By Renata Dmowska, Barry Saltzman
This sequence offers a venue for longer reports of present advances in geophysics. Written at a degree available to graduate scholars, the articles serve to develop wisdom of varied fields and will be worthwhile in classes and seminars.
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Extra resources for Advances in Geophysics, Vol. 41
1. 9 in Fig. 10.. 99, the observed spectrum is quite close to that for the white-noise case. 9999 1. does the distribution of the LFV spectrum noticeably depart from that of the pure white-noise case. 1 far exceeds unity. A more thorough experiment employing ensembles of 1000 random trials ŽTable II. demonstrates that the correct rates of chance exceedence of given conﬁdence levels are indeed obtained for all but the largest value of . Thus, the null distribution of the LFV spectrum has been shown to conform to the pure white-noise distribution under precisely those conditions for which our a priori deﬁnition of a smoothly varying colored-noise spectrum is satisﬁed.
One may want to choose L 30 years with a 100-year record. , ENSO. with dominant time scales less than 6 years in this case. More importantly, in the multivariate context, the M-SSA approach runs up against severe dimensional limitations for large data sets. The introduction of multiple channels in the covariance estimation requires the statistical decomposition of a matrix in the time, spatial index, and lag domains. , a unique eigendecomposition of the 30 MICHAEL E. MANN AND JEFFREY PARK variance is not possible.
A more thorough experiment employing ensembles of 1000 random trials ŽTable II. demonstrates that the correct rates of chance exceedence of given conﬁdence levels are indeed obtained for all but the largest value of . Thus, the null distribution of the LFV spectrum has been shown to conform to the pure white-noise distribution under precisely those conditions for which our a priori deﬁnition of a smoothly varying colored-noise spectrum is satisﬁed. , a ‘‘locally white’’ noise background.. This generality of the null hypothesis invoked in the signal detection procedure is a signiﬁcant strength of the MTM-SVD methodology.