On the scattering-greenhouse effect of CO2 ice clouds

We offer some remarks on the greenhouse effect due to high clouds which reflect thermal infrared radiation, but do not absorb or emit it. Such clouds are an idealization of the CO2-ice clouds which are thought to have existed early in the history of Mars. Clouds of this type enter also in the ability of the Earth to recover from a globally glaciated "cold start," and in the determination of habitable zones of planetary systems. A simplified model of cloud optical effects is used to estimate the effect of high CO2-ice clouds on the planetary radiation budget in the solar and infrared spectrum. It is argued that the scattering greenhouse effect certainly cancels out a large part of the cooling effect due to the cloud's visible albedo, and in some circumstances may even lead to a net warming as compared to the no-cloud case. Speculative implications for the climate of Early Mars are discussed. Scattering Greenhouse Effect on Early Mars Page 3 Indications that young Mars was warm enough to support flowing water present a continuing enigma (Squyres and Kasting 1994). Kasting (1991) showed that, owing to the effects of CO2 condensation on temperature lapse rate, the phenomenon cannot be accounted for on the basis of a CO2 greenhouse effect. Kasting did not model the optical effects of CO2-ice clouds, but remarked that because CO2-ice (unlike water-ice) has very low infrared absorbance, CO2-ice clouds should cool the planet through reflection of solar radiation uncompensated by infrared trapping. The formation of CO2-ice clouds also affects the prospects of recovery of the early Earth from a "cold start" (Caldeira and Kasting 1992), and the extent of the habitable zone around stars (Kasting et al 1993). Kasting (1991) also noted that infrared scattering is important in CO2-ice clouds. The purpose of this Note is to point out the existence of an infrared-scattering greenhouse effect due to high CO2 clouds, which is strong enough to have major climatic effects under Early Mars conditions. We can argue with some confidence that the effect is strong enough to cancel out a substantial portion of the cooling that would ordinarily result from the visible albedo of the CO2 clouds. However, our calculations are too idealized to provide a definitive answer to the question of whether the scattering greenhouse effect is potent enough to lead to a net cloud-induced warming of the planet. An early discussion of the scattering greenhouse effect in the context of Venus can be found in Samuelsen (1967,1969). Infrared scattering by clouds has been extensively studied as a means of accounting for the observed infrared spectrum of Mars (Forget 1995) and Venus (Pollack et al 1993; Crisp et al 1991). The scattering greenhouse effect has some impact on the polar climate of the present Mars (Forget and Pollack 1996). McKay et al. (1989) considered the impact of the scattering greenhouse effect of methane clouds on the climate of Titan, though the effect there turned out to be inconsequential for cloud parameters consistent with spectroscopic observations of the satellite. We will argue in the following that, in contrast, the scattering greenhouse effect of CO2 clouds could have had a highly significant effect on the climate of Early Mars. Since the scattering greenhouse effect is not widely appreciated, and since it operates rather differently from the conventional absorption/emission greenhouse effect, it is useful to see how it works in a highly idealized setting. Our calculation also serves this didactic purpose. Consider an atmosphere-clad planet with net albedo o in the solar spectrum. If it is illuminated by a solar flux So and radiates infrared to space at a rate Io, it is in equilibrium when (1o)So = Io. Now introduce a high CO2-ice cloud with albedo c in the visible and c' in the infrared, but which absorbs neither solar nor infrared radiation. Scattering Greenhouse Effect on Early Mars Page 4 This perturbs both the solar and infrared terms in the radiation budget, as shown in Fig. 1. Let the cloud be high enough that it is above virtually all of the infrared-radiating mass of the atmosphere, and suppose that the subcloud atmosphere-surface system is a perfect infrared absorber. Taking into account the effects of multiple scattering between the high cloud and the subcloud regions, the cloud changes the planetary solar albedo to = c + o { (1c)2/(1c o) }. (1.) If I1 is the upward infrared flux from the subcloud atmosphere, the flux escaping to space is (1c')I1. To restore equilibrium with the insolation So, the temperature must change so as to make I1 = { (1 )/(1c') }So. The I1 required to balance the absorbed solar radiation becomes infinite if c' 1 with <1, in which case the planetary temperature also becomes infinite. In this limit, the cloud acts like a one-way mirror which lets solar radiation in, but does not let any planetary radiation out. This state of affairs would violate the Second Law of Thermodynamics, as the planetary temperature would exceed the solar blackbody temperature. In fact, the temperature limits itself because, once the surface warms to solar temperatures, it radiates at solar wavelengths and the albedo for solar and planetary radiation become identical. This limit nevertheless shows the potency of the cloud-mirror effect. In contrast, the conventional greenhouse effect for a single-layer IR-absorbing cloud could increase the unperturbed temperature by no more than a factor of 21/4 . Unlike the conventional greenhouse effect, the scattering greenhouse effect blocks IR emission to space without the clouds having to absorb any IR themselves. The clouds therefore do not have to heat up in response to the absorbed radiation, which removes a limit to warming inherent in the conventional single-layer case. Instead of determining the cloud-induced temperature change using a radiativeconvective model, we instead ask the question of how we must change the incident solar flux so as to restore equilibrium at the original temperature. The assumption of unchanged temperature implies I1 = Io = (1o)So, and if the new solar constant needed to maintain equilibrium is called S1 we then have So = {(1 )/((1c')(1o)) } S1 S1. (2.) The high clouds make the planet act as if the sun were brighter by a factor . The warming factor has two especially significant limiting behaviors which can be inferred from (1). When o = 0, = (1c)/(1c'), which is the solar/infrared coalbedo ratio for the cloud, and which will henceforth be referred to by the notation c. Regardless of o, Scattering Greenhouse Effect on Early Mars Page 5 on the other hand, when c then c/(1o), which is the coalbedo ratio amplified by 1/(1o).