# alg\_shd\_nl

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](/io-docs/theoretical-documentation/section-7-main-channel-processes/in-stream-nutrient-processes/algae/algal-growth/local-specific-growth-rate-of-algae.md)

#### 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.


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