Distributional infilling missing data and interpolating rainfields using copulas

在本研究的框架内，我们计划研究持续时间在1小时到1天之间的强降水和极端降水的空间结构。作为第一个任务，我们打算回到降水插值和模拟问题。在这里，空间平稳性假设被通过空间联结耦合的局部降水分布所取代。这个程序需要插值分布函数。下一步是使用这些分布来插值和模拟降水量。第二个任务是研究降水插值和模拟的误差结构。在过去，由于估计误差被认为是纯粹随机的，因此忽略了对可能的系统偏差的明确考虑。然而，先前的调查表明，无偏误差的假设往往是不正确的。在本研究的框架中，我们打算将偏差与随机误差进行明确的分离，以便在模拟过程中明确考虑偏差。该程序基于使用插值分布函数的降雨空间模拟（见任务1）。第三项任务与极端空间范围的更复杂处理有关。空间缩减因子将用于获得降水的面积极值。这些是使用不同的假设从点插值估计。在之前DFG支持的项目中，我们表明极端降水在空间上具有很强的相关性，因为它们具有更高的阶依赖性。这种高阶相关性不能用经典的尾相关性来描述。第一个目标是找到依赖性的适当统计描述。随后，将设想一种将这些统计数据纳入降水模拟程序的方法。

In the framework of this research we plan to investigate the spatial structure of heavy and extreme precipitation for durations between 1 hour and 1 day. As a first task we intend to return to the precipitation interpolation and simulation problem. Here the spatial stationarity assumption is replaced by local precipitation distributions coupled through a spatial copula. This procedure requires the interpolation of distribution functions. The next step is to use these distributions for interpolation and simulation of precipitation amounts. The second task is to investigate the error structure of precipitation interpolation and simulation. In the past, as estimation errors were considered to be pure random, the explicit consideration of a possible systematic bias was neglected. However, previous investigations have shown that the assumption of an unbiased error is very often not true. In the framework of this research we intend to perform an explicit separation of bias from the random error, what enables their explicit consideration during the simulation. This procedure is based on the spatial simulation of rainfall using interpolated distribution functions (see task 1). The third task is related to the more complex treatment of the spatial extent of extremes. Spatial reduction factors are to be used to obtain areal extremes of precipitation. These are estimated using different assumptions from pointwise interpolation. In the previous DFG supported project we showed that precipitation extremes are strongly related in space due to a higher order dependence. This higher order dependence cannot be described by the classical tail dependence of copulas. The first goal is to find an appropriate statistical description of the dependence. Subsequently a method to include these statistics in a precipitation simulation procedure will be envisaged.