The estimation of a spatially varying parameter in a time-periodic boundary-value parabolic system is considered. We show that the parameter can be identified in the corresponding initial boundary-value problem. The minimization of the output least-squares criterion via the adjoint state method is implemented (using the ‘discrete’ gradient). Numerical experiments are presented on a problem taken from oceanography: the identification of the CO2turbulent diffusion coefficient in a column of water. Cubic spline approximations of the parameter are tested on different sets of data.