Results from a high resolution model of horizontally homogeneous radiative-convective equilibrium, Romps 2011. Left: equilibrium temperature profiles for 3 values of CO2 compared to an observed tropical profile. Right: the temperature differences compared to the response to doubling CO2 in an ensemble of CMIP3 global climate models.
As a moist parcel of air ascends it cools as it expands and does work against the rest of the atmosphere. If this were the only thing going on, the temperature of the parcel would decrease at 9.8K/km. But once the water vapor in the parcel reaches saturation some of this vapor condenses and releases its latent heat, compensating for some of the cooling (you get about 45K of warming from latent heat release when a typical parcel rises from the tropical surface to the upper troposphere). A warmer parcel contains more water vapor when it becomes saturated, so it condenses more vapor as it rises, and temperature decreases with height more slowly. That is, the moist adiabatic lapse rate, , decreases with warming.
To say something about the warming of the tropical atmosphere, rather than that of a moist adiabat, we need to argue that the tropical troposphere is close to a moist adiabat and remains close as it warms. The upper troposphere will then warm more than the lower troposphere. This is precisely what happens in our global climate models. The consistency or inconsistency of this prediction with observations, particularly the Microwave Sounding Unit (MSU) temperatures, is a long-standing and important issue A failure of the upper troposphere to warm as much as anticpated by this simple argument would signal a destabilization of the tropics — rising parcels would experience a larger density difference with their environment, creating more intense vertical accelerations — affecting all tropical phenomena involving deep convection. I like to refer to warming following the moist adiabat as the most “conservative” possible — having the least impact on tropical meteorology.
(One sometimes sees the argument that a consequence of smaller upper tropospheric warming in the tropics would be lower climate sensitivity, since a large fraction of water vapor feedback originates in this region, and the large vapor increase could not occur without the temperature increase. But this is not the case, because of the cancellation between negative lapse rate and positive water vapor feedbacks produced by upper tropospheric warming. In fact, the negative lapse rate feedback is generally the larger of the two, so a weaker upper level tropical warming would probably increase climate sensitivity a bit, holding everything else fixed.) [This statement continues to be a source of confusion -- sorry -- see discussion in the comments. The water vapor feedback that I am referring to here is the part associated with the lapse rate change, if relative humidity is fixed, after subtracting off the part due to uniform warming of the troposphere (IH- Jan 26, 2013)]
The tropical atmosphere, and models of moist radiative-convective equilibrium, are dominated by concentrated saturated updrafts taking up a small fraction of the total area, with the rest of the flow experiencing very slow compensating subsidence. The behavior of such a skewed flow field can be counterintuitive. The picture that most of us have, I think, is that within the convective updrafts themselves the temperature profile takes its moist adiabatic value; this profile is then communicated efficiently to the rest of the tropics, since the atmosphere is unable to maintain substantial horizontal temperature gradients within the tropics. Horizontal gradients in pressure and temperature, above the boundary layer, are flattened by wave propagation rather than by mixing, a fundamentally different process than the homogenization of entropy in a dry convecting layer.
I remain somewhat confused as to how best to translate this picture into a scaling argument for how hard one has to push the tropical atmosphere to create a given departure from the moist adiabat. Arguments of the type summarized in Emanuel, Neelin, and Bretherton, 1994 suggest that attempts to alter the free tropospheric temperature profile will modify temperatures by a rather indirect path — heating perturbations will modify the circulation in a way that then modifies the temperature and humidity of the air near the surface, which finally puts you on a different moist adiabat. The calculations by Kuang 2010 in which a dynamic model of radiative-convective equilibrium is perturbed systematically with different heat (and moisture) sources suggests that this is the path of least resistance for a convecting atmosphere, but that there are other possibilities as well — I need to understand this paper better.
It doesn’t take much of a departure form an adiabat to be dynamically significant. A 3K temperature difference between parcel and environment averaged over a height naively produces an acceleration of and velocities at the top of the convective layer of — which is larger than vertical motions observed in tropical convection. But it is not that easy to relate vertical motions quantitatively to departures from an adiabat in the tropics. There are subtleties in the definition of the moist adiabat itself associated with what happens to the condensate — temperatures are slightly different if the condensate is retained by the parcel, in which case its heat capacity must also be taken into account, or if the condensate falls out immediately, in which case we refer to the “pseudo-adiabatic” lapse rate. Real parcels are somewhere between these two extremes. You also needs to worry about the latent heat of fusion when ice forms, the presence of supercooled water making it tricky to predict when this transition to ice occurs. In addition, when computing the density difference between a rising parcel and its environment, and the associated vertical accelerations, you must account for the “condensate loading” — the pressures associated with the suspension of the condensate within the rising parcel. Finally, if a parcel entrains some dry environmental air as it rises, it has less latent heat to release per unit mass, and its temperatures will fall faster with height than the temperature profile generated by an undilute parcel.
Several of these effects can be of the order of a degree or two — they are big enough to matter when trying to estimate the magnitude of the departure of the tropical atmosphere from a moist adiabat — the CAPE (Convective Available Potential Energy) of the tropics (see, for example, Xu and Emanuel 1989 and Williams and Renno 1993). But none of them are large enough to alter the expectation that the tropical atmosphere will roughly follow a moist adiabat as it warms. One of these effects would have to change by an O(1) amount (doubling or halving its amplitude) in response to a 2K warming, say, to have a substantial effect on the sensitivity of lapse rates to warming, but why should that happen?
This conclusion is confirmed by high resolution models of horizontally homogeneous radiative-convective equilibrium, every one of which, to my knowledge, predicts a warming profile that is more or less moist adiabatic. The figure at the top is from Romps 2011, mentioned in the last post as well, which has 200m horizontal resolution. The figure on the left shows the model’s equilibrated temperature profiles at three values of CO2 along with an observed tropical profile, while the panel on the right shows the changes in temperature in this model along with an average over CMIP3 global models (with grid sizes roughly 100 times larger). The profile of temperature change is essentially identical. There is actually a rather large fractional increase in CAPE and increase in the magnitude of vertical motions as the climate warms in these simulations, but this increase is nowhere near large enough to compensate for the upper level maximum in warming.
(The fact that the overall amplitude of the warming for doubled CO2 is nearly identical in the ensemble mean of GCMs and in this cloud resolving model is a coincidence — it is the vertical profile of the temperature change that I am focusing on here. The variety of results on sensitivity with cloud resolving models of radiative-convective equilibrium is as large as that obtained with GCMs, due primarily to differing cloud feedbacks associated with differences in organization of convection. These high resolution simulations are not necessarily more relevant to nature than GCMs, due to the idealized geometry and small domain, absence of rotation etc. The value of these dynamic radiative convective equilibrium models, even in these small idealized domains, is in testing our undersatanding of moist convection. )
The change in CO2 itself has very little to do with this moist adiabatic response; you get essentially the same temperature response if you just just prescribe and then warm the surface temperature. Here, for example, is an early attempt at a dynamic radiative-convective model, from Held et al, 1993, for a 5K surface warming with fixed CO2 (the solid lines are moist adiabats):
A dramatic change in convective organization can change the relevant moist adiabat constraining tropical temperatures. The self-aggregation transition described in the previous post, is a good example. The aggregated state is warmer by several degrees averaged over the troposphere than the state with more homogeneous convection, because the near surface relative humidity is higher in the region in which the convection is occurring — due, in turn, to increased winds and evaporation. (Thanks to Caroline Muller for confirming this for me.)
As one moves upwards and convection peters out, there is presumably some potential to change local temperatures with local perturbations in ozone or aerosols, perhaps above 12 km or so. But below that, if you are trying to change the relationship between surface and tropospheric warming, it seems that one is better off trying to change the relevant moist adiabat, by changing low level humidities or temperatures in the convecting regions, rather than creating huge departures from a moist adiabatic profile.
In addition to the analyses of MSU temperatures (which I won’t try to summarize here) , there is other relevlant observational work that we need to focus on. One is the study of Allen and Sherwood 2008, using thermal wind balance to relate trends in the vertical gradient of the zonal winds to trends in the north-south temperature gradient The thermal wind equation is very accurate for zonal mean winds throughout the atmosphere, a simple consequence of the assumptions that the mean state of the atmosphere is in hydrostatic balance and that winds are in geostrophic balance. One can use an even more accurate relation, gradient wind balance, but given the large uncertainties in atmospheric warming trends, thermal wind balance is certainly accurate enough. I would like to see more attention on this use of wind trends, since these are totally independent of the temperature measurements, satellite or radiosonde.
Another study deserving attention is Johnson and Xie 2010 which argues that one can look at the distribution of deep convection in the tropics and rule out a trend towards overall destabilization. The temperature (and associated water vapor content) of near surface air has to reach a certain threshold for this air to rise close to the tropopause — currently 26-28C. If the atmosphere follows a moist adiabat as it warms, this critical temperature will increase along with the surface warming. If the upper troposphere does not keep up, this critical temperature would not increase as fast as the surface temperature itself, favoring more widespread convection — which, according to the paper, is not observed. This is another paper that I have to think about more carefully.
[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.]