Parameter estimation and model identification for stochastic models of annual hydrological data: Is the observed record long enough?

Abstract

Summary Observed hydrological records are typically not more than 100–150 years in length. This study quantifies the effect this relatively short length of data has on parameter uncertainty and model identification for two stochastic models of annual hydrological data: the common lag-one autoregressive model [AR(1)] and the two-state hidden Markov model (HMM). Both models were calibrated to synthetic data generated by different HMM and AR(1) scenarios. For the HMM the separation of the wet and dry states had a greater impact on the uncertainty than the state residence time. For the AR(1) model the uncertainty was lower than the HMM and largely independent of the persistence structure. For data lengths typical of observed data the parameter uncertainty was substantial for both models. Based on the metrics used for model identification if there was strong persistence then 100–200 years of data was required to identify both models. For weaker persistence structures typical of Australian data the length required increased to 200–500 years, well beyond observed record lengths. The analysis of six rainfall sites from across Australia showed none provided strong evidence in favour of the AR(1), HMM or an independent model. It is concluded that the limited information from observed hydrological data produces high parameter uncertainty for the AR(1) and HMM. The result is the unequivocal identification of a stochastic model to describe the underlying long-term persistence structure remains elusive. It is argued that if more complex stochastic models are proposed to represent long-term persistence they will require additional information beyond the observed hydrological data to enable their identifiability.