Estimation of Quasi-Geostrophic Modal Amplitudes from XBT/CTD Survey Data

Jerome A. Smith Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943

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Christopher N. K. Mooers Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943

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Allan R. Robinson Center for Earth and Planetary Physics, Pierce Hall, Harvard University, Cambridge, MA 02138

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Abstract

The skill with which amplitudes of quasi-geostrophic modes can be estimated is important in the analysis and modeling of data from mixed CTD/XBT surveys. Here, several methods for estimation of quasi-geostrophic vertical mode amplitudes (QGMs) are compared, both in the context of idealized estimation and (especially) in application to some recent CTD and XBT data from the California Current Systems (CCS). The methods compared are: 1) direct least-squares fitting by QGMs (LSF); 2) projection of “empirical orthogonal function” amplitudes onto QGM amplitudes at each station (EOF); 3) ridge regression (RR); 4) an “optimal estimate” using covariances between QGM amplitudes (OE); and 5) another optimal estimate using covariances between EOF amplitudes and QGM amplitudes (CEOF). For deep CTD casts (>1500 m), all methods perform well. For shallow CTD and XBT casts (<750 m), method five (CEOF) is recommended, using EOFs and amplitude covariances derived from just the deeper CTD casts. Since low-frequency internal waves have the same modal structure for density as the QGMS, they are not distinguishable from the QGMs in the present analysis. The analysis is applied to a recent survey to produce amplitude maps for the first few baroclinic modes. Comparisons with another survey indicate that the density analysis is transportable, but the T-S characteristics are so variable that the temperature analysis is not (the surveys are approximately three months apart).

Abstract

The skill with which amplitudes of quasi-geostrophic modes can be estimated is important in the analysis and modeling of data from mixed CTD/XBT surveys. Here, several methods for estimation of quasi-geostrophic vertical mode amplitudes (QGMs) are compared, both in the context of idealized estimation and (especially) in application to some recent CTD and XBT data from the California Current Systems (CCS). The methods compared are: 1) direct least-squares fitting by QGMs (LSF); 2) projection of “empirical orthogonal function” amplitudes onto QGM amplitudes at each station (EOF); 3) ridge regression (RR); 4) an “optimal estimate” using covariances between QGM amplitudes (OE); and 5) another optimal estimate using covariances between EOF amplitudes and QGM amplitudes (CEOF). For deep CTD casts (>1500 m), all methods perform well. For shallow CTD and XBT casts (<750 m), method five (CEOF) is recommended, using EOFs and amplitude covariances derived from just the deeper CTD casts. Since low-frequency internal waves have the same modal structure for density as the QGMS, they are not distinguishable from the QGMs in the present analysis. The analysis is applied to a recent survey to produce amplitude maps for the first few baroclinic modes. Comparisons with another survey indicate that the density analysis is transportable, but the T-S characteristics are so variable that the temperature analysis is not (the surveys are approximately three months apart).

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