Pendergrass and Hartmann (2014): The Atmospheric Energy Constraint on Global-Mean Precipitation

Understanding how the global-mean precipitation rate will change in response to a climate forcing is a useful thing to know. We have strong evidence that the hydrologic cycle will become more intense in response to CO2, but quantifying what drives this change is a bit more complicated, and can be understood from a few different perspectives. This paper takes a unique approach that really helped my understanding of the problem.

Pendergrass, A. G. and D. L. Hartmann, 2014: The Atmospheric Energy Constraint on Global-Mean Precipitation Change. J. Climate, 27, 757–768.

The approach of this paper is different than many previous papers that focus on the energy budget at the surface or the top of the atmosphere (TOA). Instead, the authors use the energy budget of the entire atmosphere itself. The authors show how the global-mean precipitation is constrained by the atmospheric cooling.

In the above equation for the global energy budget, latent and sensible heat fluxes (LE and SH) transfer energy from the surface to the atmosphere. On long time scales, evaporation (i.e LE) balances precipitation. Sensible heat flux is the turbulent transfer of heat, but it is generally much smaller than the latent or radiative energy flux. So, to first order, the main balance from this perspective is between radiation and precipitation. Radiation generally cools the atmosphere and precipitation generally warms it.

The novel aspect of this perspective that I had not appreciated before is how the atmosphere radiates out to space AS WELL AS down to the surface. This cooling to the surface can actually be a pretty large source of cooling.To illustrate how important this is, the authors put this really informative table from some idealized radiative calculations.

For example, the first row describes a uniform warming of the atmosphere, which increases the cooling to space by 2.3 W m2, but also increases downward emission to the surface by 3.3 W m2. There are plenty of other interesting examples here that I found useful to work through in my head.

TABLE 2. Clear-sky radiative response to various … changes at the TOA, [SFC, and ATM], calculated with Fu and Liou (1992) column radiation code. Signs are chosen so that a positive response contributes to increasing precipitation: increased cooling is positive for the atmospheric column, upwelling is positive at the TOA, and downwelling is positive at the surface. Note that the atmospheric cooling is the sum of net downwelling surface radiative flux and net upwelling TOA radiative flux: ATM = SFC + TOA…

A interesting result from this table is the different effects of moisture enhancement in the upper and lower troposphere. The 4th line of the table shows the longwave effect of uniformly increasing temperature by 1 K and adjusting the water vapor to maintain constant relative humidity. The result is increased cooling (and precip) mostly from the increase in downward emission from the atmosphere to the surface. The air near the surface is warmer, and consistent with Clausius–Clapeyron, the dew point should increase more in the lower troposphere, which means the absolute humidity will increase more in the lower troposphere than in the upper troposphere. The thing that I found surprising was that this means the response of precipitation depends on the vertical distribution of water vapor. A more humid upper troposphere could contribute to a reduction in precipitation. The authors also add this sentence about absorption bands, but I didn’t quite understand this.

“The wavelengths of water vapor continuum absorption are most important in determining surface emission, while upper tropospheric emission is determined by the wavelengths of rotation and vibrational bands (Mitchell et al. 1987; Inamdar et al. 2004).”

The authors go on to compare their calculations to CMIP5 model output, and the idealized calculations do a good job predicting the result of the models. They also do some idealized calculations of cloud effects which I found interesting. The shortwave effect of low clouds is often discussed in terms of a feedback mechanism, however they show here that the LW effect easily dominates the energy budget. Their idealized increase of high cloud amount has the strongest impact on global precipitation (see their table 4 below).

“Here we encounter one of the great advantages of the atmospheric energy budget perspective over the surface perspective: reflection of SW by clouds has little effect on the atmospheric energy budget. There is a modest change in SW absorption when clouds are present, but this is far overwhelmed by the clouds’ effects in the LW.”

TABLE 4. Radiative response (W m-2) to idealized clouds. As in previous tables, signs are chosen so that increased atmospheric cooling is positive.

This quote below was something I didn’t actually know. I always feel like an idiot when I read “It is well know…” followed by something I didn’t know…

“It is well known that the lapse rate and water vapor feedbacks compensate each other at the TOA (e.g., Cess 1975;Zhang et al. 1994; Soden and Held 2006; Held and Shell 2012).”

One last note, the energy budget framework can also be used to understand the consequences of geo-engineering scenarios that block incoming solar radiation to compensate the warming by CO2:

McCusker et al. (2012) performed an experiment in which global-mean surface temperature was held constant by increasing CO2 while simultaneously increasing sulfate aerosol… to compensate. …precipitation decreased steadily as CO2 and stratospheric sulfate aerosol increased….The CO2 forcing caused the atmospheric cooling rate to decrease. The temperature did not change, so the surface temperature-dependent responses of atmospheric radiative cooling also did not change. The sulfate aerosol acts by reflecting SW …, but this has little effect on the atmospheric energy budget and precipitation. The CO2 forcing can be viewed as directly suppressing the precipitation in this experiment, causing precipitation to decrease even without surface temperature change.


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