A wavelet-based analysis of surface air temperature variability

We study the Hölder regularity of surface air temperature signals using the wavelet leaders method (WLM). This method has been successfully applied in several domains such as DNA analysis, fully developped turbulence analysis, internet data traffic analysis,... to name just a few, and we now use it in climatology. We first define the notions of Hölder exponent, monofractal functions and spectrum of singularities before explaining the WLM. Then we use it to study surface air temperature signals from weather stations spread across Western and Eastern Europe and show that they are monofractal, i.e. their irregularity (in the sense of variability) is regular. After, we show that the stations can be classified according to their Hölder exponent and that this classification matches with the worldwide used Köppen-Geiger climate classification. A blind test is performed in order to confirm the results, which can be partly explained by the influence of the North Atlantic Oscillation. Our results can be helpful to test the accuracy of current climatic models.