Open Access

Wei Qiu

• Rain gauges are considered to provide the best available information about absolute point rainfall intensity at ground level but are limited in estimating the precipitation fields. Radar measured precipitation fields provide the spatial patterns aloft but are biased with respect to the absolute rain fall intensities. Recently, it was shown that the microwave link attenuation is a promising complement to the traditional devices such as gauge and radar. This dissertation contributes to the problem of how to estimate precipitation fields by assimilating information from gauge, radar and MW-link, combining their advantages. Since the dependence structure between different precipitation observations is usually non-Gaussian, Copulas are applied to describe the dependence structure between observations from rain gauges and radar at the corresponding grid cells. As rain gauges are not available for each radar grid cell, two Copula-based approaches namely the Copula parameter map andRain gauges are considered to provide the best available information about absolute point rainfall intensity at ground level but are limited in estimating the precipitation fields. Radar measured precipitation fields provide the spatial patterns aloft but are biased with respect to the absolute rain fall intensities. Recently, it was shown that the microwave link attenuation is a promising complement to the traditional devices such as gauge and radar. This dissertation contributes to the problem of how to estimate precipitation fields by assimilating information from gauge, radar and MW-link, combining their advantages. Since the dependence structure between different precipitation observations is usually non-Gaussian, Copulas are applied to describe the dependence structure between observations from rain gauges and radar at the corresponding grid cells. As rain gauges are not available for each radar grid cell, two Copula-based approaches namely the Copula parameter map and interpolated Copula parameter field are used to model the spatial distribution of the dependence structure between gauge and radar positive pairs. Finally precipitation fields are simulated which retain the radar derived spatial patterns but are corrected for biases in their intensities. From theoretical point of view, all Copula-based techniques require independent and identically distributed (i.i.d.) data as a pre-requisite which is often neglected. Therefore, in this dissertation, the sensitivity of the Copula-based approaches to the violation of the i.i.d. assumption is studied and the influence of the ARMA-GARCH transformation to the final estimated precipitation fields is investigated. In addition to the pure dependence structure, the marginal distributions of the time series are another key aspect of each Copula model. Therefore, the temperature and altitude driven approach is developed to represent the spatial distribution of marginal distribution for rain gauges. Simulation results from various combinations of the spatial dependence structures and marginal distributions are compared to reveal the advantages and disadvantages of the different approaches. The microwave link attenuation, measuring the line integrated precipitation at near-ground level, can be either directly included in the Copula-based approach or used to adjust the radar derived rainfall fields first. It is proven that, by integrating the observations from MW-links, the estimated precipitation fields are further improved, leading to the better simulations of the precipitation fields at the near-ground level. The performance of the Copula-based data assimilation approaches is demonstrated for the Bavarian Alps and Alpine Forelands. The simulated precipitation fields are compared to the interpolated gauge fields (Ordinary Kriging) and also cross-validated with the available 31 rain gauges at grid scale, as well as the operationally corrected radar precipitation (Radolan). The Copula-based approaches perform similarly well as indicated by different validation measures and successfully estimate precipitation fields by combining data from various observation sources.…