# Remote Sensing Reflectance (Rrs)

## 1 - Product Summary

This algorithm derives the spectral radiance upwelling from beneath the ocean surface, normalized by the downwelling solar irradiance and expressed as spectral "remote sensing" reflectance, $R_{rs}(\lambda)$ at each sensor wavelength, $\lambda$, in the visible domain with units of sr-1. $R_{rs}(\lambda)$ is the fundamental quantity to be derived from ocean color sensors, as it provides the basic input to many derived product algorithms such as chlorophyll-a, diffuse attenuation, or inherent optical properties. A by-product of the $R_{rs}(\lambda)$ derivation is the retrieved atmospheric aerosol optical properties of aerosol optical depth (AOT; dimensionless) and aerosol angstrom exponent ($\alpha$; dimensionless). These aerosol properties provide a diagnostic on algorithm performance. The $R_{rs}(\lambda)$ algorithm is applicable to all current ocean color sensors. The $R_{rs}(\lambda)$ and associated AOT and $\alpha$ products are included as part of the standard Level-2 OC product suite and the Level-3 RRS product suite.

Algorithm Point of Contact: Bryan Franz, NASA Goddard Space Flight Center

## 2 - Algorithm Description

The fundamental quantity to be derived from ocean color sensors is the spectral distribution of reflected visible solar radiation upwelling from below the ocean surface and passing though the sea-air interface. Spaceborne ocean color sensors, however, measure the spectral radiance exiting the top of the atmosphere (TOA). The majority of that observed TOA radiance is light reflected by air molecules and aerosols within the atmosphere, and those contributions must be accurately modeled and removed from the observed signal. Similarly, surface contributions from whitecaps and sun glint, the specular reflection of the sun into the sensor field of view, must be estimated and removed. Finally, the attenuating effects of absorbing atmospheric gases and scattering losses due to transmittance of the water-leaving radiance through the atmosphere must be corrected. The process of retrieving water-leaving radiance from TOA radiance is typically referred to as atmospheric correction.

The retrieved water-leaving radiances, $L_{w}(\lambda)$, at each sensor wavelength, $\lambda$, are then normalized to remove remaining effects of solar orientation and atmospheric attenuation of the downwelling radiation to produce normalized water-leaving radiance, $nL_{w}(\lambda)$, which is often expressed as a radiance reflectance, $R_{rs}(\lambda)$ or Remote Sensing Reflectance, by simply dividing by the mean extraterrestrial solar irradiance, $F_{0}(\lambda)$.

In this algorithm, the TOA radiance is assumed to be partitioned linearly into various distinct physical contributions as shown below:

$$L_{t}(\lambda)=[L_{r}(\lambda) +L_{a}(\lambda) +t_{d_v}(\lambda) L_{f}(\lambda) +t_{d_v}(\lambda) L_{w}(\lambda)] t_{g_v}(\lambda) t_{g_s}(\lambda) f_{p}(\lambda)$$

...where:

$L_{r}(\lambda)$ = the radiance contribution due to Rayleigh scattering by air molecules

$L_{a}(\lambda)$ = the contribution due to scattering by aerosols, including multiple scattering interactions with the air molecules

$L_{f}(\lambda)$ = the contribution from surface whitecaps and foam

$L_{w}(\lambda)$ = the water-leaving component

$t_{d_v}(\lambda)$ = the transmittance of diffuse radiation through the atmosphere in the viewing path from surface to sensor

$t_{d_s}(\lambda)$ = the transmittance of diffuse radiation through the atmosphere in the viewing path from Sun to surface

$t_{g_v}(\lambda)$ = the transmittance loss due to absorbing gases for all upwelling radiation traveling along the sensor view path

$t_{g_s}(\lambda)$ = the transmittance of diffuse radiation through the atmosphere in the viewing path from Sun to surface

$f_{p}(\lambda)$ = is an adjustment for effects of polarization.

The atmospheric correction algorithm retrieves $L_{w}(\lambda)$ by estimating and subtracting the terms on the right-hand side of the above equation from $L_{t}(\lambda)$. The $R_{rs}(\lambda)$ is then computed as:

$$R_{rs}(\lambda) = (L_w(\lambda)/(F_0 f_s cos(\theta_s) t_{d_s}) f_b(\lambda) f_{\lambda}$$

...where:

$F_0$ = extraterrestrial solar irradiance (Thuillier et al. 2003)

$f_s$= adjustment of $F_0$ for variation in Earth-Sun distance

$f_b$ = bidirectional reflectance correction

$f_{\lambda}$ = correction for out-of-band response

Most of the terms in the above equations are estimated through precomputed radiative transfer simulations or models that depend only on the sensor spectral response, solar and sensor viewing geometry, and ancillary information such as atmospheric gas concentrations, surface windspeeds, and surface pressure. The primary challenge in ocean color atmospheric correction is the estimation of the aerosol contribution, as aerosols are highly variable and must be inferred from the sensor observations. The aerosol estimation follows the work of (Gordon and Wang, 1994), with updated aerosol models and model selection approach detailed in (Ahmad et al. 2010). This algorithm relies on sensor observations from two bands in the near-infrared region (e.g., 748nm and 869nm for MODIS), where the water leaving radiance contributions are generally small and can be accurately estimated through an iterative bio-optical modeling approach as described in (Bailey et al. 2010).

For a full description of the atmospheric correction algorithm, including details on the estimation of each term in the above equations and the operational process through which aerosol contributions are estimated and removed, the reader is referred to the document titled Atmospheric Correction for Satellite Ocean Color Radiometry and the associated Web Book on Atmospheric Correction. The web book was developed as an online resource for the theoretical basis and implementation of the current standard atmospheric correction algorithm employed by NASA for all ocean color missions, and it will be maintained as the algorithm evolves.

## 3 - Implementation

 Product Short Name Rrs_vvv, where vvv = sensor specific center wavelength in nm (see table below). Additional products associated with the Rrs retrieval algorithm are the aerosol angstrom exponent, angstrom, and the aerosol optical thickness, aot_nnn, where nnn is the longest aerosol selection band (see table below) and angstrom is the powerlaw exponent that relates aot_443 to aot_nnn. Level-2 Product Suite OC Level-3 Product Suite RRS Level-3 Masking ATMFAIL,LAND,HILT,HISATZEN,STRAYLIGHT,CLDICE,COCCOLITH,LOWLW,CHLWARN,CHLFAIL,NAVWARN,MAXAERITER,ATMWARN,HISOLZEN,NAVFAIL,FILTER,HIGLINT

The table below lists the sensor-specific center wavelengths,$\lambda$, at which $Rrs(\lambda)$ is generated for the standard OC product. Also shown are the default band pair used in standard processing to derive the aerosol contribution. Alternative Bands, when available, can also be used to form alternate band pairs for aerosol determination in special circumstances (e.g., very turbid waters), but they are not currently used in the generation of standard products. Note, however, that some of these alternative bands suffer from low signal-to-noise in ocean applications, and some are specifically located in regions of absorbing gas contamination (e.g., 762, oxygen A-band), so they are not well placed for aerosol determination.

 Sensor Rrs Wavelengths (nm) Aerosol Bands (nm) Alternative Bands (nm) VIIRS 410,443,486,551,671 745,862 1238,1601,2257 SeaWiFS 412,443,490,510,555,670 765,865 OLI (Landsat-8) 443,482,561,655 865,2201 1609 OLCI 400,412,442,490,510,560,620,665,674,681,709 779,865 754,761,764,885,900,940,1012 OCTS 412,443,490,516,565,667 765,862 MODIS 412,443,469,488,531,547,555,645,667,678 748,869 859,1240,1640,2130 MERIS 413,443,490,510,560,620,665,681,709 779,865 754,762,885,900 HICO hyperspectral, 350-1079 by 5.7nm GOCI 412,443,490,555,660,680 745,865 CZCS 443,520,550,670 670

For further details on the implementation, go to the algorithm source code or the graphical description of the algorithm implementation in the NASA ocean color processing code (l2gen).

## 4 - Assessment

Gordon and Wang (1994) developed the basic atmospheric correction algorithm, originally for SeaWiFS. Its performance was then validated through simulations, and after launch, through direct application of the algorithms to SeaWiFS and MODIS imagery and comparison with in situ data (e.g., Bailey & Werdell, 2006; Zibordi, Mélin, & Berthon, 2006). For the current operational products, assessments are routinely performed using in situ matchups available from the SeaWiFS Bio-Optical Archive and Storage System (SeaBASS). Hyperlinks to mission-specific assessment data are provided below.

## 5 - References

Ahmad, Z., Franz, B. A., McClain,C. R., Kwiatkowska, E. J., Werdell, P. J., Shettle, E.P., & Holben, B.N. (2010). New aerosol models for the retrieval of aerosol optical thickness and normalized water-leaving radiances from the SeaWiFS and MODIS sensors over coastal regions and Open Oceans. Applied Optics, 49(29). doi:10.1364/ao.49.005545

Bailey, S. W., & Werdell, P. J. (2006). A multi-sensor approach for the on-orbit validation of ocean color satellite data products. Remote Sensing of Environment 102, 12-23. doi:10.1016/j.rse.2006.01.015

Gordon, H. R., & Wang, W. (1994). Influence of oceanic whitecaps on atmospheric correction of SeaWiFS. Applied Optics 33(33), 7754-7763. doi:10.1364/ao.33.007754

Zibordi, G., Mélin, F., Berthon, J. F. (2006). Comparison of SeaWiFS, MODIS and MERIS radiometric products at a coastal site. Geophysical Research Letters 33(6), L06617. doi:10.1029/2006gl025778