Solving the problems in Ocean Biogeochemical Dynamics — Chapter I — Part I

In this article I would like to summarise the solutions for the problems in each chapter of the book Ocean Biogeochemical Dynamics. As a beginner in this topic, I follow the book written by Jorge Sarmiento and Nicolas Gruber. To me it is important to put the knowledge gained, in this article as a summary.

At the end, the aim of the project I will be involved in, is to apply ML methods to speed up the Ocean Models, which I will put in an upcoming article. For this purpose, I have to learn about the problem at hand, and as a first step, this book might be a good starter.

In the first chapter, one is introduced with different ocean hypothesis and models, which essentially uses the so called box models. These box models are a rough simplifications of how the ocean can be modelled by dividing the ocean into surface and deep ocean, equatorial or arctic areas. The importance of the life cycles of the nutrients, mixture, river intake, phytoplanktons and minerals induced from the rivers. There are three hypothesis for explaining the distribution of the chemical minerals in the oceans: The accumulution hypothesis, kinetic control hypothesis, and the equilibrium hypothesis.

Accumulation hypothesis:

• Ocean concentrations = River inflow

Kinetic control hypthesis:

• Ocean concentrations = Balance (Input vs. Bio-Removal )

Equilibrium hypothesis:

• Equilibria between seawater, chemicals from seawater, solid particles, sediments, and oceanic crust.

The valuable method to start asking the questions raised in the problems part, is then to reinforce oneself to rehearse knowledge gained passively by reading the book.

1. Explain in words why we think that neither the accumulation hypothesis nor the equilibrium control hypothesis is correct for explaining the huge variations that we observe for the mean oceanic concentration of the different elements in the ocean? Describe the test that we devised for the accumulation hypothesis and what information we used to reject this hypothesis

• The accumulation hypothesis violates with the age of the ocean which is 30 times older than the calculation made based on the accumulation time.

2. Do the same for the equilibrium hypothesis

• The equilibrium hypothesis neglects the fact of bio removal process and concentration of rivers does not explain the different concentration in oceans

3. If we nevertheless accept the hypothesis that the mean concentraton of elements in the ocean is a result of the accumulation from river input, how large would today`s ocean concentration be of magnesium, arsenic, chlorine, and gold? Use an ocean age of 3.85 billion years and the river concentrations given in table 1.1.1:

• t_acc (Element) = C_ocean/C_River * V_ocean/v_River
• C_Ocean(Mg) = v_River/V_Ocean * C_River(Mg) * t_acc

4. List two elements that fall into each of the following categories: biolimiting, biointermediate, and biounlimited. Explain the basis of your choice.

Biounlimited: Uniform concentraion B, F, Na, Mg, S, Cl, K, Ca,Br

Biolimiting: Nearly depleted at surface: N, Si, P,Cu, Zn, Ag

Biointermediate: Partial depletion at surface: Cu, As, Se, Be, Ge, Bi, Ba, Ra, La, Pr

5. During photosynthesis, how many free oxygen molecules are produced per nitrogen atom consumed?

Oxygen per Nitrogen 150:16

This is the structure of the article that I plan to compose. But the question remains if this method is valuable or a better approach or a summary should be used.