dosycorps / swdlyt

Master's Thesis - Math Modeling of the Light Field in Kelp Aquaculture

swdlyt

It's a light model for seaweed!

Numerically solve the Radiative Transfer Equation in Fortran 90 in order to model the light field in a vertical-line kelp aquaculture environment.

This is the code used in my Master's Thesis in applied math. The full thesis can be found at https://github.com/OliverEvans96/msthesis

Abstract:

A mathematical model is developed to describe the light field in vertical line seaweed cultivation to determine the degree to which the seaweed shades itself and limits the amount of light available for photosynthesis. A probabilistic description of the spatial distribution of kelp is formulated using simplifying assumptions about frond geometry and orientation. An integro-partial differential equation called the radiative transfer equation is used to describe the light field as a function of position and angle. A finite difference solution is implemented, providing robustness and accuracy at the cost of large CPU and memory requirements, and a less computationally intensive asymptotic approximation is explored for the case of low scattering. Conditions for applicability of the asymptotic approximation are discussed, and depth-dependent light availability is compared to the predictions of simpler light models. The 3D model of this thesis is found to predict significantly lower light levels than the simpler 1D models, especially in regions of high kelp density where a precise description of self-shading is most important.