Estimating extremes from global ocean and climate models: a Bayesian hierarchical model approach

Estimating oceanic and atmospheric extremes from global climate models is not trivial as these models often poorly represent extreme events. However, these models do tend to capture the central climate statistics well (e.g., the mean temperature, variances, etc.). Here, we develop a Bayesian hierarchical model (BHM) to improve estimates of extremes from ocean and climate models. This is performed by first modeling observed extremes using an extreme value distribution (EVD). Then, the parameters of the EVD are modeled as a function of climate variables simulated by the ocean or atmosphere model over the same time period as the observations. By assuming stationarity of the model parameters, we can estimate extreme values in a projected future climate given the climate statistics of the projected climate (e.g., a climate model projection under a specified carbon emissions scenario). The model is demonstrated for extreme sea surface temperatures off southeastern Australia using satellite-derived observations and downscaled global climate model output for the 1990s and the 2060s under an A1B emissions scenario. Using this case study we present a suite of statistics that can be used to summarize the probabilistic results of the BHM including posterior means, 95% credible intervals, and probabilities of exceedance. We also present a method for determining the statistical significance of the modeled changes in extreme value statistics. Finally, we demonstrate the utility of the BHM to test the response of extreme values to prescribed changes in climate.