pyPDAF.PDAF.assimilate_etkf

pyPDAF.PDAF.assimilate_etkf()

It is recommended to use pyPDAF.PDAF.omi_assimilate_global() or pyPDAF.PDAF.omi_assimilate_global_nondiagR().

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

Using ETKF (ensemble transform Kalman filter) [1] for a single DA step without OMI. The implementation is baed on [2].

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

6. py__obs_op_pdaf (for each ensemble member)

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

8. py__prodRinvA_pdaf

9. core DA 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_global() and pyPDAF.PDAF.omi_assimilate_global_nondiagR()

References

[1]

Bishop, C. H., B. J. Etherton, and S. J. Majumdar (2001) Adaptive Sampling with the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects. Mon. Wea. Rev., 129, 420–436, doi: 10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2.

[2]

Nerger, L., Janjić, T., Schröter, J., Hiller, W. (2012). A unification of ensemble square root Kalman filters. Monthly Weather Review, 140, 2335-2345. doi:10.1175/MWR-D-11-00102.1

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__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_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__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 HV

  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__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__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:

flag – Status flag

Return type:

int