Twilight sky colors: Observations and the status of modeling Freeman F. Hall, Jr.

Wave Propagation Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado 80303 (Received 22 January 1979)

Twilight is usually defined as the interval of incomplete darkness following sunset or preceding sunrise.1 Rozenberg2

would extend the definition of twilight to cover times when the sun is above the horizon but the illuminance on a hori­zontal surface is rapidly changing; this expanded definition is not widely used.

Consider the predominant spectral-luminance character­istics of the twilight sky. When the sun is just below the ho­rizon, the sky immediately above this horizon appears as a bright orange or red segment, the primary twilight arch. With a solar depression of 2°, the sky above the arch at zenith angles of 30°-75° develops a purple color that shows the maximum color contrast with a solar depression of 4°. The purple light, shown in color in Plate 111, disappears when the sun is more than 6° below the horizon. All the while the zenith remains a deep blue.

Just after sunset the Earth casts a shadow on the atmo­sphere above the horizon opposite the sun. This shadow is called the dark segment, and it will appear on a clear night as a dark blue color. The segment is capped by a rosy purple zone, the antitwilight arch, shown in the color Plate 116.

Each twilight, evening or morning, shows these general properties, but each twilight is different because the lumi­nance effects are modified by clouds and cloud shadows, or crepuscular rays. In Fig. 1 we depict the observed twilight spectral luminance on a chromaticity diagram,3 at least with

FIG. 1. Chromaticity diagram of the observed twilight spectral luminance for 4° solar depression.

1179 J. Opt. Soc. Am., Vol. 69, No. 8, August 1979

qualitative accuracy. The solid line indicates colors in the solar direction; the dashed line is for the antisolar meridian. Notice the highly nonuniform angular scale on the diagram; most of the sky remains blue across the entire solar meridian, the vertical arc passing through the zenith and the sun. This chart was prepared by on-the-spot visual comparison with Plate 24 in Ref. 3.

When the twilight is observed from an aircraft, the dark segment fades to gray at the horizon. The dashed line of Fig. 1 seems to continue looping around to meet the white color at the center of the diagram for zenith angles of 93°. That this is not a Mach band effect4 can be demonstrated by eclipsing the antitwilight arch and the top of the dark segment with the outstretched hand. Even under these conditions, the horizon region appears much nearer to white than the uneclipsed part of the dark segment.

How well do theoretical models of twilight spectral lumi­nance predict these observed colors? Two recent papers on the subject by Dave and Mateer5 and by Adams et al.6 predict the solar-hemisphere luminance curve rather well but fail to duplicate observations of the antisolar hemisphere by a wide margin. Both models are based only on single scattering, however, and clearly multiple-scattering theory must be used to accurately describe the antitwilight arch luminance, where no direct solar rays are incident. The scattering geometry depicted in Fig. 2 illustrates this point. Single scattering in the incident, parallel solar rays occurs at Sl·, S3, and S5. The latter ray is seen by the observer at o. In the shadow zone, however, multiple scatter, as at the points S2 and S4, is the only way sunlight can reach the observer from the dark seg­ment.

A typical prediction by Adams et al. is shown in Fig. 3. It was necessary to include the Chappuis atmospheric-ozone absorption bands for the model to predict a blue zenith, and an approach toward the purple light did not occur without some atmospheric turbidity. This model clearly misses the mark, however, in predicting a yellow or orange color in the antitwilight arch.

Professor Plass has recently informed me that a multiple-scattering model is coded and ready to run on the Texas A &

FIG. 2. Scattering geometry of the twilight, with the observer at 0.

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FIG. 3. Predicted twilight spectral luminance for a single scattering model with ozone absorption and nominal atmospheric turbidity for 2° solar de­pression.

M computer. Until the results of this new model are avail­able, let us try a gedanken perturbation to the single-scat­tering model.

Clearly the twilight arch is the brightest part of the sky il­luminating the Earth-shadowed sector, and the arch color is deep orange or red. This contribution of light will bend the color curve for the antitwilight arch downward toward the complementary color line joining 380 and 700 nm. But the red, forward scattered sunlight is distributed through a narrow solid angle, typically only a few degrees wide at the 10 dB — down points.7 Therefore, at angles even deeper into the an­titwilight arch, the twilight arch contribution to illuminance rapidly fades. The remainder of the sky scatters bluish light into the Earth's shadow. Thus the color curve must continue to bend around toward the blue, as our observations tell us actually does occur. Why the curve continues toward a col­orless intercept for zenith angles greater than 90° is hard to understand by physical reasoning. Perhaps when Plass' model is run, we shall understand this anomaly.

1 Glossary of Meteorology, edited by R. E. Huschke (American Me­teorological Society, Boston, 1959).

2G. V. Rozenberg, Twilight, A Study in Atmospheric Optics (Plenum, New York, 1966), 359 pp.

3The Science of Color (Crowell, New York, 1953). 4R. M. Lowry and J. J. DePaJma, "Sine-wave response of the visual

system. I. The Mach phenomenon," J. Opt. Soc. Am. 51, 740-746 (1961).

5J. V. Dave and C. L. Mateer, "The effect of stratospheric dust on the color of the twilight sky," J. Geophys. Res. 73, 6897-6913 (1968).

6C. N. Adams, G. N. Plass, and G. W. Kattawar, "The influence of ozone and aerosols on the brightness and color of the twilight sky," J. Atmos. Sci. 31, 1662-1674 (1974).

7K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Advances in Geophysics, 10, Edited by H. E. Landsberg and J. Van Meighem (Academic, New York, 1964), pp. 99-260.

1180 J. Opt Soc. Am., Vol. 69, No. 8, August 1979 0030-3941/79/081180-04$00.50 © 1979 Optical Society of America 1180