The Postspinel Phase Boundary in Mg 2 SiO 4 Determined by in Situ X-ray Diffraction

(1992). 22. P. J. Mouginis-Mark et al., in Mars, H. H. Kieffer, B. M. Jakosky, C. W. Snyder, M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1992), p. 424; W. B. Banerdt et al., ibid., p. 249; G. Schubert et al., ibid., p. 147. 23. M. T. Zuber and D. E. Smith, J. Geophys. Res., 102, 28,673 (1997 ). 24. R. J. Phillips et al., ibid. 95, 5089 (1990). 25. J. Phipps Morgan et al., ibid. 100, 8045 (1995). 26. K. L. Tanaka et al., in Mars, H. H. Kieffer, B. M. Jakosky, C. W. Snyder, M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1992), p. 345. 27. S. C. Solomon and J. W. Head, J. Geophys. Res. 82, 9755 (1982). 28. D. H. Scott and K. L. Tanaka, U.S. Geol. Survey Map I-1802-A (1986). 29. R. M. C. Lopes et al., Moon Planets 22, 221 (1980); P. W. Francis and G. Wadge, J. Geophys. Res. 88, 8333 (1983). 30. M. H. Carr, Water on Mars (Oxford Univ. Press, New York, 1996). 31. G. Komatsu and V. R. Baker, J. Geophys. Res. 102, 4151 (1997 ). 32. We use the Chezy equations [R. A. Granger, Fluid Mechanics (Dover, New York, 1995)] to estimate average flow velocity; v, is given by v 5 C(Rs)1/2, where C is the Chezy coefficient, s is local slope, and R is hydraulic radius, defined as the ratio of flow crosssectional area to perimeter of the wetted channel. In SI units, C 5 (1/n)R1/6, where n is the Manning roughness coefficient, here square-root-gravity scaled from an assumed terrestrial value of 0.02. Hydraulic radius is obtained directly from MOLA data, assuming that the water level reached the paired-terraces and attempting to adjust the channel perimeter for post-flow mass wasting. A more difficult problem is estimation of slope. In principle, the apparent slope measured along the groundtrack can be projected into the downstream direction to yield true channel slope. The orbital track makes an angle of 50° with the downstream vector and true slope 5 apparent slope/ cos(50°). The presence of debris flows on the channel floor could locally modify this slope. 33. This velocity and the channel depth of 1300 m yield a Froude number [Fr 5 V/(hg)1/2, where h is channel depth and g is gravity] of 2.0. This value indicates supercritical flow. 34. The filter of the Viking Orbiter Camera nearest to the MOLA wavelength is red [0.5 mm to 0.7 mm; M. H. Carr et al., Icarus 16, 17 (1972)]. We have adopted a scaling factor of 0.8 to convert those images to 1.064 mm to be consistent with spectroscopic observations of the average martian surface in visible and infrared wavelengths [L. A. Soderblom, in Mars, H. H. Kieffer, B. M. Jakosky, C. W. Snyder, M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1992), p. 557]. It is not possible to obtain unbiased values of opacity using the above method, because the Viking images are not themselves corrected for the relevant atmospheric opacity. We used only Viking images that exhibited little or no obscuration. Such opacities in the Viking images may either darken or brighten them, unlike the effect in MOLA reflectivities, which is pure extinction. We estimated that average Viking images were darkened with an opacity of 0.4 and added this to the MOLA opacities. 35. M. C. Malin et al., Science 279, 1681 (1998). 36. We thank MOLA Instrument Manager R. Follas and the rest of the instrument team, and G. Cunningham, B. McAnally, and the MGS spacecraft and operation teams. We also acknowledge helpful reviews from M. Carr and an anonymous reviewer, and contributions from J. Abshire and J. Smith in instrument calibration and performance assessment, G. Neumann, G. Elman, P. Jester, and J. Schott in altimetry processing, F. Lemoine, D. Rowlands, and S. Fricke in orbit determination, and O. Aharonson, D. Brown, J. Frawley, P. Haggerty, S. Hauk, A. Ivanov, P. McGovern, C. Johnson, S. Pratt, and N. Siebert in analysis. The MOLA investigation is supported by the NASA Mars Global Surveyor Project.