A semi-analytical ocean color inherent optical property model: approach and application.

Tim Smyth, Gerald Moore, Takafumi Hirata and Jim Aiken

Plymouth Marine Laboratory, UK

Overview

• Model description

• Implementation

• Validation

• Sensitivity study - summary

• Application to satellite data

• Further work

1) Model description

• Morel (1980): “ … the inverse system can be theoretically solved using simultaneous equations, if a spectral law is assumed for backscattering.”

– Not implemented (or implementable!) for either in situ or satellite data

• Sugihara & Kishino (1988) and Roesler & Perry (1995): implemented schemes for in-water reflectance data

– Not scaled up to satellite data (problems with Q)

• We have developed a scheme using simultaneous equations: solved using empirically derived spectral slopes in combination with radiative transfer modelling.

Interface terms (Fresnel and f/Q): angular and IOP dependency

Total absorption:

aph(λ), ad(λ), ay(λ)

• Two unknowns of bbp(λ) and a(λ): therefore require two equations … achieve this using two neighbouring wavelengths (i, j) and empirically derived spectral slopes.

Simultaneous equations

1) Model description

Spectral slope in total absorption

Spectral slope in total backscatter

• solve equations simultaneously for a(j) and bbp(j) – nasty maths!

• then can solve for a(i) and bbp(i) using spectral slopes.

• need to work out which wavelength pairing to use for spectral slopes – based on empirical data.

1) Model description

• Spectral slopes from COLORS dataset (predominantly coastal stations)

• εa(490,510) converged to narrow range of values with low σ

• εa(490,510) = 1.268; εbb(490,510) = 1.0202

• Is this because only 20 nm difference between bands?

• observationally: chlorophyll-a has greatest effect between 400 – 470 nm; minor effect between 490 and 510 nm.

N=216

1) Model description

• Once have a(490,510) and bbp(490,510), then use assumed shape of backscatter to extrapolate to other wavelengths:

• can then work out the entire spectrum of a(λ)

• bio-geochemical parameters of ady(λ) and aph(λ) can be determined using spectral slope method

• εdy(412,443) and εph(412,443) selected as they are distinct with low variance. Used in combination with standard CDOM exponential function to extrapolate to other wavelengths.

2) Implementation

3) Validation

• Validation using NOMAD in situ dataset:– Points selected on basis that each entry

contained ρw(SeaWiFS); a(λ); aph(λ) and ady(λ);

– 439 data points met this criterion;

– 88 data points for bbp(λ).

– Comparison with Lee et al. (2002) model

3) Validation: Total absorption (PML model), a(λ)

R2: 0.835RMS: 0.192

R2: 0.851RMS: 0.161

R2: 0.840RMS: 0.202

R2: 0.819RMS: 0.118

R2: 0.637RMS: 0.148

R2:0.061 RMS: 0.362

N=418

Signal to noise ratio?

Raman scattering?

Good retrievals over 2 orders of magnitude

3) Validation: Total absorption (Lee model), a(λ)

R2: 0.549RMS: 0.362

N=439

R2: 0.464RMS: 0.376

R2: 0.206RMS: 0.415

R2: 0.006RMS: 0.435

R2: 0.509RMS: 0.475

R2: 0.556RMS: 0.308

Limitation at higher absorption

3) Validation: Total backscatter, bb(λ)

N=88

R2: 0.400RMS: 0.148

R2: 0.395RMS: 0.148

R2: 0.387RMS: 0.192

R2: 0.383RMS: 0.217

R2: 0.375RMS: 0.270

R2: 0.354RMS: 0.390

Increasing bias with increasing λ: problem with assumed spectral shape?

3) Validation: CDOM absorption, ady(λ)

R2: 0.568RMS: 0.507

R2: 0.532RMS: 0.500

R2: 0.477RMS: 0.516

R2: 0.453RMS: 0.519

R2: 0.406RMS: 0.538

R2: 0.313RMS: 0.595

Noisy at low ady(λ): possible measurement error?

3) Validation: phytoplankton absorption, aph(λ)

R2: 0.666RMS: 0.298

R2: 0.759RMS: 0.230

R2: 0.744RMS: 0.263

R2: 0.677RMS: 0.358

R2: 0.394RMS: 0.857

R2: 0.099RMS: 0.178

Problems with retrievals at 555 and 670

4) Sensitivity study - summary

• a(λ) and bb(λ):

– Model most sensitive to εa(490,510)

• NOMAD 1.317 cf. COLORS 1.268

– Relatively insensitive to εbb(490,510)

• NOMAD 1.040 cf. COLORS 1.0202

• ady(λ) and aph(λ)

– Most sensitive to εph(412,443)

• NOMAD 1.065 cf. COLORS 0.954

– Relatively insensitive to εdy(412,443) and S

• NOMAD 1.638 cf. COLORS 1.579

5) Application to satellite data

• Implemented on HRPT and GAC SeaWiFS imagery using an Intel Xeon 1.8 GHz processor:– 15 mins proc HRPT– 1.5 mins process on GAC entire orbit

Phytoplankton – fine eddy structure

Sediment

Coccolithophores

CDOM

bloom?

Clear blue ocean

18 May 1998 13.14 GMT “True color” composite - qualitative

a) a(443): high values (0.2 – 0.5 m-1) in coastal seas; ca. 0.3 m-1 in bloom.

b) ady(443): coastal seas dominated by CDOM;

c) aph(443): phytoplankton bloom off W. Ireland;

d) bbp(555): Emiliana huxleyi bloom in Western Approaches (in situ confirmed this)

IOP model allows us to quantify these features.

a(443)

bbp(555)aph(443)

ady(443)

10 Oct 2002 10.26 GMT

a(443) aph(443) ady(443)

• BENCAL experiment (October 2002)

• upwelling combination of ady and aph; offshore bloom dominated by aph

South Africa

Namibia

5) Further work

• 490:510 pairing used for SeaWiFS / MERIS– Develop 488:532 spectral slopes for use with MODIS

• 412:443 pair for ady and aph subject to ρw(412) problems (atmospheric correction); could use 443:490 pairing instead

• IOP models can form building block for many applications:– Determination of phytoplankton functional types;– Data assimilation into process oriented models:

address rate equations, cf. chlorophyll which is a model derived variable;

– Primary production modelling without recourse to chlorophyll