Introduction to Data Assimilation for Scientists and Engineers

Data assimilation can be used to control the initial condition of a model.

The analysis \(\underline x^a\) minimizes the cost function:

\(\displaystyle J(\underline{x}) ={1\over 2} \left(\underline{x} - \underline{x}^b\right)^T \underline{\underline B}^{-1} \left(\underline{x} - \underline{x}^b\right)+ {1\over 2} \left[\underline{y}^o - {\cal G}(\underline{x})\right]^T \underline{\underline R}^{-1}\left[\underline{y}^o - {\cal G}(\underline{x})\right]\)

• \(\underline x^b\) : the previous forecast

• \(\underline y^o\) : measurements on the real system

• \(\cal G\) : the link between an initial condition and the model observations

• \(\underline {\underline B}\) : background error covariance matrix

• \(\underline {\underline R}\) : observation error covariance matrix