A new data abimilation technique based on EnKF and Brownian bridges in the context of Richards' equation

A new data abimilation technique is presented, based on the ensemble Kalman filter (EnKF), and makes particularly sense whenever few observations in time are available, and a stiff evolutionary equation such as the Richards' equation is integrated forward in time. Because of the Monte Carlo nature of EnKF, a cheap numerical method would be conve-nient to integrate the Richards'equation, thus a lot of observations are desiderable in order to frequently correct the numerical solution. Nevertheleb, abuming to have few observations in time, a grid of fictitious observations is settled just by interpolating the available observations. The measurement error covariance matrix abociated to these fictitious observations is estimated abuming that these errors evolve in time as Brownian bridges, with diffusion coefficients depending on the goodneb-To-fit of the polinomial curves with respect to the observed data.