One of the most common descriptors of the penetration of sunlight in water is the diffuse attenuation coefficient, K(λ), or Kd(λ) when calculated from vertical profiles of downwelling irradiance, Ed(λ). Where z is depth, this relationship is:
For homogeneous waters, a plot of the logarithm of Ed(λ,z) versus z forms a straight line, and Kd(λ,z) is the localized slope of that line (Figure 1).
Figure 1: Downwelling irradiance (x-axis) as a function of depth (on y-axis). Note that the x-axis is logarithmic. In this presentation, the change of irradiance with depth is a straight line, and the slope of the line is K(λ,z). The signal at the bottom 4 meters of the 710 nm plot originates from Raman scattering.
The equation defining Kd can also be written as
This is a linear equation of the form Y=mx where m=Kd is the slope.
When calculating Kd from vertical profiles of irradiance, irradiance values do not have to be calibrated as the irradiance units drop out.