SIAM News Blog

Seasonal Marine Phytoplankton Blooms: Understanding the Phenomenon’s Dynamics

By Seth Cowall, Matthew Oliver, and L. Pamela Cook

Phytoplankton are microscopic organisms that are crucial to Earth’s ecosystems. They comprise the base of the marine food web and are a significant source of oxygen in the atmosphere. Their life cycles also result in a sink of atmospheric carbon dioxide, a process known as the biological pump. Many regions of the world's oceans experience a seasonal phytoplankton bloom — a rapid increase in the phytoplankton population. Understanding the timing of seasonal blooms is important for both marine ecology and atmospheric science, although the precise threshold definition of blooms has been debated. For a bloom to occur, biomass gains due to sufficient access to light and nutrients must be greater than losses due to predation, sinking, and mixing [4]. These conditions depend on seasonal changes in sunlight intensity, oceanic turbulence, and thickness of the ocean’s upper mixed layer. 

Since the mid-20th century, researchers have proposed various theories on how these seasonally-changing environmental conditions affect phytoplankton physiology and cause blooms. One idea predicts that as depth of mixing increases in the ocean in the winter, zooplankton (predator) have a more difficult time finding phytoplankton (prey). This could be the dominant cause of phytoplankton blooms, rather than seasonal variation nutrients and light availability [1]. 

The results of our research suggest a potential source of the ecological disruption described in [2]. We model the marine planktonic ecosystem with a depth- and time-dependent nutrient-phytoplankton-zooplankton (NPZ) model. The model is a system of three coupled reaction-diffusion equations with three state variables—\(N\) (nutrients), \(P\) (phytoplankton), and \(Z\) (zooplankton)—and time-varying coefficients. We examined the three equilibrium states of the model [3]: a plankton-free equilibrium (at which phytoplankton and zooplankton do not exist), a phytoplankton-only equilibrium (at which phytoplankton exist without zooplankton), and a coexisting equilibrium (where phytoplankton and zooplankton coexist). In nature, we do not expect an ecosystem to reach a plankton-free state or a phytoplankton-only state. However, our model has revealed that the phytoplankton-only equilibrium (which is dynamic in time) has attracting properties that significantly affect the phytoplankton population throughout an annual cycle.

Low winter sunlight limits phytoplankton growth. Since sunlight decays with depth in the water, high winter vertical diffusion in the ocean’s upper mixed layer limits phytoplankton access to sunlight. These seasonal conditions’ effect on the model have been tested with solar radiation data (photosynthetically active radiation) from NASA’s MODIS-Aqua satellite and mixed layer depth data from the HYbrid Coordinate Ocean Model (HYCOM). Incorporating this data into the model has the following effect on our simulated populations of phytoplankton and zooplankton. 

In the winter, when sunlight intensity is low and the vertical diffusion in the ocean mixed layer is high, the phytoplankton population decreases. Likewise, the zooplankton population decreases because their food source becomes scarce. With the onset of spring, the sunlight intensity increases and the vertical diffusion decreases. These environmental conditions—along with low grazing pressure from the depleted zooplankton population—facilitate rapid growth of the phytoplankton population. The planktonic ecosystem is attracted towards the dynamic phytoplankton-only equilibrium state. In our model, this rapid attraction corresponds with a phytoplankton bloom. As a consequence of this attractive state, the zooplankton population grows. The resulting grazing pressure reduces the phytoplankton population and terminates the bloom. By late spring, the planktonic ecosystem is restored to a pre-winter balance. The results indicate a mathematical representation of an ecological mechanism that contributes to seasonal phytoplankton blooms.

See the subsequent animation for more detail.

Seth Cowall presented this work during a minisymposium presentation at the 2019 SIAM Conference on Applications of Dynamical Systems, which took place last May in Snowbird, Utah.

[1] Behrenfeld, M.J. (2010). Abandoning Sverdrup's critical depth hypothesis on phytoplankton blooms. Ecology, 91, 977-989. 
[2] Behrenfeld, M.J., & Boss, E.S. (2014). Ressurecting the ecological underpinnings of ocean plankton blooms. Annu. Rev. Mar. Sci., 6, 167-194. 
[3] Cowall, S.T., Oliver, M.J., & Cook, L.P. (2019). Effects of different levels of solar radiation and depth-varying vertical diffusion on the dynamics of a reaction-diffusion NPZ model. J. Plankton Res., 41(6), 879-892. 
[4] Sverdrup, H. (1953). On conditions for the vernal blooming of phytoplankton. J. Cons., Cons. Int. Explor. Mer., 18, 287-295. 

Seth Cowall is a visiting professor of mathematics at Mercer University, where his research focuses on mathematical modeling of planktonic ecosystems from a dynamical systems perspective. He specializes in modeling with differential equations and nonlinear dynamics. Cowall's research interests also include applied mathematics problems in climate science and environmental issues.  
Matthew Oliver is the Patricia and Charles Robertson Distinguished Professor of Marine Science and Policy in the School of Marine Science and Policy at the University of Delaware. His research interests are in phytoplankton oceanography and physiology, remote sensing, polar marine systems, and related topics in oceanography.
L. Pamela Cook is a Unidel Professor of Mathematical Sciences at the University of Delaware. Her research focuses on modeling and simulations of physical systems, particularly nonlinear phenomena as evidenced in complex (viscoelastic) fluids.
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