Spatio-Temporal Synthesis of Continuous Precipitation Series Using Vine Copulas

Ana Callau Poduje,Uwe Haberlandt

doi:10.3390/w10070862

Abstract

Long and continuous series of precipitation in a high temporal resolution are required for several purposes, namely, urban hydrological applications, design of flash flood control structures, etc. As data of the temporally required resolution is often available for short period, it is advantageous to develop a precipitation model to allow for the generation of long synthetic series. A stochastic model is applied for this purpose, involving an alternating renewal process (ARP) describing a system consisting of spells that can take two possible states: wet or dry. Stochastic generation of rainfall time series using ARP models is straight forward for single site simulation. The aim of this work is to present an extension of the model to spatio-temporal simulations. The proposed methodology combines an occurrence model to define in which locations rainfall events occur simultaneously with a multivariate copula to generate synthetic events. Rainfall series registered in different regions of Germany are used to develop and test the methodology. Results are compared with an existing method in which long independent time series of rainfall events are transformed to spatially dependent ones by permutation of their order. The proposed model shows to perform as a satisfactory extension of the ARP model for multiple sites simulations.

Highlights

Stochastic modeling of precipitation aims at conceptually representing the natural process through some mathematical relationships in order to generate synthetic series that reproduce the statistical properties of observations
The developed method consists of an extension of the model based on alternating renewal process presented by [23] for single site simulations to multisite applications
The developed method consists of an extension of the model based on alternating renewal process presented by [23] for single site simulations to multi-site applications

Summary

Introduction

Stochastic modeling of precipitation aims at conceptually representing the natural process through some mathematical relationships in order to generate synthetic series that reproduce the statistical properties of observations. Synthetic series are used for different purposes, e.g., planning and design, deriving long extended time series or regionalization of rainfall to areas without measurements. Multi-point models are able to simultaneously generate time series at different sites while preserving temporal and spatial cross-correlation of the process. Many examples of multi-site models can be found in the literature; most of them are based on monthly, weekly, and up to daily time scales. Some of the models become complex and the parameters increase drastically. Their performance declines as a result of the difficulty

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