Joseph A. Shaw
NOAA
[Published in Optics and Photonics News volume 10 no. 3, March 1999, pages 43-45, 68.]
On a November evening in 1982 I was on a train slowly wandering around the edge ofa bay in southern Japan. The setting sun created a magical streak of glittering light reachingacross the water (Figure 1). Even though I had no formal optics training at that time, I tookspecial care to photograph this optical treat, even thinking that someday I would like tounderstand this glittering light better. I knew, at least, that this would be a nice addition tothe slide show I would share with my family and friends back home when telling them aboutJapan - the "Land of the Rising Sun" (or setting sun in this case).
Figure 1.
Thirteen years later I was on an inverted ship in the Pacific Ocean (Figure 2)measuring glitter patterns created with a laser. With the passage of time, I have discoveredthat understanding how glitter patterns are formed, and even forming my own glitter patternsto measure sea-surface roughness, helps me enjoy nature's glitter even more.
Figure 2.
How Glitter Patterns are Formed
The name "glitter pattern" implies a moving and changing phenomenon. Glitterpatterns consist of many bright points of light that come and go, blending together to form asmooth path of glittering light when viewed at a distance. If you look closely at a glitterpattern, you can see individual points of light. Each of these points of light is a specularreflection of the sun, called a sun glint. Glints occur on the water where the local slopeprovides a direct specular reflection of the sun. A perfectly smooth surface would containonly one glint. It is this kind of glass-smooth surface that produces the nearly perfect imageswe see in nature calendars of mountains reflected in a lake. But if the water surface isrippled by even the slightest wind, reflected images become wrinkled and indistinct. A lightsource, such as the sun or moon, or even a streetlight or distant illuminated window, is thenreflected from multiple spots on the surface (Figure 3). As the wind-rippled surface moves,so do individual glints. But the ensemble of glints produces a glitter pattern whose shape andsize can be related to the roughness of the water and the viewing geometry.
Figure 3.
Glitter patterns are roughly elliptical, with an aspect ratio that depends on the sourceelevation angle.1,2 For example, the sun produces a circular glitter pattern when it is directlyoverhead (90 elevation angle) and produces an elongated elliptical pattern near sunset orsunrise (small elevation angle). This all assumes a uniformly rough surface; quite often,however, wind gusts increase the roughness or surface slicks reduce the roughness in alocalized region. These kinds of effects are evident in Figure 1, especially close to the nearshore where the glitter pattern is much wider than elsewhere (perhaps partly because of thewind generated by the passing train).
For a high light source, the angular length of a glitter pattern is equal to four times theangle of the maximum wave slope (figure 3). Waves inclined both toward and away from theobserver create glints, resulting in a factor of two times the maximum wave slope; theadditional factor of two is a result of angular doubling on reflection. The ratio of the glitter-pattern width to its length is given by the sine of the source elevation angle. If the lightsource is at the same elevation as the observer, the glitter pattern dimensions are half as largeas with an infinitely high source, but the width-to-length ratio is the same. As the sun ormoon drops lower in the sky, the glitter pattern gets progressively narrower until the width-to-length ratio reaches a minimum when the source elevation angle is twice the maximum waveslope. Beyond this angle, as the sun or moon approaches the horizon, the glitter patternbecomes shorter because of shadowing and eventually disappears.
Glitter patterns on water are similar to vertical light pillars in the sky, caused byreflection from ice crystals floating or falling with a distribution of slopes.1-5 Growing up inAlaska, I often saw light pillars above city lights during the winter when the ice-ladenatmosphere was calm and cold. But sun pillars can be seen even in more temperate climates,especially near sunrise or sunset in the vicinity of thin cirrus clouds.
Better Weather Forecasts from Glitter Patterns
Have you ever been rained on during an afternoon forecast as "mostly sunny?" Thiskind of event could happen less often with improved knowledge of the wind speed anddirection over the ocean three or four days earlier. Satellite sensors can see large regions ofocean where there are no people to measure winds, but they rely on models to infer windspeed and direction from surface roughness. It turns out that much of the information relatingsurface roughness to the wind came from studying patterns of light glittering on the oceansurface.
Recall that the maximum wave slope can be determined from the geometry of glitterpatterns. In 1951, Charles Cox and Walter Munk found a more quantitative way of usingglitter patterns to derive a statistical model for the complete wave-slope distribution.6,7 Theyused cameras in the bomb bay of a World War II surplus B-17G aircraft to photograph sunglitter on the Pacific Ocean near Hawaii.6,7 By relating the photographic density to theprobability of a sun-glint wave slope, Cox and Munk derived a wave-slope probability densityfunction (pdf). The photographs used to derive this model actually were recorded with thecamera lenses removed, resulting in a blob of light with continuously decaying brightness atthe edges. This experiment was limited to measuring slopes smaller than about 28 becausethe light from larger slopes, which occur with lower probability, was lost in the background.
By examining multiple images in this way at different wind speeds, Cox and Munkwere able to show that the pdf for ocean wave slopes can be described as a Gaussian plushigher-order skewness and kurtosis terms. The actual pdf tends to have higher probability forvery small and very large slopes than a Gaussian distribution. Furthermore, the along-winddistribution is skewed, showing a higher probability for downwind slopes than for upwindslopes. This makes sense because the wind pushing the small wind waves causes them tolean downwind. The pdf variance (mean-square slope) increases approximately linearly withwind speed, indicating that the surface gets steadily rougher as the wind blows harder.
Forty-four years after Cox and Munk flew their B-17G over the Hawaiian Islands, mycolleagues and I set out to examine the ocean wave-slope probability model in more detail.8,9 This time, however, we used laser-glitter patterns to avoid the explicit dependence on solarangle and sky conditions. In September 1995, we measured laser-glint patterns from the shipshown in Figure 2 about 20 km off the Oregon Coast in the Pacific Ocean. By counting thenumber of glints in angular bins as a narrow laser beam was scanned repeatedly over theocean surface, we derived wave-slope probability density functions that agreed well with theCox and Munk model under similar conditions. We also found, however, that the surfaceroughness depends on the air-sea temperature difference (which was nearly zero in the Cox-Munk experiment).8 At a given wind speed, water warmer than the adjacent air leads to arougher surface than predicted by the Cox & Munk model and water colder than air results ina smoother surface. Therefore, the wind cannot be determined uniquely from the surfaceroughness alone.
We also used video cameras to record images of the surface illuminated by a widecone of laser light. The image at the top of Figure 4 is a laser-glint pattern seen by a videocamera looking straight down at a smooth ocean surface (1 m/s wind speed). Nine successivevideo frames have been averaged to provide a 0.3 second integration time, resulting in animage similar to what would be seen by a human observer. Large closed loops are formed byglints moving in pairs around waves of finite length and width as the surface undulates. Similar loops can be seen in the reflection of overhead street lights or the moon from water,or, as shown on the bottom of Figure 4, in the reflection of a camera flash from the water ina swimming pool.1,2 To see such loops, the surface must be smooth enough that the wavecrests are large and slowly varying. When the surface roughness increases, the loops becomesmaller and change rapidly. In fact, we found that a time series of the number of brightregions in these glint images is a fractal process whose fractal dimension varies with surfaceroughness.9 So, in addition to being beautiful and fun to watch (especially in motion), theselight loops also convey quantitative information about the surface and its environment.
 Figure 4a. |
 Figure 4b. |
Where Glitter Paths Lead
You do not have to be a remote sensing expert to appreciate glitter patterns. Fromsidewalk puddles to the ocean, beautiful light shows can be seen by anyone with the attentionto notice. Depending on the amount of patience you have for such things, you can eithercasually notice these patterns or spend hours examining them in detail. Either way, there ismuch to be learned and much to be appreciated about nature by watching light glittering onwater.
References
- M.G.J. Minnaert, Light and Color in the Outdoors, Translated and Revised by L. Seymour, Springer-Verlag, New York, 1993.
- D.K. Lynch and W. Livingston, Color and Light in Nature, Cambridge Univ. Press, 1995.
- R. Greenler, Rainbows, Halos, and Glories, Cambridge Univ. Press, 1980.
- A.J. Mallman et al., "Comparison of Sun pillars with light pillars from nearby light sources," Appl. Opt. 37, 1441-1449, 1998.
- W. Tape, Atmospheric Halos, American Geophysical Union, Wash., D.C., 1994.
- C. Cox and W. Munk, "Statistics of the sea surface derived from sun glitter," J. Marine Res. 13, 198-227, 1954.
- C. Cox and W. Munk, "Measurement of the roughness of the sea surface from photographs of the Sun's glitter," J. Opt. Soc. Am. 44, 838-850, 1954.
- J.A. Shaw and J.H. Churnside, "Scanning-laser glint measurements of sea-surface slope statistics," Appl. Opt. 36, 4202-4213, 1997.
- J.A. Shaw and J.H. Churnside, "Fractal laser glints from the ocean surface," J. Opt. Soc. Am.-A 14, 1144-1150, 1997.
