By Renata Dmowska, Barry Saltzman
This sequence presents a venue for longer stories of present advances in geophysics. Written at a degree available to graduate scholars, the articles serve to increase wisdom of assorted fields and will be important in classes and seminars.
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Extra resources for Advances in Geophysics, Vol. 41
May yield more physically sensible patterns, but only under certain restrictive assumptions regarding the spatial structure of signals; in fact, the true linear transformations of the eigenmodes required to yield physically distinct climate signals cannot a priori be known. In the case of MTM-SVD, a corresponding alternative linear transformationᎏthe Fourier transformᎏis in fact speciﬁable a priori. The MTM-SVD procedure assumes that a signal has a very speciﬁc narrowband frequency-domain structure, and under that assumption assures quite high spatial signal-to-noise ratios in signal reconstruction.
The signiﬁcance of putative narrowband signals detected in the LFV spectrum is estimated by diagnosing the likelihood that a given value of the LFV would arise from random ﬂuctuations of such a process. Spatial correlation in the climate noise background which is largely local, but is, to a lesser extent, at the larger planetary wave scale also, strongly limits the true number of spatial degrees of freedom in the sampling of any climatic ﬁeld. , peaks in the LFV spectrum. are likely. We guard against contaminations from long-range spatial correlations in the climate background noise by a bootstrap resampling of the multivariate data in time.
While there is considerable power in the synthetic data Žsignalplus-noise. at all gridpoints at all frequencies, the regional as well as the large-scale spatial structure of the reconstructed signals were shown above to be quite faithful to their true counterparts. The ambiguities in distinguishing regional vs global spatial structures, inherent in conventional PCA, are thus relatively alleviated in the MTM-SVD approach. Similarly, FIG. 11. Local fractional variance spectrum of SVD based on Ža.
Advances in Geophysics, Vol. 41 by Renata Dmowska, Barry Saltzman