One of the most common descriptors of the penetration of sunlight in water is the diffuse attenuation coefficient, K(λ), or K_d(λ) when calculated from vertical profiles of downwelling irradiance, E_d(λ). Where z is depth, this relationship is: 

For homogeneous waters, a plot of the logarithm of E_d(λ,z) versus z forms a straight line, and K_d(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 K_d can also be written as 

 Ln[E_d(λ,z)/E_d(λ,z+dz)]=K_d(z)

This is a linear equation of the form Y=mx  where m=K_d is the slope. 

When calculating K_d from vertical profiles of irradiance, irradiance values do not have to be calibrated as the irradiance units drop out.