Constructing multivariate distribution of rainfall characteristics: A Bayesian vine algorithm

Abstract

Constructing a multivariate distribution model for rainfall characteristics is an important task for risk-based hydrologic design. However, most stochastic rainfall models are limited to bivariate frequentist distribution and cannot be easily generalized to multivariate (≥3) Bayesian settings. Towards this problem, this study presents a Bayesian vine algorithm. The presented algorithm translates the high-dimensional Bayesian update task into multiple lower-dimensional update tasks using the vine approach. The algorithm also computes the evidence, allowing Bayesian model selection of marginals and copulas in the joint distribution. Two numerical examples, a synthetic rainfall data from Canada, and a real rainfall data from China are utilized to demonstrate the algorithm’s capability. The results suggest that the algorithm can satisfactorily identify and characterize the underlying marginal and dependence for the rainfall characteristics. Since the high-dimensional Bayesian update task is translated into lower-dimensional Bayesian updates, the algorithm is scalable, stable, and computationally efficient in higher dimensions. A 20-year continuous hourly rainfall record can be characterized for its depth, duration, and intensity in around 60 s without any convergence or tuning issues. Overall, this study provides a powerful Bayesian tool for constructing stochastic rainfall models, which in turn can be used in multiple civil engineering disciplines concerned with rainfall interaction. This study does not consider temporal/serial dependence but only the cross-dependence among the rainfall characteristics.