  This paper investigates the solution of a parabolic inverse problem based
upon the convection-diffusion-reaction equation, which can be used to estimate
both water and air pollution. We will consider both known and unknown source
location: while in the first case the problem is solved using a projected
damped Gauss-Newton, in the second one it is ill-posed and an adaptive
parametrization with time localization will be adopted to regularize it. To
solve the optimization loop a model reduction technique (Proper Orthogonal
Decomposition) is used.
