Covariance models
The forecast covariance matrix is essential for variational algorithm (and also Ensemble Kalman's filter).
But the huge size of such matrices,
coefficients, implies it has to be approximated (ensemble) or modelized.
Model of covariance matrix should ensure properties of covariance matrix:
symmetry
positivity
full rank (but, actually, this is not essential)
There exists several covariance model, among them one can mention:
Spectral digonal assumption [CAaJP+98]
Wavelet diagonal assumption [Fis03, PBD07, Pan09]
Diffusion based formulation [WC01, PM08]
Deformation based formulation [Des97, Mic12, PET12]
Recursive filter [PWDR03]
