*Journal of the Atmospheric Sciences*, **59**, 1744-1752.

Lorenzo M. Polvani and Adam H. Sobel

Department of Applied Physics and Applied Mathematics and Department of Earth and Environmental Sciences,
Columbia University, New York, NY.

**Abstract**

The weak temperature gradient (WTG) approximation is applied to simple shallow-water models of the Hadley circulation. While it is difficult to formally justify the use of the WTG approximation for this problem, the derived WTG solutions are shown to agree well with numerical solutions of the full equations and to converge to the traditional angular momentum-conserving (AMC) solutions in the inviscid limit. Heuristic arguments are given to explain this. The WTG method also provides semi-analytical solutions in the case of nonvanishing viscosity, in contrast to the AMC solutions which are strictly inviscid.