  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.
