Lection 6 Optical phenomena in the atmosphere By

Lection 6 Optical phenomena in the atmosphere By Edward Podgaisky 1. Brightness, polarization and form of the sky Brightness of the sky, as well as its colour, is determined by the solar light diffusion conditions in the atmosphere. These conditions include: - transparency of the atmosphere; - form of the scattering phase function; - the Sun position on the sky; - reflecting features of the underlying surface.

Fig. 1. Brightness distribution over the sky The main brightness maximum is always observed near the Sun position and is known as solar aureole. This maximum is related to a well stretched aerosol scattering phase function. The aureole is a bright ring around the solar disk. The angular radius of the ring is 1012 o, and it is observed at the clear sky condition. The brightness of the solar aureole depends on the size and number of the aerosol particles. The larger the particles and the bigger their number, the brighter the aureole. The secondary sky brightness maximum is observed just above the horizon. It appears due to the increase of the atmosphere mass participating in scattering as the view beam approaches the horizon. The sky brightness minimum is observed at the point situated at 90 o angle apart from the Sun being at horizon. In case the Sun is above the horizon, this angle is a bit smaller The brightness of the sky part, where the Sun is situated, is significantly brighter than the other part

Solar diffused radiance at channels 870 and 340 nm The depth-transformation of the radiation field above (1178 -804 m), within (770 -404 m), and below (393 -371 m) cloud. Altitudes are pointed in the figure.

the light reflected from the earth surface plays a noticeable role in the sky brightness increasing, i. e. albedo is a very important feature in this respect. For instance, over snow surfaces the brightness is remarkable larger than over open water. The measurements made from satellites have revealed a layer near 19 km where the scattering index has somewhat larger value due to higher concentration of aerosol. This layer makes the largest input into the light scattering at twilight time. It is why this layer is called twilight layer. It is to recall Rayleigh's formula discussing the scattered light polarization, : The conclusion Rayleigh made from this formula is not fully correct. The measurements have shown the maxima of the scattered light polarization are observed along the directions perpendicular to incident light. However, the polarization degree does never reach 100%. Usually it does not exceed 80 -85 %. The reason for that is the existence of so called depolarizing factors (they were not accounted by the Rayleigh's theory). Among them are multiple and aerosol scattering, anisotropy of molecular structure, etc.

Fig. 2. The neutral points position. According to the formula, the sky polarization degree in the Sun direction ( = 0 o) and in the antisolar point As ( = 180 o) is equal to zero, and the maximum is at = 90 o (Solar zenith). In fact, the distribution of the light polarization on the sky is much more complicated. There are four points at the sky (not two) where polarization degree is equal to zero. These points are known as neutral points. The angular distance of the points from the Sun and the antisolar point changes from 12 o to 30 o depending on the Sun altitude, atmosphere transparency, surface albedo, and wavelength of the light. As the atmosphere turbidity and surface albedo increase, and the Sun approaches the horizon, the distance between the neutral points and the Sun (or antisolar point) increase, too.

Fig. 3. The flattenness of the sky The form of the sky. An interesting observation can be made if the observer is at an open site, for instance at a flat field, or at a sea. He would easily discover that the sky is not a hemisphere. It rather has a form of an overturned chalice, i. e. the sky appears as if it is flattened in vertical direction. The measure of the sky flattenness is the altitude over horizon of a point which divides the arc of the sky from zenith (Z) to horizon (H) in two. This point on the Fig. 3 is denoted by M. The altitude of the point is measured with the angle . It should be noted that one must divide the arc ZH in two, but not the angle ZOH. If the sky were hemisphere, the angle would be equal to 45 o. Actually this angle is much smaller (18 o 30 o). The appearing flattenness of the sky depends on illumination of the atmosphere and the surface. At overcast condition is larger than at clear sky. The mean value of the angle are: 22 o at day time, 27 o at moonlight night 30 o at moonless night

The form of sky causes a number of optical illusions. Fig. 4. Apparent augmentation of objects. 1) Angular altitudes of all objects and phenomena over horizon are overestimated as they are observed visually without instruments. These are the Sun, the Moon, stars, aurora, and clouds. For example, a cloud altitude over horizon is 10 o, but for an observer (at visual observation) it seems to have the altitude equal to 25 o. 2). The angular sizes of objects being near horizon appear to be larger than in reality. Those above 35 o appear to be smaller than in reality. For example the moon appears to be 2. 2 times larger when it is near horizon, and about twice smaller when it is in zenith. Apparent enlargement (augmentation) of the sizes and altitudes of the objects observed at the horizon can be partly explained by the fact that they are projected on the sky as on a screen located on a variable distance from an observer due to flattenness of the sky. The real angular sizes of the Sun, moon and other objects naturally remain the same at any position in the sky. The Fig. 4 is explaining the matter above. In reality both the sky shape and apparent augmentation of objects at horizon are explained by the psychophysiological features of our eyesight.

3. Illumination of the Earth surface The natural illumination of the earth surface is the light flux arriving to a unit of the surface. At day time, this light flux is created by direct and diffused solar radiation, at night by some other illumination sources. The unit of the illumination is flux (l). The direct solar illumination varies in a wide range from 0 (sunrise) to 120 kl (kiloluxes) at noon. Somewhat smaller one is the range of the diffused light illumination variation: from 0. 5 kl (sunrise, sunset) to 15 kl (noon). The sums of the illumination by direct and diffused light for various time intervals (one hour, day, month, year) characterize so called illumination climate of a given region. Twilight. After sunset the illumination of the earth surface decreases at first very rapidly, but after a while it occurs slower and gradually transfers into night darkness. Due to the presence of the atmosphere and its ability to diffuse the light, the transfer from day to night does not occur instantly, it lasts some period of time. This period is called twilight. There are several types of twilight.

1) Civil twilight begins at sunset moment and comes to end as the Sun submerges down the horizon by 6 o - 8 o. At this moment people usually have to switch on an artificial light in houses. On the sky, one can see stars of the first magnitude. 2) Maritime (nautical) twilight begins at the end of the civil twilight and lasts up to the moment the Sun will have submerged by 12 o. At the end of the maritime twilight the navigators of sea vessels are not able to orient themselves by non-illuminated objects. At that moment all marking and signal lights (beacons, lighthouses) must be switched on. 3) Astronomic twilight begins at the end of the maritime twilight and lasts until the Sun will have submerged by 18 o. That is the starting point for night time. All stars can be seen in the sky. During twilight the earth surface illumination changes significantly. At the twilight beginning it is 10 -3 – 10 -4 l and at the end (night time) it is 10 -4 – 10 -5 l.

The twilight duration depends upon latitude and season. The higher the latitude the longer the twilight duration. In summer, at some latitudes the evening and morning twilight merge with each other. In this case no night time appears. This phenomenon is known as white nights. Cloudiness makes illumination decrease during twilight. The thicker the clouds are, the more noticeably the illumination decreases. Snow cover causes illumination to increase only at the twilight beginning.

Fig. 5. Explanation of a twilight The flux of the Sun beams S is tangent to the earth surface at the point E, where an observer watches sunset. The line SEB is known as terminator, i. e. the boundary between light and shadow. The part of the atmosphere situated above the terminator is illuminated with direct Sun beams. It diffuses the light and sends it in all directions creating illumination at the point E as well. The other part of the atmosphere (that situated below the terminator) is shaded by the Earth, it does not take part in any light diffusion. The angle (EOA) is equal to the Sun submerge angle under the horizon. As the Sun continues submerging below the horizon, the terminator is ascending higher and higher above the observer, and the illuminated by the Sun part of the atmosphere becomes smaller and smaller. Due to this fact the illumination at the point E decreases.

The rapid change of illumination during twilight causes various optical phenomena. The latter are very quick to appear, to develop and disappear. Descending to horizon, the Sun becomes less bright and changes its colour from bright golden, through yellow and orange, to dark-red. Simultaneously the sky is also coloured; it is yellow near the Sun and orange at a distance from it. Along the horizon, at the sunset side, one can watch a bright strip of evening glow. This strip appears as dark-red at its bottom, a bit higher it is yellowish-orange and greenishblue at the top. In the opposite to the sunset part of the sky a leaden-gray coloured shadow of the Earth bordered with a pink belt ascends from the horizon. As the Sun submerges, the evening glow colour becomes richer and a pink spot appears over the glow at the altitude 20 o- 25 o. It is also called purple light

This light is the brightest when the Sun submerge depth reaches 4 o- 5 o. The tops of mountains covered with snow and clouds are coloured in purple and scarlet tint. If there are high mountains or Cumulus clouds beyond the horizon, their shadows are seen on the background of bright-coloured sky in form of radial dark beams. The latter are known as Buddha beams. By the end of the civil twilight the shadow of the Earth covers a significant part of the sky, the pink belt (purple light) pales and disappears. The clouds occurred to be in the shadow become gray. By the end of the astronomic twilight, the narrow coloured strip at the sunset side also pales and goes out

Illumination at night. At night, the main source of the earth surface illumination is the Moon. The full moon makes the illumination of a plane facing the beams at the top of the atmosphere equal to 0. 34 l. At the bottom of atmosphere the illumination is 0. 25 l in case of cloudless sky and average transparency of the atmosphere. In moonless conditions, the earth surface is not absolutely dark. It is illuminated by the night light. The light arriving at the surface from the night sky is called night-sky luminescence. The reasons for this luminescence are: a) Inherent luminescence of atmospheric gases (the night atmospheric luminescence), b) aurora light, c) solar light diffused by most upper layers of the atmosphere, d) star lights, e) the light diffused by interplanetary dust (zodiacal light) f) the light diffused by the interstellar dust (galaxy light) General illumination at moonless nights at clear condition varies from 0. 0005 to 0. 001 l. In case of overcast and rainy weather the illumination may decrease 10 times (and ever more).