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Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity

Article Link

Manabe, Syukuro and Richard T. Wetherald, 1967. Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity. Journal of Atmospheric Science 24, 241-259.

Essay about this article

General circulation models (GCMs) trace their origins to the work of Norman Phillips (1956) who focused on emulating the dynamics of atmospheric flows. In the decades that followed, Syukuro Manabe led a team at NOAA’s Geophysical Fluid Dynamics Lab that extended this work to diagnostic climate models that incorporated additional complexity.

In 1967 Manabe and Wetherald presented a radiative-convective model of the atmosphere with a given distribution of relative humidity in order to investigate the important issue of climate sensitivity. The model was designed so that net incoming solar radiation was equal to net outgoing longwave radiation at the top of the atmosphere and there were no internal temperature discontinuities. The surface equilibrium temperature of their model and the vertical temperature structure were extremely sensitive to changes in factors such as the solar constant and the concentrations of ozone and carbon dioxide. In addition, a new requirement was added, that the atmosphere maintain a specified vertical distribution of relative humidity. This meant that water vapor and cloud feedbacks increased with increasing temperature.

The model contained representations of low, middle, and high clouds, which have very different radiative properties. Low and middle clouds tend to cool the climate, while high clouds can cause additional warming. Manabe and Wetherald predicted that heating caused by a doubling of CO2 could be offset by a ten percent increase in low or middle clouds. On the other hand the amplifying effect of a twenty percent increase in high clouds could itself double the effect of increased CO2.

Manabe and Wetherald computed a ±0.033 oC temperature sensitivity for a ±1 percent change in CO2 concentration. This was later adjusted to ±0.027 oC. A doubling of the CO2 content in the model had the effect of raising the temperature of the atmosphere by about 2.3 oC. This model was also used to study the radiative properties of the stratosphere. The National Academy of Sciences was concerned about a possible increase of water vapor in the stratosphere for a fleet of proposed supersonic transport (SST) airplanes. Manabe and Wetherald concluded that a five-fold increase of stratospheric water vapor would cause an unacceptably high 2 oC increase in surface temperature. They also pointed out that the stratosphere would be expected to cool with increasing concentrations of CO2.

This influential one-dimensional model produced convincing results and constituted an important step toward the ultimate goal of designing realistic three-dimensional climate models that account for additional factors such as oceans, ice sheets, and even weather patterns (Manabe, 1997).

Discussion Questions

a. What is a radiative-convective model of the atmosphere, and why is holding relative humidity constant an important approximation?

b. Using Moore’s “law” describing a long-term trend in the history of computing hardware, estimate the power of the largest computer of 1967 compared to (i) the largest computer today and (ii) a desktop personal computer.

c. What is a one-dimensional model, compared to a three-dimensional one?


Manabe, S., 1997. Early development in the study of greenhouse warming: The emergence of climate models. Ambio 26, 47-51.

Phillips, N.A., 1956. The General Circulation of the Atmosphere: A numerical experiment. Quart. J. Roy. Meteorol. Soc. 82, 123-164.

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Select articles citing this paper

Cess, R. D., G. L. Potter, et al. (1990). "INTERCOMPARISON AND INTERPRETATION OF CLIMATE FEEDBACK PROCESSES IN 19 ATMOSPHERIC GENERAL-CIRCULATION MODELS." Journal of Geophysical Research-Atmospheres 95(D10): 16601-16615.

Chylek, P., U. Lohmann, et al. (2007). "Limits on climate sensitivity derived from recent satellite and surface observations." Journal of Geophysical Research-Atmospheres 112(D24).

Huang, Y. and V. Ramaswamy (2007). "Effect of the temperature dependence of gas absorption in climate feedback." Journal of Geophysical Research-Atmospheres 112(D7).


Lilly, D. K. (1968). "MODELS OF CLOUD-TOPPED MIXED LAYERS UNDER A STRONG INVERSION." Quarterly Journal of the Royal Meteorological Society 94(401): 292-&.


Manabe, S. and R. J. Stouffer (1980). "SENSITIVITY OF A GLOBAL CLIMATE MODEL TO AN INCREASE OF CO2 CONCENTRATION IN THE ATMOSPHERE." Journal of Geophysical Research-Oceans and Atmospheres 85(NC10): 5529-5554.

Manabe, S. and R. T. Wetherald (1975). "EFFECTS OF DOUBLING CO2 CONCENTRATION ON CLIMATE OF A GENERAL CIRCULATION MODEL." Journal of the Atmospheric Sciences 32(1): 3-15.

Pierrehumbert, R. T. (1995). "THERMOSTATS, RADIATOR FINS, AND THE LOCAL RUNAWAY GREENHOUSE." Journal of the Atmospheric Sciences 52(10): 1784-1806.

Ramanathan, V., R. J. Cicerone, et al. (1985). "TRACE GAS TRENDS AND THEIR POTENTIAL ROLE IN CLIMATE CHANGE." Journal of Geophysical Research-Atmospheres 90(ND3): 5547-5566.

Schwarzkopf, M. D. and V. Ramaswamy (2008). "Evolution of stratospheric temperature in the 20th century." Geophysical Research Letters 35(3).

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