Adjoint models are powerful tools for many studies that require an estimate of sensitivity of model output (e.g., a forecast) with respect to input. Actual fields of sensitivity are produced directly and efficiently, which can then be used in a variety of applications, including data assimilation, parameter estimation, stability analysis, and synoptic studies.

The use of adjoint models as tools for sensitivity analysis is described here using some simple mathematics. An example of sensitivity fields is presented along with a short description of adjoint applications. Limitations of the applications are discussed and some speculations about the future of adjoint models are offered.

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*The National Center for Atmospheric Research is sponsored by the National Science Foundation.