Algorithm for Retrieval of Remote Sensing Reflectance from Satellite Ocean Color Sensors

Bryan A. Franz

NASA Ocean Biology Processing Group

Last updated on 2015-03-20

- Under Construction -

1. Introduction

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 (Gordon and Wang, 1994). 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 accounted for. 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, $F_{0}(\lambda)$.

This document describes the standard algorithm employed by NASA for retrieval of $R_{rs}(\lambda)$ from TOA radiance. This algorithm is used to produce all standard products generated and distributed by the OBPG for MODIS, SeaWiFS, OCTS, and CZCS, and it is the default method for all sensors supported by L2GEN and SeaDAS.

2. Atmospheric Correction Algorithm

2.1. Overview

The radiance observed over oceans by the satellite sensor in the visible to infrared spectral range, $L_{t}(\lambda)$ , can be considered as the sum of atmospheric scattering components, surface components, and a water-leaving component. These components interact with each other and with absorbing atmospheric gases as they are transmitted through the atmosphere and scattered into the satellite sensor field-of-view. In addition, the surface and atmospheric scattering alters the polarization state of the radiance exiting the TOA, and this affects the apparent radiance observed by instruments with significant polarization sensitivity. In the standard atmospheric correction algorithm employed for NASA ocean color, the TOA radiance is modeled as shown in Equation 1,

where $L_{r}(\lambda)$ is the radiance contribution due to Rayleigh scattering by air molecules, $L_{a}(\lambda)$ is the contribution due to scattering by aerosols, including multiple scattering interactions with the air molecules, $ L_{f}(\lambda)$ is the contribution from surface whitecaps and foam, and $L_{w}(\lambda)$ is the water-leaving component. The $t_{d_v}(\lambda)$ multiplier on $L_{f}(\lambda)$ and $L_{w}(\lambda)$ represents the transmittance of diffuse radiation through the atmosphere in the viewing path from surface to sensor (Figure 1), and $t_{g_v}(\lambda)$ is the transmittance loss due to absorbing gases for all upwelling radiation traveling along the sensor view path. Similarly, the $t_{g_s}(\lambda)$ term represents the transmittance to the downwelling solar radiation due to the presence of absorbing gases along the path from Sun to surface. Finally, the $f_{p}(\lambda)$ adjusts for effects of polarization. Each of these components is discussed in more detail in the sections that follow.


2.2. Sensor-specific Band-pass Information

2.3. Sun Glint

2.4. Whitecaps and foam

2.5. Absorbing gases

2.6. Rayleigh Radiance

2.7. Aerosol Radiance

2.8. Polarization Effects

2.9. Algorithm Limitations

3. Normalized Water-Leaving Radiance and Rrs

4. Alternative Algorithms

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Updated: 13 April 2015