Some limitations of statistical interpolation
3D-Var: background-error covariances are considered to be stationary and representative of forecast error averaged over a period of a few months (1-3 months)
- No flow dependency to take into account the spatio-temporal variability of forecast error
Kalman filter: error statistics are only described by their covariances
- Extension to more general probability distributions requires knowledge of higher-order statistical moments (Lorenc, 1986; Tarantola, 1987)
- van Leeuwen, P.J. and G. Evensen, 1996: Data assimilation and inverse methods in terms of a probabilistic formulation. Mon. Wea. Rev., 124, 2898-2913.
Forecast and observation error are assumed to be unbiased