Distributional infilling missing data and interpolating rainfields using copulas

• Applicant: Professor Dr.-Ing. András Bárdossy
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 271221982

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.

• DFG Programme: Research Grants
• International Connection: South Africa
• Cooperation Partner: Professor Geoffrey Pegram