Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II Applications

Abstract

The Fourier amplitude method developed in Paper I as a diagnostic tool for determining the sensitivity of the results of complex calculations to the parameters which enter these calculations has been applied to two chemical reaction systems involving sets of coupled, nonlinear rate equations. These were: (a) a five reaction set describing the high temperature (6000 °K) dissociation of air and (b) a nine reaction set describing the constant temperature (2000 °K) combustion of H2 and O2. We have evaluated the Fourier amplitudes for all the species at a number of different times for both reaction systems. The analysis of these results verifies the claims made in Paper I. The relative magnitudes of the Fourier amplitudes showed a several order of magnitude distribution which permitted a clear distinction of the relative sensitivity of the species concentration to uncertainties in the rate coefficients. The conclusions based on the Fourier amplitude method for these two reaction systems are in excellent agreement with sensitivity predictions which could be made on the basis of previous kinetic studies of these systems.

A review of techniques for parameter sensitivity analysis of environmental models

“…In this approach, 'exact' (Downing et al 1985) sensitivities are calculated as defined by partial derivatives. The Fourier amplitude sensitivity test (FAST) (Cukier et al 1973(Cukier et al , 1978 has been used to solve coupled nonlinear rate equations by Schaibly and Shuler (1973) and Cukier et al, (1975). FAST has also been used by Dickinson and Gelinas (1976) to study sensitivities of parameters used to model atmospheric chemical kinetics, by Koda et al (1979) to study atmospheric diffusion, and several others (Leipmann and Stephanopoulos, 1985;Kim etal., 1988).…”

Global sensitivity analysis—a computational implementation of the Fourier Amplitude Sensitivity Test (FAST)

“…However, the difference between x and <x> for a well chosen integer frequency set can be made arbitrarily small [ 2,3].…”

Towards simplification of hydrologic modeling: identification of dominant processes

“…This is determined by partitioning the total variability in the model output or change in performance statistics to individual calibration parameters . The Fourier amplitude sensitivity test (FAST) (Schaibly and Shuler, 1973;Cukier et al, 1973Cukier et al, , 1975Saltelli et al, 2006) was selected for this study because it has been demonstrated that it can efficiently estimate non-linear hydrologic model parameter sensitivity (Guse et al, 2014;Pfannerstill et al, 2015;. FAST is a variance-based global sensitivity algorithm that estimates the first-order partial variance of model output explained by each calibration parameter (hereafter referred to as parameter sensitivity).…”