Data worth analysis within a model-free data assimilation framework for soil moisture flow

Abstract. Conventional data-worth (DW) analysis for soil water problems depends on physical dynamic models. The widespread occurrence of model structural errors and the strong nonlinearity of soil water flow may lead to biased or wrong worth assessment. By introducing the nonparametric data-worth analysis (NP-DWA) framework coupled with ensemble Kalman filter (EnKF), this real-world case study attempts to assess the worth of potential soil moisture observations regarding the reconstruction of fully data-driven soil water flow models prior to data gathering. The DW of real-time soil moisture observations after Gaussian process training and Kalman update was quantified with three representative information metrics, including the trace, Shannon entropy difference, and relative entropy. The sequential NP-DWA framework was examined by a number of cases in terms of the variable of interest, spatial location, observation error, and prior data content. Our results indicated that the overall increasing trend of the DW from the sequential augmentation of additional observations was susceptible to interruptions by localized surges due to never-experienced atmospheric conditions (i.e., rainfall events) within the NP-DWA framework. Fortunately, this performance degradation can be effectively alleviated by enriching training scenarios or the appropriate amplification of observational noise under extreme meteorological conditions. Nevertheless, a substantial expansion of the prior data content may cause an unexpected increase in DW of future potential observations due to the possible introduction of ensuing observation noises. Hence, high-quality and representative “small” data may be a better choice than unfiltered “big” data. Compared with the observations in the surface layer with the strongest time-variability, the soil water content in the middle layer robustly exhibited remarkable superiority in the construction of model-free soil moisture models. An alternative monitoring strategy with a larger data-worth was prone to a higher DW assessment accuracy within the proposed NP-DWA framework. We also demonstrated that the DW assessment performance was jointly determined by ‘3C’, i.e., capacity of potential observation realizations to “capture” actual observations, correlation of potential observations with the variables of interest, and choice of DW indicators. Direct mapping from regular meteorological data to soil water content within the NP-DWA mitigated the adverse effects of nonlinearity-related interference, which thus facilitated the identification of the soil moisture covariance matrix, especially the cross-covariance.