'Calibrate it twice': A simple resampling method for incorporating parameter uncertainty in stochastic data generation

Abstract

Stochastically generated data are used to assess the impact of climate variability on water resources systems. The CRC for Catchment Hydrology has produced a toolkit product SCL to generate rainfall and climate data but all the models in SCL except the annual rainfall model do not take into account parameter uncertainty. One of the objectives of the eWater CRC is to incorporate parameter uncertainty in stochastic models. The source of parameter uncertainty is insufficient sample size in calibration and is equally applicable to parametric and nonparametric models. The traditional way of incorporating parameter uncertainty is via Bayesian analysis using Markov chain Monte Carlo simulation. This technique requires formulation of a likelihood function which is not straightforward for all the models in SCL. Therefore, a simple resampling method is investigated to incorporate parameter uncertainty in both parametric and nonparametric models. The model is applied to generate annual rainfall data at 10 Australian rainfall stations and the results are compared with those from the SCL. Also, the method is evaluated for different record lengths by applying to Melbourne data with different data lengths. The comparison shows that the resampling method adequately describes the effect of parameter uncertainty in most tested statistics for record lengths of the order of 50 years or more. Although this conclusion is model specific, one would expect similar results for other models employing efficient estimators, sufficiently long records and quantities that avoided extrapolation.