Exploration of the critical depth hypothesis with a simple NPZ model

The critical depth hypothesis (CDH) is a predictive criteria for the onset of phytoplankton blooms that comes from the steady-state analytical solution of a simple mathematical model for phytoplankton growth presented by Sverdrup in 1953. Sverdrup's phytoplankton-only model is very elementary compared with state-of-the-art ecosystem models whose numerical solution in a time-varying environment do not systematically conform to the CDH. To highlight which model ingredients make the bloom onset deviate from the CDH, the complexity of Sverdrup's model is incrementally increased, and the impact that each new level of complexity introduced is analysed. Complexity is added both to the ecosystem model and to the parameterization of physical forcing. In the most complete experiment, the model is a one-dimensional Nutrient-Phytoplankton-Zooplankton model that includes seasonally varying mixed layer depth and surface irradiance, light and nutrient limitation, variable grazing, self-shading, export, and remineralization. When complexity is added to the ecosystem model, it is found that the model solution only marginally deviates from the CDH. But when the physical forcing is also changed, the model solution can conform to two competing theories for the onset of phytoplankton blooms—the critical turbulence hypothesis and the disturbance recovery hypothesis. The key roles of three physical ingredients on the bloom onset are highlighted: the intensity of vertical mixing at the end of winter, the seasonal evolution of the mixed-layer depth from the previous summer, and the seasonal evolution of surface irradiance.