We consider inverse problems in atmospheric modelling. Instead of using the ordinary least squares, we add a weighting matrix based on the topology of measurement points and show the connection with Bayesian modelling. Since the source--receptor sensitivity matrix is usually ill-conditioned, the problem is often regularized, either by perturbing the objective function or by modifying the sensitivity matrix. However, both these approaches are heavily dependent on specified parameters. To ease this burden, we intend to use techniques looking for a sparse solution with a small number of positive elements. We summarize several known sparse optimization techniques and propose their modifications to handle selected constraints such as nonnegativity of released amounts. We compare these techniques from the point of implementation simplicity and approximation capability. Moreover, we show that they are less parameter dependent. Finally, we compare these methods with the currently used techniques on the European Tracer Experiment (ETEX) data.
L. Adam, M. Branda: Sparse optimization for inverse problems in atmospheric modelling. Journal of Optimization Theory and Applications. DOI 10.1016/j.envsoft.2016.02.002