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

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.