fips.Estimator.desroziers

property Estimator.desroziers: ndarray

Desroziers et al. (2005) diagnosed observation error covariance.

Estimates the observation error covariance from the innovation (prior departure) and analysis departure (posterior residual):

\[R_{diag} = \frac{1}{2}(d^a {d^b}^T + d^b {d^a}^T)\]

where \(d^b = z - Hx_0 - c\) (innovation) and \(d^a = z - H\hat{x} - c\) (analysis departure).

Symmetrized since the single-realization outer product is not symmetric but the expectation is.

Returns:

Diagnosed observation error covariance matrix (n_z × n_z).

Return type:

np.ndarray

References

Desroziers, G., Berre, L., Chapnik, B., & Poli, P. (2005). Diagnosis of observation, background and analysis-error statistics in observation space. Q.J.R. Meteorol. Soc., 131, 3385–3396.