Direct data assimilation method for convection-diffusion models based on splitting scheme
Modern urban and industry areas emit large number of airborne chemical substances that can seriously pollute the environment. These processes can be studied with multidimensional convection-diffusion models. Both high spatial dimensionality and large variety of considered chemical species impose strong requirements to the performance of direct and inverse modeling algorithms. In this work, we consider a data assimilation problem for a nonstationary multidimensional convection-diffusion model with in situ concentration measurements. Data are assimilated at each time step of time discretized model. From theoretical point of view, data assimilation problem is considered as a sequence of inverse problems for different compositions of measurement data. Hence Tikhonov regularization can be a theoretical background to study the problem as an ill-posed measurement operator inversion problem with convection-diffusion model as a regularizer. The model is augmented with control functions that are added to the source term in order to resolve uncertainty of the emission rate inherent to the atmospheric chemistry models. They are sought as the minimum of the target functional in which a control function norm is combined with the misfit between measured and corresponding modeled values. Original element in the model lies in variational approach that has been applied to the weak-constraint formulation for each splitting stage of the multidimensional model. Because of the efficient algorithm for one-dimensional data assimilation to the convection-diffusion model, the resulting algorithm doesn''t take iterations with given data assimilation parameter that regulates the measurements reproduction quality. This parameter can be chosen with Morozov discrepancy principle. Algorithm efficiency has been shown in computational experiments.