Fig. 6.10 Ratio of scalar to downward irradiance at the mid-point of the euphotic zone as a function of the ratio of scattering to absorption coefficients. Data obtained by Monte Carlo calculation for vertically incident monochromatic light using the method of Kirk (1981a, c).

by light flux as its zenith angle increases), at any point in the water the value of scalar irradiance is always higher than that of downward irradiance.

From the radiance distribution data for Lake Pend Oreille, USA,1076,1380 it is possible to calculate that in the 480 nm waveband the ratio E0/Ed is 1.30 to 1.35 for various depths within the euphotic zone. The higher the ratio of scattering to absorption, the more diffuse the underwater light field becomes, and the greater the difference between E0 and Ed. Figure 6.10 shows the way E0/Ed at the mid-point of the euphotic zone (zm) increases as the ratio of the scattering coefficient to the absorption coefficient increases: E0/Ed is equal to 1.5, 1.75 and 2.0 for b/a values of 6, 10 and 18, respectively. Since the absorption coefficient of natural waters can vary markedly with wavelength, the ratios of scalar to downward irradiance will vary across the spectrum. Taking the whole photosynthetic waveband, for clear oceanic waters the average b/a ratio is low enough to give rise to E0/Ed values of up to about 1.2. For typical inland and some coastal waters, however, with b/a values in the region of 4 to 10, or even up to 20 or 30 in the most extreme cases, we might commonly expect E0/Ed to be in the region of 1.4 to 1.8, rising to 2.0 to 2.5 in the very turbid waters.

Thus, if it is wished to determine the absolute amount of light available for photosynthesis at a given depth in a water body, a measurement of downward irradiance may seriously underestimate this, particularly in turbid waters. On the other hand, the vertical attenuation coefficient, Kd, for downward irradiance is close in value to the vertical attenuation coefficient, K0, for scalar irradiance. Monte Carlo calculations (Kirk, unpublished) show that for media with b/a ranging from 0.3 to 30, Kd/ K0 varies only between about 1.01 and 1.06. The measured value of Kd can therefore be taken as a reasonable estimate of the value of K0, and used to predict the attenuation of scalar irradiance with depth.

It would be useful to have, for any given water body, a measure of the total amount of light available for photosynthesis at a given instant, throughout the whole water column, 1 m square. We shall give this parameter the symbol, Qt: it has the units joules or quanta. Assuming that no light reaches the bottom, it can be shown that

Where E0(0) is the scalar irradiance just below the surface, cw is the speed of light in water and wK0(av) is the irradiance-weighted vertical attenuation coefficient for scalar irradiance (ยง1.3). Thus, if one water body has a wK0(av) value twice that in another water body, then for a given subsurface scalar irradiance it has about half the total amount of light available for photosynthesis.

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