1. Lecture 12: Models of IOPs and AOPs Collin Roesler 11 July 2007

2. Why should I model the IOPs, I own an ac9 and vsf? Separating component absorption spectra using the ac9 measurements hyperspectral from multispectral volume scattering function (Hydrolight) sensitivity analyses checking the observations (QA/QC) modeling

3. a =  a i ( ) b =  b j ( )  (  ) =   j ( , ) Mother Nature helps out as the IOPs are additive i=1 j=1 N M M Since we cannot measure every single compound we look for components that exhibit like IOPs

4. a =  a i ( ) Mother Nature helps out as the IOPs are additive i=1 N = a w +  a  i +  a CDOMj +  a CPOMk +  a CPIMn = a w + C  a *  + C CDM a * CDM + C CPOM a * CPOM + C CPIM a * CPIM a* is a “concentration-specific absorption coefficient” that is representative of the component e.g. C  = chlorophyll concentration (mg m -3 ) a *  = chlorophyll-specific absorption (m 2 mg -1 ) NAP

5.  =   i ( ) works for phase functions too i=1 N what components make sense for b? =  (b i /b)  i ~ = b w /b  w + b  /b   + b CPOM /b  CPOM + b CPIM /b  CPIM ~ ~  is a phase function representative of the component e.g. b i /b = fraction of total scattering by particle type i  i = particle type i phase function (sr -1 ) ~ ~

6. IOP Models water phytoplankton CDOM NAP –CPOM –CPIM (min)

7. IOP Models (absorption): water no analytic function for water absorption type in the values for Pope and Frye’s Measurements Google water absorption but watch units

8. IOP Models (absorption): phytoplankton e.g. Bidigare et al. 1989 but see Sosik and Mitchell 1990 a  ( ) = P{C chla a * chla + C chlc a * chlc + C fuco * a fuco …} Sum a pigments ( ) Perform solvent shifts Package pigments P

9. IOP Models (absorption): Phytoplankton measure absorption by a range of species compute the average spectrum 0.04 0.03 0.02 0.01 0 a*  (m 2 mg -1 ) scale to chlorophyll concentration use a*  for your environment with the magnitude determined by local chl a  ( ) = Chl a *  ( )

10. IOP Models (absorption): Phytoplankton Bricaud et al. 1995 JGR At low [Chl], the ecosytem tends to be picoplankton dominated with low packaging At high [Chl], ecosystem tends to be dominated by large cells with high packaging so parameterize a*  ( ) as a function of chlorophyll a *  ( ) = A( ) [chl] -B( ) Recognition that the spectral shape changes and that change is a function of biomass (i.e. ecosystem) a* phyt ( ) m 2 /mg a* phyt ( )

11. IOP Models (absorption): Phytoplankton Ciotti et al. 2002 JGR Two endmembers Large packaged cells, Micro Small unpackaged cells, Pico In situ is some combination a  ( ) = f a pico ( ) + (1 – f) a micro ( ) Taken a step further, allow a mixture of size dependent phytoplankton absorption spectra a* phyt ( ) m 2 /mg a* phyt ( )

12. IOP Models (absorption): Phytoplankton Lee et al. 1996 a  ( ) =a  (570) a  (656) – a  (570) ( -570) 570 <  < 656 nm 656-570 a  ( ) =a  (440)exp(-F*{[ln( -340)]^2}) 400 <  < 570 nm 100 a  ( ) =a  (676)exp(-( -676) 2 ) 656 <  < 700 nm 2  2

13. IOP Models (absorption): CDOM Kirk 1983 a CDOM ( ) = a CDOM ( o )e -S(  o) But see Twardowski et al. 2004 Mar. Chem. Depends on wavelength interval

14. IOP Models (absorption): CDOM a CDOM ( ) = a CDOM ( o )e -S(  o) Babin et al. 2003 Roesler et al. 1989

15. IOP Models (absorption): NAP a NAP ( ) = a NAP ( o )e -S(  o) Roesler et al. 1989 Babin et al. 2003

16. IOP Models (scattering): water scattering spectrum b w ( ) = 0.003 (  ) -4.32 water volume scattering function  w (  ) =  w (,90 o ) (  o ) -4.32 *(1+0.835 cos 2  ) phase function  w (  ) =  w (,90 o ) (1+0.835 cos 2  ) ~ ~

17. IOP Models (scattering): CDOM b CDOM ( ) = 0 ?

18. IOP Models (scattering): Phytoplankton and NAP Morel & Bricaud 1981

19. IOP Models (scattering): Phytoplankton and NAP Smoothly varying function Not so smoothly varying function

20. IOP Models: Particle Scattering Babin et al. 2003

21. IOP Models (backscattering): Phytoplankton and NAP independent of imaginary refraction index varies with real refraction index Ulloa et al. 1994 Appl.Opt.  backscattering has same spectral shape as scattering

22. Analytic models for the phase function There are tons of analytic phase function models, particularly for atmospheric and interstellar studies. While the shape looks approximately similar to those measured in the ocean (e.g. Petzold), upon closer inspection, they can be very different. Henyey Greenstein, Reynolds-McCormick…

23. Analytic models for the phase function So Petzold is a measurement and the others are models Note the Fournier-Forand function

24. Analytic models for the phase function Hydrolight has the option of using the measured Petzold function or the Fournier-Forand model with a prescribed backscattering ratio

25. What does the function look like? A lot of math Mie theory –homogeneous spheres with real refractive index, n –hyperbolic (Junge) size distribution with slope,  –integrate over particles sizes from 0 to infinity Emmanuel will cover Mie Theory and Mie Modeling Later single particle approach

26. IOP Models: The old fashioned way IOPs are parameterized as a function of [chl] Case I Waters: Case II Waters: Waters for which the IOPs are determined by phytoplankton and the covarying organic components (particulate and dissolved) Waters for which the IOPs are determined by components that do not covary with phytoplankton Coastal vs Open Ocean Waters?

27. IOP Models: The old fashioned way IOPs are parameterized as a function of [chl] Phytoplankton CDOM CPOM CPIM absorption scattering

28. IOP Models: The old fashioned way e.g. scattering as a function of [chl] Morel 1987 DSR factor of 5 > factor of 10

29. There are a number of “Case I, chlorophyll- based” IOP models, each of which provide a different estimate of the total IOPs and each of which will provide a different estimate of the AOPs when used as input to Hydrolight. Before you use them, think carefully about the inherent assumptions. Where is the division between case I and II? Developed to use satellite-retrieved chl for IOPs Global relationships not appropriate regionally And certainly not as a function of depth Or in shallow waters Read Mobley et al. 2004

30. Models for AOPs empirical Case I approximations solved through Monte Carlo simulations of in water light field (i.e.Kirk) solved through approximations to the radiative transfer equation (i.e. Gordon) –successive order scattering –single scattering approximation –quasi-single scattering approximation

31. Jerlov Water Types Relationship between K (%T) and R?

32. Jerlov Diffuse Attenuation Classification ~ K d (m -1 ) Wavelength (nm) %transmission of E o (m -1 ) Type Kd(440) Chl I 0.017 0.01 … III 0.14 2.00 1 0.20 >2.00 … 9 1.00 >10.0 Variability in Kd attributed primarily To chlorophyll. This suggested that the inverse problem to estimate Kd from Chl might be tractable.

33. AOP Models: The old fashioned way AOPs are parameterized as a function of [chl] Morel 1988 JGR Let K w ( ) = a w ( ) + 0.5 b w ( ) K( ) = K w ( ) +  ( ) C e( ) See also Gordon 1989 and Phinney and Yentsch 1986

34. K parameterized as a function of [chl] Case I Morel 1988 JGR K( ) = K w ( ) +  ( ) C e( )

35. K d inversion…? Back when only AOPs were measured in situ there was an approach to estimate chl from Kd using the following approximation: K d = K dw + K dchl + K dother And K dchl = K dchl * * Chl Chl KdKd Slope=K dchl * K dw +K dother

36. K d inversion…? K d = K dw + K dchl + K dother And K dchl = K dchl * * Chl Chl KdKd Slope=K dchl * K dw +K dother

37. R parameterized as a function of [chl] Case I Morel 1988 JGR R = 0.33 b b /a R = 0.33 b b  d /K d where b b = 0.5 b = 0.5*(bw + b chl ) K( ) = K w ( ) +  ( ) C e( )  d ( ) = constant

38. R parameterized as a function of [chl] Case I Morel 1988 JGR Morel and Prieur 1977 LO

39. John Kirk Approach to AOP Models Monte Carlo Simulations –homogeneous ocean or homogeneous layers –define a and b (  (  )) –Define incident radiance field –follow photons through model water column –use random numbers to determine probability of a or b and of  –follow a million photons, assign to L(  ) –compute AOPs K = (a 2 + 0.256 ab) 1/2 R ~ b b /a

40. K d : dependence on b/a K d = (a 2 +G ab) 1/2 G is a function of  o (~ 0.256)

41. Reflectance: dependence on b/a R = G b b /a G is a function of  o (~ 0.33 to 0.36)

42. Howard Gordon Approach to AOP Models Howard Gordon Ocean –homogeneous water –plane parallel geometry –level surface –point sun in black sky –no internal sources Make a number of assumptions… R ~ bb/(a + bb)

43. AOP Models: reflectance R = E u /E d R = 0.33 b b /a+b b Which leads to reflectance inversion….

44. Take home messages for AOPs In order to conceptualize the behavior of the AOPs, you must understand how the radiance distribution varies with depth and with the IOPs The average cosine often shows up in the relationships between the AOPs and the IOPs, this is because it is sensitive to the volume scattering function

45. General Take Home Messages Case I algorithms –useful for global relationships –useful for remote sensing applications when only chlorophyll is available (but what are the inherent limitations on satellite-derived chlorophyll?) –applications to Case II waters or local/regional scales very risky (think about underlying relationships) Analytic models –independent of “case” –physically based –suitable for inversion –good for sensitivity analyses