### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3pUW21. Empirical orthogonal function representations of stochastic
sound-speed ensembles.

**M. J. Longfritz
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W. L. Siegmann
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M. J. Jacobson
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*Rensselaer Polytech. Inst., Troy, NY 12180-3590
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The representation of stochastic ensembles of sound-speed profiles by
convenient and efficient means is examined. The procedure is based on using
discrete empirical orthogonal functions (EOFs) with random coefficients. The
eventual objective is to use the EOF representations in random wave propagation
models, for which their efficiency is expected to reduce significantly the
computational expense. To illustrate the procedure, two specific model
ensembles are considered. The first consists of deep-water (Munk) sound-speed
profiles, and the second has shallow-water profiles obtained from temperature
profiles generated by a portion of the generalized digital environmental model
(GDEM). After a statistical distribution of stochastic environmental input
parameters is assumed, EOFs are calculated for ensembles of up to 10 000
profile samples. Relations between the statistics of the input parameters and
the sound speed profiles that are obtained from EOF representations are
investigated. In each case examined, the number of EOFs needed to account for
virtually all of the sample variance is at most four. Additional cases are
considered using Continental Shelf data by assuming measured profiles represent
ensemble samples. [Work supported by ONR.]