Session 3
Common Phytoplankton Models & The Spring Bloom
Papers to Read Before!
Riley 1946: a classic model for phytoplankton ecology
Siegel 2002: evaluating Sverdrup's critical depth hypothesis & the North Atlantic spring bloom
The Spring Bloom
The beautiful phenomenon of the North Atlantic spring bloom is a “greening” of the surface of the ocean that corresponds to rapid growth of phytoplankton as temperatures warm too match rising nutrient concentrations as winter stratification disappears. As noted by Siegel et al. (2002), this “greening” can move as quickly as 20 km/day.
Sverdrup’s Critical Depth Hypothesis
The defining equation for Sverdrup’s critical depth hypothesis is:
Where \(P(z)\) is a measure of primary productivity and \(I(z)\) is a measure of irradiance at some depth. \(\alpha\) is some slope that quantifies the linear dependence of primary productivity on irradiance, and \(I_0\) is the irradiance (or photosynthetically active radiation, PAR) at the surface. \(K\) is the “diffuse attenuation coefficient” of PAR, or in simple terms, how much PAR is reduced by the accumulation of overhead water with depth. \(R(z)\) is the loss processes at a given depth \(z\).
The reason this defines the critical depth hypothesis (CDH) is because the critical depth is where the integrated rates of photosynthesis and respiration are equal. We know that we will have more production than respiration whenever \(P(z) > R_0\) (“net production”). This defines the compensation depth (\(Z_C = \frac{1}{K} \textrm{ln} \left( \frac{P_0}{R_0} \right)\)). The critical depth, by contrast, happens whenever across all depths, we have balanced all of the effects of higher production at the surface and comparatively high respiration at depth (\(Z_{CR}\)).
Sverdrup’s assumptions
Sverdrup assumed a compensation depth \(I_C = 0.6\) mol photons m\(^{-2}\) day\(^{-1}\). We know that culture experiments are different than the real deal, and based on real-world estimates, this assumption is probably six times too small.
Community Composition Irradiance as a Metric
The tricky part about assessing Sverdrup’s hypothesis is that our metrics are imperfect. The spring bloom progresses northward, which means that as it travel,s the irradiance at the surface will be different relative to the commmunity composition irradiance, which is where the respiration use equals the production help. Functionally in this paper, the critical depth was later taken as the depth of the mixed layer when the bloom happens. This is troublesome because when the bloom happens is biased towards the local niche & temperature conditions…and because we don’t always have a reliable mixed layer depth at the time that the bloom happens.
The Sum Total from Siegel’s Analysis
Siegel et al. found that there’s a sharp division of the section of the North Atlantic basin that does react the way that Sverdrup predicted - north of around 40 degrees of latitude - and the section of the North Atlantic that is south of this latitude and doesn’t behave as Sverdrup expected.
This is because the year-long warm water conditions south of 40N mean that nutrient limitation is a lot more important, which means that spring mixing is the real culprit for the bloom starting. Even though irradiance plays a role, it’s not the real trigger for the bloom. There’s too much light throughout the year for this to be the case!
Siegel's Bottom Line
Phytoplankton Mathematical Modeling
Our main required reading of this session is a seminal work of distinguished biological oceanographer Dr. Gordon A. Riley. In order to connect to how important and lasting this work was to be for marine ecosystem modeling, you can check out this perspective from Thomas Anderson (2012):
Classical Models
Because much of this class will be focused on quantitative approaches to assessing phytoplankton physiology and community ecology, we’ll need a discussion of a cousple of classical models that have applications far beyond the phytoplankton world.
Lotka-Volterra
Classically known as the predator-prey model, Lotka-Volterra is applicable even to phytoplankton. Papers have been published just this year that leverage classical Lotka-Volterra dynamics to explain phytoplankton ecology.