Calibrating climate models using inverse methods: case studies with HadAM3, HadAM3P and HadCM3

Optimisation methods were successfully used to calibrate parameters in an atmospheric component of a climate model using two variants of the Gauss-Newton line-search algorithm: (1) a standard Gauss-Newton algorithm in which, in each iteration, all parameters were perturbed and (2) a randomised block-coordinate variant in which, in each iteration, a random sub-set of parameters was perturbed. The cost function to be minimised used multiple large-scale multi-annual average observations and was constrained to produce net radiative fluxes close to those observed. These algorithms were used to calibrate the HadAM3 (third Hadley Centre Atmospheric Model) model at N48 resolution and the HadAM3P model at N96 resolution. For the HadAM3 model, cases with 7 and 14 parameters were tried. All ten 7-parameter cases using HadAM3 converged to cost function values similar to that of the standard configuration. For the 14-parameter cases several failed to converge, with the random variant in which 6 parameters were perturbed being most successful. Multiple sets of parameter values were found that produced multiple models very similar to the standard configuration. HadAM3 cases that converged were coupled to an ocean model and run for 20 years starting from a pre-industrial HadCM3 (3rd Hadley Centre Coupled model) state resulting in several models whose global-average temperatures were consistent with preindustrial estimates. For the 7-parameter cases the Gauss-Newton algorithm converged in about 70 evaluations. For the 14-parameter algorithm, with 6 parameters being ran-domly perturbed, about 80 evaluations were needed for convergence. However, when 8 parameters were randomly perturbed, algorithm performance was poor. Our results suggest the computational cost for the Gauss-Newton algorithm scales between P and P-2, where P is the number of parameters being calibrated. For the HadAM3P model three algorithms were tested. Algorithms in which seven parameters were perturbed and three out of seven parameters randomly perturbed produced final configurations comparable to the standard hand-tuned configuration. An algorithm in which 6 out of 13 parameters were randomly perturbed failed to converge. These results suggest that automatic parameter calibration using atmospheric models is feasible and that the resulting coupled models are stable. Thus, automatic calibration could replace human-driven trial and error. However, convergence and costs are likely sensitive to details of the algorithm.