Direct data assimilation algorithms for advection-diffusion models with the increased smoothness of the uncertainty functions

Direct variational data assimilation algorithm for the non-stationary one-dimensional advection-diffusion model and in situ measurements is presented. Data assimilation is carried out by adjusting the uncertainty (control) function that has the sense of the emission sources. In the algorithm a target functional containing the misfit between the modeled and measured values and a regularizer, containing a norm of the control function derivative, is minimized on every time step of the discretized advection-diffusion model. The minimum is obtained by the solution of the tri-diagonal matrix system. The performance of the algorithm was evaluated in the numerical experiments.