Temperature dependent atmospheric circulation models.

Author: MattVerey
Composed: 9/2/06
Last modified: 12/2/06

Abstract – pure speculation at how temperature change might alter the atmospheric circulation on Earth. Specifically, the number and interaction of convection cells are discussed. PLEASE BE AWARE: THIS IS PURE FICTION. THERE IS NO HARD EVIDENCE TO SUPPORT THE ALTERNATIVE MODELS PRESENTED. The true objective of this essay is to provoke the ire or interest of someone who does know about atmospheric circulation and have them tell me why the following models are correct or otherwise.

In Figure 1, the familiar present-day simplistic model of atmospheric circulation is shown on only one quarter of the Earth for clarity. This figure depicts the thermal equator coinciding with the geographic equator which approximates the conditions during the equinox. It is crucial to observe in each of the figures (1, 2 and 3), that the colours red and blue represent relative warm and cool temperatures (low and high pressures) within the cell and are not intended to be compared to other cells. In other words, the absolute average temperature of a given cell is expected to be different to another and has not been indicated in the figure. Note also the difference in thickness of the cells is only a reminder of the difference in the thickness of the troposphere at varying latitudes and is not drawn to scale. Also the size of the arrows depicting the prevailing advective wind do not correspond to the magnitude of those winds. Indeed, winds in the polar regions are some of the strongest on Earth. Jet streams are not shown, nor are any of the other atmospheric layers.

It is understood that due to the Coriolis force, the Earth has not one but three atmospheric cells: two strong conveyors of heat, the Hadley and Polar cells, and the weaker Ferrel cell which acts like a bearing between the two. This conventional explanation is not disputed here. What is examined is the effect of increased global average temperature (GAT) on these three cells. There are numerous assumptions that have been made in the proposal of the following models of atmospheric circulation. Some are more spurious than others. The first assumption is that any moderate rise in GAT will not fundamentally change the direction of flow of the the Hadley or Polar cells (depicted as a clockwise direction for the North-West quarter of the Earth shown in the figures). Due to the strength of these weather patterns, this is thought to be a reasonable assumption. A second assumption is that while the composition of the atmosphere is changing, its Prandtl number is not expected to change significantly. The third assumption is that the increase in GAT will result in an increased heat gradient across the vertical (altitude) of the troposphere. The fourth assumption is that an increase in the heat gradient is anticipated to result in a change in the geometry and number of the cells: specifically, the breaking up the flow of air in the Ferrel cell. In controlled conditions, using purpose built laboratory apparatus, it has been demonstrated that an increase the heat gradient across various fluids does result in a change in the geometry and number of the cells [1, 2, 3].

Figure 2 depicts an unlikely model where the Ferrel cell splits into two. This scenario assumes that if the Hadley and Polar cells maintain a clockwise rotation (with reference to the North-West quarter of the Earth depicted), the two newly generated cells will find wind shear conflict with at least one other cell regardless of which direction they turn. There are no known convection experiments that provide any analogues for this situation. Only if either the Hadley or Polar cell were to change direction would an arrangement be possible where the cells engage in synchronous rotation. Note that the geometry of each of the cells is assumed to span equally sized arcs across the quarter of the Earth shown (at the equinox). This assumption is based on the observations in [1, 2, 3] where the cells are of the same size.

The scenario in Figure 3 is considered to be somewhat more probable that that of Figure 2. Not only do the cells exhibit synchronous rotation with the Hadley and Polar cells it has been speculated that the two cells rotating counter clockwise (labeled Chaos cell A and Chaos cell B) will substitute for the variable weather patterns found in the present day Ferrel cell, but instead span a total of 36 degrees of the idealised equinox right angle as compared to the 30 degrees presently occupied by the Ferrel cell. This small but significant increase is speculated to reflect the trend toward turbulence as heat gradients increase. Important factors that might prevent this scenario from occurring are firstly the annual fluctuation of the thermal equator by 23 degrees north and south of the geographic equator. This would result in a 23/5 degree reduction or increase in the latitudinal regions covered by each cell such that each cell influences somewhere between about 13 and 23 degrees. It is possible, for example, that a cell region spanning only 13 degrees (about 1400 Km) could be too unstable. It is for this reason that a scenario of seven cells appears to be even more unlikely. Secondly, the transition from three to five cells may require extremely unfavourable conditions, even if it were found that the five cell scenario were more energetically favorable. It might be the case that the transition phase involve the four cell scenario, which would appear to be very energetically unfavourable.

If in fact the five cell scenario in Figure 3 is possible and has or will occur in the history of the Earth, it is interesting to note the effect it would have on the heat gradient from equator to pole. Extra cells would slow the transfer of heat and might have the effect of preserving the ice sheets in the polar regions, assuming the vertical heat gradient needed to induce this scenario didn't require the regions to melt first.

1. http://www.nls.physics.ucsb.edu/papers/HEA97_PRE.pdf
2. http://www.nls.physics.ucsb.edu/papers/TBA01.pdf
3. http://www.isi.edu/~lerman/binmix/My_work.html