The random field approach for gravel-bed roughness characterization, which is based on the presentation of bed elevations as a three-dimensional random field, is justified as an alternative to the characteristic particle size approach. We first show that the bed elevation distribution is close to Gaussian and then investigate gravel-bed roughness using the second-order structure function. The latter reveals two distinct regions: a scaling region at small spatial lags and a saturation region at large scales. The scaling exponent H (a form of Hurst exponent) appears to be isotropic and universal for both manually created unworked gravel beds (H=0.5) and natural water-worked gravel beds (H=0.79). However, the gravel-bed roughness, in general, is not isotropic and should be characterized by three independent characteristic scales. A simple model of gravel-bed roughness based on the structure function parameterization is developed and compared with the characteristic particle size approach. ¿ 1998 American Geophysical Union