Radiative Transfer in Coupled Atmosphere and Ocean Systems: Impact of Surface Roughness on Remotely Sensed Radiances
Following from: Radiative transfer in coupled atmosphere and ocean systems: the Hybrid Method
Impact of Surface Roughness on Remotely Sensed Radiances
To analyze remotely sensed radiances obtained by instruments such as the Sea-viewing Wide Field of view Sensor (SeaWiFS, on-board SeaStar) or the Moderate-resolution Imaging Spectroradiometer (MODIS, deployed on both the Terra and Aqua spacecrafts), and the Medium Resolution Imaging Spectrometer (MERIS, deployed onboard the European Space Agency (ESA)’s Envisat platform, NASA has developed a comprehensive data analysis software package (SeaWiFS Data Analysis System, SeaDAS), which performs a number of tasks, including cloud screening and calibration, required to convert the raw satellite signals into calibrated top-of-the-atmosphere (TOA) radiances. In addition, the SeaDAS software package has tools for quantifying and removing the atmospheric contribution to the TOA radiance (“atmospheric correction”) as well as contributions due to whitecaps and sunglint caused by reflections from the wind-roughened ocean surface (Gordon, 1997).
The scattering geometry is shown in Fig. 1. The tilted facet with normal n makes a polar angle β with respect to the vertical, and azimuth angle α. Solar radiance I_{i} is incident on the facet with solar zenith angle θ_{0}. The reflected radiance I_{r} is in polar direction θ, and Δφ is the relative azimuth between direction of incidence and reflection.
Figure 1. Scattering geometry. The tilted surface facet makes a polar angles β and relative azimuth α. The incident solar radiance I_{i} is at a zenith angle θ_{0}, and the reflected radiance I_{r} at zenith angle θ. The relative azimuth between I_{i} and I_{r} is Δφ.
Directly Transmitted Radiance Approach
The sunglint radiance can be expressed as a function of the following variables:
where the angles μ_{0},μ, and Δφ = φ^{'}- φ define the sun-satellite geometry, WS is the wind speed, and λ the wavelength. The atmosphere is characterized by its total optical depth τ_{tot}, and the choice of an aerosol model (AM).
In the SeaDAS algorithm, a sunglint flag is activated for a given pixel when the reflectance or BRDF, as calculated from
(1) |
exceeds a certain threshold. Here, r(m_{1},m_{2},μ,μ_{0},Δφ) is the Fresnel reflectance, μ_{n} = cosθ_{n}, θ_{n} ≡ β is the tilt angle between the vertical and the normal to the tangent plane (see Fig. 1), σ^{2} = 0.003 + 0.00512 WS, and WS is the wind speed in meters per second. If the reflectance for a given pixel is above the threshold, then the signal is not processed. If the reflectance is below the threshold, then a directly transmitted radiance (DTR) approach is used to calculate the TOA sunglint radiance in the SeaDAS algorithm. Thus, it is computed assuming that the direct beam and its reflected portion only experience exponential attenuation through the atmosphere (Wang and Bailey, 2001), i.e.,
(2) |
(3) |
where the normalized sunglint radiance I_{GN} is the radiance that would result in the absence of the atmosphere if the incident solar irradiance were F^{s} = 1, and where τ_{M} and τ_{A} (τ_{tot} = τ_{M} + τ_{A}) are the Rayleigh (molecular) and aerosol optical thicknesses. Multiple scattering is ignored in the DTR approach, implying that light removed from the direct beam path through scattering will not be accounted for in the computed TOA radiance.
Multiply Scattered Radiance Approach
Wheres the DTR approach accounts only for the direct beam (beam 2 in Fig. 2), the multiply scattered radiance (MSR) approach is based on computing the TOA radiance by solving the RTE [see Eq. (3)] subject to the boundary condition,
(4) |
thereby allowing multiple scattering to be included in the computation. Here, τ_{1} is the optical thickness of the atmosphere, and B_{glint}(μ,φ;-μ_{0},φ_{0}) = B_{r}(μ,-μ_{0},Δφ) [see Eq. (1)] is the BRDF of the air-ocean interface. For consistency with the definition of sunglint, radiation reflected from the surface after being scattered on its way down to the ocean surface (beam 1 in Fig. 2) is ignored by not including a downward diffuse term in Eq. (4). The complete solution [of Eqs. (3) and (4)] gives the total TOA radiance I_{TOA}^{tot}(μ,μ_{0},Δφ), which includes light scattered into the observation direction without being reflected from the ocean surface (beam 4 in Fig. 2). This contribution is denoted by I_{TOA}^{bs}(μ,μ_{0},Δφ), since it can be computed by considering a black or totally absorbing ocean surface, for which B_{glint} = 0 in Eq. (4). To isolate the glint contribution, one must subtract this “black-surface” component from the complete radiation field,
(5) |
Equation (5) includes multiply scattered reflected radiation, but ignores multiply scattered sky radiation undergoing ocean-surface reflection (beam 1 in Fig. 2). Thus, it guarantees that the difference between the TOA radiances obtained by the DTR and MSR approaches is due solely to that component of the TOA radiance, which is scattered along its path from the ocean surface to the TOA (beam 3 in Fig. 2). In order to quantify the error introduced by the DTR assumption, Ottaviani et al. (2008) used a coupled atmosphere-ocean discrete ordinate code with a Gaussian surface slope distribution (Spurr, 2008).
Figure 2. Schematic illustration of various contributions to the TOA radiance in the case of a wind-roughened ocean surface. (1) Diffuse downward component reflected from the ocean surface; (2) direct, ocean-surface reflected beam; (3) beam undergoing multiple scattering after ocean-surface reflection, and (4) (multiply) scattered beam reaching the TOA without hitting the ocean surface [adapted from Ottaviani et al. (2008)].
Comparison of DTR and MSR
To correct for the sunglint signal, Wang and Bailey (2001) added a procedure to the SeaDAS algorithm based on the DTR assumption, which ignores multiple scattering in the path between the ocean surface and the TOA as well as in the path from the TOA to the ocean surface. To quantify the error introduced by the DTR assumption, Ottaviani et al. (2008) ignored the effect of whitecaps as well as the wavelength dependence of the refractive index. Figure 3 shows a comparison of DTR and MSR results at 490 nm for several wind speeds and different aerosol types and loads. The incident solar irradiance was set to F^{s} = 1, giving the sun-normalized radiance, and in the computation of the Fresnel reflectance in Eq. (1), the imaginary part of the refractive index was assumed to be zero. A standard molecular atmospheric model (midlatitude) with a uniform aerosol distribution of <2 km was used in the computations. Thus, of <2 km, the aerosol optical thickness due to scattering (τ_{A}^{s}) and absorption (τ_{A}^{a}) was added to the molecular optical thickness τ_{M},
(6) |
The IOPs for aerosols were computed by a Mie code (Tsay and Stephens, 1990), and the IOPs of a multi-component mixture were then obtained as a concentration-weighted average of the IOPs of each aerosol component (Yan et al., 2002; Zhang et al., 2007).
Figure 3. Sun-normalized sunglint TOA radiance (solid and thin curves) at 490 nm for a SZA of 15 deg, along the principal plane of reflection, and relative error incurred by ignoring multiple scattering along the path from the surface to the TOA (dotted curves). Each plot contains three representative wind speeds (1, 5, and 10 m/s). The upper row pertains to small aerosol particles in small amounts ( τ = 0.03, left panel) and larger amounts ( τ = 0.3, right panel). The bottom row is similar to the top one, but for large aerosol particles. The error curves have been thickened within the angular ranges in which retrievals are attempted (corresponding to 0.0001 ≤ I_{TOA}^{tot} ≤ 0.001 in normalized radiance units) [adapted from Ottaviani et al. (2008)].
The upper panels in Fig. 3 pertain to small aerosol particles with optical depths of 0.03 and 0.3, while the lower panels are for large aerosol particles. The DTR curves are shown for wind speeds of 1, 5, and 10 m/s, while only one MSR curve at 5 m/s is shown for clarity. The errors incurred by ignoring multiple scattering in the path from the surface to the TOA typically range from 10 to 90% at 490 nm (Fig. 3). These error ranges are determined by the radiance threshold values that mark the retrieval region boundaries; the errors are smaller closer to the specular reflection peak (higher threshold). Surface roughness only affects the angular location and extent of the retrieval region, where these errors occur. The minimum errors grow significantly in an atmosphere with a heavy aerosol loading, and asymmetries are found close to the horizon, especially in the presence of large (coarse-mode) particles.
Figure 3 pertains to the principal plane. Similar computations showed that the errors are azimuth dependent (Ottaviani et al., 2008). Thus, in a typical maritime situation the errors tend to grow as the radiance decreases away from the specular direction, and the high directionality of the radiance peak at low wind speeds causes larger minimum errors away from the principal plane. Correcting for sunglint contamination including multiple scattering effects in future processing of ocean color satellite data is feasible, and would be desirable in view the magnitude of the errors incurred by the DTR approach.
REFERENCES
Gordon, H. R., Atmospheric correction of ocean color imagery in the Earth Observing Observation System era, J. Geophys. Res., vol. 102, pp. 17081-17106, 1997.
Ottaviani, M., Spurr, R., Stamnes, K., Li, W., Su, W., and Wiscombe, W. J., Improving the description of sunglint for accurate prediction of remotely-sensed radiances, J. Quant. Spectrosc. Radiat. Transfer, vol. 109, pp. 2364-2375, 2008.
Spurr, R. J. D., LIDORT and VLIDORT: Linearized pseudo-spherical scalar and vector discrete ordinate radiative transfer models for use in remote sensing retrieval algorithms, Light Scattering Reviews, Vol. 3, Kokhanovsky, A. (Ed.), Springer, Berlin, 2008.
Tsay, S.-C. and Stephens, G. L., A Physical/Optical Model for Atmospheric Aerosols with Application to Visibility Problems, Department of Atmospheric Sciences, Colorado State University, Fort Collins, 1990.
Wang, M. and Bailey, S., Correction of sun glint contamination on the SeaWiFS ocean and atmosphere products, Appl. Opt., vol. 40, pp. 4790-4798, 2001.
Yan, B., Stamnes, K., Li, W., Chen, B., Stamnes, J. J., and Tsay, S.-C., Pitfalls in atmospheric correction of ocean color imagery: How should aerosol optical properties be computed? Appl. Opt., vol. 41, pp. 412-423, 2002.
Zhang, K., Li, W., Stamnes, K., Eide, H., Spurr, R., and Tsay, S. C., Assessment of the MODIS algorithm for retrieval of aerosol parameters over the ocean, Appl. Opt., vol. 46, pp. 1525-1534, 2007.
Verweise
- Gordon, H. R., Atmospheric correction of ocean color imagery in the Earth Observing Observation System era, J. Geophys. Res., vol. 102, pp. 17081-17106, 1997.
- Ottaviani, M., Spurr, R., Stamnes, K., Li, W., Su, W., and Wiscombe, W. J., Improving the description of sunglint for accurate prediction of remotely-sensed radiances, J. Quant. Spectrosc. Radiat. Transfer, vol. 109, pp. 2364-2375, 2008.
- Spurr, R. J. D., LIDORT and VLIDORT: Linearized pseudo-spherical scalar and vector discrete ordinate radiative transfer models for use in remote sensing retrieval algorithms, Light Scattering Reviews, Vol. 3, Kokhanovsky, A. (Ed.), Springer, Berlin, 2008.
- Tsay, S.-C. and Stephens, G. L., A Physical/Optical Model for Atmospheric Aerosols with Application to Visibility Problems, Department of Atmospheric Sciences, Colorado State University, Fort Collins, 1990.
- Wang, M. and Bailey, S., Correction of sun glint contamination on the SeaWiFS ocean and atmosphere products, Appl. Opt., vol. 40, pp. 4790-4798, 2001.
- Yan, B., Stamnes, K., Li, W., Chen, B., Stamnes, J. J., and Tsay, S.-C., Pitfalls in atmospheric correction of ocean color imagery: How should aerosol optical properties be computed? Appl. Opt., vol. 41, pp. 412-423, 2002.
- Zhang, K., Li, W., Stamnes, K., Eide, H., Spurr, R., and Tsay, S. C., Assessment of the MODIS algorithm for retrieval of aerosol parameters over the ocean, Appl. Opt., vol. 46, pp. 1525-1534, 2007.