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This work introduces a novel approach for generating conditionalprobabilistic rainfall forecasts with temporal and spatial dependence. Atwo-step procedure is employed. Firstly, marginal location-specificdistributions are jointly modelled. Secondly, a spatial dependency structure islearned to ensure spatial coherence among these distributions. To learnmarginal distributions over rainfall values, we introduce joint generalisedneural models which expand generalised linear models with a deep neural networkto parameterise a distribution over the outcome space. To understand thespatial dependency structure of the data, a censored latent Gaussian copulamodel is presented and trained via scoring rules. Leveraging the underlyingspatial structure, we construct a distance matrix between locations,transformed into a covariance matrix by a Gaussian Process Kernel depending ona small set of parameters. To estimate these parameters, we propose a generalframework for the estimation of Gaussian copulas employing scoring rules as ameasure of divergence between distributions. Uniting our two contributions,namely the joint generalised neural model and the censored latent Gaussiancopulas into a single model, our probabilistic approach generates forecasts onshort to long-term durations, suitable for locations outside the training set.We demonstrate its efficacy using a large UK rainfall data set, outperformingexisting methods.

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