Ensemble Kalman Filter and Extended Kalman Filter for State-Parameter Dual Estimation in Mixed Effects Models Defined by a Stochastic Differential Equation

Abstract. The performance of the ensemble Kalman filter (EnKF) in soil moisture assimilation applications is investigated in the context of simultaneous state-parameter estimation in the presence of uncertainties from model parameters, soil moisture initial condition and atmospheric forcing. A physically based land surface model is used for this purpose. Using a series of identical twin experiments in two kinds of initial parameter distribution (IPD) scenarios, the narrow IPD (NIPD) scenario and the wide IPD (WIPD) scenario, model-generated near surface soil moisture observations are assimilated to estimate soil moisture state and three hydraulic parameters (the saturated hydraulic conductivity, the saturated soil moisture suction and a soil texture empirical parameter) in the model. The estimation of single imperfect parameter is successful with the ensemble mean value of all three estimated parameters converging to their true values respectively in both NIPD and WIPD scenarios. Increasing the number of imperfect parameters leads to a decline in the estimation performance. A wide initial distribution of estimated parameters can produce improved simultaneous multi-parameter estimation performances compared to that of the NIPD scenario. However, when the number of estimated parameters increased to three, not all parameters were estimated successfully for both NIPD and WIPD scenarios. By introducing constraints between estimated hydraulic parameters, the performance of the constrained three-parameter estimation was successful, even if temporally sparse observations were available for assimilation. The constrained estimation method can reduce RMSE much more in soil moisture forecasting compared to the non-constrained estimation method and traditional non-parameter-estimation assimilation method. The benefit of this method in estimating all imperfect parameters simultaneously can be fully demonstrated when the corresponding non-constrained estimation method displays a relatively poor parameter estimation performance. Because all these constraints between parameters were obtained in a statistical sense, this constrained state-parameter estimation scheme is likely suitable for other land surface models even with more imperfect parameters estimated in soil moisture assimilation applications.

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Efficient State/Parameter Estimation in Nonlinear Unsteady PDEs by a Reduced Basis Ensemble Kalman Filter

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/16m1078598 ◽

2017 ◽

Vol 5 (1) ◽

pp. 890-921 ◽

Cited By ~ 4

Author(s):

Stefano Pagani ◽

Andrea Manzoni ◽

Alfio Quarteroni

Keyword(s):

Parameter Estimation ◽

Kalman Filter ◽

Ensemble Kalman Filter ◽

State Parameter ◽

Reduced Basis

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A comparison of assimilation results from the ensemble Kalman Filter and a reduced-rank extended Kalman Filter

Nonlinear Processes in Geophysics ◽

10.5194/npg-10-477-2003 ◽

2003 ◽

Vol 10 (6) ◽

pp. 477-491 ◽

Cited By ~ 8

Author(s):

X. Zang ◽

P. Malanotte-Rizzoli

Keyword(s):

Kalman Filter ◽

State Space ◽

Extended Kalman Filter ◽

Ensemble Kalman Filter ◽

Forecast Error ◽

High Viscosity ◽

Empirical Orthogonal Functions ◽

Reduced Rank ◽

Low Viscosity ◽

Reduced State

Abstract. The goal of this study is to compare the performances of the ensemble Kalman filter and a reduced-rank extended Kalman filter when applied to different dynamic regimes. Data assimilation experiments are performed using an eddy-resolving quasi-geostrophic model of the wind-driven ocean circulation. By changing eddy viscosity, this model exhibits two qualitatively distinct behaviors: strongly chaotic for the low viscosity case and quasi-periodic for the high viscosity case. In the reduced-rank extended Kalman filter algorithm, the model is linearized with respect to the time-mean from a long model run without assimilation, a reduced state space is obtained from a small number (100 for the low viscosity case and 20 for the high viscosity case) of leading empirical orthogonal functions (EOFs) derived from the long model run without assimilation. Corrections to the forecasts are only made in the reduced state space at the analysis time, and it is assumed that a steady state filter exists so that a faster filter algorithm is obtained. The ensemble Kalman filter is based on estimating the state-dependent forecast error statistics using Monte Carlo methods. The ensemble Kalman filter is computationally more expensive than the reduced-rank extended Kalman filter.The results show that for strongly nonlinear case, chaotic regime, about 32 ensemble members are sufficient to accurately describe the non-stationary, inhomogeneous, and anisotropic structure of the forecast error covariance and the performance of the reduced-rank extended Kalman filter is very similar to simple optimal interpolation and the ensemble Kalman filter greatly outperforms the reduced-rank extended Kalman filter. For the high viscosity case, both the reduced-rank extended Kalman filter and the ensemble Kalman filter are able to significantly reduce the analysis error and their performances are similar. For the high viscosity case, the model has three preferred regimes, each with distinct energy levels. Therefore, the probability density of the system has a multi-modal distribution and the error of the ensemble mean for the ensemble Kalman filter using larger ensembles can be larger than with smaller ensembles.

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