Hydrological modelling using ensemble satellite rainfall estimates in a sparsely gauged river basin: The need for whole-ensemble calibration

The potential for satellite rainfall estimates to drive hydrological models has been long understood, but at the high spatial and temporal resolutions often required by these models the uncertainties in satellite rainfall inputs are both significant in magnitude and spatiotemporally autocorrelated. Conditional stochastic modelling of ensemble observed fields provides one possible approach to representing this uncertainty in a form suitable for hydrological modelling. Previous studies have concentrated on the uncertainty within the satellite rainfall estimates themselves, sometimes applying ensemble inputs to a pre-calibrated hydrological model. This approach does not account for the interaction between input uncertainty and model uncertainty and in particular the impact of input uncertainty on model calibration. Moreover, it may not be appropriate to use deterministic inputs to calibrate a model that is intended to be driven by using an ensemble. A novel whole-ensemble calibration approach has been developed to overcome some of these issues.This study used ensemble rainfall inputs produced by a conditional satellite-driven stochastic rainfall generator (TAMSIM) to drive a version of the Pitman rainfall-runoff model, calibrated using the whole-ensemble approach. Simulated ensemble discharge outputs were assessed using metrics adapted from ensemble forecast verification, showing that the ensemble outputs produced using the whole-ensemble calibrated Pitman model outperformed equivalent ensemble outputs created using a Pitman model calibrated against either the ensemble mean or a theoretical infinite-ensemble expected value.Overall, for the verification period the whole-ensemble calibration provided a mean RMSE of 61.7% of the mean wet season discharge, compared to 83.6% using a calibration based on the daily mean of the ensemble estimates. Using a Brier's Skill Score to assess the performance of the ensemble against a climatic estimate, the whole-ensemble calibration provided a positive score for the main range of discharge events. The equivalent score for calibration against the ensemble mean was negative, indicating it showed no skill versus the climatic estimate.