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• W2012910545 abstract "We examine leakage and aliasing problems in a seasonal multiple linear regression model of data taken during the NORPAX Hawaii-to-Tahiti Shuttle Experiment. The model includes a mean, trend, annual harmonic, and semiannual harmonic. Inclusion of the trend can exacerbate leakage, particularly for record lengths of 13 months or less. This is not a major problem for the 15-month shuttle record. The irregularity of the shuttle shipboard time series reduces the potential aliasing of single unresolved high frequencies. Confidence limits for regression model coefficients are determined empirically from Monte Carlo subsampling experiments on moored current meter and sea level data taken during the shuttle. These limits are generally narrower than the standard regression error estimates because there is lack of fit in the regression model. Confidence limits used here pertain only to the determination of model coefficients for a given data set; they say nothing about whether the annual cycle during the shuttle period is typical of any other time interval. The shuttle sampling at each of three longitudes (150 o , 153 o , and 158oW) was in general not adequate to reveal significant differences in low-frequency signals from one longitude to another. If data from the three longitudes are analyzed together without regard for longitude, the multiple linear regression parameters for temperature and zonal velocity component are fairly well determined. The meridional velocity component is so dominated by higher-frequency variability that the model parameters do not differ significantly from zero. The NORPAX Hawaii-to-Tahiti Shuttle Experiment was a study of currents and hydrography in the central equatorial Pacific during one seasonal cycle [Wyrtki et al., 1981]. Measurements were made on 15 cruises at roughly monthly intervals. The central purpose of this experiment was to observe one realization of the seasonal cycle and to accurately determine the mean during that cycle. In this paper we quantify how well that was accomplished. We were motivated by the need for reliable confidence limits for multiple linear regression (MLR) parameters calculated from the shuttle data [Lukas and Firing, 1984, 1985] using McPhaden's [1982] model. McPhaden [1982] used a seasonal MLR model consisting of a mean, linear trend, and annual and semiannual harmonics to analyze a time series sampled irregularly at 1- to 4-week intervals. He showed that occasional gaps in weekly wind observations substantially affected the estimated trend and seasonal cycle when important peaks of short duration were missed. All such errors due to inadequate sampling are now commonly referred to as aliasing, although the term arose in the narrower context of Fourier analysis of evenly spaced data. In this original sense, sinusoids are aliases of each other if they are indistinguishable given a particular sample spacing. Any sinusoid with frequency greater than the Nyquist frequency (one half cycle per sample interval) will be seen as its alias in the frequency interval from zero to Nyquist. The seriousness of this type of aliasing depends critically on the periodicity of both the process and the sampling. Shapiro and Silverman [1960] studied aliasing with different schemes of nonperiodic sampling. Leakage was avoided by considering infinite record lengths and therefore an infinity of samples. They showed that aliasing persists when periodic sample times are perturbed by random variations (jitter)." @default.
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• W2012910545 title "Sampling and aliasing during the NORPAX Hawaii-to-Tahiti Shuttle Experiment" @default.
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• W2012910545 doi "https://doi.org/10.1029/jc090ic06p11709" @default.
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