Theor. Comp. Fluid Dyn., 20, 323-350.
Adam H. Sobel
Department of Applied Physics and Applied Mathematics and Department of Earth and Environmental Sciences, Columbia University, New York, NY.
J. David Neelin
Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, CA.
Theories for the position and intensity of precipitation over tropical oceans on climate time scales have a perplexing disagreement between those that focus on the momentum budget of the atmospheric boundary layer (ABL), and those that focus on thermodynamic factors. In the case of narrow intertropical convergence zones (ITCZs), there is some evidence for both classes of theories, and there are large open questions on the interpretation of the moist static energy and momentum budgets of these regions. We develop a model in which both types of mechanisms can operate, and the interaction between them can be analyzed. The model includes a mixed-layer ABL, coupled to a free troposphere whose vertical structure follows the quasi-equilibrium tropical circulation model (QTCM) of Neelin and Zeng. The case analyzed here is axisymmetric, using a fixed sea surface temperature (SST) lower boundary condition with an idealized off-equatorial SST maximum. We examine a regime with small values of the gross moist stability associated with tropospheric motions, which is realistic but poses theoretical challenges. In both rotating (equatorial $\beta$-plane) and nonrotating cases, the model ITCZ width and intensity are substantially controlled by horizontal diffusion of moisture, which is hypothesized to be standing in for non-axisymmetric transients. The inclusion of the ABL increases the amplitude and sharpness of the ITCZ, contributing to the importance of diffusion. Analytical solutions under simplifying assumptions show that the ABL contribution is not singular in the nondiffusive limit; it just features an ITCZ more intense than observed. A negative gross moist stability contribution associated with the flow component driven by ABL momentum dynamics plays a large role in this. Because of the ABL contribution, the flow imports, rather than exports, moist static energy in the ITCZ, but we show that this can be understood rather simply. The ABL contribution can be approximately viewed as a forcing to the tropospheric thermodynamics. The ABL forcing term is in addition to thermodynamic forcing by net flux terms in the moist static energy budget, which otherwise is much as in the standard QTCM. The ABL momentum budget suggests that divergent flow in the ABL is controlled to a significant extent by the pressure gradient imprinted on the ABL by the SST gradient---termed the Lindzen-Nigam contribution---although we also find that the thermodynamics mediating this is nontrivial, especially in the rotating case. Nonetheless, when this component of the pressure gradient is artificially removed, the peak ITCZ precipitation is reduced by a fraction on the order of 30-40\%, less than might have been expected based on the diagnosis of the ABL momentum budget.