Statistical analysis of air and sea temperature anomalies Page: 1
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Statistical analysis of air and sea temperature anomalies
Nicola Scafetta-"~*. Tim Imholt2. Paolo Grigolini2 3 and Jim Roberts2.
1Pratt School EE Dept., Duke University. P.O. Bor 90291, Durharrm, North Carolina 27708
2 Center for Nonlinear Science, University of North Texas. P.O. Box 311427, Denton, Texas 76203-1427
:'Dipartimento di Fisica dell'Universita di Pisa and INFM. Piazza Torricelli 2. 56127 Pisa, Italy
4Istituto di Biofisica CNR. Area della Ricerca di Pisa. Via A/fierci 1, San Cataldo 56010 Ghezzano-Pisa. Italy
(March 11. 2013)
This paper presents a global air and sea temperature anomalies analysis based upon a combination
of the wavelet miultiresohltion analysis and the scaling analysis methods of a tine 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 tempnoral 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.
The statistical analysis of time series is a challenging
problem of statistical mechanics. This is due to the fact
that there are still many unsettled problems. The most
irmportaint seems to be that the techniques of analysis
that are curre nrtly used are based on the asslumniption that
the time series under study are generated by stationary
processes. In general this is not the case. The time series
mirroring complex processes are usually non-stationary
in nature. Tihe non-stationary condition seerls to be a
very general property, although it has any minlber of pos-
sible sources ini any system. For instance the origin of
non-stationarity in the case of solar flares is given by the
solar cycles (for a recent review about this interesting is-
sue. see R ef. ) and a special caution must be adopted
to take the effects of this non-stationarity into account
. In fact, it has been recently shown  that the mrien-
ory left after detrending annual periodicity is much less
intense than imagined in earlier publications . Another
issue. which seems to be still unsettled, is as to the sta-
tistical nature of the fluctuations, once their genuinely
stationary nature has been assessed. Are these flulCtua-
tions Gaussian? Are these fluctuation of Levy in nature?
In this paper we want to illustrate an efficient approach
to the solution of these difficulties. To stress the efficiency
of this approach we apply it to the analysis of global air
and sea temperature ' allnomalie's, a problemnn where, as we
shall see. properly detrending non-stationary components
is an essential request to shed light into the nature of the
process under study. The approach we intend to use rests
on their joint uise of the Diffusion Entropy Analysis (DEA)
and wavelet analysis of time series. DEA was born as
an efficient way to detect scaling [3,5.6]. with applica-
tions to sociological  and astrophysical  processes.
This technique of analysis has been applied with suc-
cess also to the study of DNA sequences [7,8] and heart
beat rhythms in cardiac patients . Furthermore, some
attention has been devoted to establish the connection
between DEA and the Kolmogorov complexity  and
it is beconirg clear that this technique can also be lsed
to stltudy the transition from dynamics to tlhermlodnam-rn
ics, a, crucial property that is used with success to study
small portions of large sequences , thereby establishing
a possible way to address the problem of non-stationality.
Research work is currently being done to make it possible
to utilize this technique to address the cases of multiple
Wavelet techniques are a powerful method of analysis
 that localizes a signal simultaneously in time and fre-
qimency. We use wavelets for the purpose to deconlmp)ose
the signal in smooth, detail and residual components.
Tihe wavelet tdecolnpositionL has beenl shown to be an ef-
ficient way of detrending from the data a non-stationary
component in a natural way. so as to bypass the main dif-
ficulties concerning the non-stationary nature of the data
under study . The adoption of DEA makes the scal-
ing emerge and also sheds light into the statistical nature
of the fluctuations around the non-stationary bias.
Let us now illustrate the time series under study in this
paper. The time series of annually averaged global sur-
face temperature anomalies have attracted the attention
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Scafetta, Nicola; Imholt, Timothy; Grigolini, Paolo & Roberts, James A. Statistical analysis of air and sea temperature anomalies, paper, March 11, 2013; (digital.library.unt.edu/ark:/67531/metadc174686/m1/1/: accessed April 28, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.