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 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 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 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.

Automated model optimisation using the Cylc workflow engine (Cyclops v1.0)

“…In the particular wave modelling case we have investigated, our approach would not be sufficient on its own to identify suitable values of the large set of WW3 parameters without guidance from previous studies. Tett et al (2017) point out that the inherently chaotic nature of the climate system means that a certain level of noise is introduced into evaluations of an atmospheric model simulation, which can cause problems in evaluating the termination criteria. They describe a procedure to rerun a simulation that had nominally satisfied the prescribed convergence criteria, with randomised perturbations before determining whether or not to terminate.…”

“…More recently, Tett et al (2013) applied a Gauss-Newton line search optimisation algorithm to climate simulations with the Hadley Centre Atmosphere Model version 3 (HadAM3) forced with observed sea surface temperature and sea ice, optimising an objective function derived from reflected shortwave radiation and outgoing longwave radiation comparisons. The Tett et al (2013) method was subsequently applied to optimise the sea ice component of the global coupled HadCM3 climate model (Roach et al, 2017;Tett et al, 2017).…”

Reducing climate model biases by exploring parameter space with large ensembles of climate model simulations and statistical emulation

“…Older-generation Hadley Centre coupled models (HadCM2 and HadCM3), and atmosphere-only global (HadAM) and regional (HadRM), models have been used in numerous attribution studies (e.g., Tett et al, 1996;Stott et al, 2004;Otto et al, 2012;Rupp et al, 2017a;van Oldenborgh et al, , 2017Schaller et al, 2016;Uhe et al, 2018), and the same models have been used for future projections (e.g., Rupp and Li, 2017;Rupp et al, 2017b;Guillod et al, 2018). These model families exhibit warm and dry biases during JJA over continental midlatitudes, biases that have persisted over model generations and enhancements (e.g., Massey et al, 2015;Li et al, 2015;Guillod et al, 2017).…”

“…The second category uses a PPE to train a statistical emulator or establish some cost function, which is then used to automatically search for optimal parameter values that produce simulations closest to observations (e.g., Bellprat et al, 2012aBellprat et al, , 2016Zhang et al, 2015;Tett et al, 2017). Different approaches have been used in optimization, including ensemble Kalman filters (Annan et al, 2005;Annan and Hargreaves, 2007, and the references therein), stochastic Bayesian approaches (e.g., Jackson et al, 2004), Markov chain Monte Carlo integrations (Jackson et al, 2008;Järvinen et al, 2010), and optimization over multiple objectives (Neelin et al, 2010).…”

Adjoint‐Based Climate Model Tuning: Application to the Planet Simulator

“…Using a minimization algorithm and the gradients, Tett et al () and Zhang et al () iteratively tuned several parameters to calibrate climate models. In these methods, computational cost increases linearly with the number of parameters and convergence is likely sensitive to the minimization algorithms (Tett et al, ).…”