Characterizing errors in areal rainfall estimates: application to uncertainty quantification and decomposition in hydrologic modelling

Abstract

Calibration and prediction in conceptual rainfall-runoff (CRR) modelling is affected by the sampling and measurement uncertainty in the observed input/output data and by the structural error of the model conceptualisation. The Bayesian Total Error Analysis methodology (BATEA) provides the opportunity to directly and comprehensively address these sources of uncertainty. BATEA is based on Bayesian hierarchical methods and uses explicit error models for input/output data and structural errors. Previous studies demonstrated that simultaneous inference on forcing (e.g. rainfall) and structural errors requires strong prior knowledge of the error mechanisms (e.g., statistical properties of rainfall errors).This paper investigates a geostatistical approach to estimate the sampling error made in approximating the areal rainfall by averaging point-values from a raingauge network. The geostatistical model generates an ensemble of rainfall fields conditioned on gauged values. This ensemble is treated as a distribution of the “true” areal rainfall over the catchment and used as a prior in the BATEA framework. A case study shows that the inclusion of such prior knowledge allows simultaneous estimation of input and structural errors, whereas in the absence of such information the inference is ill-posed.