Quantifying changes in seasonal temperature variations using a functional data analysis approach

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 actually rarely uniform throughout the year. 

The shape of the annual cycle and its changes differ significantly between regions around the globe. Therefore, performing a global analysis implies the necessity to focus on diagnostics that can be evaluated for all these different shapes (e.g., single and double waves, different timing of seasons, etc.). Many previous studies relied on Fourier-transform-based methods, which assume a sinusoidal shape of the mean annual cycle. Here, we introduce an innovative approach based on functional data analysis. The evolution of the mean annual cycle is estimated from daily long-term mean temperature values, which are converted to functional form. This way, we can assess arbitrary shapes of the annual cycle. We concentrate on diagnostics that evaluate the change in absolute temperature, its seasonal slope, and the position of the maximum. We analyze two reanalysis datasets (coupled CERA20C and atmospheric ERA5) and a subset of CMIP6 Earth system models (ESMs). Recent changes in the second half of the 20th century are assessed, and the ability of ESMs to represent them is evaluated. Then, 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. Further, the projections show, for example, 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.