Development and validation of the automatic calibration method for FDR soil moisture measurement based on data assimilation

Accurate measurement of soil moisture is often required for hydrology, agriculture, and environmental science. Frequency-domain reflectometry (FDR) has been widely used during indirect measurement due to the available soil moisture sensors. However, the measurement biases are attributed to the susceptibility of field calibration to environmental interference. This study aims to calibrate soil moisture under FDR measurement using data assimilation. A robust framework of data assimilation was also presented to integrate the ensemble Kalman filter (EnKF) with in-situ meteorological data. The EnKF was combined with different models of bias calibration. Specifically, the meteorological observation data were employed to drive a physics-based one-dimensional soil hydrodynamic model. The dynamic migration and distribution of soil moisture were simulated within the soil profile. The unknown sensor bias parameters and inherent soil hydraulic properties were treated as joint state variables to be estimated in the data assimilation system. These variables were simultaneously inverted and continuously updated during the iterative EnKF assimilation, which effectively constrained sensor observations with hydrological physical laws. The outdoor experiments were conducted to verify the universality and performance of the calibration. Soil moisture data were collected at three specific depths of 10, 20, and 50 cm below the soil surface. A systematic evaluation was conducted to compare the performance of two bias correction structures, namely the linear and the power function bias model. Meanwhile, extensive sensitivity analysis was performed to explore the effects of assimilation parameters on the overall calibration efficacy. Experimental results demonstrate that the uncalibrated FDR sensors exhibited significant systematic biases in soils of different textures. Statistical analysis showed that the uncalibrated sensor measurements shared a high average relative error (RE) of 32.7%, an average root mean square error (RMSE) of 0.045 cm³/cm³, and an average mean absolute error (MAE) of 0.037 cm³/cm³. Calibration models significantly improved the measurement accuracy of the sensors after data assimilation. Once the linear bias calibration model was used, the average RE was drastically reduced to 18.6%, and the RMSE and MAE decreased to 0.027 and 0.023 cm³/cm³, respectively. When the power function bias model was adopted, the average RE, RMSE, and MAE were 19.2%, 0.029 cm³/cm³, and 0.024 cm³/cm³, respectively. The statistical indicators revealed that the linear calibration model delivered superior performance, stronger overall stability, and higher physical authenticity, where the systematic errors were effectively reduced after comparison. Furthermore, the critical thresholds of EnKF parameters were determined for the optimal performance: An assimilation duration of 20 to 30 days can provide the optimal data window to capture sufficient soil moisture dynamics, and the optimal ensemble size was between 100 and 150 members. In summary, the systematic biases can be effectively corrected without sampling. The finding can also provide an efficient and low-cost technical solution for soil moisture monitoring.