Abstract 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.

中文翻译：

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连续数据价值分析结合 Ensemble Kalman 滤波器用于土壤水流：一个真实案例研究

摘要 鉴于土壤水问题中数据采集的高成本，尽可能经济高效地收集测量数据变得越来越重要。通过引入数据价值分析框架以及集成卡尔曼滤波器 (EnKF)，这个真实案例研究试图在数据收集之前评估潜在土壤水分观测的价值。实施了一项现场实验，以证明在实际情况下以顺序方式量化未来数据对不确定性减少的影响的可行性。未来观测的数据价值是关于土壤水力参数估计或土壤水分剖面检索的。四种信息度量，包括迹（Tr）、香农熵差（SD）、相对熵（RE）和信号自由度（DFS），引入量化信息内容。序列数据价值分析框架通过多种案例进行检验，包括在不同灌溉强度下，使用不同的先验数据（已经收集的现有观察），以及使用不同深度和不同测量误差的数据。我们展示了按顺序量化数据价值的能力和挑战。我们的结果表明，关于土壤水分剖面检索的值得评估的数据比关于参数识别的数据更难。方差类型和协方差类型度量对潜在观测（未来可能收集的观测）的准确度要求相对宽松，而均值协方差类型度量需要更高的准确度。土壤水分的垂直协方差易受大气边界条件的影响，这最终对包含协方差指标的数据价值的量化提出了挑战。通过同化更多的先验数据，可以改进预期数据和参考数据之间的匹配。然而，更多的先验数据无法弥补由于前一阶段和后或前后阶段之间的场景变化而可能造成的模型结构错误的损害。在我们的研究中，浅层土壤水分数据通常比深层观测具有更大的数据价值，但如果采用协方差型或平均协方差型指数，用浅层数据评估数据价值会受到相当大的不确定性。较小的测量误差并不总是导致值得估计的改进数据。