An Efficient Stochastic Bayesian Approach to Optimal Parameter and Uncertainty Estimation for Climate Model Predictions

Abstract

One source of uncertainty for climate model predictions arises from the fact that climate models have been optimized to reproduce observational means. To quantify the uncertainty resulting from a realistic range of model configurations, it is necessary to estimate a multidimensional probability distribution that quantifies how likely different model parameter combinations are, given knowledge of the uncertainties in the observations. The computational cost of mapping a multidimensional probability distribution for a climate model using traditional means (e.g., Monte Carlo or Metropolis/Gibbs sampling) is impractical, requiring 104–106 model evaluations for problems involving less than 10 parameters. This paper examines whether such a calculation is more feasible using a particularly efficient but approximate algorithm called Bayesian stochastic inversion, based on multiple very fast simulated annealing (VFSA). Investigated here is how the number of model parameters, natural variability, and the degree of nonlinearity affect the computational cost and accuracy of estimating parameter uncertainties within a surrogate climate model that is able to approximate the noise and response behavior of a realistic atmospheric GCM. In general, multiple VFSA is one to two orders of magnitude more efficient than the Metropolis/Gibbs sampler, depending primarily on dimensionality of the parameter space analysis. The average cost of estimating parameter uncertainties is only moderately affected by noise within the model as long as the signal-to-noise ratio is greater than 5. Also the average cost of estimating parameter uncertainties nearly doubles for problems in which parameters are nonlinearly related.