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

35 m

25 m

Sunglint from the Ocean:

Cox and Munk 50 Years Later

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

March 6, 2002 Scripps Sunglint Seminar 2

Sun Glint: Specular ReflectionSun Glint: Specular ReflectionSun Glint: Specular ReflectionSun Glint: Specular Reflection

• Flat sea: mono-directional (–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 –function reflection pattern spreads out as seen here.


Sea Surface Slopes Change Sunglint Pattern

Sea Surface Slopes Change Sunglint Pattern


Sun Glint: Good News, Bad NewsSun 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 m wavelengths

Cox & Munk (1954): Measuring Sunglint to Study Sea Surface Roughness

Cox & Munk (1954): Measuring Sunglint to Study Sea Surface Roughness

• Width of glint pattern indicates maximum wave slope

• Measured density 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!


2D Gram-Charlier Distribution2D Gram-Charlier Distribution

c, u are the crosswind and upwind root mean square slopecomponents. 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=c

2+u2=0.003+5.1210-3U

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

⎭⎬⎫

⎩⎨⎧ +−+−−++−+−−−−

⎥⎦⎤

⎢⎣⎡ +−= −

)36(24

1)1)(1(

4

1)36(

24

1)3(

6

1)1(

2

11

)(2

1exp)2(

2404

2222

2440

303

221

221

ηηηξξξηηηξ

ηξσπσ

ccccc

p uc


Cox/Munk Sea Surface Roughness Measurements (cont)

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


Cox/Munk Sea Slope Probability Distribution

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


Microscale Microscale Macroscale MacroscaleMicroscale Microscale Macroscale 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


* After Cox Munk

Sea Surface Roughness Measurements ACM*

Sea Surface Roughness Measurements ACM*

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


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 distributions is 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




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


Cox and Munk results versus others?Cox and Munk results versus others?Cox and Munk results versus others?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


Current State of Theoretical Calculations of Ocean Reflectivity

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


35 m

25 m

CERES Ocean Validation Experiment (COVE) CERES Ocean Validation Experiment (COVE) SiteSite

CERES Ocean Validation Experiment (COVE) CERES Ocean Validation Experiment (COVE) SiteSite

Located 25 km off the coast of Virginia Beach

Rises up to 35 m from ocean surface

Sea depth is 11 m


I fly out by Helicopter! I fly out by Helicopter!


COVE InstrumentationCOVE 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


My Instrument at COVE: SP1ASP1AMy Instrument at COVE: SP1ASP1A

for measuring ocean bidirectional reflectance


Elevation (deg) AC BC Diameter (m) 2 664 663 266.0012 111 109 9.0022 62 57 2.8032 44 37 1.4042 35 26 0.8952 29 18 0.6562 26 12 0.5272 24 8 0.4590 23 0 0.40

SP1A at COVE: Sun Glint SP1A at COVE: Sun Glint MeasurementMeasurement

SP1A at COVE: Sun Glint SP1A at COVE: Sun Glint MeasurementMeasurement


Reflectance Distribution Reflectance Distribution

200

2

)cos(

),,(),,(

dE

dL

ss

vsvs θ

ϕΔθθπϕΔθθρ =


Simulations of Measured Sunglint at Simulations of Measured Sunglint at COVECOVE

Simulations of Measured Sunglint at Simulations of Measured Sunglint at COVECOVE

• 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


Different Mean Square Slopes: Different Mean Square Slopes: SZA=58SZA=58oo


cm2 is the

mean square slope given by Cox and

Munk

Red: cm2;

Blue: cm2/2;

Green: cm2 *2




Red: cm2;

Blue: cm2/2;

Green: cm2

*2




Red: cm2;

Blue: cm2/2;

Green: cm2

*2


Different Peakedness Different Peakedness CoefficientsCoefficients

Solar Zenith Angle=58Solar Zenith Angle=58oo

Different Peakedness Different Peakedness CoefficientsCoefficients

Solar Zenith Angle=58Solar Zenith Angle=58oo

Red: C/M peak; Blue: C/M Peak/2;

Green: C/M Peak*2


Sensitivity Study: SummarySensitivity Study: SummarySensitivity Study: SummarySensitivity 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.


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.

Reflectances of Jan. 6, 13 UTCReflectances of Jan. 6, 13 UTCReflectances of Jan. 6, 13 UTCReflectances of Jan. 6, 13 UTC

Measured Simulated


Reflectances for Jan. 6, 17UTCReflectances for Jan. 6, 17UTCReflectances for Jan. 6, 17UTCReflectances for Jan. 6, 17UTC

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.

Measured Simulated


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.

Influence of Wind Speed on Sun Glint Influence of Wind Speed on Sun Glint distributiondistribution

Influence of Wind Speed on Sun Glint Influence of Wind Speed on Sun Glint distributiondistribution

(a) (b)


Reflectance vs. Azimuth at Reflectance vs. Azimuth at Specular Zenith AnglesSpecular Zenith Angles

Reflectance vs. Azimuth at Reflectance vs. Azimuth at Specular Zenith AnglesSpecular Zenith Angles

(a)for 13:30 UTC, Jan. 62001 at view elevation

angleof 12o when SZA is 78.4o

(a)(a) (b)(b)

((b) for 17:00 UTC, Jan. 6, 2001 at view elevation angle of 32o when SZA is 59.3o


(a) Normalized reflectances for 13:30 UTC, Jan. 6 2001 at view elevation angle of12o when SZA is 78.4o

Normalizing to the Maximum Normalizing to the Maximum ReflectanceReflectance

Normalizing to the Maximum Normalizing to the Maximum ReflectanceReflectance

(b)Normalized reflectances for 17:00 UTC, Jan. 6 2001 at view elevation angle of 32o when SZA is 59.3o


Ratio of Maximum reflectances Ratio of Maximum reflectances (RM)(RM)

Ratio of Maximum reflectances Ratio of Maximum reflectances (RM)(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 :

RMcm

2/2


Wind Speed and RM

Wind Speed and RM

• RM increases with wind speed.

• RM decrease with increasing view elevation angles.

12o

22o 32o


Width of Sun GlintWidth of Sun GlintWidth of Sun GlintWidth of Sun Glint

Width=WidthL+WidthR

The observed sun glint covers a larger region than what is simulated.

RLrefo

RL absWidth /1.0/ )180( =−= ϕ


StabilityStabilityStabilityStabilityRelationship between cm

2

normalized mean square slope and stability given by Shaw and Churnside (sc

2) is:

sc2/cm

2=1.42-2.80Ri

(-0.23<Ri<0.27)sc

2/cm2=0.65

(Ri0.27)Where Ri is the Richardson

number, given byRi=gΔTa-wZ/TwUz

2Maximum RM is found

at neutral stability


Effect of Stability on Mean Square Effect of Stability on Mean Square SlopeSlope

Effect of Stability on Mean Square Effect of Stability on Mean Square SlopeSlope

Shaw and Churnside:sc

2>cm2 for Ri<0.15,

sc2<cm

2 for Ri>0.15.

Us: No dependence of 2/cm

2 on Ri.

2 < cm2 for both negative and positive

stabilities maximum deviation happens at neutral

stability, except for very calm conditions.


Future WorkFuture Work

• Including Shadowing

- Nakajima included shadowing factor

- Wu’s formula of wave shadowing• Wavelength dependence


ConclusionsConclusionsConclusionsConclusions

• 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


Conclusions (cont.)Conclusions (cont.)Conclusions (cont.)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.

Documents

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