Conclusion

Because strong explosive volcanic eruptions are known to have a pronounced impact on the climate it is important to estimate the spatio-temporal patterns of volcanic forcing. For the most recent eruptions instrumental observations from satellites and ground based measurements are available. For historical volcanic eruptions climate forcing has to be reconstructed. Therefore we introduced a stratospheric aerosol-transport parameterization based on nonlocal unisotropic diffusion. Exchange coefficients are obtained from recent studies of stratospheric mass transport. Strength, date and latitude of an eruption have to be known to apply the parameterization. We take this information from the $VEI$ series, although the estimated strength of eruptions is not accurate, especially for eruptions a long time ago. Therefore, we correct the $VEI$ with respect to observations for the strongest eruptions of the last century. While the parameterization is linear with respect to the strength of the eruption, errors in the estimated strength have no impact on the spatio-temporal structure of $AOD$. However, latitude and season of an eruption strongly affects the aerosol distribution and therefore the impact on the climate. If the required information is available we are able to reconstruct spatio-temporal patterns of $AOD$ for volcanic eruptions not included in the calibration of the parameterization and even for historic eruptions. For most of the historic eruptions only the year of the eruption is known. This has an impact on the temporal structure of the forcing (Figure 7). Nevertheless, as we have shown in an example (Table 7), the three year average forcing is not necessarily affected significantly by this lack of information. The knowledge of volcanic stratospheric optical depth is neccessary to estimate its climate impact, but the most important information is the forcing itself. It depends dramatically on the length of a ray path through the layer and the undisturbed radiation uptake. Also a pronounced aerosol cloud has no dramatic influence if it exists only in a winter polar region where there is nearly no radiation supply. Thus we introduce a radiation-transfer parameterization which takes into account these properties in their latitudinal and seasonal dependence to provide estimates of volcanic aerosol forcing. We hope that our investigations of the volcanic climate forcing will be helpful for other researchers to study the relationship between volcanic forcing and the observed climate response.