Page updated: February 13, 2021
Author: Curtis Mobley
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The contribution of white caps and foam to the TOA radiance depends on two factors: the reflectance of whitecaps per se and the fraction of the sea surface that is covered by whitecaps.

Following Gordon and Wang (1994b), the contribution of whitecaps and foam at the TOA is

t(𝜃v,λ)ρwc(λ) = [ρwc(λ)]Nt(𝜃s,λ)t(𝜃v,λ),

where t(𝜃v,λ) is the diffuse atmospheric transmission in the viewing direction, t(𝜃s,λ) is the diffuse transmission in the Sun’s direction, and [ρwc(λ)]N is the non-dimensional normalized whitecap reflectance. [ρwc(λ)]N is defined in the same manner as was the normalized water-leaving reflectance [ρw(λ)]N in Eq. (3.3) of the Normalized Reflectances page, namely

[ρwc]N π Fo[Lwc]N = π R Ro 2L wc(𝜃s) Fo cos 𝜃st(𝜃s), (1)

where Lwc is the whitecap radiance. It is assumed that the whitecaps are Lambertian reflectors, so that (unlike for Lw) Lwc does not depend on direction 𝜃v,ϕ. This gives the interpretation (Gordon and Wang (1994b), page 7754) that ”ρ is the reflectance–the reflected irradiance divided by the incident irradiance–that a Lambertian target held horizontally at the TOA would have to have to produce the radiance L.” [ρwc]N can be interpreted as the average reflectance of the sea surface that results from whitecaps in the absence of atmospheric attenuation.

The effective whitecap irradiance reflectance is taken from Koepke (1984) to be 0.22 (albeit with ± 50% error bars). This reflectance is independent of wavelength. This gives [ρwc]N = 0.22Fwc, where Fwc is the fraction of the sea surface that is covered by whitecaps. The fractional coverage is taken from Stramska and Petelski (2003), who give two models for for Fwc:

Fwc = 5.0 × 105(U 10 4.47)3fordevelopedseas (2) Fwc = 8.75 × 105(U 10 6.33)3forundevelopedseas (3)

where W is the wind speed in ms1 at 10 m. Formula (3) for undeveloped seas is used on the assumption that if the seas are well developed it is probably stormy, hence cloudy, so that remote sensing is not possible. The blue curve in Fig. (4) shows Fwc for undeveloped seas.

The final model for [ρwc]N is then taken to be

[ρwc]N(λ) = awc(λ) × 0.22 × Fwc = awc(λ) × 1.925 × 105(U 10 6.33)3. (4)

A whitecap correction is applied for wind speeds in the range 6.33 U10 12ms1. The factor awc(λ) is a normalized whitecap reflectance that describes the decrease in reflectance at red and NIR wavelengths. This factor is taken from Figs. 3 and 4 of Frouin et al. (1996); the values are

λ =412443490510555 670 765 865
awc =

Linear interpolation is used as needed between these values. Figure 1 shows the whitecap reflectance as given by Eq. (4) when awc = 1.


Figure 1: Whitecap normalized reflectance as given by Eq. (4) with awc = 1, and the fraction of sea surface whitecap coverage as given by Eq. (3).

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