pyPDAF.PDAF.put_state_etkf

pyPDAF.PDAF.put_state_etkf()

It is recommended to use pyPDAF.PDAF.omi_put_state_global() or pyPDAF.PDAF.omi_put_state_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].

Compared to pyPDAF.PDAF.assimilate_etkf(), 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.

This function should be called at each model time step.

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

Deprecated since version 1.0.0: This function is replaced by pyPDAF.PDAF.omi_put_state_global() and pyPDAF.PDAF.omi_put_state_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__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 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__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

Returns:

flag – Status flag

Return type:

int