Distributional infilling missing data and interpolating rainfields using copulas

在这项研究的框架内，我们计划调查的空间结构之间的持续时间为1小时和1天的强降水和极端降水。作为第一个任务，我们打算返回到降水插值和模拟问题。在这里，空间平稳性假设被替换为通过空间copula耦合的局部降水分布。这个过程需要分布函数的插值。下一步是使用这些分布进行降水量的插值和模拟。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随机的，因此忽略了对可能的系统偏差的明确考虑。然而，以前的研究表明，无偏误差的假设往往是不正确的。在这项研究的框架中，我们打算执行一个明确的分离偏差的随机误差，使他们明确考虑在模拟过程中。这一程序的基础是使用插值分布函数对降雨量进行空间模拟（见任务1）。第三项任务涉及对极端情况的空间范围进行更为复杂的处理。空间折减系数将用于获得降水量的区域极值。这些是使用逐点插值的不同假设估计的。在以前的DFG支持的项目中，我们表明，由于高阶依赖性，降水极值在空间上密切相关。这种高阶相关性不能用经典的copula尾相关性来描述。第一个目标是找到一个适当的统计描述的依赖。随后将设想一种方法，将这些统计数据纳入降水模拟程序。

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.