Bio-optical modeling of IOPs (PFT approaches)

Transcription

1 Bio-optical modeling of IOPs (PFT approaches) Collin Roesler July note: the pdf contains more information than will be presented today

2 Some History It started with satellite observations of El Niño

3 Some History MS - ecosystem response to climate-scale forcing

4 Some History nd Ocean Optics summer course in Friday Harbor, Washington Drs Mary Jane Perry and Ken Carder PhD-The Determination of In Situ Phytoplankton Spectral Absorption Coefficients: Direct Measurements, Modeled Estimates, and Applications to Bio-optical Modeling

5 Some History and now

6 leads into today's lecture time series of satellite-estimated and moored fluorometer chlorophyll

7 lots of advantages to band ratio approaches but there are some disadvantages too SeaWiFS Mobley, Light and Water

8 coastal waters are problematic time series of satellite-estimated and moored fluorometer chlorophyll CDOM dynamics dominate shelf optical properties

9 lots of advantages to band ratio approaches but there are some disadvantages too MODIS Mobley, Light and Water requires separating CDM and phytoplankton IOPS via inversion Sauer, Roesler, Werdell, Barnard 2012 Opt Exp V20

10 semi-analytical reflectance inversion models to obtain IOPs, focus on phytoplankton absorption spectra FORWARD MODEL: IOPs RTE Reflectance INVERSE MODEL: Reflectance Inversions* IOPs e.g. Hydrolight, Monte Carlo *empirical (including neural network), semi-empirical, semianalytical

11 A reminder on how you measure Reflectance Ratios Sample spectra

12 semi-analytic Reflectance inversion starts with simplification of radiative transfer equation, RTE "Howard Gordon Ocean" homogeneous water plane parallel geometry level surface point sun in black sky no internal sources

13 Solving RTE for Reflectance cos d L( ) = -a L(z, ) -b L(z, ) + (z,, )L( ) dz successive order scattering, SOS separate radiance into unscattered, single scattered, twice scattered contributions, L o, L 1, L 2 L n single scattering approximation, SSA consider only the unscattered and single scattered radiance terms, L o and L 1 quasi-single scattering approximation, QSSA noting that volume scattering functions in the ocean are highly peaked in the forward direction forward scattering is like no scattering at all so replace b with b b

14 QSSA b b b c a + b b o = b/c b b /(a + b b ) solve the ssa (see optics web book) R ~ b b /(a + b b ) R(0) exact solution QSSA SSA o Gordon 1994

15 semi-analytic Reflectance inversion starts with this simplification of radiative transfer equation, RTE Other Models: R x = G b b /a when b b <<<a R x = G b b /(a+b b ) R x = G 1 b b /(a+b b ) + G 2 (b b /(a+b b )) 2 x and G are defined by measurement of R (L u, E u, 0 +, 0 - ) see papers by Gordon, Zaneveld, Kirk, Morel

16 Homework #1 Starting with "measured" IOPs (a, b, and b b ) Use Hydrolight to generate R HL =L u (0-)/E d (0+) compute R = fcn(a,b b ) from RTE approximations R = G 1 b b /a R = G 1 b b /(a+b b ) R = G 1 b b /(a+b b ) + (G 2 b b /(a+b b )) 2 Save your R spectra and the IOPs used Compare How do the three model compare with each other? How do they compare with the exact solution? Does it matter what your IOPs are?

17 My results for one case, let's compare when you do your homework

18 You have heard how to estimate chl from spectral ratios of reflectance but back in 1977 Morel and Prieur were investigating the IOP R relationship

19 Measurements of R = E u /E d QSSA leads to: R = 0.33 b b /(a+b b ) R = E u E d Explain variations in R with respect to b b, a model the IOPs to predict R Morel and Prieur 1977 These results are the basis for semi-analytic inversions

20 Parameterize the Spectral Backscattering b( ) = b w ( ) + b p ( ) and b b ( ) = b bw ( ) + b bp ( ) = b bw ( ) b bp ( ) np b b (380) b b (700) when water dominates the spectral slope is dominated by that of water n p = - 1 n p =0 but as particles dominate the spectral slope is very reduced and dependent upon the slope of the power function (n p ) b bw :b b

21 Case 1: Blue Water R = b bw + b bp a w Only b bp varies Crater Lake Sargasso Sea T 1 to T 5 increasing [particle] n p =1 (dotted) n p =0 (solid) Compared Modeled T 3 T 4 with Measured Spectra

22 Case 1: Green Waters V-type Chl-dominated R = b bw + b bp a w + a ph a ph and b bp chl chl =0.2 chl =18.1

23 Case 2: Green Waters U-type Sediment-dominated R = b bw + b bp a w + a ph + a p a ph chl, and a p,b bp chl

24 The generalized semi-analytic model a = a w + [chl+pheo]a* ph + b a p obs --- mod b b = b bw + (b-b w ) b bp b p (know b w,b bw, measure b) Assume backscattering ratio for particles is spectrally flat, adjust to match R(500), b p

25 The results Order of magnitude variations exist between reflectance ratios and pigment due to combined spectral variations of absorption and backscattering Variations in ocean color are explained by more than variations in pigment concentration.

26 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) So starting in 1995 there was an explosion of papers (well, ok less than 5) focused on semianalytic inversion models to obtain IOPs from reflectance Here is how it works

27 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) Step 1. The IOPs are additive, separate into absorbing and backscattering components a( ) = a w ( ) + a ( ) + a nap ( ) + a CDOM ( ) b b ( ) = b bw ( ) + b bp ( ) particles large water small

28 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) Step 2. Beer's Law indicates that the IOP for a component is proportional to its concentration, define the concentrationspecific spectral shape, for example the chl-specific phytoplankton absorption spectrum a ( ) = Chl a * ( ) component IOP = concentration = scalar *vector = eigenvalue eigenvector concentration-specific IOP spectrum

29 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) Step 3. Put it all together, e.g. R ( ) = f/q b bw ( ) + A bp b bp* ( ) b bw ( )+A bp b bp* ( )+a w ( )+A a * ( ) +A nap a * nap( ) + A CDOM a * CDOM( ) water IOPs are known eigenvectors are spectra, representative of each constituent eigenvalues are scalars to be estimated

30 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) Step 4. put in known eigenvectors (spectral shapes), perform regression against measured reflectance spectrum to estimate the eigenvalues (magnitudes, A's) R ( ) = f/q b bw ( ) + A bp b bp* ( ) b bw ( )+A bp b bp* ( )+a w ( )+A a * ( ) +A nap a * nap( ) + A CDOM a * CDOM( ) How much of each absorbing and backscattering component is needed (in a least squared sense) to reconstruct the measured spectrum? particles large water small

31 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) So starting in 1995 there was an explosion (well, about 5) of inversion models utilizing this approach. Roesler and Perry 1995 Lee et al QAA Hoge and Lyon 1996 Garver and Siegel GSM Roesler and Boss 2003

32 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) The biggest differences between them lies in: 1) definition of the eigenvectors (spectral shapes of the absorbing and backscattering spectra) particles large water small

33 e.g. Phytoplankton absorption spectrum Roesler & Perry 1995 Lee 1996 Maritorena 2002

34 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) The biggest differences between them lies in: 1) definition of the eigenvectors (spectral shapes of the absorbing and backscattering spectra) 2) method of inversion non-linear least square regression constrained regression for global functions optimized non-linear least square regression linear matrix inversion

35 1990 s Invert R to obtain IOPs R ( ) = f/q b b ( )/ (b b ( ) +a( )) The biggest differences between them lies in: 1) definition of the eigenvectors (spectral shapes of the absorbing and backscattering spectra) 2) method of inversion (non-linear least square, linear matrix inversion ) 3) validation and error analysis was the model validated with measurements? was the validation data set truly unique from the data set used to derive eigenvectors? is model tested over broad range of conditions?

36 we will not go through each one in detail but will look at an example to see how the approach works 1. non-linear regression of R = f/q bb/(a+bb) Roesler and Perry 1995 Lee et al (used to derive empirical coeffic) Garver et al. 1997

37 Eigenvectors particles large b bw ( ) water small b bpl ( ) = b(440) ( 0 b bps ( ) = b(440) ( -1 a w ( ) a ( ) (from 1989 data) a NAP ( ) + a CDOM ( ) a CDM (440) exp[ ( -440)] Roesler and Perry 1995

38 a note on the slope of backscattering from ten thousand observations of spectral scattering obtained via acs on the TARA the slope is closer to -0.7 rather than -1.0 appears to be due to the impacts of absorption Boss et al. 2013

39 Measured R( ) = E u ( )/E d ( ) Large Optical Range Chl = 0.07 to 25.6 g/l a (440) = to 0.5 m -1 b bp (440) ~ to 0.04 m -1 Roesler and Perry 1995

40 Results I: R( ) Model Test reconstructing R( ) measured modeled R b bw + b bpl + b bps a w + a + a CDM 6-component model explains most of the observed variability

41 Results II: IOP model validation Chl a (440) b bp (440) Estimated chl from a (676)[m -1 ]/0.014[m 2 mg -1 ] no b b meter, so from particle size distribution (Coulter Counter) Roesler and Perry 1995

42 Results III: residuals to assess a spectral variations QFT measured model + residual R=R meas -R mod convert R to a First estimate: a ( ) = A a ( ) Second estimate: add in R( ) residual Compare with Basis Vector a ( )

43 So simple semi-analytic inversions provide good estimates of IOPs assumption about spectral shapes of the eigenvectors spectral variations in eigenvectors provide additional information so what to do? For example phytoplankton absorption spectra contain a wealth of information

44 Phytoplankton come in all colors This is due to taxon-specific pigments Which have distinct absorption spectra Why limit inversions to a single average spectrum?

45 Hyperspectral Remote Sensing provides a means to estimate highly resolved spectral variations in phytoplankton absorption from ocean color taxonomy (PFT) Benguela - Annual, expansive red tides, variable species composition

46 Transect variations in water color

47 Satlantic Tethered Hyper-Spectral Radiometer Buoy Deployed from boat, towed, moored Run semi-analytic inversion with 5 species-specific phytoplankton absorption spectra as eigenvectors rather than just 1 average Day to day variations in water color Downward irradiance Upward radiance

48 Examples from South African Time Series Measured and modeled reflectance spectra Wavelength (Y) Time (X) Brightness (Z) measured modeled Pre-bloom condition

49 Examples from South African Time Series Measured and modeled reflectance spectra Wavelength (Y) Time (X) Brightness (Z) measured modeled Diatom bloom condition

50 Examples from South African Time Series Measured and modeled reflectance spectra Wavelength (Y) Time (X) Brightness (Z) measured modeled Mesodinium bloom condition

51 Examples from South African Time Series Measured and modeled reflectance spectra Wavelength (Y) Time (X) Brightness (Z) measured modeled Dinophysis bloom condition

52 a ( ) a (440) (m -1 ) Inverting ocean color: species composition based upon phytoplankton absorption spectra Diatom 1. Performed daily microscopic cell counts 2. converted cell counts to absorption accounting for species-specific cell sizes and intracellular pigment concentration (Bricaud and Morel approach) Dinoflagellate Dinophysis Diatom Dinoflagellate Dinophysis Mesodinium Chlorophyte Mesodinium Chlorophyte Wavelength (nm) Roesler et al

53 a ( ) a (440) (m -1 ) Inverting ocean color: species composition based upon phytoplankton absorption spectra 3. eigenvalues (a PFT (440)) for each species-specific absorption spectrum estimated daily from reflectance spectrum inversion (dark symbols) notice model resolved accurate proportions of each species/group even over large range Diatom Dinoflagellate Dinophysis Mesodinium Chlorophyte Diatom Dinoflagellate Dinophysis Mesodinium Wavelength (nm) Roesler et al Chlorophyte

54 Hyperspectral Inversion for PFTs is an overconstrained problem (many more measured wavelengths than unknown eigenvalues) allow resolution of spectral gradients in R( ), hence spectral gradients in a( ) this resolution is what makes this approach sensitive to variations in pigment-based phytoplankton taxonomy by using pigment-based taxonomic eigenvectors, PFTs can be estimated

55 Reformulate the reflectance equation to retrieve more information 2. non-linear regression of R( ) to additionally retrieve beam c, slope of beam c and backscattering ratio

56 Roesler and Boss 2003 GRL: Semianalytic inversion to retrieve beam attenuation let where is the particle backscattering ratio so not spectral?

57 What do we know about the particle backscattering ratio? varies with real index of refraction mineral range nap range phyto range independent of imaginary index of refraction and so insensitive to absorption and thus spectrally independent*

58 if we know and c p ( ) is generally a smoothly varying function so

59 Regression Model Where 7 unknowns, 3 absorption eigenvectors

60 R( ) Standard Model Fit Better fit with c-model Results: Model fit to reflectance 0.1 Gyre 0.01 GoM SA SA

61 ap modeled Results: comparison with measured IOPs Gyre GoM SA00 SA01 slope = 1.02 intercept = m -1 r 2 = a p measured cp modeled r 2 = slope = 0.82 intercept = 0.26 m -1 r 2 = c p measured Gyre GoM SA00 SA01 extreme monospecific algal bloom

62 bb( ) (m -1 ) Results: backscattering C-model realistic bb spectrum, spectral features under high absorption conditions as predicted by Mie theory

63 we will not go through each one in detail but will look at a few examples to see how the approach works 3a. linear matrix inversion Hoge and Lyon b. with uncertainties Peng et al Boss and Roesler 2006

64 linear matrix inversion This is linear??? R ( ) = f/q b bw ( ) + A bp b bp* ( ) b bw ( )+A bp b bp* ( )+a w ( )+A a * ( ) +A nap a * nap( ) + A CDOM a * CDOM( ) (a w + a + a cdm + b bw +b bp ) = (f/qr) (b bw +b bp ) (a + a cdm +b bp ) - (f/qr) *b bp = (f/qr) *b bw (a w + b bw ) which is of the form for linear regression: A1 a* + A2 a* cdm + A3 b* bp = [(f/qr) -1] b bw a w

65 because it is linear regression yields exact solution fast (good for image processing) allows for computation of uncertainties in retrieved IOPs based upon our uncertainties measured Rrs spectral shapes of basis vectors

66 For each measured R( ), allow the spectral shapes of the basis vectors to vary for each linear regression for hundreds of combinations of eigenvectors (spectral shapes) retrieve a unique set of associated eigenvalues look at histogram of eigenvalues allow statistics to determine best value and uncertainties Results from one run: 1. one measured R( ) spectrum 2. >1000 difference combinations of eigenvectors

67 For a very large set of R( ) spectra each spectrum is inverted hundreds of time and the average estimate for each eigenvalue comes with uncertainties COMPARE the figures below linear inversion yields 100s eigenvalue estimates for each R( ) errorbars in figures non-linear inversion yields only single eigenvalue estimate for each R( )

68 What about other sources of variability in measured spectra chlorophyll fluorescence is not in model

69 What about other sources? natural fluorescence spectrum R F ( ) = R meas ( )-R mod ( ) for chlorophyll fluorescence wavelength range ( nm)

70 What about other sources chlorophyll fluorescence water raman Percent contribution of Raman scatter to Rrs(λ) expressed as the ratio of Rrs,R(λ) : Rrs(λ) times 100 Westbury, Boss, Lee

71 What about other sources chlorophyll fluorescence water raman a ph (443) [m -1 ] a cdm (443) [m -1 ] b bp (443) [m -1 ]

72 Take Home Messages Semi-analytic reflectance inversion models are powerful tools for estimating spectral IOPs from ocean color the devil is in the details eigenvector definitions (These are the empirical parts of models! check assumptions and applicability over large range in optical regimes) over constrained (hyperspectral vs multispectral) solution methods: non-linear regression, optimized non-linear regression, linearized regression important considerations testing against independent measured observations sensitivity analysis uncertainties You will get the opportunity to run these inversions later this week

73 Any questions?