Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models

This paper presents an investigation of rainfall error models used in hydrological model calibration and prediction. Traditional calibration methods assume input error to be negligible: an assumption which can lead to bias in parameter estimation and compromise model predictions. In response, a growing number of studies now specify an error model for rainfall input, usually simple in form due to both difficulties in understanding sampling errors in rainfall, and to computational constraints during parameter estimation. Such rainfall error models have not typically been validated against experimental evidence. In this study we use data from a dense gauge/radar network in the Mahurangi catchment (New Zealand) to directly evaluate the form of basic statistical rainfall error models. For this catchment, our results confirm the suitability of a multiplicative error formulation for correcting mean catchment rainfall values during high-rainfall periods (e.g., intensities over 1 mm/h); or for longer timesteps at any rainfall intensity (timestep 1 day or greater). We show that the popular lognormal multiplier distribution provides a relatively close approximation to the true error characteristics but does not capture the distribution tails, especially during heavy rainfall where input errors would have important consequences for runoff prediction. Our research highlights the dependency of rainfall error structure on the data timestep.