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

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method