Probabilistic Rainfall Downscaling: Joint Generalized Neural Models with Censored Spatial Gaussian Copula

TL;DR

This paper presents a novel probabilistic rainfall forecasting method that combines neural network-based marginal models with a censored Gaussian copula to capture spatial dependence, outperforming existing approaches on UK data.

Contribution

It introduces a joint neural model for marginal rainfall distributions and a censored Gaussian copula for spatial dependence, enabling accurate probabilistic forecasts.

Findings

Outperforms existing rainfall forecasting methods on UK data.

Effectively models spatial and temporal dependence in rainfall data.

Generates reliable short to long-term probabilistic forecasts.

Abstract

This work introduces a novel approach for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly modelled. Secondly, a spatial dependency structure is learned to ensure spatial coherence among these distributions. To learn marginal distributions over rainfall values, we introduce joint generalised neural models which expand generalised linear models with a deep neural network to parameterise a distribution over the outcome space. To understand the spatial dependency structure of the data, a censored latent Gaussian copula model is presented and trained via scoring rules. Leveraging the underlying spatial structure, we construct a distance matrix between locations, transformed into a covariance matrix by a Gaussian Process Kernel depending on a small set of parameters. To estimate these parameters, we propose a general framework for the estimation of Gaussian copulas employing scoring rules as a measure of divergence between distributions. Uniting our two contributions, namely the joint generalised neural model and the censored latent Gaussian copulas into a single model, our probabilistic approach generates forecasts on short to long-term durations, suitable for locations outside the training set. We demonstrate its efficacy using a large UK rainfall data set, outperforming existing methods.