Available at: https://digitalcommons.calpoly.edu/theses/3237
Date of Award
3-2026
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Paul Choboter
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
Near-bottom hypoxia occurs when dissolved oxygen levels drop to a level that is harmful to marine biology, creating biological dead zones along the ocean floor. Recent years have seen a dramatic increase in the percentage of coastal, near-bottom, hypoxic water, with the average in 2021 nearly double that of the average from 2009 to 2018 and about twenty-eight times the average from 1950 to 1980. Recent literature has linked this increase in oceanic hypoxia to the increase in upwelling-favorable winds caused by climate change. Upwelling brings low-oxygen, nutrient-rich water up to the surface, leading to plankton blooms and mass consumption of oxygen as the bacteria decompose the increase in biological matter.
Attempts to replicate this process numerically are often done with complex numerical simulations with high fidelity. However, simple mathematical models that recreate this system through differential equations of just a few state variables are far less common. Addressing this gap in the literature, we take a simple oxygen-phytoplankton-zooplankton model and add idealized upwelling forces via two smooth, multiplicative forcing functions. Simple upwelling-induced hypoxia is achieved by perturbations causing trajectories to leave non-trivial basins of attraction. Survival under upwelling forces is shown to be much more nuanced, with the character of that survival changing depending on upwelling strength and frequency.