Computational methods for parameter estimation in climate models

Intensive computational methods have been used by Earth scientists in a wide range of problems in data inversion and uncertainty quantication such as earthquake epicenter location and climate projections. To quantify the uncer- tainties resulting from a range of plausible model congurations it is necessary to estimate a multidimensional probability distribution. The computational cost of estimating these distributions for geoscience applications is impractical using traditional methods such as Metropolis/Gibbs algorithms as simulation costs limit the number of experiments that can be obtained reasonably. Several alternate sampling strategies have been proposed that could improve on the sampling e- ciency including Multiple Very Fast Simulated Annealing (MVFSA) and Adaptive Metropolis algorithms. The performance of these proposed sampling strategies are evaluated with a surrogate climate model that is able to approximate the noise and response behavior of a realistic atmospheric general circulation model (AGCM). The surrogate model is fast enough that its evaluation can be embed- ded in these Monte Carlo algorithms. We show that adaptive methods can be superior to MVFSA to approximate the known posterior distribution with fewer forward evaluations. However the adaptive methods can also be limited by inad- equate sample mixing. The Single Component and Delayed Rejection Adaptive Metropolis algorithms were found to resolve these limitations, although challenges remain to approximating multi-modal distributions. The results show that these advanced methods of statistical inference can provide practical solutions to the cli- mate model calibration problem and challenges in quantifying climate projection uncertainties. The computational methods would also be useful to problems out- side climate prediction, particularly those where sampling is limited by availability of computational resources.