pyPDAF.PDAF.omi_assimilate_nonlin_nondiagR

pyPDAF.PDAF.omi_assimilate_nonlin_nondiagR()

Global nonlinear filters for a single DA step using non-diagnoal observation error covariance matrix.

See pyPDAF.PDAF.omi_assimilate_global_nondiagR() for simpler user-supplied functions using diagonal observation error covariance matrix.

Here, this function call is used for global NETF [1], and particle filter [2]. The filter type is set in pyPDAF.PDAF.init(). This function should be called at each model time step.

The function is a combination of pyPDAF.PDAF.omi_put_state_global_nondiagR() 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_dim_obs_pdaf

4. py__obs_op_pdaf (for ensemble mean)

5. py__obs_op_pdaf (for each ensemble member)

6. py__likelihood_pdaf

7. core DA algorithm

8. py__prepoststep_state_pdaf

9. py__distribute_state_pdaf

10. py__next_observation_pdaf

References

[1]

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.

[2]

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]]) –

  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__likelihood_pdaf (Callable[step:int, dim_obs_p:int, obs_p : ndarray[tuple[dim_obs_p], np.float64], resid : ndarray[tuple[dim_obs_p], np.float64], likely:float]) –

  Compute observation likelihood for an ensemble member

  Callback Parameters

  • stepint

    • Current time step

  • dim_obs_pint

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

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

    • Vector of observations

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

    • Input vector holding the residual

  • likelyfloat

    • Output value of the likelihood

  Callback Returns

  • likelyfloat

    • Output value of the likelihood

• 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__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:

outflag – Status flag

Return type:

int