Temperature dependence of a phytoplankton population in a 2D model of a coastal area

Abstract

Due to climate change, the sea temperature is rising. This temperature change has an effect on the phytoplankton population. Phytoplankton is responsible for more than 50 percent of the oxygen production on earth, and is therefore crucial for life on earth. In this report, the research question is: is the temperature increase of the water important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean?

To investigate this, first a 2D model for a coastal area of an ocean is formed. As a basis for this model the 0D model of Steele and Henderson is used to describe the predator-prey model for zooplankton and phytoplankton. Due to this model a repeating pattern in time arises, which is called a limit cycle. This predator-prey
model is expanded to a 2D model by applying convection (v) and diffusion (D) to it, representing the current and dispersion in the water. The chosen parameters and boundary conditions are inspired by the coastal area of the west coast of Portugal.

To evaluate the effect of the water temperature rising, first, the effect of diffusion and convection are studied by answering the following questions: is the convection important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean? And: is the diffusion important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean?

The diffusion is dominant in the direction perpendicular to the coast. Due to the diffusion the limit cycle of the predator-prey model is suppressed. Its range gets smaller until the plankton population is completely constant for D > 2.5 m^2/s. This critical value is included in the realistic value of D, which varies from 1 to 2000 m^2/s.

Due to convection, the limit cycle corresponding to the boundary condition occurs in the direction parallel to the coast, making every point in the domain steady state. The higher the velocity v corresponding to the convection is, the less oscillations in phytoplankton density there are in the domain, thus the larger the wavelength of the oscillation is. For v > 0.06 m/s the current is so fast that the predator-prey model has little time to develop before it reaches the right boundary, making the left boundary value more important. This critical value is included in the realistic value of v, which varies from 0.03 to 0.28 m/s.

The model experiences both diffusion and convection more or less equally when the Péclet number vH^2/DL≈1, resulting in D/v≈50 m. If this number is significantly larger than 50 m, diffusion dominates the solution. If the number is significantly smaller than 50 m, convection dominates the solution.

Now the main research question can be answered. By increasing the temperature of the water the growth rate of phytoplankton increases. Due to this increase, the timescale of the predator-prey (τpp ) decreases. The value of D and v for which the predator-prey model and diffusion and convection all influence the solution
equally depends on the timescale with the factor 1/τpp . A smaller time scale means that the predator-prey model contributes more to the model. However, this change is very small in comparison to the scale of the realistic values. In conclusion, in the formed 2D model the temperature increase of the water is not important for the development of the plankton population in space and time.

The results of this report are influenced by the assumptions and approximations made. In this study, several processes, both physical and biological, are described with constants and simplifications. Improving the models of these processes is left for further research.