GENERAL METEOROLOGICAL OPTICS 65 
are sensibly independent of the assumption regarding 
the vertical density distribution and the concentricity 
of isopyenic surfaces [28, 42, 59]. Court® pointed out the 
inadequacy of these correction tables particularly for 
cold climates; he suggests the use, instead of air tem- 
perature, of “refractive temperature,” 7e., that tem- 
perature for which the correction obtained from tables 
is the one actually required, and he presents rules for 
estimating these refractive temperatures. 
For zenith distances > 70°, Esclangon [12] attributes 
the greatest optical effect to the layer up to about 15 
km, whereas according to Wtinschmann [59] the mass 
distribution in the stratosphere between 15 and 45 km 
height and the orientation of the isopyenic surfaces in 
this layer play a dominant role. More frequent and 
systematic soundings of the upper atmosphere with 
modern equipment would enable us to solve this prob- 
lem and to obtain more direct values of stratospheric 
density variatio 1s. 
Wiinschmann, by means of upper-air soundings, con- 
structed charts showing the topography of the optical 
surfaces. He found that the influence of density varia- 
tions in the lower troposphere up to 6.5 km is generally 
compensated by an opposite influence in the upper 
tropospheric region between 6.5 and 15 km, leaving an 
insignificant net effect of the troposphere. The inclina- 
tions of isopycnic surfaces owing to local horizontal 
temperature gradients, fronts, or orographic features, 
generally change the astronomical refraction by only a 
fraction of a second of are. 
The large astronomical refraction for zenith dis- 
tances of 90° or more generally lengthens the day, since 
it causes the sun to rise somewhat earlier and set some- 
what later than is computed from purely geometrical 
considerations. This is of practical importance for the 
prediction of illumination conditions in polar regions, 
where the strong density gradient, built up in the lower 
atmosphere during the winter night, may advance the 
date of sunrise by several days [42]. The great decrease 
in normal refraction with slight elevation above the 
horizon causes a deformation of the sun’s or moon’s 
disk; for the difference in refraction between the lower 
limb, touching the horizon, and the upper limb amounts 
to 6’, so that the vertical axis of the disk appears shorter 
by 14. The large refraction is connected with a rela- 
tively large prismatic dispersion which is of the order 
of 20 to 40 seconds of are between blue and red wave 
lengths [19, 42]. This dispersion occasionally causes the 
last segment of the setting sun or planets [54] to appear 
green for a few seconds, the so-called green flash [21] 
or green segment [19]. Sometimes the color is blue or it 
changes continuously from yellow to violet. This phe- 
nomenon can occur only when the atmosphere is so 
clear that the shorter wave lengths are not attenuated. 
Whereas Hulburt [19] believes that normal dispersion 
is sufficient to cause this phenomenon, most observa- 
tions seem to be associated with refractions in excess of 
the normal [35, 54]. To what extent selective absorption 
3. See A. Court, “Refractive Temperature,” J. Franklin 
Inst., 247: 583-595 (1949). 
by water vapor [42] or other gases contributes to this 
phenomenon is still undecided. 
The curvature of the rays from artificial lights is 
due to terrestrial refraction. In Fig. 5, an observer at A 
sees a point B in the direction of incidence AC of the 
curved light ray; the angle a between the straight line 
AB and the tangent AC is the terrestrial refraction. 
Similar conditions obtain for an observer at B sighting 
point A; im this case the terrestrial refraction is meas- 
ured by angle 8. The sum a + 6 = e is called the total 
refraction. For an average density gradient the terres- 
trial refraction imereases roughly from 2” to 42” when 
the distance between the two points increases from 1 to 
20 km [42]. The curve of the light ray can, in most cases, 
be assumed as a circular arc, so that a = B = e/2. The 
path of the light ray is then determined by its radius of 
curvature rz. In Fig. 5 the angular distance between 
points A and B is ¢ at the earth’s center, and e is the 
central angle of the are AB. Since the heights of A and 
B above the earth’s surface are small as compared to the 
Fig. 5.—Schematie diagram of terrestrial refraction. 
earth’s radius 7o, and the angles e and g are small, the 
ratio 
=< (4) 
= or g 
2 2ry ‘ 
As g and r, are known, the terrestrial refraction can be 
computed from the radius of curvature of the light 
ray. Its reciprocal, the curvature of the ray, is (ac- 
cording to Wegener [56]) determined by 
1 Dy Zila ay u 
esi (@ — 1) T= 700 GH) (5) 
where 7 is the refractive index, p the barometric pres- 
sure in mm Hg, 7’, the virtual temperature in °K, y 
the temperature lapse rate (counted as negative in case 
of inversions), and y’ the autoconvective lapse rate. 
The curvature of the light ray is proportional to the 
barometric pressure and inversely proportional to the 
square of the virtual temperature, showing the dominat- 
ing influence of temperature on refraction. The curva- 
ture decreases as the lapse rate increases, and the light 
ray becomes rectilinear for a homogeneous atmosphere 
(y = 7’). For large lapse rates, however, the convective 
activity causes scintillation. For strong inversions 
(y << 0) the curvature of the light rays approaches 
