The numerical solution of Richards' equation by means of method of lines and ensemble Kalman filter

Here a numerical technique based on the method of lines (MoL) for solving Richards' equation is presented. The Richards' equation deals with modeling infiltration of water into the unsaturated zone. By means of any kind of observations, some values of the state variable are assumed to be available at certain time points, in order to "correct" the numerical solution in the light of these observations. This is done by means of ensemble Kalman filter (EnKF), that is a data assimilation technique based on a Monte Carlo approach. Advantages of this approach are discussed, in the light of existing bibliography.