Quantifying changes in seasonal temperature variations using a functional data analysis approach
Abstract. Ever-worsening climate change increases near-surface air temperatures for almost the entire Earth and threatens living organisms and human society. While annual mean changes are frequently used to quantify past and expected future changes, the increase is rarely uniform throughout the year. In addition, the shape of the annual cycle and its changes can differ considerably between regions around the globe. Therefore, we perform a global analysis resolving the annual cycle and its changes in different regions, focusing on diagnostics that can be evaluated for various existing annual cycle shapes (e.g., single and double waves, different timing of seasons, etc.). Many previous studies relied on parameter-based methods, assuming a sinusoidal shape of the mean annual cycle. Here, we introduce an innovative approach based on Functional Data Analysis (FDA), a relatively new statistical approach. The evolution of the mean annual cycle is estimated from daily long-term mean temperature values, which are converted to functional form. We concentrate on diagnostics that evaluate the change in absolute temperature, its seasonal slope, the position of the maximum, and the amplitude of the annual cycle. We analyze two reanalysis datasets (coupled CERA20C and atmospheric ERA5) and a subset of five CMIP6 Earth system models (ESMs). Observed changes in the second half of the 20th century are assessed, and the ability of ESMs to represent them is evaluated. Further, the changes projected for the end of the 21st century under the SSP3-7.0 pathway are analyzed. Among other results, we highlight distinct differences between the two reanalyses, especially over equatorial and polar regions across diagnostics. Our approach also reveals that differences in the historical period between 1951–1980 and 1981–2010 can be negative during (short) parts of the year in many regions. Further, the ESMs future projections show different rates of warming between seasons, resulting in changes in the amplitude. The largest amplitude increase is projected over the Mediterranean region, and the largest decrease over the Arctic Ocean, the latter being due to the considerably stronger warming in the northern hemisphere winter. The ESMs also project a delayed maximum near the poles and an earlier maximum in many tropical continental regions. In Europe, the southern and eastern regions experienced a delay of the maximum of up to 10 days, whereas a slightly earlier maximum is found for northern Europe. A similar dipole pattern can be seen between eastern and western regions in North America. Regarding the slope of the annual cycle, higher latitudes detect a higher magnitude of change in the historical period than lower latitudes. The geographical pattern remains the same for future slope changes, with the magnitude twice as high in most regions. The FDA diagnostics introduced here can be tailored for different purposes and applied to other climatic variables, without making any prior assumptions about the annual cycle shape. Potential applications include, e.g., explicitly evaluating the climate model performance or ensemble mean and spread assessment beyond annual or seasonal means.
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 20th century and projections into the end of the 21st 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.