pyPDAF.PDAF.assimilate_lnetf

pyPDAF.PDAF.assimilate_lnetf()

It is recommended to use pyPDAF.PDAF.localomi_assimilate() or pyPDAF.PDAF.localomi_assimilate_lnetf_nondiagR().

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

Local Nonlinear Ensemble Transform Filter (LNETF) [1] for a single DA step. The nonlinear filter computes the distribution up to the second moment similar to Kalman filters but it uses a nonlinear weighting similar to particle filters. This leads to an equal weights assumption for the prior ensemble at each step. This function should be called at each model time step.

The function is a combination of pyPDAF.PDAF.put_state_lnetf() 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_n_domains_p_pdaf

  4. py__init_dim_obs_pdaf

  5. py__obs_op_pdaf (for each ensemble member)

  6. loop over each local domain:

    1. py__init_dim_l_pdaf

    2. py__init_dim_obs_l_pdaf

    3. py__g2l_state_pdaf

    4. py__init_obs_l_pdaf

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

    6. py__likelihood_l_pdaf

    7. core DA algorithm

    8. py__l2g_state_pdaf

  7. py__prepoststep_state_pdaf

  8. py__distribute_state_pdaf

  9. py__next_observation_pdaf

Deprecated since version 1.0.0: This function is replaced by pyPDAF.PDAF.localomi_assimilate() and pyPDAF.PDAF.localomi_assimilate_lnetf_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__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_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__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 observation likelihood for an ensemble member

    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__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_state_pdaf (Callable[step:int, domain_p:int, dim_p:int, state_p : ndarray[tuple[dim_p], np.float64], dim_l:int, state_l : ndarray[tuple[dim_l], np.float64]]) –

    Get state on local ana. domain from full state

    Callback Parameters
    • stepint

      • current time step

    • domain_pint

      • current local analysis domain

    • dim_pint

      • pe-local full state dimension

    • state_pndarray[tuple[dim_p], np.float64]

      • pe-local full state vector

    • dim_lint

      • local state dimension

    • state_lndarray[tuple[dim_l], np.float64]

      • state vector on local analysis domain

    Callback Returns
    • state_lndarray[tuple[dim_l], np.float64]

      • state vector on local analysis domain

  • py__l2g_state_pdaf (Callable[step:int, domain_p:int, dim_l:int, state_l : ndarray[tuple[dim_l], np.float64], dim_p:int, state_p : ndarray[tuple[dim_p], np.float64]]) –

    Init full state from state on local analysis domain

    Callback Parameters
    • stepint

      • current time step

    • domain_pint

      • current local analysis domain

    • dim_lint

      • local state dimension

    • state_lndarray[tuple[dim_l], np.float64]

      • state vector on local analysis domain

    • dim_pint

      • pe-local full state dimension

    • state_pndarray[tuple[dim_p], np.float64]

      • pe-local full state vector

    Callback Returns
    • state_pndarray[tuple[dim_p], np.float64]

      • pe-local full state 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__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