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Experiments with a Spectral Tropical Cyclone Model

Mark DeMariaDepartment of Atmospheric Science, Colorado State University, Fort Collins, CO 80523

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Wayne H. SchubertDepartment of Atmospheric Science, Colorado State University, Fort Collins, CO 80523

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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.

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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