Residence time of volcanic aerosol

Explosive volcanism injects precursors of aerosols like sulfate dioxide ($SO_{2}$) into the stratosphere which are converted into stratospheric aerosol by gas-to-particle conversion. This leads to very small particles which coagulate to larger ones. Eventually the large particles fall out by sedimentation (Kasten, 1968). The interaction of all these microphysical processes is extremly complicated and hard to handle in detail. Furthermore, the radiative properties of the aerosol depend not only on the concentration but also on the size distribution and shape of the particles, which hampers the derivation of a complete microphysical model. Fortunately we are not primarily interested in the microphysical processes, but in the impact of volcanism on the climate. Therefore we use macroscopic observational information to deal with that problem, i.e. we suggest a certain formulation of the temporal evolution of an aerosol cloud and calibrate it with respect to observed data. In fact, we assume a linear increase of the total aerosol mass up to 5 months after eruption leading to a maximum mass according to the strength of the eruption. This seems to be a compromise between the estimates of build-up times to the peak $AOD$ reaching from one month (Pinto et al., 1989) over six months (Deshler et al., 1993) to nine to twelve months (Ardanuy et al., 1992). Grant et al. (1996) found a peak loading 20 weeks after the Pinatubo eruption in 1991. After that we assume a mainly exponential decrease of the stratospheric $AOD$. According to Ardanuy et al. (1992) and Grant et al. (1996) we use a mean e-folding time of stratospheric aerosol of one year. This is supported by more detailed observations of the Pinatubo stratospheric aerosol cloud by Lambert et al. (1993). An optical depth of $5.5\cdot 10^{-3}$ in April 1992 and $4.4 \cdot 10^{-3}$ in July 1992 was observed. According to these observations an e-folding time of 13.44 months can be estimated. Nevertheless, Hofmann and Rosen (1987) found shorter decay times for the Fuego aerosols (Guatemala, 1974) of about 8 to 10 months and about 10 to 12 months for the El Chichón eruption (1982). The major sink of stratospheric aerosol is the stratosphere-troposphere flux of air which is described by Rosenlof and Holton (1993) and Holton et al. (1995) to be in the order of $10^{9}$ to $10^{10} kg/s$ in the extratropics (Table 4). Within the tropics tropospheric air enters the statosphere and thus hampers the sedimentation of aerosol. Therefore the tropical stratosphere is often seen as a tropical stratospheric reservoir (TSR, Grant et al., 1996). According to Grant et al. (1996) we assume that sedimentation is not an important aerosol removing mechanism within the TSR. In fact, we allow no sedimentation in the tropical regions and therefore have to increase the removal rates in the extra-tropics to reproduce the observed average removal e-folding times. Thus we need an e-folding time of only 5 months in the extratropics to obtain the latitudinal averaged e-folding time of 12.2 months for the Pinatubo eruption in 1991. By using this information we may describe the impact of all microphysical processes on the temporal evolution of a volcanic stratospheric cloud by one function that depends on the latitude belt $i$, the season $s$, and the time after eruption $n$. An additional sink in the winter polar vortex is wash-out by polar stratospheric clouds (PSC's). This is neglected because of the short residence time and the small spatial fraction covered by PSC's (Volk, 1998). The calibration coefficient $p_{1}$ in equation (2) can be taken from fitting the parameterization results to observations as described in section 4.