Tropical Cyclone Motion in a Nondivergent Barotropic Model

Mark DeMaria National Center for Atmospheric Research, Boulder, CO 80307

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Abstract

Tropical cyclone motion is investigated in the context of a nondivergent barotropic model. For this purpose, the nondivergent barotropic vorticity equation is solved on a doubly-periodic midlatitude, β-plane using a spectral method with Fourier basis functions. The results from previous studies are summarized and illustrated in idealized model simulations. It is shown that the absolute vorticity gradient of the steering current (∇ζa) causes an axisymmetric vortex to drift relative to the steering current with a component in the direction of the gradient and a component 90° to the left of the gradient. The implications of the basic principles of vortex motion for operational track prediction models are discussed. By consideration of the horizontal variation of ∇ζa, it is shown that a vortex track will be more sensitive to initial position errors in regions where ∇2ζa> 0 than in regions where ∇ζa< 0. It is also shown that the vortex track is much more sensitive to changes in the outer regions (size changes) than to changes in the inner regions (intensity changes) of the vortex, and that the vortex track is more sensitive to size changes in regions where | ∇ζa| is large.

The effect of numerical approximation on the vortex track is studied by comparing the spectral model to a second-order finite difference version of the model. These results suggest that the resolution used in some operational tropical cyclone track prediction models is inadequate.

Abstract

Tropical cyclone motion is investigated in the context of a nondivergent barotropic model. For this purpose, the nondivergent barotropic vorticity equation is solved on a doubly-periodic midlatitude, β-plane using a spectral method with Fourier basis functions. The results from previous studies are summarized and illustrated in idealized model simulations. It is shown that the absolute vorticity gradient of the steering current (∇ζa) causes an axisymmetric vortex to drift relative to the steering current with a component in the direction of the gradient and a component 90° to the left of the gradient. The implications of the basic principles of vortex motion for operational track prediction models are discussed. By consideration of the horizontal variation of ∇ζa, it is shown that a vortex track will be more sensitive to initial position errors in regions where ∇2ζa> 0 than in regions where ∇ζa< 0. It is also shown that the vortex track is much more sensitive to changes in the outer regions (size changes) than to changes in the inner regions (intensity changes) of the vortex, and that the vortex track is more sensitive to size changes in regions where | ∇ζa| is large.

The effect of numerical approximation on the vortex track is studied by comparing the spectral model to a second-order finite difference version of the model. These results suggest that the resolution used in some operational tropical cyclone track prediction models is inadequate.

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