Surface roughness has a strong controlling influence on radar scattering and other types of remote sensing observations. We compare field measurements of surface topography and dielectric constant for a range of lava flow textures to aircraft multipolarization radar observations at 5.7, 24, and 68 cm (C, L, and P band) wavelengths. The roughness is found to vary with scale in a self-affine (fractal) manner for scale lengths between 25 cm (the smallest horizontal step size) and 3--5 m. This result is used to demonstrate that a two-component surface description, consisting of the fractal dimension and rms height or slope at some reference scale, can resolve some of the ambiguities in previous efforts to quantify roughness. At all three radar wavelengths, the HV backscatter cross section is found to vary in an approximately exponential fashion with the rms height or Allan deviation at some reference scale, up to a saturation point, where the surface appears entirely diffusely scattering to the radar. Based on these observations, we use a parameter, &ggr;, defined as the ratio of rms height to the particular scale of measurement. Backscatter values at 24-cm wavelength and the topographic profile data were used to derive expressions which link the HV radar cross section to &ggr; or to the analogous wavelength-scale rms slope. These equations provide a reasonable fit to 24- and 68-cm echoes and for rough surfaces at 5.7 cm, but yield poor results for 5.7-cm echoes on smooth terrain. We conclude that the roughness at the two larger scales is well described by a single fractal dimension and rms height, but that texture at very small scales is characterized by different statistics. This inference is supported by analysis of 5-cm horizontal spacing topographic profiles. The relationships defined here allow determination of the surface rms height or slope at the scale of the radar wavelength. Given radar data at additional wavelengths, a more complete view of the statistical properties of the surface can be developed. Such techniques may be useful in analyses of synthetic aperture radar images for terrestrial volcanic areas, Magellan data for Venus, and other planetary radar observations. ¿ 1996 American Institute of Physics.