# Ensemble Radar-Based Rainfall Forecasts for Urban Hydrological Applications
## 1 Introduction
Elevated terrain can cause occultation of the main part of the radar beam in some cases. This can only be corrected if less than 60% of the radar beam is obstructed [16]. Variation in the Vertical Profile of Reflectivity (VPR) is related to changes in size, in phase, and in shape distribution of hydrometeors [22]. Using dual polarisation radars permits the measurements of hydrometeor characteristics such as rain and melting snow, and snow to be identified and corrections to be applied [23]. This can be used to improve the rainfall estimation on the ground. When the distance from a radar increases, there is naturally an increase in the radar sampling volume as well. At a higher altitude, the distribution of hydrometeors changes, leading to a difference between measured rainfall and rainfall that actually falls on the ground [17; 24]. During heavy rainfall events, attenuation might occur when radars with small wavelengths are used (e.g., C-band or X-band radars) [16; 19; 25; 26]. Finally, the radar rainfall can be adjusted using ground rain gauge measurements using bias correction methods or geostatistical approaches [27; 28]. Once the radar data have been corrected for the different error sources, a radar-based rainfall forecasting model, such as nowcasting, can be applied. Nowcasting models based on the extrapolation of Lagrangian trajectories produce rainfall forecasts with a few hours lead-time (with increased loss of performance after 2-3 h ahead). They have a significant role in enhancing rainfall warning systems, especially when predicting extreme events or flash floods [29; 30]. Nowcasting models use a sequence of weather radar images, and the generated precipitation forecasts produced with this technique have a high spatial and temporal resolution [7]. However, uncertainties inherent to the nowcasting model result in an increasing loss of forecasting skill after 1 h lead-time. Uncertainties in radar nowcasts are caused mainly by [31; 30; 32]: uncertainties inherent in the specific nowcasting model used, errors in radar rainfall estimation, uncertainties due to the temporal development of the velocity field and uncertainties caused by precipitation processes such as growth and decay not being taken into account. [PERSON] [33] developed a pattern recognition model based on a correlation coefficient to calculate motion vectors in storms known as TREC (tracking radar echo with correlation). The TREC algorithm has been modified, and new models are based on this approach. [PERSON] et al. [34] compared forecasts produced using two different models. The COTREC model (Continuity of Tracking Radar Echoes by Correlation vectors), which is based only on extrapolation from radar images and assumes that rainfall trajectories do not change with time, and the SAMR model (Statistical Advective Method Radar) that utilizes the same technique, but in addition factors in a statistical model to correct precipitation estimations. Results showed that SAMR provides slightly better results, but it is not capable of predicting new storms or of forecasting any significant changes in existing ones accurately. The GANDOLF scheme (Generating Advanced Nowcasts for Deployment in Operational Land-based Forecasts) was developed to increase the predictability of convective rainfall. An object-oriented model of convection is used that incorporates a model of the life cycle of convective clouds [6]. This advection scheme showed deficiencies in severe rainfall events. An attempt to address this issue was made by dividing the rain analysis into blocks and forcing adjacent blocks to have a smooth transitional variation of the velocity. [PERSON] et al. [12] derived a new optical flow algorithm, enhancing the GANDOLF system's capability to calculate the advection field. This algorithm was used to further develop the STEPS (Short-Term Ensemble Prediction System) [7]. In the STEPS model, ensemble radar nowcasts are blended with Numerical weather prediction (NWP) forecasts.