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

A Monte Carlo computer simulation has been used to determine the ratio of the scalar irradiance E(0) to the downwelling irradiance E(d). These E(0)/E(d) 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 </= theta' </= 89 degrees plus a diffuse cardioidal distribution). Mathematical expressions were curve fitted to the Monte Carlo outputs to yield relationships between E(0)/E(d) 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 E(0)/E(d) ratio at the 1% downwelling irradiance depth is the same for theta' = 0 degrees as for diffuse cardioidal incidence, and (b) for R>0.08, the E(0)/E(d) ratio at the 10% downwelling irradiance depth for theta'= 0 degrees is nearly the same as the E(0)/E(d) ratio at the 1% downwelling irradiance depth for diffuse cardioidal incidence.