The Sensitivity to Parametric Variation in Direct Minimization Techniques

S. D. Meyers Mesoscale Air-Sea Interaction Group, The Florida State University, Tallahassee, Florida

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C. Stephens Jones Mesoscale Air-Sea Interaction Group, The Florida State University, Tallahassee, Florida

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D. M. Legler Mesoscale Air-Sea Interaction Group, The Florida State University, Tallahassee, Florida

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K. F. Miles Mesoscale Air-Sea Interaction Group, The Florida State University, Tallahassee, Florida

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J. J. O'Brien Mesoscale Air-Sea Interaction Group, The Florida State University, Tallahassee, Florida

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Abstract

Solutions of some objective analysis techniques are known to depend upon the subjective values of internal parameters. The change in the solution per change in the parameter is the sensitivity. Parameters with low sensitivity can be varied with large increments during preliminary searches for near-optimal parameter values. Only terms with high sensitivity must be thoroughly investigated once the parameters are determined to be close to optimal. Both absolute and relative sensitivities are discussed and a sensitivity-based definition of the solution uncertainty is proposed. The sensitivity of direct minimization analysis to parametric variation is evaluated using a set of “response functions” that characterize different aspects of the solution. It is shown that solutions of direct minimization techniques have low absolute sensitivity.

Two examples are used to illustrate the usefulness of the technique. Both involve measurements of air-sea quantities (e.g., wind stress and latent heat flux) from a variety of data sources using a direct minimization technique. The examples demonstrate that sensitivity analysis is capable of quantifying regional sensitivities as well as indicating the magnitude and relationship between the various parameters.

Abstract

Solutions of some objective analysis techniques are known to depend upon the subjective values of internal parameters. The change in the solution per change in the parameter is the sensitivity. Parameters with low sensitivity can be varied with large increments during preliminary searches for near-optimal parameter values. Only terms with high sensitivity must be thoroughly investigated once the parameters are determined to be close to optimal. Both absolute and relative sensitivities are discussed and a sensitivity-based definition of the solution uncertainty is proposed. The sensitivity of direct minimization analysis to parametric variation is evaluated using a set of “response functions” that characterize different aspects of the solution. It is shown that solutions of direct minimization techniques have low absolute sensitivity.

Two examples are used to illustrate the usefulness of the technique. Both involve measurements of air-sea quantities (e.g., wind stress and latent heat flux) from a variety of data sources using a direct minimization technique. The examples demonstrate that sensitivity analysis is capable of quantifying regional sensitivities as well as indicating the magnitude and relationship between the various parameters.

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