### Abstract

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, z0. Here we propose a predictive formula for z0 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 z0 value of sinusoidal microtopography as a function of the amplitude and slope. The effective z0 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 z0 values measured in ∼ 10^{5} wind-velocity profiles from southwestern US playa surfaces. Our equation is capable of predicting z0 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.

Original language | English (US) |
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Pages (from-to) | 391-405 |

Number of pages | 15 |

Journal | Earth Surface Dynamics |

Volume | 4 |

Issue number | 2 |

DOIs | |

State | Published - May 19 2016 |

### ASJC Scopus subject areas

- Earth-Surface Processes
- Geophysics

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## Cite this

*Earth Surface Dynamics*,

*4*(2), 391-405. https://doi.org/10.5194/esurf-4-391-2016