Atmospheric Models: Keeping It Simple
Levine, X.J., and Schneider, T. 2011. Response of the Hadley Circulation to Climate Change in an Aquaplanet GCM Coupled to a Simple Representation of Ocean Heat Transport. Journal of the Atmospheric Sciences 68: 769-783.
The HC is what emerges in the tropics if we average atmospheric motions on the time-scale of a month or more. In a classical view of this circulation, there are upward motions and low pressure at the equator, poleward moving air aloft, downward motion around 30° N (S) and the subtropical highs, and equatorward moving air (the trade winds) in the lower atmosphere. There are studies which have shown that the HC may have widened in the last few decades.
Levine and Schneider (2011) use a crude atmospheric general circulation model (GCM) to examine the strength and span of the HC over a wide range of climates. They perform this study since in global warming scenarios, some studies show the HC strengthens while others show it and weakens in the future. As the authors state; "Despite a large body of observations and numerous studies with GCMs, it remains unclear how the width and strength of the Hadley Circulation are controlled."
In the Levine and Schneider (2011) GCM, they use an idealized radiative transfer scheme and moist thermodynamics. The model is based on one used at the Geophysical Fluid Dynamics Laboratory. It is a model with relatively coarse resolution (about 2.8° latitude / longitude) and 30 levels in the vertical. The planet "surface" is water covered only. The oceans include simple dynamics for heat transport (which is turned "on" and "off"), and the model was driven with the annual mean insolation. Thus, there is no diurnal or annual cycle. In this way the authors could isolate two variables, the strength of the HC versus global temperature (controlled by the absorption of longwave radiation only).
The authors then establish a baseline climate for their aqua-planet. They ran the model with and without ocean dynamics. The results were more realistic with the ocean dynamics. Then, the longwave absorption, which is a function of latitude and pressure (height), is varied by a constant amount between 0.2 and 6.0 times the control value. This produces a global climate with planetary temperatures varying between 260 - 315 K (roughly 10°F and 110°F - today it is roughly 59°F). The equator-to-pole temperature differences decreased linearly with increasing temperature.
The strength of the HC did not change linearly (Fig. 1), and in fact the function is more parabolic in shape which makes the situation more complicated. The HC in their model was actually weaker in both very cold and very warm climates. Also, Fig. 1 implies that ocean dynamics becomes less important in determining the strength of the HC as climate warms. This is true because the equator-to-pole temperature difference becomes negligible. In colder climates, the weakening is the result of a more geostrophic, or zonal, atmospheric flow. A more zonal flow would imply less wave action in the jet stream, which means less energy exchange. Today's climate is roughly at the maximum in the ocean dynamics curve (Fig. 1).
Figure 1. (Adapted from Levine and Schneider, 2011 - their Fig. 4) The strength of HC in simulations with (solid, circles) and without (dashed, squares) ocean dynamics. Shown is the absolute value of the mass flux at the latitude of its maximum and at the level σc = 0.7, averaged for both hemispheres. The filled symbols are the reference simulations.
Then the behavior of atmospheric systems can be complicated even when there are few variables. This can lead to studies which find what at first blush seem to be contradictory results in, for example, a warmer climate. The behavior of changes in the strength of the HC is non-linear even in this simpler model. Then adding complexity to the model will make interpretation of the output more difficult. This stresses the importance of understanding the fundamental behavior of phenomena like the HC.