= PDAF_diag_diffstats = 

This page documents the routine `PDAF_diag_diffstats` of PDAF, which was introduced with PDAF V3.1.

The routine is provided two vector of the same length and returns a vector with 6 statistics comparing the two vectors. The statistics can, for example, be used to plot a Taylor diagram.

The routine can be called in the pre/poststep routine of PDAF both before and after the analysis step to compute the ensemble statistics. 

The interface is: 
{{{
  SUBROUTINE PDAF_diag_diffstats(dim_p, vec1, vec2, stats, verbose)

    INTEGER, INTENT(in) :: dim_p     !< Size of vector
    REAL, INTENT(inout) :: vec1(:)   !< Vector 1
    REAL, INTENT(inout) :: vec2(:)   !< Vector 2
    REAL, INTENT(inout) :: stats(6)  !< Vector holding statistics
          ! Included statistics are:
          !  (1,:) correlations between vec1 and vec2 (corr)
          !  (2,:) centered RMS difference between vec1 and vec2 (cRMSD)
          !  (3,:) mean bias (vec1-vec2)
          !  (4,:) mean absolute difference between vec1 and vec2 (MAD)
          !  (5,:) standard deviation of vec1 (STDDEV(vec1))
          !  (6,:) standard deviation of vec2 (STDDEV(vec2))
    INTEGER, INTENT(in) :: verbose   !< Verbosity flag
}}}


For verbose>0 a list of statistics is printed for each observation type in the form
{{{
PDAF   corr      cRMSD       bias         MAD      STDDEV(1)   STDDEV(2)
PDAF   0.611   7.084E-01   4.376E-02   5.774E-01   8.787E-01   7.179E-01
}}}

**Note:**
 * The statistics are computed for the global domain. Thus, with parallelization the values in `stats(6)` will be identical for all processes.
 * The routine performs MPI operations to obtain the global result. These operations are performed within the communicator `COMM_filter`, i.e. within the communicator computing the analysis step.
 * To compare the assimilated observations with the ensemble mean, one can use the PDAF-OMI routine [wiki:PDAFomi_diag_diffstats].