Total Least Squares (TLS) or orthogonal regression is used to remedy attenuation bias in optimal fingerprinting regressions. Consistency properties in multivariate applications require strong assumptions about unobservable variance ratios. Monte Carlo analysis is used herein to examine coefficient biases when the explanatory variables are correlated and have heterogeneous error variances. Ordinary Least Squares (OLS) exhibits the expected attenuation bias patterns which vanish as the noise variances on the explanatory variable disappear. TLS is generally more biased than OLS except under homogeneous noise variances. When the explanatory variables are negatively correlated TLS imparts a large upward bias which gets worse as the noise variance on the explanatory variable gets smaller. In general without specific diagnostic information TLS should not be considered an improvement on OLS and can yield extremely biased coefficients.

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- and mid-troposphere layers both globally and in the tropics, all 38 models overpredict warming in every target observational analogue, 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.