Deep inflow transport and dispersion in the Gulf of St. Lawrence revealed by a tracer release experiment

Abstract

The Gulf of St. Lawrence is increasingly affected by bottom water hypoxia; however, the timescales and pathways of deep water transport remain unclear. Here, we present results from the Deep Tracer Release eXperiment (TReX Deep), during which an inert SF₅CF₃ tracer was released inshore of Cabot Strait at 279 m depth to investigate deep inflow transport and mixing rates. Dispersion was also assessed via neutrally-buoyant Swish floats. Our findings indicate that the tracer moves inland at 0.5 cm s⁻¹, with an effective lateral diffusivity of 2 × 10² m² s⁻¹ over 1 year. Simplified 1D simulations suggest inflow water should reach the estuary head in 1.7 years, with the bulk arriving after 4.7 years. Basin-wide effective vertical diffusivity is around 10⁻⁵ m² s⁻¹ over 1 year; however, vertical diffusivity increases near the basin slopes, suggesting that turbulent boundary processes influence mixing. These results are compared to Lagrangian simulations in a regional 3D model to evaluate the capacity to model dispersion in the Gulf.

Introduction

The Gulf of St. Lawrence (or simply the Gulf, hereafter) is an important waterway that links 25% of the world’s freshwater reserves with the western North Atlantic through its connection to the Great Lakes of North America. In recent years, this region has become increasingly exposed to natural and human-induced drivers of environmental change^1,2, including a notable shift in ocean source water composition³ which has caused a recent Gulf-wide reduction in bottom water dissolved oxygen content^4,5,6. Hypoxia is a growing issue in coastal seas globally^7,8, and is approaching critical levels in some areas of the Gulf with adverse health effects for various organisms^9,10. Given transit time estimates of 3–7 years from the shelf to the estuary^11,12,13, the full ramifications of this deoxygenation signal on the St. Lawrence Estuary may only become evident in the next half-decade, thus more detailed estimates of bottom water spreading dynamics are necessary. Furthermore, considering that the Gulf is a busy shipping region, there are concerns surrounding the possibility of widespread contamination following a marine traffic incident¹⁴, yet the specific transport pathways and timescales that would allow for an accurate assessment of subsurface contaminant dispersal remain obscure.

Obtaining measurements of subsurface dispersion in semi-enclosed seas can be challenging¹⁵ and mixing rate measurements are rare in the Gulf region outside of the Lower St. Lawrence Estuary (LSLE, Fig. 1a)^16,17. One resource-intensive but effective method of studying long-term dispersion involves releasing an inert chemical tracer and then tracking its movement over a period of time¹⁸. While surface experiments often use short-lived fluorescent dyes to measure dispersion^19,20, subsurface tracer release studies generally inject long-lived inert compounds and monitor them over periods of months to years^21,22,23,24, sometimes decades²⁵. While examples of large-scale tracer releases in inland seas are uncommon, recent experiments in the Baltic Sea (BATRE)²⁶ and Gulf of Mexico²⁷ have provided valuable insights into subsurface transport timescales and the effect of basin geometry on spreading and mixing in marginal seas. However, the use of subsurface tracer release experiments to track circulation pathways, mixing rates, and residence times in a large, semi-enclosed estuarine systems is rare.

Fig. 1: Maps, sampling information, and hydographic properties from TReX Deep.

Maps (a) and (b) show the Gulf of St. Lawrence, TReX Deep sampling locations, and regional bathymetry. Black contour lines represent the injection depth bathymetric contour, h = 279 m. Abbreviated location names are: TS Tadoussac, QC Quebec, AI Anticosti Island, CS Cabot Strait, NL Newfoundland, BI Belle Ille Strait. The Lower St. Lawrence Estuary (LSLE), immediately east of Tadoussac, is shaded gray. Plot (c) shows hydrographic conditions from a single CTD profile immediately following the tracer injection with a dashed line indicating the injection depth. Shading represents the 95% confidence limits (mean conditions ± 2σ) of an October–December hydrography climatology from the Atlantic Zone Monitoring Program in the eastern Gulf between 1998 and 2022. Histogram (d) denotes the number of samples in z^* = 10 m depth bins from Leg 1 and Leg 2 cruises.

Here, we report results from the Gulf of St. Lawrence Deep Tracer Release eXperiment (TReX Deep), the first (to our knowledge) deep water tracer release conducted in the Gulf of St. Lawrence and one of very few in any marginal sea globally. This project aimed to define transport pathways and mixing rates by labeling inflowing water at the entrance to the Gulf in October 2021 with trifluoromethyl sulfur pentafluoride (SF₅CF₃) and subsequently measuring this tracer spread via ship surveys 8 and 12 months later. The experiment also utilized neutrally buoyant Swish floats²⁸ to define transport pathways on shorter timescales and provide complimentary Lagrangian measurements of dispersion. In this study, our observations reveal the tracer advecting shoreward while also undergoing pronounced lateral mixing. Additionally, we evaluate the evolving vertical tracer distribution to help gauge spatially varying mixing processes, finding evidence that vertical mixing along the basin slopes plays an important role in basin-wide vertical transport. Based on these findings, we predict the future evolution of this tracer in the Gulf to motivate and inform future sampling efforts, and compare our results to simulations from a regional 3D model to diagnose the current capacity to model dispersion in the Gulf.

Results

The Gulf of St. Lawrence Deep Tracer Release Experiment 2021 (TReX Deep): background and experimental details

The Gulf of St. Lawrence is a collection of straits and channels in eastern North America (Fig. 1a, b) with an estuarine circulation driven primarily by outflow from the St. Lawrence River²⁹. The estuary is relatively shallow until Tadoussac, after which it abruptly deepens into the 1240 km long Laurentian Channel with depths exceeding 300 m. This channel communicates with the North Atlantic Ocean primarily through Cabot Strait via a 500 m deep channel that cuts through the shelf offshore. While Belle Isle Strait also connects the Gulf to the North Atlantic in the north of the region, this channel is only 50 m deep with relatively limited deep-water exchange compared to Cabot Strait³⁰.

The water column of the Laurentian Channel can be broadly described as a three-layer system, with a 25–50 m deep fresh surface layer flowing seaward, and both a Cold Intermediate Layer (CIL), located between 50–150 m, and a deep layer, located at depths exceeding 150 m, flowing landward²⁹. During winter, the CIL is primarily formed locally as the surface layer progressively cools, becomes denser, and merges with the intermediate layer below^31,32. The deep layer has a broad cyclonic circulation^33,34 and the core of the Atlantic inflow can be identified by an oxygen minimum located between 200–250 m in vertical profiles (Fig. 1c). Model simulations suggest a mean residence time (defined as the average lifetime of a water parcel in the Gulf) of about 1 year^12,35, although estimates of transit time for water parcels from Cabot Strait to the LSLE range between 2 and 4 years^11,12,13. Diapycnal diffusivities derived from microstructure measurements near the LSLE vary spatially, increasing from ${{{{{{{\mathcal{O}}}}}}}}(1{0}^{-5}\,{{{{{{{{\rm{m}}}}}}}}}^{2}\,{{{{{{{{\rm{s}}}}}}}}}^{-1})$ in the basin interior to ${{{{{{{\mathcal{O}}}}}}}}(1{0}^{-4}\,{{{{{{{{\rm{m}}}}}}}}}^{2}\,{{{{{{{{\rm{s}}}}}}}}}^{-1})$ in the bottom boundary layer¹⁶ due largely to turbulence driven by internal tides¹⁷.

On October 25th, 2021, a SF₅CF₃ tracer was injected using GEOMAR’s Ocean Tracer Injection System (OTIS)³⁶ as part of a larger multi-investigator tracer release experiment which took place over 2021–2022 at various locations in the St. Lawrence estuary. The OTIS was towed behind the R/V Coriolis II at ~1 knot while injecting a liquid emulsion of tracer through 25 μm orifices. The SF₅CF₃ tracer is a stable, non-toxic compound with a very low detection limit and an undetectable background concentration that has been used in various open ocean²⁴ and marginal sea^26,27 experiments. The target isopyncal was σ_θ = 27.26 kg m⁻³ at a depth of about 280 m.

Two follow-up tracer surveys have been conducted to date. Due to ice cover from December through April, winter sampling was not possible during the period immediately following the injection. The first mission (Leg 1) was a dedicated tracer survey that took place from June 12th to 22nd, 2022, collecting 515 samples at 111 stations with an average horizontal station spacing of ~15 km. Vertical sampling was concentrated in a ~ 100 m region around the injection isopycnal to maximize the number of tracer-labeled samples (Fig. 1d). The second survey (Leg 2), occurred from October 25th to November 10th, 2022 as part of an Atlantic Zone Monitoring Program mission^5,37, collecting 225 samples at 51 stations with an average horizontal station spacing of ~31 km. Though the Leg 2 lateral sampling resolution was reduced and sampling below 300 m was limited (Fig. 1a, d), the vertical resolution was fairly uniform throughout large portions of the tracer-labeled area of the water column. Along with tracer inventories, comprehensive biogeochemical sampling was conducted during both legs in order to relate transport processes to changes in other chemical parameters of interest.

A total of 14 neutrally buoyant expendable Swish floats²⁸ were deployed with resurfacing timescales of 1–6 weeks during the injection and Leg 1 cruises (Fig. 2a, d). These floats descend immediately to a pre-selected density surface following deployment at a known time and location, after which they become neutrally buoyant and drift for a predetermined period of time before jettisoning a sufficient mass to resurface and communicate their positions through a Global Navigation Satellite System telemetry link. Each float provides a single-point Lagrangian displacement at a low cost. These instruments were primarily used to provide early indications of deep layer transport to inform tracer sampling efforts; however, it is also possible to utilize these floats to provide a Lagrangian comparison to tracer-derived estimates of lateral advection and diffusion. The precise equilibrium depth of the expendable floats is not known, but given the float ballasting and observed stratification, post-cruise analysis suggests that neutral buoyancy occurred somewhat shallower than the tracer at ~150 m with an uncertainty as large as 20% due to errors in ballasting procedures at that time²⁸.

Fig. 2: Observations of SF₅CF₃ tracer and Swish float dispersion.

Interpolated maps of vertically integrated observed tracer I_j from (a) Leg 1 at 8 months after injection; and (d) Leg 2 at 12 months after injection. The dashed gray line represents the Anticosti Island-Newfoundland transect, gray x’s represent sampling stations. Swish floats were deployed at the injection site during the injection cruise and in the Laurentian Channel during Leg 1. The float deployment locations are denoted by a violet star in (a) and the black `x' in (d) for the injection cruise and Leg 1, respectively. Float resurfacing locations are marked by translucent white circles, with circle diameter representing float resurfacing time (see reference). Vertical profiles of SF₅CF₃ concentrations are plotted for from Leg 1 (b) and Leg 2 (c) in z^* coordinates with A(z^*) and ${A}_{0}{e}^{-{z}^{* }/L}$ hypsographies. Leg 1 and Leg 2 SF₅CF₃ vs. σ_θ profiles are plotted in (e) and (f), respectively.

Injection cruise observations

The SF₅CF₃ tracer was injected in a streak in the northeastward region of Cabot Strait (Fig. 1a). Two independently logging frame-mounted conductivity-temperature-depth (CTD) sensors confirmed that the injection occurred at the target isopycnal σ_θ = 27.26 kg m⁻³ within a ±0.016 kg m⁻³ interval (2σ), centered at a depth z = 279 ± 3 m. Initially, the OTIS was filled with 4.5 kg of SF₅CF₃; however, after pumping for a short period of time, the OTIS was recovered to the surface for diagnostic purposes. During recovery, a surface-side rupture in one of the pump’s internal membranes allowed an unknown mass of tracer to escape into the atmosphere. While post-cruise examination of the OTIS pump data confirm that an amount of tracer was injected at the target isopycnal, the exact mass is unclear and thought to be substantially less that the initial 4.5 kg payload. Despite these challenges, tracer concentrations were observed throughout the Gulf in quantities exceeding the detection limit of our gas chromatography system (refer to “Sample Analysis”) and we observed no evidence of tracer at depths other than the target depth, aside from that resulting from mixing. Thus, regardless of the uncertainty surrounding the initial tracer injection mass, we found that the injection process had effectively labeled the inflow waters with detectable concentrations of SF₅CF₃, allowing us to assess the dispersion of inflow waters.

Post-injection CTD measurements confirmed typical seasonal deep water conditions in Cabot Strait and verified that the tracer had effectively labeled the inflow waters of Atlantic origin, as indicated by its location in the core of the oxygen minimum (Fig. 1c). Shorter timescale Swish floats deployed during the injection cruise resurfaced mainly around the injection site within a few weeks (Fig. 2a); however, floats with resurfacing timescales of a month or longer traveled northward, indicating the initial direction of post-injection transport was as predicted based on the general cyclonic circulation of the region’s deep waters^33,34. Cumulatively, the floats from this deployment were advected at a mean speed u_f = 2.1 ± 0.3 cm s⁻¹ (1σ; Fig. 2a; Table 1; “Swish Float Dispersion Statistics”).

Table 1 Summary of advection-diffusion characteristics from tracer and float observations

Leg 1 observations (8 months post-injection)

After the first winter, the tracer core was located 100 km northwest of the injection site in the Laurentian Channel, as indicated by a peak in the depth-integrated tracer concentration I_j = 3–4 × 10⁴ fmol m⁻² (Fig. 2a), with isolated tracer patches located at 300 km and 420 km along the Laurentian Channel. Additionally, moderately high tracer concentrations were observed near the entrance to Cabot Strait, suggesting that some tracer might have exited the Gulf since injection via deep water transport along the south side of the Laurentian Channel’s assumed cyclonic circulation. The analysis of tracer simulations suggests, however, that the amount of tracer having exited the Gulf at this time is likely small (see “Tracer Budget” and “Implications For Regional Modeling”). Swish floats deployed during Leg 1 consistently resurfaced westward further into the Laurentian Channel at a mean speed of u_f = 1.7 ± 0.5 cm s⁻¹ (1σ; Fig. 2d; Table 1), suggesting that the tracer would continue to spread along-channel after Leg 1.

To remove the influence of heaving and large-scale changes in isopycnal depth on the vertical displacement of the tracer, we interpolated the tracer measurements onto a reference density profile $\overline{{\sigma }_{\theta }}({z}^{* })$ to produce an isopycnally-mapped vertical coordinate z^* (see “Processing Tracer Profiles” for details)^21,24,26. The maximum measured SF₅CF₃ concentration was found to be 0.75 fmol kg⁻¹ at z^* ≈ 292 m, σ_θ ≈ 27.29 kg m⁻³ (Fig. 2b, e). The vertical distribution was Gaussian with an approximate full width at half maximum (FWHM) of 60 m in z^* coordinates and 0.2 kg m⁻³ in σ_θ coordinates. Spatial variations in vertical tracer distribution were observed (blue points in Fig. 3a); notably, enhanced tracer spreading and shoaling was observed north of the injection site where depths are generally shallower than the injection depth.

Fig. 3: Spatial distribution of vertical SF₅CF₃ tracer dispersion and corresponding 1D model simulations.

Map (a) shows the vertical distribution of tracer from seven regional subsets selected using a K-means clustering algorithm. The geographical extents of each subset is represented on the map as translucent, colored shapes, and displayed on each region is a z^* vs. tracer profile from each leg compiled from the corresponding area, with the injection depth marked with a black dashed line. Also included is a hypsography A(z) for each region (black line), which has been normalized by tracer concentration. Plot (b) shows profiles of normalized tracer concentration r vs. $\hat{z}$, where $\hat{z}={z}^{* }-$279 m is the vertical coordinate referenced to the injection depth, with error bars representing 95% confidence limits (2σ) derived from a bootstrapping analysis with 1000 random subsets. The wide curves show the best-fitting advection-diffusion model solutions based on the optimization routine explained in “1D Model Fitting”. Plot (c) is similar to (b), showing r and best-fitting 1D model solutions for boundary and interior regions; (Leg 1 is plotted with lighter curves, Leg 2 with darker curves).

Leg 2 observations (12 months post-injection)

The tracer core was observed near the injection site (I_j ≈ 3 × 10⁴ fmol m⁻²), but extended further west along the Laurentian Channel, consistent with the Leg 1 Swish float trajectories (Fig. 2d). The peak of the Leg 2 vertical distribution was observed at z^* ≈ 294 m, σ_θ ≈ 27.29 kg m⁻³ at a concentration of 0.69 fmol kg⁻¹ (Fig. 2c, f). The vertical distribution was well-resolved between z^* = 100 m (σ_θ = 26.70 kg m⁻³) and z^* = 320 m (σ_θ = 27.35 kg m⁻³); however, due to sampling limitations, the distribution was poorly-resolved at z^* > 320 m and σ_θ > 27.35 kg m⁻³. Assuming an approximately Gaussian distribution, we can estimate an FWHM of 110 m in z^* coordinates and 0.34 kg m⁻³ in σ_θ coordinates. This suggests increased overall vertical spreading since Leg 1, though again this vertical spreading was not spatially uniform, with less spreading and shoaling occurring in Cabot Strait compared to other regions (Fig. 3a).

Tracer inventory

We can estimate the tracer mass during each leg (M_L) as follows:

$${M}_{{{{{{{{\rm{L}}}}}}}}}=\int\overline{{c}_{{{{{{{{\rm{L}}}}}}}}}}({z}^{* }){A}_{{{{{{{{\rm{L}}}}}}}}}({z}^{* })\,d{z}^{* }$$

(1)

where

$$\overline{{c}_{{{{{{{{\rm{L}}}}}}}}}}({z}^{* })=\frac{1}{{N}_{{{{{{{{\rm{L}}}}}}}}}}\sum\limits_{j=1}^{N}{c}_{j}({z}^{* })$$

(2)

Here, c is SF₅CF₃ concentration; subscript L denotes the Leg number; c_j(z^*) denotes continuous vertical tracer profiles that have been interpolated using a log-linear scheme onto a regular z^* grid with 1 m spacing, where j is an index of our individual tracer profiles; $\overline{{c}_{{{{{{{{\rm{L}}}}}}}}}}({z}^{* })$ is the mean SF₅CF₃ concentration profile for each leg; N_L is the number of SF₅CF₃ profiles from each leg (111 for Leg 1 and 51 for Leg 2) and A(z^*) is the regional hypsography mapped onto the z^* coordinate (see Fig. 2b, c)^26,36. A bootstrap resampling technique is used to compute a 95% confidence interval (2σ) for M by creating 1000 random subsets of c_j profiles.

Using this technique, we estimate a Leg 1 inventory of M₁ = 71 ± 16 g and a Leg 2 inventory of M₂ = 61 ± 25 g. The majority of the Leg 1 inventory was located in the Laurentian Channel inshore of the injection site (~70 g), with only ~1 g of tracer located in the northern Gulf region (i.e., north of the gray line in Fig. 2a). The majority of the Leg 2 inventory was again located in the Laurentian Channel (>59 g). Moderate Leg 2 tracer concentrations in Cabot Strait (I_j = 1.4 × 10⁴ fmol m⁻²) suggest some eastward motion may have occurred; however, the small decrease in total inventory between legs is likely within the uncertainty of our estimates, given the available spatial sampling. Therefore, the potential for deep-water advective loss appears to be minimal over the duration of our experiment to date, and appears small in numerical tracer simulations (see “Implications For Regional Modeling”)—we further discuss these tracer inventories in “Tracer Budget”.

Diffusivity analysis

Our surveys show that tracer is mostly moving inshore, spreading both vertically and horizontally while the peak concentration appears at greater depths with increasing time. Although a small amount of tracer sinking of ${{{{{{{\mathcal{O}}}}}}}}$(1 m) might be initially expected due to the finite time necessary for the tracer emulsion to fully dissolve^24,26,36, an overall downwelling of the tracer mass of ${{{{{{{\mathcal{O}}}}}}}}$(10 m) is surprising given that the tracer-labeled inflow waters represent the oceanic component of a broadly estuarine circulation, in which we expect a net upwelling of deep waters. To gain insight into the observed spreading processes, we first interpret our observations using some simple advection-diffusion models, before considering the additional complications that arise from the relatively complex bathymetry of the region.

First, we focus on lateral spreading in the Laurentian Channel, where the majority of the tracer was detected. We employ a 1D advection-diffusion pipe model—previously used to model deep estuarine inflow in other systems¹⁵—to study the along-channel transport of depth- and channel-width-integrated tracer concentration c(x):

$$\frac{\partial c}{\partial t}+\frac{\partial }{\partial x}\left(uc-{\kappa }_{{{{{{{{\rm{h}}}}}}}}}\frac{\partial c}{\partial x}\right)=0$$

(3)

where u is a constant advection velocity and κ_h is a constant horizontal diffusivity. In response to an initial spike input of mass M, c(x, t = 0) = Mδ(x), the depth-integrated tracer concentration ${I}^{{\prime} }(x,t)=c(x,t)/Y$ in this model spreads diffusively through a channel of transverse width Y into a patch of axial width $\sqrt{2{\kappa }_{{{{{{{{\rm{h}}}}}}}}}t}$ around an initial point that moves in time as x = ut:

$${I}^{{\prime} }(x,t)=\frac{M}{\sqrt{4\pi {\kappa }_{{{{{{{{\rm{h}}}}}}}}}t}}\exp \left(-\frac{{(x-ut)}^{2}}{4{\kappa }_{{{{{{{{\rm{h}}}}}}}}}t}\right)\frac{1}{Y{M}_{{{{{{{{\rm{m}}}}}}}}}\overline{\rho }}$$

(4)

where x is distance in an along-channel coordinate system (Fig. 4), t is time since injection, M_m = 196.06 g mol⁻¹ is the molar mass of SF₅CF₃, $\overline{\rho }=$1026 kg m³ is a density conversion factor for the deep waters of the Laurentian Channel, and Y = 75 km is a channel width scale. Using the mass inventories from each cruise (M = M_L), we can then vary u and κ_h over a reasonable range to find the best-fitting solution at known time t (see “1D Model Fitting” for fitting routine details).

Fig. 4: Laurentian Channel horizontal SF₅CF₃ tracer dispersion and corresponding 1D model simulations.

Map (a) shows Laurentian Channel stations from both legs and an along-channel axis with x = 50 km spacing between individual points on the axis. Plot (b) shows station-wise vertically integrated tracer I_j as a function of along-channel distance: blue is used for Leg 1, and red for Leg 2. The dashed lines represent a 50 km overlapping window mean for Leg 1 and a 75 km overlapping window for Leg 2, both with a 50% window overlap. In (c), $I{\prime}$(x, t) is estimated from the 1D pipe model by substituting $\overline{u}$ and $\overline{{\kappa }_{{{{{{{{\rm{h}}}}}}}}}}$ into Equation (4). Plot (d) shows modeled $I{\prime} (x,t)$ transit time distributions at points along the channel, where line colors correspond to colored axis markers in map (a).

Our model estimates along-channel inflow advection velocities of u = 0.53 ± 0.16 cm s⁻¹ and u = 0.50 ± 0.23 cm s⁻¹, and effective lateral diffusivities of κ_h = 227 ± 91 m² s⁻¹ and κ_h = 157 ± 67 m² s⁻¹ (±2σ, estimated using a bootstrap resampling scheme with 1000 random subsets) over the first 8 months and 12 months after the release, respectively (Fig. 4b, Table 1). These estimates are approximated on timescales of months to years and spatial scales of hundreds of kilometers, and include the effects of shear dispersion from vertical spreading and horizontal circulation. Note that the reasonable ${I}_{j}^{{\prime} }$ values produced by the 1D model when using calculated mass inventories M = M_L in Eq. (4) imply that the inventories are plausible approximations of the amount of tracer in the channel at the time of both surveys. Some experimentation shows that dispersion estimates remain robust to moderate variations (±25%) in M and to normalization routines which scale ${I}^{{\prime} }(x,t)$ to match observations.

We can also use the Swish floats to provide a Lagrangian comparison to the tracer spreading estimates. Advection speed and dispersion in the deep layer can be estimated from the mean displacement and pair separation of the floats (see “Swish Float Dispersion Statistics”), resulting in estimates of u_f ≈ 2 cm s⁻¹ and lateral relative diffusivity of κ_f ≈ 480 m² s⁻¹ (Table 1). These values are comparable but somewhat larger than those estimated from the observed tracer fields; we discuss possible reasons for this discrepancy in “Inflow Transport”.

If we ignore horizontal dispersion and consider instead a mean vertical profile of tracer concentrations within the Gulf, we observe the tracer spreading vertically in an approximately Gaussian manner (Fig. 2b, c, e, f). It therefore seems reasonable to use a horizontally averaged vertical 1D advection-diffusion system to initially estimate the vertical diffusion at rate κ_v and vertical advection at a velocity w of a tracer $c(\hat{z},t)$ in a basin with a hypsography $A(\hat{z})$, where $\hat{z}$ is a vertical coordinate referenced to the injection depth $\hat{z}={z}^{* }-$279 m. The vertical advection velocity w (positive downwards, negative upwards) would model the effects of the estuarine upwelling.

An initial tracer distribution $c(\hat{z},0)=M\delta (\hat{z})/{A}_{0}$ will then evolve vertically according to:

$$\frac{\partial (cA)}{\partial t}+\frac{\partial }{\partial \hat{z}}\left(wcA-{\kappa }_{{{{{{{{\rm{v}}}}}}}}}A\frac{\partial c}{\partial \hat{z}}\right)=0$$

(5)

To simplify, we assume constant effective vertical velocity w and diffusivity κ_v and approximate the hypsography near the injection depth as $A(\hat{z}) \, \approx \, {A}_{0}{e}^{-\hat{z}/L}$ (dashed gray lines in Fig. 2b, c) for a scale depth L, where L is large for a steep basin, small for a wide shallow basin, and is about 200 m for the Gulf (Fig. 2b); A₀ corresponds to basin surface area $A(\hat{z}=-279\,{{{{{{{\rm{m}}}}}}}})$, that is, the basin area at z = 0 m. We can then find a solution:

$$c(\hat{z},t)=\frac{M}{{A}_{0}\sqrt{4\pi {\kappa }_{{{{{{{{\rm{v}}}}}}}}}t}}\exp \left(-\frac{{(\hat{z}-Wt)}^{2}}{4{\kappa }_{{{{{{{{\rm{v}}}}}}}}}t}+\frac{wt}{L}\right)$$

(6)

The concentration peak shifts vertically at speed W = w + κ_v/L. With an upward estuarine advection (negative w), the peak will also tend to move upwards if the basin has steep walls and weak diffusion (large L, small κ_v, Fig. 5b). Conversely, in scenarios where the basin has more gradual slopes and higher diffusivity (small L, large κ_v, Fig. 5a), the peak of the tracer distribution may actually sink: this would occur as the tracer dilutes while spreading upward into the widening basin, reducing concentrations above the injection point. However, in the simplified system presented in Eqs. (5) and (6), the distribution will remain Gaussian, spreading into a vertical patch of thickness $\sqrt{2{\kappa }_{{{{{{{{\rm{v}}}}}}}}}t}$; note that there will be an overall decrease in concentration at all levels due to the dilution that occurs as the tracer moves upwards into depth ranges with a greater surface area, with a timescale L/w. Both the 1D model and the observed vertical tracer distribution are subject to an identical normalization routine (see Ledwell and Watson, 1991³⁶ and “Processing Tracer Profiles”), which allows us to compare the time-evolution of distribution shape and ensures that the fitting regime is robust to changes in M Eq. (6), eliminating dependency on the uncertain original tracer mass.

Fig. 5: Tracer spreading in shallow and steep-sided basins.

A schematic depicting the spreading of tracer in (a) a shallow-sided basin and (b) a steep-sided basin. Note that while w is constant and negative (i.e., upward) in both basins, the apparent advection velocity of the tracer peak W = w + κ_v/L can be positive (i.e., downward) when L is small and diffusivity κ_v is large.

By varying w and κ_v over a reasonable range to find the best-fitting solution (see “1D Model Fitting” for information on the fitting routine), we estimate a bulk effective diapycnal diffusivity and vertical advection velocity of κ_v = (1.0 ± 0.3) × 10⁻⁵ m² s⁻¹ and w = 9.5 ± 5.0 m yr⁻¹ for Leg 1 and κ_v = (0.7 ± 0.4) × 10⁻⁵ m² s⁻¹ and w = 6.5 ± 7.0 m yr⁻¹ for Leg 2 (Fig. 3b, Table 1). While the Gaussian model explains a large portion of the spreading, both the observed Leg 1 and Leg 2 vertical distributions exhibit skewness with longer tails extending towards the shallower end of the distribution, and we see a downwelling velocity w that far exceeds the dilution factor κ_v/L ≈ 1.5 m yr⁻¹. These findings indicate that there is a bulk downwelling of the tracer, but vertical mixing rates may be spatially inconsistent.

Interior and boundary spreading

Although horizontal averaging over the entire Gulf provides some insight into vertical advection and diffusion, our observations suggest that in areas where the target isopycnal approaches the seafloor (circular markers in Fig. 1a), tracer has spread and shoaled considerably in comparison to the deeper portions of Laurentian Channel (Fig. 3). This indicates that boundary regions may be undergoing a qualitatively different tracer evolution due to mixing in a bottom boundary layer. To evaluate bottom boundary layer effects on vertical mixing, we divide observations from each cruise into boundary and interior subsets²⁷. The boundary subset includes stations with I_j > 0 fmol m⁻² and h < 279 m, mainly north of the Anticosti Island-Newfoundland transect and on Laurentian Channel banks (circular markers in Fig. 1a; 33 stations from Leg 1, 10 from Leg 2). The interior subset includes stations with I_j > 0 fmol m⁻² and h > 279 m, mainly in the Laurentian Channel (triangular markers in Fig. 1a; 44 stations from Leg 1, 16 from Leg 2). Both subsets undergo the same normalization and optimization as per Eqs. (10)–(13) and uncertainties are presented as 95% confidence intervals assigned from a bootstrap analysis with 1000 random subsets (±2σ).

Averaged over both legs, observations from the interior have an effective vertical diffusivity of $\overline{{\kappa }_{{{{{{{{\rm{in}}}}}}}}}}=$(6.5 ± 1.8) × 10⁻⁶ m² s⁻¹ and a positive (i.e., downwelling) advection velocity of $\overline{{w}_{{{{{{{{\rm{in}}}}}}}}}}=11\pm$3 m yr⁻¹, whereas observations from the boundary regions have an effective vertical diffusivity of $\overline{{\kappa }_{{{{{{{{\rm{b}}}}}}}}}}= \,$(1.5 ± 1.0) × 10⁻⁵ m² s⁻¹ and a negative (i.e., upwelling) advection velocity of $\, \overline{{w}_{{{{{{{{\rm{b}}}}}}}}}}=-23\pm$11 m yr⁻¹ (Fig. 3c). The increased uncertainty in the boundary subset reflects more variable tracer profile shapes and reduced data coverage in these areas. However, these estimates suggest that mixing and upwelling are enhanced in areas where the tracer contacts the slopes of the basin.

Discussion

In October 2021, we injected an inert tracer into deep inflow waters entering the Gulf of St. Lawrence from the Atlantic. Observations 8 and 12 months later show the tracer advecting inshore and undergoing considerable lateral dispersion that plays an important role in the horizontal circulation. The tracer also exhibits downward vertical displacement and moderate vertical dispersion in the basin interior with contrasting upward displacement and enhanced dispersion along the boundaries.

Tracer budget

Given the initial 4.5 kg tracer payload, the subsequent 60–70 g inventories invoke questions about the fate of the remaining tracer. These relatively small inventories imply some combination of the following: a substantial amount of the injected tracer had exited the Gulf via lateral advection prior to the first survey; some portion of the injected tracer was located in high-concentration streaks or patches that were not sampled during either survey; and/or only a small portion of the tracer was actually injected at the target isopycnal. To gain a first order estimate of the amount of tracer that may have laterally advected out of the Gulf, we can evaluate tracer release simulations in a regional 3D model (described in “Implications For Regional Modeling”). In these simulations, 0.8% of the virtual tracer had exited the Gulf by Leg 1 and 1.7% by Leg 2 (Fig. 6a, b). These results indicate that a large majority of the tracer would have remained in the Gulf during the survey period, even accounting for any substantial mismatch between the model simulations and our observations.

Fig. 6: Lagrangian 3D simulations of tracer spreading using CIOPS-E velocity fields.

Simulated tracer release maps of depth-integrated particle count P_j after (a) 8 months and (b) 12 months. Black contours represent the h = 279 m depth level. Station-wise comparisons between simulated and observed bulk 1D transport are provided for along-channel spreading in (c) and (d) and vertical spreading in (e) and (f), with simulated and observed vertical spreading provided for interior and boundary subsets in (g) and (h).

The likelihood of a streaky tracer distribution can be evaluated by comparing the Gulf deep water hypsography to a tracer spreading length scale. Garrett, 1983³⁸ showed that a tracer distribution may remain streaky up until a timescale t₂, whereby the area of occupation A_d—that is, the region containing most of the tracer as defined by Taylor’s (1922)³⁹ dispersion formula 4πκ_ht—matches the actual area of the tracer A_t. At times exceeding t₂, the dispersion process evolves such that the tracer becomes more homogenized, leading to the establishment of a more uniform distribution. Consider a scenario where the TReX Deep tracer has maximally spread to fill the entire Gulf on the injection surface A(z^* = 290 m) ≈ 0.5 × 10¹¹ m² (see gray lines in Fig. 2b, c for hypsographies). Provided κ_h = 2 × 10² m² s⁻¹, the timescale t₂ ≈ 6 months, suggesting that the during both the Leg 1 (8 months) and Leg 2 (12 months) surveys, the likelihood of high variance in the tracer distribution is low—realistically, A_t < A(z^* = 290 m), therefore the timescale t₂ is presumably smaller than the 6 month estimate provided here. This is echoed in simulated tracer releases (see “Implications For Regional Modeling”), which have fairly smooth, uniform lateral distributions with the exception of a few patches near the initial injection location, which cumulatively contain less than 5% of the Gulf-wide tracer content.

Given the unlikelihood that a large portion of the tracer exited the Gulf or remained unsampled during either survey, it seems plausible that only a small portion of the tracer, on the order of a few hundred grams or less, was injected into the deep inflow of the Gulf. This supposition is consistent with post-injection diagnostics from the OTIS pump and with Gulf-wide tracer concentration observations. Fortunately, due to the low detection limit of SF₅CF₃ in seawater using purge and trap gas chromatography systems (see “Sample Analysis” and Köllner, 2016⁴⁰), this smaller-than-planned mass of tracer was sufficient to effectively label the inflow waters and quantify dispersion in the Gulf on timescales of at least 1 year and likely much longer, given flushing times on the order of years³⁵.

Inflow transport

The along-channel 1D model (defined in “Diffusivity Analysis”) provides a useful new opportunity to estimate transit time distributions along the Laurentian Channel and further characterize lateral spreading. One regional issue that we address is the deep water transit time from Cabot Strait to the head of the Laurentian Channel, near Tadoussac, QC (Fig. 1; brown station at x ≈ 800 km on Fig. 4a, d), with estimates ranging from 2 years¹³ to 4 years¹¹ based the propagation of temperature signals along the channel. To estimate along-channel inflow dynamics based on the tracer spreading, we can simulate transport in the 1D pipe model by substituting mean $\overline{u}$ and $\overline{{\kappa }_{{{{{{{{\rm{h}}}}}}}}}}$ into Equation (4) to provide detailed long-term estimates of tracer concentrations throughout the channel.

Our 1D simulations show tracer concentrations increasing above trace amounts at Tadoussac after ~1.7 years and peaking at 4.7 years, with small amounts of tracer remaining up to a decade after injection (Fig. 4d). This 1D model, while a basic approximation, provides insight into the influence of the local advection/diffusion balance on tracer transport which can serve as a framework for modeling the dispersion of other tracers through the Laurentian Channel. Given the extensive TReX Deep measurements of CFCs and key biogeochemical species, minor model adjustments to incorporate time-varying boundary conditions (as has been done for the Laurentian Channel⁴¹ and the Strait of Georgia¹⁵) and internal sources and sinks may yield realistic distributions of these tracers. This capability may prove particularly useful given recent changes in the composition of source waters^4,42.

An estimated lateral diffusivity of ~200 m² s⁻¹ is comparable to that of subsurface layers in basins such as the Baltic Sea (${{{{{{{\mathcal{O}}}}}}}}[1{0}^{2}\,{{{{{{{{\rm{m}}}}}}}}}^{2}\,{{{{{{{{\rm{s}}}}}}}}}^{-1}]$)²⁶ and the Strait of Georgia (88–167 m² s⁻¹)¹⁵. It is also consistent with apparent diffusivities in similar scale surface ocean circulation as described by Okubo, 1971⁴³ and numerical estimates of surface diffusivity in the Gulf (150–300 m² s⁻¹)⁴⁴. The predominance of lateral diffusion over mean transport observed here is a noteworthy new feature of the circulation, and is confirmation of a similar characteristic recently noted in the Strait of Georgia, a smaller but comparable basin located in the Salish Sea¹⁵. While Swish float dispersion exceeded that of the tracer by a factor of two, these instruments have offered valuable tracer-independent evidence that our lateral 1D tracer spreading model is reasonably estimating advection and diffusion. The enhanced float dispersion likely results from the floats’ shallower neutral buoyancy coupled with the expectation of larger float-derived currents near the channel edges due to the Laurentian Channel’s mean cyclonic circulation (Fig. 2a, d)^34,45. A detailed comparison between the Swish float dispersion and simulated trajectories would be useful to provide more insight into the differences in float and tracer-derived spreading estimates, but is beyond the scope of this study.

While the observed basin-wide effective vertical diffusivity of ~1 × 10⁻⁵ m² s⁻¹ aligns with tracer measurements in BATRE ([1–2] × 10⁻⁵ m² s⁻¹)²⁶ and some larger-scale mid-depth ocean experiments ([1–1.5] × 10⁻⁵ m² s⁻¹)^23,24, it is between three and thirty times smaller than measurements in various other tidal basins (i.e., the Santa Monica³⁶ and Santa Cruz⁴⁶ basins) and open-ocean mixing hot-spots^25,27,47. Closer inspection of tracer profiles suggest local increases in vertical mixing rates near the basin slopes (Fig. 3a, c)^27,48, likely due to turbulent boundary layer processes such as bottom shear stress and internal wave scattering^17,49,50, in addition to possible isopycnal spreading through the boundary layer^26,51. These findings are of the same magnitude as microstructure measurements from the LSLE, where depth-averaged diapycnal mixing rates of ${{{{{{{\mathcal{O}}}}}}}}(1{0}^{-5}\,{{{{{{{{\rm{m}}}}}}}}}^{2}\,{{{{{{{{\rm{s}}}}}}}}}^{-1})$ were observed with a similar relative increase in effective diffusivity when comparing between boundary and interior regions¹⁶.

In other tracer release experiments, diapycnal diffusivity has been observed to increase dramatically once the tracer contacts the boundary layer⁴⁶. In TReX Deep, horizontal tracer distributions suggest that initial contact with the basin slopes occurred between the injection and Leg 1, indicating that boundary layer processes have been incorporated into our bulk estimates of vertical diffusivity. One noteworthy result in the tidally-energetic Gulf is the relatively low basin-wide vertical diffusivity of ${{{{{{{\mathcal{O}}}}}}}}(1{0}^{-5}\,{{{{{{{{\rm{m}}}}}}}}}^{2}\,{{{{{{{{\rm{s}}}}}}}}}^{-1})$, which more closely resembles the low-energy, non-tidal Baltic Sea basins²⁶ rather than the tidal Santa Monica or Santa Cruz Basins^36,48. One reason for this may be the considerably larger area of the Gulf in comparison to the relatively small basins in which other tracer experiments have been conducted, where spatial scales are smaller and the effects of enhanced boundary mixing might be more influential throughout the measurement region.

Furthermore, our observations reveal asymmetrical vertical advection of the tracer, characterized by a downwelling tracer peak in the basin interior and an upwelling peak near the basin boundaries (Fig. 3c). This pattern deviates from a typical estuarine circulation, where deep waters are generally expected to shoal as part of the regional exchange flow, and is likely influenced locally by complex and spatially-varying freshwater inputs and exchange pathways^37,45. A small portion of the downwelling velocity can be explained by an immediate deepening of the tracer emulsion before it dissolves, a phenomenon previously estimated to result in a 1–2 m downwelling of the tracer peak^24,26,36. Aside from advection, other contributors to the vertical velocity may include pseudo-velocities associated with the dilution of tracer due to the spreading basin walls or a depth-variable diffusivity. However; the pseudo-velocities associated with the hypsographic correction κ_v/L entail a downwelling of only a few meters per year, and a depth-variable κ_v varying proportionally with the Gulf’s hypsographic scale (L = 200 m) would introduce an upwelling pseudo-velocity −∂κ_v/∂z of a few meters per year. These corrections are smaller components of the larger observed bulk downwelling velocity w ≈ 5–10 m, which implies that diffusive processes alone are insufficient to account for the interior deepening.

Given these findings, the basin slopes are identified as key upwelling regions that warrant close attention in future surveys. Recent evidence from near-bottom dye release experiments indicates that diapycnal upwelling rates can reach ${{{{{{{\mathcal{O}}}}}}}}(100\,{{{{{{{\rm{m}}}}}}}}\,{{{{{{{{\rm{day}}}}}}}}}^{-1})$ within bottom boundary layers⁵¹, which would designate these processes as vital components of a regional overturning circulation. In light of the apparent asymmetrical nature of the tracer spreading, more complex models could build upon the 1D models presented here by incorporating space and time variations in spreading parameters to better characterize the asymmetry and improve our understanding of its regional significance to vertical mixing processes in the Gulf.

Implications for future gulf circulation

We can summarize our findings to predict the future tracer evolution in the Gulf. Assuming stable Gulf dynamics over interannual timescales, we expect the tracer to have spread laterally through the Laurentian Channel and reached the LSLE by winter 2023, with concentrations predicted to peak there by mid-2026. Current observations suggest that the tracer peak will sink and mix steadily in the interior of the basin; however, basin-wide effective vertical diffusivity may appear to increase as more tracer reaches the basin slopes and turbulent boundary layer processes further contribute to mixing and local shoaling of the tracer peak. Several factors, however, limit the certainty of these predictions, including the reduced sampling resolution of Leg 2 and the ambiguity around the initial tracer injection mass. For these reasons, continued and detailed monitoring of tracer spreading over the next few years is required to refine our mixing estimates; better understand and model the effects of boundary mixing on the basin-wide transport of inflow waters; and provide a robust estimate of the overall tracer (or contaminant) flushing time for the Gulf.

The rate of tracer lateral spreading in the Gulf indicates a strongly diffusive circulation which may be influenced by the effects of tides on lateral mixing rates⁵². The regional balance between advection and diffusion has implications for the transport of tracers and contaminants in this region and other analogous systems. In a diffusion-dominated basin, we expect flatter tracer transit time distributions with long tails, which suggests rapid horizontal dispersal, prolonged residence times, and ultimately a uniform distribution throughout the system. This finding implies different outcomes for different tracers: for a long-lived pollutant, this behavior could entail undesirable rapid and widespread contamination following a subsurface pollution event. Conversely, consider recent proposals to artificially inject oxygen into subsurface water masses to mitigate hypoxia⁵³, an approach that has been tested on a small-scale in a Swedish fjord⁵⁴ and contemplated specifically for the Gulf of St. Lawrence⁵⁵: in this scenario, it may be desirable that injected oxygen be distributed quickly and evenly throughout the bottom waters, which might occur given the strong diffusivity that we have measured in the system. Given the growing concerns surrounding hypoxia in the Gulf^3,4,5,6 and in coastal systems globally⁸, understanding the regional balance of advection and diffusion would be key in managing any remediation efforts of this nature.

Implications for regional modeling

Tracer release experiments offer unique and valuable opportunities to directly evaluate our ability to predict dispersion in regional numerical models. To estimate the tracer distribution and assist with cruise planning logistics, a virtual tracer release was simulated prior to the tracer surveys by implementing a Lagrangian model using archived daily velocity fields from the Coastal Ice-Ocean Prediction System East (CIOPS-E)^56,57,58,59, an operational NEMO version 3.6 configuration for the Gulf Region developed by Environment and Climate Change Canada (ECCC; see “Regional 3D Simulations” for details of the CIOPS-E model). This prognostic offline simulation was used to seed 300,000 virtual particles at the tracer release point to estimate tracer spreading over a period of 1 year following the injection, providing a best-estimate of the tracer distribution during the Leg 1 and Leg 2 surveys. The Lagrangian model used here (see “Regional 3D Simulations” for details) was initially developed by Chassé and Miller (2010)⁶⁰ for modeling lobster larvae movement in the Gulf, and several subsequent applications have since employed the same particle tracking software in the Gulf region^61,62,63.

The modeling goal prior to the tracer surveys was to provide a prognostic estimate of the tracer distribution at the time of sampling. However, we can here utilize tracer observations to retroactively evaluate the accuracy of these forecasts. Thus, the goal of this exercise is to identify the capacity to predict three-dimensional dispersion in the Gulf given the available numerical tools, and to utilize this comparison to identify possible improvements to these forecasts, which has clear implications for improving predictions of tracer and/or contaminant dispersal in the region.

We first qualitatively assess the lateral tracer spreading by mapping vertically integrated particle count P_j (see “Implications For Regional Modeling”) throughout the Gulf region (Fig. 6a, b). The simulation depicts comparable along-channel transport pathways to tracer observations (Fig. 2a, d) at the time of the Leg 1 and Leg 2 surveys, though with enhanced northward spreading past the Anticosti-Newfoundland line (gray dashed line in Fig. 2a) which is less apparent in our observations. This northward spreading is, however, consistent with the post-injection transport of neutrally buoyant floats with longer resurfacing timescales (Fig. 2a). Simulated particles are located in areas considerably shallower than the h = 279 m contour in the north of the region, though this phenomenon is less apparent along the walls of the Laurentian Channel. The simulations also depict some tracer escaping eastwards along the southern side of Cabot Strait, but the amount is relatively minimal compared to the simulated tracer mass remaining inside the Gulf (Tracer Budget).

To quantify spreading in the 3D simulations, we perform a station-wise comparison with the tracer observations using a ~5 km region of the model grid surrounding each observation station. We then quantify along-channel and vertical spreading by applying the same normalization and 1D model fitting techniques that were employed for tracer observations in “Diffusivity Analysis”. The analysis of simulated along-channel lateral spreading provides effective diffusivities of κ_h = 181 ± 78 m² s⁻¹ and κ_h = 157 ± 125 m² s⁻¹, and advection rates of u = 0.58 ± 0.15 cm s⁻¹ and u = 0.53 ± 0.34 cm s⁻¹ for the first 8 and 12 months after the release, respectively (Fig. 6c), which show good agreement with those derived from observations (Table 1).

In contrast to the general agreement between simulated and observed horizontal evolution of the tracer field, the simulated vertical diffusivity is κ_v = (1.1 ± 0.2) × 10⁻⁴ m² s⁻¹ for Leg 1 and κ_v = (1.3 ± 0.3) × 10⁻⁴ m² s⁻¹ for Leg 2 (Fig. 6e). This finding suggests that the simulations overestimate the observed vertical diffusivity by a factor of ten. Further, vertical velocities w = −116 ± 24 m yr⁻¹ for Leg 1 and w = −49 ± 30 m yr⁻¹ for Leg 2 predict a considerable overall shoaling of the tracer, contrary to what is observed in the tracer observations. Subsetting the data into boundary and interior regions does not result in largely different spreading rates ($\overline{{\kappa }_{{{{{{{{\rm{b}}}}}}}}}} \, \approx \, \overline{{\kappa }_{{{{{{{{\rm{in}}}}}}}}}} \, \approx \, 1\times 1{0}^{-4}$ m² s⁻¹), although upwelling velocities are generally larger in the boundary regions compared to the interior ($\overline{{w}_{{{{{{{{\rm{b}}}}}}}}}} \, \approx \, -$100 m yr⁻¹, $\overline{{w}_{{{{{{{{\rm{in}}}}}}}}}} \, \approx \, -$60 m yr⁻¹).

While simulated lateral transport rates compare favorably with tracer observations and qualitatively resemble observed tracer distributions, simulated vertical diffusivity is a factor of ten larger than observations. Note that extending these analyses from station-wide comparisons to the entire Gulf-wide does not result in dramatically different dispersion estimates. The agreement between simulated and tracer-derived horizontal dispersion estimates suggests that the random walk diffusion parameter κ_p = 10 m² s⁻¹ provides a realistic estimate of horizontal transport along the Laurentian Channel using this specific modeling framework. However, these simulations suggest that a more stringent scheme is required to realistically forecast vertical spreading in the Gulf—this is especially important as enhanced vertical spreading will change effective lateral diffusivity due to vertical shear.

The results from these simulations suggest that future attempts to forecast dispersion in the Gulf might provide realistic horizontal tracer distributions, but will spread the tracer too rapidly in the vertical dimension. This discrepancy has implications for predictions of tracer transport, as increased vertical spreading in simulations can lead to shortened bottom water residence time estimates, increased shear dispersion, and the underestimation of tracer concentrations given future deliberate (i.e., oxygen enrichment⁵⁵) or unintentional (i.e., contamination events) releases of substances into the Gulf. Future work aimed at enhancing modeling capabilities could address model shortcomings by using inverse techniques on measurements from the TReX Deep experiment to formulate an improved model for Gulf dispersion, similar to what has been achieved for the BATRE project⁶⁴.

Methods

Sample analysis

Tracer samples were collected from a rosette sampler into 200 ml glass syringes. Samples were analyzed on-board using a custom purge and trap gas chromatography system, standardized using a commercially prepared gaseous SF₅CF₃ standard. The analytical precision was 0.06 fmol kg⁻¹ with a quantification limit of 0.1 fmol kg⁻¹. Tracer analysis protocols were identical for Leg 1 and Leg 2.

Swish float dispersion statistics

For each float deployment, we can calculate the mean float drift speed u_f of n floats to estimate an advection speed:

$${{{{{{{{\bf{u}}}}}}}}}_{{{{{{{{\rm{f}}}}}}}}}=\frac{1}{n}\sum\limits_{i=1}^{n}\left[\frac{{{{{{{{{\bf{x}}}}}}}}}_{i}-{{{{{{{{\bf{x}}}}}}}}}_{0}}{\Delta {t}_{i}}\right]$$

(7)

where x_i are the resurfacing positions, x₀ is the deployment site, and Δt_i is the time interval until surfacing.

We can also calculate the float relative diffusivity κ_f as the time rate of mean square pair separation. As the resurfacing periods of the floats vary, we pair any floats from the same deployment that resurface with timescales Δt ± 36 h and calculate their average resurfacing timescales ($\overline{\Delta t}$). There are N = 8 pairs of floats that fit this criteria. We then calculate the relative diffusivity κ_f as being proportional to the time rate of the mean square separation, which we estimate by averaging over the separation rate of N particle pairs which all appear at different times:

$${\kappa }_{{{{{{{{\rm{f}}}}}}}}}=\frac{{\sigma }^{2}}{2t}\approx \frac{1}{2N}\sum\limits_{i\ne j}^{N}\frac{| {{{{{{{{\bf{x}}}}}}}}}_{i}-{{{{{{{{\bf{x}}}}}}}}}_{j}{| }^{2}}{\overline{\Delta t}}$$

(8)

where σ² is the mean square separation of the floats, and i and j are the paired float indices.

Processing tracer profiles

To remove effects of vertical displacements from heaving and large-scale changes in isopycnal depth, tracer measurements at a depth z associated with a measured potential density σ_θ(z) are mapped onto a new vertical coordinate z^* (positive downwards) which defines the location of that density in a reference profile $\overline{{\sigma }_{\theta }}(z)$ using ${\sigma }_{\theta }(z)=\overline{{\sigma }_{\theta }}({z}^{* })$^21,24,26. The reference profile is defined as the mean potential density profile from observations in the vicinity of Cabot Strait, the deepest area of the basin containing the densest water. The mapping generally results in vertical adjustments of less than 20 m. Samples in a given profile are interpolated using a log-linear interpolation scheme to create continuous vertical tracer profiles c_j(z^*), where c is concentration of SF₅CF₃ and j is an index of our individual tracer profiles. The log-linear interpolation scheme used here is a linear interpolation scheme applied to concentration values in $\log (c)$ coordinate space to reduce the effects of changes in curvature at the edges of the distribution.

To assess the lateral spreading of the tracer, we calculate vertical integrals of the tracer profiles from both surveys as follows:

$${I}_{j}=\int\nolimits_{{z}_{{{{{{{{\rm{b}}}}}}}}}^{* }}^{{z}_{{{{{{{{\rm{t}}}}}}}}}^{* }}{c}_{j}({z}^{* })\,d{z}^{* }$$

(9)

where ${z}_{{{{{{{{\rm{b}}}}}}}}}^{* }=$ 400 m and ${z}_{{{{{{{{\rm{t}}}}}}}}}^{* }=$ 1 m. Kriging⁶⁵ is used to produce horizontally interpolated I_j fields (Fig. 2a, d). Areas outside of the survey area were removed from the interpolated fields.

We create normalized, weight-averaged tracer profiles $r(\hat{z})$ to compare the vertical tracer distribution between surveys³⁶, where $\hat{z}$ is a vertical coordinate referenced to the injection depth $\hat{z}={z}^{* }-$279 m. This normalization is achieved using the relation:

$$r(\hat{z})=\sum\limits_{j}\frac{{W}_{j}{c}_{j}(\hat{z})}{{I}_{j}}$$

(10)

where

$${W}_{j}=\frac{{I}_{j}}{{\sum }_{j}{I}_{j}}$$

(11)

is a weighting function using the integrated amount of observed tracer. We use a bootstrap resampling technique to compute uncertainty for r by creating 1000 random subsets of our profiles and calculating 2σ to represent the 95% confidence interval of the mean tracer profile.

1D model fitting

We find the best-fitting solution to Eq. (4) at known time t by varying u and κ_h over a reasonable range and minimizing the cost function:

$$\chi (x,{\kappa }_{{{{{{{{\rm{h}}}}}}}}},u)=\int{\left[{I}_{j}(x)-{I}^{{\prime} }(x)\right]}^{2}dx$$

(12)

where I_j(x) represents the station-wise tracer observations, ${I}^{{\prime} }(x)$ represents the corresponding 1D model values, and x is distance in an along-channel coordinate system (Fig. 4).

To estimate κ_v and w from our observations, we optimize our solution to Eq. (6) by varying κ_v and w minimizing the cost function at known times t:

$$\chi (\hat{z},{\kappa }_{{{{{{{{\rm{v}}}}}}}}},w)=\int{[r(\hat{z})-{r}^{{\prime} }(\hat{z})]}^{2}d\hat{z}$$

(13)

where $r(\hat{z})$ is the normalized observed tracer profile and ${r}^{{\prime} }(\hat{z})$ is modeled concentration $c(\hat{z})$ normalized by substituting model values into Eqs. (10)–(11).

To assign uncertainty to our model estimates, we use a bootstrap resampling technique to create 1000 random subsets of our observed I_j values in Eq. (12) and our observed normalized tracer profiles r in Eq. (13) and apply the above nonlinear optimization to find the best-fitting solution for each subset. From this subset of solutions, we calculate 2σ to represent the 95% confidence intervals of u, v, κ_h, and κ_v.

Regional 3D simulations

Tracer spreading was simulated in three dimensions using archived velocity fields from the Coastal Ice-Ocean Prediction System East (CIOPS-E)^56,57,58,59, a NEMO version 3.6 configuration for the Gulf Region developed by Environment and Climate Change Canada (ECCC). The CIOPS-E model domain follows the ORCA tri-polar grid projection at a nominal 1/36^∘ horizontal resolution, equivalent to a horizontal grid resolution of about 2 km. The vertical grid has 100 vertical points, spaced about 15 m apart at the depth of the tracer injection. CIOPS-E is forced at the ocean boundaries by daily mean temperature, salinity, currents and sea surface height fields from ECCC’s Regional Ice-Ocean Prediction System (RIOPS)⁶⁶ with tides from the Oregon State University TPXO model⁶⁷. At the surface, CIOPS-E is forced by a blend of atmospheric parameters from the High Resolution Deterministic Prediction System⁶⁸ and Global Deterministic Prediction Systems⁶⁹ models and uses a monthly river discharge climatology except for daily estimates for the St. Lawrence River⁷⁰. Background vertical eddy viscosity and diffusivity in CIOPS-E are set to 1.0 × 10⁻⁴ m² s⁻¹ and 1.0 × 10⁻⁵ m² s⁻¹, respectively, and turbulent kinetic energy (TKE) is calculated using a κ − ϵ scheme with generic length scales⁷¹. The model has been evaluated against water level, hydrography, current, and sea surface temperature observations⁵⁶.

The Lagrangian model employed in “Implications For Regional Modeling” was initially developed by Chassé and Miller (2010)⁶⁰ and has been used in various other studies^61,62,63. This particle tracking method calculates trajectories using a fourth-order Runge-Kutta algorithm with a predictor-corrector scheme. Given that dispersion due to tides is mostly removed in the CIOPS-E daily-averaged velocity fields, we initially modeled tidal dispersion by utilizing small-scale diffusion values of a magnitude similar to those previously estimated in the Gulf⁷². This diffusion was implemented as a random walk in the horizontal plane with a diffusion coefficient κ_p, which is translated into random horizontal movements ranging from 0 to $\sqrt{2{\kappa }_{p}\Delta t}$, where Δt is the time step. Various trials were conducted with varying κ_p to estimate dispersion in the system: following comparisons with Swish float information and early tracer observations during Leg 1, simulations incorporating a diffusivity κ_p = 10 m² s⁻¹ were chosen as a best-representation of the tracer dispersion. Moreover, vertical speeds are not available with the CIOPS-E output. Instead, assuming incompressibility, the divergence of the horizontal velocity field is used to estimate the vertical speeds for each day. Due to the inherent numerical errors in calculating vertical speeds, which result in artificial diffusion, no random walk was included in the vertical. All apparent vertical diffusion is therefore only caused by advection and its perturbation errors in the model.

Vertically integrated particle counts are calculated as:

$${P}_{j}=\sum\limits_{j=1}^{n}{p}_{j}({z}^{* })$$

(14)

where p is the vertical distribution of particles at each station j.