Photoclinometry:

     Photoclinometry is the measurement of the height of lunar features using the shading produced by oblique illumination.  This is a complex field and many reflectance algorithms can be used.  The most accurate are based on lunar Lambertian reflectance, but these are also the most complex to use and are often based on the Hapke photometric function which requires input of multiple parameters including surface roughness.  However, if area imaged is not too close to the lunar limb, the solar elevation does not exceed 20 degrees, and the albedo of the surface is uniform; then it is possible to use a less complex algorithm. Because of its simplicity, I prefer an algorithm put foward by Mark Carlotto in 1996, which in my experience only underestimates feature heights by an average of about 9 percent as compared to the more complex lunar lambertian reflectance functions.  I recently studied eleven lunar domes using the Carlotto algorithm.  The mechanics of applying this algorithm to lunar height determinations using Microsoft EXCEL are described in a paper that I wrote for the first issue of the on-line journal Selenology Today. 

http://webzoom.freewebs.com/revans_01420/Photoclinometry/Excel-Carlotto-Algorithm.pdf

For those that are interested, the process of applying the Carlotto-Algorithm in EXCEL has now been fully automated thanks to the efforts of Kurt Fisher. The fully automated spreadsheet template is available at:

http://members.csolutions.net/fisherka/astronote/Photometry/sfs/SFS.html

In addition, the basic algorithm has now been corrected for lunar phase angle, lunar longitude and latitude etc. by Raffaello Lena of the GLR group.  The corrected algorithm now very closely approximates results using more complex lunar lamberterian schemes. This excellent work will soon be published in Selenology Today (see issue #16).  The free on-line journal is available for download at: http://digilander.libero.it/glrgroup/ . Eventually I hope that this corrected algorithm will also become available in automated spreadsheet format.

Rheology:

Finally, geometric information about a lunar dome obtained from shape from shading estimates (i.e. the dome height and dome radius) and dome morphology can be used in rheologic studies (i.e. studies of volcanic flow).  Specifically they can be used to calculate the effusion rate of magma that formed the dome, the length of time necessary for the dome to form, and in some cases the ascent rate of magma in the dike that fed the dome and the width and length of the dike itself.  The effusion rate of magma forming a single dome in cubic meters per second is approximately equal to [0.00102 *  (radius of the dome in meters)^2] / Height of the dome in meters.  The time necessary to form the dome (in years) is given by the volume of the dome in cubic meters divided by [effusion rate in cubic meters/second * 3.154 x 10^7]. These calculations assume a lava density of 2000 kg/cubic meter and that the dome formed on a flat plain with lava spreading in all directions.  The yield strength and plastic viscosity of the magma can also be calculated, again assuming a lava density of 2000 kg/cubic meter and formation on a flat plain.  The yield strength in Pascals is approximated by [1053 * (dome height in meters)^2] / dome radius in meters.  The plastic viscosity in Pascal seconds is approximated by 0.0006 * (yield strength)^2.4.

Those interested in these issues can consult a few papers on the subject that are listed below. However, be aware that (at least in my opinion), the Wilson & Head paper has a typesetting error in equation 13 and in that equation I believe that 0.72 should actually be 0.7^2. The paper by Rubin is important for those interested in volcanic dike calculations.

Wilson L and Head JW: Lunar Gruithuisen and Mairan domes: Rheology and mode of emplacement. Journal of Geophysical Research. Vol 108 No E2 pp. 6-1 to 6-7. (2003).

Woehler C; Lena R; Pau KC: The lunar dome complex Mons Rumker: Morphometry, Rheology and Mode of Emplacement. Lunar and Planetary Science Conference XXXVIII abstract #1091 League City, Texas (2007).

Allan M. Rubin: Dikes vs diapirs in viscoelastic rock. Earth Planet Sci Lett, 119 issue 4. pp. 641-659 Oct 1993.