Investigations of solar forcing of climate variability have focused on longer-term periodicities associated with the near-absence of sunspot cycles (e.g., Stuiver et al., 1991). Sunspot records have been deduced from observations, although they are quite uncertain prior to 1800, and from variations in carbon and beryllium isotopes. In periods of high solar activity, the stronger solar wind deflects cosmic rays and decreases the production of cosmogenic isotopes, so solar activity is typically thought to be responsible for much of the natural decade-to-century-scale changes in 14C and 10Be (Stuiver et al., 1991; Stuiver and Braziunas, 1988). Long-term 14C variations can be determined by comparing 14C dates with dates obtained from analyses of tree rings, whereas records of 10Be variations are obtained from ice cores. Although care needs to be taken in interpreting 14 C changes, since they are affected by the intensity of the geomagnetic-field polar dipole and carbon-cycle/climate variations, the covariation between 14C and 10Be suggests strong solar control of isotope production for the time scales of concern here (Stuiver et al., 1991).
Spectral analyses of the 14C record indicate apparent fluctuations in periods ranging from decades up to several thousand years, including the 11- and 22-year (Hale) cycles, the 88-year (Gleisberg) cycle, and approximately 200-year and approximately 2500-year cycles (see, e.g., Damon and Linick, 1986; Stuiver et al., 1991). Hints of these cycles have also been identified in the climate record, e.g., the 2500-year cycle in marine, glacier, and polar ice core records (Pestiaux et al., 1987; Denton and Karlen, 1973; Wigley and Kelly, 1990; Dansgaard et al., 1984), and the 88- and 200-year cycles in varved sediments (Halfman and Johnson, 1988; Peterson et al., 1991; Anderson, 1992). Whether these are truly periodic in nature is doubtful, and the relationship of the geologic indicators to climate is itself uncertain, but the similarities in periodicities are indicative of a general coincidence of apparently reduced 14C production and colder temperatures (de Vries, 1958; Eddy, 1976), with the Maunder Minimum/Little Ice Age being the most recent example.
To quantify this connection, it is necessary to know the magnitude of the possible solar irradiance variations. Recent observations during the last solar cycle (solar cycle 21) indicated close to 0.1 percent peak-to-peak change from solar maximum to solar minimum (e.g., Willson and Hudson, 1991). What these observations imply about past solar irradiance variations is a more difficult question. Various indicators of insolation changes have been generated. These include 10Be and 14C variations, indicative of solar activity (Beer et al., 1988, 1990; Stuiver et al., 1991); solar-radius variations, thought to be representative of solar luminosity (Ribes et al., 1987); the envelope of the sunspot cycle, perhaps representative of solar irradiance and apparently correlated with decade-to-century-scale sea surface temperature variations (Reid, 1991); and the length of the solar cycle, also seemingly correlated (Friis-Christensen and Lassen, 1991). These latter correlations have been used to suggest the possibility of solar dominance of climate variability over the last several centuries. In recent publications, Kelly and Wigley (1992) and Schlesinger and Ramankutty (1992) both found that including solar irradiance variations related to the length of the solar cycle improved their reconstruction of global temperature changes for the last 150 years. Nevertheless, it is difficult to translate these solar properties into absolute irradiance changes and prove the causal connection.
Another approach to understanding solar variations has been to observe other stars that have a nature similar to the sun's. Decadal-scale stellar-activity variations are apparent (Radick et al., 1990), including the complete absence of "sunspot" conditions (Baliunas and Jastrow, 1990). Accompanying variations in luminosity are as much as 0.4 percent, or somewhat higher than the variation recorded in solar cycle 21. While the relevance of these observations to solar irradiance variations is uncertain, they do serve to provide some constraint on the magnitude of likely changes.
Lean et al. (1992) estimate that the Maunder Minimum reduction in solar insolation was on the order of 0.25 percent, due to changes in sunspots, faculae, and network radiation. Current GCMs give a climate sensitivity of approximately 4°C for a 2 percent change in solar constant (Hansen et al., 1984); whether the 0.25 percent reduction is sufficient depends on how cool the Little Ice Age was. Estimates range from 0.5°C (Wigley and Kelly, 1990) to 1°C to 1.5°C (Crowley and North, 1991). The nominal value we have used above, about one-fifth the cooling of the full glacial age, implies values of 0.7°C to 1.0°C (e.g., see Rind and Peteet (1985) for estimates of the full ice-age cooling of 3.5°C to 5°C). A GCM simulation with the GISS model, using the 0.25 percent reduction, produced a global annual-average cooling of about 0.45°C, which is probably somewhat smaller than would be required to explain the Little Ice Age if solar variability were acting alone. Of course, if the climate sensitivity were greater or the global temperature change smaller than indicated, the required solar variability would be reduced.
The geographical variation of the temperature change generated by the 0.25 percent reduction (Table 1) is shown in Figure 5. Significant cooling occurs in the tropics, and there is no obvious high-latitude amplification of the climate change. Note that not all regions are cooler than they are today; the forcing is small enough that regional changes in advection patterns can produce local warming. A similar response occurred in the colder-North-Atlantic experiment, which produced advective warming over the Arctic (Figure 3). These results imply too that advection changes may also alter the sources of water vapor sufficiently to confound isotope/temperature reconstructions when the cooling is of such small magnitude (Cole et al., 1992).
The low-latitude cooling led to a reduction in the intensity