  This paper presents a global air and sea temperature anomalies analysis based
upon a combination of the wavelet multiresolution analysis and the scaling
analysis methods of a time series. The wavelet multiresolution analysis
decomposes the two temperature signals on a scale-by-scale basis. The
scale-by-scale smooth and detail curves are compared and the correlation
coefficients between each couple of correspondent sets of data evaluated. The
scaling analysis is based upon the study of the spreading and the entropy of
the diffusion generated by the temperature signals. Therefore, we jointly adopt
two distinct methods: the Diffusion Entropy Analysis (DEA) and the Standard
Deviation Analysis (SDA). The joint use of these two methods allows us to
establish with more confidence the nature of the signals, as well as their
scaling, and it yields the discovery of a slight Levy component in the two
temperature data sets. Finally, the DEA and SDA are used to study the wavelet
residuals of the two temperature anomalies. The temporal regions of persistence
and antipersistence of the signals are determined and the non-stationary effect
of the 10-11 year solar cycle upon the temperature is studied. The temperature
monthly data cover the period from 1860 to 2000 A.D.E.

Statistical Mechanics;Atmospheric and Oceanic Physics