The Linear Response of a Stratified Global Atmosphere to Tropical Thermal Forcing

The linear response of model normal modes in a stratified atmosphere to tropical thermal forcing is investigated by using global primitive equations which are linearized with respect to a resting state and include a prescribed thermal forcing and momentum dissipation. By the method of separation of the variables, the basic equations are split up into vertical and horizontal equations. The homogeneous parts of these equations are solved spectrally to obtain the model normal modes. The forced problem is then solved by using a normal mode expansion. For a parabolic form of heating in the vertical, it is shown that the internal modes corresponding to the equivalent height of a few hundred meters are favorably excited. This implies that the disturbances created by diabatic heating tend to have a typical baroclinic vertical structure. Numerical results are presented for the forced solutions generated by stationary and transient beat sources. For the case of stationary tropical heating, most of the excited energy goes into the rotational modes, but a significant portion also goes to the Kelvin modes, while other gravity wave modes play insignificant roles in general. For the case of transient tropical heating, the generation of gravity wave modes, except for the Kelvin modes, depends strongly on the time scale of heating, while the rotational modes and the Kelvin modes are dependent only weakly on the heating rate. The unique behavior of the Kelvin modes may be explained by the resemblance of the heating pattern to the horizontal structure of Kelvin modes and the closeness of their frequencies to those of rotational modes.