pyPDAF.PDAF.omi_put_state_enkf_nondiagR

pyPDAF.PDAF.omi_put_state_enkf_nondiagR()

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_global() for simpler user-supplied functions using diagonal observation error covariance matrix.

The stochastic EnKF is implemented based on [1].

Compared to pyPDAF.PDAF.omi_assimilate_enkf_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.

This function executes the user-supplied functions 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 ensemble mean)

  5. py__add_obs_err_pdaf

  6. py__init_obscovar_pdaf

  7. py__obs_op_pdaf (for each ensemble member)

  8. core DA algorithm

References

Parameters:

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

    Routine to collect a state vector

    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]) –

    Initialize dimension of observation vector

    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 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__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

  • py__prepoststep_pdaf (Callable[step:int, dim_p:int, dim_ens:int, dim_ens_p: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]) –

    User supplied pre/poststep routine

    Callback Parameters
    • stepint

      • current time step (negative for call after forecast)

    • dim_pint

      • pe-local state dimension

    • dim_ensint

      • size of state ensemble

    • dim_ens_pint

      • pe-local size of ensemble

    • 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 not generally not initialized in the case of seik. it can be used freely here.)

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

      • inverse of matrix u

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

      • pe-local state ensemble

    • flagint

      • pdaf status flag

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

      • pe-local forecast/analysis state (the array ‘state_p’ is not generally not initialized in the case of seik. it can be used freely here.)

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

      • inverse of matrix u

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

      • pe-local state ensemble

Returns:

outflag

Return type:

int