A new data assimilation technique based on ensemble Kalman filter and Brownian bridges: An application to Richards’ equation

In this paper a new data assimilation technique is proposed which is based on the ensemble Kalman filter (EnKF). Such a technique will be effective if few observations of a dynamical system are available and a large model error occurs. The idea is to acquire a fine grid of synthetic observations in two steps: (1) first we interpolate the real observations with suitable polynomial curves; (2) then we estimate the relative measurement errors by means of Brownian bridges. This technique has been tested on the Richards’ equation, which governs the water flow in unsaturated soils, where a large model error has been introduced by solving the Richards’ equation by means of an explicit numerical scheme. The application of this technique to some synthetic experiments has shown improvements with respect to the classical ensemble Kalman filter, in particular for problems with a large model error.