Space-time Uncertainty Propagation of Input Precipitation across a coupled Rainfall-Runoff Urban Drainage Model

Rainfall is one important source of uncertainty in the simulation of combined sewer overflows and the emissions of pollutants to the receiving water body. Studies often ignore the spatial dimension treating input rainfall as a non-spatially distributed time series. Neglecting spatial and space-time distribution of rainfall entering urban drainage systems may result in inaccurate quantification of rainfall and, hence, in substantial uncertainties associated to water quantity and quality predictions. We developed a space-time interpolation model for rainfall, based on space-time Kriging, using point rainfall measurements as the primary variable. We then interpolated rainfall over space and time and built a 90\% confidence interval of rainfall for the Haute-Sûre urban drainage system catchment in North-West Luxembourg. The resulting rainfall maps were fed into a rainfall-runoff model simulating the routing of the runoff across the catchment. The space-time rainfall uncertainty propagation demonstrated that an over estimation of CSO spill volume and consequently pollutants (COD and NH$_4$) is done when we consider only the deterministic simulation without taking into account the space-time model for rainfall. Furthermore, the presented methodology is generic and can be applied to a wider range of integrated environmental assessment models. Future work will focus on the space-time simulation implementation to replace space-time Kriging to produce more realistic and less smooth rainfall maps to propagate through the run-off model. Also, this will be realised as a generic approach to be applied to spatio-temporal integrated environmental assessment models.