pyPDAF.PDAF.omi_put_state_global

pyPDAF.PDAF.omi_put_state_global()

Global filters except for 3DVar for a single DA step using diagnoal observation error covariance matrix without post-processing, distributing analysis, and setting next observation step.

See pyPDAF.PDAF.omi_put_state_enkf_nondiagR(), or pyPDAF.PDAF.omi_put_state_global_nondiagR(), or pyPDAF.PDAF.omi_put_state_nonlin_nondiagR() for non-diagonal observation error covariance matrix.

OMI functions need fewer user-supplied functions and improve DA efficiency.

Here, this function call is used for global stochastic EnKF [1], E(S)TKF [2], SEEK [2], SEIK [2], NETF [3], and particle filter [4]. The filter type is set in pyPDAF.PDAF.init(). Compared to pyPDAF.PDAF.omi_assimilate_global(), 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.

The ESTKF is a more efficient equivalent to the ETKF.

The 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]

Evensen, G. (1994), Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99(C5), 10143–10162, doi:10.1029/94JC00572.

[2] (1,2,3)

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

[3]

Tödter, J., and B. Ahrens, 2015: A second-order exact ensemble square root filter for nonlinear data assimilation. Mon. Wea. Rev., 143, 1347–1367, doi:10.1175/MWR-D-14-00108.1.

[4]

Van Leeuwen, P. J., Künsch, H. R., Nerger, L., Potthast, R., & Reich, S. (2019). Particle filters for high‐dimensional geoscience applications: A review. Quarterly Journal of the Royal Meteorological Society, 145(723), 2335-2365.

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__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__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

Returns:

flag – Status flag

Return type:

int