Rrs Modeling and BRDF Correction Zhong Ping Lee
Rrs Modeling and BRDF Correction Zhong. Ping 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.
Acknowledgement: The support from NASA Ocean Biology and Biogeochemistry Program and NRL is greatly appreciated. Michael Twardowski Scott Freeman David Mc. Kee
Outline: 1. Background 2. Decision on particle phase function shape 3. Rrs model 4. IOP-centered BRDF correction & validation 5. Summary
1. 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)
1. Background (cont. ) Rrs is a function of angles, too. Define subsurface remote-sensing reflectance as Cross-surface parameter
1. Background (cont. ) further From radiative transfer equation (Zaneveld 1995)
1. Background (cont. ) The angular component: Phase function shape is the key on the model parameter! bb/b = 0. 015 0. 025 Rrs [sr-1] But not necessarily the bb/b number! Wavelength [nm]
1. Background (cont. ) 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. ) In general: Case-1 approach a = f 1(Chl) b = f 2(Chl) β = f 3(Chl) g(Ω) = Table(Chl, Ω) Advantages: need Chl only. Caveats: (Loisel et al 2002) 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.
1. Background (cont. ) Objectives of IOP-based BRDF Correction: 1. reduce or minimize the dependency on empirical biooptical relationships. 2. avoid the Case-1 assumption. 3. coefficients vary with angular geometry only.
2. Decision on particle phase function shape Locations of VSF measurements relative distribution [%] Distribution of bbp (wide range) bbp [m-1]
2. Decision on particle phase function shape (cont. ) Phase function normalized at 120 o Examples of newly measured phase function shape Scattering angle [deg]
2. Decision on particle phase function shape (cont. ) Cruise average of measured shape They are not the same! But very similar.
2. Decision on particle phase function shape (cont. ) bbp [m-1] relative distribution [%] Distribution of the shapes β(160 o)/β(120 o) Apparently there is a dominant appearance for wide range of b bp!
2. Decision on particle phase function shape (cont. ) Phase function normalized at 120 o An average shape is determined from the measurements Scattering angle [deg]
3. Rrs model Hydrolight simulations: θs: 0, 15, 30, 45, 60, 75 θv: 0, 10, 20, 30, 40, 50, 60, 70 ψ: 0 – 180 o with a 15 o step λ: 400 – 760 nm bb/(a+bb): 0 – 0. 5 With the new average phase function shape θS θv Lw(Ω) ψ
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)
G from HL simulation [sr-1] 3. Rrs model (cont. ): Example of G parameter variation (Ω: 60, 40, 90) bb/(a+bb) 1. G is not a monotonic function of bb/(a+bb) 2. G flats out when bb/(a+bb) gets large (saturation)
3. Rrs model (cont. ): Analytical G models G from model [sr-1] Gordon et al formulation (1988): 1: 1 (Ω: 60, 40, 90) G from HL simulation [sr-1]
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 …
3. Rrs model (cont. ) G from model [sr-1] Lee et al (2004) 1: 1 (Ω: 60, 40, 90) G from HL simulation [sr-1] Caveats: Cannot invert a&bb algebraically.
3. Rrs model (cont. ) A practical choice for algebraic inversion G from model [sr-1] Global distribution of Rrs(443) 1: 1 (Ω: 60, 40, 90) G from HL simulation [sr-1] Rrs 443 [sr-1] G ~ 0. 07
3. Rrs model (cont. ) bbp(555) [m-1] Retrieved Chl and bbp(555) of North Pacific Gyre (from Sea. Wi. FS) Chl [mg/m 3] After the separation of molecular and particle scatterings on the model parameter, derived bbp compared much better with in situ measurements.
3. Rrs model (cont. ) Impact of wind speed Distribution of Rrs difference between 0 m/s and 10 m/s distribution 94. 4% within 5%! Difference = impact of wind speed is small (consistent with earlier studies).
3. Rrs model (cont. ) (with 5 m/s wind) Table ((7 x 13+1)x 4 x 6) array, 2208 elements) of {G(Ω)} (if based on Chl, it is 6 x 13 x 7 = 546 elements per band per Chl) 0. 0593 0. 012 0. 0529 0. 1277 0. 0581 0. 0178 0. 0483 0. 1511 0. 0575 0. 0178 0. 0463 0. 1642 … 0. 0584 0. 0177 0. 0502 0. 1402 0. 0601 0. 0157 0. 0527 0. 1324 0. 0598 0. 0176 0. 0506 0. 1438 … 0. 0586 0. 0177 0. 0504 0. 14 0. 06 0. 0177 0. 0525 0. 1342 0. 0599 0. 0176 0. 0505 0. 1456 … 0. 0585 0. 0176 0. 0503 0. 14 0. 0598 0. 0176 0. 0514 0. 138 0. 0598 0. 0123 0. 0496 0. 1488 … 0. 0588 0. 0176 0. 0506 0. 1404 0. 06 0. 0113 0. 0504 0. 1445 0. 0596 0. 0137 0. 0488 0. 1547 … 0. 0583 0. 0163 0. 0502 0. 1392 0. 059 0. 0123 0. 0489 0. 1481 0. 0584 0. 0178 0. 0474 0. 1578 … 0. 0586 0. 0169 0. 0504 0. 1398 0. 0587 0. 0146 0. 0482 0. 1535 0. 0581 0. 0158 0. 0466 0. 165 … 0. 0583 … 0. 0131 … 0. 05 … 0. 1397 … 0. 0577 … 0. 0178 … 0. 047 … 0. 1569 … 0. 057 … 0. 0179 … 0. 0455 … 0. 1709 … …… Angular-dependent model coefficients for Rrs(Ω) are now available.
4. IOP-centered BRDF correction & validation IOP approach Rrs(Ω) {a&bb} G[0] Rrs[0] QAA, optimization, linear matrix, etc.
4. IOP-centered BRDF correction & validation (cont. ) Algebraic algorithm (e. g. , QAA, linear matrix) (Lee et al. 2002, Hoge and Lyon 1996) Optimization algorithm (e. g. GSM 01, HOPE) (Roesler and Perry 1996, Lee et al. 1996, Maritorena et al. 2001) Rrs( ) Y Input-data focus Input-model focus
4. IOP-centered BRDF correction & validation (cont. ) Retrieval and correction examples HL simulated data: Sun at 60 o, 10 -70 o view angles and 0 -180 o azimuth Wavelength: 400 – 760 nm Derived a from Rrs(Ω) [m-1] Derived bbp from Rrs(Ω) [m-1] Comparison of IOPs (via QAA) Known a [m-1] Known bbp [m-1]
4. IOP-centered BRDF correction & validation (cont. ) Distribution [%] Comparison of Rrs[0] Before correction: 63% & 38% are within 10% and 5%, respectively. After correction: 99% & 95% are within 10% and 5%, respectively
4. IOP-centered BRDF correction & validation (cont. ) QAA vs Spectral optimization (HOPE) Distribution [%] Rrs(Ω) {a&bb} G[0] Rrs[0] 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. ) Ω(15, 10, 165) Rrs[0] [sr-1] Absorption coefficient [m-1] Rrs(Ω) QAA bbp [m-1] Rrs(Ω) QAA a [m-1] Scattering angle [deg] Rrs(Ω) QAA Rrs[0] [sr-1] 120 o-normalized part. phase function Impact of wrong phase function shape bbp [m-1]
4. IOP-centered BRDF correction & validation (cont. ) Field measured data Mediterian Sea, 2004; Sun at 30 o a 440 = 0. 024 Zeu = 108 m m-1, 411 nm, 60 o view L(Ω)/L[0] Blue: from Rrs Red: from Nu. RADS 436 nm, 60 o view 486 nm, 60 o view L(Ω)/L[0]
4. IOP-centered BRDF correction & validation (cont. ) Field measured data Mont. Bay 20060915; Sun at 60 o a 440 = 1. 1 m-1, Zeu = 6. 8 m 411 nm, 60 o view L(Ω)/L[0] 436 nm, 60 o view Blue: from Rrs Red: from Nu. RADS Black: Hydrolight L(Ω)/L[0]
4. IOP-centered BRDF correction & validation (cont. ) Remote-sensing domain
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 bb/(a+bb). Separating the angular effects of molecule and particle scatterings are important for deriving particle scattering coefficient in oceanic waters.
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 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!
Thank you!
2. Decision on particle phase function shape (cont. ) Measurement of shape difference (Mobley et al 2002) Distribution [%] (compared with average shape) Δβ [%]
4. IOP-centered BRDF correction & validation (cont. ) Field measured data AOPEX 081404; Sun at 70 o a 440 = 0. 035 m-1, Zeu = 82 m 486 nm, 60 o view Blue: from Rrs Red: from Nu. RADS 548 nm, 60 o view
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