pyPDAF.PDAF.omi_assimilate_global_nondiagR

pyPDAF.PDAF.omi_assimilate_global_nondiagR()

Global filters except for 3DVar and stochastic EnKF for a single DA step using non-diagnoal observation error covariance matrix.

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

Here, this function call is used for global, E(S)TKF [1], SEEK [1], SEIK [1]. The filter type is set in pyPDAF.PDAF.init(). This function should be called at each model time step.

The function is a combination of pyPDAF.PDAF.omi_put_state_global() and pyPDAF.PDAF.get_state().

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 ensemble mean)

  5. py__obs_op_pdaf (for each ensemble member)

  6. py__prodRinvA_pdaf

  7. core DA algorithm

  8. py__prepoststep_state_pdaf

  9. py__distribute_state_pdaf

  10. py__next_observation_pdaf

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

    distribute a state vector from pdaf to the model/any arrays

    Callback Parameters
    • dim_pint

      • PE-local state dimension

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

      • PE-local state vector

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

      • PE-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__prodRinvA_pdaf (Callable[step:int, dim_obs_p:int, rank:int, obs_p : ndarray[tuple[dim_obs_p], np.float64], A_p : ndarray[tuple[dim_obs_p, rank], np.float64], C_p : ndarray[tuple[dim_obs_p, rank], np.float64]]) –

    Provide product R^-1 A

    Callback Parameters
    • stepint

      • Current time step

    • dim_obs_pint

      • Number of observations at current time step (i.e. the size of the observation vector)

    • rankint

      • Number of the columns in the matrix processes here. This is usually the ensemble size minus one (or the rank of the initial covariance matrix)

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

      • Vector of observations

    • A_pndarray[tuple[dim_obs_p, rank], np.float64]

      • Input matrix provided by PDAF

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

      • Output matrix

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

      • Output matrix

  • 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__next_observation_pdaf (Callable[stepnow:int, nsteps:int, doexit:int, time:float]) –

    Routine to provide number of forecast time steps until next assimilations, model physical time and end of assimilation cycles

    Callback Parameters
    • stepnowint

      • the current time step given by PDAF

    • nstepsint

      • number of forecast time steps until next assimilation; this can also be interpreted as number of assimilation function calls to perform a new assimilation

    • doexitint

      • whether to exit forecasting (1 for exit)

    • timefloat

      • current model (physical) time

    Callback Returns
    • nstepsint

      • number of forecast time steps until next assimilation; this can also be interpreted as number of assimilation function calls to perform a new assimilation

    • doexitint

      • whether to exit forecasting (1 for exit)

    • timefloat

      • current model (physical) time

Returns:

outflag – Status flag

Return type:

int