How bright the moon: correcting a propagated figure error in the literature

How bright the moon: correcting a propagated figure error in the literature

Last year, the National Park Service released our report, Artificial night lighting and protected lands: Ecological effects and management approaches (Longcore and Rich 2016), which had been in the works for quite a while. Our colleague Andrej Mohar, while enthusiastic about the report overall, pointed out that a figure that we had included of natural illumination under various conditions was wrong, and by quite a bit, when it came to the levels under a “quarter moon.”  This is the story of that error, where it came from, and its correction.

The figure we used in the 2016 NPS report was re-printed with very minor adjustments from Paul Beier’s chapter in our 2006 edited book, Ecological Consequences of Artificial Night Lighting (Island Press).


This figure was published in Ecological Consequences of Artificial Night Lighting and re-published with slight adjustment of the icons in our 2016 NPS report.

The “quarter moon” is shown as causing ground-based illumination of 0.1 lux or thereabouts.  This is obviously and very wrong, and in fact is contradicted in Chapter 1 of the book, which indicates 0.01-0.03 lux for a quarter moon. We should have caught it then, but did not.

Furthermore, a quarter moon, technically, is half of the disk of the moon illuminated, which is one quarter of the entire moon. The icon we used for the “quarter moons” in the figure, however, is that of a crescent moon, with closer to one quarter of the disk  illuminated. We had switched the icon for the “quarter moons” from a depiction of three quarters of the disk illuminated to one quarter of the disk illuminated to match this commonsense language.

Beier (2006) had adapted the graphic from McFarland et al. (1999), who cited their sources as Blaxter (1970) and Brown (1952).  It was McFarland et al. (1999) who introduced the error.  They correctly copied the illumination line from a moon with three-quarters of the face illuminated (a gibbous moon) and incorrectly labeled it as “quarter moons.” They  had three-quarters of the face illuminated in the icon, which was correct, but inconsistent with the label.


 Illuminations produced by the sun and moon as reported by McFarland et al. (1999). Note that “quarter moons” identifies the same line as a three-quarter moon in Brown (1952) once the conversion from footcandles to lux is made.

Compare the figure from McFarland et al. (1999) with the figure produced by Brown for the Department of Navy in 1952. The Brown figure is in footcandles.


Illumination produced by the phases of the moon reported by Brown (1952). The text “1st and 3rd Quarters” indicates the “apparent half moon.”

The 1952 Brown report provides curves of illumination from the moon at four phases: full (phase angle 0º), three-quarters full (phase angle 60º), half full (phase angle 90º, which is technically a “quarter moon”) and one-quarter full (phase angle 120º). In the McFarland et al. (1999) diagram, two curves are given: one for the full moon and one for “quarter moons.” The full moon line is correct. The “quarter moons” line is the same as the three-quarters full moon in Brown (1952), meaning that the lunar disk is three-quarters illuminated (phase angle 60º) and not a “quarter moon” in the sense of one quarter of the disk being illuminated or even a quarter moon meaning one quarter of the entire moon visible and illuminated (half of the disk visible and illuminated).

Unfortunately, this error propagated forward to Beier (2006), our 2016 report (which is being reissued with a corrected figure), and Gaston et al. (2014), who changed the icon to a crescent moon (as we did in our report) and might have shifted the line down slightly, but not enough to be accurate, especially given the icon depiction of a crescent moon and textual description.



Illumination from the sun and moon reported by Gaston et al. (2014). The curve for the “quarter moons” is shifted downward slightly but is an order of magnitude higher than a crescent moon (a quarter of the face illuminated) and higher than a quarter moon (half of the face illuminated).

I regret not catching the error when editing Beier’s chapter or when updating the figure in 2016. But Andrej did catch it and now the record can be set straight.


This corrected version of the figure shows maximum values for a full moon (0.3 lux) and quarter moons (0.03 lux) with the proper icon for quarter moon showing half of the face illuminated.

For the record, the approximate values for the maximum clear-sky illumination from the moon directly overhead at its phases are as follows.


Phase Angle

Brown (1952) (lux)

(Krisciunas & Schaefer 1991) (lux)

100% illuminated



75% illuminated




First and Last Quarter
50% illuminated




25% illuminated




These values can vary based on the distance between the sun and the moon and whether the moon is waxing or waning because of the differing characteristics of the face of the moon. Illuminations this high are unlikely to occur under most circumstances, especially at temperate latitudes. A working estimate of illumination from the full moon is closer to 0.1 lux on the ground than the ~0.4 lux potential maximum illumination, a fact that has been recently discussed by Kyba et al. (2017).

Travis Longcore, Ph.D.
August 5, 2017

Literature Cited

Beier, P. 2006. Effects of artificial night lighting on terrestrial mammals. Pages 19–42 in C. Rich, and T. Longcore, editors. Ecological consequences of artificial night lighting. Island Press, Washington, D.C.

Blaxter, J. H. S. 1970. Light, Animals, Fishes. Pages 213–230 in O. Kinne, editor. Marine ecology: a comprehensive integrated treatise on life in oceans and coastal waters. Wiley-Interscience, London.

Brown, D. R. 1952. Natural illumination charts. Research and Development Project NS 714-100. Pages 1–11, 43 plates. Department of the Navy, Bureau of Ships, Washington, D.C.

Gaston, K. J., J. P. Duffy, S. Gaston, J. Bennie, and T. W. Davies. 2014. Human alteration of natural light cycles: causes and ecological consequences. Oecologia 176:917–931.

Krisciunas, K., and B. E. Schaefer. 1991. A model of the brightness of moonlight. Publications of the Astronomical Society of the Pacific 103:1033–1039.

Kyba, C., A. Mohar, and T. Posch. 2017. How bright is moonlight? Astronomy & Geophysics 58:1.31–31.32.

Longcore, T., and C. Rich. 2016. Artificial night lighting and protected lands: Ecological effects and management approaches. Natural Resource Report NPS/NRSS/NSNS/NRR—2016/1213. National Park Service, Fort Collins, Colorado.

McFarland, W., C. Wahl, T. Suchanek, and F. McAlary. 1999. The behavior of animals around twilight with emphasis on coral reef communities. Pages 583–628 in S. N. Archer, M. B. A. Djamgoz, E. R. Loew, J. C. Partridge, and S. Vallerga, editors. Adaptive mechanisms in the ecology of vision. Kluwer Academic Publishers, Dordrecht.


CubeSats to measure light pollution

CubeSats to measure light pollution

I had the fortune of being able to offer some examples of environmental applications in a paper by Dee Pack and Brian Hardy from Aerospace Corporation for the Small Satellite Conference this summer in Utah.  We (mostly they) show the feasibility of using small satellites to measure upward radiance from Earth at night, with examples ranging from the Middle East to Southern California.  I’m glad to have offered the concept of “darkest path” modeling for wildlife connectivity and perspectives on the usefulness of spectral information at this scale. The work we have been doing with the VIIRS Day-Night Band shows up for the identification of a very bright greenhouse on the Oxnard Plain.  Here is the citation, abstract, and download link.

Pack, D. W., B. S. Hardy, and T. Longcore. 2017. Studying Earth at night from CubeSats. Proceedings of the 31st Annual AIAA/USU Conference on Small Satellites, Leo Missions, SSC17-WK-35.

This paper presents examples of the latest imaging data of the Earth at night from multiple CubeSat platforms. Beginning in 2012, with AeroCube-4, The Aerospace Corporation has launched multiple CubeSat platforms in different orbits equipped with a common suite of CMOS sensors. Originally designed as utility cameras to assist with attitude control system studies and star sensor development, we have been using these simple camera sensors to image the Earth at night since 2014. Our initial work focused on observing nighttime urban lights and global gas flare signals at higher resolution than is possible with the VIIRS sensor. To achieve optimum sensitivity and resolution, orbital motion is compensated for via the use of on-board reaction wheels to perform point-and-stare experiments, often with multiple frame exposures as the sensor moves in orbit. Ground sample distances for these systems range from approximately 100 to 130 meters for the narrow-field-of-view cameras, to 500 meters for the medium-field-of-view cameras. In our initial work, we demonstrated that CMOS sensors flown on AeroCube satellites can achieve a nighttime light detection sensitivity on the order of 20 nW-cm-2-sr-1. This resolution and sensitivity allows for detection of urban lighting, road networks, major infrastructure illumination, natural gas flares, and other phenomena of interest. For wide-area surveys, we can also program our cameras to observe regions of interest and co-add pixels to reduce the data bandwidth. This allows for a greater number of frames to be collected and downloaded. These results may then be used to task later satellite passes. Here, we present new examples of our nighttime Earth observation studies using CubeSats. These include: 1) detecting urban growth and change via repeat imaging, 2) investigating the utility of color observations, 3) spotting major sources of light pollution, 4) studying urban-wildland interface regions where lighting may be important to understanding wildlife corridors, 5) imaging lightning and cloud cover at night using wide-area imaging, 6) observations of the very bright lights of fishing boats, and 7) observing other interesting natural phenomenon, including airglow emissions, and the streaking caused by proton strikes in the South Atlantic Anomaly. Our ongoing work includes utilizing a diversity in overpass times from multiple satellites to observe nighttime scenes, imaging high-latitude cities not optimally accessed by the international space station’s cameras, and building a catalogue of observations of rapidly developing megacities and global infrastructure nodes. Data from CMOS sensors flown in common on 5 different AeroCubes in 4 different orbits have been collected. Our results show that enhanced CubeSat sensors can improve mapping of the human footprint in targeted regions via nighttime lights and contribute to better monitoring of: urban growth, light pollution, energy usage, the urban-wildland interface, the improvement of electrical power grids in developing countries, light-induced fisheries, and oil industry flare activity. Future CubeSat sensors should be able to contribute to nightlights monitoring efforts by organizations such as NOAA, NASA, ESA, the World Bank and others, and offer low-cost options for nighttime studies.

Spatial and Temporal Analysis of Nighttime Lighting In and Around National Parks


Yu Chuan Shan, Ben Banet, and I have been working the past couple of years on developing a monthly database of upward radiance from within and buffers around all of the National Park units in the United States.  They are presenting the research today at the USC undergraduate research symposium.  The results presented only scratch the surface of what we can do to analyze this high-resolution database over space and time.

Shan also put together a website to walk through the project.

The poster can be downloaded here. Please cite as:

Shan, Yu Chuan, Ben Banet, and Travis Longcore. 2017. Spatial and Temporal Analysis of Nighttime Lighting In and Around National Parks. USC Undergraduate Symposium for Scholarly and Creative Work (Los Angeles, April 12, 2017).

Unintentional Media Blitz

As a result of the new atlas of of artificial night sky brightness I ended up doing a lot of interviews for national and international outlets, including Science Magazine,, Christian Science Monitor, Scientific American, and USA Today.

Then the American Medical Association released a statement on LED lighting (for which I had provided some background information) and a few more stories came out in and Christian Science Monitor.

A couple of Los Angeles Times stories also happened to include me:

Rare toads (presumably) love him; off-roaders do not 

The sunset that takes an hour to go from date palms to to redwoods

Heading to New Orleans: Ecologically Sensitive Lighting Design

Landscape architects, mark your calendars.  I’ll be part of a joint presentation on Ecologically Sensitive Lighting Design that was just accepted to the American Society of Landscape Architects annual meeting in New Orleans this fall.  I teamed up with lighting designer Linnaea Tillett and lighting engineer Nancy Clanton, two of the top landscape lighting experts in the country on the session proposal.  We will use a case study format to explore approaches to landscape lighting (and not lighting…) that incorporate the psychology of place-making, consideration for nature, and technical advances in the field.

Boulder City Hall lighting design by Clanton and Associates.

Boulder City Hall lighting design by Clanton and Associates.

Optics and Photonics News Covers Environmental Impacts of Lighting

Optics and Photonics News Covers Environmental Impacts of Lighting

The message that lights can have environmental consequences becomes more and more mainstream. Optics and Photonics News this month has an article by freelance writer Jeff Hecht, with whom I’ve spoked for other stories before. His article is a multi-page spread and emphasizes both spectrum and intensity and their potential impacts, as well as the potential to mitigate those impacts by customizing both. Here’s my pull quote:

Longcore’s ideal would be very low blue to reduce wildlife impact, with only enough blue added to raise color temperature to 2700 K if necessary for good color rendering.

I actually think that most outdoor lighting can do without blue light and might put an “absolutely” before the “necessary” in the quote. Manufacturers are starting to deliver LEDs that cut out nearly all the blue light, have a reasonable color rendering index, and can be dimmed without an efficiency penalty.

Expert quote on exciting new light pollution research

Australian zoologist Kylie Robert and colleagues have published an exciting new paper on the disruption of breeding patterns and melatonin levels in a free-ranging native mammal. I had the chance to comment on the significance of this research for Science News and am delighted that Dr. Robert will also be presenting at the Annual General Meeting of the International Dark-Sky Association on November 15 in Phoenix. To my knowledge, this paper is one of the first showing these kinds of effects, such as lowered blood melatonin levels, in the field and joins recent work by Davide Dominoni, who showed impacts from night lighting on the physiology of wild birds.