The tendency of climate models to overstate warming in the tropical troposphere has long been noted. Here we examine individual runs from 38 newly released Coupled Model Intercomparison Project Version 6 (CMIP6) models and show that the warm bias is now observable globally as well. We compare CMIP6 runs against observational series drawn from satellites, weather balloons, and reanalysis products. We focus on the 1979–2014 interval, the maximum span for which all observational products are available and for which models were run using historically observed forcings. For lower‐troposphere and midtroposphere layers both globally and in the tropics, all 38 models overpredict warming in every target observational analog, in most cases significantly so, and the average differences between models and observations are statistically significant. We present evidence that consistency with observed warming would require lower model Equilibrium Climate Sensitivity (ECS) values.

Comparisons of trends across climatic data sets are complicated by the presence of serial correlation and possible step‐changes in the mean. We build on heteroskedasticity and autocorrelation robust methods, specifically the Vogelsang–Franses (VF) nonparametric testing approach, to allow for a step‐change in the mean (level shift) at a known or unknown date. The VF method provides a powerful multivariate trend estimator robust to unknown serial correlation up to but not including unit roots. We show that the critical values change when the level shift occurs at a known or unknown date. We derive an asymptotic approximation that can be used to simulate critical values, and we outline a simple bootstrap procedure that generates valid critical values and p‐values. Our application builds on the literature comparing simulated and observed trends in the tropical lower troposphere and mid‐troposphere since 1958. The method identifies a shift in observations around 1977, coinciding with the Pacific Climate Shift. Allowing for a level shift causes apparently significant observed trends to become statistically insignificant. Model overestimation of warming is significant whether or not we account for a level shift, although null rejections are much stronger when the level shift is included. © 2014 The Authors. Environmetrics published by John Wiley & Sons, Ltd.

Overall climate sensitivity to CO₂ doubling in a general circulation model results from a complex system of parameterizations in combination with the underlying model structure. We refer to this as the model's major hypothesis, and we assume it to be testable. We explain four criteria that a valid test should meet: measurability, specificity, independence, and uniqueness. We argue that temperature change in the tropical 200‐ to 300‐hPa layer meets these criteria. Comparing modeled to observed trends over the past 60 years using a persistence‐robust variance estimator shows that all models warm more rapidly than observations and in the majority of individual cases the discrepancy is statistically significant. We argue that this provides informative evidence against the major hypothesis in most current climate models.

Allen and Tett (1999, herein AT99) introduced a Generalized Least Squares (GLS) regression methodology for decomposing patterns of climate change for attribution purposes and proposed the “Residual Consistency Test” (RCT) to check the GLS specification. Their methodology has been widely used and highly influential ever since, in part because subsequent authors have relied upon their claim that their GLS model satisfies the conditions of the Gauss-Markov (GM) Theorem, thereby yielding unbiased and efficient estimators. But AT99 stated the GM Theorem incorrectly, omitting a critical condition altogether, their GLS method cannot satisfy the GM conditions, and their variance estimator is inconsistent by construction. Additionally, they did not formally state the null hypothesis of the RCT nor identify which of the GM conditions it tests, nor did they prove its distribution and critical values, rendering it uninformative as a specification test. The continuing influence of AT99 two decades later means these issues should be corrected. I identify 6 conditions needing to be shown for the AT99 method to be valid.