A method has been developed to investigate the sensitivity of the solutions of large sets of coupled nonlinear rate equations to uncertainties in the rate coefficients. This method is based on varying all the rate coefficients simultaneously through the introduction of a parameter in such a way that the output concentrations become periodic functions of this parameter at any given time t. The concentrations of the chemical species are then Fourier analyzed at time t. We show via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to 〈∂ci/∂kl〉, the rate of change of the concentration of species i with respect to the rate constant for reaction l averaged over the uncertainties of all the other rate coefficients. Thus a large Fourier coefficient corresponds to a large sensitivity, and a small Fourier coefficient corresponds to a small sensitivity. The amount of numerical integration required to calculate these Fourier coefficients is considerably less than that required in tests of sensitivity where one varies one rate coefficient at a time, while holding all others fixed. The Fourier method developed in this paper is not limited to chemical rate equations, but can be applied to the study of the sensitivity of any large system of coupled, nonlinear differential equations with respect to the uncertainties in the modeling parameters.

In Parts I and II of this series [J. Chem. Phys. 59, 3873, 3879 (1973)] we developed a new method of sensitivity analysis for large sets of coupled nonlinear equations with many parameters. In developing this theory and in carrying out the computer calculations involved in this analysis we made a number of approximations. We present here a quantitative analysis of these approximations and, where applicable, develop rigorous error bounds. Our analysis shows that we can specify the approximations which enter into our theory so as to obtain sensitivity measures of known accuracy. On this basis we feel that the techniques developed in this series of papers provide a useful and efficient method of sensitivity analysis of large systems with many parameters.

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.

The concept validation phase (Phase I) of the Navstar GPS program will evaluate the performance of User receiving equipment and the Control Segment. The purpose of this paper is to describe how the Control Segment supports the User test program, and how Control Segment prediction errors in satellite ephemerides and atomic frequency standard behavior are propagated into User error. A summary of projected performance is also presented based on simulation results.

Existing software packages for target/background signature analysis generate radiometrically accurate results, but may be difficult to use because of the complexity involved in coordinating model inputs and in 'mating' intermediate model outputs into a final result In addition, tools used to display and analyze model results are not always available on the model's host computer. Horizons Technology, Incorporated UITI) has undertaken the development of integrated workstations for the analysis of earth background and target signatures in the visible and infrared wavelengths. The first of these products, available now, is the Infrared Atmospherics and Signatures Predic1on Model (JASPM). IASPM is hosted on 80386 and 80486 PC/AT desktop computers, and incorporates three widely used electro-optical simulation codes: LOWTRAN (atmospheric propagation), SPIRITS (target signature) and EOSSIM (sensor performance). Also included are image display and analysis utilities. IASPM is controlled by an interacthre menu-driven graphical user interface which assists the analyst in selecting, comparing, and then analyzing meaningful target/background image scenarios. In addition, IASPM can also be used to display, analyze, and extend measured imageiy into new and unmeasured cases.