pyPDAF.PDAF.omi_assimilate_en3dvar_estkf

pyPDAF.PDAF.omi_assimilate_en3dvar_estkf()

3DEnVar for a single DA step using diagnoal observation error covariance matrix.

See pyPDAF.PDAF.omi_assimilate_en3dvar_estkf_nondiagR() for using non-diagonal observation error covariance matirx.

Here, 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 function is a combination of pyPDAF.PDAF.omi_put_state_en3dvar_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. the iterative optimisation:

   1. py__cvt_ens_pdaf

   2. py__obs_op_lin_pdaf

   3. py__obs_op_adj_pdaf

   4. py__cvt_adj_ens_pdaf

   5. 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. core ESTKF algorithm

8. py__prepoststep_state_pdaf

9. py__distribute_state_pdaf

10. py__next_observation_pdaf

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__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

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

  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

• outflag (int) – Status flag

Returns:

outflag – Status flag

Return type:

int