The estimation of whitecap (foam) reflectance correction follows the form:
rhowc = awhite ∗ 0.4 ∗ 6.49E-7 ∗ ws3.52
The 'awhite' coefficient is a wavelength dependent factor to address the decreasing reflectance vs wavelength in the red/nir following Frouin (1996)
The 6.49E-7 ∗ ws^3.52 is the wind speed (ws) dependent fractional coverage for whitecaps from Monahan and O'Muircheartaigh (1980) multiplied by the effective reflectance of whitecaps from Koepke. The Monahan and O'Muircheartaigh power function is: 2.95e-6 ∗ ws^3.52 (ws taken at 10m)
The Koepke effective reflectance for whitecaps is 22%:
2.95E-6 ∗ 0.22 = 6.49E-7
The 0.4 is a wavelength independent "albedo modifier" designed to produce an effective modifier of ~25% of the Koepke-derived whitecap reflectance for 865nm. The reason for this dates back to reprocessing #2. At that time, there was a wavelength-independent correction (i.e. no Frouin spectral dependence), and it was determined that under high wind conditions, the whitecap correction was causing Lt-Lr-tLf to go negative and thus fail retrievals that should otherwise have been OK. It was suggested that a 75% reduction was needed. It worked, in that retrievals in these high wind cases were now possible.
We subsequently added the Frouin spectral dependence, which reduces whitecap reflectance in the NIR relative to the nearly constant visible reflectance. This reduction was on the order of 35% for 865 nm. To get back to the 75% Gordon suggested, we added the albedo modifier of 0.4 to ALL bands.
The big problem with the whitecap correction is the uncertainty. Koepke's effective reflectance for whitecaps as we use it is 22% (Koepke took Whitlock's (1982) value of 55% reflectance for fresh, dense foam in the visible (up to 800 nm) to be too large for real world applications and derived an efficiency factor of 0.4 &2212;0.2) That 22% has a HUGE error bar associated with it, could be 11%, could be 33%.
Another problem is the uncertainty in the wind speed. The wind speed not only affects the fractional coverage estimate for whitecaps, but also the Rayleigh calculation (and glint...). In cases where Lt-Lr-fLf went negative, we find that Lt-Lr goes negative. So, we implemented a rhoamin threshold so that in these cases (where the ability to estimate the aerosol type is shot) we fix the aerosol type and set the concentration to a small value - effectively disabling the aerosol correction.
Somewhere along our journey, we added a threshold to the wind speed that we allow to be used for the whitecap correction. This threshold is currently 8 m/s. The global average is 6-8 m/s. So, basically we've instituted a fixed whitecap correction for most of the globe. Given the power function used to relate wind speed to fractional coverage, wind speeds below about 6 m/s result in nearly zero whitecap reflectance.
In 2000, Moore published a paper on the augmentation to Lw by the spectral reflectance of whitecaps. He reports 'reasonable agreement' with previous work - reasonable meaning within a factor of 2 - for the 9–12 m/s range. He suggests the following:
rhowc = 3.4E-6 ∗ ws2.55 (for 412nm, based on rhowc of 0.0012 @ 10m/s)
Moore uses a different fractional coverage model (hence the 2.55 power vs 3.52), and derived the 3.4e-6 coefficient from a fit to his data. This results in a rhowc that is not much different from our current approach.
A paper by Stramska and Petelski (2003) suggests that the fractional coverage vs wind speed relationship needs revision. The current model is from 1975 and many argue that the interpretation of the photographic imagery as done in that Monahan paper is quite subjective.
The following are suggested for the next reprocessing:
The following figure shows the wavelength independent whitecap reflectance (the value used for the visible wavelengths) for the current correction (blue), Moore's suggested update (green), the Stramska model without the 0.4 albedo modifier (black) and with the albedo modifier (yellow). The red line is the suggested new wind speed maximum.
The following figure shows the histogram of wind speed for a single day - wind speeds that were ACTUALLY seen in the L2 process, not the wind speeds that the planet saw on that day. This is just to show where the new wind speed threshold falls is in a global sense.
