This book contains a detailed presentation of general principles of sensitivity analysis as
well as their applications to sample cases of remote sensing experiments. An emphasis is made
on applications of adjoint problems because they are more efficient in many practical cases
although their formulation may seem counterintuitive to a beginner. Special attention is paid
to forward problems based on higher-order partial differential equations where a novel matrix
operator approach to formulation of corresponding adjoint problems is presented. Sensitivity
analysis (SA) serves for quantitative models of physical objects the same purpose as
differential calculus does for functions. SA provides derivatives of model output parameters
(observables) with respect to input parameters. In remote sensing SA provides
computer-efficient means to compute the jacobians matrices of partial derivatives of
observables with respect to the geophysical parameters of interest. The jacobians are used to
solve corresponding inverse problems of remote sensing. They also play an important role
already while designing the remote sensing experiment where they are used to estimate the
retrieval uncertainties of the geophysical parameters with given measurement errors of the
instrument thus providing means for formulations of corresponding requirements to the specific
remote sensing instrument. If the quantitative models of geophysical objects can be formulated
in an analytic form then sensitivity analysis is reduced to differential calculus. But in most
cases the practical geophysical models used in remote sensing are based on numerical solutions
of forward problems - differential equations with initial and or boundary conditions. As a
result these models cannot be formulated in an analytic form and this is where the methods of
SA become indispensable. This book is intended for a wide audience. The beginners in remote
sensing could use it as a single source covering key issues of SA from general principles
through formulation of corresponding linearized and adjoint problems to practical applications
to uncertainty analysis and inverse problems in remote sensing. The experts already active in
the field may find useful the alternative formulations of some key issues of SA for example
use of individual observables instead of a widespread use of the cumulative cost function. The
book also contains an overview of author's matrix operator approach to formulation of adjoint
problems for forward problems based on the higher-order partial differential equations. This
approach still awaits its publication in the periodic literature and thus may be of interest to
readership across all levels of expertise.
