This study uses a new methodology based on Functional Data Analysis (FDA) to analyze changes in the annual cycle of temperature for different regions of the globe. Changes are examined for the second half of the 20^th century and projections into the end of the 21^st century. Two reanalysis products (CERA20C and ERA5) and five CMIP6 earths system models are analyzed. Specific diagnostics of the annual cycle documented are the changes in absolute temperature, shifts in the maximum temperature, absolute velocity, and changes in the amplitude of the seasonal cycle.

The study is interesting and presents valuable diagnostics for understanding past and future changes in the annual cycle.  I feel this paper is a valuable contribution to the literature.  A few comments are listed below.

Line 193-194: Can you expand here on why there may be disagreement between the reanalyses in these situations, and if one may be more believable?

Line 277-278: In Figure 9, it appears to me that the EEU and NWN have experienced an increase in amplitude.  Please clarify. 

Discussion: I think it should also be considered how the number of assimilated observations in the reanalysis products changes between the 2 observed periods (1951-1980 and 1981-2010), and what effect this may have on the results.

See attached file with comments