alg_shd_nl

Nonlinear algal self-shading coefficient

The light extinction coefficient, $k_l$, is calculated as a function of the algal density using the nonlinear equation:

$k_l=k_{l,0}+k_{l,1}*\alpha_0*algae+k_{l,2}*(\alpha_0*algae)^{2/3}$

where $k_{l,0}$ is the non-algal portion of the light extinction coefficient ($m^{-1}$), $k_{l,1}$ is the linear algal self shading coefficient ($m^{-1}(\mu g - chla/L)^{-1})$, $k_{l,2}$ is the nonlinear algal self shading coefficient $m^{-1}(\mu g - chla/L)^{-2/3})$, $\alpha_0$is the ratio of chlorophyll a to algal biomass ($\mu g$ chla/mg alg), and $algae$ is the algal biomass concentration (mg alg/L).

This equation allows a variety of algal, self-shading, light extinction relationships to be modeled. When both $k_{l,1}$ and $k_{l,2}$ are set to 0, no algal self-shading is simulated. When $k_{l,1}$ is set to a value other than 0 and $k_{l,2}$ is set to 0, linear algal self-shading is modeled. When both $k_{l,1}$ and $k_{l,2}$ are set to a value other than 0, non-linear algal self-shading is modeled.

The Riley equation (Bowie et al., 1985) defines $k_{l,1} = 0.0088 m^{-1}(\mu g - chla/L)^{-1}$ and $k_{l,2} = 0.054 m^{-1}(\mu g - chla/L)^{-2/3})$.

Relevant chapter in the Theoretical Documentation:

Local Specific Growth Rate of Algae

References

Bowie, G.L., W.B. Mills, D.B. Porcella, C.L. Campbell, J.R. Pagenkopt, G.L. Rupp, K.M. Johnson, P.W.H. Chan, and S.A. Gherini. 1985. Rates, constants, and kinetic formulations in surface water quality modeling, 2nd ed. EPA/600/3-85/040, U.S. Environmental Protection Agency, Athens, GA.