Pacific ENSO Update1st Quarter, 2005 Vol. 11 No. 1 |
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SPECIAL SECTION: ENSO and Sea-Level Variability (3):
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Guam | Palau | Saipan | Kwajalein | Yap | Pago Pago | ||
Guam | 1.000 | ||||||
Palau | 0.642** | 1.000 | |||||
Saipan | 0.743** | 0.680** | 1.000 | ||||
Kwajalein | 0.763** | 0.777** | 0.661** | 1.000 | |||
Yap | 0.771** | 0.952** | 0.808** | 0.681** | 1.000 | ||
Pago Pago | 0.348 | 0.001 | 0.217 | 0.14 | 0.086 | 1.000 |
Note: Correlation is a statistical technique which can show whether and how strongly pairs of variables (here sea level of each of the stations) are related. A correlation coefficient of 1.00 or -1.00 is a perfect relationship between two variables. The closer the correlation coefficient is to zero, the less relationship there is between the two variables. In this example sea level variations in Palau and Yap are very closely related (correlation coefficient = .952) where as the sea level variations between Palau and Saipan are less closely related (correlation coefficient = .680)
Significance levels show how likely a result is due to chance. The most common level, used to mean something is good enough to be believed, is “0.01” or “0.05” meaning that the finding has a one percent (0.01) or five percent (0.05) chance of not being true. In our data, all north Pacific stations were significant at the .01 level.
While a qualitative variation of the climatology of annual cycle is identifiable from the monthly average sea level data records (as discussed before) (Figure 2 – solid line), it is the harmonic analysis that can give a picture of quantitative variation in these data (Figure 2 – dashed line). Therefore, to quantitatively evaluate the importance of the annual cycle from these data, harmonic analysis has been performed. Harmonic analysis consists of representing the fluctuations or variation in a time series as having arisen from the adding together of a series of sine and cosine functions. These trigonometric functions are “harmonic” in the sense that they are chosen to have frequencies exhibiting integer multiples of the “fundamental” frequency determined by the sample size of the data series. For example, a common physical analogy is the musical sound produced by a vibrating string, where the pitch is determined by the fundamental frequency, but the aesthetic quality of the sound depends on also on the relative contributions of the higher (1st and 2nd) harmonics. The 1st harmonics represents the annual cycle and explains the maximum variances.
The first harmonic, here in this case, explained about a considerable percentage of variance of the sea level variability in the north Pacific Islands (Fig. 2a-2e). The first harmonic for all islands explained variances of 64-88%. For the western most islands in the north Pacific (Guam, Saipan, Palau and Yap), maximum rise of sea level occurs in summer months (June to August). The annual cycle is relatively weak (though still explaining over 40% of the variance for sea level) in Kwajalein (Fig. 2e), and the annual cycle is extremely weak in Pago Pago (only 2% variance) (Fig. 2f). However, a second harmonic, which represents the semiannual cycle, explains 3-17% of variances (not reported here). This component adds considerably to the variance of Kwajalein (17%) and Pago Pago (11%).