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# cvt_adj_pdaf

The page document the user-supplied call-back routine `cvt_adj_pdaf`

.

The routine `cvt_adj_pdaf`

(`U_cvt_adj`

inside the PDAF library routines) is a call-back routine that has to be provided by the user.

The routine is used with the parameterized 3D-Var and the hybrid 3D-Var methods.

The routine is called during the iterative optimization. It has to perform the adjoint of the control vector transform (preconditioning) which is usually a multiplication with the transponse square-root of the background covariance matrix **B**. The routine is provided with a state vector and hos to return a vector in control space. The routine allows a user to implement the control vector transform in form of covariance operators.

The interface is the following:

SUBROUTINE cvt_adj_pdaf(iter, dim_p, dim_cvec, Vcv_p, cv_p) INTEGER, INTENT(in) :: iter ! Iteration of optimization INTEGER, INTENT(in) :: dim_p ! PE-local observation dimension INTEGER, INTENT(in) :: dim_cvec ! Dimension of control vector REAL, INTENT(in) :: Vcv_p(dim_p) ! PE-local result vector (state vector increment) REAL, INTENT(inout) :: cv_p(dim_cvec) ! PE-local control vector

Hints:

- If the state vector is decomposed in case of parallelization one needs to take care that the application of the trasformation is complete. This usually requries a communication with MPI_Allreduce to obtain a global sun.