pyPDAF.PDAF.omi_put_state_lenkf_nondiagR

pyPDAF.PDAF.omi_put_state_lenkf_nondiagR()

Covariance localised stochastic EnKF for a single DA step using non-diagnoal observation error covariance matrix without post-processing, distributing analysis, and setting next observation step.

See pyPDAF.PDAF.omi_put_state_lenkf() for simpler user-supplied functions using diagnoal observation error covariance matrix.

This function is implemented based on [1].

This is the only scheme for covariance localisation in PDAF.

Compared to pyPDAF.PDAF.omi_assimilate_lenkf_nondiagR(), this function has no get_state() call. This means that the analysis is not post-processed, and distributed to the model forecast by user-supplied functions. The next DA step will not be assigned by user-supplied functions as well. This function is typically used when there are not enough CPUs to run the ensemble in parallel, and some ensemble members have to be run serially. The pyPDAF.PDAF.get_state() function follows this function call to ensure the sequential DA.

This function should be called at each model time step.

User-supplied functions are executed in the following sequence:

  1. py__collect_state_pdaf

  2. py__prepoststep_state_pdaf

  3. py__init_dim_obs_pdaf

  4. py__obs_op_pdaf (for each ensemble member)

  5. py__localize_pdaf

  6. py__add_obs_err_pdaf

  7. py__init_obscovar_pdaf

  8. py__obs_op_pdaf (repeated to reduce storage)

  9. core DA algorithm

References

Parameters:

  • py__collect_state_pdaf (Callable[dim_p:int, state_p : ndarray[tuple[dim_p], np.float64]]) –

    Collect state vector from model/any arrays to pdaf arrays

    Callback Parameters
    • dim_pint

      • pe-local state dimension

    • state_pndarray[tuple[dim_p], np.float64]

      • local state vector

    Callback Returns
    • state_pndarray[tuple[dim_p], np.float64]

      • local state vector

  • py__init_dim_obs_pdaf (Callable[step:int, dim_obs_p:int]) –

    The primary purpose of this function is to obtain the dimension of the observation vector. In OMI, in this function, one also sets the properties of obs_f, read the observation vector from files, setting the observation error variance when diagonal observation error covariance matrix is used. The pyPDAF.PDAF.omi_gather_obs function is also called here.

    Callback Parameters
    • stepint

      • current time step

    • dim_obs_pint

      • dimension of observation vector

    Callback Returns
    • dim_obs_pint

      • dimension of observation vector

  • py__obs_op_pdaf (Callable[step:int, dim_p:int, dim_obs_p:int, state_p : ndarray[tuple[dim_p], np.float64], m_state_p : ndarray[tuple[dim_obs_p], np.float64]]) –

    Observation operator

    Callback Parameters
    • stepint

      • Current time step

    • dim_pint

      • Size of state vector (local part in case of parallel decomposed state)

    • dim_obs_pint

      • Size of PE-local observation vector

    • state_pndarray[tuple[dim_p], np.float64]

      • Model state vector

    • m_state_pndarray[tuple[dim_obs_p], np.float64]

      • Observed state vector (i.e. the result after applying the observation operator to state_p)

    Callback Returns
    • m_state_pndarray[tuple[dim_obs_p], np.float64]

      • Observed state vector (i.e. the result after applying the observation operator to state_p)

  • py__prepoststep_pdaf (Callable[step:int, dim_p:int, dim_ens:int, dim_ens_l:int, dim_obs_p:int, state_p : ndarray[tuple[dim_p], np.float64], uinv : ndarray[tuple[dim_ens-1, dim_ens-1], np.float64], ens_p : ndarray[tuple[dim_p, dim_ens], np.float64], flag:int]) –

    Preprocesse the ensemble before analysis and postprocess the ensemble before distributing to the model for next forecast

    Callback Parameters
    • stepint

      • current time step (negative for call before analysis/preprocessing)

    • dim_pint

      • PE-local state vector dimension

    • dim_ensint

      • number of ensemble members

    • dim_ens_lint

      • number of ensemble members run serially on each model task

    • dim_obs_pint

      • PE-local dimension of observation vector

    • state_pndarray[tuple[dim_p], np.float64]

      • pe-local forecast/analysis state (the array ‘state_p’ is generally not initialised in the case of ESTKF/ETKF/EnKF/SEIK, so it can be used freely here.)

    • uinvndarray[tuple[dim_ens-1, dim_ens-1], np.float64]

      • Inverse of the transformation matrix in ETKF and ESKTF; inverse of matrix formed by right singular vectors of error covariance matrix of ensemble perturbations in SEIK/SEEK. not used in EnKF.

    • ens_pndarray[tuple[dim_p, dim_ens], np.float64]

      • PE-local ensemble

    • flagint

      • pdaf status flag

    Callback Returns
    • state_pndarray[tuple[dim_p], np.float64]

      • pe-local forecast/analysis state (the array ‘state_p’ is generally not initialised in the case of ESTKF/ETKF/EnKF/SEIK, so it can be used freely here.)

    • uinvndarray[tuple[dim_ens-1, dim_ens-1], np.float64]

      • Inverse of the transformation matrix in ETKF and ESKTF; inverse of matrix formed by right singular vectors of error covariance matrix of ensemble perturbations in SEIK/SEEK. not used in EnKF.

    • ens_pndarray[tuple[dim_p, dim_ens], np.float64]

      • PE-local ensemble

  • py__localize_covar_pdaf (Callable[dim_p:int, dim_obs:int, hp_p : ndarray[tuple[dim_obs, dim_p], np.float64], hph : ndarray[tuple[dim_obs, dim_obs], np.float64]]) –

    Apply localization to HP and HPH^T

    Callback Parameters
    • dim_pint

      • pe-local state dimension

    • dim_obsint

      • number of observations

    • hp_pndarray[tuple[dim_obs, dim_p], np.float64]

      • pe local part of matrix hp

    • hphndarray[tuple[dim_obs, dim_obs], np.float64]

      • matrix hph

    Callback Returns
    • hp_pndarray[tuple[dim_obs, dim_p], np.float64]

      • pe local part of matrix hp

    • hphndarray[tuple[dim_obs, dim_obs], np.float64]

      • matrix hph

  • py__add_obs_err_pdaf (Callable[step:int, dim_obs_p:int, C_p : ndarray[tuple[dim_obs_p, dim_obs_p], np.float64]]) –

    Add obs error covariance R to HPH in EnKF

    Callback Parameters
    • stepint

      • Current time step

    • dim_obs_pint

      • Dimension of observation vector

    • C_pndarray[tuple[dim_obs_p, dim_obs_p], np.float64]

      • Matrix to that observation covariance R is added

    Callback Returns
    • C_pndarray[tuple[dim_obs_p, dim_obs_p], np.float64]

      • Matrix to that observation covariance R is added

  • py__init_obs_covar_pdaf (Callable[step:int, dim_obs:int, dim_obs_p:int, covar:float, obs_p : ndarray[tuple[dim_obs_p], np.float64], isdiag:bool]) –

    Initialize obs. error cov. matrix R in EnKF

    Callback Parameters
    • stepint

      • Current time step

    • dim_obsint

      • Global size of observation vector

    • dim_obs_pint

      • Size of process-local observation vector

    • covarfloat

      • Observation error covariance matrix

    • obs_pndarray[tuple[dim_obs_p], np.float64]

      • Process-local vector of observations

    • isdiagbool
    Callback Returns
    • covarfloat

      • Observation error covariance matrix

    • isdiagbool

Returns:

outflag – Status flag

Return type:

int