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Analysis of forward models using the singular value decomposition algorithm

For microwave remote sensing of atmospheric composition or temperature an inversion of the measured primary data is in general necessary to obtain the desired profiles. In addition to the atmospheric quantities some unknown instrumental parameters might also need to be estimated from the data. Especially when designing a new instrument the question arises, whether the suggested data set contains enough information to retrieve the profiles and parameters with the desired accuracy. The singular value decomposition algorithm is shown to be a universal and powerful tool to analyze any linear or moderately nonlinear forward model and quantify the amount of retrievable parameters. In addition the method can be used as a simple and robust inversion technique, thus giving in one step not only an analysis of the relationship between measurement and parameter space, but also a solution of the inverse problem. The application of this method is illustrated using data obtained by ground-based measurements of ozone at 142 GHz.