Stochastic Reconstruction and Interpolation of Precipitation Fields Using Combined Information of Commercial Microwave Links and Rain Gauges

For the reconstruction and interpolation of precipitation fields, we present the application of a stochastic approach called Random Mixing. Generated fields are based on a data set consisting of rain gauge observations and path-averaged rain rates estimated using Commercial Microwave Link (CML) derived information. Precipitation fields are received as linear combination of unconditional spatial random fields, where the spatial dependence structure is described by copulas. The weights of the linear combination are optimized such that the observations and the spatial structure of the precipitation observations are reproduced. The innovation of the approach is that this strategy enables the simulation of ensembles of precipitation fields of any size. Each ensemble member is in concordance with the observed path-averaged CML derived rain rates and additionally reflects the observed rainfall variability along the CML paths. The ensemble spread allows additionally an estimation of the uncertainty of the reconstructed precipitation fields. The method is demonstrated both for a synthetic data set and a real-world data set in South Germany. While the synthetic example allows an evaluation against a known reference, the second example demonstrates the applicability for real-world observations. Generated precipitation fields of both examples reproduce the spatial precipitation pattern in good quality. A performance evaluation of Random Mixing compared to Ordinary Kriging demonstrates an improvement of the reconstruction of the observed spatial variability. Random Mixing is concluded to be a beneficial new approach for the provision of precipitation fields and ensembles of them, in particular when different measurement types are combined.