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.