Introduction to Data Assimilation for Scientists and Engineers

Most of the data assimilation methods lead to the minimization of a cost function involving quadratic forms based on the both the background and observation covariance matrices. Basic algebra and minimization methods are recalled.

When the observation operator is linear, this formulation of the cost function leads to the Best Linear Unbiased Estimation (BLUE) method and the analyis is the sum of the background plus a gain matrice times the "innovation". This algebra can be used in the nonlinear case with an incremental approximation of the cost function.

The 4D-Var method deals with a time evolution model and measurement spread on a time interval. The minimization of the cost function involves the computation of adjoint model.