  We study a local data inverse problem for the time-dependent
Convection-Diffusion Equation (CDE) in a bounded domain where a part of the
boundary is treated to be inaccessible. Up on assuming the inaccessible part to
be flat, we seek for the unique determination of the time-dependent convection
and the density terms from the knowledge of the boundary data measured outside
the inaccessible part. In the process, we show that there is a natural gauge in
the perturbations, and we prove that this is the only obstruction in the
uniqueness result.
