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Rrs Modeling and BRDF Correction

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.

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Rrs Modeling and BRDF Correction

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  1. Rrs Modeling and BRDF Correction ZhongPing Lee1, Bertrand Lubac1, Deric Gray2, Alan Weidemann2, Ken Voss3, Malik Chami4 1Northern Gulf Institute, Mississippi State University 2Naval Research Laboratory 3University of Miami 4Laboratoire 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: • Background • Decision on particle phase function shape • Rrs model • IOP-centered BRDF correction & validation • Summary

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

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

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

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

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

  9. Background (cont.) In general: Case-1 approach a = f1(Chl) b = f2(Chl) β= f3(Chl) g(Ω) = Table(Chl, Ω) Advantages: need Chl only. 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. (Loisel et al 2002)

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

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

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

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

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

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

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

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

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

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

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

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

  23. 3. Rrs model (cont.) Retrieved Chl and bbp(555) of North Pacific Gyre (from SeaWiFS) bbp(555) [m-1] Chl [mg/m3] After the separation of molecular and particle scatterings on the model parameter, derived bbp compared much better with in situ measurements.

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

  25. 3. Rrs model (cont.) (with 5 m/s wind) Table ((7x13+1)x4x6) array, 2208 elements) of {G(Ω)} (if based on Chl, it is 6x13x7 = 546 elements per band per Chl) Angular-dependent model coefficients for Rrs(Ω) are now available.

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

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

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

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

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

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

  32. 4. IOP-centered BRDF correction & validation (cont.) Field measured data Mediterian Sea, 2004; Sun at 30o a440 = 0.024 m-1, Zeu = 108 m L(Ω)/L[0] Blue: from Rrs Red: from NuRADS 411 nm, 60o view 436 nm, 60o view 486 nm, 60o view L(Ω)/L[0] L(Ω)/L[0]

  33. 4. IOP-centered BRDF correction & validation (cont.) Field measured data Mont. Bay 20060915; Sun at 60o 411 nm, 60o view a440 = 1.1 m-1, Zeu = 6.8 m L(Ω)/L[0] 436 nm, 60o view Blue: from Rrs Red: from NuRADS Black: Hydrolight L(Ω)/L[0]

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

  35. 5. Summary • Angular distribution of remote-sensing reflectance (Rrs) highly depends on particle phase function shape (PPFS). • 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. • Without known PPFS precisely, BRDF correction is an approximation. • The model parameter for Rrs is not a monotonic function of bb/(a+bb). 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. 2. Decision on particle phase function shape (cont.) Measurement of shape difference (compared with average shape) Distribution [%] (Mobley et al 2002) Δβ [%]

  39. 4. IOP-centered BRDF correction & validation (cont.) AOPEX 081404; Sun at 70o Field measured data a440 = 0.035 m-1, Zeu = 82 m 486 nm, 60o view Blue: from Rrs Red: from NuRADS 548 nm, 60o view

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