The evolution of a wind turbine wake situated downstream of an abrupt change in surface roughness is investigated using large-eddy simulations (LES). The results are compared with the evolution of the wake of a turbine sited on a homogeneously rough surface, and with the flow over a surface undergoing an abrupt roughness transition without a turbine. The changed surface roughness affects the turbulent statistics such as streamwise velocity, turbulence intensity, and shear stress. Different velocity deficits can be constructed based on different definitions of "background"velocity. The usual definition, that is, the difference between the velocity upstream and downstream of a turbine, attains negative values over a significant portion of the turbine wake, rendering it difficult to model using the usual Gaussian radial shape-based framework. An alternative definition, that is, the difference between the velocity over a heterogeneous surface in the absence and in the presence of a turbine, has mostly positive values and is amenable to modeling. A new model accounting for streamwise and vertical variations of the background velocity profile is developed. The new model yields more accurate predictions of the LES results than the existing Gaussian wake-shape model, which is applicable only for turbines sited on homogeneously rough surfaces. © 2022 Author(s).