Inversion study on pollutant discharges in the Bohai Sea with the adjoint method

Abstract

The adjoint method is presented which could be used to estimate the time-varying contamination concentration (CC) from pollution source (PS). Then the pollutant flux is calculated. In order to guarantee the continuity of pollutant distribution and make the calculated results more accurate, the independent point (IP) scheme is proposed. The contamination concentrations (CCs) at some time steps are selected as the independent points (IPs), and only CCs at these IPs are optimized while CCs at other points are calculated through linear interpolation of the independent CCs. In twin numerical experiments, all the given distributions are successfully inverted with the adjoint method. The cost functions and the mean absolute errors (MAEs) in concentrations and pollutant fluxes decrease greatly after assimilation, and the cost functions are reduced by about 5 orders of magnitude compared with their initial values. The results indicate that the adjoint method is computationally efficient to recover CCs from PS. It is easier to invert the given distribution which is less complex. The inversion efficiency with IP scheme is raised compared to that without this scheme. The IP scheme is significant for the inversion result, in which appropriate IP number could yield better inversion results. More work will be done to apply this method to real experiment.