Sensitivity Analysis of Analytic Models: Linearization and Adjoint Approaches

Part of the SpringerBriefs in Earth Sciences book series (BRIEFSEARTH)


In this chapter we apply the linearization and adjoint approaches of sensitivity analysis to three analytic models, for which we have obtained the solutions earlier, in Chap.  4, using the formalism of differential calculus (for discrete parameters) and variational calculus (for continuous parameters). We will reproduce these results using the approaches of sensitivity analysis described in general form in Chap.  3, which will provide a form of validation of these approaches.


Analytic models Linearization approach Adjoint approach 


  1. Sensitivity analysis of the linear and non-linear demo models using the linearization and adjoint approaches in the form presented in this chapter was developed by the author for the course on sensitivity analysis mentioned in the previous chapter. The concept of assembling the linear operator and the right-hand term of the operator forward problem in the form of weighted sums of the operators and right-hand terms of the differential equation(s) and initial and/or boundary conditions was developed in the author’s paper:Google Scholar
  2. Ustinov EA (2001) Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. J Quant Spectr Rad Transf 68:195–211CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA

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