Distribution of brightness and colour over the sky

P h y s i c a X l I , no. 5

DISTRIBUTION

A u g u s t u s 1946

OF BRIGHTNESS OVER THE SKY

AND

COLOUR

by J. J. M. R E E S I N C K Laboratory of Physics and Meteorology of the Agricultural College at Wageningen, Director Prof. Dr J. A. Prins Summary P r e l i m i n a r y results a r e g i v e n of v i s u a l o b s e r v a t i o n s of t h e b r i g h t n e s s o[ t h e s k y in red and blue l i g h t .

In this paper the results are given of measurements of the spectral brightness of the sky with a visual brightness meter, devised in the laboratory of the N. V. K.E.M.A. at Arnhem. A beginning was made with the observations in June 1944 at Arnhem ; they were continued till September ~944, when Arnhem was evacuated and the instrument was destroyed. As the period of the observations is short and a check on the calibration of the instrument at the end of the period was impossible, the results are to be considered as only preliminary. Fig. la gives the principle of the instrument. By the lens L 1 and the mirrors $2 and $3 an image of the lamp A is formed in the pupil of the eye. The lens L2 is focussed on the upper edge of the mirror Sa. This edge divides the field of view into two halves. The eye sees the lower part uniformly illuminated by the lamp A. By rotating the mirror SI about the axis SIL2 and the whole instrument about the axis PQ the upper half of the field of view can be illuminated b y an arbitrary part of the sky, the altitude and azimuth of which can be read on scales. By means of the rotating disk D colour filters can be placed in the beam of light. The light from the sky can be reduced in intensity b y means of the neutral filters Fl, F 2 and F3, with transmission factors resp. 1/10, 1/100 and 1/lO00nominally; three neutral filters F4, Fs and F6 can be placed in the beam of the lamp A, each with a transmission factor of 1/1o nominally; a further reduction of the light from A is possible with a cylinder T, bearing a strip of photographic film, the optical density of which varies gradually b y a factor 40; the position of T can be read on a scale. With this instru- -

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DISTRIBUTION OF BRIGHTNESS AND COLOUR OVER THE SKY

297

ment it is possible to compare brightnesses differing by a factor 107. Measurements were made with Schott-filters RG 2 (thickness 1 mm) and BG 12 (2 mm) and incidentally with VG 2 (2 mm), with effective wave-lengths 648 m~, 472 m~x and 542 m~ respectively. The instrument was calibrated in the laboratories of the K.E.M.A. by measuring the brightness of an image, formed on a surface covered with MgO, of a tungsten bandlamp, the. true temperature of which is known as a function of the input and by measuring the standard I p .

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Fig. la. P r i n c i p l e of K . E . M . A . b r i g h t n e s s m e t e r . H o r i z o n t a l d i m e n s i o n n e a r l y 20 c m . In r e a l i t y t h e lens L l is p l a c e d m u c h n e a r e r to t h e m i r r o v S a. Fig. lb. C u b e for r e l a t i v e c a l i b r a t i o n ; e d g e 16 cm.

brightness, described in a former paper *). A calibration in relative values was also obtained by measuring the brightness of the inside of a white cardboard cube (fig. l b), into which sunlight is admitted through a hole the diameter of which can be varied. The calibration curve and the transmission factors of the filters m a y contain systematic errors to such an extent that the uncert a i n t y in the slope of the logarithmic curve of the brightness is some 0.05 per unit, perhaps somewhat different for red and blue light. As the calibration was carried out at a brightness about 100 times smaller than that of the sky, the absolute spectral brightness and colour index are less accurate than the relative values of these quantities. *) J. J. M. R e e s i n c k ,

Metingen van de schemering, Physica XI, 61, 1944.

298

J . j . M . REESINCK

The observations were m a d e on a roof of the technical school (,,Ambachtsschool") at A r n h e m ; 38 series with 1540 observations were obtained, m o s t l y with a r a t h e r clear (16 series) or a c o m p l e t e l y overcast (15 series) skv. The time between two observations was a b o u t one minute. 0 I

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Fig. 2. Examples of separate series of observations. Upper part : clear sky (argument: distance from the sun); solar altitude 45o--55 ° . Left: red; right: blue. Crosses are observations at 70 ° zenith distance. Lower part: overcast sky (argument: zenith distance); solar altitude 330--45 °. Left: red; right: blue. On d a y s with an overcast s k y (scattering layer of great optical depth) the brightness B (in this p a p e r always expressed in erg cm -2 ster -I A -I sec -1) will be a function of the zenith distance z. On d a y s with a clear s k y (scattering layer of small optical depth) B cos z is to a first a p p r o x i m a t i o n a function of the distance r from the sun; this a p p r o x i m a t i o n is not valid for large values of z; our m e a s u r e m e n t s h o w e v e r were as a rule m a d e at zenith distance not exceeding 70 ° .

DISTRIBUTION OF BRIGHTNESS AND COLOUR OVER THE SKY 299

F o r each series with clear or slightly veiled sky log (B cos z) was p l o t t e d against r and represented b y a s m o o t h curve. An example is given in fig. 2, upper part. The shape of the curve is n e a r l y the same for all the series, the curves are however shifted with respect to each o t h e r in the direction of ordinates ; the m e a n value of this shift is 0.20 for red and 0.12 for blue. T h e differe]:ce between these two numbers corresponds to the well k n o w n fact t h a t a slight cloudiness, h a r d l y visible t h r o u g h a blue filter m a y be v e r y conspicuous when seen !

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Fig. 3. T h e q u a n t i t y log (B cos z) as a f u n c t i o n of t h e d i s t a n c e r f r o m t h e s u n for d a y s w i t h a c l e a r sky, for red (648 m~) a n d blue (472 mt~) a n d t h e d i f f e r e n c e b l u e m i n u s red. B is t h e s p e c t r a l b r i g h t n e s s in erg c m -2 s t e r -1 /~-I s e c - I ; z is t h e z e n i t h d i s t a n c e . A b o v e t o t h e r i g h t : log B as a f u n c t i o n of z for d a y s w i t h a n o v e r c a s t sky. for red a n d blue.

t h r o u g h a red filter. Mean curves are given in fig. 3. The curve blue minus red shows t h a t the light from p a r t s of the sky in the neighb o u r h o o d of the sun is less blue t h a n f a r t h e r off (0.51 near the sun against 0.66 at 90 ° distance). In fig. 4 B cos z is given in a polar d i a g r a m ; this gives the distribution of the light scattered in various directions b y a vertical column of air with a basis of 1 cm 2. The difference from R a v 1 e i g h scattering is conspicuous and indicates the presence of large particles in the air. The difference in colour between the n e i g h b o u r h o o d of the sun and the rest of the sky is due to a combined effect of scattering b y smaller

309

DISTRIBUTION OF BRIGHTNESS AND COLOUR OVER THE SKY

and by larger particles. "['he molecules and in general particles much smaller than the wave-length of light scatter principally the shorter wave-lengths with only a small preponderance in the direction of the incident light and the opposite direction (R a y 1e i g h scattering ; dotted in fig. 4) ; the larger particles scatter unselectively and principally under small angles with the incident light. So the colour of the sky in the neighbourhood of the sun is mainly determined b y the larger particles, at a large distance from the sun Rayleigh scattering gains in importance.

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Fig. 4. P o l a r d i a g r a m of B cos z (erg c m - 2 s t e r -1 .~-1 s e c - l ) . I n n e r c u r v e red, o u t e r c u r v e blue. T h e d o t t e d c u r v e gives t h e r e l a t i v e i n t e n sities in t h e case of p u r e R a y l e i g h s c a t t e r i n g . To o b t a i n a b s o l u t e i n t e n s i t i e s for 648 a n d 472 m~z m u l t i p l y R a y l e i g h c u r v e b y 0.05 a n d 0.21 r e s p e c t i v e l y .

For series with an overcast sky log B was plotted against z (fig 2, lower part). The divergence between the observations is of course greater than in the case of a clear sky; with stratus it is smaller than with stratocumulus. All curves however have essentially the same shape. Their mean deviation in the direction of ordinates is 0.17 and 0.16 for red and blue respectively. Mean curves are given in fig. 3. The difference blue minus red is 0.27, independent of zenith distance. The theoretical background of these facts will be considered more in detail in another paper. This preliminary research has shown the usefulness of the method. It is intended to continue the measurements of the brightness of the sky at the Laboratory of Physics and Meteorology at Wageningen. The author is greatly indebted to the management of the N.V. K.E.M.A. who put the instrument at his disposal, to Dr D. V e rmeulen and M r J . B. d e B o e r for devising the apparatus, to Dr G. A. W. R u t g e r s who kindly helped with the calibration and to Mr C o v e n s, Director of the technical school at Arnhem, for the permission to use this school for the observations. Received March 26th, 1946