pyPDAF.PDAF.put_state_letkf

pyPDAF.PDAF.put_state_letkf()

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

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

Local ensemble transform Kalman filter (LETKF) [1] for a single DA step without OMI. Implementation is based on [2].

Compared to pyPDAF.PDAF.assimilate_letkf(), 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.

Note that the LESTKF is a more efficient equivalent to the LETKF.

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_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_state_pdaf

   4. py__g2l_obs_pdaf (localise mean ensemble in observation space)

   5. py__init_obs_l_pdaf

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

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

   8. py__prodRinvA_l_pdaf

   9. core DA algorithm

   10. py__l2g_state_pdaf

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

References

[1]

Hunt, B. R., Kostelich, E. J., & Szunyogh, I. (2007). Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D: Nonlinear Phenomena, 230(1-2), 112-126.

[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]]) –

  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__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_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

• 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__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__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

Returns:

flag – Status flag

Return type:

int