Bidirectional Reflectance Distribution Function ( BRDF )

1. Bidirectional Reflectance Function in Coastal Waters And its Application to the Validation of the Ocean Color Satellites Alexander Gilerson1, Soe Hlaing1, Tristan Harmel1, Alberto Tonizzo1, Robert Arnone2, Alan Weidemann2, Samir Ahmed1 1Optical Remote Sensing Laboratory, City College, New York 2 Naval Research Laboratory, Stennis Space Center

2. Bidirectional Reflectance Distribution Function (BRDF) Above water radiometer Water Body • Radiance emerging from the sea, in general, is not isotropic. • Varies directionally depending on viewing and illumination conditions. • Bi-directionality property depends on Inherent Optical Properties (IOP) of the water constituents which are highly variable, especially in coastal environment •  This bidirectional effect needs to be corrected to get standardized parameters suitable for : • Oceanic and Coastal waters monitoring • Calibration-validation of ocean-color satellite data

3. Correction for Bidirectional Reflectance Distribution •  Adjust the remote-sensing reflectance for • Hypothetical configuration of : • Nadir Viewing • Sun at zenith • Current standard BRDF correction algorithm [Morel & Gentili 2002 et. al] : • Optimized for the open ocean water conditions. • Correction is based on the prior estimation of chlorophyll concentration. • But, inappropriate for typical coastal waters usually dominated by sediment or by colored dissolved organic matters (CDOM)

4. BRDF-CORRECTION Algorithm

5. Outline • To analyze Case 2 BRDF, a dataset of remote sensing reflectances typical for coastal (Case 2) water conditions was generated through radiative transfer simulations for a large range of viewing and illumination geometries. • Based on this simulated dataset, a Case 2 water-focused remote sensing reflectance model is proposed to correct above-water and satellite water leaving radiance data for bidirectional effects. • Proposed model is validated with a one year time series of in situ above-water measurements acquired by collocated multi- and hyperspectral radiometers which have different viewing geometries. • With the use of proposed BRDF correction, match-up comparisons of in situ time series and the MODIS satellite data has been improved. 5

6. Theoretical Background Fundamental equation which relates Rrs to optical properties [Morel 2002 et. al]: merges reflection and refraction effects that occur when downward irradiance and upward radiance propagate through the air-water interface f relates the magnitude of the irradiance reflectance just below the surface to IOP Q= bidirectional function W = wind speed ω= single back-scattering albedo ω = bb / ( a + bb )  determined by IOP BRDF correction: Rrs(W,IOP)_corrected Angular Coordinate Convention θv ~ Viewing angle θs ~ solar Zenith φ ~ solar-sensor relative azimuth Set f and Q for Sun at zenith and nadir view

7. Bio-optical model and radiative transfer simulation Obtain Rrs(λ) & equivalent ω(λ) from 500 sets of IOPs to investigate Rrs – ω relatioships for large sets of viewing and illumination geometries. ω = bb / ( a + bb ) can be directly connected to Rrs through modeling 500 sets of IOP Inherent Optical Properties (IOP) Four Components Bio-optical Model Absorption (a) Remote-sensing Reflectance Rrs(λ) Scattering (b, bb) Algal Particles [Chl] Radiative transfer simulations (Hydrolight) Non - Algal Particles [CNAP] CDOM 1053 sets of Viewing & illumination geometries Viewing angle ( θv )0o ~ 80o solar Zenith ( θs )0o ~ 800 relative azimuth ( φ )0o ~ 180o Wavelength: 412,443, 491, 551, 668 nm Particle Scattering Phase Function Varied with particle Concentration & Composition Pure Sea-water Range of input parameters [Chl] = 1 to 10mg/m3 CNAP = 0.01 to 2.5mg/m3 aCDOM = 0 to 2m-1 Generated as random variables in the prescribe ranges typical for coastal water conditions

8. Rrs (λ) vs Single back-scattering albedo (ω) at various illumination and viewing geometries [Gordon 1988, Lee 2002 & Park 2005 ]. Rrs ~ function(ω) with • Rrs~f(ω) relationship also depends on the viewing and illumination geometries. • Spectral dependency of the ω ~ Rrs relationship can be also observed [Gilerson 2007 et.al]. •  Rrs can be fitted to ω with a third order polynomial: coefficients are generated for each set of viewing / illumination geometries as well as for each wavelength. These coefficients are applicable to typical coastal water conditions.

9. CCNY-BRDF correction algorithm Optimized for typical Case-2 water conditions Use of third order polynomial parameterization based on radiative transfer computation for large range of optical properties  generalized expression ω – single backscattering albedo θs – Solar zenith angle θv – Viewing zenith angle φ – Solar-sensor relative azimuth λ – Wavelengths Tabulatedcoefficients based on radiative transfer computation • CCNY algorithm in 2 steps: • (1) From the measuredRrs(θs, θv, φ, λ): Solve and retrieve ω(λ)with the use of the least mean square fitting & tabulated αi (θs, θv, φ, λ) coefficients. • (2) Use the retrieved ω(λ ) in the equation with αi (θs=0, θv=0, φ=0, λ ) coefficients for nadir viewing and illumination to calculate the BRDF-correctedRrs(θs=0, θv=0, φ=0, λ )

10. Statistical Analysis/Comparison of the standard MG (Morel/Gentili) and proposed CCNY Algorithms Based on Simulated Dataset (1/2) Standard Algorithm CCNY Algorithm Dispersion y = 0.93*x – 8.4e-5 (Standard) Regression lines y = 1.00*x – 8.5e-6 (CCNY) AAPD(Standard Algo)=9.5% AAPD(CCNY Algo)=0.6% • The standard use of Case 1-water based BRDF MG correction induce almost 10% uncertainty in the remote sensing reflectance retrieval in typical coastal waters. • The proposed algorithm permit to reduce this dispersion below 1% without adding any bias

11. Statistical Analysis of the Algorithms Based on Simulated Dataset (2/2) • Up to 26% in bi-directional variation is observed addressing the need for a BRDF correction. • Standard MG algorithm: helps, but 57% of the dataset still have relative percent difference more than 5% which is the required accuracy for Ocean Color Sensor • CCNY algorithm: ~98% of the cases have relative percent difference less than 5% CCNY algorithm Standard algorithm Without correction in % • Important need to incorporate Case-2 water based BRDF correction in the current data processing • Possible suitability of CCNY-algorithm to fulfill the Ocean Color Radiometry requirements

12. ASSESSMENT OF BRDF-CORRECTION APPLICATION TO ABOVE-WATER DATA AT LONG ISLAND SOUND COASTAL OBSERVATORY

13. LISCO Site Characteristics LISCO Multispectral SeaPRISM system as part of AERONET – Ocean Color network LISCO [Zibordi et al., 2006] • Identical measuring systems and protocols, calibrated using a single reference source and method, and processed with the same code; •  Standardized products of exact normalized water-leaving radiance and aerosol optical thickness

14. LISCO Site Characteristics Location and Bathymetry Depth in meters (GEBCO data) Water type: Moderately turbid and very productive (Aurin et al. 2010) Bathymetry : plateau at 13 m depth

15. LISCO site Characteristics Platform: Collocated multispectral SeaPRISM and hyperspectral HyperSAS instrumentations since October 2009 LISCO Tower Instrument Panel Retractable Instrument Tower 12 meters

16. SeaPRISM instrument LISCO Instrumentation HyperSAS Instrument • Sea Radiance • Sky Radiance • Downwelling Irradiance • Linear Polarization measurements • Hyperspectral: 180 wavelengths [305,900] nm • Sea Radiance • Direct Sun Radiance and Sky Radiance • Bands: 413, 443, 490, 551, 668, 870 and 1018 nm Data acquisition every 30 minutes for high time resolution time series 16

17. Features of the LISCO site Unique Capability of Making Near-Concurrent Water-Leaving Radiance From Different Viewing Geometries N Instrument Panel W • Both instrument makes measurements with viewing angle, θv = 40o. • Thanks to the rotation feature of SeaPRISM, its relative azimuth angle, φ, is always set 90o with respect to the sun (resulting in water scattering angle range of 132 ~ 145o). • HyperSAS instrument is fixed pointing westward position all the time, thus φ is changing throughout the day and resulting scattering angle range from 110 -175o. • LISCO site instrumentations configuration permits to assess accuracy of the bi-directionality correction of the water leaving radiances. HyperSAS SeaPRISM

18. Above Water Signal decomposition Above-Water Data Processing Down-welling Irradiance LT=Lw+ ρ(W) Li+ Lg Sun Ed Li Total radiance Sky radiance Sun glint radiance θ Li θ Water leaving radiance Sea surface reflectivity Lw Remote-sensing reflectance: Rrs = Lw /Ed Needs to be corrected for the bidirectionality property

19. Comparison of SeaPRISM and HyperSAS Both instrument pointing same direction (within ±10° in Azimuth) For all the viewing geometries Rrs HyperSAS [sr-1] Rrs HyperSAS [sr-1] Rrs SeaPRISM [sr-1] Rrs SeaPRISM [sr-1] • Increased dispersion in the right figure is mainly due to BRDF • (filters exclude data from some geometries, specifically where relative azimuth angle, φ < 60° to eliminate glint effects) 19

20. Comparison between the Standard MG and Proposed CCNY Algorithm with the LISCO Dataset Before BRDF Correction Corrected with MG Corrected with CCNY • Current MG algorithm does not reduce significantly the dispersion and induces a weaker correlation with R2 •  The proposed CCNY algorithm reduce dispersion by 2% in absolute value and by more than 3% in relative values

21. APPLICATION TO OCEAN COLOR MODIS IMAGERY

22. Satellite Validation Satellite Pixel Selection for Matchup Comparison Validation of MODIS-Aqua against the LISCO Data Satellite Data Processing: Standard NASA Ocean Color Reprocessing 2009 3km×3km pixel box for matchup comparison Exclusion of pixel box if presence of cloud-contaminated pixels in this 9km×9km pixel box Also exclusion of any pixel flagged by the NASA data quality check processing (Atmospheric correction failure, sun glint contamination,…)

23. Comparison between LISCO and MODIS Ocean Color data Rrs Time series for the match-up comparison  Qualitative consistency in variations is observed between the in-situ and satellite data. How will the Satellite / in situ data comparison be improved by application of the CCNY BRDF-correction ?

24. Application to the Satellite Data Corrected with Standard Algo Corrected with CCNY • Application of the CCNY algorithm induces stronger correlation (0.926) • Spectral average absolute percent difference is improved by more than 3%. • Suitability of CCNY BRDF-correction to significantly improve OCR satellite data accuracy in coastal areas

25. Conclusions • We proposed a new algorithm for BRDF correction of the remote-sensing reflectance based on extensive radiative transfer calculations for typical coastal (case-2) waters conditions • Theoretical analysis showed that significant improvement are observed with the proposed algorithm reducing the uncertainty of this correction below 1% • This algorithm has been tested over the two years time series of LISCO observations. • It has been shown that the CCNY BRDF-correction algorithm improve the accuracy of the above-water data by more than 3% • Application of CCNY-algorithm to MODIS satellite data showed the same order of improvement. Suitability of CCNY BRDF-correction to significantly improve OCR satellite data accuracy in coastal areas As a consequence of this work the operational application of this algorithm to current and future (VIIRS) OCR satellite is planned

26. ACKNOWLEDGMENTS NASA AERONET team for SeaPRISM calibration, data processing and support of the site operations NASA Ocean Color Processing Group for satellite imagery Partial support from: Office of Naval Research (ONR) National Oceanographic and Atmospheric Administration (NOAA)