A Bayesian Hierarchical Time Series Model for Reconstructing Hydroclimate from Multiple Proxies

We propose a Bayesian model which produces probabilistic reconstructions of hydroclimatic variability in Queensland Australia. The approach uses instrumental records of hydroclimate indices such as rain and evaporation, as well as palaeoclimate proxy records derived from natural archives such as sediment cores, speleothems, ice cores and tree rings. The method provides a standardised approach to using multiple palaeoclimate proxy records for hydroclimate reconstruction. Our approach combines time series modelling with an inverse prediction approach to quantify the relationships between the hydroclimate and proxies over the instrumental period and subsequently reconstruct the hydroclimate back through time. Further analysis of the model output allows us to estimate the probability that a hydroclimate index in any reconstruction year was lower (higher) than the minimum (maximum) hydroclimate value observed over the instrumental period. We present model-based reconstructions of the Rainfall Index (RFI) and Standardised Precipitation-Evapotranspiration Index (SPEI) for two case study catchment areas, namely Brisbane and Fitzroy. In Brisbane, we found that the RFI is unlikely (probability between 0 and 20%) to have exhibited extremes beyond the minimum/maximum of what has been observed between 1889 and 2017. However, in Fitzroy there are several years during the reconstruction period where the RFI is likely (> 50% probability) to have exhibited behaviour beyond the minimum/maximum of what has been observed. For SPEI, the probability of observing such extremes since the end of the instrumental period in 1889 doesn't exceed 50% in any reconstruction year in the Brisbane or Fitzroy catchments.