Sequential data-worth analysis coupled with ensemble Kalman filter for soil water flow: A real-world case study

Given the high cost of data acquisition in soil water problems, it is becoming increasingly essential to collect the measurements as cost-efficient as possible. By introducing the data-worth analysis framework coupled with Ensemble Kalman Filter (EnKF), this real-world case study attempts to assess the worth of potential soil moisture observations before data collection. A field experiment was implemented to demonstrate the feasibility of quantifying the effect of future data on uncertainty reduction under real circumstances in a sequential way. The data worth of future observations is defined regarding soil hydraulic parameter estimation or soil moisture profile retrieval. Four information measures, including the trace (Tr), Shannon entropy difference (SD), relative entropy (RE) and degrees of freedom for signal (DFS), are introduced to quantify the information content. The sequential data worth analysis framework is examined by a number of cases, including under different irrigation intensities, with different prior data (existing observations that have already been collected), and with data of various depths and different measurement errors. We demonstrated the ability, and the challenge as well, of quantifying the data worth sequentially. Our results showed that data worth assessment regarding soil moisture profile retrieval is more difficult than that regarding parameter identification. Variance-type and covariance-type metrics have relatively loose accuracy requirement on potential observations (future possible observations to be collected), while mean-covariance-type metrics require higher accuracy. The vertical covariance of soil moisture is susceptible to the effect of atmospheric boundary condition, which eventually imposes a challenge on the quantification of data worth with covariance involved indices. The match between the expected and reference data worth can be improved by assimilating more prior data. However, more prior data cannot compensate for the damage from possible model structural error due to the changed scenarios between the prior stage and the posterior or preposterior stage. Shallow soil moisture data generally has larger data worth than deep observations in our study, but evaluating data worth with shallow data is subject to considerable uncertainty if covariance-type or mean-covariance-type index is employed. Smaller measurement error does not always lead to improved data worth estimation.