Description

The Ensemble Kalman Filter (EnKF?) was developed by Evensen (1994) as an alternative to the Extended Kalman Filter (EKF) approach. The EnKF? is the adaptation of the Kalman Filter (KF) model to non-linear systems using Monte Carlo sampling (in the propagation step) and linear updating (correction or analysis step). In the ensemble Kalman filter (EnKF?) an ensemble of model states is integrated forward in time using the nonlinear forward model with replicates of system noise. At update times, the error covariance is calculated from the ensemble. The traditional update equation from the classical Kalman filter is used, with the Kalman gain calculated from the error covariances provided by the ensemble. It has been applied to rainfall-flow modelling by Vrugt et al. (2005) and Moradkhani et al.(2005).

Software

no information

Advantages

The advantages of the EnKF? are as follows: any model can be used; model does not need to be differentiable; noise can be placed anywhere, for example, on uncertain parameters and forcing; noise can be non-Gaussian and non-additive; uses all data in a batch window to estimate the state.

Disadvantages

Estimates are conditioned on past measurements only and it uses a linear analysis step. This may lead to physically non-feasible solutions of the propagation step (e.g. negative flow). Another problem – is that it is computationally intensive, requiring many Monte Carlo realizations at each propagation step. Moreover, due to the high complexity of these approaches, there may be questions about the identifiability of parameters involved in the different aspects of the applied routines (e.g. the choice of the variance during the state and parameter estimation processes).

References and Further Reading

Bertino, L., Evensen, G. and Vackernagel, H., 2003. Sequential data assimilation techniques in oceanography. International Statistical Review, 71: 223-242.

Evensen, G., 1994. Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research, 99: 10143-62.

Moradkhani, H., Sorooshian, S., Gupta, H.V. and Houser, P.R., 2005. Dual state-parameter estimation of hydrological models using ensemble Kalman filter. Advances In Water Resources, 28(2): 135-147.

Vrugt, J.A., Diks, C.G.H., Gupta, H.V., Bouten, W. and Verstraten, J.M., 2005. Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation. Water Resources Research, 41: doi:10.1029/2004WR003059.

(very) Usefull links

• Evensen paper reviewing methods: Evensen, G. (2003) The Ensemble Kalman Filter: theoretical formulation and practical implementation, Ocean Dynamics 53: 343–367, DOI 10.1007/s10236-003-0036-9: Link http://enkf.nersc.no/Publications/eve03a.pdf.

• Greir Evensen's web site: link http://enkf.nersc.no/.