Dual form of the 3D-Var: the 3D-PSAS(Physical Space Assimilation System)

• Cohn et al., 1998; Courtier, 1997:

where w is such that

Minimisation is performed in observation space

• Remark
  • Number of observations is less than the number of degrees of freedom characterizing X
  • Formulation is similar to what had been used for optimal interpolation which can facilitate the implemention
  • Equivalence is only true if H is linear.
  • Preconditioning of the minimisation is more difficult.
  • Same elementary operators as those used for the 3D-Var.

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