A comment on jovian greenhouse models

A comment on jovian greenhouse models

ICARUS 19,244-246 (1973) A Comment on Jovian Greenhouse Models L. TR’AFTON Astronomy Department and Received September Radiative greenhous...

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ICARUS

19,244-246

(1973)

A Comment

on Jovian

Greenhouse

Models

L. TR’AFTON Astronomy

Department

and

Received

September

Radiative greenhouse the temperature of the transport of heat.

McDonald Austin,

models lower

Observatory, Texas 78712

16, 1972; of Jupiter’s cloud level

Neglecting convection, Sagan and Mullen (1972) performed a two-level radiative equilibrium calculation to derive a temperature between 270 and 340°K at the “effective reflecting level” of Jupiter’s lower cloud layer. As a consequence, they suggest that water, its compounds, and solutions form this reflecting layer. They reconcile this result with the measured rotational temperatures by suggesting that these are means over two distinct layers, ammonia cirrus at 120°K and dense water cumulus at 270-340°K. Assuming that infrared abundances near the center of the Jovian disk refer to gas quantities overlying the lower cloud layer, their analysis overestimates the temperature at the top of the lower clouds by 64 124°K. The amount depends on which thermal opacities their models include and arises from their neglect of the convective heat transport. In the convecting layers of Jupiter’s atmosphere, the vertical atmospheric motion transports part of the heat. What this means is that the temperature gradient must be less than that for radiative equilibrium because the net energy flux is fixed by solar insolation and the internal source of heat. For a reflecting level fixed by the overlying gas abundances, the shallower temperature gradient causes this level to be cooler than the temperature predicted by the corresponding radiative solution. I pointed out (Trafton, 1967) that less than 3Okm-atm H, provides sufficient thermal opacity to bring about convection Copyright 0 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.

244

revised

University

November

atmosphere because they

of Texas

at Austin,

22, 1972 seriously neglect

the

overestimate convective

in the underlying layers of Jupiter’s atmosphere. A model which I have recently computed (cf., Wildey and Trafton, 197 1) verifies that the top of Jupiter’s convective zone lies near 142’K and underlies 20kmatm H,. These results are not sensitive to the likely range of He/HZ abundance ratios. The opacities include H, and the rotational band of ammonia. Table 1 compares P(T) for this radiative-convective model and for the corresponding model in purely radiative equilibrium. Comparison of radiative models should be made for common compositions and pressure levels. The radiative portion of Table 1 corresponds approximately to Sagan and Mullen’s HZ-NH, model, except that they include the vibrational bands of ammonia. The latter, however, have only a minor effect on the structure which can be estimated on the basis of a comparison with the H,-CH, model. Interpolating the opacities in their models, we find that the temperature of the lower cloud zone of their model including H, and only the rotational band of ammonia would be near 246°K. This result is directly comparable to the corresponding level of the radiative model in Table 1. Observed HZ abundances fall typically in the range 50-80km-atm for Jupiter. If we take 80km-atm H, above Jupiter’s lower cloud layer, this puts this layer at a temperature of 237°K and a pressure of 1.8 atm in the radia,tive model. The difference between this temperature and the 246°K of the corresponding model of Sagan and Mullen is presumably due to

JOVIAN

TABLE

I

P(T)STRUCT~REFORJUPITER

T (“K)

Radiative convective” 1ogP (c.g.s.)

Purely radiative 1ogP (c.g.s.)

100.5 102.3 104.4 105.0 105.6 106.1 106.6 107.1 108.7 110.3 112.5 113.8 114.9 116.0 117.1 119.0 120.7 122.3 123.7 126.4 128.8 131.0 133.1 135.1 137.0 141.8 146.6 151.4 156.4 164.5 170.4 181.4 190.1 204.5 216.0 225.9 234.6 242.3 258.7 272.4 284.2

3.783 3.934 4.173 4.325 4.436 4.587 4.675 4.738 4.889 4.987 5.091 5.140 5.180 5.214 5.244 5.294 5.335 5.369 5.399 5.450 5.491 5.526 5.556 5.583 5.608 5.659 5.704 5.750 5.795 5.865 5.913 6.000 6.067 6.171 6.250 6.315 6.370 6.417 6.515 6.591 6.655

5.659 5.702 5.738 5.769 5.822 5.866 5.936 5.991 6.076 6.140 6.192 6.236 6.273 6.350 6.409 6.458

a Convection begins starting tabulated values in the purely column. For lower temperatures, pressures in the two models are The point-by-point convergence 0.5% in the flux. The maximum is ratio is 6.7 x 10m4; ammonia to be saturated when its vapor gives a smaller mixing ratio.

with the radiative the the same. is to NHJH, assumed pressure

GREENHOUSE

245

their approximate treatment of the band transmissions and to a somewhat different choice of gas abundance overlying the lower cloud tops. In our radiative-convective model, this pressure level has a temperature of 2 16°K ; convection cools this level by 21°K. We note here that this result is compatible with a fairly transparent cloud layer at the 120°K level, at least for observations near the center of the disk. The essential point to realize now is that the addition of further thermal opacities, which are minor constituents to this radiative-convective model, will slightly elevate the top of the convective zone but leave the adiabatic gradient essentially unaltered. Adding such thermal opacities to the convecting region of the atmosphere does not affect the temperature of the lower cloud top (in the first approximation) as it definitely would if added to the purely radiative model. The radiative models of Sagan and Mullen illustrate the sensitivity of the lower cloud temperature to opacity. The 340°K value derived by including the opacity of water in their models is over 120°K higher than the temperature of the same pressure level in the same model where convective motion is permitted. These considerations suggest that the spectroscopically-determined temperatures really are representative of the absorbing layer and that any lower cloud layer is too cold to consist primarily of water cumulus clouds. My model neglects the high-altitude absorption of sunlight by methane, but this has only a small influence on the deeper structure because the magnitude of the internal heat source insures that convection occurs throughout this region. It remains to verify that the P(T) . relation in the convecting region (cf., Trafton, 1967) holds in spite of the short time constants for large scale dynamics in Jupiter’s atmosphere. Gierasch and Goody (1969) showed that this time constant is much shorter than that for radiative processes in these layers. Stone (1972), however, has recently shown that the Jovian atmospheric dynamics specify a lapse rate which differs from the convective

246

TRAFTON

one by only one part in 1 04. Since radiation to space sets a boundary value to the resulting P(T) relation, the use of a radiative-convective model for supporting my above conclusions should be adequate. REFERENCES

GIERASCH, P., AND GOODY, R.(1969).Radiative time constants J. Atmos. Sci.

in the 26, 979.

atmosphere

of Jupiter.

SAGAN,C.,ANDMULLEN,

G.(1972).TheJupiter greenhouse. Icarus 16, 397. STONE, P. (1972). A simplified radiativedynamical model for the static stability of rotating atmospheres. J. Atmos. Sci. 29, 405. TRAFTON, L. (1967). Model atmospheres of the major planets. Astrophys. J. 147, 765. WILDEY, R., AND TRAFTON, L.(1971).Studiesof Jupiter’s equatorial thermal limb darkening during the 1965 apparition. Astrophys. J. Suppl. 23, l-34.