Mitigating parameter bias in hydrological modelling due to uncertainty in covariates

SummaryThe uncertainty in hydrological model covariates, if ignored, introduces systematic bias in the parameters estimated. We introduce here a method to determine the true value of parameters given uncertainty in model inputs. This method, known as simulation extrapolation (SIMEX) operates on the basis of an empirical relationship between parameters and the level of input noise (or uncertainty). The method starts by generating a series of alternate model inputs by artificially adding white noise in increasing multiples of the known error variance. The resulting parameter sets allow us to formulate an empirical relationship between their values and the level of noise present. SIMEX is based on theory that the trend in alternate parameters can be extrapolated back to the notional error free zone.We illustrate the strength of SIMEX in improving skills of predictive models that use uncertain sea surface temperature anomaly (SSTA) data over the NINO3 region as predictor to the southern oscillation index (SOI), an alternate measure of the strength of the El Nino southern oscillation. Our hypothesis is that the higher magnitude of noise in the pre 1960 data period introduces bias to model parameters where SSTA is the input variable. The relatively error invariant southern oscillation index (SOI) is regressed over SSTA and calibrated using a subset of the series from 1900 to 1960. We validate the resulting models using the less erroneous 1960–2003 data period. Overall the application of SIMEX is found to reduce the residual predictive errors during the validation period.