Spatial-temporal rainfall models based on poisson cluster processes

Nanda R Aryal,Owen D Jones

doi:10.1007/s00477-021-02046-5

Abstract

We fit stochastic spatial-temporal models to high-resolution rainfall radar data using Approximate Bayesian Computation (ABC). We consider models constructed from cluster point-processes, starting with the model of Cox, Isham and Northrop, which is the current state of the art. We then generalise this model to allow for more realistic rainfall intensity gradients and for a richer covariance structure that can capture negative correlation between the intensity and size of localised rain cells. The use of ABC is of central importance, as it is not possible to fit models of this complexity using previous approaches. We also introduce the use of Simulated Method of Moments (SMM) to initialise the ABC fit.

Highlights

We introduce the use of Simulated Method of Moments (SMM) to initialise the Approximate Bayesian Computation (ABC) fit
Our interest in spatial-temporal rainfall models comes from the use of rainfall simulators to understand the responses of hydrological systems to rainfall events
It has been argued by many authors that using simulated rainfall with realistic spatial and temporal variation is an effective way of understanding the range and frequency of responses from any given hydrological system

Summary

Introduction

Our interest in spatial-temporal rainfall models comes from the use of rainfall simulators to understand the responses of hydrological systems to rainfall events. In this paper we are concerned with the latter, for which we consider stochastic cluster-type models These models are structed to mimic the cell-like structure of rainfall events, and are straight-forward to simulate. The thesis of Aryal [1] considers other rainfall events at the same and different locations and obtains similar results Because it has an intractible likelihood function, in the past the CIN model has been fitted using the Generalized Method of Moments (GMM) [18]. ABC fitting compares the observed process to simulations, and places no restrictions on the statistics used to compare them. It has the advantage of providing credible intervals for the estimated parameters. Some recent examples of these can be found in the papers of Paschalis et al [12] and Benoit et al [4]

The data

The Cox-Isham-Northrop model and extensions

Generalisations of the CIN model

Model Fitting Using ABC