GENERAL METEOROLOGICAL OPTICS 
By HANS NEUBERGER 
The Pennsylvania State College 
The phenomena of meteorological optics are not as 
generally well known as those of other branches of 
meteorology. For this reason, the subsequent sections 
are introduced with a brief description of the major 
phenomena and a summary of known facts. For ab- 
normal variations the reader is referred to the multi- 
tude of meteorological, astronomical, and general 
science periodicals. Visible sound waves in the sky, 
frequently observed during World War II,' could not 
be considered here. 
In order to keep the number of references within 
space limits, authors whose contributions have been 
discussed in standard works are, where possible without 
ambiguity, cited from these works; this is indicated by 
a ‘“‘c” preceding the respective reference number. 
SUBJECTIVE PHENOMENA IN THE 
ATMOSPHERE 
The Apparent Shape of the Sky. When scanning the 
daytime sky, an observer perceives a more or less 
flattened vault. For some observers, this impression 
persists even at night, although the multitude of stars 
in their different magnitudes tends to convey the idea of 
a rather undefinable space. The variety of impressions 
is the result of a complex psychometric coordination of 
the visual and the physical space. This coordination is 
not a simple transformation of a geometric reality such 
as obtains for an overcast sky, because, in the case of 
the clear daytime sky, we look into an indefinite depth 
of the luminous atmosphere. Indeed, if we fix our sight 
in any elevated direction, we fail to perceive a ‘“‘surface” 
on which our eyes may rest. However, if we let our 
eyes wander between zenith and horizon, the impression 
of such a surface is inescapable. The problem of the sky 
shape, although some of its aspects lie within the realm 
of psychophysics, is of meteorological interest because 
of its bearing on the practice of estimating cloudiness. 
Smith [c. 42] introduced a method by which a numeri- 
cal value can be assigned to the apparent flatness of the 
sky, by measuring the elevation angle a (Fig. 1) of the 
Ha 
Fic. 1.—Half-are angle a as a measure of the apparent shape 
of the sky. 
estimated position of point M that bisects the imagi- 
1. For example, see W. E. K. Middleton, J. R. astr. Soc. 
Can., 38: 432 (1944). 
61 
nary are ZH from zenith to horizon. The half-arc angle 
a is then a measure of the flatness of the sky, becoming 
smaller as the sky appears flatter. Another method for 
expressing the sky flatness numerically is the estima- 
tion of the ratio of the apparent distances OH/OZ, 
which increases with increasing flatness of the sky. 
The estimation of this ratio is a more difficult task than 
bisecting the are ZH and is a much coarser measure. 
Assuming, for example, a circular sky profile, we can 
compute corresponding values of OH /OZ and a [c. 42]; 
OH/OZ = 1, 2, 3, 4, corresponds to a = 45°, 33°, 25°, 
20°, respectively. Since most observations fall in the 
range 20° < a < 40° and are reproducible within 1°, 
while OH /OZ can be estimated, at best, only in whole 
numbers, OH /OZ is obviously an inadequate measure. 
Various authors have deduced the curvature of the 
sky profile as circular, elliptic, parabolic, hyperbolic, or 
helmet-shaped [8, 9, 22, 23, c. 42]. The angle at which 
the sky appears to meet the horizon plane is one 
criterion of the geometric form. This angle would be 90° 
only in the cases of elliptic and parabolic shapes, but 
more or less acute in all others. A parabolic profile would 
also be distinguished by the pointed appearance of the 
zenith sky. Another criterion is derived from compari- 
son of observed overestimation of elevation angles of 
objects with those computed under the assumption of 
various sky shapes [42]. Variations of a psychological 
nature among different observers and physical varia- 
tions of sky conditions undoubtedly preclude the as- 
sumption of any unique sky shape. For the discussion 
of observational results, consideration of the half-are 
angle a may suffice. 
Table I shows the effect of general sky brightness and 
cloudiness on the depression of the sky as seen by vari- 
ous observers. Although the large differences among 
TaBLE I. AvERAGE Hatr-Arc ANGLES FOR VARIOUS 
Sky ConpIvTIoNs 
Daytime An Clear night 
Observer = pile a. Twilight 
cloudy clear moonlit | moonless 
Dember and Uibe [8]..| 29.0° | 32.0° | 32.2° | 36.7° | 40.1° 
INMUilller [Billo oc ogecores 29.9 | 34.0 = — — 
Reimann [c. 42]....... Pil) |) 2s) - 26.6 | 30.0 
Mendelssohn and Dem- 
laa (BBiloscosscse cee — 31.9 — 36.6 R= 
observers reflect the strong subjectivity of the phe- 
nomenon, the same trend appears in the effect of the 
various sky conditions. The cloudy daytime sky looks 
flattest, the moonless night sky most arched. Some of 
the individual differences may be due to effects of 
locality, since the observations cited were made at 
different places and altitudes. 
