Utilizing the components of vector irradiance to estimate the scalar irradiance in natural waters

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Abstract
A Monte Carlo computer simulation has been used to determine the ratio of the scalar irradiance E0 to the downwelling irradiance Ed. These E0/Ed ratios were calculated at depths corresponding to the 100, 10, and 1% downwelling irradiance levels. A range of volume reflectance 0 ≤ R ≤ 0.14 was considered, as were six conditions of incident radiation (collimated beams with incident angles 0 ≤ θ′ ≤ 89° plus a diffuse cardioidal distribution). Mathematical expressions were curve fitted to the Monte Carlo outputs to yield relationships between E0/Ed and R for the depths and incident conditions considered. It was found that in many cases a single relationship would not accommodate the entire range of volume reflectances and that R = 0.055 provided an appropriate demarcation for mathematical curve fitting. Curves, tables, and equations are presented which indicate (a) for all R > ~0.02, the E0/Ed ratio at the 1% downwelling irradiance depth is the same for θ′ = 0° as for diffuse cardioidal incidence, and (b) for R > ~0.08, the E0/Ed ratio at the 10% downwelling irradiance depth for θ′ = 0° is nearly the same as the E0/Ed ratio at the 1% downwelling irradiance depth for diffuse cardioidal incidence.