Rainfall is the main input to most hydrological systems. To assess flood risk for a catchment area, hydrologists use models that require long series of subdaily, perhaps even subhourly, rainfall data, ideally from locations that cover the area. If historical data are not sufficient for this purpose, an alternative is to simulate synthetic data from a suitably calibrated model. We review stochastic models that have a mechanistic structure, intended to mimic physical features of the rainfall processes, and are constructed using stationary point processes. We describe models for temporal and spatial-temporal rainfall and consider how they can be fitted to data. We provide an example application using a temporal model and an illustration of data simulated from a spatial-temporal model. We discuss how these models can contribute to the simulation of future rainfall that reflects our changing climate.

中文翻译：

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降雨的随机模型


降雨是大多数水文系统的主要输入。为了评估集水区的洪水风险，水文学家使用的模型需要一系列低于每日甚至每小时以下的降雨数据，最好来自覆盖该区域的位置。如果历史数据不足以实现此目的，另一种方法是从经过适当校准的模型模拟合成数据。我们回顾了具有机械结构的随机模型，旨在模拟降雨过程的物理特征，并使用稳态点过程构建。我们描述了时间和时空降雨模型，并考虑了如何将它们拟合到数据中。我们提供了一个使用时间模型的示例应用程序，并提供了从时空模型模拟的数据图例。我们讨论了这些模型如何有助于模拟反映我们不断变化的气候的未来降雨。