scholarly journals Soil Moisture Assimilation Using a Modified Ensemble Transform Kalman Filter Based on Station Observations in the Hai River Basin

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Guocan Wu ◽  
Bo Dan ◽  
Xiaogu Zheng
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Water Budget ◽  
Forecast Error ◽  
Estimation Accuracy ◽  
Surface Model ◽  
Common Land Model ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Ensemble Transform

Assimilating observations to a land surface model can further improve soil moisture estimation accuracy. However, assimilation results largely rely on forecast error and generally cannot maintain a water budget balance. In this study, shallow soil moisture observations are assimilated into Common Land Model (CoLM) to estimate the soil moisture in different layers. A proposed forecast error inflation and water balance constraint are adopted in the Ensemble Transform Kalman Filter to reduce the analysis error and water budget residuals. The assimilation results indicate that the analysis error is reduced and the water imbalance is mitigated with this approach.

scholarly journals An Estimate of Inflation Factor and Analysis Sensitivity in Ensemble Kalman Filter

2016 ◽  
Author(s):  
Guocan Wu
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Estimation Accuracy ◽  
Error Matrix ◽  
Spatially Correlated ◽  
Inflation Factor ◽  
Analysis Error ◽  
Lorenz 96 ◽  
Assimilation Scheme

Abstract. The estimation accuracy of forecast error matrix is crucial to the assimilation result. Ensemble Kalman filter (EnKF) is a widely used ensemble based assimilation method, which initially estimate the forecast error matrix using a Monte Carlo method with the short-term ensemble forecast states. However, this estimate needs to be further improved using inflation technique. In this study, the forecast error inflation factor is estimated based on cross validation and the analysis sensitivity is also investigated. The improved EnKF assimilation scheme is validated by assimilating spatially correlated observations to the atmosphere-like Lorenz-96 model. The experiment results show that, the analysis error is reduced and the analysis sensitivity to observations is improved.

scholarly journals The Gaussian Approach to Adaptive Covariance Inflation and Its Implementation with the Local Ensemble Transform Kalman Filter

2011 ◽  
Vol 139 (5) ◽  
pp. 1519-1535 ◽  
Author(s):  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Forecast Error ◽  
Grid Point ◽  
Circulation Model ◽  
Error Variance ◽  
Model Errors ◽  
Variable Model ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

In ensemble Kalman filters, the underestimation of forecast error variance due to limited ensemble size and other sources of imperfection is commonly treated by empirical covariance inflation. To avoid manual optimization of multiplicative inflation parameters, previous studies proposed adaptive inflation approaches using observations. Anderson applied Bayesian estimation theory to the probability density function of inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied a Kalman filter analysis update to the inflation parameters based on the Gaussian assumption. In this study, Li et al.’s Gaussian approach is advanced to include the variance of the estimated inflation as derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson’s general Bayesian approach. An advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally varying adaptive inflation technique is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; numerical experiments show promising results both with and without model errors.

Improving Land Data Assimilation Performance with a Water Budget Constraint

2011 ◽  
Vol 12 (5) ◽  
pp. 1040-1055 ◽  
Author(s):  
M. Tugrul Yilmaz ◽  
Timothy DelSole ◽  
Paul R. Houser
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Land Surface ◽  
Water Budget ◽  
Land Surface Model ◽  
Statistical Characteristics ◽  
Surface Model ◽  
Ensemble Kalman Filters ◽  
Land Data Assimilation ◽  
Ensemble Transform Kalman Filter

Abstract A weak constraint is introduced in ensemble Kalman filters to reduce the water budget imbalance that occurs in land data assimilation. Two versions of the weakly constrained filter, called the weakly constrained ensemble Kalman filter (WCEnKF) and the weakly constrained ensemble transform Kalman filter (WCETKF), are proposed. The strength of the weak constraint is adaptive in the sense that it depends on the statistical characteristics of the forecast ensemble. The resulting filters are applied to assimilate synthetic observations generated by the Noah land surface model over the Red Arkansas River basin. The data assimilation experiments demonstrate that, for all tested scenarios, the constrained filters produce analyses with nearly the same accuracy as unconstrained filters, but with much smaller water balance residuals than unconstrained filters.

scholarly journals Assimilating shallow soil moisture observations into land models with a water budget constraint

2020 ◽  
Vol 24 (11) ◽  
pp. 5187-5201
Author(s):  
Bo Dan ◽  
Xiaogu Zheng ◽  
Guocan Wu ◽  
Tao Li
Keyword(s):  
Soil Moisture ◽  
Moisture Content ◽  
Water Balance ◽  
Water Budget ◽  
Soil Moisture Content ◽  
Forecast Error ◽  
Deep Layers ◽  
Assimilation Process ◽  
Analysis Error ◽  
Vertical Localization

Abstract. Assimilating observations of shallow soil moisture content into land models is an important step in estimating soil moisture content. In this study, several modifications of an ensemble Kalman filter (EnKF) are proposed for improving this assimilation. It was found that a forecast error inflation-based approach improves the soil moisture content in shallow layers, but it can increase the analysis error in deep layers. To mitigate the problem in deep layers while maintaining the improvement in shallow layers, a vertical localization-based approach was introduced in this study. During the data assimilation process, although updating the forecast state using observations can reduce the analysis error, the water balance based on the physics in the model could be destroyed. To alleviate the imbalance in the water budget, a weak water balance constrain filter is adopted. The proposed weakly constrained EnKF that includes forecast error inflation and vertical localization was applied to a synthetic experiment. An additional bias-aware assimilation for reducing the analysis bias is also investigated. The results of the assimilation process suggest that the inflation approach effectively reduces the analysis error from 6.70 % to 2.00 % in shallow layers but increases from 6.38 % to 12.49 % in deep layers. The vertical localization approach leads to 6.59 % of the analysis error in deep layers, and the bias-aware assimilation scheme further reduces this to 6.05 %. The spatial average of the water balance residual is 0.0487 mm of weakly constrained EnKF scheme, and 0.0737 mm of a weakly constrained EnKF scheme with inflation and localization, which are much smaller than the 0.1389 mm of the EnKF scheme.

scholarly journals Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator

2014 ◽  
Vol 1 (1) ◽  
pp. 543-582
Author(s):  
G. Wu ◽  
X. Zheng ◽  
L. Wang ◽  
X. Liang ◽  
S. Zhang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Second Order ◽  
Observation Operator ◽  
Strongly Nonlinear ◽  
Taylor Approximation ◽  
Inflation Factor ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
Ensemble Transform

Abstract. The Ensemble Transform Kalman Filter (ETKF) assimilation scheme has recently seen rapid development and wide application. As a specific implementation of the Ensemble Kalman Filter (EnKF), the ETKF is computationally more efficient than the conventional EnKF. However, the current implementation of the ETKF still has some limitations when the observation operator is strongly nonlinear. One problem is that the nonlinear operator and its tangent-linear operator are iteratively calculated in the minimization of a nonlinear objective function similar to 4DVAR, which may be computationally expensive. Another problem is that it uses the tangent-linear approximation of the observation operator to estimate the multiplicative inflation factor of the forecast errors, which may not be sufficiently accurate. This study seeks a way to avoid these problems. First, we apply the second-order Taylor approximation of the nonlinear observation operator to avoid iteratively calculating the operator and its tangent-linear operator. The related computational cost is also discussed. Second, we propose a scheme to estimate the inflation factor when the observation operator is strongly nonlinear. Experimentation with the Lorenz-96 model shows that using the second-order Taylor approximation of the nonlinear observation operator leads to a reduction of the analysis error compared with the traditional linear approximation. Similarly, the proposed inflation scheme leads to a reduction of the analysis error compared with the procedure using the traditional inflation scheme.

scholarly journals Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator

2014 ◽  
Vol 21 (5) ◽  
pp. 955-970 ◽  
Author(s):  
G. Wu ◽  
X. Yi ◽  
L. Wang ◽  
X. Liang ◽  
S. Zhang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Second Order ◽  
Observation Operator ◽  
Strongly Nonlinear ◽  
Taylor Approximation ◽  
Inflation Factor ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
Ensemble Transform

Abstract. The ensemble transform Kalman filter (ETKF) assimilation scheme has recently seen rapid development and wide application. As a specific implementation of the ensemble Kalman filter (EnKF), the ETKF is computationally more efficient than the conventional EnKF. However, the current implementation of the ETKF still has some limitations when the observation operator is strongly nonlinear. One problem in the minimization of a nonlinear objective function similar to 4D-Var is that the nonlinear operator and its tangent-linear operator have to be calculated iteratively if the Hessian is not preconditioned or if the Hessian has to be calculated several times. This may be computationally expensive. Another problem is that it uses the tangent-linear approximation of the observation operator to estimate the multiplicative inflation factor of the forecast errors, which may not be sufficiently accurate. This study attempts to solve these problems. First, we apply the second-order Taylor approximation to the nonlinear observation operator in which the operator, its tangent-linear operator and Hessian are calculated only once. The related computational cost is also discussed. Second, we propose a scheme to estimate the inflation factor when the observation operator is strongly nonlinear. Experimentation with the Lorenz 96 model shows that using the second-order Taylor approximation of the nonlinear observation operator leads to a reduction in the analysis error compared with the traditional linear approximation method. Furthermore, the proposed inflation scheme leads to a reduction in the analysis error compared with the procedure using the traditional inflation scheme.

scholarly journals Assimilating Shallow Soil Moisture Observations into Land Models with a Water Budget Constraint

2020 ◽  
Author(s):  
Bo Dan ◽  
Xiaogu Zheng ◽  
Guocan Wu ◽  
Tao Li
Keyword(s):  
Soil Moisture ◽  
Moisture Content ◽  
Water Balance ◽  
Water Budget ◽  
Soil Moisture Content ◽  
Forecast Error ◽  
Deep Layers ◽  
Assimilation Process ◽  
Analysis Error ◽  
Vertical Localization

Abstract. Incorporating observations of shallow soil moisture content into land models is an important step in assimilating satellite observations of soil moisture content. In this study, several modifications of an ensemble Kalman filter (EnKF) are proposed for improving this assimilation. It was found that a forecast error inflation-based approach improves the soil moisture content in shallow layers, but it can increase the analysis error in deep layers. To mitigate the problem in deep layers while maintaining the improvement in shallow layers, a vertical localization-based approach was introduced in this study. During the data assimilation process, although updating the forecast state using observations can reduce the analysis error, the water balance based on the physics in the model could be destroyed. To alleviate the imbalance in the water budget, a weak water balance constrain filter is adopted. The proposed weakly constrained EnKF that includes forecast error inflation and vertical localization was applied to a synthetic experiment and two real data experiments. The results of the assimilation process suggest that the inflation approach effectively reduce both the short-lived analysis error and the analysis bias in shallow layers, while the vertical localization approach avoids increase in analysis error in deep layers. The weak constraint on the water balance reduces the degree of the water budget imbalance at the price of a small increase in the analysis error.

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