Results of experiments on decaying turbulence in shallow water flow bounded by a solid bottom and a free surface are presented. The evolution of the turbulence structures generated by a grid, with horizontal mesh dimensions larger than the water depth, is measured using laser Doppler velocimetry and particle image velocimetry (PIV). The vertical confinement of the flow forces the large turbulence structures to move in the horizontal plane, thus attaining strongly two-dimensional features. This two-dimensionality and its consequences for the intensities and length scales of the large structures are analysed. It is shown that the decay of the vortices that are shed from the grid is determined by the characteristic size of the grid elements rather than the grid spacing. Furthermore, during the decay process the merging of vortices is observed in combination with a $-3$ slope in the energy density spectrum of the velocity fluctuations. Using the PIV data, spatial properties like divergence and enstrophy can be derived for the velocity field near the free surface. The distinct effect of water depth that is found in the velocity fluctuations is almost insignificant in the enstrophy decay.