AbstractThe goal of this work is the formulation of a model for the parameterization of homogeneous roughnessâinduced drag in turbulent flow simulations. We characterize rough surfaces using their surfaceâarea moments of roughnessâpeaks. Additionally, we consider a probabilistic selfâsimilar power law distribution for the roughness heights, in such a way that an assumed set of discrete roughness elements can behave as a probabilistic fractal set. Upon these assumptions, the surface characterization is complete and yields wallânormal profiles of porosity, average roughness element diameter, and equivalent pore diameter of the roughness affected porous flow. The profiles are supplied to a (poreâbased) Reynolds number and porosityâbased drag parameterization for staggered cylinder arrays available in the literature, as well as a oneâdimensional mapâbased turbulence model, the oneâdimensional turbulence (ODT) model. The purpose of the latter is a way to provide the missing effects of the equivalent dispersion tensor in the porous flow close to the rough surface, as well as that of the nonlinear turbulent transport away from the wall. Simulations are then carried out in order to evaluate the effects of two different rough surfaces on a turbulent channel flow, comparing results with existing direct numerical simulation (DNS) data. Overall, reasonable agreement is obtained, which suggests that, by using the proposed model, it is possible to model the effects of rough surfaces on wallâbounded turbulent flows, without the explicit need of the full topological representation of the surface on the numerical domain. To that extent, one clear flow control application for the suggested approach would be that of dragâbased surface optimization.