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Singular-Vector Perturbation Growth in a Primitive Equation Model with Moist Physics

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  • 1 Institute for Meteorology and Geophysics, University of Vienna, Vienna, Austria
  • | 2 National Center for Atmospheric Research,* Boulder, Colorado
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Abstract

Finite-time growth of perturbations in the presence of moist physics (specifically, precipitation) is investigated using singular vectors (SVs) in the context of a primitive equation regional model. Two difficulties appear in the explicit consideration of the effect of moist physics when studying such optimal growth. First, the tangent-linear description of moist physics may not be as straightforward and accurate as for dry-adiabatic processes; second, because of the consideration of moisture, the design of an appropriate measure of growth (i.e., norm) is subject to even more ambiguity than in the dry situation.

In this study both of these problems are addressed in the context of the moist version of the National Center for Atmospheric Research Mesoscale Adjoint Modeling System, version 2, with emphasis on the second problem. Leading SVs are computed in an iterative fashion, using a Lanczos algorithm, for three norms over an optimization interval of 24 h; these norms are based on an expression related to (total) perturbation energy. The properties of these SVs are studied for a case of explosive cyclogenesis and a case of summer convection.

The consideration of moisture leads to faster growth of perturbations than in the dry situation, as well as to the appearance of new growing structures. Apparently, moist processes provide for new mechanisms of error growth and do not simply lead to a modulation of SVs obtained with the dry version of the model. Consequently, consideration of the linearized moist processes is essential for revealing all structures that might potentially grow in a moist primitive equation model. In the context of this investigation growth rates depend more on the choice of the basic state and linearized model (moist vs dry) than on the choice of the norm (moist vs dry total energy norm). A reference is cited that supports the validity of the moist tangent-linear SV perturbation growth studied here in the nonlinear regime.

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

Email: martin.ehrendorfer@univie.ac.at

Abstract

Finite-time growth of perturbations in the presence of moist physics (specifically, precipitation) is investigated using singular vectors (SVs) in the context of a primitive equation regional model. Two difficulties appear in the explicit consideration of the effect of moist physics when studying such optimal growth. First, the tangent-linear description of moist physics may not be as straightforward and accurate as for dry-adiabatic processes; second, because of the consideration of moisture, the design of an appropriate measure of growth (i.e., norm) is subject to even more ambiguity than in the dry situation.

In this study both of these problems are addressed in the context of the moist version of the National Center for Atmospheric Research Mesoscale Adjoint Modeling System, version 2, with emphasis on the second problem. Leading SVs are computed in an iterative fashion, using a Lanczos algorithm, for three norms over an optimization interval of 24 h; these norms are based on an expression related to (total) perturbation energy. The properties of these SVs are studied for a case of explosive cyclogenesis and a case of summer convection.

The consideration of moisture leads to faster growth of perturbations than in the dry situation, as well as to the appearance of new growing structures. Apparently, moist processes provide for new mechanisms of error growth and do not simply lead to a modulation of SVs obtained with the dry version of the model. Consequently, consideration of the linearized moist processes is essential for revealing all structures that might potentially grow in a moist primitive equation model. In the context of this investigation growth rates depend more on the choice of the basic state and linearized model (moist vs dry) than on the choice of the norm (moist vs dry total energy norm). A reference is cited that supports the validity of the moist tangent-linear SV perturbation growth studied here in the nonlinear regime.

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

Email: martin.ehrendorfer@univie.ac.at

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