Master in Marine Sciences

The Global Oceanic Nitrogen Cycle

• Different forms of reactive nitrogen and biogeochemical reactions.
• Reservoirs and fluxes - ocean, continent, atmosphere.
• Anthropogenic perturbations.
• Control processes of the oceanic nitrogen cycle.
  • Deep nitrate reservoir and thermohaline circulation.
  • Biological control.
  • Dugdale & Goering model: new vs. regenerated production.
  • Exportable production.
  • Exported production.
• Global-scale diazotrophy/nitrification/denitrification coupling.
• Coupling between the continental and oceanic cycles.

The Phosphorus Cycle

• Distribution and control factors of phosphate in marine environments.
  • The role of phosphate in limiting nitrogen fixation and oceanic production.
  • Distribution, composition, and availability of phosphate pools in the ocean.
  • Sources - rivers, atmosphere, volcanoes, hydrothermal processes.
  • Sinks - burial of organic matter, adsorption on clays and iron oxyhydroxides, burial of phosphorites.
  • Residence times.
• The biogeochemical cycle of phosphate.
  • Cycle in the World Ocean.
  • Broecker & Peng 1st order model.
  • Cycle in the surface ocean.
  • Thingstad model.
  • Climate change and Karl's shift hypothesis.
  • Coupling with the cycles of other biogenic elements (C, N, Si).
  • Case studies in environments with low mineral phosphate availability (Mediterranean Sea, South West Tropical Pacific).

The Silicon Cycle

• The biogeochemical cycle of silicon.
  • Techniques for studying stocks and fluxes.
  • Silica dissolution in the natural environment.
  • Reactivity of particulate silica and dissolution constants.
  • Temperature effect.
  • Relationship with bacterial degradation processes.
  • Influence of aluminum content.
• The global silicon cycle in the oceans.

The Biogeochemical Cycles of Iron in the Ocean (variables, processes, stocks and fluxes, budgets)

• Iron limitation of primary production in "High-Nutrient, Low-Chlorophyll (HNLC)" oceanic regions.
• Techniques for studying the iron cycle in the ocean.

Numerical Modeling in Biogeochemistry

• Forward modeling and inverse modeling.
• An example of a simple model.
  • Optimum Multiparameter (OMP) analysis models to assess water mass distribution from physical (temperature, salinity) and biogeochemical (nutrients, dissolved oxygen, alkalinity...) measurements.

Tutorials

• Nutrient availability, primary production, and carbon export in the Mediterranean Sea.
• Carbon and nitrogen uptake and export in the Equatorial Pacific.
• Phosphorus-33 method for estimating phosphate availability.
• Methods for determining lithogenic and biogenic silica fractions.
• Processes controlling the distribution of trace elements in the global ocean.
• Use of an Optimum Multiparameter (OMP) model to estimate water mass origins and remineralization. Analysis of results and their uncertainties.

Part I

• Inertial vs. Earth-rotating reference frames.
• Rotation-related accelerations.
• Conservation equations (global and local forms, application to mass, heat, tracer, and momentum).
• Main approximations.
• Conservation of vorticity and consequences.
• Geostrophic balance.
• Thermal wind.
• Shallow water equations (original, linearized, integrated).
• Viscous stress and Reynolds stress tensors.
• Turbulence and turbulent closure.
• Ekman solutions in infinite and finite depth.
• Bottom Ekman spiral.
• Sverdrup, Stommel, and Munk solutions.
• Basin circulation analysis.

Part II

• Gravity waves without Earth rotation effects and applications (basin seiches, eigenresonances, tidal bores, tsunamis).
• Waves with periods close to or greater than the local inertial period and applications (Kelvin, Sverdrup, Poincaré waves, tides, storm surges).
• Wave celerity modifications induced by Earth's rotation.
• Pattern of currents associated with the presence of waves.
• Wave superposition, amphidromic systems, analogy and differences with standing waves without rotation effects.
• Generalization of results in a two-layer medium (internal waves, modified or not, and their applications: internal Kelvin waves coastal-guided (upwelling), internal Kelvin waves equatorially-guided: El Niño).

Lectures

• Reference frames - positioning at sea - mapping - distance calculation.
• Measurements of T, Conductivity, P parameters and estimation of derived variables.
• Measurements of "Biogeochemical" parameters (e.g., Oxygen, Chl-A).
• Measurement of physical parameters.
• Introduction to ocean observation systems: Different platforms.
• Introduction to time series analysis.

Tutorials

• Preparation and debriefing of fieldwork at sea.
• Graphical representation of data in oceanography.
• Drafting the data collection report.

Laboratory & Practical Sessions

• Demonstration of different measurement platforms (Oceanographic cruise/Fieldwork).
• Measurement of chemical parameters on collected samples.

Lectures

• Introduction, ODE/PDE definitions, mathematical reviews, finite difference discretization.
• Development of classical discretization schemes, discretization of a parabolic PDE.
• Matrix formulation, discretization of boundary conditions, 2D/3D generalization.
• Discretization of hyperbolic and elliptic PDEs, consistency.
• Stability analysis (Fourier and matrix methods), CFL condition, Arakawa grid.
• Vertical grids and equation transformation, upwind schemes, numerical diffusion, TVD schemes.
• Temporal discretization, alternating direction implicit (ADI) method, tridiagonal systems, internal and external modes.

Tutorials

• Characterization of PDEs, development of finite difference schemes for first and second derivatives.
• Implementation and analysis of the numerical solution for a problem governed by a hyperbolic PDE.
• Study of the discretization of a Burgers' equation (QUICK scheme and associated TVD scheme), solving a tridiagonal system using Thomas algorithm.
• Discretization and stability of an advection-diffusion equation.

Laboratory & Practical Sessions

• Advection-diffusion of a contaminant, stability study, explicit/implicit schemes. Programming in Fortran 90, plotting results with Python.

Lectures

• History of numerical modeling of geophysical fluids and introduction to the CROCO community platform.
• Conservation equations for mass, momentum, heat, and salt.
• Modeling of oceanic turbulence and main closure schemes.
• Numerical grids for ocean modeling.
• Definition of initial and boundary conditions.

Tutorials

• Registering as a CROCO code user, downloading software and data.
• Implementation of the demonstration configuration.
• Implementation of a configuration for a selected oceanic region.
• Analysis of numerical results and comparison with literature.
• Online publishing of the report and presentation of results.

Content

• Common 2- or 3-species models.
• n-species models.
• Unstructured models followed by size-, age-, and space-structured models.
• Food web models and using these models to test hypotheses on the functioning of marine ecosystems.
• Lyapunov functions.
• Bendixson and Dulac negative criteria.
• Poincaré-Bendixson theorem.
• Routh-Hurwitz criteria.