Time series of volcanic induced stratospheric aerosol optical depth

There are two coefficients to fit the parameterization to observations. The first one ($p_{1}$) is given in equation (2) to fit the aerosol transport parameterization to observations given by Sato et al. (1993), Sato (1995), and Stothers (1996). Because the $AOD$ values by Stothers (1996) are valid for the visible spectral range and the $AOD$ values provided by Sato et al. (1993) and Sato (1995) relate to a wavelength of $.55 \mu m$, the latter ones have to be converted with a scale factor of 1.6 for comparison (Stothers, 1996). Thus we have two time series of volcanic stratospheric $AOD$ at our disposal. Since the calibration coefficient $p_{1}$ affects only the magnitude of the spatio-temporal pattern we decide to choose it in a way to obtain the same annual and global average value for the year 1983 as Sato (1995). Accordingly we'll get a realistic description of the globally and annually averaged influence of the El Chichón eruption as it is observed. Figure 3 shows the $AOD$ time series of Stothers (1996), Sato (1995) and of this paper for four equal area latitude belts. The global mean time series are shown in Figure 4. To obtain an objective measure of similarity of the different time series, we calculate linear correlation coefficients. These correlation coefficients are presented in Table 5. There are good linear correlations between the three time series on all regional scales considered. The $AOD$ time series, calculated in this paper, is better correlated with the time series proposed by Stothers (1996) than with the time series published by Sato (1995). Apart from the Northern Hemisphere extra-tropics, correlations between the data of Sato (1995) and Stothers (1996) are not as high as data resulting from this paper compared with both of the other series, respectively. Nevertheless, all correlations are higher than those of the ice core volcanic index ($IVI$, Robock and Free, 1995) and the index of Sato (1995), which are quantified by Robock and Free (1995) to be .4 for the Northern Hemisphere and .54 for the Southern Hemisphere. Because the explained variance is the square of the correlation coefficient, these two series reach less than 50% of combined variance. In contrast to that, the approach of this paper reaches more than half of the combined variance with both the data from Sato (1995) and Stothers (1996), respectively.