AAAR 33rd Annual Conference
October 20 - October 24, 2014
Rosen Shingle Creek
Orlando, Florida, USA
Abstract View
Bounds on Aerosol Physical and Optical Properties Using Linear Programming-based Extension of the Quadrature Method of Moments
ROBERT MCGRAW, Brookhaven National Laboratory
Abstract Number: 429 Working Group: Aerosol Physics
Abstract Moment methods have rich mathematical connections that embody orthogonal polynomials, continued fractions, and quadrature. In the quadrature method of moments (QMOM) a sequence of e.g. radial moments of a particle distribution function (pdf) is inverted using such methods to obtain a small set of quadrature abscissas and weights that can be used to accurately estimate aerosol physical and optical properties. The pdf itself is not required; only values for a, typically small, set of its moments are required. For the present study a new approach to moment inversion is presented that is not based on moment methods or limited to moments. The new approach can be applied to arbitrary kernels over the pdf with the result that many aerosol properties and/or measurement, i.e. those linear in the pdf, can be accurately represented. These new inversions, which like the QMOM lead to sparse representations for the aerosol, solve the constrained optimization problem in which of various physical and/or optical properties of the aerosol are either maximized or minimized subject to various constraints using optimization theory. The QMOM, recovered as a special case, falls into this class. The method is shown to yield nested sequences of rigorous upper and lower bound pairs that constrain a selected aerosol physical or optical property, e.g. light extinction coefficient, particle surface area, etc., based on a Bayesian-like input sequence of independent measurement/model constraints.