A Semi-Parametric Bayesian Spatial Model for Rainfall Events in Geographically Complex Domains

TL;DR

This paper introduces a flexible Bayesian semi-parametric spatial model that captures complex environmental influences on rainfall, effectively modeling spatial dependencies and geographical factors with efficient inference, demonstrated through simulations and real Italian data.

Contribution

The paper presents a novel semi-parametric Bayesian model using latent Gaussian processes for rainfall data in complex terrains, with an efficient MCMC algorithm for inference.

Findings

Model accurately captures spatial correlation and geographical influences.

Demonstrates robustness across various rainfall and spatial scenarios.

Provides detailed rainfall maps for Italian regions with complex orography.

Abstract

Environmental phenomena are influenced by complex interactions among various factors. For instance, the amount of rainfall measured at different stations within a given area is shaped by atmospheric conditions, orography, and physics of water processes. Motivated by the need to analyze rainfall across complex spatial locations, we propose a flexible Bayesian semi-parametric model for spatially distributed data. This method effectively accounts for spatial correlation while incorporating dependencies on geographical characteristics in a highly flexible manner. Indeed, using latent Gaussian processes, indexed by spatial coordinates and topographical features, the model integrates spatial dependencies and environmental characteristics within a nonparametric framework. Posterior inference is conducted using an efficient rejection-free Markov Chain Monte Carlo algorithm, which eliminates the need for tuning parameter calibration, ensuring smoother and more reliable estimation. The model's flexibility is evaluated through a series of simulation studies, involving different rainfall and spatial correlation scenarios, to demonstrate its robustness across various conditions. We then apply the model to a large dataset of rainfall events collected from the Italian regions of Veneto and Trentino-Alto Adige, these areas are known for their complex orography and diverse meteorological drivers. By analyzing this data, we generate detailed maps that illustrate the mean and variance of rainfall and rainy days. The method is implemented in a new R package available on GitHub.