Advances in Geophysics, Vol. 41 by Renata Dmowska, Barry Saltzman

By Renata Dmowska, Barry Saltzman

This sequence offers a venue for longer stories of present advances in geophysics. Written at a degree available to graduate scholars, the articles serve to expand wisdom of assorted fields and should be worthy in classes and seminars.

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15.. The ‘‘checkerboard’’ network grid of case I containing 13 of the 25 gridpoints exhibits an LFV spectrum which is virtually indistinguishable from that of the full grid. So too does the more regionally restricted network of 10 gridpoints of case II, with no differences in peak detection at the 95% or greater levels of inference. The sparser regular network of 9 gridpoints of case III begins to show signaldetection degradation, with the interannual peaks detected at a lesser Ž95᎐99%. degree of confidence than in the full data set and cases I and II.

This reconstruction tends to minimize the size of the envelope and thus favors A˜k ª 0 at the ends of the time series. , a secular trend.. A second possible inversion minimizes the numerical first derivative of A˜1Ž n⌬ t . , which favors envelopes that approach zero slope at the ends of the time series. Such an inversion does not discriminate against a zero-frequency trend in the data, for example, but is poorly suited for other describing features which change rapidly near the beginning or end of the data series.

L 1, . . , K. The time-domain signal x Ž t . and the envelope ᑬ AŽ t . are formally identical for modes referenced to f 0 0, that is, the secular modes of variability. In the multivariate case, the time-domain signal is reconstructed from the components of its corresponding spectral EOF v1 Ž f 0 .. This reconstruction is not unique and requires additional constraints. 4nN 1 , A˜1Ž n⌬ t . Ž l Žl. Žl. 1 *wn , Ž 17. 1 where 1Ž l . is the lth component of the vector v1Ž f 0 .. The ␰ l are the bandwidth retention factors of the Slepian tapers Žsee Park and Maasch, 1993..

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