pyPDAF.PDAF.omi_put_state_en3dvar_estkf_nondiagR

pyPDAF.PDAF.omi_put_state_en3dvar_estkf_nondiagR()

3DEnVar 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_en3dvar_estkf() for simpler user-supplied functions using diagonal observation error covariance matrix.

Compared to pyPDAF.PDAF.omi_assimilate_en3dvar_estkf_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.

The background error covariance matrix is estimated by an ensemble. The 3DEnVar only calculates the analysis of the ensemble mean. An ESTKF is used along with 3DEnVar to generate ensemble perturbations. This function should be called at each model time step.

The 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

  5. the iterative optimisation:

    1. py__cvt_ens_pdaf

    2. py__obs_op_lin_pdaf

    3. py__prodRinvA_pdaf

    4. py__obs_op_adj_pdaf

    5. py__cvt_adj_ens_pdaf

    6. core 3DEnVar algorithm

  6. py__cvt_ens_pdaf

  7. ESTKF:

    1. py__init_dim_obs_pdaf

    2. py__obs_op_pdaf (for ensemble mean)

    3. py__obs_op_pdaf (for each ensemble member)

    4. py__prodRinvA_pdaf

    5. core ESTKF algorithm

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__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__cvt_ens_pdaf (Callable[iter:int, dim_p:int, dim_ens:int, dim_cvec_ens:int, ens_p : ndarray[tuple[dim_p, dim_ens], np.float64], v_p : ndarray[tuple[dim_cvec_ens], np.float64], Vv_p : ndarray[tuple[dim_p], np.float64]]) –

    Apply control vector transform matrix to control vector

    Callback Parameters
    • iterint

      • Iteration of optimization

    • dim_pint

      • PE-local dimension of state

    • dim_ensint

      • Ensemble size

    • dim_cvec_ensint

      • Dimension of control vector

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

      • PE-local ensemble

    • v_pndarray[tuple[dim_cvec_ens], np.float64]

      • PE-local control vector

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

      • PE-local state increment

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

      • PE-local state increment

  • py__cvt_adj_ens_pdaf (Callable[iter:int, dim_p:int, dim_ens:int, dim_cv_ens_p:int, ens_p : ndarray[tuple[dim_p, dim_ens], np.float64], Vcv_p : ndarray[tuple[dim_p], np.float64], cv_p : ndarray[tuple[dim_cv_ens_p], np.float64]]) –

    Apply adjoint control vector transform matrix

    Callback Parameters
    • iterint

      • Iteration of optimization

    • dim_pint

      • PE-local observation dimension

    • dim_ensint

      • Ensemble size

    • dim_cv_ens_pint

      • PE-local dimension of control vector

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

      • PE-local ensemble

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

      • PE-local input vector

    • cv_pndarray[tuple[dim_cv_ens_p], np.float64]

      • PE-local result vector

    Callback Returns
    • cv_pndarray[tuple[dim_cv_ens_p], np.float64]

      • PE-local result vector

  • py__obs_op_lin_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]]) –

    Linearized observation operator

    Callback Parameters
    • stepint

      • Current time step

    • dim_pint

      • PE-local dimension of state

    • dim_obs_pint

      • Dimension of observed state

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

      • PE-local model state

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

      • PE-local observed state

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

      • PE-local observed state

  • py__obs_op_adj_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]]) –

    Adjoint observation operator

    Callback Parameters
    • stepint

      • Current time step

    • dim_pint

      • PE-local dimension of state

    • dim_obs_pint

      • Dimension of observed state

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

      • PE-local model state

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

      • PE-local observed state

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

      • PE-local model state

  • 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

  • outflag (int) – Status flag

Returns:

outflag – Status flag

Return type:

int