Inversion of Diffusion Coefficients and Effect of Related Difference Schemes

Air pollution prediction is a direct problem, and deriving diffusion coefficients from the concentration of pollutants is an inverse problem. A direct problem is different from an inverse problem in essence, and their definitions and methods of resolution are quite different. A sort of solution of the inversion of the vertical diffusion coefficients in the atmospheric boundary layer is defined based on the theory of optimum control. The adjoint model method is introduced to calculate the gradient of the objective function, and then the inverse problem is solved. It turns out that the result of the inverse problem is sensitive to the choice of difference algorithms, and is directly affected by the settlement of the sources used in the measurement. The causes of errors are analyzed both in theory and in numerical experiments. The relationships between the inverse result and the difference algorithms and sources are summarized, and then satisfactory results are shown in the resolutions. The above studies are of help to the practical experiments to measure diffusion coefficients.