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The evolution of chemical, biological, radiological, nuclear and explosive (CBRNE) clouds depends considerably on its composition. For example, cloud tracking usually relies on a diffusion model of the average atmospheric concentration of the CBRNE material; identification of its composition can benefit greatly from knowledge about the propagation of the compounds. As a result, substance classification and cloud tracking help each other significantly. However, few research efforts consider joint identification and tracking of CBRNE clouds using a network of possibly heterogeneous sensors. This paper deals with such joint identification and tracking. We assume that the chemical composition has a sparse representation in the Raman spectra with a reference library and apply a sparsity pursuit algorithm to adaptively refine the cloud propagation model based on the estimated composition. We demonstrate the benefit of joint identification and tracking of the aggregated clouds when individual substance has a different diffusion coefficient. The results also provide guidelines for selecting an appropriate sensor combination to accurately predict the cloud boundary.