We have developed a radar-echo model for Mars based on 12.6-cm continuous-wave radio transmissions backscattered from the planet. In our model, Mars' surface is divided into radar map units that are based on generalized geologic map units; the radar map units are further subdivided using thermal inertias because the geologic units are insufficient to account for the quasispecular echoes. For cratered uplands and northern plains units, model depolarized and polarized diffuse echoes are uniformly bright, but polarized-diffuse echoes are three times stronger than the depolarized ones. For volcanic units, depolarized and polarized-diffuse echoes are Lambertian and of equal strength. Quasispecular echoes are computed using Hagfors' scattering law. Assignments of depolarized-echo strengths, normal reflectivities, and root-mean-square (rms) slopes for the radar map units were guided by experience, thermal inertias, and data on quasispecular echoes, and then adjusted by trial and error methods to best fit the data. Regional slopes are not included in the model. Our model contains 118 radar-scattering units. The most important ones can be characterized as follows: (1) extensive cratered uplands (background) with weak depolarized echoes (0.01), average thermal inertias, moderate reflectivities (0.095), and moderate rms slopes (3.2-degrees); (2 ) volcanic units of the Tharsis, Elysium, and Amazons regions with strong depolarized echoes (0.04-0.133), low thermal inertias, small reflectivities (0.025-0.050), and large rms slopes (6-degrees-20-degrees); and (3) northern plains units with moderate to strong depolarized echoes (0.017-0.045), moderate to very high thermal inertias, moderate to large reflectivities (0.075-0.15), and moderate rms slopes (3-degrees-5-degrees). Arabia, an extensive unit of upland that is mantled by dust, has a weak depolarized echo (0.007), low thermal inertia, small reflectivity (0.05), and small rms slope (3.0-degrees ). Like the 1986 Goldstone observations along 7-degrees-S: (1) model depolarized-echo total cross sections vary with longitude as a one-cycle curve with a maximum near 135-degrees and a minimum near 330-degrees-W; (2) model polarized-echo total cross sections vary with longitude as a two-cycle curve with maxima near 30-degrees and 240-degrees-W and minima near 130-degrees and 330-degrees-W; (3) model ratios of depolarized-and polarized-echo total cross sections vary with longitude as a one-cycle curve; and (4) model depolarized- and polarized-echo spectra, as well as ratios of the two, resemble the complex observed spectra. Our model also broadly matches the variation in depolarized- and polarized-echo total cross sections (and their ratios) observed by Arecibo in 1980-1982 along 22-degrees-N. Our model illustrates the complexity of echo spectra that arises from a mixture of surface units with different scattering properties. We also conclude that there are two dominant populations of surfaces that have distinct echo properties and that there is general agreement between the quasispecular echo reflectivities of our model and those of many other radar observations of Mars.
