Numerical Reaction-transport Model of Lake Dynamics and Their Eutrophication Processes

Abstract

A 1D numerical reaction-transport model (RTM) that is a coupled system of partial differential equations is created to simulate prominent physical and biogeochemical processes and interactions in limnological environments. The prognostic variables considered are temperature, horizontal velocity, salinity, and turbulent kinetic energy of the water column, and the concentrations of phytoplankton, zooplankton, detritus, phosphate (H3PO4), nitrate (NO3-), ammonium (NH4+), ferrous iron (Fe2+), iron(III) hydroxide (Fe(OH)3(s)), and oxygen (O2) suspended within the water column. Turbulence is modelled using the k-e closure scheme as implemented by Gaspar et al. (1990) for oceanic environments. The RTM is used to demonstrate how it is possible to investigate limnological trophic states by considering the problem of eutrophication as an example. A phenomenological investigation of processes leading to and sustaining eutrophication is carried out. A new indexing system that identifies different trophic states, the so-called Self-Consistent Trophic State Index (SCTSI), is proposed. This index does not rely on empirical measurements that are then compared to existing tables for classifying limnological environments into particular trophic states, for example, the concentrations of certain species at certain depths to indicate the trophic state, as is commonly done in the literature. Rather, the index is calculated using dynamic properties of only the limnological environment being considered and examines how those properties affect the sustainability of the ecosystem. Specifically, the index is calculated from a ratio of light attenuation by the ecosystem’s primary biomass to that of total light attenuation by all particulate species and molecular scattering throughout the entire water column. The index is used to probe various simulated scenarios that are believed to be relevant to eutrophication: nutrient loading, nutrient limitation, overabundance of phytoplankton, solar-induced turbulence, and wind-induced turbulence.