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Sunglint from the Ocean: Cox and Munk 50 Years Later

35 m. 25 m. Sunglint from the Ocean: Cox and Munk 50 Years Later. Wenying Su Center for Atmospheric Science, Hampton University Thomas Charlock and Ken Rutledge NASA Langley Research Center. Sun Glint: Specular Reflection.

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Sunglint from the Ocean: Cox and Munk 50 Years Later

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  1. 35 m 25 m Sunglint from the Ocean:Cox and Munk 50 Years Later Wenying Su Center for Atmospheric Science, Hampton University Thomas Charlock and Ken Rutledge NASA Langley Research Center

  2. Sun Glint: Specular Reflection • Flat sea: mono-directional (d–function) specular reflection... • which is never seen in practice, because... • wind roughens the sea surface... • which creates capillary waves... • which reflect solar beam into many angles not just one. • Thus, the d–function reflection pattern spreads out as seen here. Scripps Sunglint Seminar

  3. Sea Surface Slopes Change Sunglint Pattern Scripps Sunglint Seminar

  4. Sun Glint: Good News, Bad News • Bad news: avoided by almost all current & past satellite remote sensing instruments • saturates or even blinds them • above their dynamical response range • instruments tilt away or shut down • data normally discarded (even from MODIS) • Good news: bright lamp at the surface • transmission measurement easiest to interpret • Kleidman et al (2001): use MODIS sunglint regions to retrieve water vapor column • Kaufman et al (2002): use MODIS sunglint regions to retrieve aerosol absorption • May be able to retrieve CO2 column amount using sunglint at 1.5/2.2 mm wavelengths Scripps Sunglint Seminar

  5. Cox & Munk (1954): Measuring Sunglint to Study Sea Surface Roughness • Width of glint pattern indicates maximum wave slope • Measureddensity at each pixel in defocused sunglint photographs • Related this to probability of occurrence for the wave slope defined by that pixel’s geometry • Described probability distribution of sea slopes (within 2.5 standard deviations) by a 2D Gram-Charlier distribution with two skewness coefficients and three peakedness coefficients • Solar zenith angles  35°; neutral, positive stability (air sea temperature difference) • Widely used by radiative transfer modelers today!

  6. 2D Gram-Charlier Distribution c, u are the crosswind and upwind root mean square slope components.  and  are defined as: =zx/c=zy/u zx and zy are the crosswind and upwind components of slope. The total mean square slope given by Cox and Munk (cm) is: cm2=c2+u2=0.003+5.1210-3U The skewness coefficients are: c21=0.01-0.0086U, c03=0.04-0.033U The peakedness coefficients are: c40=0.40, c22=0.12, c04=0.2 Scripps Sunglint Seminar

  7. Cox/Munk Sea Surface Roughness Measurements (cont) • solid curves: observeddashed curves: Gaussian fit • x-axis scale is normalized sea slope, =zx/cross and =zy/up • heavy vertical segments show corresponding tilts 5°, 10°, …, 25° for a wind speed of 10 m/s • note skewness in lower curve crosswind upwind Scripps Sunglint Seminar

  8. Cox/Munk Sea Slope Probability Distribution • nearly Gaussian → Gram-Charlier • skewed from Gaussian in up/downwind direction; skewness increases with wind speed • peaked than Gaussian in crosswind direction; peakedness is barely above the limit of observational error • mean square slope increase linearly with wind speed • primary axis closely aligned with wind direction • ratio of upwind to crosswind mean square slope ranges from 1.0 to 1.9 • oil slicks tend to suppress the shorter waves, reduce mean square slope by a factor of 2 to 3 Scripps Sunglint Seminar

  9. Microscale  Macroscale • Cox/Munk pioneered method of using macroscale sunglint photographs to get microscale slope distribution • Whether this slope distribution always provides a correct macroscale image from a calibrated radiometer hasn’t been tested • mainly because radiometers would need to have such a large dynamical range • Why might it not work? • All Cox/Munk photos were for solar zenith angles < 35°...but • reflectance a strong function of solar geometry, increasing rapidly as sun ––> horizon • ...so, C/M high-sun photographs might cause bias in the derived mean square slope Scripps Sunglint Seminar

  10. Sea Surface Roughness Measurements ACM* * After Cox Munk Refractive laser slope gauge (1980+): • Slopes determined from refraction of light passing from an immersed laser source through the water-air interface to a receiver above the water • Greater range of stability considered than C/M: found that mean square sea slope increases with negative stability at roughly the same rate as it decreases with moderately positive stability Scripps Sunglint Seminar

  11. Sea Surface Roughness Measurements ACM Sea surface radar backscatter (1980+): • prompted by SeaSat (1970’s) and possibility of satellite radar remote sensing of ocean surface winds • Gram-Charlier distributionsis valid only in the range of small slopes • a new probability distribution function (PDF) is derived over the full range of sea surface slopes • slope peakedness generated by nonlinear wave-wave interactions in the range of gravity waves • slope skewness generated by nonlinear coupling between short waves and underlying long waves Scripps Sunglint Seminar

  12. Sea Surface Roughness Measurements ACM Polarimetric microwave measurements (1980+) • sea surface microwave brightness temperature is determined by surface waves of different scales • analyze polarized microwave radiation emitted by sea surface at several viewing angles and frequencies • convert observed brightness temperatures to the mean square slope Scripps Sunglint Seminar

  13. Cox and Munk results versus others? Some new results agree with Cox/Munk, some don’t… • largest reported differences from Cox/Munk mean square slopes is a factor of 3 (Laser slope gauge) • Dependence on stability • The dependence of skewness and peakedness on stability was also studied • skewness is very weakly correlated with stability • peakedness is much more strongly correlated and tends to increase with negative stability Scripps Sunglint Seminar

  14. Current State of Theoretical Calculations of Ocean Reflectivity • All calculations are based on Cox/Munk plus Fresnel reflection equations • What assumption does this imply? - Fresnel equations assume radiation wavelength much smaller than capillary wavelengths (geometric optics) - Sea surface not curved; made up of flat facets - Mean sea surface is flat - No shadowing • What improvements have been made? - Shadowing factor • In what parameter regions will current calculations be likely to break down? - Large SZA Scripps Sunglint Seminar

  15. 35 m 25 m CERES Ocean Validation Experiment (COVE) Site Located 25 km off the coast of Virginia Beach Rises up to 35 m from ocean surface Sea depth is 11 m Scripps Sunglint Seminar

  16. I fly out by Helicopter! Scripps Sunglint Seminar

  17. COVE Instrumentation • Up- and down-looking pyranometers, pyrgeometers • pyrheliometer on a solar tracker • Multi-Filter Rotating Shadowband Radiometer • Cimel sunphotometer (part of AERONET ) • GPS column water vapor • met obs: temperature, humidity, pressure, wind speed, wind direction • NOAA provides measurements of • wave height • dominant and average wave period • swell height • large scale wave steepness • water temperature Scripps Sunglint Seminar

  18. My Instrument at COVE: SP1A for measuring ocean bidirectional reflectance Scripps Sunglint Seminar

  19. Elevation (deg) AC BC Diameter (m) 2 664 663 266.00 12 111 109 9.00 22 62 57 2.80 32 44 37 1.40 42 35 26 0.89 52 29 18 0.65 62 26 12 0.52 72 24 8 0.45 90 23 0 0.40 SP1A at COVE: Sun Glint Measurement Scripps Sunglint Seminar

  20. Reflectance Distribution Scripps Sunglint Seminar

  21. Simulations of Measured Sunglint at COVE • Radiative transfer model used: "6S" (Second Simulation of Satellite Signal in the Solar Spectrum) • uses Cox-Munk distribution of wave slopes to parameterize the effect of wind on sunlight reflection by the sea • Compare measured radiance distributions around the sun glint region for clear sky conditions with "6S". The input data needed for 6S include: • Aerosol optical depths (AOD) for COVE site (from AERONET) • Pigment concentrations (from SeaWiFS) • Wind speed and direction (measured once/minute at COVE) • All results provided here are for 500 nm Scripps Sunglint Seminar

  22. Different Mean Square Slopes: SZA=58o cm2is the mean square slope given by Cox and Munk Red: cm2; Blue: cm2/2; Green: cm2 *2 Scripps Sunglint Seminar

  23. Different Mean Square Slopes: SZA=68o Red: cm2; Blue: cm2/2; Green: cm2 *2 Scripps Sunglint Seminar

  24. Different Mean Square Slopes: SZA=78o Red: cm2; Blue: cm2/2; Green: cm2 *2 Scripps Sunglint Seminar

  25. Different Peakedness CoefficientsSolar Zenith Angle=58o Red: C/M peak; Blue: C/M Peak/2; Green: C/M Peak*2 Scripps Sunglint Seminar

  26. Sensitivity Study: Summary • For SZA of 58o and 68o, and for the wind speeds considered in our study, the simulated maximum reflectances at the specular point are in reverse proportion to the mean square slopes, but at different ratios (1.5-2). • For SZA of 78o, and for wind speed ranging from 2-8 m/s, maximum reflectance happens at the mean square slopes given by Cox and Munk. Increasing or decreasing mean square slopes gives smaller reflectances • Changing sea slope peakedness by up to a factor of two has at most a 10% effect on max reflectance at the specular point. • 6S reflectance distributions are not sensitive to the skewness coefficients. Scripps Sunglint Seminar

  27. Reflectances of Jan. 6, 13 UTC Measured Simulated Measured (a) and simulated (b) reflectances. Solar Zenith Angle (SZA) is 83.1 and Solar Azimuth Angle (SAA) is 124.7. Wind speed is 5.8 m/s and wind direction is 251.4. Aerosol Optical Depth (AOD) is 0.056. Scripps Sunglint Seminar

  28. Reflectances for Jan. 6, 17UTC Measured Simulated Measured (a) and simulated (b) reflectances. SZA is 59.3 and SAA is 178.0. Wind speed is 4.9 m/s and wind direction is 244.5. AOD is 0.056. Scripps Sunglint Seminar

  29. Influence of Wind Speed on Sun Glint distribution (a) (b) Observed reflectance distributions for Jan. 10 and 11 at 17:30 UTC, SZA is about 58o, wind speeds are 4.8 (a) and 0.6 (b) m/s. AODs are 0.033 and 0.036. Scripps Sunglint Seminar

  30. Reflectance vs. Azimuth at Specular Zenith Angles (a) (b) • for 13:30 UTC, Jan. 6 2001 at view elevation angle of 12o when SZA is 78.4o ((b) for 17:00 UTC, Jan. 6, 2001 at view elevation angle of 32o when SZA is 59.3o Scripps Sunglint Seminar

  31. Normalizing to the Maximum Reflectance (a) Normalized reflectances for 13:30 UTC, Jan. 6 2001 at view elevation angle of12o when SZA is 78.4o (b)Normalized reflectances for 17:00 UTC, Jan. 6 2001 at view elevation angle of 32o when SZA is 59.3o Scripps Sunglint Seminar

  32. Ratio of Maximum reflectances (RM) Define RM as the ratio of observed maximum reflectance to simulated maximum reflectance at the specular viewing zenith angle. At SZAs of 58o and 68o and the wind speed range that we considered, the peak reflectance is in reverse proportion to mean square slope 2, thus : RMcm2/2 Scripps Sunglint Seminar

  33. 12o Wind Speed and RM • RM increases with wind speed. • RM decrease with increasing view elevation angles. 22o 32o Scripps Sunglint Seminar

  34. Width of Sun Glint Width=WidthL+WidthR The observed sun glint covers a larger region than what is simulated. Scripps Sunglint Seminar

  35. Stability Relationship between cm2 normalized mean square slope and stability given by Shaw and Churnside (sc2) is: sc2/cm2=1.42-2.80Ri (-0.23<Ri<0.27) sc2/cm2=0.65 (Ri0.27) Where Ri is the Richardson number, given by Ri=gTa-wZ/TwUz2 Maximum RM is found at neutral stability Scripps Sunglint Seminar

  36. Effect of Stability on Mean Square Slope Shaw and Churnside: sc2>cm2 for Ri<0.15, sc2<cm2 for Ri>0.15. Us: • No dependence of 2/cm2 on Ri. • 2 < cm2 for both negative and positive stabilities • maximum deviation happens at neutral stability, except for very calm conditions. Scripps Sunglint Seminar

  37. Future Work • Including Shadowing - Nakajima included shadowing factor - Wu’s formula of wave shadowing • Wavelength dependence Scripps Sunglint Seminar

  38. Conclusions • 6S-model-simulated reflectance distributions (using Cox and Munk slope statistics) around sun glint region capture the measured distributions....but the measured sun glint is • more intense, and • covers a larger area than simulation • The differences between the observed and simulated maximum reflectance • increase with increasing wind speed, and • are larger for smaller viewing elevation angles Scripps Sunglint Seminar

  39. Conclusions (cont.) • At very low wind speed, the reflectance distribution is close to what classical Fresnel flat-surface reflection equation predicts, with the largest reflectance near the specular point... • while as wind speed increases, the largest reflectance shifts to the horizon. • Differences between observed and simulated maximum reflectance are largest at neutral stability. • Our measurements do not show a dependence of mean square slope on stability. Scripps Sunglint Seminar

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