Spatio-temporal evolution of global surface temperature distributions.

Climate is known for being characterised by strong non-linearity and chaotic behaviour. Nevertheless, few studies in climate science adopt statistical methods specifically designed for non-stationary or non-linear systems. Here we show how the use of statistical methods from Information Theory can describe the non-stationary behaviour of climate fields, unveiling spatial and temporal patterns that may otherwise be difficult to recognize. We study the maximum temperature at two meters above ground using the NCEP CDAS1 daily reanalysis data, with a spatial resolution of 2.5 by 2.5 degree and covering the time period from 1 January 1948 to 30 November 2018. The spatial and temporal evolution of the temperature time series are retrieved using the Fisher Information Measure, which quantifies the information in a signal, and the Shannon Entropy Power, which is a measure of its uncertainty -- or unpredictability. The results describe the temporal behaviour of the analysed variable. Our findings suggest that tropical and temperate zones are now characterized by higher levels of entropy. Finally, Fisher-Shannon Complexity is introduced and applied to study the evolution of the daily maximum surface temperature distributions.