Spatial bootstrapping for model-free estimation of subcatchment parameter uncertainty for a semi-distributed rainfall runoff model

Semi-distributed rainfall runoff models are widely used in hydrology, offering a compromise between the computational efficiency of lumped models and the representation of spatial heterogeneity offered by fully distributed models. In semi-distribute models, the catchment is divided into subcatchments, which are used as the basis for aggregating spatial characteristics. During model development, uncertainty is usually estimated from literature, however, subcatchment uncertainty is closely related to subcatchment size and level of spatial heterogeneity. Currently, there is no widely accepted systematic method for determining subcatchment size. Typically, subcatchment discretisation is a function of the spatiotemporal resolution of the available data. In our research, we evaluate the relationship between lumped parameter uncertainty and subcatchment size. Models with small subcatchments are expected to have low spatial uncertainty, as the spatial heterogeneity per subcatchment is also low. As subcatchment size increases, as does spatial uncertainty. Our objectives are to study the trade-off between subcatchment size, parameter uncertainty, and computational expense, to outline a systematic and precise framework for subcatchment discretisation. A proof of concept is presented using the Stormwater Management Model (EPA-SWMM) platform, to study a semi-urban catchment in Southwestern Ontario, Canada. Automated model creation is used to create catchment models with varying subcatchment sizes. For each model variation, uncertainty is estimated using spatial statistical bootstrapping. Applying bootstrapping to the spatial parameters directly provides a model free method for calculating the uncertainty of sample estimates. A Monte Carlo simulation is used to propagate uncertainty through the model and spatial resolution is assessed using performance criteria including the percentage of observations captured by the uncertainty envelope, the mean uncertainty envelope width, and rank histograms. The computational expense of simulations is tracked across the varying spatial resolution, achieved through subcatchment discretisation. Initial results suggest that uncertainty estimates often disagree with typical values listed in literature and vary significantly with respect to subcatchment size; this has significant implications on model calibration.

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