UC Merced

Soil moisture is essential for many applications, such as agricultural irrigation, water resources management, and natural disasters, such as landslides and droughts. With the advancement of measurement technology, a vast amount of soil moisture data is available from ground-based sensors and remote sensing. How can we use such abundant data in a meaningful way? For better interpretability and extrapolation capability, soil moisture data should be analyzed based on a known physical model through an inverse modeling framework. In the dissertation, I explored the inverse modeling of soil moisture dynamics based on the Richardson-Richards equation (RRE) via techniques recently developed in applied mathematics. In Chapter 1, a general introduction is presented. Chapter 2 investigated the application of a neural network-based inverse method called physics-informed neural networks (PINNs). I demonstrated that PINNs with domain decomposition could approximate the solution to the RRE for layered soils by comparing PINNs with an analytical solution of the RRE. Chapter 3 estimated soil hydraulic properties from upward infiltration experiments using the Peters-Durner-Iden (PDI) model. I demonstrated that the PDI model better captured soil moisture dynamics for dry conditions than the van-Genuchten Mualem model. Chapter 4 discusses the estimation of surface water flux from soil moisture measurements through inverse modeling. I compared an adjoint method with PINNs and demonstrated through numerical examples that both methods gave reasonable estimates of surface water flux from soil moisture measurements. However, the adjoint method was more robust than PINNs regarding the reconstructed soil moisture profile for a data-limited case. In Chapter 5, I summarized the limitations of the current approaches and discussed future perspectives of inverse modeling of soil moisture dynamics.