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Luminance and polarization of the sky light at Seville (Spain) measured in white light
Armospheric Enkmmenr
Vol. 22. No. 3. pp 595-599.
ooo4d9981 :a $3.00 + 0.00
1988.
Pergamon Press plc.
Printed in Great Britain.
LUMINANCE AND POLARIZATION OF THE SKY LIGHT AT SEVILLE (SPAIN) MEASURED IN WHITE LIGHT C. BELLVER Departamento de Optica, Facultad de Fisica, Universidad de Sevilla, Apartado 1065. 41080~Seville. Spain (First received 16 February 1987 and
injnalform
2 September
1987)
Abstract-An extensive study on certain optical characteristics of the sunlit sky at Seville was carried out from March 1980 to September 1984. Values of luminance Land degree of polarization p of diffuse sky light were measured in white light throughout the day by observing two points in the sun’s vertical plane: the zenith and the point situated, at each instant, at 90” to the sun. The very large amounts of data from these measurements have provided reliable corroboration of results obtained from similar observations at three wavelengths in the visible spectrum, previously reported in this Journal. In addition a study on the behaviour of luminance due to polarized light is included. Changes in luminance and polarization during periods near sunset have been studied for several months and for solar angles ranging from 5” to - 5”. One of the Rubenson empirical formulae was used giving a reasonably good fit when comparing values of p at 90” from the sun with those calculated from this expression. A brief reference to a set of measurements performed at a rural location is also included. Finally, shifts in the position of maximal polarization in the sun’s vertical plane were detected. Key word pollution.
index:
Sky
luminance, sky light polarization, light scattering, degree of polarization, particulate
1. INTRODUCHON
As experimental measurements have shown (Sekera, 1956; Co&on, 1980, 1981, etc.), the sunlit sky always exhibits remarkable variations of colour, luminance and polarization that would be produced by Rayleigh scattering alone, even taking into account the contribution of multiple scattering and molecular anisotropy. This discrepancy is attributed to the presence of the atmospheric aerosol particles whose scattering properties are different from those of gas molecules. Particles with radii 2 0.03 times the wavelength of the light scatter according to Mie theory. Then, for instance, particles are much less efficacious polarizers than are gaseous molecules and consequently the degree of polarization exhibited by the actual atmosphere is less than that which would exist without the presence of aerosols (McCartney, 1976; Bohren and Huffman, 1983; van de Hulst, 1981). So the depolarization effect depends on aerosol characteristics such as particle size-frequency distribution, index of refraction of the materials, number concentration of the particles, etc. Since all these parameters characterize the condition of atmospheric turbidity, the degree of polarization is usually measured to get information about the turbidity in the atmosphere. On the other hand, variations in polarization at the zenith during periods near sunrise or sunset have been attributed to the existence of layers of aerosols in the stratosphere (Rozenberg, 1966). Thus one can obtain valuable information about the atmospheric aerosol from measurements of the in-
tensity and polarization of diffuse sky light taking into account the effects of molecular (Rayleigh) scattering (Bullrich, 1964, Liou, 1980; Magill and Holden, 1956, etc.). The work reported in this paper represents the most extensive part of a general study on the luminance and polarization of diffuse sky light at Seville. Previous results on the behaviour of both luminance and polarization at three wavelengths in the visible spectrum for solar elevations higher than 5” were described in an earlier paper (Bellver, 1987). Measurements were carried out by observing two points in the sun’s vertical plane (the zenith and the point situated, at each instant, 90” from the sun). In the present work, the same analysis has been performed for white light. Nevertheless the number of observations is much larger and considerable amounts of data were taken for solar angles < 5” at dusk. Moreover, several points not covered in the previous paper are discussed.
2. EXPERIMENTAL
The measurement urban site was the flat roof of the Main Building of Seville University, close to the city centre but surrounded by a green belt. Luminance is measured with a ‘Tektronix J-16 digital photometer. The photometer calibrated probe is mounted on a ‘Zeiss ‘I&I’ theodolite, in such a way that any point of the sky can be easily and accurately located. Luminance is determined with an accuracy of 5 “/,. In order to determine the degree of polarization, a rotating circular-shaped analyzer is placed in front of the probe. Keeping the direction of observation constant, the analyzer is 595
596
C.
BELLVER
rotated and for three positions separated by angles of 60”, the corresponding brightness is read from the photometer display. L, , 15, and L3 being the three values of brightness, the degree of polarization is given by,
p=2JLI(L,-L~)+L,(L,-L3)+L3(L3-L,), _____ L,+L,+L,
The analyzer could be easily removed to provide measurements of brightness. Values of p are measured with an estimated accuracy of 15 ‘;;, In order to gain information about atmospheric particulate content, systematic collection of samples was carried out at the reference sun elevation h = 30”. These samples are obtained by the filtration of a measured volume of air (usually 500 !) through a ‘Whatman 1’ paper filter, where particles settle forming a greyish spot. The darkening of the sample is determined by means of an ‘EEL reflectometer. An experimental calibration curve provided by the O.C.D.E. (1964) for an ‘EEL’ reflectometer and for a l-in. diameter ‘Whatman 1’ paper filter allows us to convert the reflectometer readout into surface particulate concentration on the filter spot (expressed in pg m -‘). This value is then converted into volumetric concentration using the spot surface and the amount of filtered air. The mass of particulate matter per unit volume is expressed in pg mm3 and it is denoted by M. Simultaneously with pollution measurements, mean wind speed w and air relative humidity U were evaluated at the same site. Relative humidity determinations were also used to restrict measurements to those days on which U was below 70” II 3. RESULTS This section has been divided into subsections: subsection 3.1 presents an analysis similar to that performed in a previous work (Bellver, 1987), but now deals only with measurements in white light. The other subsections study certain points not previously described. 3.1. Luminance and polarization for sun elevations higher than 5” During the period March 1980-September 1984, photo-polarimetric determinations were carried out by measuring the luminance and the degree of polarization of diffuse light from two points of the sky lying in the vertical plane through the sun: the zenith and the point situated, at each instant, 90” from the sun. Measurements were performed at sun elevations h varying from 5” to 65” at 5” intervals on cloudless days. Subscripts z and 90 denote the measurements in the direction of the zenith or at 90” from the sun, respectively. For a total of 374 dates, diurnal evolution of L,, L,,, pz and ppO have been studied. Although all these parameters undergo considerable variations from day to day, their diurnal evolutions always show the same general trends: an increase in h leads to a decrease in pZ and puo and to an enhancement of the values of L,and L 90. Even high values of the atmospheric turbidity on certain days cause no essential change in this pattern. Moreover, the diurnal evolution curves for every day are very similar to those obtained at other places in the
world (Vassy, 1966; de Bary, 1964, Adams, 1981, etc.). The characteristic diurnal behaviour of luminance and polarization provides high correlations between L, and 1 lp, and between L,, and 1 ipso at every sun elevation. The corresponding correlation coefficients r remain high for every h at the zenith as well as at 90’ from the sun, attaining values close to 0.90 in certain cases (see Table 1). These high values of r can be considered very significant because of the illustrative number of data intervening in the correlation (more than 400 pairs of values at h = 25” and at h = 30 ). Figure 1 shows the plot of 1ip, vs L, at h : 30’. The possible seasonal and environmental dependence of these parameters is investigated during 5 years by considering only the data taken at the reference sun elevation /I = 30”. It is observed that only environmental (especially turbidity) factors seem to influence the values of L,, L,,, pz and psO, and no definite dependence with the season or the month of the year is found. A general trend is observed: an increase in atmospheric particulate content leads to an increase in the values of luminance (L, and L,*) and to a decrease in the values of the degree of polarization (p, and psn). For this reason, correlation coefficients of the mass of suspended particulate matter in the air M against these optical parameters are calculated. For a total of 425 pairs of values on each case, marked correlations appear (see Table 2). The plot of M vs L,, at h = 30” is shown in Fig. 2. Limitations of the results listed in Table 2 can be summarized as follows: The method used for determining M provides reasonably good information about local atmospheric particulate content and the results obtained by its application agree fairly well at our urban site with those obtained by weighing the samples obtained by the filtration of a certain volume of air through a paper filter for 34 h in an electrobalance. Nevertheless, in certain aspects, it can be considered particularly coarse.
Table 1. Correlation coefficients r between luminance of the diffuse sky light L and the inverse of its corresponding degree of polarization p measured in white light at the zenith and at 90” from the sun and at several sun elevations h (n is the number of pairs of values) h(“) 5 10 15 20 25 30 35 40 45 50 55 60
r(L,,
l/P,)
0.79 0.75 0.75 0.84 0.86 0.90 0.87 0.84 0.83 0.83 0.82 0.72
r(Lm
l/P,,)
0.79 0.77 0.75 0.85 0.89 0.9 1 0.89 0.88 0.86 0.88 0.86 0.75
n
89 130 197 279 411 425 341 271 252 229 148 88
59-l
of sky light in white light
Luminance and polarization
l-
’
!
.
.
I
l
’
:
:
2
4
6
6
10
12
14
16
INVERSE OF THE DEGREE OF POLARIZATION
Fig. 1. Inverse of the degree of polarization of diffuse sky light vs luminance. both measured at the zenith in white light, and at a solar elevation of 30”.
Table 2. Correlation coefficients r of particulate mass per unit volume M against luminance and degree of polarization of diffuse sky light measured in white light at the zenith and at 90” from the sun, at a sun elevation of 30” (n is the number of pairs of values)
r W,. Ml r(Ls.0. M) r (p, M) r(p90.
W
r
n
0.70 0.71 - 0.70 -0.72
425 425 425 425
However, measurements have been performed at ground level. For these and other reasons, correlations of M against optical parameters can only be regarded as an estimation of the important influence of nonmolecular scattering on the spatial distribution and polarization of sky light. Again, the use of the Milch-Tikhanovskii semiempirical formula (Stamov, 1972) has been investigated in order to relate zenith polarization to that obtained at 90” from the sun
Pz =
pyo sin4 * 1 - p9()cos4@
where 1/1is the scattering angle. In the course of this work, experimental data of pro have been substituted into (1) obtaining values of pz that do not depart markedly from those measured. The corresponding correlation coefficient between
measured and calculated values is I = 0.89 for 2926 pairs of values. Hence all the studied characteristics of these parameters and their mutual relationships corroborate previous reported results obtained at three wavelengths in the visible spectrum.
3.2. Luminance due to polarized light The luminance due to polarized light is equal to the product of total luminance and the corresponding degree of polarization. This parameter is denoted by Lp. Subscripts ‘z’ and ‘90’ have the same meaning. The diurnal evolution of Lp,departs markedly from that of Lp,,: in most cases, Lp, decreases and Lp,, increases with increasing h. This feature is due to the peculiar diurnal behaviour of p,, pgo, L, and L,,. As the sun elevation becomes greater, L, tends to increase much more rapidly than Lye but the precipitous decrease of pz compared to that of pgo produces the observed behaviour. So, in the middle of the day close to the local noon, Lp,turns out to be rather lower than Lp,, . However, in the early morning and evening, Lp, and Lp,, exhibit very similar values. At sun elevations ranging from 5” to 15” the lowest values of Lp,, are usually reached, as the corresponding values of luminance are also very low (see Fig. 3). At the reference sun elevation (h = 30”) Lp, and Lp,, scarcely vary from day to day. This feature is less marked at values of h >50”and ~15”. As above, no definite seasonal dependence of Lp
values is observed. On the other hand, the possible influence of M on these parameters is found to be negligible.
598
c.
25
BELLVER
50
75
100
PARTICULATE POLLUTION
125
lpg m-al
Fig. 2. Particie mass per unit volume vs luminance ofdiffuse sky light measured in white light at 90” from the sun and at a solar elevation of 30”.
Fig. 3. Typical diurnal evotution of the luminance due to polarized iight, u Determinationsat the zenith, a determinations at 90” from the sun.
The remarkable changes of sky illumination and potarization that take place during short time intervals before and after sunset can be summarized as follows: A rapid decrease in luminance as the sun approaches and sinks below the horizon is found: values of luminance decrease more than SOY{,when the sun elevation diminishes by only I’.. During these months, the maximum polarization throughout the day was found at sun elevations ranging from 2.5” to - 2.5’. On most occasions (i.e. almost 60 days), the maximum was found when the sun was on the horizon (h = 0”). Note that values of the degree of poIari~tion ZZ.+ 0.80 have never been measured at our urban site. Moreover, regular behaviour of p during the period from 5” to - 5” is observed and no secondary maxima were detected. 3.4. Ruhenson empiricul formula
eletiations
One of the empirical formulae developed by Rubenson (Kartschaguin, 1925: Stamov, 1972) allows us to evaluate the diurnal evolution of the degree of polarization at 90” from the sun
Lummance and polarization of the sky at dusk have been measured for a total of 73 dates during the autumn-winter months from 1980 to 1982. Measurements were carried out at sun elevations ranging from 5” to -5”, at l”, and even at 0.5 intervals. As above, measurements were performed in the direction of the zenith and at 90” from the sun, except when the sun is on the horizon, since the two points coincide.
In this expression, x is the time (in h) between the focal noon and the instant of the measurements, a, b and k being three parameters that vary from day to day. In generat, small discrepancies between measured and calculated values of psO are observed. The cor-
3.3. l~eus~re~e~ts
d~f~~g
twi~~g~t and at
low
sun
599
Luminance and polarization of sky light in white light responding correlation coefficient (r = 0.75) is lower than that obtained by applying the MilchTikhanovskii formula. 3.5. Rural photo-polarimetric determinations Together with urban measurements, a much smaller set of determinations of L, I!+,,, pZand pso were made at a rural location close to the village of Sanlucar la Mayor, 18 km W of Seville, during the summer of 1980. The behaviour exhibited by all these parameters is similar to that observed at the urban site showing regular diurnal evolution curves. The main result was the occurrence of very high values of the degree of polarization close to 0.90. Values of 0.88 and 0.86 were found during the evening twilight. These extremely high values of polarization, characteristic of very clear atmospheres, like those of the Australian outback (Adams, 1981), are very difficult to find in urban areas. It should be mentioned again that values of p higher than 0.80 have never been measured at our urban site over a period of 5 years. 3.6. Positions of maximal polarization It is well known that all the discrepancies between the polarization values calculated from Rayleigh’s theory and those experimentally found are covered by the general term known as ‘polarization defect’. One of the most noticeable features of the defect is the phenomenon of neutral points (where polarization vanishes) occurring in directions different from those predicted. Also, a shift in the position of maximal polarization from the theoretical right angles from the sun can be considered as another ostensible feature of this defect. In the course of our work, several determinations of the actual positions of maximal polarization were carried out by exploring the sky regions below and above the theoretical position. These explorations were performed by measuring the degree of polarization over these zones to get a maximum. When the point of maximal polarization was found, the angular distance between it and the predicted position was measured. This angular distance is named 6. Results have shown that 6 always has the same sign. Thus positions of maximum are shifted away from presupposed locations and lie at angular distances
ranging between 90” and 94” to the sun. So, 6 varies from 0 to 4” for all measurements taken at different sun elevations. Acknowledgements-I am indebted to Prof. Dr V. Hernandez for his continuous help and advice. I also thank Prof. Dr J. Lea1 and Prof. Dr R. Marquez for their valuable help.
REFERENCES Adams K. H. J. (1981) The detection of very thin aerosol layers by the measurement of spectral sky radiance. Atmospheric Environment 15, 371-378. Bellver C. (1987) Study of luminance and polarimetry of the sky at Seville (Spain) from May 1982 to September 1984. Atmospheric
Environment 21, 1477-1482.
Bohren C. F. and Huffman D. R. (1983) Absorption and Scattering of Light by Small Particles. Wiley, New York. Bullrich K. (1964) Scattered radiation in the atmosphere and the natural aerosol. Advances in Geophysics, Vol. 10.
Academic Press, New York. Coulson K. L. (1980) Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity-l. Degree of polarization. Appt. Optics 19, 3469. Coulson K. L. (1981) Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity-2. Intensity and color ratio. Appt. Optics 20, 1516. de Bary E. (1964) Influence of multiple scattering on the intensity and polarization of diffuse sky radiation, Appt. Optics 3, 1293-1303.
Kartschaguin M. V. (1925) Polarisation de la lumitre diffuse du ciel. J. Physique Radium 6, 10.
Liou K. N. (1980)An introduction to Atmospheric Radiation. Academic Press, New York. Magill P. I. and Holden F. R. (1956) Air Pollution Handbook (edited by Ackley C.). McGraw-Hill, New York. McCartney E. J. (1976) Optics ofthe Atmosphere. Scattering by Molecules and Particles. Wiley, New York. O.C.D.E. (1964) Me’fhodes de mesure de la pollurion atmospherique.
Rozenberg G. V. (1966) Twilight. A Study in Atmospheric Optics. Plenum Press, New York. Sekdra Z. (1956) Recent development in the study of the polarization of sky light. Advances in Geophysics, Vol. 3. Academic Press, New York. Stamov D. G. (1972) The need to improve the semiempirical formula for correlation of observations of sky light polarization. Atmospheric Optics (edited by Divari N. B.), Vol. 2, p. 113. Consultants Bureau. van de Hulst H. C. (1981) Light Scattering by Small Particles. Dover Publications, New York. Vassy E. (1966) Physique de kitmosphere. Tome 111. Phenomenes d’tibsorption
et de diffusion darts i’dtmosphere.
Gauthier Villars, Montrouge, France.
Vol. 22. No. 3. pp 595-599.
ooo4d9981 :a $3.00 + 0.00
1988.
Pergamon Press plc.
Printed in Great Britain.
LUMINANCE AND POLARIZATION OF THE SKY LIGHT AT SEVILLE (SPAIN) MEASURED IN WHITE LIGHT C. BELLVER Departamento de Optica, Facultad de Fisica, Universidad de Sevilla, Apartado 1065. 41080~Seville. Spain (First received 16 February 1987 and
injnalform
2 September
1987)
Abstract-An extensive study on certain optical characteristics of the sunlit sky at Seville was carried out from March 1980 to September 1984. Values of luminance Land degree of polarization p of diffuse sky light were measured in white light throughout the day by observing two points in the sun’s vertical plane: the zenith and the point situated, at each instant, at 90” to the sun. The very large amounts of data from these measurements have provided reliable corroboration of results obtained from similar observations at three wavelengths in the visible spectrum, previously reported in this Journal. In addition a study on the behaviour of luminance due to polarized light is included. Changes in luminance and polarization during periods near sunset have been studied for several months and for solar angles ranging from 5” to - 5”. One of the Rubenson empirical formulae was used giving a reasonably good fit when comparing values of p at 90” from the sun with those calculated from this expression. A brief reference to a set of measurements performed at a rural location is also included. Finally, shifts in the position of maximal polarization in the sun’s vertical plane were detected. Key word pollution.
index:
Sky
luminance, sky light polarization, light scattering, degree of polarization, particulate
1. INTRODUCHON
As experimental measurements have shown (Sekera, 1956; Co&on, 1980, 1981, etc.), the sunlit sky always exhibits remarkable variations of colour, luminance and polarization that would be produced by Rayleigh scattering alone, even taking into account the contribution of multiple scattering and molecular anisotropy. This discrepancy is attributed to the presence of the atmospheric aerosol particles whose scattering properties are different from those of gas molecules. Particles with radii 2 0.03 times the wavelength of the light scatter according to Mie theory. Then, for instance, particles are much less efficacious polarizers than are gaseous molecules and consequently the degree of polarization exhibited by the actual atmosphere is less than that which would exist without the presence of aerosols (McCartney, 1976; Bohren and Huffman, 1983; van de Hulst, 1981). So the depolarization effect depends on aerosol characteristics such as particle size-frequency distribution, index of refraction of the materials, number concentration of the particles, etc. Since all these parameters characterize the condition of atmospheric turbidity, the degree of polarization is usually measured to get information about the turbidity in the atmosphere. On the other hand, variations in polarization at the zenith during periods near sunrise or sunset have been attributed to the existence of layers of aerosols in the stratosphere (Rozenberg, 1966). Thus one can obtain valuable information about the atmospheric aerosol from measurements of the in-
tensity and polarization of diffuse sky light taking into account the effects of molecular (Rayleigh) scattering (Bullrich, 1964, Liou, 1980; Magill and Holden, 1956, etc.). The work reported in this paper represents the most extensive part of a general study on the luminance and polarization of diffuse sky light at Seville. Previous results on the behaviour of both luminance and polarization at three wavelengths in the visible spectrum for solar elevations higher than 5” were described in an earlier paper (Bellver, 1987). Measurements were carried out by observing two points in the sun’s vertical plane (the zenith and the point situated, at each instant, 90” from the sun). In the present work, the same analysis has been performed for white light. Nevertheless the number of observations is much larger and considerable amounts of data were taken for solar angles < 5” at dusk. Moreover, several points not covered in the previous paper are discussed.
2. EXPERIMENTAL
The measurement urban site was the flat roof of the Main Building of Seville University, close to the city centre but surrounded by a green belt. Luminance is measured with a ‘Tektronix J-16 digital photometer. The photometer calibrated probe is mounted on a ‘Zeiss ‘I&I’ theodolite, in such a way that any point of the sky can be easily and accurately located. Luminance is determined with an accuracy of 5 “/,. In order to determine the degree of polarization, a rotating circular-shaped analyzer is placed in front of the probe. Keeping the direction of observation constant, the analyzer is 595
596
C.
BELLVER
rotated and for three positions separated by angles of 60”, the corresponding brightness is read from the photometer display. L, , 15, and L3 being the three values of brightness, the degree of polarization is given by,
p=2JLI(L,-L~)+L,(L,-L3)+L3(L3-L,), _____ L,+L,+L,
The analyzer could be easily removed to provide measurements of brightness. Values of p are measured with an estimated accuracy of 15 ‘;;, In order to gain information about atmospheric particulate content, systematic collection of samples was carried out at the reference sun elevation h = 30”. These samples are obtained by the filtration of a measured volume of air (usually 500 !) through a ‘Whatman 1’ paper filter, where particles settle forming a greyish spot. The darkening of the sample is determined by means of an ‘EEL reflectometer. An experimental calibration curve provided by the O.C.D.E. (1964) for an ‘EEL’ reflectometer and for a l-in. diameter ‘Whatman 1’ paper filter allows us to convert the reflectometer readout into surface particulate concentration on the filter spot (expressed in pg m -‘). This value is then converted into volumetric concentration using the spot surface and the amount of filtered air. The mass of particulate matter per unit volume is expressed in pg mm3 and it is denoted by M. Simultaneously with pollution measurements, mean wind speed w and air relative humidity U were evaluated at the same site. Relative humidity determinations were also used to restrict measurements to those days on which U was below 70” II 3. RESULTS This section has been divided into subsections: subsection 3.1 presents an analysis similar to that performed in a previous work (Bellver, 1987), but now deals only with measurements in white light. The other subsections study certain points not previously described. 3.1. Luminance and polarization for sun elevations higher than 5” During the period March 1980-September 1984, photo-polarimetric determinations were carried out by measuring the luminance and the degree of polarization of diffuse light from two points of the sky lying in the vertical plane through the sun: the zenith and the point situated, at each instant, 90” from the sun. Measurements were performed at sun elevations h varying from 5” to 65” at 5” intervals on cloudless days. Subscripts z and 90 denote the measurements in the direction of the zenith or at 90” from the sun, respectively. For a total of 374 dates, diurnal evolution of L,, L,,, pz and ppO have been studied. Although all these parameters undergo considerable variations from day to day, their diurnal evolutions always show the same general trends: an increase in h leads to a decrease in pZ and puo and to an enhancement of the values of L,and L 90. Even high values of the atmospheric turbidity on certain days cause no essential change in this pattern. Moreover, the diurnal evolution curves for every day are very similar to those obtained at other places in the
world (Vassy, 1966; de Bary, 1964, Adams, 1981, etc.). The characteristic diurnal behaviour of luminance and polarization provides high correlations between L, and 1 lp, and between L,, and 1 ipso at every sun elevation. The corresponding correlation coefficients r remain high for every h at the zenith as well as at 90’ from the sun, attaining values close to 0.90 in certain cases (see Table 1). These high values of r can be considered very significant because of the illustrative number of data intervening in the correlation (more than 400 pairs of values at h = 25” and at h = 30 ). Figure 1 shows the plot of 1ip, vs L, at h : 30’. The possible seasonal and environmental dependence of these parameters is investigated during 5 years by considering only the data taken at the reference sun elevation /I = 30”. It is observed that only environmental (especially turbidity) factors seem to influence the values of L,, L,,, pz and psO, and no definite dependence with the season or the month of the year is found. A general trend is observed: an increase in atmospheric particulate content leads to an increase in the values of luminance (L, and L,*) and to a decrease in the values of the degree of polarization (p, and psn). For this reason, correlation coefficients of the mass of suspended particulate matter in the air M against these optical parameters are calculated. For a total of 425 pairs of values on each case, marked correlations appear (see Table 2). The plot of M vs L,, at h = 30” is shown in Fig. 2. Limitations of the results listed in Table 2 can be summarized as follows: The method used for determining M provides reasonably good information about local atmospheric particulate content and the results obtained by its application agree fairly well at our urban site with those obtained by weighing the samples obtained by the filtration of a certain volume of air through a paper filter for 34 h in an electrobalance. Nevertheless, in certain aspects, it can be considered particularly coarse.
Table 1. Correlation coefficients r between luminance of the diffuse sky light L and the inverse of its corresponding degree of polarization p measured in white light at the zenith and at 90” from the sun and at several sun elevations h (n is the number of pairs of values) h(“) 5 10 15 20 25 30 35 40 45 50 55 60
r(L,,
l/P,)
0.79 0.75 0.75 0.84 0.86 0.90 0.87 0.84 0.83 0.83 0.82 0.72
r(Lm
l/P,,)
0.79 0.77 0.75 0.85 0.89 0.9 1 0.89 0.88 0.86 0.88 0.86 0.75
n
89 130 197 279 411 425 341 271 252 229 148 88
59-l
of sky light in white light
Luminance and polarization
l-
’
!
.
.
I
l
’
:
:
2
4
6
6
10
12
14
16
INVERSE OF THE DEGREE OF POLARIZATION
Fig. 1. Inverse of the degree of polarization of diffuse sky light vs luminance. both measured at the zenith in white light, and at a solar elevation of 30”.
Table 2. Correlation coefficients r of particulate mass per unit volume M against luminance and degree of polarization of diffuse sky light measured in white light at the zenith and at 90” from the sun, at a sun elevation of 30” (n is the number of pairs of values)
r W,. Ml r(Ls.0. M) r (p, M) r(p90.
W
r
n
0.70 0.71 - 0.70 -0.72
425 425 425 425
However, measurements have been performed at ground level. For these and other reasons, correlations of M against optical parameters can only be regarded as an estimation of the important influence of nonmolecular scattering on the spatial distribution and polarization of sky light. Again, the use of the Milch-Tikhanovskii semiempirical formula (Stamov, 1972) has been investigated in order to relate zenith polarization to that obtained at 90” from the sun
Pz =
pyo sin4 * 1 - p9()cos4@
where 1/1is the scattering angle. In the course of this work, experimental data of pro have been substituted into (1) obtaining values of pz that do not depart markedly from those measured. The corresponding correlation coefficient between
measured and calculated values is I = 0.89 for 2926 pairs of values. Hence all the studied characteristics of these parameters and their mutual relationships corroborate previous reported results obtained at three wavelengths in the visible spectrum.
3.2. Luminance due to polarized light The luminance due to polarized light is equal to the product of total luminance and the corresponding degree of polarization. This parameter is denoted by Lp. Subscripts ‘z’ and ‘90’ have the same meaning. The diurnal evolution of Lp,departs markedly from that of Lp,,: in most cases, Lp, decreases and Lp,, increases with increasing h. This feature is due to the peculiar diurnal behaviour of p,, pgo, L, and L,,. As the sun elevation becomes greater, L, tends to increase much more rapidly than Lye but the precipitous decrease of pz compared to that of pgo produces the observed behaviour. So, in the middle of the day close to the local noon, Lp,turns out to be rather lower than Lp,, . However, in the early morning and evening, Lp, and Lp,, exhibit very similar values. At sun elevations ranging from 5” to 15” the lowest values of Lp,, are usually reached, as the corresponding values of luminance are also very low (see Fig. 3). At the reference sun elevation (h = 30”) Lp, and Lp,, scarcely vary from day to day. This feature is less marked at values of h >50”and ~15”. As above, no definite seasonal dependence of Lp
values is observed. On the other hand, the possible influence of M on these parameters is found to be negligible.
598
c.
25
BELLVER
50
75
100
PARTICULATE POLLUTION
125
lpg m-al
Fig. 2. Particie mass per unit volume vs luminance ofdiffuse sky light measured in white light at 90” from the sun and at a solar elevation of 30”.
Fig. 3. Typical diurnal evotution of the luminance due to polarized iight, u Determinationsat the zenith, a determinations at 90” from the sun.
The remarkable changes of sky illumination and potarization that take place during short time intervals before and after sunset can be summarized as follows: A rapid decrease in luminance as the sun approaches and sinks below the horizon is found: values of luminance decrease more than SOY{,when the sun elevation diminishes by only I’.. During these months, the maximum polarization throughout the day was found at sun elevations ranging from 2.5” to - 2.5’. On most occasions (i.e. almost 60 days), the maximum was found when the sun was on the horizon (h = 0”). Note that values of the degree of poIari~tion ZZ.+ 0.80 have never been measured at our urban site. Moreover, regular behaviour of p during the period from 5” to - 5” is observed and no secondary maxima were detected. 3.4. Ruhenson empiricul formula
eletiations
One of the empirical formulae developed by Rubenson (Kartschaguin, 1925: Stamov, 1972) allows us to evaluate the diurnal evolution of the degree of polarization at 90” from the sun
Lummance and polarization of the sky at dusk have been measured for a total of 73 dates during the autumn-winter months from 1980 to 1982. Measurements were carried out at sun elevations ranging from 5” to -5”, at l”, and even at 0.5 intervals. As above, measurements were performed in the direction of the zenith and at 90” from the sun, except when the sun is on the horizon, since the two points coincide.
In this expression, x is the time (in h) between the focal noon and the instant of the measurements, a, b and k being three parameters that vary from day to day. In generat, small discrepancies between measured and calculated values of psO are observed. The cor-
3.3. l~eus~re~e~ts
d~f~~g
twi~~g~t and at
low
sun
599
Luminance and polarization of sky light in white light responding correlation coefficient (r = 0.75) is lower than that obtained by applying the MilchTikhanovskii formula. 3.5. Rural photo-polarimetric determinations Together with urban measurements, a much smaller set of determinations of L, I!+,,, pZand pso were made at a rural location close to the village of Sanlucar la Mayor, 18 km W of Seville, during the summer of 1980. The behaviour exhibited by all these parameters is similar to that observed at the urban site showing regular diurnal evolution curves. The main result was the occurrence of very high values of the degree of polarization close to 0.90. Values of 0.88 and 0.86 were found during the evening twilight. These extremely high values of polarization, characteristic of very clear atmospheres, like those of the Australian outback (Adams, 1981), are very difficult to find in urban areas. It should be mentioned again that values of p higher than 0.80 have never been measured at our urban site over a period of 5 years. 3.6. Positions of maximal polarization It is well known that all the discrepancies between the polarization values calculated from Rayleigh’s theory and those experimentally found are covered by the general term known as ‘polarization defect’. One of the most noticeable features of the defect is the phenomenon of neutral points (where polarization vanishes) occurring in directions different from those predicted. Also, a shift in the position of maximal polarization from the theoretical right angles from the sun can be considered as another ostensible feature of this defect. In the course of our work, several determinations of the actual positions of maximal polarization were carried out by exploring the sky regions below and above the theoretical position. These explorations were performed by measuring the degree of polarization over these zones to get a maximum. When the point of maximal polarization was found, the angular distance between it and the predicted position was measured. This angular distance is named 6. Results have shown that 6 always has the same sign. Thus positions of maximum are shifted away from presupposed locations and lie at angular distances
ranging between 90” and 94” to the sun. So, 6 varies from 0 to 4” for all measurements taken at different sun elevations. Acknowledgements-I am indebted to Prof. Dr V. Hernandez for his continuous help and advice. I also thank Prof. Dr J. Lea1 and Prof. Dr R. Marquez for their valuable help.
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Gauthier Villars, Montrouge, France.