PDAF_diag_CRPS_mpi

This page documents the routine PDAF_diag_CRPS_mpi of PDAF, which was introduced with PDAF V2.2.1.

This routine computes the Continuous Ranked Probability Score (CRPS) and its decomposition into resolution and reliability. The CRPS provide information about the statistical consistency of the ensemble with the observations. In toy models, the CRPS can also be computed with regard to the true state.

With parallelization, the computation for the CRPS, reliability, etc. are performed over the global state vector utilizing appropriate MPI operations.

Inputs are an array holding the observed ensemble and a corresponding vector of observations.

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

The interface is:

SUBROUTINE PDAF_diag_crps_mpi(dim_p, dim_ens, element, oens, obs, &
    COMM_filter, mype_filter, npes_filter, &
    CRPS, reli, pot_CRPS, uncert, status)

  INTEGER, INTENT(in) :: dim_p                ! PE-local state dimension
  INTEGER, INTENT(in) :: dim_ens              ! Ensemble size
  INTEGER, INTENT(in) :: element              ! index of element in full state vector
       !< If element=0, mean values over dim_p grid points/cases are computed
  INTEGER, INTENT(in) :: COMM_filter          ! MPI communicator for filter
  INTEGER, INTENT(in) :: mype_filter          ! rank of MPI communicator
  INTEGER, INTENT(in) :: npes_filter          ! size of MPI communicator
  REAL, INTENT(in)    :: oens(dim_p, dim_ens) ! State ensemble
  REAL, INTENT(in)    :: obs(dim_p)           ! Observation / truth
  REAL, INTENT(out)   :: CRPS                 ! CRPS
  REAL, INTENT(out)   :: reli                 ! Reliability
  REAL, INTENT(out)   :: pot_CRPS             ! potential CRPS (resolution)
  REAL, INTENT(out)   :: uncert               ! uncertainty
  INTEGER, INTENT(out) :: status              ! Status flag (0=success)

Hints:

• using element one can select a since element of the observation vector for which the CRPS is computed (by multiple computations, it allows to computed a CRPS individually for each entry of the state vector). For element=0 the CRPS over all elements is computed
• A perfectly reliable system gives reli=0. An informative system gives resol << uncert.
• Compared to Hersbach (2000), resol here is equivalent to CPRS_pot.
• The routine uses parallelization utilizing the parallelization variables given as aguments (COMM_filter, mype_filter, npes_filter). With these specifications, the routine can be used also when PDAF was not initialized by calling PDAF_init.
• The routine uses a rather simple sorting algorithm. Accordingly, the performance is likely suboptimal for high-dimensional cases.