pyPDAF.PDAF.assimilate_lenkf

pyPDAF.PDAF.assimilate_lenkf()

It is recommended to use pyPDAF.PDAF.omi_assimilate_lenkf() or pyPDAF.PDAF.omi_assimilate_lenkf_nondiagR().

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

Stochastic EnKF (ensemble Kalman filter) with covariance localisation [1] for a single DA step without OMI.

This is the only scheme for covariance localisation in PDAF.

This function should be called at each model time step. The function is a combination of pyPDAF.PDAF.put_state_lenkf() and pyPDAF.PDAF.get_state().

The user-supplied function is 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 each ensemble member)

5. py__localize_pdaf

6. py__add_obs_err_pdaf

7. py__init_obs_pdaf

8. py__init_obscovar_pdaf

9. py__obs_op_pdaf (repeated to reduce storage)

10. core DA algorith

11. py__prepoststep_state_pdaf

12. py__distribute_state_pdaf

13. py__next_observation_pdaf

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

References

[1]

Houtekamer, P. L., and H. L. Mitchell (1998): Data Assimilation Using an Ensemble Kalman Filter Technique. Mon. Wea. Rev., 126, 796–811, doi: 10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2.

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__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__localize_covar_pdaf (Callable[dim_p:int, dim_obs:int, hp_p : ndarray[tuple[dim_obs, dim_p], np.float64], hph : ndarray[tuple[dim_obs, dim_obs], np.float64]]) –

  Apply localization to HP and HPH^T

  Callback Parameters

  • dim_pint

    • pe-local state dimension

  • dim_obsint

    • number of observations

  • hp_pndarray[tuple[dim_obs, dim_p], np.float64]

    • pe local part of matrix hp

  • hphndarray[tuple[dim_obs, dim_obs], np.float64]

    • matrix hph

  Callback Returns

  • hp_pndarray[tuple[dim_obs, dim_p], np.float64]

    • pe local part of matrix hp

  • hphndarray[tuple[dim_obs, dim_obs], np.float64]

    • matrix hph

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

  Provide time step and time 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:

flag – Status flag

Return type:

int