pyPDAF.PDAF.local_put_state_lknetf

pyPDAF.PDAF.local_put_state_lknetf()

It is recommended to use pyPDAF.PDAF.localomi_put_state() or pyPDAF.PDAF.localomi_put_state_lknetf_nondiagR().

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

A hybridised LETKF and LNETF [1] for a single DA step.

Compared to pyPDAF.PDAF.local_assimilate_lknetf(), 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 LNETF computes the distribution up to the second moment similar to Kalman filters but using a nonlinear weighting similar to particle filters. This leads to an equal weights assumption for the prior ensemble. The hybridisation with LETKF is expected to lead to improved performance for quasi-Gaussian problems. The function should be called at each model step.

User-supplied functions are executed in the following sequence:

  1. py__collect_state_pdaf

  2. py__prepoststep_state_pdaf

  3. py__init_n_domains_p_pdaf

  4. py__init_dim_obs_pdaf

  5. py__obs_op_pdaf (for each ensemble member)

  6. py__init_obs_pdaf (if global adaptive forgetting factor type_forget=1 is used in pyPDAF.PDAF.init())

  7. py__init_obsvar_pdaf (if global adaptive forgetting factor is used)

  8. loop over each local domain:

    1. py__init_dim_l_pdaf

    2. py__init_dim_obs_l_pdaf

    3. py__g2l_obs_pdaf (localise each ensemble member in observation space)

    4. py__init_obs_l_pdaf

    5. py__init_obsvar_l_pdaf (only called if local adaptive forgetting factor type_forget=2 is used)

    6. py__prodRinvA_pdaf

    7. py__likelihood_l_pdaf

    8. core DA algorithm

  9. py__obs_op_pdaf (only called with HKN and HNK options called for each ensemble member)

  10. py__likelihood_hyb_l_pda

  11. py__init_obsvar_l_pdaf (only called if local adaptive forgetting factor type_forget=2 is used)

  12. py__prodRinvA_hyb_l_pdaf

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

References

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 PE-local 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__init_obs_l_pdaf (Callable[domain_p:int, step:int, dim_obs_l:int, observation_l : ndarray[tuple[dim_obs_l], np.float64]]) –

    Init. observation vector on local analysis domain

    Callback Parameters
    • domain_pint

      • Index of current local analysis domain

    • stepint

      • Current time step

    • dim_obs_lint

      • Local size of the observation vector

    • observation_lndarray[tuple[dim_obs_l], np.float64]

      • Local vector of observations

    Callback Returns
    • observation_lndarray[tuple[dim_obs_l], np.float64]

      • Local 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_l_pdaf (Callable[domain_p:int, step:int, dim_obs_l:int, rank:int, obs_l : ndarray[tuple[dim_obs_l], np.float64], A_l : ndarray[tuple[dim_obs_l, rank], np.float64], C_l : ndarray[tuple[dim_obs_l, rank], np.float64]]) –

    Provide product R^-1 A on local analysis domain

    Callback Parameters
    • domain_pint

      • Index of current local analysis domain

    • stepint

      • Current time step

    • dim_obs_lint

      • Number of local observations at current time step (i.e. the size of the local 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_lndarray[tuple[dim_obs_l], np.float64]

      • Local vector of observations

    • A_lndarray[tuple[dim_obs_l, rank], np.float64]

      • Input matrix provided by PDAF

    • C_lndarray[tuple[dim_obs_l, rank], np.float64]

      • Output matrix

    Callback Returns
    • C_lndarray[tuple[dim_obs_l, rank], np.float64]

      • Output matrix

  • py__prodRinvA_hyb_l_pdaf (Callable[domain_p:int, step:int, dim_obs_l:int, dim_ens:int, obs_l : ndarray[tuple[dim_obs_l], np.float64], gamma:float, A_l : ndarray[tuple[dim_obs_l, dim_ens], np.float64], C_l : ndarray[tuple[dim_obs_l, dim_ens], np.float64]]) –

    Provide product R^-1 A on local analysis domain with hybrid weight

    Callback Parameters
    • domain_pint

      • Index of current local analysis domain

    • stepint

      • Current time step

    • dim_obs_lint

      • Number of local observations at current time step (i.e. the size of the local observation vector)

    • dim_ensint

      • 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_lndarray[tuple[dim_obs_l], np.float64]

      • Local vector of observations

    • gammafloat

      • Hybrid weight provided by PDAF

    • A_lndarray[tuple[dim_obs_l, dim_ens], np.float64]

      • Input matrix provided by PDAF

    • C_lndarray[tuple[dim_obs_l, dim_ens], np.float64]

      • Output matrix

    Callback Returns
    • C_lndarray[tuple[dim_obs_l, dim_ens], np.float64]

      • Output matrix

  • py__init_n_domains_p_pdaf (Callable[step:int, n_domains_p:int]) –

    Provide number of local analysis domains

    Callback Parameters
    • stepint

      • current time step

    • n_domains_pint

      • pe-local number of analysis domains

    Callback Returns
    • n_domains_pint

      • pe-local number of analysis domains

  • py__init_dim_l_pdaf (Callable[step:int, domain_p:int, dim_l:int]) –

    Init state dimension for local ana. domain

    Callback Parameters
    • stepint

      • current time step

    • domain_pint

      • current local analysis domain

    • dim_lint

      • local state dimension

    Callback Returns
    • dim_lint

      • local state dimension

  • py__init_dim_obs_l_pdaf (Callable[domain_p:int, step:int, dim_obs_f:int, dim_obs_l:int]) –

    Initialize dim. of obs. vector for local ana. domain

    Callback Parameters
    • domain_pint

      • index of current local analysis domain

    • stepint

      • current time step

    • dim_obs_fint

      • full dimension of observation vector

    • dim_obs_lint

      • local dimension of observation vector

    Callback Returns
    • dim_obs_lint

      • local dimension of observation vector

  • py__g2l_obs_pdaf (Callable[domain_p:int, step:int, dim_obs_f:int, dim_obs_l:int, mstate_f : ndarray[tuple[dim_p], np.intc], dim_p:int, mstate_l : ndarray[tuple[dim_l], np.intc], dim_l:int]) –

    Restrict full obs. vector to local analysis domain

    Callback Parameters
    • domain_pint

      • Index of current local analysis domain

    • stepint

      • Current time step

    • dim_obs_fint

      • Size of full observation vector for model sub-domain

    • dim_obs_lint

      • Size of observation vector for local analysis domain

    • mstate_fndarray[tuple[dim_p], np.intc]

      • Full observation vector for model sub-domain

    • dim_pint

      • Size of full observation vector for model sub-domain

    • mstate_lndarray[tuple[dim_l], np.intc]

      • Observation vector for local analysis domain

    • dim_lint

      • Size of observation vector for local analysis domain

    Callback Returns
    • mstate_lndarray[tuple[dim_l], np.intc]

      • Observation vector for local analysis domain

  • 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__init_obsvar_l_pdaf (Callable[domain_p:int, step:int, dim_obs_l:int, obs_l : ndarray[tuple[dim_obs_p], np.float64], dim_obs_p:int, meanvar_l:float]) –

    Initialize local mean observation error variance

    Callback Parameters
    • domain_pint

      • Index of current local analysis domain

    • stepint

      • Current time step

    • dim_obs_lint

      • Local dimension of observation vector

    • obs_lndarray[tuple[dim_obs_p], np.float64]

      • Local observation vector

    • dim_obs_pint

      • Dimension of local observation vector

    • meanvar_lfloat

      • Mean local observation error variance

    Callback Returns
    • meanvar_lfloat

      • Mean local observation error variance

  • py__likelihood_l_pdaf (Callable[domain_p:int, step:int, dim_obs_l:int, obs_l : ndarray[tuple[dim_obs_l], np.float64], resid_l : ndarray[tuple[dim_obs_l], np.float64], likely_l:float]) –

    Compute likelihood

    Callback Parameters
    • domain_pint

      • Index of current local analysis domain

    • stepint

      • Current time step

    • dim_obs_lint

      • Number of local observations at current time step (i.e. the size of the local observation vector)

    • obs_lndarray[tuple[dim_obs_l], np.float64]

      • Local vector of observations

    • resid_lndarray[tuple[dim_obs_l], np.float64]

      • nput vector holding the local residual

    • likely_lfloat

      • Output value of the local likelihood

    Callback Returns
    • likely_lfloat

      • Output value of the local likelihood

  • py__likelihood_hyb_l_pdaf (Callable[domain_p:int, step:int, dim_obs_l:int, obs_l : ndarray[tuple[dim_obs_l], np.float64], resid_l : ndarray[tuple[dim_obs_l], np.float64], gamma:float, likely_l:float]) –

    Compute likelihood with hybrid weight

    Callback Parameters
    • domain_pint

      • Index of current local analysis domain

    • stepint

      • Current time step

    • dim_obs_lint

      • Number of local observations at current time step (i.e. the size of the local observation vector)

    • obs_lndarray[tuple[dim_obs_l], np.float64]

      • Local vector of observations

    • resid_lndarray[tuple[dim_obs_l], np.float64]

      • Input vector holding the local residual

    • gammafloat

      • Hybrid weight provided by PDAF

    • likely_lfloat

      • Output value of the local likelihood

    Callback Returns
    • likely_lfloat

      • Output value of the local likelihood

Returns:

outflag – Status flag

Return type:

int