Posted on November 15th, 2014 in Isaac Held's Blog
Fractional change in global mean precipitation (blue) and global mean (horizontally and vertically integrated) water vapor (red) as a function of change in global mean surface air temperature, over the 21st century in the A1B scenario in CMIP3 models. Redrawn from fig. 2 in Held and Soden 2006.
The figure at the top describes a very robust result in the responses to warming in global climate models: the fractional increase in the total amount of water vapor in the atmosphere is much larger than the fractional increase in global mean precipitation. While this figure shows the responses in CMIP3 models for a particular scenario of increasing forcing over the 21st century, the results from CMIP5 and different scenarios are all similar. This disparity in the magnitude of the increases in water vapor and precipitation and its important consequences for many other aspects of the climate response have been discussed since relatively early days in GCM simulations of climate change (e.g., Mitchell et al 1987). Perhaps the most fundamental consequence is the reduction in the vertical mass exchange between the lower and upper troposphere. That is, the “amount of convection” in the atmosphere decreases — or, by this particular measure, the atmospheric circulation slows down, especially in the tropics where a large fraction of this exchange takes place.
The connection with the atmospheric circulation is most easily understood by a simple argument that goes back at least to Betts and Ridgway 1988. Think of a picture in which parcels of air leave the boundary layer and enter the drier free troposphere, carrying a mass of dry air per unit time and unit area and therefore carrying the water vapor , where is the mixing ratio (the ratio of the mass of water vapor to the mass of dry air) in the boundary layer. The same amount of mass returns to the boundary layer carrying where is a typical mixing ratio in the returning air, which is a lot drier. The water that is lost equals the precipitation. Suppose that is negligible compared to so that the precipitation is . Since the vertically integrated water vapor is dominated by the vapor in the lowest few kilometers, will look like the integrated water vapor in the figure at the top. If the precipitation increases more slowly, the mass flux must decrease. If is not negligible and does not change proportionally to then this will change the quantitative result, but with small compared to the qualitative result should hold up. (In response to an email: you can think of this exchange of air as partly in shallow non-precipitating circulations for which and partly in deeper precipitation-generating circulations; if this distinction is sharp then it is only the mass flux in the deeper precipitation-generating flows that are constrained in this way.)
The slope in the temperature vs total water vapor plot is about what you expect from the Clausius-Clapeyron (C-C) dependence of saturation vapor pressure on temperature, but you have to be a little careful. For example, Back et al 2013 point out that the proportionality constant is smaller for more equilibrated climate changes, like glacial-interglacial differences. This is because the ratio of tropical warming to global warming is smaller when the climate is more equilibrated due to greater warming in polar latitudes, especially in the Southern Hemisphere. Since water vapor is dominated by the tropics, you get get less increase per unit global warming. But the bottom line is that fixed relative humidity in the lower troposphere still explains the results to first approximation. The proportionality constant is well-defined in the figure because the spatial patterns of warming are similar enough across these different models that there is a consistent relation between the changes in the globally averaged saturation vapor pressure in the lower troposphere and the globally averaged temperature change. As discussed in post #48, models beautifully reproduce satellite observations of vertically integrated water vapor averaged over the tropical oceans when these models use observed ocean surface temperatures as a boundary condition. So I think the relation between total water vapor vs temperature is very solid.
The global strength of the hydrological cycle is not determined by the C-C scaling but rather by the the energy balance of the free troposphere, the troposphere above the planetary boundary layer, where the release of latent heat associated with precipitation balances the radiative cooling to first approximation — see O’Gorman et al, 2012 for a recent review. (Focusing on the troposphere above the boundary layer allows you to avoid thinking about the turbulent sensible heat flux which is important in the boundary layer.) The radiative transfer is such that the radiative cooling (in our models) just can’t increase fast enough to keep up with the C-C increase in water vapor. If the atmosphere tries to increase precipitation a lot without balancing it with increased radiative cooling, the free troposphere will warm, creating a more stable environment which will eventually reduce the mass exchange and precipitation to rebalance things. It is interesting to explore the routes by which this rebalancing occurs, but whatever the mechanisms the reduction in mass exchange needs to occur for the atmosphere to re-equilibrate.
The observational record is not nearly as clear cut in this respect. In fact, there are claims (Wentz et al, 2007) that precipitation has increased at close to the C-C rate over the satellite era. Others see differences between models and observations in the tropics but estimate weaker overall trends in mean precipitation (see the O’Gorman et al review for some references). I am not aware of a convincing proposal for how atmospheric radiative cooling can increase by the amount needed to balance such a large increase in precipitation per unit warming– so my working hypothesis is that there is, in fact, a substantial difference between the rates of increase of water vapor and precipitation with warming. It is important to clarify this issue. Its resolution can affect estimates of climate sensitivity as well as circulation changes. You can change the atmospheric cooling of the free troposphere by either changing the fluxes at the tropopause or at the top of the boundary layer. If you do it at the tropopause you also affect climate sensitivity, with increasing radiative cooling per unit warming decreasing temperature sensitivity while increasing the sensitivity of the mean precipitation. If you do it at the bottom of the free troposphere without compensating changes at the top, as is the case if you modify how the absorption of solar radiation responds to warming you change the precipitation sensitivity with minimal change in temperature sensitivity. (modified for clarity on Nov. 17)
Regarding circulation changes, it is sometimes assumed that a reduction in vertical mass exchange in the troposphere, dominated by the tropics, would result in weaker mean tropical circulations — weaker Hadley and Walker circulations in particular. This doesn’t necessarily follow. A simple (oversimplified) picture of the tropics that I have discussed before in these pages is that most of the air is descending at a rate determined by the radiative cooling, with upward motion confined to a relatively small fraction of the area. If there are more than the average number of plumes of rising air in some large region, the Western Pacific warm pool or the ITCZ in the eastern Pacific say, the mean motion is upward, while the mean motion is downward where convective plumes are relatively scarce. In the regions of mean upward motion there has to be convergence of air at low levels, and low level divergence out of the regions with mean descent – and the surface flow can be thought of a driven by this pattern of convergence and divergence (rotation makes the connection between this convergence/divergence pattern and the flow itself a little counterintuitive). The average of the north-south flow around latitude circles is referred to as the Hadley circulation, while the Walker circulation is a strong westward flow at low levels over the Pacific. Even if the total mass exchange decreases, if the patten of convection becomes more organized the large-scale circulation could be enhanced — for example, if more convection moved to the regions where convection is already prevalent and even less occurred in the relatively quiescent regions.
But having said all that, if not much happens to the pattern of convection, you would expect the large-scale circulation to weaken on average. In models a lot of this weakening occurs in the east-west Walker circulation rather than the north-south Hadley circulation. It seems like the latter is prevented by other constraints from changing as much. Models generally do predict a weakening Walker circulation with warming, and I think that this overall weakening of the mass exchange in the tropics is part of the explanation for this model result. And this did seem to be an emerging signal in observations (Vecchi et al 2006) — until the recent 15 years or so in which the continuing hiatus/persistent La Nina/strong Walker circulation has muddied the picture of what the long-term forced trend might be. (I hope to return to this issue soon.)
[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.]