Large-Scale Response of the Tropical Atmosphere to Transient Convection

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  • 1 National Center for Atmospheric Research, Boulder, CO 80307
  • 2 Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523
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Abstract

We consider the problem of the linear response of a stratified, equatorial, β-plane model atmosphere to specified transient sources of heat and momentum. The method of solution involves transforms in all three spatial coordinates. A finite Stürm-Liouville transform is used in z, a Fourier transform in x, and a generalized Hermite transform in y. The resulting spectral equations can then be solved analytically for a specified forcing. Of particular interest is the case of a Gaussian-shaped heat source centered at latitude yo and with e-folding radius a. The heat source is transient and has time scale 1/α. Using the Parceval relation we compute how the forced energy is partitioned between Kelvin, mixed Rossby-gravity, Rossby and gravity modes as a function of a, yo, α. Model results using a heat source centered at 11°S with an e-folding radius of 750 km and a time scale of about a day indicate that many aspects of the summertime upper tropospheric circulation over South America can be explained by the dispersive properties of Rossby and mixed Rossby-gravity waves. These results also show that the transient heat source excites Kelvin waves which propagate rapidly eastward as a nondispersive wave group. The existence of the Kelvin waves has implications for the initialization of tropical forecast models. By applying a nonlinear normal mode initialization procedure in the middle of a model simulation we investigate how the initialization distorts the subsequent evolution. Much of the distortion is associated with the Kelvin wave response.

Abstract

We consider the problem of the linear response of a stratified, equatorial, β-plane model atmosphere to specified transient sources of heat and momentum. The method of solution involves transforms in all three spatial coordinates. A finite Stürm-Liouville transform is used in z, a Fourier transform in x, and a generalized Hermite transform in y. The resulting spectral equations can then be solved analytically for a specified forcing. Of particular interest is the case of a Gaussian-shaped heat source centered at latitude yo and with e-folding radius a. The heat source is transient and has time scale 1/α. Using the Parceval relation we compute how the forced energy is partitioned between Kelvin, mixed Rossby-gravity, Rossby and gravity modes as a function of a, yo, α. Model results using a heat source centered at 11°S with an e-folding radius of 750 km and a time scale of about a day indicate that many aspects of the summertime upper tropospheric circulation over South America can be explained by the dispersive properties of Rossby and mixed Rossby-gravity waves. These results also show that the transient heat source excites Kelvin waves which propagate rapidly eastward as a nondispersive wave group. The existence of the Kelvin waves has implications for the initialization of tropical forecast models. By applying a nonlinear normal mode initialization procedure in the middle of a model simulation we investigate how the initialization distorts the subsequent evolution. Much of the distortion is associated with the Kelvin wave response.

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