Space-time modelling of rainfall using Copulas - a quasi meta-gaussian approach

降水的随机时空模拟是一项具有重要现实意义的科学挑战。有两个关键挑战：第一，降雨量在空间和时间分布上高度可变。其次，在一个雨场内，有些地方的降雨强度为零(这种特性称为“间歇性”)。其现实意义在于，空间分布的雨量场对于防洪设计和规划人员来说是至关重要的。此外，天气预报领域对正确的空间分布雨量场以提高天气预报的能力越来越感兴趣。目前，还没有能充分考虑这两个性质的方法。我们建议开发一种方法，能够描述雨场的时空变化，并正确地考虑到间歇性。这项提议的目的是开发一种基于Copulas的多站点降水模拟的新方法。Copula是描述空间和时间依赖结构的选择方法，因为Copula允许以最纯粹的形式描述这种依赖。这一方法应适用于德国和南非的不同气候条件。不同的气候条件意味着不同的降雨量时空分布，应用所提出的模型将对该模型进行终极检验。开发的第一步是使用常规观测创建和测试每日时间尺度的模型。随后，模型将进行更小的时间步长测试，小到一个小时。该模式既应作为降水产生程序，也应作为内插器和条件模拟器的基础。这项研究计划在德国和南非进行双边研究，目的是补充目前关于Copulas和降水模拟的研究活动。

Stochastic space time modelling of precipitation is a scientific challenge with great practical importance. There are two key challenges: Firstly, rainfall is highly variable in its spatial and temporal distribution. Secondly, within a rain-field there are locations where the rainfall intensity is zero (a property referred to as “intermittence”). The practical importance lies in the fact that spatially distributed rainfall fields are of key importance for designers and planners for flood protection. Moreover, the field of weather forecasting is more and more interested in correct spatially-distributed rainfall fields to enhance weather forecasts. Currently, there are no methods available which take these two properties adequately into account. We are suggesting the development of a method that can describe the spatial and temporal variability of rain fields and correctly takes intermittence into account. The purpose of this proposal is to develop a novel methodology for multisite precipitation modelling which is based on Copulas. Copulas are the method of choice to describe spatial and temporal dependence structures, because Copulas allow to describe such a dependence in its purest form. This methodology should be applied to different climatic conditions in Germany and in South-Africa. Different climatic conditions imply a different spatial and temporal distribution of rainfall, and applying the proposed model there will be an ultimate test for the model. First step of the development is to create and test the model for the daily time scale using conventional observations. Subsequently, the model will be tested for smaller time steps, as small as one hour. The model should serve both as a precipitation generating procedure and as the basis for an interpolator and a conditional simulator. The research is planned to be conducted bilaterally in Germany and South Africa and is aimed to complement present research activities both on Copulas and precipitation modelling.