contributions Radiance distribution over a ruffled sea: from glitter, sky, and ocean

Transcription

1 Radiance distribution over a ruffled sea: from glitter, sky, and ocean contributions Gilbert N. Plass, George W. Kattawar, and John A. Guinn, Jr. The upward radiance just above the ocean surface and at the top of the atmosphere is calculated for a realistic model including an ocean surface with waves. The separate contributions of the sun glitter, the reflected sky radiance, and the upwelling photons from the ocean are calculated. The Monte Carlo method takes account of both Rayleigh scattering by the molecules and Mie scattering by the aerosols as well as molecular and aerosol absorption in the atmosphere. Similarly, in the ocean, both Rayleigh scattering by the water molecules and Mie scattering by the hydrosols as well as absorption by the water molecules and hydrosols are considered. Separate single-scattering functions are used for the aerosols and hydrosols calculated from the Mie theory. Both the reflected and refracted rays, as well as the rays that undergo total internal reflection, are followed at the ocean surface. The wave slope is chosen from the Cox-Munk distribution. The upward radiance just above the ocean surface outside of the sun glitter region is dominated by the reflected sky radiation from the horizon to a nadir angle of observation of from 680 to 23 depending on the azimuthal angle and the solar zenith angle; the upwelling photons from the ocean dominate over the remainder of the hemisphere, except in the region of the sun glitter which centers around the mirror image of the sun on a calm ocean. It is possible to answer various questions about the interaction of light with the ocean from the quantitative results presented here. 1. Introduction Although the majority of the earth's surface is covered by water, there has been remarkably little research done on the influence of various atmospheric and oceanic properties on the quantitative interaction between sunlight and the oceans. What is the distribution of the sunlight reflected from the ocean surface with waves? What is the angular distribution of the radiation within the ocean and what fraction of the radiation enters the upwelling stream and passes back into the atmosphere through the ocean surface? At what angles can an observer above the ocean surface see down into the ocean instead of seeing radiation reflected by the surface? Why can an observer in an airplane seated on the sunlit side easily see the shadows of isolated cumulus clouds upon the ocean, while an observer on the other side of the plane cannot see any trace of such shadows? A qualitative answer to some of these questions is given by Minnaert 1 in his delightful and provocative book on various types of phenomena about light and color. Both the theoretical and experimental knowledge about light in the oceans is reviewed by Jerlov 2 and Jerlov and Nielsen 3 in their excellent books. The path of a solar photon through the atmosphere The authors are with the Texas A&M University, Physics Department, College Station, Texas Received 14 June and ocean can be very complex. It may undergo absorption and multiple scattering by aerosols and atmospheric molecules, reflection and refraction at the ocean surface, and further absorption and multiple scattering by hydrosols and water molecules of the ocean. Additional complexity arises from scattering and absorption by the ocean floor, from waves on the ocean surface, and from the refraction and reflection (including total internal reflection at some angles) of the upwelling light at the ocean boundary. Various techniques have been proposed to obtain numerical solutions of the equations of radiative transfer including multiple scattering. The only successful technique that has so far been used for a model, of a system as complicated as that of the earth's ocean-atmosphere is the Monte Carlo method. Some of the advantages are: all relevant orders of multiple scattering are taken into account; accurate solutions can be obtained for optically deep layers that may be inhomogeneous; interior radiances can be calculated; waves on the ocean surface can be taken into account; highly asymmetric phase functions for the hydrosols and aerosols are easily incorporated into the theory. The basic Monte Carlo method has been described by Plass and Kattawar. 4 5 The method has been extended to calculate the flux and radiance in an atmosphere-ocean system, 6-8 to include the Stokes vector so that the polarization and ellipticity of the radiation is obtained, 9 and to include the effect of waves on the December 1976 / Vol. 15, No. 12 / APPLIED OPTICS 3161

2 lot ANGLE Fig. 1. Total upwelling radiance at the top of the atmosphere (crosses) and just above the ocean surface (solid curve) as a function of the nadir angle of observation for the sun at the zenith. The three contributions to the upward radiance just above the ocean surface are shown separately: (1) sun glitter (open circles); (2) reflected sky radiance (triangles); (3) upwelling photons from ocean (solid circles). Waves appropriate for a 20-knot (37.1-km/h) wind are assumed. A wavelength of 0.46 um is assumed. ocean surface. 10 Raschke 1 " has considered the effect of ocean waves. Gordon and Brown 1 2 have used Monto Carlo techniques to compute the radiation flux in a calm ocean, but their calculations are for either an isotropic radiance distribution or a solar beam without sky radiation incident on the ocean; they did not couple the radiation fields of the atmosphere and ocean. In this article a particular model of the atmosphereocean including waves at the ocean surface is used to calculate the radiance just above the ocean surface as well as that at the top of the atmosphere. The radiance is divided into parts so that the relative contributions of the sun glitter, reflected sky radiance, and upwelling light from the ocean may be studied. 11. Method of Calculation The method of calculation is identical with that described by Plass et al. 10 and thus will not be repeated here. All calculations were done at a wavelength of 0.46 Aim, which is near the wavelength of maximum transparency for clear ocean water. The absorption and scattering cross sections used are those of the clear ocean model of Kattawar et al. 9 The distribution of wave slopes in all cases was the one appropriate for a wind speed of 20 knots (37.1 km/h), as given by Cox and Munk. 13 The ocean was assumed to have an optical depth of ten with a totally absorbing surface at the bottom; this is equivalent to an infinitely deep ocean as far as any observed effects on the radiance above the ocean surface are concerned. The atmosphere is assumed to be without clouds and with an aerosol and ozone distribution given in Ref. 9. Ill. Radiance The results of these Monte Carlo calculations of the radiance are shown in Figs. 1-5 for solar zenith angles Oo ot 00, 15, 320, 570, and 80. The total upward radiance is shown in each case both at the top of the atmosphere and just above the ocean surface. When the *sun is at the zenith, the radiance i azimuthally symmetric, so that the complete radiance distribution is given in Fig. 1. In the other four cases the radiance is given in the principal plane with the solar horizon on the left of the figure, the zenith at the center, and the antisolar horizon on the right. Photons with three different types of history contribute to the upward flux just above the ocean surface. These three contributions are indicated separately in each figure: (1) sun glitter (time-average radiance of photons from direct solar beam reflected from wave facets); (2) reflected sky radiance (photons from the blue sky that have been scattered one or more times in the atmosphere and are subsequently reflected upward by wave facets); (3) upwelling photons from the ocean (photons that entered the ocean and then were scattered one or more times within the ocean into an upward direction such that they passed through the ocean surface back into the atmosphere). First, consider the contribution from the sun glitter to the upward radiance just above the ocean surface. - TOTAL, TOP OF ATMOSPHERE i TOTAL RADIANCE -0-- SUN LITTER ~ OBSERVES JUST ABOVE X- U O REFLECTED SKY RADIANCE UPWELLING OCEAN PHOTONS SURFACE FROM ANGLE - Fig. 2. Same as Fig. 1, except solar zenith angle is 150. The solar horizon is at the left of the figure, the nadir at the center, and the antisolar horizon at the right edge. These curves are for the principal plane ( = and 1800). Z a~ l., I I I, I, I -, I I I I I, I 80 -x-total, TOP OF ATMOSPHERE - TOTAL RADIANCE G9-32' - REFLECTED SKY RADIANCE -4- UPWELLING PHOTONS FROM OCEA ABOVE OCEAN SURFACE ANGLE Fig. 3. Same as Fig. 1, except solar zenith angle is APPLIED OPTICS / Vol. 15, No. 12 / December 1976

3 0- S~ ~ ~~~~~WELN.. OON FRO OCAN o (I 40 W 80 ANGLE- Fig. 4. Same as Fig. 1, except solar zenith angle is B80 TOTAL, TOP OF ATMOSPHERE TOTAL RADIANCE SUN GLITTER OBSERVED JUST REFLECTED SKY RADIANCE SURFACE ---- UPWELLING PHOTONS FROM OCEAN contribution increases rapidly as the horizon is approached. This increase is due to the increased reflectivity of the ocean surface for rays at near grazing incidence and to the greater sky radiance near the horizon compared to the zenith. The reflected sky radiance has a minimum value between the solar horizon and the nadir in all cases when the sun is not at the zenith; for example, the minimum is at a zenith angle 0 = 260 when Oo = 15. The reflected sky radiance is always the dominant factor in the upwelling radiance just above the ocean surface when observing near the horizon, except in those limited angular ranges where the sun glitter dominates. Third, consider the contribution of the upwelling photons from the ocean. This contribution is largely independent of the angle of observation. At a particular angle of observation this contribution decreases as the solar zenith angle increases. Figures 6 and 7 were prepared to show the dominant factor in the total radiance just above the ocean surface over the entire hemisphere (the previous figures only give data for the principal plane). The data for 00 = O are not included in this figure, since it is azimuthally symmetric and can easily be read from Fig. 1, i.e., the sun glitter dominates from 0 < 0 < 300, the upwelling light from the ocean from 300 < 0 < 640, and the reflected sky radiance from 640 < 0 < 90. As the sun moves from the zenith toward the horizon, the region dominated by the reflected sky radiation, marked sky in the figures, increases in size. In this region it is difficult to observe anything within the ocean. It is nat- '0-I 10.4i2l 80 60, , ANGLE - Fig. 5. Same as Fig. 1, except solar zenith angle is 80. When the sun is at the zenith, the maximum glitter is, of course, observed at the nadir; it decreases to 0.1 of its maximum value at a nadir angle 0 of about 410. When 00 = 150 and 320, the maximum value for the glitter is at 0 = 170 and 380, respectively. When Oo = 570, the maximum value is at the horizon because of the increased reflectivity of the water surface at near grazing angles. When 00 = 150, the sun glitter is 0.1 of its maximum value for 0 = 600 and 0 = O and for 0 = 250 and 0 = When 0o = 320, it is 0.1 of its maximum value for 0 = 30 and k = 1800, but does not reach this low a value for 0 = 00 due to the increased reflectance near the horizon. The curves for Oo = 570 and 80 show that the sun glitter increases monotonically from the nadir to the solar horizon. Second, consider the radiance from the sky that is reflected by the ocean surface. At all solar angles this Fig. 6. The right half of the figure indicates the dominant terms in the upwelling radiance for a solar zenith angle 0 = 15, while the left half is for 0o = 32. The nadir is at the center of the figure, while the horizon is at the edge. The position of the reflected sun is indicated. The word sun indicates that the sun glitter dominates, sky that the reflected sky radiance dominates, and ocean that the upwelling photons from the ocean dominate. In the sun glitter region, the next most important term contributing to the total radiance is also indicated. December 1976 / Vol. 15, No. 12 / APPLIED OPTICS 3163

4 Fig. 7. Same as Fig. 6, except for 0o = 570 and 800. the opposite side of the airplane ( = 1800). For the solar zenith angles just mentioned, the upwelling radiation from the ocean dominates the upward radiation over all angles from the nadir to at least 0 = 60. When the cloud shadow falls on the water, there is no effect on the contribution from the sun glitter which does not reach these angles, and the change in the small contribution from the reflected sky radiance (reflection of radiation from the underside of the clouds instead of the blue sky over part of the sky) is insignificant compared to the much larger contribution from the upwelling photons from the ocean. This last contribution is not changed sufficiently in the shadow region to cause the shadow to be noticeable, due to the horizontal diffusion of the photons from the illuminated areas of the ocean into the relatively small shadow regions. When flying over islands and observing from the shady side of the plane, it is quite striking to observe the cloud shadows very clearly when they fall on islands and then to see them suddenly disappear as the shadow moves over the water. ural to look as straight down as possible when attempting to observe details within the ocean. The angular range over which this upwelling radiation from the ocean is dominant, marked ocean in the figures, can be seen from these figures. This range decreases appreciably as the sun sinks toward the horizon. The region dominated by the sun glitter is marked sun in the figures. In addition the next most important contribution to the total radiance is indicated for these regions. The time average of the sun glitter is computed, whereas it is actually composed of flashes of light; thus, in principle, this time varying component could be separated from the steady background radiation. The radiance at the top of the atmosphere is also shown in Figs The radiance is greater at the top of the atmosphere for a given angle of observation than it is at the ocean surface, except for a few angles near the horizon when the sun is also near the horizon. A comparison of these two curves indicates the contribution to the radiance at the top of the atmosphere from scattering processes within the atmosphere itself. These figures answer quantitatively the questions asked at the beginning of Sec. I, at least for this particular model of the ocean and atmosphere. The results should be largely independent of changes in the ocean turbidity. They would, of course, be different for a cloudy day instead of the cloudless atmosphere assumed here. A further comment about the visibility of the shadows of isolated cumulus clouds on the ocean surface. When these are observed from an airplane, they are easily seen on the water surface from the sunlit side of the plane. When the sun is moderately high in the sky, i.e., 00 = 320 or 570 (Figs. 3 and 4), the largest contribution to the total upward radiance is from the sun glitter. Any interruption in this pattern, as by the shadow of a cloud, is very noticeable. The situation is quite different when looking out of IV. Conclusions The radiance is calculated for five different solar zenith angles as observed just above the ocean's surface. The relative contributions from the sun glitter, the reflected sky radiance, and the upwelling photons from the ocean are shown separately. The sun glitter dominates over a region around the mirror angle of reflection whose size depends on the wind speed (and thus the steepness of the wave slopes). Outside of the region of the sun glitter, it is only possible to observe details within the ocean over the region where the upwelling photons from the ocean are the dominant term in the upwelling light. This region extends from the nadir to a nadir angle which may be as large as 680 when the sun is high in the sky. However, this region, where it is possible to observe objects within the ocean from above the surface, becomes much smaller as the sun nears the horizon (Fig. 7). Reflected sky radiation dominates over the remainder of the hemisphere out to the horizon. In this region it is difficult to observe anything within the ocean, since the reflected sky radiation is the major contributor to the total upward radiance. In this region the color of the ocean is determined largely from the color of the sky as reflected by the surface. The color near the nadir is largely determined, on the other hand, by the properties of the ocean water itself including the hydrosol, chlorophyll, and yellow substance concentrations. The research was supported by the Office of Naval Research through contract N C APPLIED OPTICS / Vol. 15, No. 12 / December 1976

5 References 1. M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954). 2. N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968). 3. N. G. Jerlov and E. S. Nielsen, Eds., Optical Aspects of Oceanography (Academic, New York, 1974). 4. G. N. Plass and G. W. Kattawar, Appl. Opt. 7, 415 (1968). 5. G. N. Plass and G. W. Kattawar, J. Atmos. Sci. 28, 1187 (1971). 6. G. N. Plass and G. W. Kattawar, Appl. Opt. 8, 455 (1969). 7. G. N. Plass and G. W. Kattawar, J. Phys. Oceanogr. 2, 249 (1972). 8. G. W. Kattawar and G. N. Plass, J. Phys. Oceanogr. 2, 146 (1972). 9. G. W. Kattawar, G. N. Plass, and J. A. Guinn, Jr., J. Phys. Oceanogr. 3, 353 (1973). 10. G. N. Plass, G. W. Kattawar, and J. A. Guinn, Jr., Appl. Opt. 14, 1924 (1975). 11. E. Raschke, Beitr. Phys. Atmos. 45, 1 (1972). 12. H. R. Gordon and 0. B. Brown, Appl. Opt. 12, 1549 (1973). 13. C. Cox and W. Munk, J. Opt. Soc. Am. 44, 838 (1954). Preliminary CALL FOR PAPERS UNIVERSITY q SURGH THE INSTITUTE OF ELECTRICAL AND ELECTRONIC ENGINEERS THE SYSTEMS, MAN AND CYBERNETICS SOCIETY EIGHTH ANNUAL PITTSBURGH CONFERENCE ON MODELING AND SIMULATION April 21-22, 1977 SPONSORED BY SCHOOL OF ENGINEERING - UNIVERSITY OF PITTSBURGH IN COOPERATION WITH THE PITTSBURGH SECTIONS OF AND THE INTERNATIONAL ASSOCIATION FOR MATHEMATICS AND COMPUTERS IN SIMULATION (FORMERLY AICA) THE INSTRUMENT SOCIETY OF AMERICA THE SOCIETY FOR COMPUTER SIMULATION Special emphasis for the 1977 Conference will include energy, social, economic, and global modeling and simulation as well as papers on all traditional areas of modeling and simulation. Only papers which have not been published previously will be considered. These papers should describe significant contributions which add to the knowledge in a particular area or which describe the origin and progress of research that is being currently conducted. All papers submitted and accepted for presentation at the Conference will be considered for publication in the PROCEEDINGS. There will be a length limitation on all such papers but additional space in the PROCEEDINGS may be purchased at a nominal cost. INFORMATION FOR AUTHORS: Two copies of titles, authors, all authors' addresses, abstracts and summaries should be submitted by January 28, The abstract should be approximately 50 words in length and the summary should be of sufficient length and detail to permit careful evaluation. Identify one author as the correspondent for the paper. All communications will be with this author. Notification of acceptance for presentation will be given by March 4, Instructions and model paper for the preparation of accepted papers will be mailed to each author. The final typed manuscript will be due by April 22, Direct all correspondence to: William G. Vogt or Marlin H. Mickle Modeling and Simulation Conference 348 Benedum Engineering Hall University of Pittsburgh Pittsburgh, Pennsylvania PROCEEDINGS: The Instrument Society of America will publish the 1977 PROCEEDINGS shortly after the conference. Registration will include a copy of the 1977 PROCEEDINGS. PROCEEDINGS of past conferences (1969, 1971, 1973, 1974, 1975, 1976) can be obtained by contacting the Publications Department, Instrument Society of America, 400 Stanwix Street, Pittsburgh, Pennsylvania,