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The Total Energy Norm in a Quasigeostrophic Model

Martin EhrendorferInstitute for Meteorology and Geophysics, University of Vienna, Vienna, Austria

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Abstract

Total energy E as the sum of kinetic and available potential energies is considered here for quasigeostrophic (QG) dynamics. The discrete expression for E is derived for the QG model formulation of Marshall and Molteni. While E is conserved by the nonlinear unforced model equations, an analogous expression in terms of perturbed fields is, in general, not conserved for tangent-linearized versions of the model, thereby allowing for growth (or decay) in this total energy norm. Examples for structures linearly growing optimally (i.e., the so-called singular vectors) in terms of either the total energy or just the kinetic energy norm are briefly illustrated and contrasted. It is argued that E might preferably be used (rather than kinetic energy) in predictability and data assimilation studies that are based on the QG model considered here.

Corresponding author address: Dr. Martin Ehrendorfer, Institute for Meteorology and Geophysics, University of Vienna, Hohe Warte 38, A-1190 Vienna, Austria.

Email: martin.ehrendorfer@univie.ac.at

Abstract

Total energy E as the sum of kinetic and available potential energies is considered here for quasigeostrophic (QG) dynamics. The discrete expression for E is derived for the QG model formulation of Marshall and Molteni. While E is conserved by the nonlinear unforced model equations, an analogous expression in terms of perturbed fields is, in general, not conserved for tangent-linearized versions of the model, thereby allowing for growth (or decay) in this total energy norm. Examples for structures linearly growing optimally (i.e., the so-called singular vectors) in terms of either the total energy or just the kinetic energy norm are briefly illustrated and contrasted. It is argued that E might preferably be used (rather than kinetic energy) in predictability and data assimilation studies that are based on the QG model considered here.

Corresponding author address: Dr. Martin Ehrendorfer, Institute for Meteorology and Geophysics, University of Vienna, Hohe Warte 38, A-1190 Vienna, Austria.

Email: martin.ehrendorfer@univie.ac.at

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