Uncertainty propagation in coupled hydrological models using winding stairs and null-space Monte Carlo methods

Abstract By integrating disciplinary sub-models, coupled hydrological models allow the exchange of output and input fluxes among their sub-models. While such coupling of models can mirror the conceptual representation of the water-cycle, potential uncertainty propagation and aggregation across the sub-models may limit their overall performance. There are limited studies dealing with uncertainty in coupled hydrological models due to the high computational needs, the absence of detailed data, and the lack of efficient uncertainty propagation frameworks. This study presents an effective uncertainty propagation framework using a combination of statistical techniques, multi-variable calibration, and parallel computation. The framework was tested using a synthetic mathematical coupled model and a real‐world, coupled surface water (PRMS) and subsurface (MODFLOW) model. For the synthetic coupled model, the framework has shown its effectiveness to reveal the interplay of input variables, quantify the uncertainties within each sub-model and track their propagation through the coupled modeling system. For the PRMS-MODFLOW model, the framework has demonstrated how uncertainty in input precipitation, surface water, and subsurface water sub-models influences the different segments of a hydrograph. The results also indicate that improved predictions of high flow require a better quantification of input uncertainty. In contrast, baseflow and recession flow uncertainties largely depend on the subsurface and surface water sub-models, respectively. The presented framework, in addition to providing relatively comprehensive uncertainty information on the integrated model outputs, it helps to identify the potential sources of uncertainty that can be used for further model improvement and guide new data collection campaigns.