Time series of volcanic radiative forcing

To calibrate the radiative forcing parameterization, we compare the estimated forcing with observations and calculations from more sophisticated models. Dutton and Christy (1992) show that monthly clear-sky total solar irradiance at Mauna Loa, Hawaii, decreased about 5% after the Pinatubo eruption (June 1991) with a ten month average of 2.7%. The latter value corresponds to more than 10 $W/m^{2}$ clear-sky forcing at the surface (at an elevation of about 3.400 m). Minnis et al. (1993) used ERBE data between $\pm 40^{\circ}$ latitude and showed that in August 1991 the reflected shortwave radiation at the top of the atmosphere increased about 10 $W/m^{2}$. Hansen et al. (1996) calculated a global and seasonal mean net radiation forcing of about 4 $W/m^{2}$ from the end of 1991 to summer 1992 using a GCM. Graf et al. (1996) found the strongest volcanic forcing in summer polar regions with a magnitude of about 5 $W/m^{2}$, and no forcing at the winter polar regions performing equilibrium simulations with an atmosphere-ocean general circulation model (AOGCM). Realizing such differences even in sophisticated models, we choose the parameter $p_{2}$ to obtain a magnitude of monthly and northern hemisphere tropical volcanic forcing of 10 $W/m^{2}$ following the Pinatubo eruption (1991). This leads to a forcing of about 5.1 $W/m^{2}$ in global average for the last quarter of 1991. Using the time series of $AOD$ provided by Sato (1995) and by Stothers (1996) and the crude radiation parameterization given by Lacis et al. (1992) (equation (1) in this paper), we get time series of volcanic forcing (in $W/m^{2}$) for the same equal area latitude belts as they are used in Figure 3. These are presented in Figure 5. Figure 6 shows the related annual and global averages. The linear correlation coefficients of the different forcing time series are listed in Table 6. Because the parameterization by Lacis et al. (1992) is linear, the correlations between the forcings calculated from $AOD$ series by Sato (1995) and by Stothers are the same as for the $AOD$ series itselves and therefore not explicitely given in Table 6. Similar to the $AOD$ series, the volcanic forcing series of Stothers (1996) and the approach of this paper are in better agreement, too, than the series of Stothers (1996) and Sato (1995) and our approach compared to the series of Sato (1995). Changes due to the non-linear radiation parameterization are very weak on the spatial and temporal scales under consideration. This will change considerably if one is interested in a more detailed spatial and temporal resolution, as will be seen in section 4.4.