Predicting the Appearance of the Lunar Umbra at Future Total Solar Eclipses

Jeffrey R. Charles

© Copyright 1994, 1995,1996, Jeffrey R. Charles, All Rights Reserved.



Predicting the Appearance of the Lunar Umbra at Future Total Solar Eclipses

Contents:


Introduction:

The primary purpose of this ongoing project is to obtain and analyze data that will facilitate predicting the appearance of the lunar shadow (or umbra) and related atmospheric phenomena at future total solar eclipses.

To the eclipse observer using only the unaided eye, the approach of the lunar umbra can be a very dramatic and memorable part of the eclipse experience. In cases where the solar corona is obscured by clouds during totality (as was my experience in 1991) a view of the umbra may be the ONLY memorable part of one's eclipse experience. Knowing the approximate appearance of the umbra in advance can allow the eclipse observer to get the most out of being engulfed by it!

The boundary of the lunar umbra is obviously invisible in space; it is only visible where it intercepts light scattering elements in the earth's atmosphere. As a result, the lunar umbra can usually be seen as a large dark (though not black) area in the sky before, during, and after the total phase of the eclipse. Direct sunlight is absent within the umbra, so the normal light blue color of the sky caused by atmospheric scattering is absent as well.

From a distance of ~50 km or more, the diffuse umbral boundary can appear to be surprisingly well defined. This implies that the atmospheric scattering which makes the umbral boundary visible is stronger at certain altitudes. In order to predict the appearance of the lunar umbra at future total solar eclipses, it is first necessary to determine these prominent projection altitude(s) of the lunar umbra on the earth's atmosphere. While it may be possible to extrapolate some probable projection altitudes from existing atmospheric data, a total solar eclipse can cause unusual local atmospheric conditions. This indicates empirical observation of the local phenomena caused by the interaction of the lunar umbra and the earth's atmosphere.

At second and third contact (the beginning and end of the total phase of the eclipse) the edge of the umbra crosses directly between the observer and the sun. When the shape, size, orientation, and horizontal velocity of the umbra are known, and the times of the umbral observations and second or third contact are also known, the distance from the edge of the umbra to a point at the atmospheric projection altitude that is directly between the observer and the sun can be determined. This information can be used to calculate the altitude(s) at which the edge of the umbra is the most prominently projected. If the elevation angle of the umbral boundary is measured at various sets of opposing azimuths during totality, one need only triangulate (while compensating for various physical factors) to get the results.

Due to the large size of the umbra and the relatively long distances between the observer and the umbral boundary, calculations must include compensation for the curvature of the earth. Under exceptionally clear weather conditions, the curvature of the earth ultimately determines the extent of time that the umbra can be observed from a given site. Due to the irregular profile of the limb of the moon and other factors, the edge of the umbra is not a razor sharp line. This imparts a certain degree of uncertainty in the results taken from photographic data.

Knowing the apparent projection altitude of the umbra can be useful for predicting the appearance of the umbra at future eclipses and for atmospheric study. A total solar eclipse is the only natural phenomenon that can create a predictable circumstance where the lower atmosphere is illuminated by direct sunlight while the upper atmosphere is in shadow.

Most solar eclipses are observed from sites where the sun is at a low to moderate elevation angle. Atmospheric scattering effects and the geometry of the lunar umbra usually dictate that observations of multiple azimuths must be made in order to obtain reliable results, particularly when the sun is at a low elevation angle. To collect data used in the study of the umbral boundary, I designed and fabricated the instrumentation required to take 360 degree panoramic photos of the twilight conditions typically present during totality. In addition to the panoramic photographs, other time indexed photos and video and were taken to collect lunar umbra data, as was a light meter. A large part of this work is based on data I obtained from a high altitude site near Sevaruyo, Bolivia during the total solar eclipse of November 3, 1994.

This work requires good weather conditions and good site selection. The weather was not favorable for all observed eclipses (cirrus clouds were the most common problem) but after I observed my third eclipse in 1994, I had enough data to calculate results and prepare the first version of this paper. It was presented to a limited group at JPL on March 23, 1995, and at the RTMC on May 26, 1995.

Thus far, my experiments show two prominent altitudes for the visible projection of the lunar umbra on a cloudless sky; ~15 km and ~22 km. The latter 22 km figure figure is the altitude at which the umbral boundary is typically the most obvious. This corresponds to an altitude in the lower stratosphere at which relatively high concentrations of ozone and volcanic material are typically present. Above the 22 km altitude, the umbral boundary is nearly invisible except during totality itself and during times within about one minute of totality. At these times, very subtle evidence of the umbral boundary can apparently be observed up to altitudes as high as ~30 km. Below the 22 km altitude, the umbral boundary becomes less and less obvious and typically becomes difficult to detect in a clear sky at altitudes below ~15 km; therefore, the difference between the 22 km altitude and the 15 km altitude relates to the definition of the observed umbral boundary in a clear sky.

Atmospheric cooling caused by an eclipse can often result in the development of cirrus clouds over eclipse sites. It is not uncommon for these eclipse related cirrus clouds to occur at altitudes between 9 and 11 km at low and moderate latitude sites, and at lower altitudes near the poles. Such conditions are unfavorable for the above umbral experiment; clouds can obscure the view of the umbral boundary at higher altitudes. In addition, cirrus clouds will obscure the outer extremes of the solar corona. While unfavorable for most eclipse work, cirrus clouds can act as a "projection screen" for the lunar umbra, making it very easy to see. Under such conditions, the umbral boundary can be projected so sharply that its motion across the sky can often be easily detected.

Local haze conditions present a different condition. Haze can completely obscure the umbra from view until within one or two minutes of totality. When the umbra finally becomes visible, it may be visible high in the sky as well as on the haze layer near the horizon. The effect often appears subtle to the naked eye, but a good view of the phenomena may be obtained by looking through a wide angle optic such as a video fisheye conversion lens or a wide angle "door peeper".

Without haze, the umbra can typically be detected at least 5 minutes before and after totality. The theoretical maximum time before or after totality that the umbra should be detectable is about 15 minutes. This longer time would only apply to a total eclipse observed near local noon from a site near the equator. Thus far, the maximum time before totality that I have actually observed the umbra is a little over 9 minutes. This observation was made from Mazatlan, Mexico at the July 11, 1991 eclipse. Footage from a popular film entitled "The Great Eclipse" confirmed this observation.

Several minutes before to totality, the sky in the west may appear to be darker than that in the east, but this effect is not always caused by the umbra itself. Rather, it can be caused by virtue of the fact that the west is in an area of deeper partial eclipse than the east. When it initially appears, the umbra usually looks like a subtly dimmer blue or blue gray color that is confined to an area very low on the western horizon. The umbra usually does not appear very dark at this point, since there is still a considerable amount of sunlit atmosphere between it and the observer. As it approaches, the umbra typically appears to get larger, higher, and darker.

Additional atmospheric effects are observable during and immediately before or after totality: sunlight that is scattered or reflected to the observer from outside the umbra will often to appear yellow or orange (and occasionally even red) due to atmospheric scattering. These effects are typically most pronounced beyond the most distant parts of the umbral boundary.

This chapter includes results from my umbral experiments as well as some observations concerning factors which influence the appearance of the umbra, the color around the horizon, and the times at which the umbra can be observed from a given eclipse site. It also references some of my panoramic photographs of the umbra at previous total solar eclipses, my predictions for the appearance of the umbra at selected future total solar eclipses, and my photos of the solar corona, some of which show 4-5 diameter long coronal streamers and easily visible earthshine on the moon.


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Experiment for Determination of the Prominent Projection Altitude(s) of the Lunar Umbra on the Earth's Atmosphere


Objectives:


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Challenges:


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Assumptions, variables, and resulting maximum theoretical uncertainty; as applicable to November 3, 1994 eclipse data.

(Maximum errors apply only to data taken from an edge of the umbra that is at an elevation angle of 3 degrees or less)

					1st Order	Uncert. (%);
Assumption or Variable:			Uncert. (%)	2nd Iteration

Perfectly spherical Earth		0.007		0.007

Reference to center of moon		0.7		0.7 (corrected in results)

Fixed elevation angle over 3 minutes	0.9		0.9 (corrected in results)

Atmospheric refraction at 3 deg. elev.	1.1		0.08 (% wtd.)

50% error in estimated curvature of
earth between observer and visible 
limit of umbra at 36 deg. elev. angle	3.0		0.18

Repeatability of measurements		0.4		0.4

Calculations (sans assumptions)		0.1		0.1

Variation in actual solutions for
different data points. Includes timing
and path width prediction errors.	9.3		8.6

Total uncertainty for clear sky		15.5		11.0

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Applicable methods for calculating projection altitude from observations made at same azimuth as the sun.

The high altitude of the Bolivian altiplano made the November 3, 1994 total solar eclipse very favorable for collecting umbral data. Unfortunately, local cultural problems beyond my control interfered with my local preparations for this eclipse and my work at it. As a result, my data did not included reliable measurements for the minor axis of the umbra. These measurements were to have been taken during totality at opposing azimuths which were nearly parallel to the minor axis. Reliable umbral data was also sparse at every other azimuth except for that which was taken near the same azimuth as the eclipse. This was one of the least favorable azimuths for good umbral data, but there was significant redundancy in the data at this azimuth because multiple wide angle cameras had been used to take photographs and video of the eclipse over the horizon for purely aesthetic purposes. This made it possible to salvage the experiment, but the calculations used in reducing the data had to be more complex.

Due to the large size of the umbra, the curvature of the earth must be taken into account when reducing data. This adds complexity to the problem, particularly in cases where the eclipse occurs at a low elevation angle. A single observation of the umbra at the same azimuth as the sun will only provide a solution analogous to a triangle for which only one angle and the length of the opposite side are known. The "solution" for such a triangle is the locus of all points from which the side of known length will subtend the known angle. This locus is defined as an arc which nearly touches both ends of the known side of the triangle. The length of this arc is 360 degrees, minus twice the angular subtense of the known side of the triangle. Fortunately, the umbral projection altitude can be determined from a few of these observations, since the loci from the different observations will all intersect at the observation point. Simpler calculation methods are also reasonably accurate, as shown below:

Calculation Method		Advantages		Disadvantages

Triangulation above the		Simple to perform,	Init. requires
earth's surface, initially	easy to explain.	assumptions about
incorporating assumptions				minor variables.
about minor factors.					2nd iteration has	
							~0.3% error.

Triangulation above and		Less 1st order		Still requires
below the earth's surface	uncertainty.		assumptions.

Defining the arcs which		Fewer assumptions	More difficult 
describe the ambiguous		required.  1st order	to perform.
"solutions" for the triangles	uncertainty ~0.17%.
from multiple observations.	(= error in est. umbra
These arcs all intersect at	altitude/radius of earth)
the observation point.

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Results from My 1994 Umbral Data:

Altitudes for the most prominent projections of the lunar umbra on the earth's atmosphere:

Atmospheric	Projection
Condition	Altitude	Uncertainty	Comments

Clear Sky	21.8 km		9.4%		Upper visible limit.
		(71,500')			High ozone concentration.
						Volcanic material may
						obscure true limit.

Clear Sky	14.6 km		11.6%		Underexposed data.
		(48,000')			Possible minimum 
						clear sky limit.
						(Relates to observable
						definition of boundary)

Cirrus clouds	9.0 km		2.8%		Separate projection
		(29,000')			visible on cloud bands.
						High site elevation
						reduces uncertainty.

Data shows that clouds are probably 0.3 km 50% thick, moving east at ~50km/hr.


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Weighted Results from My 1994 and 1995 Umbral Data, and from 1994 Video Provided by Astronomia Sigma Octante, (ASO) Bolivia.

Altitudes for the most prominent projections of the lunar umbra on the earth's atmosphere:

Atmospheric	Projection	Calculated	Observer/time/qty.
Condition	Altitude	Uncertainty	Comments

Clear Sky	21.8 km		9.4%		J. Charles 1994 (14)
Maximum		(71,500')			Best data

Clear Sky	19.0 km		9.5%		ASO 1994 (2)
Maximum		(62,300')			Video data

Clear Sky	28.6 km		20.0%*		J. Charles 1995 (7)
Maximum		(93,800')			Hazy conditions
---------
Clear Sky	14.6 km		11.6%		J. Charles 1994 (14)
Minimum		(48,000')			Partly cloudy

Clear Sky	14.8 km		11.5%		ASO 1994 (2)
Minimum		(48,600')			Video data

Clear Sky	19.3 km		8.0%*		J. Charles 1995 (7)
Minimum		(63,300')			Hazy conditions
----------------------------------------------------------------
Clear Sky	23.6 km		12.6%		Weighted average
Maximum		(77,500')			of combined data

Clear Sky	16.0 km		10.5%		Weighted average
Minimum		(52,600')			of combined data

* Preliminary results from cursory observation of 1995 data. 1995 projection altitude data will not be incorporated into final conclusions until a detailed analysis has been performed.


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Summary of Conclusions from Total Solar Eclipse Observations of Umbral Boundary:


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Summary of Conclusions from Total Solar Eclipse Observations of "Sunset" Colors Near Horizon:


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Additional Details from Total Solar Eclipse Observations:

The true maximum umbral projection altitude may not be observable from the ground. Reports from high altitude balloon and airplane flights indicate that the daytime sky above ~21.8 km should be bright enough to support visible projection of the umbra. The relatively low level of sky brightness at this altitude or the presence of light scattering elements such as volcanic material at ~21.8 km may prevent the detection of this higher altitude projection from most ground based sites. The presence of scattering elements at the observed projection altitude appears to be very likely, given the fact that measurements taken from both inside and outside of the umbra revealed the same projection altitude. This conclusion indicates that the observable projection altitude could change according to a function of time and location, with latitude being the most significant location factor.

"Sunset" colors around and below the observable edge of the umbra: Thus far, my total eclipse observations (1979, 1991, 1994, and 1995) indicate that the "sunset" colors are usually the strongest near the most distant observable edge of the umbra. The color is generally yellow near the edge of the umbra, turning to a pale orange near the horizon. These observations would support the conclusions in earlier work by Glenn E. Shaw which suggests that the color results from light being "single-scattered of into the umbra from the penumbra and from the usual absorption of blue light by dust and haze". Additionally, it is possible that the relatively deep blue color which is often visible inside the umbra would by contrast make the color outside the umbra visually appear to be more yellow than it really is.

Atmospheric scattering effects are sometimes observable in the absence of a sunset or eclipse. On occasions when exceptionally clear visibility exceeds 80 km or so, very distant mountain ranges and clouds (when present) can be observed, even when the sun is relatively high. At such times, it is not unusual for distant objects that within a fraction of a degree from a flat horizon to appear more yellow than usual. In addition, unobstructed sky at such low elevation angles may appear to be a low saturation green color.

Additional factors contributing to "sunset" colors. Photos and observations of the 1979 and 1994 eclipses revealed the same stronger colors near the most distant parts of the umbra, but there were some notable exceptions. High, thin clouds covered much of the sky at the 1979 eclipse, providing an impressive projection screen for the umbra. Shortly after second contact, the northeastern to eastern edge of the umbra could be seen moving away at an impressive speed, "eating up" the blue sky as it moved. The observable umbral boundary was still some 9 degrees above the horizon, and probably about 55 kilometers away. Clinging to the edge of the umbra was a dim, thin, ruby red line of color. Farther from the edge the color changed to deep orange, then yellow, which finally gave way to blue sky near the horizon. Occasional white sunlit clouds could be seen behind these colors and later through the umbra itself. I did not notice the color at all prior to second contact. The close range and high elevation angle of the edge of the umbra at this eclipse did not present atmospheric conditions favorable for producing the ruby coloration at such a high elevation angle. Some of my photos from the 1994 eclipse also subtly reveal this phenomenon. This data leads me to speculate that even though it is comparatively dim, the red light from the solar chromosphere is part of the cause for this subtle red color near the edge of the umbra.

Other possible causes for unusual color: When observed from terrestrial sites at high elevations, partial eclipses of less than 30% magnitude have occasionally impressed me as causing the ambient light to appear slightly bluer than normal. If this color shift has basis in fact, then it could indicate that the light from the extreme limb of the sun is "yellower" than the light from the center. This would explain the yellow color near the edge of the umbra at high elevation angles as well as accounting for the "golden" color of the sunlight just prior to second contact that is often reported by eclipse observers who have clear skies. Clear skies would help explain why the best displays of shadow bands often seem to coincide with the presence of this "golden" light. However, published solar data shows that solar limb reddening is probably too subtle to be detected so easily. This would lead me to speculate that the causes of the perceived color shift (if it is indeed real) are probably atmospheric.


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Proposed Future Umbral Experiments:


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Predicting the Appearance of the Lunar Umbra:

The following factors (shown in more or less descending order of influence) drive the overall visual appearance of the lunar umbra at a total solar eclipse:

Weather is a very significant factor in determining the appearance of the lunar umbra. Since we would all seek to observe an eclipse from a clear site, the following prediction criteria apply primarily to clear weather conditions.

The following information is written to be best suited for predicting the appearance of the lunar umbra at a total solar eclipse of at least 2.5 minutes duration which occurs while the sun has an elevation angle of at least 30 degrees. It assumes that the weather is clear and that there is very little haze. A rough prediction of the appearance of the lunar umbra under clear conditions can be obtained by considering only a few of the above factors. The prediction data can in turn be used to generate graphics showing the appearance of the umbra at future eclipses.

The maximum visible umbral projection altitude should be shown to be at about 22 km. The edge of the umbra should be feathered to have a boundary definition equal to between 10% and 25% of its elevation angle above the horizon. There is minimal change in the brightness of the sky above this altitude. At all times except within one minute of totality and during totality, the area inside the umbra should appear to be a blue color of medium saturation. When the umbra is very distant, it should appear only slightly darker than the surrounding sky, and it should appear to get darker and larger as totality approaches. By about one or two minutes before totality, the umbra should appear somewhat like the blue color visible under a late afternoon thunderstorm, but the blue should be slightly less saturated. By one minute before totality, a pale yellow color should appear below the most distant parts of the umbra. By 30 seconds before totality, the yellow color should be stronger, and it may give way to an orange color of moderate saturation under the most distant part of the umbra. At this time, brighter planets should begin to appear and the entire outline of the moon should gradually become visible against the inner corona.

By second contact, the area within the umbra appears to be a dark blue-gray, but not black. The area occupied by the moon does not appear black either; it is about the same brightness and color as the sky surrounding the corona. During totality, yellow color is usually visible all the way around the horizon, but it is typically strongest (and may even be orange or red) under the most distant parts of the umbra. Clouds near the horizon outside the umbra may also appear to be yellow. Clouds at elevation angles above about 8 degrees typically appear to be white while they are sunlit. When totality ends, the appearance of the umbra (in regard to brightness and color) changes in the reverse of its appearance before totality.

In addition to what is described above, the following attributes should be incorporated into umbral prediction images:

If the prediction is for a site under strong haze, the umbra probably will not become very easy to see until within about 3 minutes of totality. At all times except during totality, the umbra will appear to be much brighter than usual. Within about 1 minute before or after totality, and in cases where the umbra appears near the horizon in directions opposite the solar azimuth, the umbra probably will become visible on the haze layer in addition to being visible higher in the sky. During totality, the yellow colors near the horizon may be stronger than usual. Most other attributes should remain the same.

If the prediction is for a site under continuous but thin cirrus clouds, show the umbra projected at an altitude of about 10 km. No umbral information should be shown in the sky above or below this altitude. During totality, the area within the umbra should be a dark blue-gray of very low saturation. Most other attributes should remain the same. These conditions can give the umbra a very dramatic appearance!

Enjoy your encounter with the lunar umbra!


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Linked Graphics and Recommended Reading:


Linked Graphics are Under Construction.

Steps to a Successful Eclipse Expedition, by Jeffrey R. Charles

Eclipse Chaser's Journal

Getting Your Film & Equipment Through Airports and to Your Eclipse Site

Cultural Reality at Your Eclipse Destination; When Caution may be in Order




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© Copyright 1996, Jeffrey R. Charles, All Rights Reserved. Any form of reproduction or posting of any part of this document at web sites other than "eclipsechaser.com", "eclipsemovie.com", or "versacorp.com" without including this notice and without the prior express written consent of Jeffrey R. Charles is strictly prohibited.

This material is the intellectual property of Jeffrey R. Charles, and all content is protected by intellectual property laws. Commercial use (such as in a seminar, publication, program, or motion picture) of data or other material in this paper or of related material by the same author (whether said material was obtained directly or indirectly) without the prior express written consent of Jeffrey R. Charles is strictly prohibited.

With prior written permission, selected astronomy software developers are free to use data from this paper (entitled "Predicting the Appearance of the Lunar Umbra at Future Total Solar Eclipses") in generating umbral simulations for their programs so long as: they prominently reference this work and my authorship of it in said software, they include the above copyright and intellectual property notice in said software, and, they agree and prominently indicate that commercial and intellectual property rights to data and other material from this paper, or to material derived therefrom, are not transferable.

Mail to: Jeffrey R. Charles (jcharles@versacorp.com)

Document Last Modified: 27 February, 1997
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