Distributional infilling missing data and interpolating rainfields using copulas

在本研究的框架中，我们计划调查持续时间为 1 小时至 1 天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。这里，空间平稳性假设被通过空间连接耦合的局部降水分布所取代。该过程需要分布函数的插值。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。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，之前的调查表明，无偏误差的假设通常是不正确的。在本研究的框架中，我们打算将偏差与随机误差明确分离，以便在模拟过程中明确考虑它们。该过程基于使用插值分布函数进行的降雨空间模拟（参见任务 1）。第三项任务涉及对极端空间范围进行更复杂的处理。空间折减因子用于获得降水的区域极值。这些是使用逐点插值的不同假设来估计的。在之前 DFG 支持的项目中，我们表明，由于更高的阶依赖性，极端降水量在空间上密切相关。这种高阶依赖性无法通过 copula 的经典尾部依赖性来描述。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.