MADMS: Modal Aerosol Dynamics model for multiple Modes and fractal Shapes in the free-molecular and near-continuum regimes

Atmospheric particles vary in size and shape. Moment Dynamics Equations (MDEs) of the Modal Aerosol Dynamics (MAD) approach were extended to simulate the Brownian coagulation process of multimodal aerosols covering full size ranges and arbitrary fractal dimensions for implementation in three-dimensional atmospheric aerosol chemical transport and climate models. The proposed approach is referred as the Modal Aerosol Dyanmics ʹmodelʹ for multiple Modes and fractal Shapes (MADMS). The approximation of Otto, Fissan, Park, and Lee (1997) for intramodal coagulation in the free-molecular regime was for the first time extended to intermodal coagulation with different geometric standard deviations (σ) and geometric mean diameters (Dg) for arbitrary mass fractal dimensions (Df). To evaluate the accuracy of the MADMS model and to examine temporal evolution of coagulating aerosol modes under atmospheric conditions, simple one-box simulations using the model were performed and compared with rigorous numerical solutions obtained using the difference (bin) method. Deviations of MADMS from the accurate bin method (BIN100, d log D=3.01×10−2, 100 bins between 1 nm and 1 μm and 100 between 1 μm and 1 mm) are smaller than 5% in number and volume concentrations and smaller than 2% in σ and Dg during the period for 30% of the initial number concentration to coagulate (t30). The MADMS model is four to six orders of magnitude faster than BIN100 with respect to CPU time. It was found to be sometimes comparable in accuracy to, but generally one order of magnitude more accurate than, the bin method with a coarse bin-grid resolution (BIN10, d log D=3.01×10−1, 10 bins between 1 nm and 1 μm), which is commonly used for 3-D simulations, as well as two to four orders of magnitude faster than BIN10.