Calibrating Climate Models Using Inverse Methods: Case studies with HadAM3, HadAM3P and HadCM3

Abstract

Abstract. 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. 2) A randomized block-coordinate variant in which, in each iteration, a random sub-set of parameters was perturbed. The cost function to be minimized used multiple large-scale observations and was constrained to produce net radiative fluxes close to those observed. These algorithms were used to calibrate the HadAM3 (3rd Hadley Centre Atmospheric Model) model at N48 resolution and the HadAM3P model at N96 resolution. For the HadAM3 model, cases with seven and fourteen 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 ran 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 pre-industrial estimates. For the 7-parameter cases the Gauss-Newton algorithm converged in about 70 evaluations. For the 14-parameter algorithm with 6 parameters being randomly 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 P2 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 six out of thirteen 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.

On structural errors in emergent constraints

“…where biases in climatology and historical trends are iteratively reduced and addressed through improved process representation and parameter adjustment (Hourdin et al, 2017;Mauritsen et al, 2012;Schmidt et al, 2017), or systematically through the use of perturbed ensembles and formal inference (Tett et al, 2017;Williamson et al, 2013;Zhang et al, 2018). Adequate performance on a subset of metrics is generally accepted as necessary for consideration as a member of the collection of climate models (Eyring et al, 2016) used to assess future change in IPCC assessment 40…”

Reply on CC1

“…where biases in climatology and historical trends are iteratively reduced and addressed through improved process representation and parameter adjustment (Hourdin et al, 2017;Mauritsen et al, 2012;Schmidt et al, 2017), or systematically through the use of perturbed ensembles and formal inference (Tett et al, 2017;Williamson et al, 2013;Zhang et al, 2018). Adequate performance on a subset of metrics is generally accepted as necessary for consideration as a member of the collection of climate models (Eyring et al, 2016) used to assess future change in IPCC assessment 40 reports (Pachauri et al, 2014) -for example, the need for models to conserve energy or to broadly reproduce the https://doi.org/10.5194/esd-2020-85 Preprint.…”

Earth System Model Parameter Adjustment Using a Green's Functions Approach

“…In addition, some of the computational expense of the sequential tuning method is alleviated, since only one set of sensitivity experiments is required, so there is little or no expense relative to an extensive range of observational targets or combinations of parameters. The no-iteration characteristic is also an advantage relative to the Gauss-Newton line search algorithm (Tett et al, 2013(Tett et al, , 2017Roach et al, 2018) which uses similar aproach to minimized a set of parameters simultaneously. The Green's functions methodology does assume that the effect of the perturbed parameter is approximately linear.…”