The Analytical Method

With this method, the radiative transfer equations can be simplified for the retrieval of the variables of interest, and hence, the weak benthic signal containing the desired layer of information about the seagrasses can be untangled from remote sensing image data. For instance, Eq. (11) (or the more detailed equations preceding that derivation) can be inverted for a spectral band to enable the determination of one variable such as bottom reflectance (Rb) provided that all the other variables are known or can be estimated. When based solely on the remote sensing reflectance, only (R(0-,H) is measured (after atmospheric and air-water interface correction).

As more spectral bands become available it becomes possible to determine more variables. In theory, if we have two spectral bands (containing some uncorrelated information) then two variables can be directly retrieved, with three spectral bands three variables can be directly retrieved, and so on. These variables do need to have a measurable influence (from an aircraft or space sensor) on the spectral band reflectances!

To obtain bottom reflectance (Rb), we would need to invert Eq. (11) and to do this we would need to be able to determine two reflectances (R(0-, H) and RTO), four vertical attenuation coefficients (Kd, Ku, kb , and kc) and the water column depth, which would require a minimum of eight spectral bands for direct inversion calculations. Since the vertical attenuation coefficients are spectrally similar and potentially spatially variable (e.g. Karpouzli et al., 2003), it is difficult to determine these directly from remotely sensed image bands.

A solution to this problem is to look at the inherent optical properties of absorption, scattering, or preferably backscattering of each of the components of the water. The spectral shapes of these components are more specific and thus have a better chance of being estimated from spectral information. The vertical attenuation coefficients can then be calculated from the inherent optical properties. Inversion of an 8 band, 8 variable set of equations (that contain some nonlinear effects) is virtually impossible, especially if one realizes that all the remote sensing data contain some level of noise. Solutions are possible; but these will be discussed only after considering another pathway to understanding the underwater light climate and the detection of substratum reflectance: the Radiative Transfer of Energy theory (RT) based modeling approach (see chapter 12 for introduction to RT theory and chapter 13 for the application of RT theory to seagrass canopy light interactions).

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