This paper proposes algorithms for estimating parameters in Earth System Models (ESMs), specifically focusing on simulations that have not yet achieved statistical equilibrium and display climate drift. The basic idea is to treat ESM time series as outputs of an autoregressive process, with parameters that depend on those of the ESM. The maximum likelihood estimate of the parameters and the associated uncertainties are derived. This method requires solving a nonlinear system of equations and often results in unsatisfactory parameter estimates, especially in short simulations. This paper explores a strategy for overcoming this limitation by dividing the estimation process into two linear phases. This algorithm is applied to estimate parameters in the convection scheme of the Community Earth System Model version 2 (CESM2). The modified algorithm can produce accurate estimates from perturbation runs as short as 2 years, including those exhibiting climate drift. Despite accounting for climate drift, the accuracy of these estimates is comparable to that of algorithms that do not. While these initial results are not optimal, the autoregressive approach presented here remains a promising strategy for model tuning since it explicitly accounts for climate drift in a rigorous statistical framework. The current performance issues are believed to be technical in nature and potentially solvable through further investigation.
