Using Commercial Microwave Links for a stochastic reconstruction of precipitation field ensembles

Precipitation is one of the crucial variables within the hydrological system, and accordingly one of the main drivers for terrestrial hydrological processes. The quality of many hydrological applications such as climate prediction, water resource management, and flood forecasting, depends on the correct reproduction of its spatiotemporal distribution. However, the global network of precipitation observations is relatively sparse in large areas of the world. Compared to these observation network, inhabited areas typically have a relative dense network of Commercial Microwave Links (CMLs). These CMLs can be used to calculate path-averaged rain rates, derived from their attenuation. One challenge when using path-averaged rain rates is the construction of spatial precipitation fields. To address these challenges, we apply Random Mixing Whittaker-Shannon (RMWSPy) to stochastically simulate precipitation fields. Therefore, we generate precipitation fields as a linear combination of unconditional spatial random fields, where the spatial dependence structure is described by copulas. The weights of the linear combination are optimized in such a way that the observations and the spatial structure of the precipitation observations are reproduced. Within this method the path-averaged rain rates are used as non-linear constrains. One big advantage when using RMWSPy is the ability to simulate precipitation field ensembles of any size, where each ensemble member is in concordance with the underlying observations. The spread of such an ensemble enables an uncertainty estimation of the simulated fields. In particular, it reflects the precipitation variability along the CML path and the uncertainty between the observation locations. We demonstrate RMWSPy using CML observations within various areas of Germany with a different density of observations. We show, that the reconstructed precipitation fields reproduce the observed spatial precipitation pattern in a comparable good quality as the RADOLAN weather radar data set provided by the German Weather Service (DWD).