Seeing gray spot shapes matching the expected distortion of shadows falling on irregular surfaces is compelling, but it is only possible to quantify if the geometry of the surface is known.  For example, the length of an object’s shadow falling on a known slope angle can be calculated and related to a shadow falling on flat ground. ​

​In image E16-00714 below, the shadow direction (dark spots) appears to be 90 degrees off from sun direction.  However, this is an example of the object in shadow appearing dark and the shadow cast on ground appearing much lighter (reference item 4 in “Property of Light“ section).  When image contrast was increased from 50% to 75% the ground shadows became noticeable.​

​If only one NASA image of Mars containing spots was used, the results may be too unusual to believe, but that is not the case.  Altogether fourteen NASA MGS MOC images were used in the analysis of the spots surrounding polar dunes. The images cover a combined area of 698 km2, contain an estimated 11,100 spots, and have a resolution ranging from 1.61 meters/pixel to 15.72 meters/pixel.​

For sun angle A  (90 degree – incidence angle), if an object height is set equal to 1, shadow length l  equals 1/tan A.  For image E18-00494 l  equals 2.003 and for image E16-00714 l  equals 3.143.  Thus gray spots in image E16-00714 should measure 56.9% longer than gray spots in identical locations in E18-00494.

Five of the clearest spots in image E16-00714 were measured and they proved to be 30-65% longer than the corresponding spots in image E18-00494.   Due to the faintness of the shadows in E16-00714, it was difficult to measure the shapes with any precision, but this agrees in magnitude and direction with the predicted 56.9% value.


3) SHADOW SHAPE

An object’s shadow will vary in shape depending on the surface it falls on.  The shadows will appear short and fat on a steep slope, long thin on flat ground, and curved on a side slope.  ​Image MOC2-323 offered very clear gray spots with image resolution of 3.38 meters/pixel.  As shown below, the gray spots matched the patterns expected of shadows.

​2) SHADOW LENGTH VARIES WITH SUN INCLINATION

Image E16-00714 was taken on 5/11/2002 and has a sun inclination of 71.79 degrees from vertical.  On 7/9/2002 image E18-00494 captured the same dune field.   This image has an inclination of 61.41 degrees.  The 10-degree difference allows for a measurable difference in shadow length.​

​2.      Shadow length varies with inclination of sun.​

To determine what may be causing the shift in this image, the ancillary data for image M20-00416 was compared to the ancillary data of the other eight images that had spot alignment with sunlight.

According to the Malin Space Science System explanation of the Ancillary Data, Emission Angle in most cases is close to 0 degree, i.e. the MOC is looking “straight down”.  In those cases the Phase Angle equals the Incidence Angle.  Of the fourteen dune images with spots, six turn out to have high Emission Angles.  In five of those cases, the Emission Angle plus the Incidence Angle equals the Phase Angle, meaning the MOC was angled toward the direction of the sun and the MOC direction of flight (side viewing angle = 0 degree).  Only image M20-00416 departed from this norm.​

​Using the 25.47 degree sun angle and the 15.2 degree slope angle in the equation, Y = TANq  / TANq + TANa, results in the following predicted ratio:  


Predicted Slope Shadow / Flat Shadow Ratio of 63.68%

In order to compare the actual Slope Shadow / Flat Shadow Ratio with the predicted value, measurements were taken of seventy gray spots in the MOC2-323 image.  Only gray spots with "two pixel" black spots were chosen for ease of measuring.  ​This resulted in the following ratio:


Measured Slope Shadow vs Flat Shadow Ratio of 66.35%.

​Eleven images of southern polar images containing spots were analyzed, but only image E05-00762 had spots that aligned with sun direction.   Either the process creating the spots in the south are creating significantly lower “mounds”, making it more difficult to see and measure shadows, or the spots in image E05-00762 are not mounds and it was only coincidence that the spots lined up with sun direction.

Factors unique to Mars, such as lower gravity and frozen CO2 in the soil, may cause the slope angles to vary from earth’s 10-15 degree range, but the nearly uniform slope angles of the windward and lee slopes of the dune should remain consistent. 

Since the dunes and dune shadows are very pronounced in the MOC2-323 image, the dune shadow length and dune length (from leading edge to brink) can be accurately measured.  From this utilizing the 25.47-degree sun angle provided in the ancillary data can derive the dune slope.

Twelve dunes were measured, yielding an average slope of 15.2 degrees.   Plotting the slope angle in relation to dune height shows the relationship of increasing windward slope angle with increasing dune height.  This is consistent with the above dune profile chart provided Sauermann, Kroy, & Herrmann.​​

Given Sun Angle, a, and Slope Angle, q,  the  expected slope shadow length can be calculated and expressed as a ratio of slope shadow / flat shadow.   Height, h, is equal to the TAN (slope angle,  q) times the length of slope shadow, Sos.  And  h is also equal to the TAN (sun angle, a) times the length of flat shadow minus the length of slope shadow, SOf - SOs, or Y, then

    TANa * Y  =  TANq * SOs

If SOf   is set equal to 1, and SOs  = 1 - Y, then

     Y = TANq  / TANq + TANa

From this the ratio of the dune slope shadow / flat shadow (1-Y / 1) can be calculated.  For q=15  and a=25, slope shadows should measure 63.5% of the length of flat land shadows.  This can then be compared to the ratio for actual measured slope and flat shadows.

It is fortunate that the gray spots in several of the images are falling on Barchen dunes.  Barchen dunes are well studied on earth.  The dunes are formed in areas where the wind blows consistently from one direction, resulting in well-defined shapes and profiles depending on size.  Per the USGS the windward slope of the dunes range from 10 to 15 degrees. 

Additional characteristics, such as the variability of dune height and brink location in relation to dune size, are described by "Saturation Transients in Saltation and their Implications in Dune Slopes", Feb 2001, Sauermann, Kroy, & Herrmann (reference figure below).​

​The NASA Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) took the image below in December of 2002.  It shows dark gray spots surrounding crescent shaped dunes that lie in the northern polar regions of Mars.​​

An alternative explanation of the gray spots is that they are shadows cast by mound-like features on the surface of Mars.  Five properties of light and shadow – orientation, length vs. inclination, shape vs. surface, intensity, and phase angle – allow measurable analysis of the spots to be conducted.

The following sketches provide a simple explanation of the five methods used to analyze the MOC images:

1.      Shadow orientation lines up with direction of sun.​

Five methods were used to analyze the images – spot orientation with respect to sunlight; spot length with respect to sun inclination; spot shape with respect to surface geometry; spot intensity versus known shadow intensity; and spot orientation compared to dune phase.  In each case the measured values were in agreement with predicted values for a surface feature causing shadows.

Although the analysis does not exclude the possibility that some spots are the result of melting CO2, no correlation is evident in these fourteen images to support the melting CO2 explanation.  One of the images in support of this theory is MOC2-168.  This side-by-side comparison of two images, one taken 6/19/1999, and the other taken 7/15/1999, does appear to show an increase in spot size.  However, the source image, M02-02528, for the 6/19 portion of the MOC2-168 image has a resolution of 4.15 meters/pixel with a cross-track summing of 3 – yielding a net resolution of 12.5 m/pixel.  Whereas the M03-02916 source image for the 7/15 half of MOC2-168 has a 5.54 m/pixel net resolution.  Therefore it is questionable if the apparent increase in size in the MOC2-168 image comparison is a function of the 2.2X increase in resolution, or due to the advancing season.

In order to check the effect of season on spot size, ten spots in seven of the images were measured.  A plot of size versus season (provided in NASA ancillary data) was created, where 0 degree = beginning of spring, and 90 degree = end of spring.  The results show that, if anything, the spots grow smaller with the advancing season.​

​Explanations for the gray spots, has been attributed to seasonal defrosting of CO2 and streaks of dark sand.  Although even NASA’s own descriptions of the spots come with qualifiers such as: “though not well understood”, “speculation”, “this is thought to be”, “unknown is whether”, and “much that remains unknown”.  If the gray spots are in fact melting CO2, then it would be expected to find examples of spots that have grown in size, or have merged to form larger irregular shapes.  However, as shown in the SIX MONTHS webpage, a search of the Malin Space Science System’s online database of over 134,000 images located 28 images of dunes taken between February and July 2004, and no correlation between advancing season and spot size could be made.​

5.      Shadow phase varies with viewing angle.

Considering the image resolution and the measurement method, the errors in measuring dune length, dune shadow length, and gray spot length can easily account for the difference in predicted value, 63.68%, and measured value, 66.35%.



4) SHADOW INTENSITY

The MGS Mars Orbiter Camera is essentially a device that records the amount of sunlight reflected upward by the various surface features of Mars. 

Bright surface images are areas reflecting more sunlight, black images are reflecting less.  Three factors affecting the amount of reflected light are:  1) Surface Slope, 2) Obstructions (causing shadows), and 3) Surface Reflectivity

1)     The dunes are a great example of the effect of slope on sunlight.  They have a nearly uniform composition, and therefore reflectance, yet the dune images vary from bright white to dark gray, depending on the slope angle in relation to the MOC.

2)     The dunes also provide examples of obstructions when the leeward slope angle of a particular dune is greater than the sun incidence angle.   This results in the dune shadow causing the leeward slope and flat ground to appear darker (see number 4 in image below).

3)     The gray spots, which usually consist of a small almost black spot and a larger gray area, could be the result of low reflectance material (dark sand exposed by melting CO2 and a lighter gray drifting sand area).  Or they could be shadows cause by obstructions.

Measuring light intensity can provide a method of comparative analysis of shadows cast by the sand dunes and the gray spots.  If the intensity is similar, it is another sign that the gray spots are shadows.  It is possible for dark sand to return the same light levels, but that would be an unlikely coincidence.

The section of dune below, which is located 1.8 km from the left side of the E16-00714 image and .4 km from the top, was measured for light intensity in order to compare the gray spots to dune shadows. ​

The M20-00416 image was taken with the MOC “looking away from the sun” with the 16.29 degree Emission Angle subtracting 7.47 degree from the Incidence Angle to arrive at the Phase Angle.  As it turns out, not only was the MOC recording this image from the opposite direction of the other images, there was also a side-view angle involved. This turns out to be the most plausible explanation of the spot direction change, as a side-view of an object in shadow would result in a shadow phase change (like the phases of a moon) if the viewpoint (MOC) changed during the image recording process.

If the spots are changing phase, so to must the dune shadows.  The samples of the M20-00416 image below are a side-by-side comparison of a portion of the top of the dune field (left) and a portion 22km lower near the bottom of the dune field (right).  It is readily apparent that the dune phase direction (indicated by blue arrows) has changed from nearly horizontal to a 45-degree angle.

A change in phase will result if there is a change in MOC viewing angle. General orbital data, ancillary data, and simple geometric calculations were used to approximate this change. An orbit period of 117.65 minutes, altitude of 378 km, and 3397.2 km radius of Mars were used to calculate the speed of the MOC (3.41 km/sec). Utilizing the ancillary data for the image, a .4821-millisecond line integration time and 7680 lines were used to arrive at image recording time for the range of dunes (2.581 seconds). This results in an 8.8 km movement of the MOC during the time needed to record the 23 km image of the dunes, causing the viewing angle to vary from 62.5 to 68.3 degrees, and Phase Angle to vary by 1.85 degrees.

The cumulative effects of viewing angle and phase angle shift would require a computer model to predict the image changes and compare those to measured changes.  Absent this, a comparison of dune shadow shift versus spot direction shift was made.​

Counter to what would be expected if the spots were melting CO2, the largest spots were measured in the earliest spring image and the smallest were found in the late spring.

Six of the spots were scanned and in each case 81% was the highest value recorded for the black spots (blue in Adobe image).  This “Feature in Shadow” value compares fairly closely to the “Dune in Shadow” high value of 84%.  The “Dune Shadow on the Plain” and the “Mound Feature Shadow on the Dune” values were comparable, with each having two zones of intensity measuring 40% and 53%.   For the intensity values of the dune shadows and the spots to be so closely matched is a good indicator that the spots are also shadows.



5) SHADOW PHASE

The spots in image M20-00416 initially presented a mystery.  The direction of the spots at the top of the image matched the 301 degree sun-angle, but near the bottom of the 23 km long range of dunes, the spots had a 230 degree alignment.  If the spots were drifts of dark sand, then changing wind direction could explain the shift.  But the alignment did not appear to be affected by local geography, as is the normal case with wind.

In the M20-00416 image the change in spot direction from 301 degree to 230 degree seemed to be related to the distance from the top of the image. To verify this, spot direction versus distance was measured and plotted.​

​Analysis of Spots on Mars

In all, fourteen images were looked at in detail. These NASA images comprise an area of 698 km2 and contain an estimated 11,100 spots, with image resolution ranging from 1.61 meter/pixel to 15.72 meter/pixel. The results of all five methods of spot analysis match the values expected of large mound-like features creating shadows visible from space.  


1) ORIENTATION

Of the 13 images in the northern polar region containing spots, eight images contain spots with directional orientation that match sun direction, as given by NASA ancillary data or derived by use of dune shadows.  The gray spot direction could not be determined in the remaining five images due to image resolution and other factors.

The images detailed below show a section of the referenced NASA MGS MOC images.  Yellow arrows have been added to indicate direction of sun (sun azimuth).  North direction, scale in meters, and some of the ancillary data are also provided for reference.  As can be readily seen, the long chord of the gray spots line up with the yellow arrows, the same way a shadow lines up with a light source.​

​4.      Shadow intensity is dependant on surface and sun angle.​

​The section of dune was imported into Adobe Photoshop 6.0 as a grayscale image.  Using the cursor, the six zones were scanned and the highest “k” value for each was recorded.  This tools reports a value ranging from 0-100%.  The following are the results:​




​Measuring the length (blue diamonds) of the 10 largest and/or clearest spots in seven of the northern polar dune images, and comparing the average length (pink squares) at each location against the sun angle at the time the image was taken, shows that, as expected, lower sun angle results in longer shadows.

The plot of dune shadow direction (blue diamonds), measured through the chord of the dark-side shadow, follows a curve upward, where at the 23 km location it meets the curve of the previously plotted spot shadow direction (pink squares).  Both the dune (phase) and spot shadow direction seem to change in relation to distance, only in opposite directions.  This should not be the case. 

The explanation for this is that the spots at the top of image M20-00416 have a resolution that captures the image of the shadow cast on the dune; whereas, the spots at the 23 km location only shows the “mound” shadow (reference Item 4 in the properties of light section).  If 90 degrees is subtracted from the first point for the spot direction, and a line is projected to the last point (pink dotted line), it results in a fairly close fit to the dune phase.

CONCLUSION

In order to get a rough check of the size calculations and to visualize what the mound-like features would look like around the dunes, a model was created and photographed, thus providing an approximation of how the ground view of the dunes and objects would look.​

​Comparing the model to similar dunes in the MOC2-323 image shows how the shadows are a fairly close match to the gray spots in the MOC2-323 image.  Note:  the dark gray spot offset from the lighter gray portion of the spot, the shorter shadows at the front edge of dune/model; and the curve of the shadow around the sides of the dune/model.​

Using the solar inclination values in the ancillary data and the average length of ten shadows in each image, the height of the Martian mound-like features casting the gray-spot shadows was derived.  They are as high as six-story buildings, ranging from 11.7 to 24.5 meters 

3.      Shadow shape varies with surface geometry.

​Using the same measured size (length) data, a second plot of size versus solar inclination results in an average spot (shadow) length (indicated by pink squares) that increases as the solar inclination increases (sun lower on the horizon).   This is inline with expectation if the spots are caused by shadows.​


DESCRIPTIONLEVEL
1)FLAT PLAIN27%
2)BRIGHTEST DUNE AREA7%
3)DUNE IN SHADOW84%
4)SHADOW OF DUNE ON FLAT PLAIN40%
5)SHADOW OF MOUND-LIKE FEATURE ON DUNE40%
6)MOUND-LIKE FEATURE IN SHADOW81%

​As can be seen from the above graph, the plot of spot direction has a very clear relationship to distance - the orientation gradually changing from 301 degrees to 230.