Predictions of the dynamic wake meandering model (DWMM) were compared to flow measurements of a scanning Doppler lidar mounted on the nacelle of a utility-scale wind turbine. We observed that the wake meandering strength of the DWMM agrees better with the observation, if the incoming mean wind speed is used as advection velocity for the downstream transport, while a better temporal agreement is achieved with an advection velocity slower than the incoming mean wind speed. A subsequent investigation of the lateral wake transport revealed differences to the passive tracer assumption of the DWMM in addition to a non-passive downstream transport reported in earlier studies. We propose to include the turbulent Schmidt number in the DWMM to improve (i) the consistency of the model physics and (ii) the prediction quality. Compared to the observations, the thus modified DWMM showed a root-mean-square error reduction by 2% for mean velocity deficit and 1% for the turbulence intensity, relative to the unmodified DWMM, in addition to better temporal agreement of the dynamics. This is in contrast to an error increase of 35% and 36% if only a more accurate downstream transport velocity is used without including the turbulent Schmidt number.