Quantifying the uncertainty corresponding to the radar rainfall estimation process: an inverse model for radar attenuation error
Authors: Green Amy , Kilsby Chris , Bardossy Andras 
Published: February 2023

Weather radar provides rainfall estimates at high resolution in both space and time, which is useful for many hydrological applications. Despite this, the radar rainfall estimation process introduces many sources of error, impacting the reliability of results obtained from the radar rainfall estimates. Key error sources include signal attenuation, radar calibration issues, ground clutter contamination, variability in the drop-size distribution and variation in the vertical profile of reflectivity. To gain an improved understanding of potential limitations, and the corresponding uncertainty of rainfall rates, the impact of these errors has been systematically investigated, developing a radar error model by inverting the rainfall estimation process.To this end, an ensemble of realistic rainfall events is simulated, and working backwards in a stochastic manner gives an ensemble of weather radar images, corresponding to each rainfall event, at each time step. The radar error model includes random noise effects, drop-size distribution errors, sampling estimation variance and importantly, attenuation effects. To allow for direct comparisons, standard radar processing methods are applied to each radar image, to obtain corrected &#8216;best guess&#8217; rainfall estimates which would be obtained from each weather radar ensemble member in real world applications. The difference between the simulated and corrected rainfall for each ensemble member is then treated as the uncertainty corresponding to the radar rainfall estimation process.A simple measure is introduced, to help understand how often errors result in a rainfall signal completely irretrievable, referred to as &#8216;rainfall shadow&#8217;. Areas of rainfall that are &#8216;shadowed&#8217; are defined as pixels where the simulated &#8216;true&#8217; rainfall rate is significant, but the ensemble member has less than 10% of the original signal. This is equivalent to considering where a significant rainfall rate has been completely lost, and would therefore be irretrievable using standard correction methods, to quantify the frequency of occurrence in real-world radar rainfall applications. The impact of location of rainfall within images is considered, by introducing the second moment of area for radar images, in order to quantify the proximity of intense rainfall to the radar transmitter.Results show relationships between rainfall shadows and high bias and uncertainty in rainfall estimates, related to the amount of rainfall (i.e. proportion and rates) in images. More central rainfall also results in higher errors and higher variability. The minimum likelihood of occurrence of rainfall shadows showed that 50% of event images have at least 3% of significant rainfall shadowed. In addition, 25% of images had a shadowed area of over 45km2, with the minimum largest shadow in one area for 5% of images exceeding an area of 50km2. This gap would result in an underestimation of the impact of potential floods, showing that weather radar has potential for important information to be lost. A model framework for representing this uncertainty in the radar rainfall estimation process provides methodology for assessing the impacts of radar rainfall errors on hydrological applications.