Distributional infilling missing data and interpolating rainfields using copulas

在这项研究的框架内，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，我们打算回到降水内插和模拟问题上来。这里用通过空间Copula耦合的局地降水分布代替了空间平稳性假设。这一过程需要对分布函数进行内插。下一步是使用这些分布对降水量进行内插和模拟。第二个任务是研究降水内插和模拟的误差结构。在过去，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，以前的调查表明，无偏误差的假设往往是不正确的。在这项研究的框架内，我们打算明确地将偏差与随机误差分开，这使得他们能够在模拟过程中明确地考虑偏差。这一程序基于使用内插分布函数的降雨量空间模拟(见任务1)。第三项任务是关于极端的空间范围的更复杂的处理。空间折减系数被用来获得降水量的面积极值。这些是使用与逐点内插不同的假设来估计的。在上一个DFG资助的项目中，我们证明了由于更高的阶数相关性，降水极值在空间上具有很强的相关性。这种高阶相关性不能用Copula的经典尾部相关性来描述。第一个目标是找到对这种依赖关系的适当统计描述。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.