North Atlantic Subtropical Mode Water (NASTMW) serves as a major conduit for dissolved carbon to penetrate into the ocean interior by its wintertime outcropping events. Prior research on NASTMW has concentrated on its physical formation and destruction, as well as Lagrangian pathways and timescales of water into and out of NASTMW. In this study, we examine how dissolved inorganic carbon (DIC) concentrations are modified along Lagrangian pathways of NASTMW on subannual timescales. We introduce Lagrangian parcels into a physical-biogeochemical model and release these parcels annually over two decades. For different pathways into, out of, and within NASTMW, we calculate changes in DIC concentrations along the path (ΔDIC), distinguishing contributions from vertical mixing and biogeochemical processes. While the mean ΔD for parcels that persist within NASTMW in one year is relatively small at +6 µmol/L, this masks underlying dynamics: individual parcels undergo interspersed DIC depletion and enrichment, spanning several timescales and magnitudes. The strongest ΔDIC is during subduction of water parcels (+101 µmol/L  in one year), followed by transport out of NASTMW due to increases in density in water parcels (+10 µmol/L). Most DIC enrichment and depletion regimes span timescales of weeks, related to phytoplankton blooms. However, mixing and biogeochemical processes often oppose one another at short timescales, so the largest net DIC changes occur at timescales of more than 30 days. Our new Lagrangian approach complements bulk Eulerian approaches, which average out this underlying complexity, and is relevant to other biogeochemical studies, for example on marine carbon dioxide removal.

To capture the effects of mesoscale turbulent eddies, coarse-resolution Eulerian ocean models resort to tracer diffusion parameterizations. Likewise, the effect of eddy dispersion needs to be parameterized when computing Lagrangian pathways using coarse flow fields. Dispersion in Lagrangian simulations is traditionally parameterized by random walks, equivalent to diffusion in Eulerian models. Beyond random walks, there is a hierarchy of stochastic parameterizations, where stochastic perturbations are added to Lagrangian particle velocities, accelerations, or hyper-accelerations. These parameterizations are referred to as the 1st, 2nd and 3rd order ‘Markov models’ (Markov-N), respectively. Most previous studies investigate these parameterizations in two-dimensional setups, often restricted to the ocean surface. On the other hand, the few studies that investigated Lagrangian dispersion parameterizations in three dimensions, where dispersion is largely restricted to neutrally buoyant surfaces, have focused only on random walk (Markov-0) dispersion. Here, we present a three-dimensional isoneutral formulation of the Markov-1 model. We also implement an anisotropic, shear-dependent formulation of random walk dispersion, originally formulated as a Eulerian diffusion parameterization. Random walk dispersion and Markov-1 are compared using an idealized setup as well as more realistic coarse and coarsened (50 km) ocean model output. While random walk dispersion and Markov-1 produce similar particle distributions over time when using our ocean model output, Markov-1 yields Lagrangian trajectories that better resemble trajectories from eddy-resolving simulations. Markov-1 also yields a smaller spurious dianeutral flux.