pyPDAF.PDAF.assimilate_hyb3dvar_estkf

pyPDAF.PDAF.assimilate_hyb3dvar_estkf()

It is recommended to use pyPDAF.PDAF.omi_assimilate_hyb3dvar_estkf() or pyPDAF.PDAF.omi_assimilate_hyb3dvar_estkf_nondiagR().

PDAF-OMI modules require fewer user-supplied functions and improved efficiency.

Hybrid 3DEnVar for a single DA step where the background error covariance is hybridised by a static background error covariance, and a flow-dependent background error covariance estimated from ensemble. The 3DVar generates an ensemble mean and the ensemble perturbation is generated by ESTKF in this implementation. This function should be called at each model time step.

The function is a combination of pyPDAF.PDAF.put_state_hyb3dvar_estkf() and pyPDAF.PDAF.get_state().

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. py__init_obs_pdaf

  6. the iterative optimisation:

    1. py__cvt_pdaf

    2. py__cvt_ens_pdaf

    3. py__obs_op_lin_pdaf

    4. py__prodRinvA_pdaf

    5. py__obs_op_adj_pdaf

    6. py__cvt_adj_pdaf

    7. py__cvt_adj_ens_pdaf

    8. core 3DEnVar algorithm

  7. py__cvt_pdaf

  8. py__cvt_ens_pdaf

  9. Perform ESTKF:

    1. py__init_dim_obs_pdaf

    2. py__obs_op_pdaf (for ensemble mean)

    3. py__init_obs_pdaf

    4. py__obs_op_pdaf (for each ensemble member)

    5. py__init_obsvar_pdaf (only relevant for adaptive forgetting factor schemes)

    6. py__prodRinvA_pdaf

    7. core ESTKF algorithm

  10. py__prepoststep_state_pdaf

  11. py__distribute_state_pdaf

  12. py__next_observation_pdaf

Deprecated since version 1.0.0: This function is replaced by pyPDAF.PDAF.omi_assimilate_hyb3dvar_estkf() and pyPDAF.PDAF.omi_assimilate_hyb3dvar_estkf_nondiagR()

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

    Routine to distribute 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__init_obs_pdaf (Callable[step:int, dim_obs_p:int, observation_p : ndarray[tuple[dim_obs_p], np.float64]]) –

    Initialize observation vector

    Callback Parameters
    • stepint

      • Current time step

    • dim_obs_pint

      • Size of the observation vector

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

      • Vector of observations

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

      • Vector of observations

  • 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 (ensemble)

    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 (ensemble var)

    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__cvt_pdaf (Callable[iter:int, dim_p:int, dim_cvec:int, cv_p : ndarray[tuple[dim_cvec], 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 observation dimension

    • dim_cvecint

      • Dimension of control vector

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

      • PE-local control vector

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

      • PE-local result vector (state vector increment)

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

      • PE-local result vector (state vector increment)

  • py__cvt_adj_pdaf (Callable[iter:int, dim_p:int, dim_cvec:int, Vcv_p : ndarray[tuple[dim_p], np.float64], cv_p : ndarray[tuple[dim_cvec], np.float64]]) –

    Apply adjoint control vector transform matrix

    Callback Parameters
    • iterint

      • Iteration of optimization

    • dim_pint

      • PE-local observation dimension

    • dim_cvecint

      • Dimension of control vector

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

      • PE-local result vector (state vector increment)

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

      • PE-local control vector

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

      • PE-local control 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__init_obsvar_pdaf (Callable[step:int, dim_obs_p:int, obs_p : ndarray[tuple[dim_obs_p], np.float64], meanvar:float]) –

    Initialize mean observation error variance

    Callback Parameters
    • stepint

      • Current time step

    • dim_obs_pint

      • Size of observation vector

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

      • Vector of observations

    • meanvarfloat

      • Mean observation error variance

    Callback Returns
    • meanvarfloat

      • Mean observation error variance

  • 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

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

    Routine to provide time step, time and dimension of next observation

    Callback Parameters
    • stepnowint

      • number of the current time step

    • nstepsint

      • number of time steps until next obs

    • doexitint

      • whether to exit forecasting (1 for exit)

    • timefloat

      • current model (physical) time

    Callback Returns
    • nstepsint

      • number of time steps until next obs

    • doexitint

      • whether to exit forecasting (1 for exit)

    • timefloat

      • current model (physical) time

Returns:

outflag – Status flag

Return type:

int