Lunar Domes and Artificial Domes: Two Tools for Lunar Observers
published on Selenology summer 2004, vol 23 n.2
By Raffaello Lena, Cristian Fattinnanzi, and Fabio Lottero
Geologic Lunar Research (GLR Group)
Introduction
In 1964, John Westfall created a dome classification scheme (1) that is widely used by the Association of Lunar and Planetary Observers’ (ALPO) Lunar Dome Survey, American Lunar Society (ALS), and GLR group. As described in (2) “the classification takes into account the size of the dome, the shape, location, surface detail, surroundings and profile. Each category is given a letter or number and their combination provides a clear encoded description of the dome in question”.
Furthermore, Ashbrook in (3) introduced the method of waiting for a dome’s black shadow to cover 1/4 of the dome, and then using the Sun’s altitude (a) at that time as an estimate of the dome’s average slope angle.
Several lunar domes observations have been made over many lunations by GLR and it is possible to compare the results of these studies.
In this paper, we illustrate two tools developed by GLR for simulating particular situations, topographies and lunar domes classification.
Instruments and measures
1. Artificial domes
FIG 1
A 50-pixel diameter 2-D model of hemispherical domes, at different D/H ratios, was built by using AutoCAD 2000 (where D is the dome’s diameter and H is its height expressed in km).
The model (included in this article) establishes the standard by which our artificial domes are compared and studied.
For every artificial dome considered here the angle b (see figure 1) was calculated with the formula:
b = 2x INV Tan (2 H/D)
b is the maximum slope of the artificial dome. b/2 is the average slope of the dome. The computed average slope values are shown in Figure 2.
FIG 2
The shadow length of each artificial dome (R in figure 1), using varying solar altitudes (a), was calculated using AutoCAD 2000®.
It should be noted that the sun’s azimuth and the lunar curvature were not considered in these calculations.
The apparent degree of illumination (labelled Is) of the nearby soil, surrounding the artificial dome, was calculated with the formula:
Is = 255 (sin a)
Where a is the solar altitude and 255 is the maximum level of white in a grey-scale (range: 0 = black shadow and 255 = white).
The apparent degree of illumination (Id) of each flank of the artificial dome was calculated with the formula:
Id = 255 sin (a + ß) [for the fully illuminated flank]
Id = 255 sin (a - ß) [for the partly illuminated flank]
The resulting Is and Idvalues are black or grey values in the grey scale 0-255. Each illuminated portion was painted using Photoshop 5.0® and then joined to the nearby soil (sloping soil was not considered).
Id <= 0 represents a real black shadow cast by a dome, whereas Id>0 corresponds to a calibrated grey value or so called “Penumbra”. For example, for low domes having D/H = 80 and solar altitude (a) = 10° we obtain two positive Id values.In fact b = 2.8 and Id1 = 57 for the illuminated flank (grey value) and Id2 = 32 for the partly illuminated flank (grey value).
In this case the dome does not cast a black shadow, only a penumbra for the partly illuminated flank. With the same procedure different sequences were recorded varying the Sun’s altitude and the D/H ratios. Frames of suitable sequences were digitally converted, as shown in figure 2.
The form of the model is:
Average Slope = b/2 = 124.12D/H (-1.0214)(R 2= 0.999)
2. Software Rete
Based on a photoclinometric theory(4-5), we developed an algorithm designed to derive a 3D view from lunar images.
Photoclinometry, sometimes referred as “shape-from-shading,” uses digital image data as a quantitative map of surface slope. In this technique (4), differences in pixel brightness are used to compute surface slope.
The assumption of the theory is summarized as follows:
a) Shading in the image is due to topography, not albedo variations
b) Photometric information can help to highlight morphology changes (it can be useful to study lunar domes)
c) Most existing topographic information comes from grey values. Every pixel of an image is related at two coordinates (in the X and Y directions) and at a grey value (range 0-255)
d) For a surface of “costant albedo” the area with the highest grey values are generally related with the highest elevations.
The program was developed using IBASIC by Pyxia Development(6).
IBASIC is similar to the BASIC languages included with personal computers in the past; it creates a stand-alone executable file compatible Microsoft Windows 98 or higher, no needing installation.The software RETE allows the user to create a density slice within the 256 grey values in a tonal grey scale (0=black and 255 =maximum level of white).
The process depends on accurate registration of the individual grey values to a pixel level, which is accomplished by several brightness measurements made at each pixel location. This cycle is then applied to all pixels to create a detailed surface topographic map, resulting in a quantitative improvement in surface morphology. This translates a texture map in perspective (oblique angle of 45°). The cycle is described in a series of steps, as proposed in figure 3.
FIG 3
In order to exalt low slopes, it was inserted a specific flag with a factor of variation “input slope parameter”(i.e. low number high slope and vice versa). The choice of the number must be based on experience and the target of the observation.
Results and discussion
1a - artificial model and lunar domes
An interesting result arising from the model is that a hemispherical dome can actually cast a black shadow (or a penumbra) of that geometry and length as figure 2 shows.
The model shows that at more than 4-5° of solar altitude the smaller domes and low profile domes become less conspicuous disappearing into their local areas. This trend is expected as the angle of illumination increase and the dome's shadow penumbra becomes broader.
The accuracy of our model is demonstrated by its ability to simulate fairly well the shadows and the penumbra appearing in our CCD images taken under similar lighting conditions. The image of one such dome is shown in figure 4 (Milichius pi -0.510 +0.175).
FIG 4
The image was taken by KC Pau on May 11, 2003 at 12:11 UT using a CN 212 telescope, 2x Barlow, and a webcam Philips Toucam Pro. The local altitude of the Sun, h and its colongitude, C, were also calculated with the Harry Jaimeson’s Lunar Observer’s Tool kit software.
Comparing this image (h = 1.16°, C = 32.43°) with our artificial domes built varying the Sun’s altitude and the D/H ratios we estimated its accuracy (see figures 2, 4 and 5). Our results are summarized in Table 1.
FIG 5
TABLE 1 Slope evaluation between artificial domes and a real dome (Milichius pi) under a solar altitude of 1°. X is the fraction of the dome east-west diameter that is covered by black shadow.
Dome |
Diameter Pixelkm |
Shadow Length Under 1° Solar Altitude Pixelkm (height) |
X |
D/H (Average Slope) |
Milichius Pi Figure 4 |
18±18.1±0.45 |
22±19.9±0.45 (0.210) |
1.2 |
40 (2.8°) |
Artificial dome D/H 80 |
50= |
23 |
0.5 |
80 (1.4°) |
Artificial dome D/H 60 |
50= |
32 |
0.6 |
60 (1.9°) |
Artificial dome D/H 50 |
50= |
42 |
0.8 |
50 (2.3°) |
Artificial dome D/H 40 |
50= |
55 |
1.1 |
40 (2.9°) |
Artificial dome D/H 30 |
50= |
76 |
1.5 |
30 (3.8°) |
From Table 1, it follows that the shadow length and the average slope angle of the artificial dome having a D/H ratio=40 matches the estimated values for Milichius Pi (Figure 3 and 4). For Milichius Pi (image taken with a low solar altitude of 1,16°) we calculated a length of its shadow of 9.9±0.45 km, X= 1.2, a height of 210 meters and an average slope of 2.8°.
FIG 6
Another image (fig.6)of the dome was taken by Pau on July, 9, 2003 at 13:23 UT .
In this frame the solar altitude over -0.510+0.175 was2.9°; it matches thecorrespondingartificial dome profile (D/H=40) under the same solar altitude.
We categorized thisdome, using the Westfall scheme as: DW/2a/6f/7j.
1b -application of artificial domes
The artificial model describes the shadow length cast by an ideal dome, hemispherical in cross section, and located in a mare. Our model can be useful for simulating particular situations for hemispherical domes. Moreover it is a tool for visual observers showing how rapidly the appearance of domes changes with increasing solar elevation.
Obviously the combined effects of variables can give some differences, summarized as follows.
FIG 7
2) Software Rete and 3-D map.
The program has been tested on several datasets. Initially our software was used to derive a 3-D map of the Rupes Recta region (figure 8). The figure shows also this slightly raised topography.
FIG 8
Using a 3-D map it is possible to analyse:
The model shows that a large patch size (or a low dome) is to “blur” the topography. On the contrary a smaller patch size (or using a large factor of multiplication of the slopes) would produce sharper map but it can give a “topographic noise.” Interesting results were obtained on Arago domes. Figures 9 and 10 show the map of Arago alpha and beta respectively.
FIG 9
Arago alpha (+362+130) shows an irregular shape, multiple summits, such as depression, elevation and valley. Arago beta (+339+106) has an irregular shape and multiple summit craterpits.
FIG 10
From the maps we categorized these irregular domes, using the Westfall scheme as: DW/3d/5i/7p8p9p.
Another map is shown in figure 11 (Mairan T). This lunar cone shows a regular shape.
FIG 11
This paper illustrated two tools developed by GLR for simulating particular situations, topographies and lunar domes classification. Our artificial model will familiarize lunar observers with the appearance of typical lunar domes. Future 3D maps are being planned to investigate domes or topographies on a case-by-case basis.
Finally the tools can contribute to confirm formations of uncertain attribution or profile.
For information on our programs and for the original digital modelling performed by us, please contact Raffaello Lena(email: gibbidomine@libero.it).
Acknowledgement.
Many thanks to KC Pau and to GLR observers for the numerous images they submitted and to U. Bacigalupo for his help in the mathematical model of the software Rete. Many thanks to B. Garfinkle, FRAS,for reviewing this article.
References
(1) John Westfall, “A Generic Classification of Lunar Domes.” JALPO 18 (1-2) (January-February 1964), 15–20.
(2) P. G. R. Salimbeni, R. Lena, G. Mengoli, E. Douglass, and G. Santacana, “The Three Domes in Rima Birt Region.” JALPO 42 (2) (August 2000), 83–87.
(3) Joseph Ashbrook, “Dimensions of the Lunar Dome Kies 1.” JALPO 15 (1-2) (January-February 1961), 1–3.
(4) Photoclinometric analysis: http://astrogeology.usgs.gov/Projects/PlanetaryIcesWorkshop/ abstracts/tscambos.html.
(5) L. S. Glaze, L. Wilson, and P.J. Mouginis-Mark, “Volcanic Eruption Plume Top Topography and Heights as Determined from Photoclinometric Analysis of Satellite Data.” Journal Geophysical Research 104 (1999), 2989-3001.
(6) IBASIC by Pyxia Development: http://www.pyxia.com/ibasic.html.