# Inherent Optical Properties (IOPs)

## Table of Contents

## 1 - Product Summary

This algorithm returns spectral marine absorption and backscattering coefficients for water column constituents (e.g., colored dissolved organic material (CDOM) and algal and non-algal particles) in m^{-1}, calculated using the default global configuration of the Generalized Inherent Optical Property (GIOP) model.

Implementation of this algorithm is contingent on the availability of $R_{rs}$ in the UV-visible spectral region. OCTS, MODIS-Aqua and -Terra, MERIS, SeaWiFS, VIIRS, and others are supported.

Algorithm Point of Contact: P. Jeremy Werdell, NASA Goddard Space Flight Center

## 2 - Algorithm Description

##### Inputs:

- $R_{rs}$ in the UV-visible spectral region
- Water temperature & salinity

##### Output:

- a_vvv_giop, total absorption coefficient (
*a*) at all visible wavelengths (*vvv*) in m^{-1} - bb_vvv_giop, total backscattering coefficient (
*b*) at visible wavelengths (_{b}*vvv*) in m^{-1} - aph_443_giop, absorption coefficient of phytoplankton (
*a*or a_{ph}_{φ}) at 443 nm in m^{-1} - adg_443_giop, absorption coefficient of non-algal material plus CDOM (
*a*) at 443 nm in m_{dg}^{-1} - bbp_443_giop, backscattering coefficient of particles (
*b*) at 443 nm in m_{bp}^{-1} - aph_unc_443_giop, the uncertainty of aph_443_giop in m
^{-1} - adg_unc_443_giop, the uncertainty of adg_443_giop in m
^{-1} - bbp_unc_443_giop, the uncertainty of bbp_443_giop in m
^{-1} - adg_s_giop, the exponential spectral slope of adg (
*S*) in nm_{dg}^{-1} - bbp_s_giop, the power-law slope of bbp (
*S*) without units_{bp} - rrs_diff, the average difference between input and modeled $R_{rs}$ from 400-600 nm in %

##### Generic Algorithm:

The $R_{rs}$ measured by the satellite are to be converted to their subsurface values (Lee et al. 2002) via:

(1) $ r_{rs}(\lambda, 0-) = \frac{\mathrm{R_{rs}(\lambda})}{\mathrm{0.52 + 1.7R_{rs}(\lambda)}} $

Subsurface remote-sensing reflectances relate to marine IOPs (Gordon et al. 1988) as:

(2) $ r_{rs}( \lambda, 0-) = 0.0949u( \lambda) + 0.0794u(\lambda)^2 $ and $ u(\lambda) = \frac{\mathrm{b_b(\lambda) } }{\mathrm{a(\lambda) } + b_b(\lambda)}, $

...where *a* and *b _{b}
* are total absorption and backscattering, respectively. Total absorption can be can be expanded as the sum of all absorbing components. Further, each component can be expressed as the product of its mass-specific absorption spectrum (eigenvector:

*a**) and its magnitude or concentration (eigenvalue:

*M*):

(3) $ a(\lambda) = a_w(\lambda) + M_{dg}a^*_{dg}(\lambda) + M_{ph}a^*_{ph}(\lambda) $

...where the subscripts *w*, *ph*, and *dg* indicate contributions by water, phytoplankton, and CDOM plus non-algal particles, respectively. Similar to absorption, total backscattering can also be expanded:

(4) $ b_b(\lambda) = b_{bw}(\lambda) + M_{bp}b^*_{bp}(\lambda), $

where the subscripts *bw* and *bp* indicate contributions by water and particles.

Constant values for *a _{w}* are used (Pope and Fry 1997), but temperature- and salinity-dependent values for

*b*are calculated on the fly using NOAA optimally interpolated sea surface temperatures and NOAA World Ocean Atlas salinities. The eigenvector

_{bw}*a**($ \lambda $) is expressed as exp(-

_{dg}*S*$ \lambda $), where

_{dg}*S*describes the rate of exponential decay and is set as 0.018 nm

_{dg}^{-1}. The eigenvector

*a**($ \lambda $) is determined at each pixel from a satellite estimate of chlorophyll

_{ph}*a*, normalized to 0.055 m

^{2}mg

^{-1}(Bricaud et al. 1998). The eigenvector

*b**($ \lambda $) is expressed as $ \lambda $

_{bp}^{ Sbp }, where

*S*determines the steepness of the power-law. This slope is determined at each pixel using a ratio of blue-to-green $R_{rs}$ (Lee et al. 2002). Three unknowns remain in equations (1)-(4), namely

_{bp}*M*,

_{dg}*M*, and

_{ph}*M*. Using $R_{rs}$ as input, these eigenvalues are estimated using Levenberg-Marquardt nonlinear least squares inversion of equation (2). A description of GIOP uncertainties calculations and quality control (data exclusion) metrics can be found in Werdell et al. 2013.

_{bp}## 3 - Implementation

Click giop.c to view source code

In practice, GIOP allows on-the-fly configuration of the above ocean reflectance inversion model within the l2gen data processing environment. For example, the three eigenvectors described in the preceding paragraph can be assigned at run-time using alternate parameterizations. The AOP-IOP relationship described in equation (2) can also be reconfigured, as can the inversion method (e.g., Levenburg-Marquardt or matrix inversion). A detailed description of GIOP parameterization options, uncertainties calculations, and similarities with other contemporary ocean reflectance inversion models can be found in Werdell et al. 2013.

GIOP is the result of two international IOP algorithm workshops that were hosted by NASA in conjunction with the Ocean Optics XIX (Oct 2008) and XX (Sep 2010) conferences. The international working group associated with these workshops proposed the preliminary consensus configuration of GIOP, with alternative model parameterizations and features defined for subsequent evaluation.

## 4 - Assessment

Satellite-to-in-situ validation results are available from the SeaWiFS Bio-Optical Archive and Storage System (SeaBASS):

## 5 - References

Bricaud, A., Morel, A., Babin, M., Allali, K., & Claustre, H. (1998). Variations of light absorption by suspended particles with chlorophyllaconcentration in oceanic (case 1) waters: Analysis and implications for bio-optical models. Journal of Geophysical Research: Oceans, 103(C13), 31033-31044. http://dx.doi.org/10.1029/98jc02712

Franz, B. A. & Werdell, P. J. (2010). A generalized framework for modeling of inherent optical properties in ocean remote sensing application, Proceedings of Ocean Optics XX, Anchorage, AK.

Gordon, H. R., Brown, O. B., Evans, R. H., Brown, J. W., Smith, R. C., Baker, K. S., & Clark, D. K. (1988). A semianalytic radiance model of ocean color. Journal of Geophysical Research, 93(D9), 10909. http://dx.doi.org/10.1029/jd093id09p10909

Pope, R. M., & Fry, E. S. (1997). Absorption spectrum (380-700 nm) of pure water II Integrating cavity measurements. Applied Optics, 36(33), 8710. http://dx.doi.org/10.1364/ao.36.008710

Werdell, P. J. (2009). Global bio-optical algorithms for ocean color satellite applications: Inherent Optical Properties Algorithm Workshop at Ocean Optics XIX, EOS Trans. AGU 90, 4, http://dx.doi.org/10.1029/2009EO010005.

Werdell, P. J., Franz, B. A., Bailey, S. W., Feldman, G. C., Boss, E., Brando, V. E., … Mangin, A. (2013). Generalized ocean color inversion model for retrieving marine inherent optical properties. Applied Optics, 52(10), 2019. http://dx.doi.org/10.1364/ao.52.002019

Werdell, P. J., Franz, B. A., Lefler, J. T., Robinson, W. D., & Boss, E. (2013). Retrieving marine inherent optical properties from satellites using temperature and salinity dependent backscattering by seawater, Optics Express 21, 32611-32622, http://dx.doi.org/10.1364/OE.21.032611.

IOCCG (2006), Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications, Z-P. Lee, Ed., Reports of the International Ocean-Colour Coordinating Group, No. 5, IOCCG, Dartmouth, Canada.

NASA IOP Algorithm Workshop #2 (Sep 2010)

NASA IOP Algorithm Workshop #1 (Oct 2008)

Summary of analyses to support Workshops #1 and #2

OceanColorWeb forum for Workshops #1 and #2

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