# Assessing the Performance of Separate Bias Kalman Filter in Correcting the Model Bias for Estimation of Soil Moisture Profiles

• Corresponding author: Shuwen ZHANG, zhangsw@lzu.edu.cn
• Funds:

Supported by the National Natural Science Foundation of China (41575098) and National Key Research and Development Program of China (2018YFC1505702)

• doi: 10.1007/s13351-019-8057-6
• The performance of separate bias Kalman filter (SepKF) in correcting the model bias for the improvement of soil moisture profiles is evaluated by assimilating the near-surface soil moisture observations into a land surface model (LSM). First, an observing system simulation experiment (OSSE) is carried out, where the true soil moisture is known, two types of model bias (i.e., constant and sinusoidal) are specified, and the bias error covariance matrix is assumed to be proportional to the model forecast error covariance matrix with a ratio λ. Second, a real assimilation experiment is carried out with measurements at a site over Northwest China. In the OSSE, the soil moisture estimation with the SepKF is improved compared with ensemble Kalman filter (EnKF) without the bias filter, because SepKF can properly correct the model bias, especially in the situation with a large model bias. However, the performance of SepKF becomes slightly worse if the constant model bias increases or temporal variability of the sinusoidal model bias becomes large. It is suggested that the ratio λ should be increased (decreased) in order to improve the soil moisture estimation if temporal variability of the sinusoidal model bias becomes high (low). Finally, the assimilation experiment with real observations also shows that SepKF can further improve the estimation of soil moisture profiles compared with EnKF without the bias correction.
• Fig. 1.  Flowchart in OSSE.

Fig. 2.  Comparison of the soil moisture estimation in SepKF-C1 and EnKF-C1 with the truth at the (a) 2nd, (b) 3rd, and (c) 4th layers with the bias of 0.01 cm3 cm–3.

Fig. 3.  Comparison with the true value of the bias estimation using SepKF respectively with λ = 0.2 and 0.8.

Fig. 4.  The soil moisture estimated by SepKF-C1 with the assimilation intervals of 6 h (dot line), 24 h (star line), 48 h (short-dashed line), and 96 h (long-dashed line), respectively.

Fig. 5.  Comparison of the soil moisture estimation in EnKF-S1 and SepKF-S1 with the truth by using the sinusoidal model bias with T = 48 days and λ = 0.2 at the (a) 2nd, (b) 3rd, and (c) 4th layers. The bias estimation in SepKF-S1 are also compared to the truth at the (d) 2nd, (e) 3rd, and (f) 4th layers.

Fig. 6.  (a) The 2nd-layer soil moisture estimation by SepKF-S2 with T = 6 days and λ = 0.2, and EnKF-S2 compared with the truth; (b) the 2nd-layer bias estimation with SepKF-S2 compared with the truth.

Fig. 7.  Comparison of the soil moisture estimation by Openloop (star line), EnKF (cross line), and SepKF (solid line) with observations (circle line) at the (a) layer 2 and (b) layer 3 during the final 30 days at SACOL.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## Assessing the Performance of Separate Bias Kalman Filter in Correcting the Model Bias for Estimation of Soil Moisture Profiles

###### Corresponding author: Shuwen ZHANG, zhangsw@lzu.edu.cn;
• 1. School of Atmospheric Sciences, Chengdu University of Information Technology, Chengdu 610225
• 2. Key Laboratory for Semi-Arid Climate Change of the Ministry of Education, College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000
• 3. No. 2 Qishan Road, Mount Wuyi 354301
• 4. Moji Co. Ltd., Beijing 100016
Funds: Supported by the National Natural Science Foundation of China (41575098) and National Key Research and Development Program of China (2018YFC1505702)

Abstract: The performance of separate bias Kalman filter (SepKF) in correcting the model bias for the improvement of soil moisture profiles is evaluated by assimilating the near-surface soil moisture observations into a land surface model (LSM). First, an observing system simulation experiment (OSSE) is carried out, where the true soil moisture is known, two types of model bias (i.e., constant and sinusoidal) are specified, and the bias error covariance matrix is assumed to be proportional to the model forecast error covariance matrix with a ratio λ. Second, a real assimilation experiment is carried out with measurements at a site over Northwest China. In the OSSE, the soil moisture estimation with the SepKF is improved compared with ensemble Kalman filter (EnKF) without the bias filter, because SepKF can properly correct the model bias, especially in the situation with a large model bias. However, the performance of SepKF becomes slightly worse if the constant model bias increases or temporal variability of the sinusoidal model bias becomes large. It is suggested that the ratio λ should be increased (decreased) in order to improve the soil moisture estimation if temporal variability of the sinusoidal model bias becomes high (low). Finally, the assimilation experiment with real observations also shows that SepKF can further improve the estimation of soil moisture profiles compared with EnKF without the bias correction.

Reference (36)

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