Copula-based conditional merging of information on different spatial and temporal scales

Abstract:

Merging data sets across spatiotemporal scales is still a critical problem in hydrology and hydrogeophysics. In particular, the often non-linear relationships and the different scales complicate the combination procedure. A well-known example is the combination of pointwise measured precipitation records with indirect precipitation measurements like radar or satellite observations.

This work presents a new developed conditional simulation technique called Random Mixing that allows merging of data sets across different scales. It is based on linear combinations of spatial random fields and uses copulas to model the dependence structure. The linear combinations need to be found such that all linear constraints, like precipitation gauge data, are fulfilled. Furthermore, certain information (e.g. zero values) can be extracted from remotely sensed data and used as additional linear constraints. Taking advantage of a specific property of Random Mixing an infinite number of conditional fields can be defined, hence non-linear constraints like large scale averages resulting from remote sensing can be incorporated via minimization of a certain objective function.

The methodology will be demonstrated using two precipitation simulation examples. First, precipitation estimations using gauge and radar data in the federal state of Baden-Württemberg in south west Germany. Second, precipitation estimations using gauge and satellite (TRMM) data in Singapore.