# Weather Radar in Complex Orography
## 4 Solutions and Results
### Modelling and Propagation of Uncertainty and End-to-End Processing Chains  
Various approaches have been presented in the literature to assess the space-time error structure of radar measurements. Most of them refer to the uncertainty in radar QPE. Two fundamentally different approaches can be used to assess QPE uncertainties. In the first approach, the radar QPE is compared with a reference, typically measurements from rain gauges; see, for instance, [168]. In the second approach, the uncertainty is estimated using a model. The methods presented in [124; 169], for instance, can be used to model the uncertainty that results from VPR and space-time variations of the drop size distribution, respectively. Not only is the _amplitude_ of the uncertainties needed for most applications, but also its _correlation_ in space and time, that is, the full covariance matrix of radar errors. The amplitude and the space-time correlation in a mountainous region exhibit a distinct dependence on the location, which needs to be taken into account, see [170].  
The uncertainties in radar QPE are large, especially for a mountainous region with severe beam shielding and VPR issues. It has often been stated that the uncertainties in rainfall measurements need to be below 10% for hydrological applications, a requirement that is difficult to satisfy with a long-range surveillance radar sited on a mountain top (or with rain gauges). It is therefore tempting to reject the use of radar QPE for hydrological modelling and for the issuing of warnings of heavy precipitation, flash floods and debris flows. From the authors' experience this is not a wise decision. First, some of the stochastic uncertainties are averaged when the rainfall is integrated in the hydrological processes in space and time, depending on the catchment and application. Second, other uncertainties of similar magnitude are involved in the hydrological system and the decision process. The decision makers are used to dealing with uncertainties. It is practically impossible to predict a debris flow. However, a simple statistical model, based on real-time radar data, and trained on a number of past events, will likely provide useful information to those decision makers who are managing the risks in a catchment prone to debris flows. In fact, thunderstorm, flash flood and debris flow warnings automatically generated from radar measurements have turned out to be of high practical value, in spite of the large uncertainties, as shown for the various applications in the Swiss Alps listed in Section 2.2.  
Ensemble approaches play a central role in the modelling of radar errors and in studies of uncertainty propagation in hydrometeorological forecasting, see [171] for a review. There have been two major related European initiatives, the COST-731 action, the aim of which was to investigate the propagation of uncertainties in end-to-end hydrometeorological forecast systems [67], and MAP D-PHASE, a WMO forecast demonstration project that was held in the European Alps [70]. COST-731 and D-PHASE brought meteorologists, hydrologists and end users together and were ideal test beds to quantify the role of uncertainties in the context of real applications. The two initiatives triggered a number of unique experiments that coupled ensembles of radar QPE, Lagrangian nowcasts and NWP forecasts with hydrological models [66; 68; 109; 170] and fostered the quantitative use of radar measurements in complex orography, despite the often large uncertainties.