Sparse particle models for data analysis and assimilation

Poster PDF

Description

This poster illustrates several members from a class of sparse particle models, with specialization to sparse aerosol models (SAMs), derived from linear programming (LP). The same approach also applies to cloud particle populations, and this application is under exploration. Examples of SAMs are presented with applications to data analysis and assimilation including the calculation of rigorous, nested, upper and lower bounds on aerosol physical and optical properties. The quadrature method of moments (QMOM), which provides a highly accurate approach to aerosol simulation while preserving computational efficiency, falls into this sparse aerosol models class. Here it is shown how other SAMs can be constructed, which are not based on moments of the particle size distribution. Examples of data assimilation will be presented based on simulated light extinction coefficient measurements (wavelengths from 0.3 to 1.1 micron) for one of the Hoppel aerosol test distributions (Hoppel et al., 1990, Journal of Geophysical Research: 3659). The examples include: (1) bounding the extinction coefficient using moments of the test distribution as LP constraints and (2) the inverse problem of bounding lower-order moments using the simulated extinction coefficient measurements as LP constraints. Next we partition the test aerosol size distribution into various numbers of sections and use the known particle number concentrations in each section as LP constraints to bound extinction coefficient and lower-order moments. The extent to which the bounds are refined through a doubling and then quadrupling the number of sections provides a quantitative measure of information achievable through sub-grid resolution. Potential applications of sparse particle models to Kalman filtering are also discussed.