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Draft for Journal of the Royal Astronomical Society of Canada (submitted Fall 2019)
Abstract
Noctilucent clouds (hereafter NLC) become visible during the summer twilight hours, when normal tropospheric clouds lie in Earth's shadow, but the Sun has yet to set for altitudes around 80km, near the mesopause. Ground-based observers have been surprised by the non-occurrence of NLCs at their longitude and latitude when a nice display was visible only two time zones (30 degrees) farther east or more rarely farther south. Is it possible that NLCs were present but lying in shadow? The geometry for this situation is examined. Shadows cast by tropospheric clouds do not play a role, and latitude ranges for potential sun-blocking NLC shields and light transmitting vacancies are identified. Further investigation is required to confirm or rule out whether shadows from the NLCs themselves play a role in the irregularity of NLC visibility.
Figure 1. Panorama of the 09:10 UT June 29, 2019 (dawn) display from Edmonton, Alberta. Credit: Alister Ling
Introduction
Noctilucent Clouds, an RASC Handbook Supplement ,provides some background on these gossamer "night-shining" clouds, which form at Earth's mesopause, about 80 km in height above sea level. They become visible to ground-based observers when the sky is sufficiently dark after sunset but the upper atmosphere located to the north remains in sunlight.
Often a nice display in the evening is followed by an absence in the morning twilight or vice versa. Observers note there is no night to night correlation of visibility. The record displays of 2019 highlighted another issue: nothing was seen at one location when sightings were made significantly to the south or to others differing by 15 degrees of longitude. Alan Dyer prompted the author to examine the geometry of NLC shadows by posing the question : could shadows from thick cirrus shields or thunderstorms explain the bewildering inconsistency of NLC displays?
Here is an outline of this article: section 1 - review of basic geometry; section 2 - "what is the latitude of that NLC?"; section 3 - shadow geometry of tropospheric clouds; section 4 - shadow geometry of NLC; and in section 5 the need of follow-up research.
Section 1. Review of basic geometry
For the sake of clarity, the following schematics are presented as cross sections with the Sun directly north (to the right), west into the page, and the view rotated in latitude to place the observer at the top, making their zenith straight up. The term altitude here is used in the angular sense where the horizon is zero and the zenith 90, with all stated values in degrees.
Most published diagrams depicting the geometry of NLC are not to scale in order to emphasize the overall situation. However, this creates a challenge for the observer to reconcile the schematic with their experience. The ones here are to scale.
Figure 2. Basic NLC geometry to scale (units in km from Earth centre), seen in cross section. The reader can manipulate the variables and see the changes in real-time at this link: https://www.desmos.com/calculator/iqyy9zvbmp
- Observer at O, center-left, zenith straight up
- Solid green is Earth in cross-section, with west into the page
- Horizontal black line is the horizon extending northward, to the right
- Blue arc is the mesopause at 81 km; NLC reside here
- Purple line is the visible upper limit of NLC as seen by the observer (in this case 25 degrees)
- Red line is a common lower limit of NLC as seen by the observer (1 degree)
- Orange line is a ray from the Sun, in this case at altitude of -10 degrees, tangent to the tropopause (here 10km). The lower left is in shadow while the upper right is in sunlight
- Green dashed line, radial from Earth's center, shows how many degrees of latitude to the north NLC at the horizon can be, refraction not included
Produced with the on-line free graphing utility at desmos.com.
Figure 3. As above except the Sun's altitude is -7 degrees. NLC are now potentially visible past the zenith and behind the observer, to 155 degrees, showing the very rapid change in NLC altitude that takes place between -7 and -10. Timetables for maximum NLC altitude for any night and any geographic location can be quickly generated at http://162.246.157.211/nlc/basic.html
Refraction by the atmosphere in the lowest couple of degrees is neglected in these diagrams, likewise the oblateness of Earth. Detailed discussion of the effects is beyond the scope of this article but does not impact the conclusions to a significant extent.
The diagrams can be interpreted in the same way for any dusk to dawn azimuth of the Sun, but the "angular difference in latitude" (variable Ldiff) becomes that of a great circle extending from the observer in the direction of the Sun.
Observers familiar with the details of lunar eclipses will be aware that the calculated size of the umbra is larger than an airless Earth. The lower atmosphere where active weather occurs (the troposphere), replete with cloud and particulates, is effectively opaque due to the long paths taken by nearly grazing solar rays. Those rays below this so-called screening height Ht will not make it through to illuminate NLCs at the upper edge of the twilight arch. A typical value is 10km [Taylor, Hapgood, Simmons], confirmed by the case study in the appendix.
Section 2. What is the latitude of that NLC?
Angles in the sky and distances by great circle can be deceptive or surprising, even to an experienced amateur astronomer. Keen NLC observers will be very familiar with the AIM (Aeronomy and Ice in the Mesosphere) satellite output "daily daisy" that depicts the extent of NLC across the polar regions. For years the author assumed that if that image showed a mass of NLC north of 60 degrees latitude, then at Edmonton (53.5N) there ought to have been a notable display - but this was incorrect.
Once the math was coded and output made available to the timetable web page via a button, it became quite obvious that we don't get to see very far north. Table 1 answers the question "when I see NLC at X degrees altitude, how many degrees of latitude farther north is the NLC overhead?"
Table 1. How much farther north is the NLC from an observer who sees it at a particular altitude above the horizon? The values are independent of an observer's location. In the real-time diagram, it is shown by the dashed green radial line, adjustable with the Ldiff slider.
The result is that observers in Winnipeg (49.9N) cannot see NLC that is north of 60 because it is below their horizon (with the exception of uncommon, extreme atmospheric refraction events).
This table also helps the NLC investigator take a report of NLC due north at 10 degrees altitude from Edmonton (53.5N) and look for NLC in the corresponding AIM image at a latitude of 57.2N, instead of mistakenly accepting the blob north of 60 to be the match.
Section 3. Shadow geometry of Tropospheric Clouds
The question posed to the author by Alan Dyer is paraphrased as follows. Can NLC be present in our skies but lie in shadow and hence be invisible? This might explain the documented sightings and images of NLC in Nevada and northern California in 2019 yet not reported in BC or Alberta.
It is instructive to explore and discuss a case study using typical values before deriving a generalized formula.
For the June 29 2019 event captured in Fig. 1, the key parameters are: time 09:10 UT; solar altitude -10.6; maximum altitude of NLC with no tropospheric screening 26.5 degrees; and with a screening height of 10 km the maximum altitude of NLC is 19.2 degrees. The NLC continues past Capella, altitude 15.8, just left of center near the very top of the frame.
Figure 4. Clouds in the troposphere cannot create shadows in the primary twilight arch. The curving red line indicating the troposphere lies 10 km above the surface while the orange line is the grazing ray tangent to the troposphere. Note that any object in the troposphere that might cast a shadow is already dark and at best would ensure a sharper cutoff at the very top of the NLC arc. Any cloud closer to the observer (above the black horizon line and below the red) appears directly in front of the distant NLC in silhouette, occulting it, so it cannot play a role in casting a shadow onto the NLC in the twilight arch to the upper right.
Figure 5. Screening height increased to 15 km. If there were a large mesoscale convective complex higher than the average 10 km lying to the north of the observer, their shadow would marginally obscure the uppermost part of the NLC display. In this case, the maximum altitude (purple line) would need to be 3 degrees lower. Practically speaking, thunderstorm tops of this height (in aviation terms 49,000 feet) would be quite rare north of 58N latitude.
Figure 6. Clouds well beyond the horizon, regardless of their latitude, cannot cast a shadow on NLC in the twilight arch. Those clouds, all lying below the curving red line of the troposphere, also lie below the orange line of the grazing sunlight ray. Clouds at the far north (right in the diagram) would be in direct sunlight, but they would cast shadows onto the solid ground at higher latitudes.
Smoke from large, intense forest fires is often lifted into the lower stratosphere, where it can remain for weeks and be transported thousands of kilometres. Due to the limited vertical motion in the stratosphere, largely a result of the stability from the temperature structure (an inversion), such smoke would not reach heights much above the troposphere. Sunsets seen through smoke can range from deep orange to intensely red, therefore it should not be surprising to see the top part of NLC tinged red.
Section 4. Shadow geometry of Noctilucent Clouds
Some readers may raise the point that NLC are too thin and translucent to cast shadows. This article deliberately does not address this in order to focus solely on the geometrical limitations.
Figure 7. NLC element at point C casts a shadow onto NLC at point P. The Sun is to the lower right, projecting parallel rays tangent to the top of the mesosphere M and M', and tangent to the top of the troposphere T and T'. The dashed green line from Earth's centre to C is the radial associated with Ldiff, the difference in latitude from the observer to that of the NLC patch casting the shadow. The red line is here set to 1 degree above the observer's horizon, while the black horizon line has been removed to reduce clutter.
An important characteristic to note about the geometry as revealed in Fig 7. is that for NLC at point L (low in the observer's sky) to be in shadow, the opaque patch is relatively closer to the observer (smaller Ldiff). Conversely, for NLC at point H (higher in the observer's sky) to be in shadow, its opaque patch must be located at a latitude difference far larger. In this case it is actually outside the diagram's boundary on the right.
The appendix contains the formula for calculating point C's difference in latitude from that of the observer. The on-line graphical calculator at https://www.desmos.com/calculator/wg43qytrba allows the reader to extract the approximate values simply by moving sliders.
In the case depicted here (Sun at -10 degrees, top of the NLC arch at 19 degrees, and bottom at 1 degree), for NLC in that arch to be in shadow as viewed from Edmonton, it would require an opaque shield of NLC to extend from 65.3N to 72, that is 13.1 to 19.2 degrees of latitude farther north than the observer.
Now consider the complement of the problem: assuming the higher latitude NLC to always be opaque enough to cast a shadow onto lower latitude NLC, then in order to see the display in Fig. 1 (Sun at -10.6) there cannot be any NLC shield from 65.4N to 71.5N. If we find out there is, then the assumption of sufficient opacity generally fails, along with the supposition that the lack of an NLC display can be attributed to shadows.
Figure 8. NLC closer to the horizon (between the black slash marks) lies in direct sunlight for solar altitude -5 degrees, and cannot be in shadow. The tangent solar ray, dashed orange, comes from "above"
A distinct difference in shadowing geometry occurs when the local solar altitude is greater than -8.2 degrees. The Sun's tangent rays match the slope of the mesopause somewhere in the arc visible to the observer. All NLC with an Ldiff north of -1 * (solar altitude) will be lit from above and therefore cannot be shadowed by anything.
Figure 9. Close-up of the left of centre portion of Fig. 8 depicting the tangent solar ray above the mesopause for a solar altitude of -5 degrees (with the Ldiff dashed green radial line set to +5 degrees). The NLC along the blue arc appearing in the observer's field from the purple line at 5.6 degrees altitude down to the red line at 1 degree lies in direct sunlight and can never be in a shadow.
This result is more useful to the observer in tabular form:
Table 3. The range in altitude of NLC in direct sunlight for a given solar altitude. It was created using the realtime online graphing utility.
It should be noted that this is almost a moot point from an observer's perspective because the foreground sky is generally too bright to see NLC in the listed ranges. The lack of NLC here is due to either physical absence or too low a contrast, not a shadow effect.
Section 5. Further research
To those unfamiliar with the details of the AIM satellite operation, it is a simple but incorrect logical chain to state "if the AIM daily daisy shows a shield of NLC in the occulting zone but ground observations record a widespread NLC display, the opacity assumption fails." The satellite is in a polar orbit that only sees in strips or "petals", essentially taking 24 hours to cover the majority of the polar region. On many occasions the satellite pass covering the area to the north may be 8 hours offset from that of the observer's. When one animates the daisy image from day to day the discontinuities or jumps in visible features are of such magnitude that tracking quickly leads to confusion.
In order to confirm or dismiss the effect of shadowing, a thorough analysis of AIM strips concurrent with ground-based observations is necessary.
What about the geometry of those cases when NLC is well to either side of the Sun-observer azimuth? Although the math is somewhat more complicated by spherical trigonometry and perspective (analogous to the spreading of crepuscular rays when they are in fact parallel), the resulting differences would be minor.
Conclusion
- Tropospheric cloud geometrically cannot contribute to shadowing NLC in the twilight arch. The troposphere however is the well-known cause of the upper limit (southern) extent of the ground-based visible display
- If NLC is optically thick enough to cast shadows, then a display spanning 1-19 degrees in altitude (solar altitude -10.6), requires a gap in the NLC shield spanning 13-19 degrees of latitude to the north
- Notably, the AIM images also show isolated patches farther south, detached from the primary mass. It is possible that displays seen from south of 55N are these patches, which could explain the perplexing absence in one location when they are present to other observers a thousand kilometres away (roughly equal to an arc of 10 degrees of latitude)
- Further research required: to document cases of simultaneous ground and space-based observations to confirm or rule out that vacancies and shields play a role in the visibility of NLC displays
- Significant challenges remain, those of spatial and temporal gaps in ground-based observations and limited temporal resolution of satellites
Acknowledgements
The author would like to thank:
Alan Dyer (amazingsky.net) for suggesting this line of enquiry;
Desmos.com on-line free graphing utility
Appendix
Case study of screening height
Figure 8. 2019 June 29 09:23 UT with 3 windows showing the maximum extent of the NLC.
Figure 9. Close-ups of 3 regions with background stars identified. The star is located just to the lower left of the constellation name label (e.g. lower left of the C in bet Cam).
The stars and their altitudes are:
23 Uma 27.5; ups UMa 24.1; bet Cam 30.4; A Per 30.3; del Per 26.8
The NLC has reached delta Persei, not alpha, but it comes close to reaching beta Camelopardalis, which is also very close to the same azimuth of the Sun, which from geometry is the line along maximum altitude (analogous to the meridian). A time-lapse of this event can be viewed here: https://www.youtube.com/watch?v=faB_Zx7Y7Fc. One can see the maximum altitude increasing with each passing minute as the rising Sun illuminates NLC farther south.
At 09:23, geometry with a tropospheric screening height (Ht) of zero (airless world) indicates a maximum height of 46.7 degrees, while an Ht of 10 km yields 29.8 degrees, confirmed by beta Cam's altitude of 30.2 degrees.
Calculation of Ldiff (latitude difference) to put point P in shadow
In Fig. 7, P represents a point at the intersection of the mesosphere and a known angle Vp degrees above the horizon. For that point to be in shadow, how far around the horizon (Ldiff) must the occulting section of NLC be? The reader may use the online graphing tool to quickly obtain approximate values or the following equations can be used for more precision, while remembering the caveat of refraction when very close to the observer's horizon.
Figure 10. The difference in latitude (Ldiff) between the observer and the occulting patch at C
References
M.J Taylor, M.A Hapgood, D.A.R. Simmons
The effect of atmospheric screening on the visible border of noctilucent clouds
Journal of Atmospheric and Terrestrial Physics Volume 46, Issue 4, April 1984, Pages 363-367, 369-372
Zalcik, M. and Boschat, M. Noctilucent Clouds RASC Handbook Supplement https://www.rasc.ca/supplements
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