The dynamic wake meandering (DWM) model is an engineering wake model designed to physically model the wake deficit evolution and the unsteady meandering that occurs in wind turbine wakes. The present study aims at improving two features of the model: 1. The effect of the atmospheric boundary layer shear on the wake deficit evolution by including a strain-rate contribution in the wake turbulence calculation. 2. The method to account for the increased turbulence at a wake-affected turbine by basing the wake-added turbulence directly on the Reynolds stresses of the oncoming wake. This also allows the model to simulate the build-up of turbulence over a row of turbines in a physically consistent manner. The performance of the modified model is validated against actuator line (AL) model results and field data from the Lillgrund offshore wind farm. Qualitatively, the modified DWM model is in fair agreement with the reference data. A quantitative comparison between the mean flow field of the DWM model with and without the suggested improvements, to that of the AL model, shows that the root-mean-square difference in terms of wind speed and turbulence intensity is reduced on the order of 30% and 40%, respectively, by including the proposed corrections for a row of eight turbines. Furthermore, it is found that the root-mean-square difference between the AL model and the modified DWM model in terms of wind speed and turbulence intensity does not increase over a row of turbines compared with the root-mean-square difference of a single turbine.