Merging and remapping modes in modal aerosol dynamics models: a “Dynamic Mode Manager”

Modal aerosol dynamics (MAD) models represent an evolving aerosol as a superposition of individual modes, which represent distinct populations of particles. Physical processes cause the formation and growth of distinct modes, and when two modes move into proximity to each other, they may become indistinguishable. Under such conditions, the number of distinct modes can be reduced by merging two indistinguishable modes into a single mode. Also, in MAD models, as modes grow they must be continually remapped into mode indices that correspond to their position in size space. Therefore, nucleated particles that begin as Mode 1 particles, may grow to eventually become Mode 2, 3, or 4 particles. In this paper, a Dynamic Mode Manager (DMM) is described for use with MAD models, which is used to determine when two modes can be merged, to control the merging rate of multiple modes, and to map individual modes into mode indices corresponding to their position in size space. The DMM calculates the flux of moments from one mode into another, and permits the complete transfer of one mode into another through this intermodal flux. The moment flux is calculated based on the relative motion of two modes towards each other, and accounts for the effect of all aerosol processes on the particle size distribution. The conceptual formulation, theoretical derivation of the governing equations, and three examples of the performance of the DMM are presented.