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

David Huk, Rilwan Akanni Adewoyin, Ritabrata Dutta

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.