Editing Covariance (section)

===In meteorological and oceanographic data assimilation===
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The covariance matrix is important in estimating the initial conditions required for running weather forecast models, a procedure known as [[data assimilation]]. The "forecast error covariance matrix" is typically constructed between perturbations around a mean state (either a climatological or ensemble mean). The "observation error covariance matrix" is constructed to represent the magnitude of combined observational errors (on the diagonal) and the correlated errors between measurements (off the diagonal). This is an example of its widespread application to [[Kalman filtering]] and more general [[state estimation]] for time-varying systems.