A closure study of extinction apportionment by multiple regression

Multiple regression has been widely used to apportion particle light scattering among distinct chemical species. The resulting scattering budgets are shown here to be unbiased estimates under certain theoretical conditions. The theory allows species’ particle size distributions and water uptakes to vary from sample to sample, as they are known to do in reality. The sole constraint is that variations in each species’ characteristics be statistically independent of all species’ concentrations. Individual violations of this condition cause identifiable biases, and multiple violations can offset each other to yield regression estimates that are accurate by accident. Detailed and summary accountings of statistical errors are illustrated using a mechanistic model derived from measurements in southern California.