The Fast Fourier Transform and its application to tidal oscillations

Franco, A. dos Santos; Rock, N. J

doi:10.1590/s0373-55241971000100007

Cited by 7 publications

(5 citation statements)

References 3 publications

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“…Thompson's (1983) low-pass filter allows its optimization by the user, who defines the main parameters of calculation, especially by imposing preselected cut-off frequencies. The harmonic components were extracted from Mesquita (1997), who analyzed the records of sea level in the coastal regions of southeastern Brazil through the application of the harmonic method developed by Franco and Rock (1971). The selected components were Q1, O1, P1, K1, N2, M2, S2 and M3, which correspond to approximately 90% of the tidal energy on the Cananeia coast (PICARELLI et al, 2002).…”

Section: Numerical Filteringmentioning

confidence: 99%

Remote wind stress influence on mean sea level in a subtropical coastal region

Costa

Bernardes

2012

Braz. j. oceanogr.

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A B S T R A C TThe purpose of this study was to assess the relative influence of remote wind stress on mean sea level (MSL) variations in the coastal region of Cananeia (Sao Paulo State, Southern Brazil) during the period from 1/1/1955 to 12/31/1993. An optimized low-pass Thompson filter for the study area, and spectral analysis (cross spectrum, coherence and phase lag) of the relationship between the MSL and both parallel (T//) and perpendicular (T|) wind stress components were applied. These were extracted from four grid points of the NCEP/NCAR global model. The predominance of annual oscillations as those of greatest coherence and energy, of periods of approximately 341 days (frequency of 0.00293 cpd) and 410 days (frequency of 0.00244 cpd), respectively, were observed. Offshore NCEP/NCAR grid points were those with the highest coherence and energy throughout the study in relation to the observed MSL. This may be linked to the restriction of the NCEP/NCAR model as regards the inland limit. It is also concluded that remote wind stress may play an important role in several MSL time scales, including the annual ones. Based on criteria such as coherence and energy peaks, the wind stress component of greatest effect on MSL was the parallel one. R E S U M OO presente estudo tem por objetivo avaliar a influência relativa de tensão do vento remoto na variação do nível médio do mar (NMM) para a região costeira de Cananéia (SP) durante o período de 1/1/1955 a 31/12/1993. Foram aplicados um filtro de passa-baixa de Thompson (1983), otimizado para a região de Cananéia, além de análise espectral (espectro cruzado, coerência e defasagem) entre o NMM e as componentes paralela (T//) e perpendicular (T|) da tensão do vento. Estas foram extraídas de quatro pontos de grade do modelo global NCEP/NCAR. Observou-se a predominância das oscilações anuais como aquelas de maior coerência e energia, destacando-se os períodos de aproximadamente 341 dias (frequência de 0,00293 cpd) e 410 dias (frequência de 0,00244 cpd), respectivamente. As maiores coerências e energia em todo estudo foram encontradas nos pontos mais distantes da costa. Este fato pode estar associado às restrições do modelo NCEP/NCAR em representar os limites continentais. Conclui-se também que a tensão do vento remoto pode ter um papel importante em várias escalas temporais do NMM, incluindo a escala anual. A partir dos valores de coerência e picos energéticos, a componente paralela da tensão do vento foi a que mostrou ser mais influente no NMM da região estudada.

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Section: Numerical Filteringmentioning

confidence: 99%

Remote wind stress influence on mean sea level in a subtropical coastal region

Costa

Bernardes

2012

Braz. j. oceanogr.

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“…In the notation of section 2.1, (3.13) that is, the spectrum of Z(t) has the form of For the theoretical spectrum we followed Godin, 1972 the spectrum of Z(t) given by (3.9), obtained from a record 1enght of one year, using a smoothed procedure and a FFT algorithm (Franco & Rock, 1971), with 8,192 digitized points.…”

Section: Theoretical and Real Tidesmentioning

confidence: 99%

“…Two constituents are considered res01ved if (3.14) where N is the number of digitized values of the record and Ôt is the sampling intervalo Some of the longest records (approximately200 years) are reported in Cartwright, 1971, but even these are insufficient to analyse for p' . Tidal analysis of short records (7 days) for some constituents is given in Franco, 1964.…”

Section: Theoretical and Real Tidesmentioning

confidence: 99%

Spectral methods in oceanography with applications

Morettin

Mesquita

1978

Bol. Inst. Oceanogr.

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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 ...

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“…Sampling intervals of the tidal records were so to give a 0.5 cy /hour Nyquist frequency ,but for Figure 2 only 75 Fouri er components were taken. In Figure 3 we have the spectrum of Z(t) given by (3.9), obtained from a record 1enght of one year, using a smoothed procedure and a FFT algorithm (Franco & Rock, 1971), with 8,192 digitized points.…”

Section: Theoretical and Real Tidesmentioning

confidence: 99%

“…where N is the number of digitized values of the record and Ôt is the sampling intervalo Some of the longest records (approximately200 years) are reported in Cartwright, 1971, but even these are insufficient to analyse for p' . Tidal analysis of short records (7 days) for some constituents is given in Franco, 1964.…”

Section: Theoretical and Real Tidesmentioning

confidence: 99%