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Wayne H. Schubert

As part of a concerted effort to reduce the publication times of submitted manuscripts,it is the goal of all American Meteorological Society (AMS) journal editorial officesto adhere to the following practices for the peer review of submissions.

1) The editor's office handling the submitted manuscript will make every effort tocontact via phone or e-mail all potential reviewers in advance to ensure that theyhave the interest and the available time to review the manuscript in a timely manner.

2) Reviewers will be asked to return the completed review within four weeks unlessspecial circumstances warrant a different schedule. (In the case of

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Wayne H. Schubert

Abstract

Lilly's model of a horizontally homogeneous cloud-topped mixed layer is studied. The model is closed by taking a weighted (weighting factor or entrainment parameter k) average of Lilly's maximum and minimum entrainment cases. The dependence of steady-state solutions on large-scale divergence, sea surface temperature and entrainment parameter k is investigated. By numerical integration the response of the mixed layer to a diurnally varying radiative flux is investigated. Significant variations in the state of the mixed layer and in the convective fluxes are found.

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Wayne H. Schubert

As part of a concerted effort to reduce the publication times of submitted manuscripts,it is the goal of all American Meteorological Society (AMS) journal editorial officesto adhere to the following practices for the peer review of submissions.

1) The editor's office handling the submitted manuscript will make every effort tocontact via phone or e-mail all potential reviewers in advance to ensure that theyhave the interest and the available time to review the manuscript in a timely manner.

2) Reviewers will be asked to return the completed review within four weeks unlessspecial circumstances warrant a different schedule. (In the case of

Full access
Wayne H. Schubert

As part of a concerted effort to reduce the publication times of submitted manuscripts,it is the goal of all American Meteorological Society (AMS) journal editorial officesto adhere to the following practices for the peer review of submissions.

1) The editor's office handling the submitted manuscript will make every effort tocontact via phone or e-mail all potential reviewers in advance to ensure that theyhave the interest and the available time to review the manuscript in a timely manner.

2) Reviewers will be asked to return the completed review within four weeks unlessspecial circumstances warrant a different schedule. (In the case of

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Wayne H. Schubert

Abstract

The geopotential tendency form of semigeostrophic theory is derived and compared with the potential vorticity form. The tendency form is compact and particularly convenient for non-Boussinesq, nonuniform potential vorticity flows.

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Wayne H. Schubert and Gudrun Magnusdottir

Abstract

A potential pseudodensity principle is derived for the quasi-static primitive equations on the sphere. An important step in the derivation of this principle is the introduction of “vorticity coordinates”—that is, new coordinates whose Jacobian with respect to the original spherical coordinates is the dimensionless absolute isentropic vorticity. The vorticity coordinates are closely related to Clebsch variables and are the primitive equation generalizations of the geostrophic coordinates used in semigeostrophic theory. The vorticity coordinates can be used to transform the primitive equations into a canonical form. This form is mathematically similar to the geostrophic relation. There is flexibility in the choice of the potential function appearing in the canonical momentum equations. This flexibility can be used to force the vorticity coordinates to move with some desired velocity, which results in an associated simplification of the material derivative operator. The end result is analogous to the way ageostrophic motions become implicit when geostrophic coordinates are used in semigeostrophic theory.

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Gudrun Magnusdottir and Wayne H. Schubert

Abstract

We develop here the isentropic–geostrophic coordinate version of semigeostrophic theory on a midlatitude β-plane. This approach results in a simple mathematical form in which the horizontal ageostrophic velocities are implicit and the entire dynamics reduces to a predictive equation for the potential pseudodensity and an invertibility relation. Linearized versions of the theory lead to a generalized Charney–Stern theorem for combined barotropic–baroclinic instability and to Rossby wave solutions with a meridional structure different from that in quasi-geostrophic theory.

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Gudrun Magnusdottir and Wayne H. Schubert

Abstract

This paper presents the combined isentropic and spherical geostrophic coordinate version of semigeostrophic theory. This is accomplished by first proposing a spherical coordinate generalization of the geostrophic momentum approximation and discussing its associated conservation principles for absolute angular momentum, total energy, potential vorticity and potential pseudodensity. We then show how the use of the spherical geostrophic coordinates allows the equations of the geostrophic momentum approximation to be written in a canonical form that makes ageostrophic advection implicit. This leads to a simple equation for the prediction of the potential pseudodensity. The potential pseudodensity can then be inverted to obtain the associated wind and mass fields. In this way the more general semigeostrophic theory retains the same simple mathematical structure as quasi-geostrophic theory—a single predictive equation which does not explicitly contain ageostrophic advection and an invertibility principle. The combined use of isentropic and spherical geostrophic coordinates is crucial to retaining this simplicity.

In order to demonstrate how the theory applies to problems of barotropic–baroclinic instability and Rossby–Haurwitz wave dispersion, we derive the semigeostrophic generalization of the Charney–Stern theorem and compare the semigeostrophic Rossby–Haurwitz wave frequencies with those of Laplace's tidal equations. The agreement between these frequencies is generally better than 0.5%. Thus, the theory appears to encompass a wide range of meteorological phenomena including both planetary-scale and synoptic-scale waves, along with their finer scale aspects such as fronts and jets.

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Wayne H. Schubert and Mark DeMaria

Abstract

Beginning with the nine nonlinear governing equations for the simplest three-layer, axisymmetric, primitive equation, tropical cyclone model, we first introduce a vertical transform which decouples the linear part of the dynamics into three sets (one external, two internal modes) of three equations. After formulating a balance model boundary condition for each of the vertical modes, we introduce a radial transform based on normal modes. The radial transformation of the governing equations then gives spectral equations which describe the time evolution of the amplitude and phase of the external and internal geostrophic and gravity-inertia modes. A transform method for calculating the nonlinear and source/sink terms is described. As a simple test of the method, numerical integrations of the frictionless form of the nonlinear spectral equations with a specified heat source are made. The results illustrate the role of gravity-inertia waves in the forced transverse circulation and the quasi-gradient rotational flow. The model provides a simple framework in which to study the effects of friction and moist physics on nonlinear normal mode initialization procedures.

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Mark DeMaria and Wayne H. Schubert

Abstract

The three-layer balanced axisymmetric tropical cyclone model presented by Ooyama is generalized to dimensions and the resultant primitive equations are solved using the spectral (Galerkin) method with Fourier basis functions on a doubly-periodic midlatitude β-plane. The nonlinear terms are evaluated using the transform method where the necessary transforms are performed using FFT algorithms. The spectral equations are transformed so that the dependent variables represent the normal modes of the linearized equations. For the three-layer model, the normal modes correspond to internal or external gravity or rotational modes or to inertial oscillations associated with the constant depth boundary layer. When the governing equations, are written in terms of the normal modes, the linear terms can be evaluated exactly and the application of the nonlinear normal mode initialization scheme proposed by Machenhauer is straightforward.

Results from a simulation with an axisymmetric initial condition on an f-plane are presented and it is shown that the model can produce a vortex similar to tropical cyclones observed in nature. The energy of the gravity modes and rotational modes are calculated for this simulation and it is shown that the gravity mode energy is more than an order of magnitude smaller than the rotational mode energy. The model is then run on the β-plane and it is shown that the variation of the Coriolis parameter with latitude causes the tropical cyclone to move toward the northwest at about 2 m s−1, in agreement with several other studies. It is also shown that the dispersion of the rotational modes causes the tropical cyclone to elongate toward the west and develop sharper geopotential gradients toward the cast. The model is also run with a basic state wind profile and it is shown that the motion of the storm produces asymmetries in the boundary layer convergence field.

The effect of initialization procedures on a tropical cyclone simulation is also studied. The results from linear and nonlinear normal mode initialization procedures and results from applying an initialization procedure based on the nonlinear balance equation are compared. It is shown that the nonlinear normal mode initialization procedure results in much smaller track and intensity forecast errors, and prevents the excitation of spurious gravity waves.

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