## Vertical attenuation coefficients for downward irradiance

As well as providing information about levels of phytoplankton, suspended solids and CDOM, remotely sensed radiances can be used to map vertical attenuation coefficients for downward irradiance. Austin and Petzold (1981) derived empirical relationships by means of which Kd(490) and Kd(520) could be obtained from the ratio of radiances in the CZCS 443 and 520 nm wavebands. Analysing SeaWiFS data mainly from Case 1 waters, Mueller (2000) arrived at the following algorithm for Kd(490)

nLw(490)

nLw(555)

-1.5401

where nLw(1) is the normalized water-leaving radiance at wavelength 1, and the 0.016 term is the Kd(490) for pure water. An updated version of this algorithm,1451 omitting the constant term is

This algorithm (SeaWiFS K[490]) does not, however, work well in waters where Kd(490) is greater than 0.25 m-1. As referred to earlier, McKee and Cunningham (2006) found that the Irish and Celtic Seas could be classified into one or other of two optical water types: A with higher scattering/ absorption and B with lower scattering/absorption ratios. McKee et al. (2007), on the basis of in situ measurements at 102 stations, found that the SeaWiFS K(490) algorithm satisfactorily predicted Kd(490) from water-leaving radiances in the clearer, B, waters but in the more turbid, A, waters an algorithm with altered coefficients

nLw(555)

-3.0054

worked better.

An alternative route to Kd(490), proposed by Morel et al. (2007) is to first use the remotely sensed data to retrieve the chlorophyll concentration and then apply the following algorithm based on [Chl]

Lee et al. (2005) have devised a more complex, semi-analytical, algorithm for remotely sensing Kd(490), which appears to be more widely applicable than the standard empirical algorithms. The first step is to use a previously devised quasi-analytical algorithm788,787 to estimate a and bb at the wavelength of choice, e.g. 490 nm, from remotely sensed radiances at 440 and 555 nm. Kd is then calculated using an equation expressing Kd as a function of a and bb, derived empirically from Hydrolight simulations790

Kd = (1 + 0.0050a)a + 4.18(1 - 0.52e-1()'8a)bb where 0a is the solar zenith angle.

In any given optical water type there should be an approximately constant relationship between Kd(490), which can be determined by remote sensing, and Kd(PAR), the coefficient for the whole photosyn-thetic waveband. To be able to map Kd(PAR) from remote sensing data would be of great value for studies of ocean productivity, but the relationship between the two coefficients is likely to vary from one water type to another. Pierson et al. (2008) used values of inherent optical properties determined at a large number of sites in the Baltic Sea to model the underwater light field. They found that Kd(PAR) could satisfactorily be expressed in terms of Kd(490), either as a linear

or a power

relationship. The Baltic Sea is, as we have noted earlier, untypical because of its high CDOM concentration. Other relationships will therefore need to be found for other parts of the ocean. On the basis of an extensive oceanic data set, primarily but not exclusively in Case 1 waters, Morel et al. (2007) propose

Kd (PAR) = 0.0665 + 0.874 Kd(490) - 0.00121 [Kd (490)]-1

Lee et al. (2007) have developed a method using values of IOPs calculated from remotely sensed Rs(1) data by the quasi-analytical algorithm (above), to determine the euphotic depth (zeu), which is equivalent, since Kd(PAR) « 4.6/ zeu, to determining Kd(PAR) itself. The method worked reasonably well for certain coastal, as well as oceanic, waters.

Another broad waveband of major ecological significance is the near-UV, 300 to 400 nm, not only because of its damaging effects on marine life forms, and its contribution to the photoinhibition of photosynthesis (§10.1), but also because of its role in the photochemical breakdown of coloured dissolved organic matter. The incident solar UV flux can now be monitored from space with ozone-mapping satellite-borne spectrometers. Remote sensing of vertical attenuation coefficients in the UV would thus make it possible to assess the underwater UV radiation field in different parts of the ocean. On the basis of in situ measurements in the Bering Sea and the Mid-Atlantic Bight, Johannessen et al. (2003) derived empirical expressions for Kd(l) at 323, 338 and 380 nm as simple power law functions of the ratio of radiance reflectance at 412 nm to that at 555 nm. Using SeaWiFS radiances at 412 and 555 nm they were then able to map the distribution of Kd(323) in the Mid-Atlantic Bight. Starting from a more wide-ranging in situ data set, and using a more complex statistical approach (principal component analysis), Fichot et al. (2008) have devised two new algorithms for mapping Kd(l) in the UV at 320, 340 and 380 nm, which give a somewhat improved performance.

Vasilkov et al. (2001) developed an algorithm for calculating UV penetration into Case 1 waters based on the simplifying assumption that the optical properties of such waters are entirely attributable to water and phytoplankton together with a CDOM contribution having an a(440 nm) corresponding to 20% of the phytoplankton plus water absorption at that wavelength. For the optical properties the starting input data were the standard SeaWiFS estimates of chlorophyll a and Kd(490). Specific absorption coefficients (absorption per mg chl a, m2mgchl a-1) for phytoplankton in the UV - where there is substantial absorption by mycosporine-like amino acids (see §3.3) - were taken from literature data for coastal waters of the Antarctic Peninsula. The authors acknowledged that these may not be entirely typical for the ocean at large, but there was a shortage of such data at the time. To estimate the backscattering coefficient, use was made of an approximate relationship developed by Gordon (1989a)

between the vertical attenuation coefficient for downward irradiance (Kd), the distribution function (D0, the reciprocal of the average downward cosine) just under the surface, and a plus bb. D0 is readily obtained as a simple function of solar angle, and the relative amount of direct sunlight and skylight. a(490) was derived from the SeaWiFS chlorophyll value together with the CDOM assumption and an appropriate CDOM spectrum. The SeaWiFS Kd(490), and the calculated D0 and a(490) values were then used in the Gordon equation to derive bb(490). The values of bb at wavelengths in the UV were calculated from bb(490) on the assumption that bb is proportional to I-1. Using the values of a(l) and bb(1) derived as above, together with the appropriate values of solar angle and the proportion of direct and diffuse sunlight, penetration of UV radiation into the water column was calculated using a simple analytical model. Data from the Total Ozone Mapping Spectrometer (TOMS) satellite instrument provided solar UV irradiance values at the ocean surface. The final output data are presented in various ways, including the distribution of the 10% UVB (280-320 nm) penetration depth over the global ocean for the month of July 1998.

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