Actinic flux and photolysis in water droplets: Mie calculations and geometrical optics limit

摘要

Photolysis of water-soluble components inside cloud dropletsby ultraviolet/visible radiation may play an important role inatmospheric chemistry. Two earlier studies have suggested that theactinic flux and hence the photolysis frequency within sphericaldroplets is enhanced relative to that in the surrounding air, but havegiven different values for this enhancement. Here, we reconcile thesediscrepancies by noting slight errors in both studies that, whencorrected, lead to consistent results. Madronich (1987) examined thegeometric (large droplet) limit and concluded that refraction leads toan enhancement factor, averaged over all incident directions, of 1.56.However, the physically relevant quantity is the enhancement of theaverage actinic flux (rather than the average enhancement factor)which we show here to be 1.26 in the geometric limit. Ruggaber etal. (1997) used Mie theory to derive energy densityenhancements slightly larger than 2 for typical droplet sizes, andapplied these directly to the calculation of photolysis rates.However, the physically relevant quantity is the actinic flux (rather thanthe energy density) which is obtained by dividing the energy density bythe refractive index of water, 1.33. Thus, the Mie-predictedenhancement for typical cloud droplet sizes is in the range 1.5, onlycoincidentally in agreement with the value originally given byMadronich. We also investigated the influence of resonances in theactinic flux enhancement. These narrow spikes which are resolved onlyby very high resolution calculations are orders of magnitude higherthan the intermediate values but contribute only little to the actinicflux enhancement when averaged over droplet size distributions. Finally,a table is provided which may be used to obtain the actinic fluxenhancement for the photolysis of any dissolved species.