Case studies

To give an idea of the spatio-temporal resolution of the parameterized $AOD$ and forcing presented in this paper, we compare the results of two special episodes with the related results of Sato (1995) or Stothers (1996), in more detail. The first episode from January 1982 till June 1986 includes the El Chichón eruption (17.4$^{\circ}$ N) in April 1982 which occurred nearly at the same latitude as the Pinatubo eruption (15.1$^{\circ}$ N) in 1991. In contrast to the Pinatubo eruption the aerosol spreading of the El Chichón eruption was very assymmetrical, as can be seen from the data adapted from Sato (1995) in Figure 9a. Figure 9b shows the spatio-temporal $AOD$ distribution as it follows from the parameterization of this paper. As can be seen both approximations are similar. Using the linear forcing parameterization by Lacis et al. (1992), the forcing pattern is a rescaled $AOD$ pattern. Using the radiation-transfer parameterization of this paper, the forcing pattern shows an annual cycle (Figure 10), which is not as pronounced as in the case of the Billy Mitchell eruption (Figure 7 for comparison). The second episode from January 1912 till June 1916 addresses the eruption of Katmai (58.3$^{\circ}$ N) in June 1912. It has the same $VEI$ as the El Chichón eruption in 1982 but due to its high latitude the aerosol spreading is completely different. We compare the $AOD$ as it is provided by Sato et al. (1995) on a 24-point grid and by Stothers (1996) on a 3-box grid with our approach on a 16 equal area box resolution (Figure 11). Although Sato (1995) used 24 grid points, they distinguish only 3 latitude zones: Southern Hemisphere, Northern Hemisphere tropics and northern hemisphere extra-tropics. They find much larger signals in the Northern Hemisphere tropics than Stothers did and we do. In respect to north of 45$^{\circ}$ N the $AOD$ series provided by Stothers is more similar to our results than the series from Sato (1995). In total, however, it can be concluded that these differences are in the range of uncertainty typical for reconstructions of volcanic stratospheric $AOD$, although Sato (1995) as well as Stothers (1996) used observations, whereas we use a parameterization without any $AOD$ observations of this period. These results encourage us to estimate forcing anomalies of historical eruptions like the Vesuvo eruption (Italy, $VEI=6$) in August 79 A.D. As can be seen in Figure 12a, $AOD$ increases nearly homogeneously within the northern hemisphere extra-tropics. This is due to the little exchange from extratropics into tropics and into the winter polar vortex. In the following spring, sedimentation and transport to the polar region became effective and $AOD$ declines dramatically. Figure 12b shows the spatio-temporal pattern of the related climate forcing which differs considerably from the $AOD$ pattern. Despite of the decrease of the $AOD$ in spring of the year 80, the forcing remains on a high level during the whole summer.