pyPDAF.PDAF.local_assimilate_hyb3dvar_lestkf¶

pyPDAF.PDAF.local_assimilate_hyb3dvar_lestkf()¶

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

Hybrid 3DEnVar for a single DA step where the background error covariance is hybridised by a static background error covariance, and a flow-dependent background error covariance estimated from ensemble. The 3DVar generates an ensemble mean and the ensemble perturbation is generated by LESTKF in this implementation. This function should be called at each model time step.

The function is a combination of pyPDAF.PDAF.local_put_state_hyb3dvar_lestkf() and pyPDAF.PDAF.get_state().

User-supplied functions are executed in the following sequence:

py__collect_state_pdaf
py__prepoststep_state_pdaf
py__init_dim_obs_pdaf
py__obs_op_pdaf
py__init_obs_pdaf
The iterative optimisation:
1. py__cvt_pdaf
2. py__cvt_ens_pdaf
3. py__obs_op_lin_pdaf
4. py__prodRinvA_pdaf
5. py__obs_op_adj_pdaf
6. py__cvt_adj_pdaf
7. py__cvt_adj_ens_pdaf
8. core DA algorithm
py__cvt_pdaf
py__cvt_ens_pdaf
Perform LESTKF:
1. py__init_n_domains_p_pdaf
2. py__init_dim_obs_pdaf
3. py__obs_op_pdaf (for each ensemble member)
4. py__init_obs_pdaf (if global adaptive forgetting factor type_forget=1 in pyPDAF.PDAF.init())
5. py__init_obsvar_pdaf (if global adaptive forgetting factor is used)
6. loop over each local domain:
  
  py__init_dim_l_pdaf
  
  py__init_dim_obs_l_pdaf
  
  py__g2l_obs_pdaf (localise mean ensemble in observation space)
  
  py__init_obs_l_pdaf
  
  py__g2l_obs_pdaf (localise each ensemble member in observation space)
  
  py__init_obsvar_l_pdaf (only called if local adaptive forgetting factor type_forget=2 is used)
  
  py__prodRinvA_l_pdaf
  
  core DA algorithm
py__prepoststep_state_pdaf
py__distribute_state_pdaf
py__next_observation_pdaf

Deprecated since version 1.0.0: This function is replaced by pyPDAF.PDAF.localomi_assimilate_hyb3dvar_lestkf() and pyPDAF.PDAF.localomi_assimilate_hyb3dvar_lestkf_nondiagR()

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_pdaf (Callable[step:int, dim_obs_p:int, observation_p : ndarray[tuple[dim_obs_p], np.float64]]) –
Initialize 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__prodRinvA_pdaf (Callable[step:int, dim_obs_p:int, rank:int, obs_p : ndarray[tuple[dim_obs_p], np.float64], A_p : ndarray[tuple[dim_obs_p, rank], np.float64], C_p : ndarray[tuple[dim_obs_p, rank], np.float64]]) –
Provide product R^-1 A
Callback Parameters
- stepint
  
  Current time step
- dim_obs_pint
  
  Number of observations at current time step (i.e. the size of the 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_pndarray[tuple[dim_obs_p], np.float64]
  
  Vector of observations
- A_pndarray[tuple[dim_obs_p, rank], np.float64]
  
  Input matrix provided by PDAF
- C_pndarray[tuple[dim_obs_p, rank], np.float64]
  
  Output matrix
Callback Returns
- C_pndarray[tuple[dim_obs_p, rank], np.float64]
  
  Output matrix
py__cvt_ens_pdaf (Callable[iter:int, dim_p:int, dim_ens:int, dim_cvec_ens:int, ens_p : ndarray[tuple[dim_p, dim_ens], np.float64], v_p : ndarray[tuple[dim_cvec_ens], np.float64], Vv_p : ndarray[tuple[dim_p], np.float64]]) –
Apply control vector transform matrix (ensemble)
Callback Parameters
- iterint
  
  Iteration of optimization
- dim_pint
  
  PE-local dimension of state
- dim_ensint
  
  Ensemble size
- dim_cvec_ensint
  
  Dimension of control vector
- ens_pndarray[tuple[dim_p, dim_ens], np.float64]
  
  PE-local ensemble
- v_pndarray[tuple[dim_cvec_ens], np.float64]
  
  PE-local control vector
- Vv_pndarray[tuple[dim_p], np.float64]
  
  PE-local state increment
Callback Returns
- Vv_pndarray[tuple[dim_p], np.float64]
  
  PE-local state increment
py__cvt_adj_ens_pdaf (Callable[iter:int, dim_p:int, dim_ens:int, dim_cv_ens_p:int, ens_p : ndarray[tuple[dim_p, dim_ens], np.float64], Vcv_p : ndarray[tuple[dim_p], np.float64], cv_p : ndarray[tuple[dim_cv_ens_p], np.float64]]) –
Apply adjoint control vector transform matrix (ensemble var)
Callback Parameters
- iterint
  
  Iteration of optimization
- dim_pint
  
  PE-local observation dimension
- dim_ensint
  
  Ensemble size
- dim_cv_ens_pint
  
  PE-local dimension of control vector
- ens_pndarray[tuple[dim_p, dim_ens], np.float64]
  
  PE-local ensemble
- Vcv_pndarray[tuple[dim_p], np.float64]
  
  PE-local input vector
- cv_pndarray[tuple[dim_cv_ens_p], np.float64]
  
  PE-local result vector
Callback Returns
- cv_pndarray[tuple[dim_cv_ens_p], np.float64]
  
  PE-local result vector
py__cvt_pdaf (Callable[iter:int, dim_p:int, dim_cvec:int, cv_p : ndarray[tuple[dim_cvec], np.float64], Vv_p : ndarray[tuple[dim_p], np.float64]]) –
Apply control vector transform matrix to control vector
Callback Parameters
- iterint
  
  Iteration of optimization
- dim_pint
  
  PE-local observation dimension
- dim_cvecint
  
  Dimension of control vector
- cv_pndarray[tuple[dim_cvec], np.float64]
  
  PE-local control vector
- Vv_pndarray[tuple[dim_p], np.float64]
  
  PE-local result vector (state vector increment)
Callback Returns
- Vv_pndarray[tuple[dim_p], np.float64]
  
  PE-local result vector (state vector increment)
py__cvt_adj_pdaf (Callable[iter:int, dim_p:int, dim_cvec:int, Vcv_p : ndarray[tuple[dim_p], np.float64], cv_p : ndarray[tuple[dim_cvec], np.float64]]) –
Apply adjoint control vector transform matrix
Callback Parameters
- iterint
  
  Iteration of optimization
- dim_pint
  
  PE-local observation dimension
- dim_cvecint
  
  Dimension of control vector
- Vcv_pndarray[tuple[dim_p], np.float64]
  
  PE-local result vector (state vector increment)
- cv_pndarray[tuple[dim_cvec], np.float64]
  
  PE-local control vector
Callback Returns
- cv_pndarray[tuple[dim_cvec], np.float64]
  
  PE-local control vector
py__obs_op_lin_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]]) –
Linearized observation operator
Callback Parameters
- stepint
  
  Current time step
- dim_pint
  
  PE-local dimension of state
- dim_obs_pint
  
  Dimension of observed state
- state_pndarray[tuple[dim_p], np.float64]
  
  PE-local model state
- m_state_pndarray[tuple[dim_obs_p], np.float64]
  
  PE-local observed state
Callback Returns
- m_state_pndarray[tuple[dim_obs_p], np.float64]
  
  PE-local observed state
py__obs_op_adj_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]]) –
Adjoint observation operator
Callback Parameters
- stepint
  
  Current time step
- dim_pint
  
  PE-local dimension of state
- dim_obs_pint
  
  Dimension of observed state
- state_pndarray[tuple[dim_p], np.float64]
  
  PE-local model state
- m_state_pndarray[tuple[dim_obs_p], np.float64]
  
  PE-local observed state
Callback Returns
- state_pndarray[tuple[dim_p], np.float64]
  
  PE-local model state
py__init_dim_obs_f_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_f_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_f_pdaf (Callable[step:int, dim_obs_f:int, observation_f : ndarray[tuple[dim_obs_f], np.float64]]) –
Initialize PE-local observation vector
Callback Parameters
- stepint
  
  Current time step
- dim_obs_fint
  
  Size of the full observation vector
- observation_fndarray[tuple[dim_obs_f], np.float64]
  
  Full vector of observations
Callback Returns
- observation_fndarray[tuple[dim_obs_f], np.float64]
  
  Full 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__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_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__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

pyPDAF.PDAF.local_assimilate_hyb3dvar_lestkf¶

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