Does stochastic modelling using instrumental data capture pre-instrumental variability? A validation study using ice core data

Abstract:

Stochastic models are used by water managers/hydrologists to generate long synthetic hydroclimate time series with statistics consistent with the instrumental record. These synthetic series contain droughts more severe than found in the instrumental record. However, instrumental records are short (~100 years long) and contain limited information about low-frequency (i.e. multidecadal) climate variability. This makes stochastic model validation with respect to low-frequency climate variability difficult. Ice core records are often >500 years in length and, being representative of local/regional precipitation, provide an opportunity to validate different stochastic models using observed data of sufficient length to characterise low-frequency climate variability. In this study, we investigated the performance of commonly used stochastic models (Gaussian white noise, AR(1), shifting mean AR(1), Long Memory ARFIMA, two-state Hidden Markov, k-Nearest Neighbor Bootstrap, and Wavelet-Autoregressive models) in capturing different statistics related to low-frequency climate variability determined using the Law Dome summer sea salt accumulation annual record. This record is teleconnected to east Australian rainfall via a broad-scale meridional atmospheric circulation, meaning that results from our analysis have implications for regional stochastic modelling and water management. We found that a) ice core data from 1900 onwards (i.e. the instrumental period) is not inconsistent with white noise; b) stochastic models calibrated to the instrumental record do not capture pre‑instrumental (i.e. 1000-1899) statistics; and c) when calibrated to the entire ice core record, stochastic models designed to replicate low-frequency climate variability (Long Memory ARFIMA, shifting mean AR(1), and Wavelet-Autoregressive) were able to capture pre‑instrumental statistics. Critically, the AR(1) stochastic model – widely used in operational hydrology - was unable to capture low-frequency climate variability when calibrated to the entire ice core record. This research highlights potentially significant limitations associated with using stochastic models calibrated to the instrumental record to characterise baseline climate variability and risk.