In this thesis we are interested in the problem of identifying point sources in an advection-diffusion model, given some measurements. By writing the problem as a minimization problem, we use a non-linear conjugate gradient method in order to estimate the source location and the corresponding intensity. Several test cases are presented. The primary motivation for this work is monitoring CO\(_2\) storage at deep geological formations, where solid monitoring tools are imperative for the storage in order to be considered safe. However, this can also be used in other situations when estimating the source location of some contamination is of interest.