Spatio-temporal quantification of climate model errors in a Bayesian framework

Numerical output from coupled atmosphere-ocean general circulation models is a key tool to investigate climate dynamics and the climatic response to external forcings, and to generate future climate projections. Coupled climate models are, however, affected by substantial systematic errors or biases compared to observations. Assessment of these systematic errors is vital for evaluating climate models and characterizing the uncertainties in projected future climates. In this paper, we develop a spatio-temporal model based on a Bayesian hierarchical framework that quantifies systematic climate model errors accounting for their underlying spatial coherence and temporal dynamics. The key feature of our approach is that, unlike previous studies that focused on empirical and purely spatial assessments, it simultaneously determines the spatial and temporal features of model errors and their associated uncertainties. This is achieved by representing the spatio-temporally referenced data using weighting kernels that capture the spatial variability efficiently while reducing the high dimensionality of the data, and allowing the coefficients linking the weighting kernels to temporally evolve according to a random walk. Further, the proposed method characterizes the bias in the mean state as the time-invariant average portion of the spatio-temporal climate model errors. To illustrate our method, we present an analysis based on the case of near-surface air temperature over the southeastern tropical Atlantic and bordering region from a multi-model ensemble mean of historical simulations from the fifth phase of the Coupled Model Intercomparison Project. The results demonstrate the improved characterization of climate model errors and identification of non-stationary temporal and spatial patterns.