Steady response to tropical heating in wavy linear and nonlinear baroclinic models

The linear, steady-state, baroclinic model response to a tropical heating superimposed on a three-dimensional basic state is examined in this study. The emphasis is on the relevance of the linear model solution as compared to a fully nonlinear baroclinic model. The direct response to heating in the fully nonlinear, time-dependent model is obtained as the day-30 model response, following the Jin and Hoskins approach. When a 15-day linear damping is included in addition to Rayleigh friction, Newtonian cooling, and a scale-selective biharmonic diffusion, the comparison of the linear and the nonlinear model responses to a 2°C/day tropical heating reveals a striking similarity in both the spatial distribution and amplitude. Thus nonlinearity appears to be a secondary effect and may be crudely represented by the 15-day linear damping, and the linear steady-state model can be a useful tool in diagnostic studies. Both the linear and the nonlinear model responses show an insensitivity to heating longitudes, especially when heating is located between 30°E and 120°W. This insensitivity is characterized by a geographically fixed response that consists of a streamfunction center over the central North Pacific and a weak wave train over the Pacific-North American region. The spatial structure of the preferred pattern does not depend on the dissipation or the amplitude of the tropical heating in the nonlinear model. The geographically fixed response is found to be prominent in the Northern Hemisphere for both the northern winter and summer climatological basic states.