From Son et al 2010, based on the CCMVal ensemble of models, the decorrelation time of the Southern annular mode (SAM) plotted against the simulated latitude of the surface westerlies. Also included is an estimate from NCEP-NCAR reanalysis.
A series of studies over the past decade, starting with Thompson and Solomon 2002, have built a very strong case that the ozone hole in the Southern Hemisphere (SH) stratosphere has caused a poleward shift in the SH surface westerlies and associated eddy fields, especially during the southern summer. The poleward shift is often described as a trend towards a more positive phase of the Southern Annular Mode (SAM). The SAM is a mode of atmospheric internal variability characterized by north-south shifts in the surface westerlies.
The mechanism by which the ozone hole causes this poleward shift is a hot topic in dynamical meteorology. Not only is this response to the ozone hole important in itself, but related mechanisms likely govern the effects on the troposphere of stratospheric perturbations due to volcanic eruptions, the solar cycle, and internal variability. The starting point is the cooling of the lower stratosphere in the vicinity of the ozone hole, due to loss of UV absorption, thereby changing the north-south temperature gradient and associated wind fields in the lower stratosphere. But there are a lot of competing ideas about how altered lower stratospheric winds and temperatures in turn affect the fluxes of angular momentum that maintain the surface westerlies. (Some of my own lectures on the basic dynamics controlling the surface westerlies, including the key role of transport of angular momentum associated with the midlatitude storm tracks, can be found here.) GCMs consistently simulate a poleward shift in response to the ozone hole but of varying magnitude. They also consistently simulate a poleward shift due to increasing CO2.
AR4 was noncommital on the relative importance of greenhouse gases and the ozone hole for the observed SH wind shift. But a number of more recent papers have argued that this shift is primarily a response to ozone depletion, rather than CO2 (see Son et al 2010, Polvani et al 2011). Does this mean that the westerlies will bounce back as the ozone hole heals, assuming that we can continue to avoid emitting CFCs? When models are used to project into the future, this bounce back typically does not occur; the tendency for the winds to return equatorward is compensated, or overcompensated in some models, by the effects of the CO2 increase — the healing is projected to occur more slowly than did the generation of the ozone hole, so the CO2 -induced trend in these models is more competitive with the ozone-induced trend in the future.
But how do we judge the ability of a model to simulate forced shifts in the midlatitude westerlies?. Gerber et al 2010 provide a nice summary of a variety of tests applied to the CCMVal model ensemble to evaluate the realism of the simulated stratosphere-troposphere coupling. I focus here on one specific test, related to the internal variability of the Southern Annular Mode.
Projecting atmospheric variability in observations or models onto the SAM index, one gets a covariance that can be approximated by exponential decay with a decorrelation, or persistence, time in the summer of 15-20 days. But this time scale varies quite a bit from model to model. Plotting the decorrelation time in the CCMVal set of models against the latitude of the mean westerlies as simulated in each model, one gets the very nice result in the figure at the top of the post: models that place the climatological westerlies further equatorward have internal variability with more persistence. Importantly, the decorrelation time of the observed SAM (in reanalyses) and the observed latitude of the westerlies falls nicely on the model ensemble regression line.
One can try to think of the SAM as a damped degree of freedom forced by weather noise with a white spectrum and perturbed by a steady external “force” :
The magnitude of the perturbation to the annular mode index due to the force, , is proportional to the decorrelation time of the internal variability . This one-degree-of-freedom linear analysis is simplistic, but it has been supported, at least qualitatively, in a series of idealized GCM experiments (e.g., Ring and Plumb 2007). There is a considerable and growing literature on the application of more general “fluctuation-dissipation” relations in the analysis of climate responses. The generalization of this simple linear 1D result to a multi-dimensional set of climate indices or fields, or the full climate state for that matter, is
is now a matrix connecting the vector of steady forcings to the vector of responses , and is the covariance matrix of the unperturbed system in the space of interest. A good reference explaining the approximations underlying this expression, followed by an impressive application to the response of the global atmosphere to tropical heating, is Gritsun and Branstator, 2007.
So the decorrelation time of the SAM index may be one of the most important things to get right if we want to model the circulation responses to the ozone hole and to CO2. As the plot at the top indicates, it seems that if one’s SH summertime westerlies are simulated too far equatorward, this correlation time will be too large, and the response of the SAM to the ozone hole will be too large, holding everything else fixed. Results described in Son et al and by Kidson and Gerber 2010 suggest that this picture does explain some of the spread among model responses, although it is not the whole story.
added on July 27:
Ed Gerber and Soek-Woo Son kindly sent me the following plot, not in the Son et al paper:
The dots correspond to the CCMval-2 model integrations for the 1980-1999 period. The poleward displacement of the westerly wind maximum (x-axis) is plotted against the SAM time scale. Because O3 is simulated in these chemistry-climate models, responding to changing CFCs in particular, the O3 perturbations differ from model to model, so the displacement is normalized by the O3 perturbation at 50mb averaged over the region polewards of 64S (which assumes that the response to ozone is dominant). The average model displacement, removing this normalization, is about 0.5 degrees/decade. The observed displacement in ERA40 over this time frame is roughly twice as large. Ignoring one outlier, the slope connecting the displacement of the westerlies and the SAM time scale is of the expected sign but somewhat smaller than if the response were simply proportional to
The CCMVal model ensemble used for the plot at the top of the post is biased, on average, with the latitude of the SH summer westerlies too far equatorward, suggesting that we should reduce the magnitude of the response estimated from the mean of the whole ensemble accordingly. It is interesting that this adjustment happens to takes us in the wrong direction compared to ERA40 trend, which is larger than in most models, so there is still a lot of work to do to figure out exactly what is going on.
It is also interesting that the surface westerlies in SH summer are harder to get right than in any other season/hemisphere, as evidenced by the spread in model results (and personal experience). It also turns out that the annular mode time scale is largest here compared to other seasons and hemispheres. So it is hard to simulate for a good reason — the restoring forces are weak and the westerlies relatively easily perturbed by model errors.
Why is the latitude of the westerlies important for the SAM time scale? This restoring strength is known to be related to the interaction between storm track eddies and the midlatitude jet (see Lorenz and Hartmann 2001). There are a number of recent papers analyzing why this feedback is weaker when the surface westerlies and storm tracks are further polewards. (I find the study of Barnes et al 2010 particularly appealing). One interesting implication of this relationship is that as one pulls the westerlies polewards it should get more and more difficult to pull them even further polewards.
Can one take a similar approach, using the covariance structure of internal variability, to constrain global climate sensitivity? People are pursuing this, and it is certainly worth pursuing. The case of the SAM index and the tropospheric response to the ozone hole is nice in that this response has a structure that is very close to that of the SAM, a dominant mode of internal variability, so the argument that the decorrelation time of this mode is relevant is pretty compelling. The question in the global warming context is whether there are aspects of internal variability that resemble the forced response sufficiently — so we can have confidence that we are looking at the relevant restoring forces.
[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]