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Abstract 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. 

Abstract The effect of the El Niño–Southern Oscillation (ENSO) teleconnection and climate change trends on observed North American wintertime daily 2-m temperature is investigated for 1960–2022 with a quantile regression model, which represents the variability of the full distribution of daily temperature, including extremes and changes in spread. Climate change trends are included as a predictor in the regression model to avoid the potentially confounding effect on ENSO teleconnections. Based on prior evidence of asymmetric impacts from El Niño and La Niña, the ENSO response is taken to be piecewise linear, and the regression model contains separate predictors for warm and cool ENSO. The relationship between these predictors and shifts in median, interquartile range, skewness, and kurtosis of daily 2-m temperature are summarized through Legendre polynomials. Warm ENSO conditions result in significant warming shifts in the median and contraction of the interquartile range in central-northern North America, while no opposite effect is found for cool ENSO conditions in this region. In the southern United States, cool ENSO conditions produce a warming shift in the median, while warm ENSO conditions have little impact on the median, but contracts the interquartile range. Climate change trends are present as a near-uniform warming in the median and across quantiles and have no discernable impact on interquartile range or higher-order moments. Trends and ENSO together explain a substantial fraction of the interannual variability of daily temperature distribution shifts across much of North America and, to a lesser extent, changes of the interquartile range.