Some refinements for global IOPs products ZhongPing Lee IOPs Workshop, Anchorage, AK, Oct 25, 2010.

1.Two not-so-minor issues: a) Phase function of molecule vs particle scattering b) Angular variation Outline: 2. QAA vs Optimization

1a). Phase function of molecule vs particle scattering (Behrenfeld et al 2005) Why a m -1 bias for b bp ?

G(0 + ) (sr -1 ) b b /(a+b b ) Rrs model commonly used: g or { g 0 & g 1 } depends on phase function shape

G or g is NOT a monotonic function of b b /(a+b b )! 1.G or g depends on phase function shape. 2.Molecular & particle scattering have significantly different phase function shapes. 3.We can have the same b b /(a+b b ) for both molecular and particle scattering phase functions, but different G or g values. 4.For oceanic waters, blue band is dominated by molecular scattering; green/red bands by particle scattering. Facts: Conclusions: Need to account for the phase function shape (molecular vs particle) effects, especially for oceanic waters.

Lee et al (2004) Complex function; cannot invert a&b b algebraically. Caveats: Explicitly separate the effects of molecule and particle phase function effects G from Hydrolight (sr -1 ) G from formula (sr -1 )

A practical model for algebraic/analytical inversion: g w &g p model g model (conventional, widely used)

MODIS Aqua Effects of separating molecular/particle phase function:

Comparison of results a443 bbp555 aph443 adg443 b bp is reduced by 40%; even more for adg443 Consistent in general with the results (Werdell & Franz) that compare f/Q LUT vs Gordon 88 formula.

Conclusion: Significantly different IOPs (in clear oceans) retrieved when the phase function shape effects are considered.

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 1b). Angular variation

400 nm640 nm Water-leaving radiance in the Sun plane, zenith dependence (arrow length indicates radiance value) Bottom line: Water-leaving radiance, or reflectance, is a function of angles.

Current, “standard”, approach to deal with angular variation: The two semi-empirical steps could be omitted with an Rrs model accounts for the angular effects. Rrs(Ω)  Chla  Rrs[0]  IOPs empirical f/Q based on Case-1

Van Der Woerd and Pasterkamp (2008) Albert and Mobley (2003) Park and Ruddick (2005) 1. Some are not visible/transparent about the physics 2. Some are not easily invertible algebraically Caveats: Candidate models for angular Rrs: Lee et al (2004)

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

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):

Rrs(Ω)  IOPs IOP retrieval from angular Rrs: QAA, optimization, linear matrix, etc. G[Ω]G[Ω] Now we get IOPs straightforwardly (one step) from Rrs(Ω)! Rrs(Ω)  Chla  Rrs[0]  IOPs empirical f/Q based on Case-1

2. QAA vs spectral optimization 2) Difference in measuring “signal” vs “noise” 1) “Philosophic” difference All start with: 3) Impact of data and/or model 4) Processing efficiency “essential” difference: 5) Stability

Δb bp, Δa will be 0 if ∆a(λ 0 ) and ∆η are 0. 1) “Philosophic” difference QAA: Total first, then individuals Optimization: Individuals first, then total or simultaneously Under QAA, the error propagation is visual and easy to quantify

(Lee and Carder 2004) Spectral shape of a ph ( λ ) is a property we want to obtain from each measured R rs ( λ ). Spectral optimization assumes a spectral shape before its derivation. Wavelength [nm] a ph ( λ ) [m -1 ] In addition:

Algebraic algorithm (QAA, LMI) (Lee et al. 2002, Hoge and Lyon 1996) Optimization algorithm (e.g., GSM01, HOPE) (Roesler and Perry 1996, Lee et al. 1996, Maritorena et al. 2001, Doerffer 1999) 2) Difference in measuring “signal” vs “noise” Every measurement is perceived as signal.Mis-match is perceived as measurement noise.

(Maritorena et al 2010) The increase trend of b bp from Aqua, by GSM01, is considered due to “error” of Aqua Rrs412. QAA will have different patterns, at least for b bp, as it does not use Rrs412 for b bp derivation. 3) Impact of data and/or model

4) Processing efficiency ‘Resolved’ for multi-band data; hyperspectral data? (Lee et al 2002) 5) Stability Optimization: software impact; optimized or closed to be optimized?

The pathway for global IOPs products by GIOP: As QAA and optimization schemes (and other semi- analytical algorithms) initiate from the same physics, then IOPs from both retrievals can serve as a consistence/reliability check: Agreeable results  highly reliable! Different results  need further diagnose …

Thank you!