On the influence of rough water surfaces on polarimetric investigations of aerosols from space

Adv. Space Res. Vol.2, No.5, pp.33—38, 1983 Printed in Creat Britain. All rights reserved.

0273—l177/83/050033—06$03.OO/O Copyright © COSPAR

ON THE INFLUENCE OF ROUGH WATER SURFACES ON POLARIMETRIC INVESTIGATIONS OF AEROSOLS FROM SPACE T. Prosch, D. Hennings and E. Raschke Instit ut für Geophysik und Meteorologie, Der Universitdt zu Koln, F.R.G.

ABSTRACT The equation of radiative transfer is solved for the complete Stokes’ vector in order to study the polarization of solar radiation on top of a turbid atmosphere. The surface characteristics (bidirectional anisotropy and polarization properties of randomly oriented water surface elements) are contained in the lower boundary condition of the integro-differential equation. Results of surface model calculations are compared with polarimeter measurements of a natural scenario. On top of the atmosphere the degree of polarization is found to depend generally on the turbidity of the atmosphere. The degree of polarization reaches its maximum in the vicinity of the angle of specular reflection on the water surface, if the sun’s zenith distance is about the Brewster’s angle According to the model calculations observation angles can be found where the degree of polarization does not depend on the surface roughness Apparently these angles have to be preferred for determination of the atmospheric turbidity INTRODUCTION Meas~uringspectral radiance by satellite borne systems has been proved as an excellent tool to determine atmospheric parameters and surface characteristics For example temperature profiles, water vapor content, ozone concentration, etc are determined on a global scale by this technique and reliable data retrieval procedures are available However, comparing data of different types of instruments one often finds discrepancies in the retrieved parameters Reasoning why differences are unavoidable one has to have in mind that two aspects might play important roles (I) Spectral and spatial responses of radiometers are different (2) An absolute calibration has to be provided and inflight calibration over a longer period of time brings up problems like degradation of sensor elements, contamination of optical components, etc. Although many successful attempts were reported to improve this situation by comparing satellite data with ground truth measurements and correcting the retrieved parameters by certain algorithms, the basic problem still remains. One method to avoid absolute calibration and related problems and to make measurements from different instruments more comparable consists in determining ratios or normalized differences and to exploit this kind of data. In optics the transversality of electromagnetic waves can be used to define a measuring technique avoiding absolute calibration: polarimetry. However, the advantage of relative measurement is accompanied by more complicated computation schemes since the solar scattering phase function in case of radiance calibration has to be replaced by 16 elements phase matrices in case of algorithms which are suitable to evaluate

33

34

T. Prosch, D. Ilennings and E. Raschke

polarization data. Positively spoken: polarization data give a deeper insight into s’-attering processes having more parameters involved in the mathematical representation in comparison to radiance formulations only.

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Fig. 1: Blockdiagram of the imaging polarimeter, which has been developed at the Institute of Geophysics and Meteorology, Cologne. Quantitative data are acquired by analog/digital converters and related electronic devices, realtime false color images are generated by color-TV—technique.

Fig. 2: The imaging polarimeter installed on board an airplane of DFVLR (Apr. 82) Therefore some efforts during recent years consisted in developing appropriate evaluation and data inversion algorithms to determine atmospheric and surface parameters from polarization measurements (Santer, Herman, 1982). A promising prospectus of the method is to be seen in the access to particulate parameters of suspended scatterers as it is shown for example by Kuriyan, Phillips and Wilson (1974) or Pearce (1979). However, satellite data inversion techniques of polarization data aiming at aerosol concentration, refractive index and size distribution can only be applied effectively with some preknowledge about surface

Rough Water

Surfaces on ~

35

characteristics. To display the influence of highly anisotropic polarizing reflectors on polarization measurements from space, model calculations are presented. Ground based measurements indicate that the model assumptions seem to be realistic. DEFINITIONS

To avoid confusions comparing data presented in this paper with results of other authors, the definitions of the basic parameters are given. The Stokes’ vector of a completely polarized wave is defined according to the representation It

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—

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MODEL CALCULATIONS

-

ASSUMPTIONS

To calculate the degree of solar radiation on top of a plane parallel atmosphere the Stokes’

vector equation of radiative transfer is solved according to a computation scheme given by Eschelbach (1972) which bases on the Gauss—Seidel iteration method. The phase matrix represents the properties of Rayleigh scatterers and polydispersed spherical Mie scatterers (Deirinendijan, 1969) and is calculated by an algorithm given by Quenzel (1976). The incoming radiation on top of the atmosphere is considered as monochromatic and unpolarized. At the bottom of the model atmosphere the downwelling~radiation is reflected taking into account reflection and polarization properties of a rough Fresnel surface, whose slope probability density function is modelled according to Cox and Munk (1956) The basic assumption consists in a linear relationship between the wind speed and the variance of a binormal distribution function (Gaussian type). Wind direction, multiple reflections, hiding effects and white cap generation at higher wind speeds are not treated within this model. Upwelling radiation from scatterers below the water surface is also neglected. Although these simplifying assumptions are believed to lead to erroneous results, specially at large zenith distances, ground based measurements indicate

that the differences of theoretical and experimental data are less than o.1 in degree of polarization (ref. Fig. 3 and 4), when the polarization is measured above clear, deep water. TECHNIQUE OF MEASUREMENT The polarization of solar radiation reflected from rough water surfaces was measured at a wavelength of 55o nm by an electronic imaging polarimeter. This type of instrument has been developed to generate false color images of a scenario. Polarization information is carried by hue and tint, radiance information is related to the screen luminosity. Quantitative data are acquired by analog/digital converters and digital signal processing is accomplished by a minicomputer system. Advantages of the system are: -

real time display of polarization information scenario identification.

The polarimeter has been used for ground based measurements and has been flown on an aircraft. Since the instrument is built up without mechanical scan parts, it is believed that this measuring method becomes of special interest for space applications. Fig. 1 shows the block— diagram of the polarimeter and Fig. 2 the equipment installed in an aircraft. MEASUREMENT RESULTS Polarization measurements of rough water surfaces are shown in Figs. 3 and 4. In both cases the sky illumination was quasi-uniform due to a low stratus layer This kind of situation is preferably suited to study the effect of the water surface itself and to obtain measurements

36

T. Prosch, 0. Hennings and E. Raschke

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Fig. 3: Isopleths of the degree of polarization measured on 5 Aug 1981, Oleftalsperre/Eifel with quasi-uniform sky illumination (stratus layer). Image centered at about Brewster’s angle. Wind 1. X = 55o nm. The low values seen speed 1 ms—right part are due to the depolari— in the ~lower zation properties of light scattered from the lake bottom.

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Fig. 4: Mean values (diamonds) and stan— dard deviations (bars) of the degree of polarization extracted from image data of Fig. 3. Model calculations results (circles) are given for two wind-speeds, 1 ms—1 and 7 ms1, taking into account uniform sky illumination.

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Fig. 5: Relative radiances of light scattered by a turbid atmosphere with a rough water surface as lower boundary condition

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which can be compared with model calculation results without treating radiation transfer in an atmosphere of several unknown constituents. MODEL CALCULATIONS Basing on the model calculations — as described in the section MODEL CALCULATIONS ASSUMPTIONS - several cases were studied. Figs. 5 and 6 display radiance and degree of polarization isopleths. On top of the atmosphere two relative maxima in the degree of polarization

Rough Water Surfaces on Polarimetric Investigations

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Fig. 6: Degree of polarization of light scattered by a turbid atmosphere, model parameters as in Fig. 5.

Fig. 7: Degree of polarization of light scattered by a turbid atmosphere with a rough water surface as lower boundary condition. Same parameters as in Fig. 6, except: Solar zenith distance G~= 55.8°.

TOP 3o Fig. 8: Degree of polarization of light scattered by a turbid atmosphere with a depolarizating Lambert surface as lower ~?d;7e1~e~m~

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of the upwelling radiation can be seen: one relates to the sun reflex on the water surface, whereas the other one is about perpendicular to the direction of incoming light and relates to Rayleigh and Mie scattering properties. Fig. 7 shows the degree of polarization with sun zenith angle at about Brewster’s angle. In comparison to Fig. 8, where the lower boundary condition of a rough Fresnel surface is replaced by boundary conditions of a depolarizing Lambert surface of a similar albedo, one finds a significant increase of the degree of polarization in the vicinity of the sun glint. Varying the wind speed in the model calculations, one finds - as it is illustrated in Figs. 9 and 1~— that the polarization of the upwelling radiation depends apparently on the surface roughness. Far off the sun glint angle the in—

38

I. Prosch, 0. Hennings and E. Raschke

fluence of the roughness of a water surface can be considered as a minor effect. As a rather strange result (ref Fig 9 and 10) there apparently exist angles near the sun reflex angle, where the degree of polarization does not depend on the surface roughness at all Additional model calculations should give a more detailed analysis of that properties. CONCLUDING REMARKS Polarimetry from space offers the advantage of a measuring technique without the necessity of absolute calibration As model calculations indicate, the degree of polarization - one of several measurable parameters — depends on the measuring geometry, on the turbidity of the atmosphere and on the reflection properties of the surface. In case of water surfaces polarization and reflection characteristics can be modelled Deriving the surface roughness parameter by an independent measuring technique Ce g micorwave scatterometer) the degree of polarization can be described as a function of atmospheric parameters only In case of unknown surface roughness the polarimeter geometry could be adjusted to angle intervals, where the surface roughness effect is small compared with the influence of atmospheric scattering processes. ~

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Fig. 9: Degree of ploarization on top of the atmosphere the and principal plane, atwind two different optical near depths three different speeds. Solar zenith angle oo (marked by arrow) is close to Brewster’s angle of water (53 deg).

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REFERENCES R. Santer, M. Herman, 1982: Aerosol properties from polarized reflected solar radiances; Ann. Met. 18, llo-112 J.G. Kuriyan, D.H. Phillips, 1974: Determination of optical parameters of atmospheric particulates from ground-based polarimeter measurements; Quart. J. Roy. Met. Soc. loo, 426, 665—677 6. Eschelbach, 1971: A direct method for the integration of the equation of radiative transfer in a turbid atmosphere; J. Qu. Spectr. Rad. Tr. 21, 757-765 D. Deirmendijan, 1969: Electromagnetic scattering on spherical polydispersions; Elsevier, NY H. Quenzel, 1976: Mie phase matrix routine; priv. comm. C. Cox, W. Munk, 1956: Slopes of the sea deduced from photographs of sun glitter; Univ. of Cal. Press, Berkeley W.A. Pearce, 1979: Influence of scatterer size distribution from single scattering matrix data, in: Light scattering by irregularly shaped particles; ed. D.W. Schuermann, Plenum Press, NY, 3o7-318