Effects of greenhouse gases on Earth, Venus, and Mars: Beyond the one-blanket model^a)

The author has covered this material in one week (three hours of lecture) immediately following a discussion of thermal radiation and its Planck spectrum.

R. T.

Pierrehumbert

, ( ., , ).

R. T.

Pierrehumbert

, ( ., , ).

T

Schneider

, “ ,” (). <http://climate-dynamics.org/wp-content/uploads/2017/04/Climate_Book.pdf>

R.

Wolfson

, , ( ., , ).

R. L.

Jaffe

and

W.

Taylor

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A. P.

Ingersoll

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F. W.

Taylor

, ( ., , ).

F. W.

Taylor

, ( ., , ).

J.-L.

Dufresne

,

V.

Eymet

,

C.

Crevoisier

, and

J.-Y.

Grandpeix

, “ ,” (), – ().

S. E.

Schwartz

, “ ,” (), – ().

S. E.

Schwartz

, “ ,” (), – ().

Y.

Huang

and

M. B.

Shahabadi

, “ ,” (), –, https://doi.org/10.1002/2014JD022466 ().

R. T.

Pierrehumbert

, “ ,” (), – ().

A.

Tomizuka

, “ ,” (), – ().

P. G.

Sieg

,

W.

Berner

,

P. K.

Harnish

, and

P. C.

Nelson

, “ ,” (), – ().

See <https://www.youtube.com/watch?v=0eI9zxZoipA> for this classroom demonstration.

In the case of Earth, there are also reflective polar icecaps, aerosols, and so on. Although we are not yet including the effects of atmosphere, we have incorporated such reflection in the data of the table via the $R$ values. Specifically, $R$ is the reflectivity averaged over the frequency range typical of the solar spectrum.

Each planet (and even some moons) also has internal energy production (geothermal energy), but this source is negligibly small for the three we have chosen to study (Ref. 4, Sec. 2.5).

The table lists distance values computed simply as the average of the closest and farthest points on each planet's orbit.

Perhaps surprisingly, even snow and ice have high IR absorptivity and, hence, also high emissivity.

Note that if Earth were literally stripped of atmosphere, then its reflectivity, currently dominated by clouds, would change, affecting the prediction. The point of the estimate made here is simply the inadequacy of neglecting absorption in the atmosphere.

The outlines of this story were already clear in the 19th century, shortly after W. Herschel's discovery of IR radiation. J. Fourier understood the role of energy balance between incoming short-wavelength and outgoing IR radiation in 1827, as well as the potential role of the atmosphere. J. Tyndall then measured the absorption spectra of many gases and correctly identified carbon dioxide and water vapor as critical for climate in 1863. At the very end of the century, S. Arrhenius constructed a simplified, but self-consistent model based in part on Tyndall's data. Modern discussions can be found in Refs. 3, 13, and 10.

P.

Pilewskie

, “ ,” , Seattle, WA, January, . <https://ams.confex.com/ams/97Annual/webprogram/Paper309519.html>

For an undergraduate laboratory measurement, see Ref. 54.

This quantity is not a “rate” in the sense of change per time. Rather, it is a spatial gradient.

K.

Stamnes

,

G. E.

Thomas

, and

J. J.

Stamnes

, , ( ., , ).

A.

Seiff

, “ ,” in , edited by

D. M.

Hunten

,

L.

Colin

,

T. M.

Donahue

, and

V. I.

Moroz

( , , ), Chap. 11, pp. –.

Rising warm air expands and, hence, cools, losing its buoyancy, so there is a minimal value for the gradient before convection turns on.

For a more detailed derivation, see Ref. 6, §34.2.2. Reference 3, p. 150 gives another detailed derivation, concluding $T surf / T last = ( p surf / p last ) R / c p$⁠, where R is the gas constant and $c p , mol$ is the specific heat at constant pressure, per mole. Substituting the exponential dependence of pressure with altitude, Taylor expanding the exponential and keeping up to linear order recovers the linear relation in the main text.

A convecting region of atmosphere with the critical lapse rate is also said to follow the “dry adiabat.”

For details, see Ref. 3. S. Manabe shared a Nobel Prize in 2021 in part for early work on radiative transport, on the role of convection, and on incorporating the effects of water condensation into a climate model.

Section V will improve upon this simplification. We continue to assume that absorption cross section is negligibly small in the visible range.

Reference 15 gives an improved formula, which, however, is numerically close to the exponential for Earth's troposphere.

We are avoiding a full radiative transport treatment; for that, see Ref. 27.

See Refs. 3 and 9. $T last$ is sometimes called the “emitting” temperature, in contrast with a lower “skin” temperature.

Changing the amount of a noncondensing trace molecule, such as carbon dioxide in Earth's atmosphere, makes a negligible change in the specific heat and, hence, in the critical lapse rate.

D. M.

Romps

,

J. T.

Seeley

, and

J. P.

Edman

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A.

Dudhia

, “ ,” , – ().

Y.

Huang

,

V.

Ramaswamy

,

X.

Huang

,

Q.

Fu

, and

C.

Bardeen

, “ ,” (), –, https://doi.org/10.1029/2007GL031409 ().

Some students will be interested to hear that this “decoupling” phenomenon is analogous to the epoch of recombination in the early Universe, after which thermal photons go out of equilibrium with matter.

M. G.

Mlynczak

,

T. S.

Daniels

,

D. P.

Kratz

,

D. R.

Feldman

,

W. D.

Collins

,

E. J.

Mlawer

,

M. J.

Alvarado

,

J. E.

Lawler

,

L. W.

Anderson

,

D. W.

Fahey

,

L. A.

Hunt

, and

J. C.

Mast

, “ ,” (), –, https://doi.org/10.1002/2016GL068837 ().

The addition of gases not naturally present in the atmosphere, such as chlorofluorocarbons, can also create entirely new absorption bands in what was previously a window region.

Thus, the spectral properties of greenhouse gases change with altitude, another complication that must be addressed in a full treatment. Indeed, on other planets with extremely high pressures, even O₂ and N₂ become IR-active.

Although carbon dioxide has a window of IR transparency, droplets of sulfuric acid forming clouds over Venus trap emission even in that spectral region.

A. P.

Ingersoll

, “ ,” (), ().

Confusingly, there are at least two different processes referred to as “weathering.” Here, we mean the conversion of silicate rocks via the Urey reaction (Ref. 2). On Earth, photosynthesis by marine organisms also removes $CO 2$ from air; they eventually fall to the bottom of the ocean, carrying their fixed carbon into sediments that ultimately reenter Earth's crust, another part of the carbon cycle that relies on liquid water (and mild temperatures). (Terrestrial plants are much less effective; much of their carbon is released back to the atmosphere after they die and decompose.)

The remaining free oxygen may, in turn, have been removed from the atmosphere, for example, by oxidizing crustal elements such as iron. Earth, too, had very little free oxygen prior to the rise of photosynthetic organisms.

N.

Jeevanjee

,

J. T.

Seeley

,

D.

Paynter

, and

S.

Fueglistaler

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Y.

Huang

,

Y.

Xia

, and

X.

Tan

, “ ,” (), –, https://doi.org/10.1002/2017JD027221 ().

Y.

Huang

,

X.

Tan

, and

Y.

Xia

, “ ,” (), –, https://doi.org/10.1002/2015JD024569 ().

T. M.

Merlis

, “ ,” (), – ().

Y.

Huang

and

M.

Zhang

, “ ,” (), –, https://doi.org/10.1002/2013GL059079 ().

G. T.

Blanchard

,

F. A.

Adesina

,

W. C.

Belkwell

,

J. R.

Dyess

,

V. A.

Frabbiele

,

C.

McGibboney

, and

R. D.

Rumsey

, “ ,” (), – ().