our findings show that the construction and analysis of the joint probability distribution between MWS and TP lead to an improved understanding of the interaction relationship between TC hazardous wind and precipitation. This study also contributes to a comprehensive investigation of the TC multihazard destructiveness.
叶妍婷, 龚俊强, 张海霞, 栗健. 基于二维Archimedean copula函数的热带气旋风雨联合概率分析[J]. 清华大学学报（自然科学版）, 2023, 63(6): 874-881.
YE Yanting, GONG Junqiang, ZHANG Haixia, LI Jian. Joint probability analysis of tropical cyclone wind and precipitation with the Archimedean copula function. Journal of Tsinghua University(Science and Technology), 2023, 63(6): 874-881.
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2023, Vol. 63 
