Analysis of the Self-Shading Effect on Algal Vertical Distribution in Natural Waters*

Self-shading of light by algae growing in a column of water plays an important:role in the dynamics of algal blooms. Thus without self-shading the algal concentration would increase more rapidly, making the nutrient limitation too strong. Apart from the practical importance of self-shading, its inherent nonlinearity in the growth dynamics leads to an interesting mathematical problem, which warrants detailed analytical investigation. Our mathematical model for the self-shading effect includes vertical diffusion; algal settling, gross production, and collective losses of algae. Steady-state solutions of the model equation are investigated in detail by the phase plane method, and their stability examined. Finally we discuss the vertical profile of algal concentration.