Probabilistic Rainfall Downscaling: Joint Generalized Neural Models with Censored Spatial Gaussian Copula
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 ens...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
18.08.2023
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2308.09827 |