How design storms with normally distributed intensities customized from precipitation radar data in Sweden affect the modeled hydraulic response to extreme rainfalls

Abstract: Intense but short-term cloudbursts may cause severe flooding in urban areas. Such short-term cloudbursts mostly are of convective character, where the rain intensity may vary considerably within relatively small areas. Using uniform design rains where maximum intensity is assumed over the whole catchment is common practice in Sweden, though. This risks overestimating the hydraulic responses, and hence lead to overdimensioning of stormwater systems. The objective of this study was to determine how the hydraulic response to cloudbursts is affected by the spatial variation of the rain in relation to the catchment size, aiming to enable improved cloudburst mapping in Sweden. Initially, the spatial variation of heavy rains in Sweden was investigated by studying radar data provided by SMHI. The distribution of rainfall accumulated over two hours from heavy raincells was investigated, based on the assumption that the intensity of convective raincells can be approximated as spatially Gaussian distributed. Based on the results, three Gaussian test rains, whose spatial variation was deemed a representative selection of the radar study, were created. In order to investigate how the hydraulic peak responses differed between the Gaussian test rains and uniform reference rains, both test and reference rains were modeled in MIKE21 Flow model. The modelling was performed on an idealised urban model fitted to Swedish urban conditions, consisting of four nested square catchments of different sizes. The investigated hydraulic peak responses were maximum outflow, proportion flooded area and average maximum water depth. In comparison with spatially varied Gaussian rains centered at the outlets, the uniform design rain with maximum rain volume overestimated the peak hydraulic response with 1-8%, independent of catchment size. Uniform design rains scaled with an area reduction factor (ARF), which is averaging the rainfall of the Gaussian rain over the catchment, instead underestimated the peak response, in comparison with the Gaussian rains. The underestimation of ARF-rains increased heavily with catchment size, from less than 5 % for a catchment area of 4 km2 to 13 - 69 % for a catchment area of 36 km2. The conclusion can be drawn that catchment size ceases to affect the hydraulic peak response when the time it takes for the whole catchment to contribute to the peak response exceeds the time it takes for the peak to be reached. How much the rain varies over the area which is able to contribute to the peak response during the rain event, can be assumed to decide how much a design rain without ARF overestimates the peak responses. If the catchment exceeds this size, an ARF-scaled rain will underestimate the peak responses. This underestimation is amplified with larger catchments. The strong pointiness of the CDS-hyetograph used in the study risks underestimating the differences in hydraulic peak responses between the test rains and a uniform rain without ARF, while the difference between test rains and uniform rains with ARF risks being overestimated.