A temperature analysis of the sea’s surface of the Brazil coast.
Jos´ Antonio dos Santos Junior and Reinaldo Roberto Rosa∗ e
LAC - INPE, Caixa Postal 5515, 12201-970, S˜o Jos´ dos Campos, Brazil. a e (Dated: October 2, 2005) In this paper we present one brief revision of some important concepts in the analysis of data: Kullback-Leibler distance and entropy. Applying them to datareferring to the temperatures of the surface of sea (TSS) in coast of Brazil, in the oceanic and coastal zone between Cabo Frio-RJ and Cabo Santa Marta-SC.
PACS numbers: Valid PACS appear here Keywords: Kullback-Liebler distance, entropy, temperature, data analysis.
Data for analysis
The Kullback-Leibler distance and the measure of the entropy of a system hasbeen eﬃcient in the analysis of data. In this article we make a revision of these concepts associating them it an amplitude grating. From Kullback-Leibler distance we can esteem the divergence of a fdp in relation to the Gaussian model, that presents an excellent distribution of probabilities. When is necessary to investigate the behavior of a system regarding its organization, a good tool is themeasure of the entropy, that it shows how much a system is “ordened” or “disordered”. The objective of this work is apply the cited methods above to analyse the data referring the temperature of the surface of the sea (TSS), that had been acquired by orbital sensor AVHRR (Advanced Very High Resolution Radiometer) installed on board the North American satellites of series NOAA. The temperatures hadbeen measured in areas located in the Southeastern coast of Brazil, in the oceanic and coastal zone between Cabo Frio - RJ and Cabo Santa Marta - SC. We choose diﬀerent localization in function of the oceanographical characteristics of the interest regions. About the organization of this article, initially is presented some preliminary concepts and information. To follow we approach the methodologyused, detailing the phases of the work. In section IV the results and the interpretation of these are presented. In section V we ﬁnish this article with remarks about this work.
The data analyzed in this paper are referring the temperature of the surface of the sea (TSS), that they had been acquired by orbital sensor AVHRR (Advanced Very High Resolution Radiometer) installed on board the NorthAmerican satellites of series NOAA. The gotten data are the monthly averages, for the period of 1998 to the 2002, with space resolution of 9km x 9km (great of pixel). Had been cut areas of 22x22 pixels and these areas are located in the Southeastern coast of Brazil, in the oceanic and coastal zone between Cabo Frio - RJ and Cabo Santa Marta - SC. We choose diﬀerent localization in function of theoceanographical characteristics of the interest regions. These data are distributed by the NASA/JPL, and can be gotten from the address http://podaac.jpl.nasa.gov/sst/. For reasons that go beyond the target of this work, opt to analyzing the ﬁve year data, however can be gotten given of ten years through the cited URL above. The ﬁrst step for the analysis, was to make a ﬁltering and interpolationof the data, therefore in the rude data had many null values and noises. To illustrate the gotten data and results always will show three data frames, the ﬁrst one, an intermediary and the last one, of the sixty frames that we possess (monthly averages of 1998 the 2002).
Entropy and Kullback-Leibler distance
In the analysis of the data had been used the entropy and Kullback-Leiblerdistance, therefore, we will describe here at great length these two important concepts in the treatment of information.
PRELIMINARY CONCEPTS AND INFORMATION.
In this section the used data in this work and the techniques used in the analysis will be described.
In Boltzmann’s deﬁnition, entropy is a measure of the...