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Pierre Tandeo, Pierre Ailliot, Marc Bocquet, Alberto Carrassi, Takemasa Miyoshi, Manuel Pulido, and Yicun Zhen

the underlying physics, including deficiencies in the numerical schemes, the cumulative effects of errors in the parameters, and the lack of knowledge of the unresolved scales. Its estimation is a challenge in general, but it is particularly so in geosciences because we usually have far fewer observations than those needed to estimate the entries of Q ( Daley 1992 ; Dee 1995 ). The sum of the two covariances P m and Q gives the forecast covariance matrix, P f (full green ellipse in Fig

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