Predicting the roughness length of turbulent flows over landscapes with multi-scale microtopography

The fully rough form of the law of the wall is commonly used to quantify velocity profiles and associated bed shear stresses in fluvial, aeolian, and coastal environments. A key parameter in this law is the roughness length, z(0). Here we propose a predictive formula for z(0) that uses the amplitude and slope of each wavelength of microtopography within a discrete-Fourier-transform-based approach. Computational fluid dynamics (CFD) modeling is used to quantify the effective z(0) value of sinusoidal microtopography as a function of the amplitude and slope. The effective z(0) value of landscapes with multi-scale roughness is then given by the sum of contributions from each Fourier mode of the microtopography. Predictions of the equation are tested against z(0) values measured in similar to 10(5) wind-velocity profiles from southwestern US playa surfaces. Our equation is capable of predicting z(0) values to 50% accuracy, on average, across a 4 order of magnitude range. We also use our results to provide an alternative formula that, while somewhat less accurate than the one obtained from a full multi-scale analysis, has an advantage of being simpler and easier to apply.