Clear- and cloudy-sky fluxes. Long-wave flux (also referred to as irradiance) is
represented by the letter F. The flux for clear-sky conditions is denoted by Fa, where the
subscript a represents the atmosphere; the flux for overcast cloud conditions is Fc. The
average flux for a mixture of clear and cloud conditions is F. Thus, if a region has a
fraction of area, C, covered by clouds, then F = (1-C) x Fa + C x Fc, where the fraction (1-
C) is the clear-sky fraction.
Up and down long-wave fluxes. The long-wave flux emitted in the upward direction is denoted by the symbol F+, and the flux in the downward direction is denoted by the symbol F-. The net flux, then, is F = F+ - F.
Before describing the role of the five factors upon which the thermostat hypothesis is based,
several terms used by Ramanathan and Collins will be reviewed.
Atmospheric greenhouse effect. The definition adopted by the global warming community (IPCC, 1990), gives the atmospheric (cloud-free) greenhouse effect (Ga) as Ga = F+(Z=0) - Fa+, where F+(Z=0) is the blackbody emission from the sea surface, and Fa+ is the outgoing long-wave radiation under clear skies, as obtained from the ERBE satellite data. Without the atmosphere the OLR would be ÓT4, where T is the surface temperature. The atmosphere, primarily water vapor and CO2, absorbs most (70 to 95%) of the surface long- wave radiation and re-emits to space at the much colder temperature of the atmosphere. The effect is to reduce OLR. Ga then represents the energy trapped by the entire atmospheric column between the surface and the top-of-the-atmosphere. The atmosphere then heats the surface by emitting absorbed energy back to the surface. This downward emission becomes another measure of the greenhouse effect (e.g., Vonder Haar, 1986). In a system in radiative-convective equilibrium, both methods are self-consistent. However, when used in a regional context, care should be taken to keep this distinction and to measure the greenhouse effect using both methods.
Ga denotes the greenhouse effect of the entire troposphere. However, with the aid of aircraft observations, it is possible to measure the vertical structure of Ga. This is denoted by Ga (Z), which is estimated from Ga(Z) = F+(Z=0) - Fa+(Z). Ga(Z) is the trapping by the atmosphere between the surface and the altitude, Z. At any altitude, Z, in the tropics, the temporal or spatial variations in Ga(Z) are mostly due to corresponding variations in water-vapor concentration and temperature profile. This is because temporal and spatial variations in other radiatively active gases are negligible compared with those of water vapor.
Cloud radiative forcing. Cloud radiative forcing denotes the effect of clouds on the surface-atmosphere column radiation budget or on the surface energy budget. Clouds reduce the long-wave energy emitted to space (i.e., OLR). Cloud long-wave forcing (Cl) for the surface-troposphere column is obtained from Cl = Fa+ - F+, where the upfluxes should be estimated at tropopause altitudes or at the top-of-the-atmosphere. Cl is the enhancement of long-wave trapping due to the presence of clouds. The total greenhouse effect combines the effect of the atmosphere with the effect of the clouds, so that G = Ga + Cl = F+(Z=0) - F+.
Clouds also enhance the downward long-wave energy at the surface. This enhancement, or cloud long-wave forcing at the surface, is given by Cl(Z=0) = Fa - Fa-. Thus, Cl(Z=0) is the effect of clouds on the surface long-wave radiation heating; Cl is the effect of clouds on the surface-troposphere long-wave radiation heating; and the difference, Cl - Cl(Z=0), is the effect of clouds on the long-wave heating of the troposphere.
In addition, clouds enhance the planetary albedo, reducing the solar radiation absorbed by the surface-atmosphere system. This effect, cloud short-wave forcing, is Cs = S - Sa, where S is the solar radiation absorbed by the surface-atmosphere column for cloudy skies (i.e., the average of clear plus overcast skies) and subscript a refers to clear skies. Cloud radiative forcing is the net of the long-wave and short-wave effects.
Let us now consider the five factors involved in the thermostat hypothesis.
Deep convection threshold temperature (Tc). The thermostat mechanism operates in regions of deep convective clouds, with bases at between the surface and 3 km and tops at between 12 and 18 km. The horizontal scale of an individual, non-entraining cell is anywhere from a few to several tens of kilometers. Such clouds typically have an anvil that begins as a thick (5–8 km) cloud deck near the convective region, then thins to a few kilometers or less at distances that are sometimes several hundreds of kilometers from the convective source (top panel of Figure 10). Systems of deep cumulonimbus-cirrus anvil clouds, referred to as super cloud clusters (Nakazawa, 1988), can grow to a size as large as 106 km2 in a matter of a day or less (e.g., WMO, 1972; Houze and Betts, 1981). The radiative effect of these clusters is dominated by the anvils and stratiform cirrus (bottom panel of Figure 10), because of their spatial extent. The albedo of these cloud systems can reach as high as 60–80% (Harrison et al., 1991), and they can reduce OLR by as much as 200 Wm-2.
These convective systems are triggered over warm oceans only when the SST > 300 K (Tc) (Gadgil et al, 1984; Graham and Barnett, 1987), where the subscript c represents convection. Satellite data of OLR clearly reveal this threshold effect (Figure 11 shows highly reflective clouds [HRC] and OLR in relation to SST). It is important to note that SST > Tc is a necessary, but not sufficient, condition for convection. In addition, convergence of moisture in the boundary-layer is required to initiate convection (Holton, 1992). In regions with SST > Tc, and where deep convection persists, the horizontal gradients in SST diminish. The maximum SST remains within a few degrees of Tc.
Super-greenhouse effect. The phrase super-greenhouse effect was first used by Vonder Haar (1986). From observations of net (upward minus downward) long-wave flux at the surface of the tropical Atlantic Ocean during GATE (GARP [Global Atmospheric Research Program] Atlantic Tropical Experiment), Vonder Haar noted that the net long-wave flux, for clear as well as for cloudy skies, decreased with an increasing SST (i.e., as SST increases, the downward emission to the surface increases at a rate faster than the increase of upward emission from the surface). The super-greenhouse effect is defined, then, as: Fa - (Z=0) / SST > F + (Z=0) / SST, where F+(Z=0)= Ó (SST)4.
The ERBE satellite data used by Ramanathan and Collins (1991) revealed—for the tropical oceans in general and over the warm oceans (SST > Tc) in particular—that the rate of increase in Ga with increasing SST indeed exceeds the rate of increase of F+(Z=0), the blackbody emission by the sea surface, ∂Ga / ∂SST > ∂F+(Z=0) / ∂SST. Ramanathan and Collins deduced this super-greenhouse behavior from analyses of spatial, seasonal, and interannual variations of Ga and SST. In addition, the cloudy sky (G) also increased significantly with SST, so that OLR decreases with an increase in SST (Figure 11). The coupling between SST and the atmospheric greenhouse effect represents a potentially unstable feedback loop, especially when cloud long-wave effects are taken into account (Figure 12). The total greenhouse effect, G = Ga + Cl, increases exponentially when SST > 300 K. The upper troposphere cirrus clouds contribute the most to this increase. Because tropical cirrus result from deep convection, and because deep convection increases with SST, a strong negative feedback is required to limit maximum SSTs and counter the super-greenhouse effect.
Radiative effects of cirrus and the f factor. The large magnitude of short-wave cloud forcing over the warm pool, as revealed by the ERBE data, indicates that the surface-atmosphere system in the warm pool absorbs significantly less solar radiation than that in the colder oceans (Figure 13) in the tropics. Ramanathan and Collins hypothesize that the oceans become warmer, and convection gets deeper, until the cirrus become sufficiently thick to reduce solar energy reaching the oceans and prevent their further warming. The large changes in planetary albedos observed in the central Pacific during the 1982 El Niño (Chertock et al., 1991) and during the 1987 El Niño (Figure 14) support this idea. That a negative feedback between surface temperature and cloud reflection of solar radiation may regulate SSTs had been suggested earlier by Monin (1972) and Sikka and Gadgil (1980) to explain ocean-atmospheric oscillations in temperature, cloudiness, and rainfall; by Graham and Barnett (1987) to explain the maximum SSTs; and by Barnett et al. (1991) to explain El Niño.
However, there is an important detail that was not addressed by these earlier studies. This concerns the long-wave-trapping effect of cirrus. As mentioned earlier, there is a near cancellation between short-wave and long-wave cloud forcing. If the warm pool were in strict radiative- convective equilibrium, the net effect of anvils on warm pool SST would be small. For the cirrus thermostat to be effective in arresting the SST increase, the long-wave energy trapped by cirrus has to be exported away from the warm pool. Ramanathan and Collins assume that between 80 and 100% of the trapped energy is exported away, and this assumption is based upon the so-called f factor. One of the key assumptions in their model is that the atmospheric long-wave trapping (Ga) warms the surface directly, whereas most of the cirrus long-wave trapping contributes to the radiative heating of the troposphere. They describe this as the f factor, where f = Cl(Z=0) / Cl. Recall that Cl is the cloud radiative forcing of the surface-troposphere column, and Cl(Z=0) is that of the surface; i.e., f describes that fraction of the long-wave cloud forcing that arrives at the sea surface.
The following example is given to clarify the terminology. Consider a 50% cloud fraction, and the clear-sky downward flux at the surface is Fa-(Z=0) = 400 Wm-2; underneath the cloud deck, the downward flux is Fc- = 440 Wm-2. The flux for the mixture of clear plus overcast skies is then F+(Z=0) = (400 x .5) + (440 x .5) = 420, and the cloud forcing at the surface is Cl(Z=0) = 420 - 400 = 20 Wm-2. Thus, long-wave cloud forcing is simply the change in radiative heating due to clouds. Now, if the corresponding values for upflux at the tropopause altitudes are Fa = 300 Wm-2 and Fc = 200 Wm-2, then F = 250 Wm-2 and Cl = 50 Wm-2. The factor for this case is f = 20 / 50 = 0.4. This implies that, out of the surface-troposphere total heating (due to clouds) of 50 Wm-2, the surface heating is 20 Wm-2, and the balance of 30 Wm-2 is the net long-wave energy heating the tropospheric column.
Ramanathan and Collins assumed that f < 0.2 for the warm-pool region, because they asserted that water-vapor opacity is large in such regions and that clouds do not influence the long-wave energy at the surface. For example, if the water vapor is optically thick in the entire long-wavelength region, then Fc-(Z=0 ) ~ Fa-(Z=0) and Cl(Z=0) ~ 0 , resulting in f ~ 0. If the f factor for cirrus is close to 1, the cirrus by itself will not be effective in limiting SSTs.
Rapid heat advection in the troposphere. A remarkable feature of the tropical atmosphere is the near-horizontal homogeneity of atmospheric temperature above the boundary layer (see Figures 1 and 2 in Wallace, 1992). Between about 750 mb and 150 mb, temperature varies by less than five degrees across an entire latitudinal circle of about 40,000 km, as seen, for example, in Figure 15 for the 200-mb level. This is remarkable, because heat sources and sinks in the tropics have significant longitudinal and latitudinal asymmetry. The temperature homogeneity is due to transport by the Walker and Hadley circulations and planetary-scale wave disturbances. This suggests that atmospheric motions and disturbances in the tropics are significantly efficient in exporting heat away from regions of heating and maintain a spatially uniform temperature profile (Wallace, 1992).
A unique feature of tropical cirrus is that the long-wave cloud effect leads to a radiative heating of the troposphere, with very little direct effect on the surface. This result (based largely upon model studies), when considered in conjunction with the efficient transport in the troposphere, leads to the deduction that the long-wave heating effect of cirrus is exported away from the warm-pool region. Thus, the only local effect of cirrus is the shielding of the sea surface from solar radiation. The magnitude of this effect is large (see Ramanathan and Collins, 1991, ERBE data) and can be in the range of 75125 Wm-2 in the monthly mean. This represents about 3050% of the total solar heating of the oceans under clear-sky conditions. The question remaining is, can SST respond to this reduction locally? The answer to this question depends upon the efficiency of dynamic heat transport in the oceans.