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

A novel approach for generating conditional probabilistic rainfall downscaling at finer scales from deterministic weather variables at coarser scales with temporal and spatial dependence is introduced. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly modelled conditional on the deterministic coarse weather variables. 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 that expand generalised linear models with a deep neural network architecture to jointly fit parameters of the distributions. The spatial dependency structure is modelled using a censored latent Gaussian copula leveraging the underlying spatial structure. We construct a distance matrix between locations, transformed into a correlation 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 latent 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 provides downscaled rainfall. We demonstrate its efficacy using a large UK data set, outperforming existing methods.