Mathematics of Critical Depth Hypothesis in Oceanography

Background and Goal

One of the most fundamental hypotheses in all of Biological Oceanography is the Critical Depth Hypothesis, which puts forward a plausible mechanism to explain the initiation of phytoplankton blooms.   While the term "Critical Depth" was coined by a famous Norwegian oceanographer named Harald Sverdup in his 1953 paper, the idea was originally developed in 1932, when oceanographers Atkins and Gran published the basic tenets from observations made in none other than….the Bay of Fundy, Canada[ Read more about the origin of biological oceanography in the Bay of Fundy in: Behrenfeld. M. and Boss, E. 2018. Student's tutorial on bloom hypotheses in the context of phytoplankton annual cycles.  Global Change Biology 24: 55-77 ].  The expedition was conducted out of what is now the Saint Andrews Biological Station in New Brunswick.  The discipline of biological oceanography was launched in our very own back yard!  Although more modern theories to explain phytoplankton bloom dynamics now exist (Critical Division Rate Hypothesis, Critical Turbulence Hypothesis, and Disturbance-Recovery Hypothesis1), they each contain elements of the original theory, and emerging theories are usually compared to the benchmark Critical Depth Hypothesis.  Critical Depth remains valid under some conditions, and is still published about today. The goal of this assignment is to explore the mathematics underlying Critical Depth.

You may answer the questions in a word document or on paper.  If you choose to use pen and paper, you will need to take photographs or scans of your written work and paste them into a word document before submitting.   If you choose to use pen and paper, ensure that your writing is neat and legible.   All submissions will be word documents submitted on D2L.   

Q1. In the early springtime at mid-day in the deep ocean off Halifax, you are sampling the ocean where the seafloor is located 2000 m below the water surface. The irradiance on the surface of the ocean here is 500  m-2 s-1.  50 % of surface radiation is PAR.  Assume the light extinction coefficient (k) is on average 0.14 m-1 in the PAR part of the irradiance spectrum.  Two species of phytoplankton are growing in this ecosystem.  Species A reaches a compensation light intensity at 1  m-2 s-1.  Species B reaches compensation light intensity at 10  m-2 s-1 .

a) At what depth in the water column does photosynthesis (P) exactly balance respiration (R) for each of the two species? ( /6 marks)

b) What is the gross rate of photosynthesis for each species at the depth calculated in part A (i.e., Species A and B will have different values), if Pmax = 10 mg C mg Chla-1 hr-1, and KI = 45  m-2 s-1  for both species?  Which population is growing more efficiently? (/6 marks)

Q2. Finding and understanding Compensation Depth

a) Sketch the Photosynthesis vs Depth (P vs D) and Respiration vs. Depth (R vs D) curves for each species.  Make a separate plot for each species.  Draw both the P vs D and R vs D curves on the same plot (as in Fig. 3.6 in your textbook).  Display and label the Compensation Depth on each plot.  Refer to the grading scheme for plots to make sure you include all of the elements that will be graded. (/11 marks)

b) What is the respiration rate at the compensation depth for each species? (/2)

c) Using the information in parts A through C, what process is driving the difference in Compensation Depth between the two species? (/2)

Q3. Scientists want to predict which of these two species will be the first to bloom with the onset of springtime conditions, assuming the Critical Depth Hypothesis holds. To do this, they collected CTD profiles from the deep ocean off Halifax from two time periods; March and May. 

a) Calculate the Critical Depth for each of Species A and Species B using the information given in Question 1.  (/5)

b) Which species (A and/or B) is likely to bloom under the conditions measured in each of spring and summer that are shown in Figure 1 on the next page? Explain your answer in the context of the Critical Depth Hypothesis. (/4)