We present a model of stratospheric aerosol optical properties (refractive index and relative size distribution) and their variability. The model's purposes are 1) providing flexible, efficient means for converting between different aerosol macroproperties (e.g., number or mass concentration, extinction or backscatter coefficient), and 2) quantifying the uncertainties in the conversion process. The latter purpose is achieved by including the results of a sensitivity analysis in the model output products.
The model has three layers, the boundaries of which are defined by tropopause height. Each layer includes a set of empirically based refractive indices and relative size distribution types. In contrast to previous models, this model allows for a range of sulfuric acid and ammonium sulfate refractive indices within the “inner stratospheric” layer (∼2 to 20 km above the tropopause, where the major peak in aerosol mixing ratio occurs). We show that nine different analytical types of size distribution previously recommended for this layer can be parameterized in terms of channel ratio—i.e., the relative size distribution indicator that has been extensively measured by dustsondes.
When so parameterized, all nine inner stratospheric function types give very similar results for the several conversion ratios of interest. This parameterization allows considerable saving of computer time while preserving the flexibility to handle certain types of size distribution change. We show that the inner stratospheric parameterization works because all nine inner stratospheric size distribution types are relatively narrow, and their optical integrals of interest are determined primarily by a size range that is well characterized by channel ratio.
Data from previous measurements made near the tropopause are used to demonstrate that, in that region, size distributions are broader than any of the inner stratospheric types, and that their optical integrals are strongly influenced by particles too large to be characterized by channel ratio. Hence, in the layer near the tropopause, conversion ratios can differ significantly from the inner stratospheric values; consequently, parameterization by channel ratios is not successful.
We develop methods for deriving vertical profiles of several conversion ratios and their uncertainties. We also demonstrate an application of the model: deriving profiles of number density and its uncertainty from satellite-measured profiles of extinction and its uncertainty. A companion paper applies the model to the task of validating satellite measurements of stratospheric aerosol extinction.