Frank, see the Pielke Sr references in my original post, the variation with altitude depends on background state of the atmosphere (primarily as it varies with latitude / season as per the calculations Pielke Sr. provides) (judithcurry.com)
The results of the study imply that Earth's climate sensitivity is strongly dependent on the climate background state with significantly larger values attained during warm phases. (usclivar.org)
New research looking at glacial - interglacial climate variability during the last 784,000 years finds that Earth's climate sensitivity is strongly dependent on the climate background state with significantly larger values attained during warm phases. (usclivar.org)