We use the discrete “wavelet transform microscope” to study the monofractal nature of surface air temperature signals of weather stations spread across Europe. This method reveals that the information obtained in this way is richer than previous works studying long range correlations in meteorological stations: the approach presented here allows to bind the Hölder exponents with the standard deviation of surface pressure anomalies, while such a link does not appear with methods previously carried out.

Fractals have been extensively used in geosciences

Let us first recall the WLM. The discrete wavelet transform (WT)
allows to decompose a signal using a single oscillating window

In order to confirm that the analyzed signals are monofractal, we used
the “surrogate data method”

Since the Fourier spectrum is preserved with the surrogate procedure, the spectrum of singularities of a monofractal signal is not affected either

We applied the WLM on daily mean surface air temperature data
collected from the European Climate Assessment and Dataset
(

For the purpose of reducing the noise, the data

As shown in Fig.

Such an observation holds for all the stations, which indicates that
air temperature signals are monofractal. However, the value of the
Hölder exponent varies from one station to another as illustrated
in Fig.

Studies about LRC in air temperature data have been carried out using
the DFA (detrended fluctuation analysis, see e.g.

A natural question arising is whether or not the observed Hölder
exponents can be bond to some climate index. A natural choice is to
try to link the surface pressure anomalies with the Hölder
exponents in the following sense: can we recover the correlation
structure observed in the pressure anomalies field from the spatial
repartition of the Hölder exponents? Moreover, can such
a structure be recovered with the DFA? To answer these questions, the
map of Europe is gridded into roughly

In order to show that the DFA method carried out in

As a conclusion, one can say that the Hölder exponents obtained here with the WLM reflect in some way the climate variability of the stations associated to the data: standard deviations of pressure anomalies and Hölder exponents are anti-correlated. Such a result does not appear with methods that first require the seasonal variations to be removed. Future work consists in investigating the possible relation between the Hölder exponents of the stations and their climate type, which could bring new information about the regularity of temperatures.

We acknowledge the data providers in the ECA&D project.
Klein Tank, A. M. G. and Coauthors, 2002. Daily dataset of 20th-century surface
air temperature and precipitation series for the European Climate Assessment, Int. J. of Climatol., 22, 1441–1453.
Data and metadata available at