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.

翻译：本文提出了一种生成具有时间和空间依赖性的条件概率降水预测的新方法。该方法采用两步流程：首先，对边缘位置特定分布进行联合建模；其次，学习空间依赖结构以确保这些分布的空间一致性。为学习降水值的边缘分布，我们引入了联合广义神经模型，该模型通过深度神经网络扩展广义线性模型，从而对结果空间上的分布进行参数化。为理解数据的空间依赖结构，提出了一种基于评分规则训练的删失潜高斯Copula模型。利用潜在的空间结构，我们构建了位置间的距离矩阵，并通过依赖于少量参数的高斯过程核函数将其转换为协方差矩阵。为估计这些参数，我们提出了一种通用框架，该框架采用评分规则作为分布间散度的度量来估计高斯Copula。通过将我们的两项贡献——即联合广义神经模型与删失潜高斯Copula——整合为单一模型，该概率方法可生成短期至长期的预测，并适用于训练集之外的位置。我们使用大规模英国降水数据集验证了其有效性，结果表明该方法优于现有技术。