The intertropical convergence zone (ITCZ) migrates north south on seasonal and longer time scales. Previous studies have shown that the zonal -mean ITCZ displacement off the equator is negatively correlated with the energy flux across the equator; when the ITCZ lies in the Northern Hemisphere, energy flows southward across the equator, and vice versa. The hemisphere that exports energy across the equator is the hemisphere with more net energy input, and it is usually the warmer hemisphere. But states with a double ITCZ straddling the equator also occur, for example, seasonally over the eastern Pacific and frequently in climate models. Here it is shown how the ITCZ position is connected to the energy balance near the equator in a broad range of circumstances, including states with single and double ITCZs. Taylor expansion of the variation of the meridional energy flux around the equator leads to the conclusion that for large positive net energy input into the equatorial atmosphere, the ITCZ position depends linearly on the cross -equatorial energy flux. For small positive equatorial net energy input, the dependence of the ITCZ position on the cross equatorial energy flux weakens to the third root. When the equatorial net energy input or its curvature become negative, a bifurcation to double-ITCZ states occurs. Simulations with an idealized aquaplanet general circulation model (GCM) confirm the quantitative adequacy of these relations. The results provide a framework for assessing and understanding causes of common climate model biases and for interpreting tropical precipitation changes, such as those evident in records of climates of the past.
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