Abstract Azouani–Olson–Titi data assimilation (often referred to as AOT, after its authors) is a computationally‐efficient algorithm that has been shown analytically and computationally to recover the true solution for a wide variety of regimes exponentially fast in time, in addition to being robust with respect to noisy data, stochastic forcing, and errors in parameters. In this paper, we apply AOT data assimilation to the Richards equation, a nonlinear degenerate system that models fluid flow in unsaturated soil. We examine convergence of the AOT approach computationally, explicitly in the case of unsaturated flow, assuming unknown initial data and sparse in time and space observations of soil water content, and show matching convergence‐in‐time and superior CPU (central processing unit) efficiency of this approach as compared to the ensemble Kalman filter algorithm. We further use the AOT algorithm to study the number, type, frequency, and placement of observations for optimal network design, and make recommendations accordingly.
Rowley et al. (Sun,) studied this question.