Notes on the Scattering Properties
of the Lunar Surface at Radio Wavelengths
The Scattering Area in Moonbounce Communication
Volker Grassmann, DF5AI
June 27, 2004
At full moon the sunlight illuminates the entire nearside of the moon resulting in bright nights and spectacular views in the sky. The term "nearside" is however misleading because regions close to the lunar limb are not facing towards the Earth but are facing into space almost perpendicular to our viewing direction. Assuming the moon would represent a perfect sphere mirroring the sunlight in accordance to the laws of optical reflection, the lunar limb would reflect no sunlight towards the Earth at all. It is the rough lunar surface which enables this magnificient view of the full moon, i.e. mountains, rocks and topographical features are scattering the sunlight towards the Earth even from the peripherials close to the lunar limb. However, the roughness of the scattering sphere depends on the probing wavelength, i.e. features appearing rough at optical wavelengths may appear smooth, more or less, at radio wavelengths. Thus, the 'radio moon' on one hand and the visible lunar disk on the other hand, may show very different scattering properties. In fact, in the 1950s it has been discovered that radiowaves, unlike light and infrared radiation, are reflected back to the Earth principally from a small region at the center of the visible disk , i.e. the moon shows a limb darkening at radio wavelengths which does not exist at optical wavelengths (detailed information on the moon's visual brightness is available, e.g., in ).
The moon's echo depth
Moon echoes in Earth-Moon-Earth radio communication cannot provide direct information about the size and the position of the scattering area on the lunar surface. However, we may obtain implicit information by analysing the echo power as a function of range. Because of the curvature of the moon, radiowaves scattered at a position close to the lunar limb travel a longer distance (i.e. twice the moon's radius) compared to radiowaves scattered at the moon's leading edge. Thus, the geometrical depth of the moon's spherical body results in a reverberation time which may vary between zero and 11.6 milliseconds,.see figure 1.
However, measuring the moon's echo depth is difficult in practice. Considering, for example, the 432 MHz amateur band (see the curve '68 cm' in figure 2), the echo power decreases by 20 dB at 1 millisecond delay time and more than 40 dB at 11 milliseconds delay time. Thus, the 'radio moon' shows a rather small but bright spot in the center of the visible disk and it shows a limb darkening, i.e. at radio and optical wavelengths, the scattering properties of the lunar surface differ significantly. Typical amateur radio EME stations can hardly detect the moon's echo depth and, in consequence, moon echo traces look simiar to figure 3 without any detectable echo components following the initial peak. The first measurements of signal reverberation were made by Trexler in 1958, who observed that about 50 percent of the reflected power was returned within the first 50 microseconds from the leading edge of the moon (see  and the references cited therein, more information on the early moon echo experiments are available, e.g. in  and ). Compared to later measurements, his equipment is considered 'insufficiently sensitive' by Evans and Pettengill  but Trexler's findings may be considered representative to moon echo tests in ham radio. Here, the echoes originate from a small region in the center of the visibile disk having a radius of one-tenth the total radius of the moon, i.e. the moon is nothing else than a point source in the main lobe of the antenna's radiation pattern.
Slim chance of measuring the moon's echo depth using ham radio techniques
Using high transmitter power at high operating frequencies (10 GHz) and arrays illuminating the entire visible disk (see  for a discussion of disadvantages resulting from too large antenna systems), sophisticated amateur radio stations may have a slim chance of detecting the moon's echo depth at least partially, perhaps. At 8.3 GHz, for example, the relative echo power is around -12 dB at 1 to 2 milliseconds delay time which appears within the reach of amateur radio stations (see the curve '3.6 cm' in figure 2). To the author's knowledge, no such measurement has been ever conducted by radio amateurs so far.
However, there is another obstacle too resulting from the fact that typical amateur radio stations cannot generate sufficient short transmitter pulses. Note that the lengths of dits and dahs in Morse code is three to ten times longer than the maximum time delay of 12 milliseconds. Thus, the echo depth effect shows little impact on CW signals, it can only modify the trailing side of a Morse code symbol. However, CW signals do not have a perfect rectanguar shape anyway, i.e. identifying the echo depth effect in a real moon echo signal trace is indeed complicated requiring careful signal analysis. Nevertheless, this type of measurement may be considered a very special challenge to the most powerful EME stations in ham radio.
Identifying the position of backscatter on the lunar surface
In total, we may view 59 percent of the lunar surface because of the moon's wobbling motion around the Earth and this libration reveals more than half of the total surface. Figure 4 displays an impressive animation of the moon's changing appearance during a complete lunar cycle . This sequence of images was produced by António Cidadão and was published on the 'Astronomy Picture of the Day' webside, it is certainly a very special example of the beauties in astronomy. Using this animation, an attempt was made at identifying the actual position of EME backscatter on the moon's surface, see figure 5.
In figure 5, the blue circle denotes the actual position of backscatter which moves along an elliptical path (yellow) during a lunation. The red frame displays an enlarged view of this area indicating that EME signals originate from highlands in the center of the visible disk representing flat terrain, more or less. However, radar interferometry draws a more complicated picture of this area. Refering to the color coded elevation model , we may find hills and mountains (red) as well as low basins (green) differing in height by several kilometers. We may therefore conclude that this area does not represent flat terrain but does include slanted surfaces and slopes which may all affect the backscatter properties of the lunar surface in EME communication.
Discussion of possible effects in EME signal strength
Considering the scatter point's motion relative to the lunar surface during a lunation, various topographical features are drifting across the backscatter area changing the area's morphology gradually from one day to another. Does this effect cause, among other effects (see, e.g., ), monthly variations in EME signal strength? This question is difficult to answer but there is no reason to exclude this assumption in general. Evans and Pettengill consider two types of scattering depending on the angle of incidence of the radiowaves to the mean lunar surface, i.e. scattering of radiowaves from a small region near the disk center describing the way in which the 'smooth' portion of the lunar surface reflects and, on the other hand, diffuse scattering by the rough component of the lunar surface which contributes only 20 percent to the echo power . This is just another description of the results we have already discussed above, i.e. the bright spot of backscatter at the disk center and, on the other hand, the limb darkening (note that contours of constant delay time are equivalent to contours of constant angle of incidence). Tilting that 'smooth' surface at the disk center, vertical incidence of radiowaves is no longer available and, using Evan's and Pettengill's above picture, EME backscatter originating from the disk center would develop from the first type of scattering towards the diffuse type of scattering resulting in a decrease in echo power.
We may certainly find local terrain features within the central area of backscatter with slopes varying over many degree (early measurements show that 'smooth' surfaces extend horizontally for 10 to 1000 meters having an r.m.s. slope of 5 to 8 degree ), considering the entire backscatter area the tilt is much smaller though. Assuming the central scatter area is 200 kilometers in diameter with a height difference of, say 3.000 meters from one end to the other, the terrain tilt is less than 1 degree. From this perspective, EME signals appear little affected by slanted terrain but, on the other hand, the echo power falls rapidly between vertical incidence and 3 degree offset  (which is also visible in figure 2) so that even a small deviation from vertical incidence may have an influence on the EME field strengths. Furthermore, an extra offset angle is present in intercontinental EME QSOs. Considering terrestrial distances of, for example, 8.000 kilometers between European and North-American EME stations, the corresponding lines of vertical incidence differ by more than 1 degree. Considering the shortest distance between the Earth and the moon (i.e. 356.000 kilometers) and EME stations located on the opposite side of the Earth, the lines of vertical incidence would differ even by 2 degree. From this perspective, the terrain slope may indeed play a role in intercontinental EME communication by supporting or, alternatively, by hindering optimum backscatter geometry. If this assumption is true, it may happen that radio operators can receive EME stations from distant continents but cannot receive their own moon echoes, and vice versa (the same effect may also result from very different reasons, of course). In the scope of this paper it means: if the scatter point moves along that elliptical path, the terrain slope may change and, in consequence, EME operators may notice a gradual change in 'EME conditions'.
Radio amateurs indeed report monthly variations in 'EME conditions' not corresponding to the variations in the earth-moon distance, i.e. the expected 2 dB difference between perigee and apogee appears amplified or, alternatively, appears cancelled for an unknown reason. Of course, many effects may contribute to this observations but we may test the above speculation by a statistical analysis quite easily, perhaps. By using modern digital noise reduction methods, even small amateur radio stations may detect moon echoes on a daily basis, i.e. sufficient data material may become available over the year in order to investigate systematical variations in the EME signal strength (assuming, amateur radio stations can fulfill the requirements in signal calibration in this type of analysis).
The three components of the moon's libration
The moon's libration has three components, i.e. the diurnal libration, the longitudinal libration and the libration in latitude, respectively. The diurnal variation results from the rotation of the Earth changing the observer's viewing angle relative to the moon's surface. The longitudinal and latitudinal libration are both clearly visible in figure 4 resulting in that elliptical motion shown in figure 5 and 6. More information on the three components of the moon's libration are available, e.g., in .
On the other hand, we may also find arguments denying the possibility of signal strength variations resulting from the scatter point's motion on the lunar surface. The above mentioned monthly variations in 'EME conditions' are not even accepted by all radio amateurs, for example: compensating the range effect and the actual sky noise in the echo strength, Leif, SM5BSZ, found a maximum deviation not exceeeding 1.5 dB in total , i.e. he considers the EME fieldstrength level constant, more or less. Refering to Leif's measurements where he found a 0.06 millisecond delay in his echo tests  (which is, by the way, in good agreement to Trexler's measurements of 50 microseconds reverberation time, see above), the corresponding backscatter area is 354 kilometers in diameter (i.e. 0.10 of the visual diameter of the moon), i.e. that area may not be considered small compared to the elliptical area in figure 5. With other words: the real backscatter area is larger than the blue circle and, in consequence, radio echoes originating from positions along that yellow path show a certain degree of correlation reducing the variability of the moon echoes.
It is also important to note that the above discussion addresses second order effects, i.e. the variability of EME signals is primarily affected by much stronger effects caused, for example, by the neutral atmosphere and the ionosphere. EME signals are in particular subject of destructive and constructive interference resulting in a highly dynamic fading characteristic. We may identify fading components contributed along the atmospheric ray paths and further components resulting from the scattering properties of the lunar surface. Here, the many scattering centers and the libration of the moon cause the way in which the returned signals recombine to change with time and exhibit marked fading. Thus, if the scatter area changes position on the moon's surface, the corresponding interference pattern will certainly change as well and, again, radio operators may notice a change in 'EME conditions'. However, separating this effect from the overall fading characteristic is difficult - it doesn't appear impossible though. Addressing possible variations in the scattering properties of the lunar surface, we also need to take polarization effects into consideration. This effects are however difficult to study in ham radio because the majority of EME stations employ plane-polarized waves which are in particular subject of the Faraday rotation in the Earth's ionosphere. However, we are primarily interested in the monthly variations of the EME signal strength, i.e. we may cancel the short-term effects of the Faraday rotation by averaging the echo power over, say, one or two hours.
Acknowledgements. The author is indebted to Leif Asbrink, SM5BSZ, for the many valuable comments, interesting discussions and for reading the manuscript. Special thanks to Stewart Nelson, KK7KA, for providing detailed information on the moon's libration and to John Yurek, K3PGP, for providing information on the early scientific moon echo experiments.