A nonparametric sequential data assimilation scheme for soil moisture flow

Various of data assimilation methods such as the ensemble Kalman filter (EnKF) have been established in physical science and engineering for the fusion of observed data with physically motivated models. However, there are cases where a physically motivated model is not available. In particular, the unsaturated flow model is often difficult to build due to the intrinsic nonlinearity and heterogeneity of soil flow process. In this paper, a nonparametric sequential data assimilation scheme (Kalman-GP) is introduced based on the filtering equations of EnKF and data-driven modeling with Gaussian process (GP). The method replaces the physical model with GP constructed directly from available multiple-source data and observations of state variables of interest, while using the Kalman update formulation to reconcile real-time observations. We tested the proposed Kalman-GP method in a real-world case study of soil moisture profile simulation. The performance of Kalman-GP was compared with two different data assimilation methods, i.e. the traditional EnKF with a physical model (Kalman-physics) and a hybrid filter which integrated a dynamic GP error model into physics-based EnKF (Kalman-physics-GP, Zhang et al., 2019). Results showed that, without knowledge of any governing equation, the Kalman-GP filter was able to reconstruct soil moisture dynamics to a level comparable with the parametric EnKF, even exhibit superior performance. The Kalman-physics-GP led to a better soil moisture estimation than Kalman-GP, however at the expense of dependence on the underlying physical model and more requirements of prior knowledge. In contrast, the proposed Kalman-GP requires only easy-to-obtain meteorological data and can be a better alternative to achieve good tradeoff between effectiveness and efficiency, especially in areas short of hydrogeological data. When less prior physical knowledge is available, the advantage of the proposed Kalman-GP over the Kalman-Physics was enhanced, while the superiority of the hybrid filter over the Kalman-GP was weakened.