endas.algorithms.EnsembleKalmanFilter

class endas.algorithms.EnsembleKalmanFilter(variant, ensemble_size, loc_strategy=None, cov_inflation=1.0, lag=0, forgetting_factor=1.0, cache=None)

Bases: object

Ensemble Kalman Filter.

This is a generic Ensemble Kalman Filter (EnKF) implementation that covers many of the EnKF variants. Ensemble Kalman Smoother (EnKS) is also implemented via the smoothing API. The filter/smoother allows both for global and localized analysis to be computed, the latter is always performed by partitioning the state space into a set of disjoint domains that are processed independently.

Parameters:
  • variant – Instance of the EnKFVariant class implementing the actual EnkF filter update
  • ensemble_size – Size of the ensemble used
  • loc_strategy – Localization strategy instance or None.
  • cov_inflation – Covariance inflation factor as a number greater or equal to 1.0. The default is 1.0, meaning no covariance inflation is applied.
  • lag – The lag length of the fixed-lag Kalman Smoother as a number of time steps. Zero Lag disables smoothing
  • forgetting_factor – Forgetting factor applied by the smoother, the value must be less or equal to 1.0.
  • cache – Large array cache instance or None. If None is given, an internal memory cache will be used.

See the DA Algorithms (endas.algorithms) page for information about implemented EnKF variants.

assimilate(z, z_coords, H, R, executor=None)

Assimilates observations as part of the analysis update.

Parameters:
  • z – Array of observations (values).
  • z_coords – Observation coordinates. See below for more information.
  • H – Observation operator, must be an instance of endas.ObservationOperator.
  • R – Observation error covariance, must be an instance of endas.CovarianceOperator.
Returns:

Nothing

The z_coords parameter contains “locations” of observations in the observation vector z and is only required when performing domain-based local analysis via localize(). What can be passed for z_coords depends on the state space partitioning (StateSpacePartitioning) used for the localization, please check the documentation of the state space partitioning you are using for information. If the analysis is not localized, None can be passed for z_coords.

begin_analysis(A, t=None)

Initiates the analysis update step.

At each time step, the analysis update must be initiated by a call to begin_analysis(), followed by one or more calls to assimilate(). After all observations have been assimilated for the current time step, end_analysis() must be called.

Parameters:
  • A – Array representing the forecast ensemble at current time step
  • t – Time corresponding to the current filter/smoother step
Returns:

Nothing
localize(loc_strategy)

Applies localization to the Ensemble Kalman Filter.

Parameters:loc_strategy – Localization strategy instance or None.
Returns:Nothing

Calling localize() is equivalent to passing loc_strategy to the __init__ method. Please note that the method must be called before smoother_begin() or begin_analysis() is called.

smoother_begin(A0, t0)

Must be called once at the beginning when smoothing solution is being calculated.

When the smoothing solution is calculated (i.e. with lag > 0), this method must be called to initialize the smoother. This method does nothing if only the filtering solution is calculated (i.e. lag==0).

Parameters:
  • A0 – Array representing the initial ensemble.
  • t0 – Time corresponding to the initial time step.
Returns:

Nothing