1. Rrs Modeling and BRDF Correction ZhongPing Lee 1, Bertrand Lubac 1, Deric Gray 2, Alan Weidemann 2, Ken Voss 3, Malik Chami 4 1 Northern Gulf Institute, Mississippi State University 2 Naval Research Laboratory 3 University of Miami 4 Laboratoire Oce´anographie de Villefranche Ocean Color Research Team Meeting, May 4 – 6, 2009, New York.

2. Acknowledgement: The support from NASA Ocean Biology and Biogeochemistry Program and NRL is greatly appreciated. Michael Twardowski Scott Freeman David McKee

3. Outline: 1.Background 2.Decision on particle phase function shape 3.Rrs model 4.IOP-centered BRDF correction & validation 5.Summary

4. 1.Background Water-leaving radiance, Lw, is a function of angles. BRDF correction: Correct this angular dependence Ω(10, 20, 30) measured photons going further away from Sun (~forward scatter) Ω(10, 20, 150) measured photons going closer to Sun (~backscatter) θSθS θvθv ψ Why BRDF Correction? Bidirectional Reflectance Distribution Function

5. Rrs is a function of angles, too. Define subsurface remote-sensing reflectance as 1.Background (cont.) Cross-surface parameter

6. 1.Background (cont.) further From radiative transfer equation (Zaneveld 1995)

7. 1.Background (cont.) The angular component: Phase function shape is the key on the model parameter! Wavelength [nm] Rrs [sr -1 ] But not necessarily the b b /b number! b b /b = 0.01 0.015 0.02 0.025

8. Only two ideal condidtions can we “precisely” correct BRDF effects: 1.Completely diffused distribution (Lambertian). 2.The phase function shape and IOPs are known exactly. Remote sensing is not in ideal conditions: BRDF correction is an approximation! 1.Background (cont.)

9. Case-1 approach a = f1(Chl) b = f2(Chl) β = f3(Chl) g(Ω) = Table(Chl, Ω) Caveats: 1. For Case-1 waters only. 2. Remotely it is difficult to know if a pixel belongs to Case-1 or not. 3. (minor) large table when (more spectral bands, more Chl) are required. Advantages: need Chl only. In general: (Loisel et al 2002)

10. 1.Background (cont.) Objectives of IOP-based BRDF Correction: 1. reduce or minimize the dependency on empirical bio- optical relationships. 2. avoid the Case-1 assumption. 3. coefficients vary with angular geometry only.

11. b bp [m -1 ] relative distribution [%] 2. Decision on particle phase function shape Locations of VSF measurements Distribution of b bp (wide range)

12. 2. Decision on particle phase function shape (cont.) Scattering angle [deg] Phase function normalized at 120 o Examples of newly measured phase function shape

13. 2. Decision on particle phase function shape (cont.) Cruise average of measured shape They are not the same! But very similar.

14. relative distribution [%] β(160 o )/β(120 o ) b bp [m -1 ] relative distribution [%] 2. Decision on particle phase function shape (cont.) Distribution of the shapes Apparently there is a dominant appearance for wide range of b bp !

15. 2. Decision on particle phase function shape (cont.) An average shape is determined from the measurements Scattering angle [deg] Phase function normalized at 120 o

16. θSθS ψ θvθv Lw(Ω)Lw(Ω) 3. Rrs model Hydrolight simulations: θ s : 0, 15, 30, 45, 60, 75 θ v : 0, 10, 20, 30, 40, 50, 60, 70 ψ : 0 – 180 o with a 15 o step λ: 400 – 760 nm b b /( a+b b ): 0 – 0.5 With the new average phase function shape

17. 3. Rrs model (cont.) (Gordon 2005) Model parameters for g[Ω] are also available. Note: This G includes the cross-surface effect and the subsurface model parameter.

18. b b /( a+b b ) G from HL simulation [sr -1 ] (Ω: 60,40,90) 1.G is not a monotonic function of b b /(a+b b ) 2.G flats out when b b /( a +b b ) gets large (saturation) 3. Rrs model (cont.): Example of G parameter variation

19. 3. Rrs model (cont.): Gordon et al formulation (1988): Analytical G models G from HL simulation [sr -1 ] G from model [sr -1 ] 1:1 (Ω: 60,40,90)

20. Other formulations Van Der Woerd and Pasterkamp (2008) 3. Rrs model (cont.) Albert and Mobley (2003) Park and Ruddick (2005) 1. Not resolving the non-monotonic dependency (contribution of molecular scattering) 2. High-order polynomials do not behave smoothly outside the range … Caveats:

21. Lee et al (2004) 3. Rrs model (cont.) Cannot invert a&b b algebraically. Caveats: G from HL simulation [sr -1 ] G from model [sr -1 ] 1:1 (Ω: 60,40,90)

22. G ~ 0.07 Rrs443 [sr -1 ] 3. Rrs model (cont.) A practical choice for algebraic inversion Global distribution of Rrs(443) G from HL simulation [sr -1 ] G from model [sr -1 ] 1:1 (Ω: 60,40,90)

23. Chl [mg/m 3 ] b bp (555) [m -1 ] After the separation of molecular and particle scatterings on the model parameter, derived b bp compared much better with in situ measurements. 3. Rrs model (cont.) Retrieved Chl and b bp (555) of North Pacific Gyre (from SeaWiFS)

24. Distribution of Rrs difference between 0 m/s and 10 m/s distribution 94.4% within 5%! Impact of wind speed 3. Rrs model (cont.) impact of wind speed is small (consistent with earlier studies). Difference =

25. Table ((7x13+1)x4x6) array, 2208 elements) of {G(Ω)} 0.05930.05840.05860.05850.05880.05830.05860.0583… 0.0120.0177 0.0176 0.01630.01690.0131… 0.05290.05020.05040.05030.05060.05020.05040.05… 0.12770.14020.14 0.14040.13920.13980.1397… 0.05810.06010.060.05980.060.0590.05870.0577… 0.01780.01570.01770.01760.01130.01230.01460.0178… 0.04830.05270.05250.05140.05040.04890.04820.047… 0.15110.13240.13420.1380.14450.14810.15350.1569… 0.05750.05980.05990.05980.05960.05840.05810.057… 0.01780.0176 0.01230.01370.01780.01580.0179… 0.04630.05060.05050.04960.04880.04740.04660.0455… 0.16420.14380.14560.14880.15470.15780.1650.1709… ……………………… (if based on Chl, it is 6x13x7 = 546 elements per band per Chl) 3. Rrs model (cont.) (with 5 m/s wind) Angular-dependent model coefficients for Rrs(Ω) are now available.

26. 4. IOP-centered BRDF correction & validation Rrs(Ω)  { a&b b }  G[0]  Rrs[0] IOP approach QAA, optimization, linear matrix, etc.

27. Algebraic algorithm (e.g., QAA, linear matrix) (Lee et al. 2002, Hoge and Lyon 1996) R rs ( ) Y 4. IOP-centered BRDF correction & validation (cont.) Optimization algorithm (e.g. GSM01, HOPE) (Roesler and Perry 1996, Lee et al. 1996, Maritorena et al. 2001) Input-model focus Input-data focus

28. 4. IOP-centered BRDF correction & validation (cont.) Known a [m -1 ] Derived a from R rs (Ω) [m -1 ] Known b bp [m -1 ] Derived b bp from R rs (Ω) [m -1 ] HL simulated data: Sun at 60 o, 10-70 o view angles and 0-180 o azimuth Wavelength: 400 – 760 nm Comparison of IOPs (via QAA) Retrieval and correction examples

29. Before correction: 63% & 38% are within 10% and 5%, respectively. After correction: 99% & 95% are within 10% and 5%, respectively Distribution [%] 4. IOP-centered BRDF correction & validation (cont.) Comparison of Rrs[0]

30. Distribution [%] Via spectral optimization: 70% & 55% are within 10% and 5%, respectively. Via QAA: 99% & 95% are within 10% and 5%, respectively. 4. IOP-centered BRDF correction & validation (cont.) QAA vs Spectral optimization (HOPE) Rrs(Ω)  { a&b b }  G[0]  Rrs[0]

31. 4. IOP-centered BRDF correction & validation (cont.) Impact of wrong phase function shape Ω(15, 10, 165) Scattering angle [deg] 120 o -normalized part. phase function Absorption coefficient [m -1 ] Rrs(Ω)  QAA  a [m -1 ] Rrs[0] [sr -1 ] Rrs(Ω)  QAA  Rrs[0] [sr -1 ] Rrs(Ω)  QAA  b bp [m -1 ] b bp [m -1 ]

32. a 440 = 0.024 m -1, Zeu = 108 m Mediterian Sea, 2004; Sun at 30 o 4. IOP-centered BRDF correction & validation (cont.) Field measured data Blue: from Rrs Red: from NuRADS 411 nm, 60 o view L(Ω)/L[0] 436 nm, 60 o view L(Ω)/L[0] 486 nm, 60 o view

33. Mont. Bay 20060915; Sun at 60 o 4. IOP-centered BRDF correction & validation (cont.) Field measured data Blue: from Rrs Red: from NuRADS Black: Hydrolight a 440 = 1.1 m -1, Zeu = 6.8 m 411 nm, 60 o view L(Ω)/L[0] 436 nm, 60 o view L(Ω)/L[0]

34. 4. IOP-centered BRDF correction & validation (cont.) Remote-sensing domain

35. 5. Summary A.Angular distribution of remote-sensing reflectance (Rrs) highly depends on particle phase function shape (PPFS). B.PPFS is not a constant, but generally varies within a limited range. An average PPFS (and particle phase function) is derived based on recent measurements. C.Without known PPFS precisely, BRDF correction is an approximation. D.The model parameter for Rrs is not a monotonic function of b b /( a +b b ). Separating the angular effects of molecule and particle scatterings are important for deriving particle scattering coefficient in oceanic waters.

36. 5. Summary (cont.) E. Models and procedures to derive IOPs from angular Rrs, and then to correct the angular dependence, are now developed. This approach can be applied to both multi-band and hyperspectral data, and not need to assume Case-1 waters. F. Excellent results (99% are within 10% error after BRDF correction) are achieved with HL simulated data. G. Reasonable results are achieved with field measured data, but more tests/evaluation are necessary. H. Impacts of wrongly assumed PPFS are mainly on the retrieval of particle backscattering coefficient, with minor impact on the retrieval of absorption coefficient. The total absorption coefficient is the least affected parameter from angles/PPFS!

37. Thank you!

38. (Mobley et al 2002) 2. Decision on particle phase function shape (cont.) Δ β [%] Distribution [%] (compared with average shape) Measurement of shape difference

39. 548 nm, 60 o view AOPEX 081404; Sun at 70 o 4. IOP-centered BRDF correction & validation (cont.) Field measured data 486 nm, 60 o view Blue: from Rrs Red: from NuRADS a 440 = 0.035 m -1, Zeu = 82 m