Application of Ensemble Kalman Smoothing in Inverse Modeling of Advection and Diffusion

To study the spread of greenhouse gases in space and time, as well as to assess the fluxes of these gases from the Earth’s surface by using a data assimilation system is an important problem of monitoring the environment. One of the approaches to estimating the greenhouse gas fluxes is based on the assumption that the fluxes are constant in a given subdomain and over a given time interval (about a week). This is justified by the properties of the algorithm and the observational data used. The modern problems of estimating greenhouse gas fluxes from the Earth’s surface have large dimensions. Therefore, a problem statement is usually considered in which the fluxes are estimated, and an advection and diffusion model is included in the observation operator. Here we deal with large assimilation windows in which fluxes are estimated in several time intervals. The paper considers an algorithm for estimating the fluxes based on observations from a given time interval. The algorithm is a variant of an ensemble smoothing algorithm, which is widely used in such problems. It is shown that when using an assimilation window in which the fluxes are estimated for several time intervals, the algorithm may become unstable, and an observability condition is violated.