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In theoretical models of tropical dynamics, the effects of both surfacefriction and upward wave radiation through interaction with the stratosphereare oft-ignored, as they greatly complicate mathematical analysis. In thisstudy, we relax the rigid-lid assumption and impose surface drag, which allowsthe barotropic mode to be excited in equatorial waves. In particular, apreviously developed set of linear, strict quasi-equilibrium troposphericequations is coupled with a dry, passive stratosphere, and surface drag isadded to the troposphere momentum equations. Theoretical and numerical modelanalysis is performed on the model in the limits of an inviscid surface coupledto a stratosphere, as well as a frictional surface under a rigid-lid. Thisstudy confirms previous research that shows the presence of a stratospherestrongly shifts the growth rates of fast propagating equatorial waves to largerscales, reddening the equatorial power spectrum. The growth rates of modes thatare slowly propagating and highly interactive with cloud-radiation are shown tobe negligibly affected by the presence of a stratosphere. Surface friction inthis model framework acts as purely a damping mechanism and increases thepoleward extent of the equatorial waves through barotropic vorticitygeneration. Numerical solutions of the coupled troposphere-stratosphere modelwith surface friction also show that the barotropic mode can betropospherically trapped when excited by surface friction but in the presenceof a highly stratified stratosphere. The superposition of phase-shiftedbarotropic and first baroclinic modes is also shown to lead to an eastwardvertical tilt in the dynamical fields of Kelvin-wave like modes.

On the Effect of Surface Friction and Upward Radiation of Energy on Equatorial Waves