Multivariate Analysis of Joint Probability of Different Rainfall Frequencies Based on Copulas

Yang Wang,Qingtai Qiu,Mengjie Zhang,Jia Liu,Chuanzhe Li,Fuliang Yu,Jiyang Tian

doi:10.3390/w9030198

Yang Wang, Qingtai Qiu + Show 5 more

Open Access

https://doi.org/10.3390/w9030198

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Abstract

The performance evaluation of a city’s flood control system is essentially based on accurate storm designs, where a particular challenge is the development of the joint distributions of dependent rainfall variables. When it comes to the research design for consecutive rainfall, the analytical investigation is only focused on the maximum of consecutive rainfalls, and it does not consider the probabilistic relations between the first day of rainfall and the overall rainfall included in consecutive rainfall events. In this study, the copula method is used to separate the dependence structure of multi-day rainfall from its marginal distribution and analyse the different impacts of the dependence structure and marginal distribution on system performance. Three one-parameter Archimedean copulas, including the Clayton, Gumbel, and Frank families, are fitted and compared for different combinations of marginal distributions that cannot be rejected by statistical tests. The fitted copulas are used to generate rainfall events for a system performance analysis, including the conditional probability and design values for different return periods. The results obtained in this study highlight the importance of taking into account the dependence structure of one-day and multi-day rainfall in the context of storm design evaluations and reveal the different impacts of the dependence structure and the marginal distributions on the probability.

Highlights

Flooding in most cities is caused by rainstorms
Rainfall depth and duration are often used in the literature [8,9,10]. When it comes to the research design for consecutive rainfall, the analytical investigation is only focused on the maximum amount of consecutive rainfall, and it does not consider the probabilistic relations between the first day of rainfall and the overall rainfall included in consecutive rainfall events
Similar to the results presented above, the Clayton copula was not appropriate to describe appropriate to describe the structure of one-day rainfall and multi-day rainfall, which overestimates the structure of one-day rainfall and multi-day rainfall, which overestimates the value of different the value of different probabilities

Summary

Introduction

Flooding in most cities is caused by rainstorms. Using rainstorm data is an indirect way to ascertain the design flood compared with the estimate based on discharge data. The discharge series in survey regions is often too short to ascertain the design flood directly, since rainfall detection is a relatively systematic process and the data sequence is long and complete [1]. Rain can be represented by such characteristics as precipitation, rainfall intensity and rainfall duration [2]. The analysis of torrential rain generally uses the design rainfall method, which is a univariate analysis based on precipitation (e.g., the designed maximum one-day precipitation and maximum three-day precipitation). Researchers realized that the analysis of torrential rain based on the distribution of univariate extremum has certain restrictions [3]

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Conclusion