aerosol injection of 2 to 3 times the magnitude of Mt. Pinatubo's. The Tambora eruption of 1815 may have been of this magnitude (Rampino and Self, 1982).
However, if volcanic aerosols were maintained continuously in the atmosphere, i.e., their climate forcing remained relatively constant, then the ocean would have sufficient time to respond to them and to initiate positive feedbacks amplifying the cooling. With an optical thickness of 0.15 (equivalent to a 2 percent decrease in solar constant), the GISS model produces an equilibrium cooling of some 4.7°C after 50 years (Rind et al., 1992; Pollack et al., 1993). To produce a 0.5°C to 1°C cooling would take an optical thickness approximately one-sixth as large, or 0.025. This is some five times larger than the ''non-volcanic" background that existed during much of the time from 1900 to 1960, and it could be achieved by the eruption of a Mt. Pinatubo once every eight years, or, equivalently, of an El Chichon every fifth year. Over the last 100 years, we have had two events of the latter magnitude (Mt. Agung and El Chichon), and one of approximately twice this magnitude (Mt. Pinatubo). Thus, volcanic-aerosol-induced cooling of the appropriate magnitude would require a substantial increase in large volcanic injections. (Also, to be effective globally, they would have to originate in low latitudes, although a big high-latitude eruption might have a significant regional or hemispheric impact.)
Is there any way to distinguish global volcanic-aerosol cooling from reduced solar insolation? We have run two experiments with the GISS GCM and GCMAM (the version of the model that extends up to 85 km altitude). In one, the solar constant was reduced by 2 percent; in the other, the volcanic-aerosol optical depth was increased to 0.15, which is equivalent to a 2 percent reduction in solar energy reaching the surface (Table 1). The relevant differences between the results from the two experiments are given in Table 2. A primary difference is that the reduction in solar irradiance cools the lower stratosphere, while volcanic aerosols induce warming in that region, via short-wave and long-wave absorption (Rind et al., 1992). In conjunction with the slightly greater sea surface cooling in the tropics from the aerosol experiment, volcanoes appear to increase the static stability at low and subtropical latitudes more than does a simple solar energy reduction. With increased stability, the Hadley cell is weakened more in the volcano experiment, and the precipitation gradient between the tropics and Northern Hemisphere subtropics is somewhat reduced. (For example, if a record of precipitation for the Little Ice Age were available at these latitudes, such a change in gradient (about 20 percent) might be observable.) Wetter subtropical deserts might occur more easily with volcanic-aerosol forcing than with a solar irradiance reduction; however, both types of forcing appear to weaken the Hadley circulation somewhat.
In this section we have been concerned with the influence of volcanic aerosols, but tropospheric aerosols may well have increased over the past few centuries, thus cooling the climate (Charlson et al., 1992). The increase in aerosol-cooling effect through time does not allow for any obvious influence on earlier cold oscillations, but if the magnitude of the reduction in solar irradiance is as large as hypothesized in the IPCC (1992) report, aerosols would counter much of the effect of trace-gas variations, discussed below. There is still much uncertainty concerning historical variations in the direct global effect of tropospheric aerosol scattering, and even more uncertainty in aerosols' influence on cloud cover.
Ice-core evidence of trace-gas concentrations during the last several centuries has indicated that CO2 levels were at approximately 270 ppm for some time prior to this century (Neftel et al., 1985) (they are currently close to 360 ppm), and that methane has increased from around 0.8 ppmv to its current value of 1.72 ppmv (Rasmussen and Khalil, 1984). Such variations in greenhouse gases undoubtedly have had an effect on the climate system. They complicate the issue of the Little Ice Age cooling because they can add a linear trend to whatever fluctuations might have occurred—that is, the cooling that would be required to reduce current temperatures to Little Ice Age values is increased due to the trace-gas-induced warming over the last several hundred years.
To estimate the influence that these trace-gas variations may have had, two facts need to be known: The equilibrium response of the system, and the response that has occurred so far. The equilibrium response can be calculated with the formulae presented in Hansen et al. (1988). For CO2, the global-average radiative surface-temperature change due to a change in gaseous concentration X (in ppm) can be calculated as
A CO2 reduction from 315 to 270 ppm thus gives a ΔT (radiative) of 0.30°C.
The equilibrium feedback factor to radiative perturbations in GCMs is between 3 and 4 (Hansen et al., 1984). Therefore, in equilibrium the CO2 change would provide for a cooling of about 1°C.
For methane, the equilibrium temperature change to a change in methane (in ppmv) can be calculated as