Traceability of Ocean Flows and Material Transport
Authors:   , Reijnders Bernardus Johannes Hendrikus Rosalius 
Published: January 2025

Tracing ocean flows and material transport has numerous applications in oceanography, climate research, ecology, and marine pollution research. This is typically done from a Lagrangian perspective, moving along the reference frame of a water parcel. Trajectories of such parcels or idealized particles can be calculated from Eulerian flow fields.

This thesis examines three questions, each related to the traceability of ocean flows and material transport:
1.	How can we simulate the dispersion of Lagrangian trajectories along neutral surfaces beyond simple random walks? (Chapter 2)
2.	How large are the biases caused by numerical errors in the presence of divergence in backward-in-time Lagrangian simulations and what are the ramifications for traceability? (Chapter 3)
3.	How can we quantify magnitudes and timescales of sources and sinks of biogeochemical tracers along Lagrangian trajectories, such as of Dissolved Inorganic Carbon along NASTMW pathways? (Chapter 4)

When simulating Lagrangian trajectories using coarse ocean model data, the dispersive effect of unresolved eddies may need to be parameterized. In Chapter 2, we introduce a three-dimensional formulation of the Markov-1 dispersion parameterization, where stochastic noise is added to the velocity vector, introducing velocity autocorrelations. The three-dimensional formulation considers the orientation of neutral surfaces, respecting ocean stratification. Unlike random walks which only simulate diffusive dispersion, Markov-1 also captures ballistic dispersion, leading to more realistic particle trajectories. Additionally, we show it is better able to constrain particles to neutral surfaces in comparison to random walks; this is key when using long integration times, such as in climate studies.

Lagrangian trajectory calculations are susceptible to numerical errors. In flows that are not divergence-free, these errors amplify in regions of divergence and are dampened in regions of convergence, consistent with the amplification or dampening of natural stochastic displacements in such regions. For source-attribution, trajectory calculations are often applied backward-in-time, but this also reverses the stability of numerical errors: divergent zones become stable and convergent zones unstable to error growth. In Chapter 3, we show that this switch in stability leads to biased estimates of material origins, for example because particles are repelled backward-in-time more quickly from areas than they were attracted forward-in-time. Experiments show that regions of persistent source under- or overestimation for experiments of 180-day and less can extend over thousands of kilometers.

North Atlantic Subtropical Mode Water (NASTMW) is a conduit for carbon to move from the ocean surface into deeper layers. In Chapter 4, we investigate how concentrations of dissolved inorganic carbon (DIC) change along Lagrangian pathways using a physical-biogeochemical model. Along pathways into, within and out of NASTMW, we calculate changes in carbon concentration (ΔDIC) and separate contributions from biogeochemistry and physical mixing. The strongest ΔDIC in a parcel occurs during subduction from the mixing layer to NASTMW, although within a year most parcels persist in NASTMW. Our Lagrangian perspective reveals how biogeochemical processes and mixing can either enhance or counterbalance each other's effects on DIC across different timescales—a complex interplay that is normally averaged out in Eulerian studies.