Release estimation of pollutants in river by the variational analysis approach

After accidental release of pollutants in rivers, the release estimation of the pollutant is necessary for the dealing of this accident. With the increase of people's attention to river pollution, the monitoring data of river pollution will become more and more abundant and diversified. At this point, data assimilation approaches will be more advantageous. In this paper, a new model called variational analysis inverse model (VAIM) based on the variational data assimilation is proposed to solve the pollutant release estimation problem. In the framework of the variational analysis, the conjugate gradient method and one-dimensional imprecise line search Wolfe-Powell conditions are combined to solve this problem. The implicit finite difference scheme is adopted to solve the one-dimensional advection-dispersion equation. Some synthetic cases are conducted to evaluate the robustness of the proposed model under the effect of the observational error and the effect of initial estimates for release rates in the iteration. Results show that VAIM successfully recovers the accurate release. There are only slight differences among estimated releases by VAIM under different initial estimates. Field tracer experiments are used to evaluate the practicability of VAIM. Results show that the relative error between the estimated release and the real release in the field tracer experiment is only 1.2%. In conclusion, VAIM is a release estimation method with high accuracy and will play an important role in river pollution management.