The decoupled direct method for calculating sensitivity coefficients in chemical kinetics

Abstract

A version of the direct method for calculating first-order sensitivity coefficients is extended to nonlinear, time-dependent models defined by stiff differential equations. In this approach the auxiliary equations for the sensitivity coefficients are solved separately from the model equations. Accuracy and stability are maintained by using exactly the same time steps and numerical approximations in calculating the sensitivities as are used in calculating the model solution. The decoupling procedure also greatly increases the efficiency of the method by taking advantage of the fact that the auxiliary equations for different sensitivity coefficients are quite similar. The decoupled direct method is applied to stiff chemical mechanisms for the oxidation of hydrocarbons in the atmosphere, the pyrolysis of ethane, and the oxidation of formaldehyde in the presence of carbon monoxide. Sensitivity coefficients are also calculated for the three mechanisms by a method employing Green's function and by actually varying the input parameters. Based on these results, the decoupled direct method has advantages in simplicity, stability, accuracy, efficiency, storage requirements, and program size over other methods, including those using Green's function. Specifically, the decoupled direct method is as much as a factor of 6 more efficient than a recent version of the Green's function method. Extensions of the decoupled direct method are also discussed.

Sensitivity analysis of a mixed‐phase chemical mechanism using automatic differentiation

“…The system of ODEs for gas and aqueous phase concentrations shown in (1) and (2) The sensitivities of the concentration of the kth species with respect to the/th parameter can be computed using a variety of techniques including the brute force method, Green's function analysis [Cho et al, 1987], adjoint Green's function analysis [Hall and Cacuci, 1983], and several variations of the direct decoupled methods [Dunker, 1984] This approach is superior to finite …”

Dynamic processes of mercury over the Mediterranean region: results from the Mediterranean Atmospheric Mercury Cycle System (MAMCS) project

“…This version of GASPAR was used to investigate the dispersion and transformation of Hg emitted from a single source in the Mediterranean, and to calculate the speciated Hg deposition flux . Sensitivity analysis of the chemistry module of GASPAR using the direct decoupled method (DDM) (Dunker, 1984;Pirrone et al, 2000a) revealed that the concentration of Hg II associated with deliquesced particles was extremely sensitive to the particle chloride content. This fact prompted the further evolution of the chemistry model, which was expanded to include gas and aqueous phase tropospheric photochemistry in the MBL.…”

ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA

“…Although the finite difference approach employed in this and other studies, sometimes termed "emissions toggling", is the most straightforward sensitivity analysis technique, it is limited in that computational requirements scale with the number of emissions investigated; perturbations to the atmospheric conditions from the changed emissions obscure nonlinear effects; and cancellation errors limit the accuracy of this method. The decoupled direct method (DDM), an implementation of a tangent linear model (TLM), can be used to understand the impact of selected emissions on the field of air quality or health metrics without changing emissions parameters (Dunker, 1984;Napelenok et al, 2006;Koo et al, 2007); second-order source-oriented sensitivities of inorganic aerosol can now quantify nonlinear contributions to sensitivity (Zhang et al, 2011). Establishing the source-receptor relationship of inorganic aerosol by these forward sensitivity analysis methods (i.e., emissions toggling, DDM/TLM) reveals emissions impacts of particular sources on the field of concentrations.…”