Application of direct regularization techniques and bounded–variable least squares for inverse modeling of an urban emissions inventory

Abstract

Inverse modeling, coupled with comprehensive air quality models, is being increasingly used for improving spatially and temporally resolved emissions inventories. Of the techniques available to solve the corresponding inverse problem, regularization techniques can provide stable solutions. However, in many instances, it is not clear which regularization parameter selection method should be used in conjunction with a particular regularization technique to get the best results. In this work, three regularization techniques (Tikhonov regularization, truncated singular–value decomposition, and damped singular–value decomposition) and three regularization parameter selection methods (generalized cross validation, the L–curve method (LC), and normalized cumulative periodograms) were applied in conjunction with an air quality model with the aim of identifying the best combination of regularization technique and parameter selection method when using inverse modeling to identify possible flaws in an urban–scale emissions inventory. The bounded–variable least–squares method (BVLS), which is not usually considered a regularization method, was also investigated. The results indicate that the choice of the regularization parameter explains most of the differences between the regularization techniques used, with the LC method exhibiting the best performance for the application described here. The results also show that the BVLS scheme provides the best agreement between the observed and modeled concentrations among the mathematical techniques tested.