Improving land data assimilation performance with a water budget constraint

A weak constraint solution was introduced to reduce the water budget imbalance that appears in land data assimilation as a result of state updates. Constrained Kalman Filter results were shown to be identical in single- or two-stages solutions for Ensemble Kalman Filter (EnKF) whereas constrained Ensemble Transform Kalman Filter (ETKF) single- and two-stage solutions form two different square root solutions. Weakly Constrained Ensemble Kalman Filter (WCEnKF) and Weakly Constrained Ensemble Transform Kalman Filter (WCETKF) were evaluated for 3-hourly and daily update frequencies with soil moisture only, or soil moisture and soil temperature assimilated together. Not perturbed observations in EnKF was revisited. Both constrained and standard solutions were performed for not perturbed observations and without the constraint anomalies. Sensitivity of the constraint error variance is analyzed by comparing the results from objectively estimating and by using tuned values. Simulations were performed using the Noah Land Surface Model (LSM) over Oklahoma, USA, using synthetic observations.;State errors of constrained and unconstrained solutions were found to be similar; neither type had significantly smaller errors for most experiments. Constrained filters had smaller water balance residuals than unconstrained standard filters for all tested scenarios. The water balance residual of the ETKF and EnKF were similar for both 3-hourly and daily update experiments. The majority of the total column water change for daily updated filters resulted from the assimilation update. Not perturbing the observations and not using the constraint anomalies affected the state prediction skill only slightly where the residuals are significantly reduced when compared to the standard filters. Tuned constraint variances gave similar performance with objective variance estimation from the ensemble for WCEnKF but the tuned variances were better than objective estimation for WCETKF.