# Ensemble Radar-Based Rainfall Forecasts for Urban Hydrological Applications
## 1 Introduction  
Flooding is a very common natural disaster around the world, and its frequency and intensity are expected to rise [1]. Structural measures are not only very expensive but also are built to protect a particular region from an estimated flood level [2; 3]. More intense floods that can overcome the protective structures will inevitably occur, and the consequences will be increasingly severe, as the concentration of people and infrastructure in urban areas is on the rise as well. Therefore alternative measures using flood forecasting and warning systems are in demand, and forecasting floods several hours ahead can allow a timely emergency response to take place [4]. Rainfall-runoff modelling has an important function when issuing flood warnings [2]. Over the last couple of decades, much research has been done to increase the reliability in forecasting rainfall [5; 6; 7; 8]. Hydrodynamic models for real-time flow predictions, utilising radar rainfall and radar-based rainfall forecasts, can be used for the real-time control of drainage systems in urban areas [9]. It is, however, essential to know the uncertainties related to the radar rainfall measurements in order to produce reliable forecasts. For urban flood forecasting applications, rainfall data should have high temporal (e.g., 5 min or lower) and spatial (e.g., 1 km or lower) resolutions [10; 11]. Weather radars measure rainfall in real-time and provide high-resolution data for short-term precipitation forecasting, which is also known as nowcasting. Accurate rainfall forecast inputs are one of the main factors that influence accurate flow predictions. Increasing the predictability of these forecasts has proven to be a challenge given the small spatial scales involved and therefore reducing radar rainfall-related uncertainties can improve radar-based rainfall forecasts [8; 12]. This paper aims at quantifying the value of radar-based rainfall forecasts and their associated uncertainties in urban flood forecasting applications. Weather radar rainfall is affected by different sources of errors that propagate into the rainfall forecasts produced by nowcasting models [13; 14]. Weather radars send microwaves and receive backscattered radiation from precipitation particles through the radar reflectivity (\(Z\)), which is related to the rainfall rate (\(R\)) using a semi-empirical equation of the form \(Z=aR^{b}\)[15; 16]. However, the parameters \(a\) and \(b\) of the \(Z\)-\(R\) equation are known to be dependent on the precipitation type and the raindrop size distribution. Using a constant \(Z\)-\(R\) equation contributes to an error in radar rainfall estimation [16; 17]. In order to reduce uncertainties due to parameter bias in the \(Z\)-\(R\) equation, [PERSON] [18] developed an error model to assess how rain gauge uncertainties impact in the \(Z\)-\(R\) equation. Although the model was shown to improve rainfall estimation, the difference is less than 5%. According to [PERSON] et al. [19], radar estimations of precipitation have a large degree of uncertainty (higher than 100%) when the reflectivity error is only a few dBZ for C-band radars. Radar calibration should regularly be made to avoid inaccurate readings [17]. Lack of accurate determination of the radar calibration constant leads to systematic errors in the observations. Some of the radar rainfall errors are associated with ground clutter echoes, which occur when the radar beam come across ground targets [16]. Much ground clutter is permanent, and a ground clutter map can be used to identify these non-meteorological echoes. However, ground clutter maps are unable to identify radar echoes caused by anomalous propagation conditions [17; 20]. In conditions of anomalous propagation, the radar beam is bent towards the ground due to changes in the refractive index of the atmosphere producing unwanted ground echoes that can be misinterpreted as heavy precipitation [17; 20]. Polarimetric weather radars have shown promise in identifying anomalous propagation [21].