Aiming to deliver improved precipitation simulations for hydrological impact assessment studies, we develop a methodology for modelling and simulating high-dimensional spatial precipitation extremes, focusing on both their marginal distributions and tail dependence structures. Tail dependence is a crucial property for assessing the consequences of an extreme precipitation event, yet most stochastic weather generators do not attempt to capture this property. We model extreme precipitation using a latent Gaussian version of the spatial conditional extremes model. This requires data with Laplace marginal distributions, but precipitation distributions contain point masses at zero that complicate necessary standardisation procedures. We therefore employ two separate models, one for describing extremes of nonzero precipitation and one for describing the probability of precipitation occurrence. Extreme precipitation is simulated by combining simulations from the two models. Nonzero precipitation marginals are modelled using latent Gaussian models with gamma and generalised Pareto likelihoods, and four different precipitation occurrence models are investigated. Fast inference is achieved using integrated nested Laplace approximations (INLA). We model and simulate spatial precipitation extremes in Central Norway, using high-density radar data. Inference on a 6000-dimensional data set is achieved within hours, and the simulations capture the main trends of the observed precipitation well.

翻译：摘要：为改善水文影响评估研究中的降水模拟，我们开发了一种建模与模拟高维空间降水极值的方法，重点关注其边缘分布与尾部依赖结构。尾部依赖是评估极端降水事件后果的关键属性，但大多数随机天气生成器并未尝试捕捉这一特性。我们采用空间条件极值模型的潜在高斯形式来建模极端降水。这要求数据具有拉普拉斯边缘分布，但降水分布中存在零点质量，使得必要的标准化过程复杂化。因此，我们采用两个独立模型：一个用于描述非零降水的极值，另一个用于描述降水发生概率。通过结合两个模型的模拟结果来生成极端降水。非零降水边缘分布采用具有伽马和广义帕累托似然的潜在高斯模型进行建模，并研究了四种不同的降水发生模型。利用集成嵌套拉普拉斯近似实现了快速推断。我们以挪威中部的高密度雷达数据为对象，建模并模拟了空间降水极值。在6000维数据集上的推断数小时内完成，且模拟结果很好地捕捉了观测降水的主要趋势。