Estimation of Mesoscale Vertical Derivatives of Potential Temperature and Density from Hydrographic Data

Arthur J. Mariano Department of Applied Science, Harvard University, Cambridge, Massachusetts

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Abstract

This study was motivated by the need to combine vertical derivative estimates of either potential density or temperature with SOFAR float data for estimating vortex stretching in the main (700 m) and lower thermocline (1300 m) of the Local Dynamics Experiment (LDE) region. Five hundred, forty-three LDE CTD casts are used to evaluate finite difference, polynomial and exponential regression models for estimating the mesoscale vertical derivative of potential density and temperature at 700 and 1300 m depth. The standard deviation and bias curves of these models were examined as a function of vertical estimation interval. Smoothing the data before derivative estimation was not necessary for estimation intervals greater than 300 m for all the models tested. An unbiased minimum variance estimator of vertical derivatives does not exist for the models tested because of a variance-bias trade-off.

An alternate criterion of merit is proposed for the estimation of vertical derivatives: We require that vortex stretching estimates be robust to small changes in the estimation interval and that the vortex stretching estimates agree with the estimates of Mariano and Rossby. According to this criterion, a cubic polynomial fit of length 800 ± 100 m to the density data is the best model for estimating vertical derivatives from hydrographic data at 700 m. Because the stretching is less at 1300 m and uncertainties are great, vortex stretching could not be estimated using this approach with sufficient accuracy at 1300 m.

Abstract

This study was motivated by the need to combine vertical derivative estimates of either potential density or temperature with SOFAR float data for estimating vortex stretching in the main (700 m) and lower thermocline (1300 m) of the Local Dynamics Experiment (LDE) region. Five hundred, forty-three LDE CTD casts are used to evaluate finite difference, polynomial and exponential regression models for estimating the mesoscale vertical derivative of potential density and temperature at 700 and 1300 m depth. The standard deviation and bias curves of these models were examined as a function of vertical estimation interval. Smoothing the data before derivative estimation was not necessary for estimation intervals greater than 300 m for all the models tested. An unbiased minimum variance estimator of vertical derivatives does not exist for the models tested because of a variance-bias trade-off.

An alternate criterion of merit is proposed for the estimation of vertical derivatives: We require that vortex stretching estimates be robust to small changes in the estimation interval and that the vortex stretching estimates agree with the estimates of Mariano and Rossby. According to this criterion, a cubic polynomial fit of length 800 ± 100 m to the density data is the best model for estimating vertical derivatives from hydrographic data at 700 m. Because the stretching is less at 1300 m and uncertainties are great, vortex stretching could not be estimated using this approach with sufficient accuracy at 1300 m.

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