**Most rain on Earth falls in the tropical rain belt known as the Intertropical Convergence Zone (ITCZ), which on average lies 6° north of the equator. Over the past 15 years, it has become clear that the ITCZ position can shift drastically in response to remote changes, for example, in Arctic ice cover. But current climate models have difficulties simulating the ITCZ accurately, often exhibiting two ITCZs north and south of the equator when in reality there is only one. What controls the sensitivity of the ITCZ to remote forcings? And how do the model biases in the ITCZ arise?**

Paleoclimate studies (e.g., Peterson et al. 2000, Haug et al. 2001) and a series of modeling studies starting with Vellinga and Wood (2002), Chiang and Bitz (2005) and Broccoli et al. (2006) have revealed one important driver of ITCZ shifts: differential heating or cooling of the hemispheres shifts the ITCZ toward the differentially warming hemisphere. So when the northern hemisphere warms, for example, because northern ice cover and with it the polar albedo are reduced, the ITCZ shifts northward. This can be rationalized as follows: When the atmosphere receives additional energy in the northern hemisphere, it attempts to rectify this imbalance by transporting energy across the equator from the north to the south. Most atmospheric energy transport near the equator is accomplished by the Hadley circulation, the mean tropical overturning circulation. The ITCZ lies at the foot of the ascending branch of the Hadley circulation, and the circulation transports energy in the direction of its upper branch, because energy (or, more precisely, moist static energy) usually increases with height in the atmosphere. Southward energy transport across the equator then requires an ITCZ north of the equator, so the upper branch of the Hadley circulation can cross the equator going from the north to the south.

To understand how far away from the equator the ITCZ is located, it helps to consider the steady-state atmospheric energy balance

$$\mathrm{div}\, F = \mathcal{R} – \mathcal{O}$$,

where $$F$$ is the vertically integrated energy flux in the atmosphere, $$\mathcal{R}$$ is the net radiative energy input to an atmospheric column (the difference between absorbed shortwave radiation and emitted longwave radiation), and $$\mathcal{O}$$ is the oceanic energy uptake at the surface. The energy balance states that the atmosphere transports energy away from regions of net energy input $$\mathcal{R}-\mathcal{O}$$ (e.g., the tropics) toward regions of net energy loss (e.g., the extratropics). Broccoli et al. (2006) and Kang et al. (2008) observed that because the ITCZ is located approximately where the meridional atmospheric mass transport in the Hadley circulation vanishes, it is typically also located close to where the atmospheric energy transport vanishes: at the “energy flux equator” (EFE) where $$F=0$$. This gives us a handle to obtain a quantitative relation between the EFE or ITCZ and quantities in the atmospheric energy balance. Focusing on the zonal mean (e.g., taken across a sufficiently wide longitude sector) and expanding the energy flux $$F$$ around the equator (denoted by subscript 0) to first order in latitude $$\delta$$ gives

$$F(\delta) \approx F_0 + (\mathrm{div}\, F)_0 a \delta$$,

where $$a$$ is Earth’s radius. Equating $$\delta$$ with the latitude of the EFE or ITCZ implies $$F(\delta) \approx 0$$, and we can solve the above expansion for $$\delta$$:

$$\delta = -\frac{1}{a} \, \frac{F_0}{\mathcal{R}_0-\mathcal{O}_0}$$,

where we have substituted $$\mathcal{R} – \mathcal{O}$$ for the equatorial energy flux divergence from the energy balance above.

The first-order relation for $$\delta$$ shows that (1) the ITCZ position is farther south the stronger northward the atmospheric energy flux $$F_0$$ across the equator, and (2) the ITCZ is farther from the equator the weaker the net atmospheric energy input $$\mathcal{R}_0 – \mathcal{O}_0$$ at the equator.

The following sketch illustrates these relations graphically:

The figure shows the atmospheric moist static energy flux $$F$$ in the zonal and annual mean in the present climate (red line). Given the equatorial values of the energy flux $$F_0$$ and of its ‘slope’ with latitude $$\mathcal{R}_0-\mathcal{O}_0$$, the energy flux equator $$\delta$$ can be determined using the arguments from above. If the northward cross-equatorial energy flux $$F_0$$ strengthens (indicated schematically by the blue line), but the slope $$\mathcal{R}_0-\mathcal{O}_0$$ remains fixed, the energy flux equator $$\delta$$ moves southward. Similarly, if $$\mathcal{R}_0-\mathcal{O}_0$$ increases, the energy flux equator moves toward the equator.

Several previous studies had pointed out that the ITCZ position is proportional to the cross-equatorial energy flux $$F_0$$ (e.g., Kang et al. 2008, Frierson and Hwang 2012, and Donohoe et al. 2013). That the net atmospheric energy input modulates the sensitivity of the ITCZ position to the cross-equatorial flux was pointed out in Bischoff and Schneider (2014).

What are some implications of these insights from the energy balance? The analysis draws attention to the importance for the ITCZ of the atmospheric energy balance near the equator. The net atmospheric energy input $$\mathcal{R}-\mathcal{O}$$ near the equator is the small residual (~20 W m^{2}) of large cancellations between absorbed shortwave radiation (~320 W m^{2}), emitted longwave radiation (~250 W m^{2}), and oceanic energy uptake (~ 50 W m^{2}). Subtle shifts in any of these large terms can lead to relatively large changes in the net atmospheric energy input near the equator and hence large ITCZ shifts. Similarly, the cross-equatorial energy flux $$F_0$$ (~-0.2 PW) represents a small residual imbalance between the two hemispheres which each have, for example, shortwave radiative energy gains and longwave radiative energy losses of tens of PW. This makes the ITCZ a sensitive recorder of the atmospheric energy balance, and it likely accounts for the large swings in the ITCZ position inferred from paleoclimatic proxies (see Schneider et al. 2014 for a review).

The results from the energy balance also point toward a way of understanding the double-ITCZ bias in climate models. The first-order expansion above breaks down when the net atmospheric energy input vanishes. In that case, one needs to go to higher order in latitude, and multiple solutions for the ITCZ position emerge. We will discuss this in a future post.

A limitation of the insights from the energy balance is that they do not provide a closed mechanistic understanding of what controls the ITCZ position. Quantities such as the net atmospheric energy input $$\mathcal{R}-\mathcal{O}$$ and the cross-equatorial energy flux $$F_0$$ depend on the strength of the Hadley circulation, among other factors, which in turn depends on the ITCZ position. How these are connected mechanistically (for example, through the angular momentum balance) remains a subject of ongoing research.