PDAF_diag_compute_moments

This page documents the routine PDAF_diag_compute_moments of PDAF, which was introduced with PDAF V3.0.

This routine computes the mean, the unbiased variance, the unbiased skewness, and the unbiased excess kurtosis from an ensemble. All moments are stored in a single array. kmax controls the highest order that should be computed. With parallized models, the moments are computed for the process-local state.

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 the following:

SUBROUTINE PDAF_diag_compute_moments(dim_p, dim_ens, ens, kmax, moments, bias) 

  INTEGER, INTENT(IN) :: dim_p              ! Local size of the state vector
  INTEGER, INTENT(IN) :: dim_ens            ! Number of ensemble members/samples
  REAL, INTENT(IN) :: ens(dim_p,dim_ens)    ! Ensemble matrix
  INTEGER, INTENT(IN) :: kmax               ! Highest order of statistical moment (1-4)
  REAL, INTENT(OUT) :: moments(dim_p, kmax) ! The statistical moments up to order `kmax` with
                                            !  - column 1: mean
                                            !  - column 2: variance
                                            !  - column 3: skewness
                                            !  - column 4: excess kurtosis
  INTEGER, OPTIONAL, INTENT(IN) :: bias     !< 0 to compute bias corrected values (default)

Note:

• The routine does not perform any MPI operations and can also be used if PDAF was not initialized by calling PDAF_init.