The domain wall motion coercivity, $H_{c}$, of magnetic materials arises from the dependence of the wall energy on localized changes in material parameters (magnetization, anisotropy, exchange energy densities). However, in an otherwise perfectly homogeneous material, the domain wall energy might change due to the change in the volume of the wall versus the wall position. Thus, any surface roughness contributes to the coercivity. Assuming different two-dimensional surface profiles, characterized by average wavelengths ${lambda}_{x}$ and ${lambda}_{y}$, and relative thickness variations dh/h, the coercivity due to the surface roughness has been calculated. Compared to the one dimensional case, the 2D coercivity is reduced. Depending on the ratio of ${lambda}$ to the domain wall width, $H_{c}$ has a maximum around 2, and increasing with dh/h. With the decreasing thickness of the thin film and GMR heads, it might be the domain factor in determining the coercivity.