SYNOPSISThis paper is a survey of the main spectra1 methods potentia11y usefu1 in Oceanography. These methods are app1ied to the ana1ysis of t ides, s easona1 variations and ocean geophys ica1 os ci 11a tions. Further topics on the Response Method, the Maximum Entropy method and Rotary Components are brief1y summarized. Examp1es of successfu1 app1i-cations are presented.
-I NTRODUCT I ONThis paper intends to be a survey of the main spectra1 methods potentia1-1y usefu1 in oceanography. Some practica1 prob1ems are discussed but they do not cover, of course, the range of a11 possib1e app1ications.Basica11y, *-This work was partia11y supported by Projeto FlNEP-IOUSP, Sub-Projeto n9 3 -Hidrodinâmica Costeira, and Fundação de Amparo ã Pesquisa do Estado de são Paulo (FAPESP).-Paper presented at the 1977 Annua1 Meeting of the Amer.ican Statistica1 Association, August 15-18, 1977, Chicago, I11inois.
PUBL. N9 425 DO INST. OCEAN. DA USP 154Bolm Inst. oceanogr., S Paulo, 27(2), 1978 there are three types of phenomena that appear in physical oceanography:first, those which present known frequencies and phases and we are interested in their amplitudes; secondly, those which possess known frequencies, and the interest is to determine phase and amplitudes and finally there are those phenomena for which frequencies, phases and amplitudes are unknown.According to other classification the hidrodynamical ocean processes are assumed to be of planetary scale (sections 3 and 5), medium scale and microscale, eventhough there is not a precise separation between these scales.Processes of medium and micro-scale are further discussed in Mesquita & Morettin, 1976.The plan of the paper is as follows: in s'ection 2 we describe some general spectral methods; in section 3 we present the fundamentaIs of tide analysis and results of a simple analysis of a tidal record are given. An application concerning seasonal variation is given in section 4 and in section 5 some preliminary analysis of GATE (GARP ATLANTIC TROPICAL EXPERIMENT) data is discussed.
-GENERAL SPECTRAL METHODSLet X = {X(t,w):teT,WEn} be a real-valued stochastic process, where for each tET, X(t,w) is a random variable defined on the probability space (n ,A, p) • Usually we take T= Z= {O ,±l ,±2, ••• } or T= R, the set of real numbers • For fixed w we have a reatization~ trajectory or sampte function of X. The set of alI these realizations is the enserrible. A problem which arises in practical situations is the determination of the ensemble. Suppose, for example, that we are interested in measuring wave heights in a given area. If an instrument is attached to a buoy and thrown in a point of this area, we / will have observations of a time series, which is part of a realization of the processo If the buoy is thrown in a different point we will observe another realiza~ion of the processo It is therefore necessary to stipulate the area in which we have some assurance that we are observing the same processo MORETTIN & MESQUITA: Spectral methods: oceanography 155We will indicate by 1J ...