M. German¹, [submesoscale co-author]², [OAE-efficiency co-author]³ ¹Steps Ventures. ²[LDEO/Columbia — TBD]. ³[Yale/[C]Worthy — TBD]. Working draft — 2026-07-11. Not for circulation.
Abstract
Ocean alkalinity enhancement (OAE) is among the most scalable candidate marine carbon-dioxide-removal (mCDR) approaches, and its realized efficiency is now guided by global model atlases that map the fraction of added alkalinity that becomes atmospheric CO₂ uptake. These atlases are produced by ocean models at roughly 1° (~100 km) resolution, which do not resolve the submesoscale (1–10 km) fronts and mixed-layer eddies that drive much of the ocean's vertical exchange. Using the 1/48° (~2 km) submesoscale-resolving MITgcm LLC4320 simulation, we measure the fraction of surface-added tracer that is permanently subducted below the winter mixed layer — the pathway that strands alkalinity before it can equilibrate with the atmosphere on crediting-relevant timescales. Across 14 globally distributed regions spanning every dynamical regime, submesoscale subduction permanently removes 16–38% of mixed-layer tracer at open-ocean fronts and deep-convection sites, and essentially none in shallow, enclosed, or ice-covered basins. When the same velocity field is coarsened to the ~100 km resolution of the efficiency atlases, the resolved subduction collapses to near zero: the atlases cannot see this pathway. The effect is not recoverable from coarse surface fields (mixed-layer depth, front strength, or eddy kinetic energy each explain ≤24% of the variance), so the atlases cannot be corrected by parameterization. Because it is not predictable from coarse fields, we project it globally only as a regime bound: applied where winter mixed layers are deep, unresolved submesoscale subduction implies current efficiency atlases over-count near-term OAE efficiency by of order 10–20% in the global mean, and by up to ~40% in the subpolar North Atlantic and Pacific, the Nordic Seas, and the Southern Ocean — the deep-mixed-layer regions where OAE is most often proposed. The result tightens the physical case for measurement-based (ex-post) rather than model-based (ex-ante) crediting of ocean CDR.
1. Introduction
Ocean alkalinity enhancement adds alkalinity to seawater, shifting the carbonate equilibrium so that the surface ocean holds more dissolved inorganic carbon at a given CO₂ partial pressure and draws down atmospheric CO₂. The climate benefit is realized only through air–sea gas exchange, which is slow: the equilibration timescale τ_eq = (h/k)(R_ion/R_f) is of order months to years (Jones et al., 2014; here validated at a global median of 0.51 yr), and CO₂ uptake occurs only while the alkalinity-enriched water remains in contact with the atmosphere. Any process that removes that water from the surface before equilibration completes strands the added alkalinity: the carbon is eventually taken up when the water re-ventilates, but that can be decades to centuries later, outside the horizon on which removal is credited.
The realized, location-dependent efficiency of OAE is increasingly represented by global atlases (Zhou et al., 2024; He & Tyka, 2023) that simulate pulsed alkalinity additions in an ocean general circulation model and report the fraction of the addition realized as atmospheric uptake over a fixed horizon. These atlases are the practical basis for siting and for efficiency assumptions in crediting protocols. They are produced at ~1° nominal resolution, which resolves the mean circulation and mesoscale (~100 km) eddies but not the submesoscale (1–10 km). Submesoscale fronts and mixed-layer instabilities generate intense, coherent vertical velocities (O(10–100) m d⁻¹) that subduct surface water into the interior (Fox-Kemper et al., 2008; Lévy et al., 2012; Su et al., 2018; Balwada et al., 2018; Omand et al., 2015). For alkalinity enhancement the relevant transport is purely physical: dissolved, alkalinity-enriched surface water and its air–sea CO2 equilibration. The same submesoscale subduction also operates in biologically mediated ocean-CDR methods, where its role differs in sign — it is part of the export pathway rather than a loss — a distinction we return to in the Discussion. Balwada et al. (2018) showed in an idealized channel that a 1 km submesoscale-permitting model subducts ~50% more of a passive tracer than a 20 km model. Whether, where, and by how much this unresolved physical subduction biases OAE efficiency atlases has not been quantified.
Here we quantify it directly, and the contribution is specific: the first global, multi-regime measurement of the fraction of surface water subducted below the winter mixed layer faster than the air–sea equilibration timescale, and the first quantification that OAE efficiency atlases, at their own ~1° resolution, resolve essentially none of it. We advect a passive surface tracer in the 3-D velocity field of a submesoscale-resolving simulation and measure the permanently subducted fraction, comparing native resolution against the same field degraded to atlas resolution. We do not simulate the carbonate system in the submesoscale model; the efficiency implication follows physically, through the competition between the subduction timescale we measure and the independently constrained equilibration timescale (§2.1), not from a simulated carbon budget.
2. Results
2.1 A retention-versus-equilibration framework
Realized near-term OAE efficiency is governed by a race between air–sea equilibration (τ_eq) and the removal of surface water from the mixed layer by subduction (τ_sub). Where τ_sub ≫ τ_eq the alkalinity equilibrates and the uptake is realized; where τ_sub ≲ τ_eq a fraction is subducted first and its uptake is deferred to the deep re-ventilation timescale. Submesoscale dynamics act on τ_sub, shortening it at fronts. The efficiency-relevant quantity is therefore the fraction of surface alkalinity subducted below the winter (permanent) mixed layer faster than τ_eq — the quantity we measure below.
2.2 Submesoscale subduction measured across 14 regions
We seed passive particles uniformly in the surface mixed layer of the LLC4320 simulation and advect them in the full 3-D (u, v, w) field through a winter month, in each of 14 regional subdomains spanning western boundary currents, the Antarctic Circumpolar Current, the Agulhas retroflection, subpolar deep-convection sites, subtropical counter-currents, shelves, and enclosed/marginal seas (Table 1; Methods). A particle is counted as permanently subducted if it remains below the winter mixed-layer base through the last quarter of the integration.
Permanent subduction is large and consistent at open-ocean fronts and deep-convection sites (Labrador Sea 0.38, NW Pacific 0.30, Agulhas 0.29, Rockall Trough 0.25, ACC 0.23, Gulf Stream 0.16–0.20) and negligible in shallow, enclosed, or ice-covered basins (Baltic Sea 0.00, Bass Strait 0.00, Weddell ice zone 0.001). In every case the same field coarsened to ~25 km subducts 0–8%. The Gulf Stream value is reproducible across two winter months (0.16, 0.20).
2.3 The atlases cannot see it: bias grows to atlas resolution
Degrading the velocity field to successively coarser resolution collapses the resolved subduction: in the ACC, permanent subduction falls from 0.28 (2 km, native) to 0.13 (25 km), 0.045 (50 km), and ~0.00 at 100 km — the nominal resolution of the efficiency atlases (Fig. 3). At their own resolution, the atlases resolve essentially none of the submesoscale subduction pathway.
The gross vertical exchange tells the same story: at the Gulf Stream, the root-mean-square vertical velocity at the mixed-layer base is 81 ± 6 m d⁻¹ at 2 km versus 27 ± 3 m d⁻¹ coarsened to 25 km (a factor 2.97, 95% CI 2.89–3.04), and the downward volume flux is enhanced 2.67× (2.51–2.79). The coarse value matches the mesoscale root-mean-square reported in the literature, confirming the calculation.
2.4 The enhancement converges to the literature value
The ratio of native to coarse subduction is unstable at short integration times because the coarse denominator is near zero, but it converges as the window lengthens: in the ACC, over 10 → 16 → 22 days the coarse fraction fills in (0.046 → 0.096 → 0.171) while the native fraction stays ~0.25, and the ratio converges 5.5 → 2.5 → 1.5 (Fig. 4), reaching the ~1.5× net enhancement reported by Balwada et al. (2018) from a fully independent model. The robust, integration-time-independent quantity is the absolute native subduction fraction; the ratio is reported only as a convergence check.
2.5 The bias is not parameterizable from coarse fields
Across the open-ocean fronts, the measured subduction fraction is not predicted by any coarse surface field: winter mixed-layer depth explains 4% of the between-region variance, front strength |∇b| explains 18%, and eddy kinetic energy 24%. A Fox-Kemper mixed-layer-eddy parameterization applied to coarse fronts anti-correlates with the measurement (r = −0.59), because coarse fields flag sharp-gradient enclosed seas that do not subduct. The process is intrinsically submesoscale: the atlases cannot be corrected by a resolution-independent formula.
2.6 Global implications
Applying the measured open-ocean penalty (median 0.27, range 0.16–0.38) as a regime map — material where the winter mixed layer is deep (open-ocean fronts and convection), zero in shallow/enclosed/ice-covered water — and overlaying it on the Zhou et al. (2024) atlas, roughly half of the atlas ocean (and of its highest-efficiency cells) is affected, and near-term efficiency is reduced by of order 10–20% in the global mean and by up to ~40% in the subpolar North Atlantic and Pacific, the Nordic Seas, and the Southern Ocean (Fig. 5). We report this as a resolution-bounded regime estimate, not a calibrated correction. These deep-mixed-layer regions are precisely those most frequently proposed for OAE deployment.
2.7 Robustness
The result is robust to the analysis choices. Permanent subduction varies smoothly with the reference depth (0.46/0.37/0.22 at 80/100/150 m) and is stable across persistence thresholds (0.23/0.20/0.17 at 0.7/0.8/0.9). Rerunning with proper vertical-velocity interpolation and with added eddy diffusion changes the result by ≤12%, within the confidence intervals. An independent parameterized estimate (Fox-Kemper on eddy-resolving GLORYS reanalysis fronts) agrees on the distribution and ordering while confirming (§2.5) that coarse fields lack point-by-point skill.
The global penalty projection is robust to the mixed-layer-depth data source: rebuilding the regime map on the observation-based de Boyer Montégut (2004; Argo) winter mixed-layer climatology, rather than one year of GLORYS reanalysis, gives a slightly larger penalized area (66% vs 53% of atlas ocean) and mean near-term reduction (16% vs 13%), so the reanalysis-based estimate is if anything conservative. The efficiency-bias argument is not specific to a single atlas: a second, independent OAE-efficiency model (Tyka, 2025; MITgcm) runs at ~2.8° resolution — coarser than the CESM atlas — and therefore resolves even less of the submesoscale subduction pathway, so the bias applies at least as strongly there.
Most importantly, the result is not an artifact of the LLC4320 model. Repeating the full permanent-subduction measurement in a completely independent simulation — NEMO eNATL60 at 1/60° (~1.7 km), a different model code — at the same Gulf Stream region and a February winter window reproduces it: the permanent subducted fraction is 0.39 (95% CI 0.33–0.44) at native resolution versus 0.044 coarsened to 25 km, mirroring the LLC4320 result of a material native fraction against a near-zero coarse fraction. The eNATL60 value is higher than the LLC4320 Gulf Stream value (0.16–0.20), consistent with its finer resolution and inclusion of tides resolving still more of the submesoscale subduction — the same resolution dependence documented in Fig. 3. Two independent submesoscale- resolving models therefore bracket the effect and agree that coarse-resolution models see essentially none of it. (An earlier vertical-exchange comparison in the eNATL60 Mediterranean subdomain gave a consistent ~2.5× native/ coarse enhancement.)
Finally, the regime map's physical basis is confirmed by observations. The map places the penalty where the winter mixed layer is deep; BGC/core-Argo float profiles show observed median late-winter mixed-layer depths of 488 m in the Labrador Sea and 404 m in the subpolar northeast Atlantic (both penalized) versus 94 m in the subtropical gyre (unpenalized). The deep-mixed-layer criterion is therefore observed, not a reanalysis artifact, and the penalized regions are the deep-convection sites where submesoscale subduction is expected to operate.
3. Discussion
Submesoscale subduction is a real, mappable, and previously unquantified bias in the OAE efficiency atlases that now guide ocean-CDR siting and crediting. It systematically over-states near-term efficiency at open-ocean fronts and deep-convection regions, the very places where efficiency and deployment interest are highest. Because the bias is intrinsically submesoscale, it cannot be removed by a coarse-field correction; resolving it requires submesoscale-resolving simulations or in-situ measurement. This strengthens the case for measurement-based, ex-post crediting of realized removal over model-based, ex-ante crediting.
The subducted alkalinity is not lost. It re-ventilates and contributes to CO₂ uptake on the deep-ventilation timescale (decades to centuries), so the century-scale efficiency the atlases report is not overturned. What is biased is the near-term, crediting-horizon efficiency — a horizon shift, not a loss — which is exactly the quantity that matters for the carbon markets financing OAE today.
The sign of this effect is method-dependent, and the distinction matters for the broader marine-CDR portfolio. For approaches that depend on air–sea equilibration of a dissolved species — alkalinity enhancement and direct ocean capture — submesoscale subduction is a near-term penalty, because it removes the treated water from atmospheric contact before it can gas-exchange. For biologically mediated approaches that fix carbon at the surface and rely on its physical export to depth — iron and nutrient fertilization, macroalgal cultivation and sinking, artificial upwelling — the same submesoscale subduction instead contributes to the sequestration pathway and can aid rather than penalize removal (Omand et al., 2015; Mahadevan, 2016), with permanence then set by the depth of export and re-ventilation rather than by air–sea exchange. A crediting and efficiency framework that spans marine CDR must therefore carry submesoscale transport as a resolved physical control whose sign flips between the chemical and biological method families, not as a single correction.
Limitations. The bootstrap confidence intervals quantify sampling over particles within a single model realization; the dominant uncertainty — a single winter, a single model configuration, one year — is not captured by them, so the CIs are a lower bound on the true uncertainty. The honest spread on the effect is the two-model bracket itself (native Gulf Stream f_perm 0.16–0.20 in LLC4320 versus 0.39 in the finer, tidal eNATL60), which also encodes the resolution and tidal dependence. Both submesoscale-resolving simulations span a single winter, so interannual variability is untested; the tracer is advected offline rather than run inside the model (mitigated by ≤12% offline-method sensitivity, by agreement with the online passive-tracer result of Balwada et al., 2018, and by the two-model agreement here); and winter-specificity is suggested but not fully established (a summer Gulf Stream mixed layer is too shallow to seed, and a summer Labrador Sea shows a modest 30% reduction). The single-model and single-atlas concerns are addressed by the region-matched eNATL60 Gulf Stream measurement, the second efficiency atlas (Tyka, 2025), and the Argo observational anchor. A passive tracer run online within a submesoscale-resolving biogeochemical model, resolving the full carbonate response, remains the definitive future test.
4. Methods
Submesoscale simulation. MITgcm LLC4320, 1/48° (~2 km), 90 vertical levels, hourly output; Pre-SWOT regional subsets (PO.DAAC) for 14 regions, hemisphere-appropriate deep-winter month (Feb 2012 NH, Jul–Aug 2012 SH). Variables: 3-D u, v, w, potential temperature, salinity, and KPP boundary-layer depth (mixed-layer depth proxy).
Lagrangian tracer. Particles seeded in the interior 50% of each domain at 5/20/40 m within the mixed layer, advected by vectorized 4th-order Runge–Kutta on the 3-D velocity field (regular lat/lon subdomains) through the winter window; permanent subduction = below the winter mixed-layer base (100 m reference) for ≥80% of the final quarter. Bootstrap 95% confidence intervals over particles.
Coarsening. Native fields block-averaged to 25/50/100 km before re-advection of the same seed set.
Regime map. Global winter-maximum mixed-layer depth from GLORYS12 reanalysis; measured open-ocean median penalty applied where MLD > 90 m (ramped to 0 below 40 m), zeroed where the coldest-month SST < −1 °C (ice). Overlaid on the Zhou et al. (2024) CESM efficiency atlas.
Parameterized cross-check (E1). Fox-Kemper (2008) mixed-layer-eddy overturning w ~ Cₑ H |∇b| / N computed on daily eddy-resolving GLORYS12 fronts at 11 candidate deployment sites; permanent-subduction fraction from the competition with τ_eq.
Equilibration timescale. τ_eq = (h/k)(R_ion/R_f) with Wanninkhof gas transfer and PyCO2SYS carbonate chemistry; validated against Jones et al. (2014).
Data and code availability
Analysis code and derived data: gs://airloom-marine-cdr/outputs and github.com/steps-re/marine-cdr-investability. LLC4320 from NASA PO.DAAC; GLORYS12 from CMEMS; OAE efficiency atlas from Zhou et al. (2024) / [C]Worthy.
Figures
- Fig. 1. Schematic: the retention-versus-equilibration race; horizontal dilution conserves the integral while vertical submesoscale subduction strands alkalinity below the winter mixed layer.
- Fig. 2. Measured permanent submesoscale subduction fraction (native 2 km) across 14 regions, ordered by magnitude, with bootstrap 95% CIs; regimes color-coded (fronts/convection vs shelf vs enclosed/ice). (outputs/e_campaign_global.csv; fig_e3_lagrangian.png shows the Gulf Stream depth distribution.)
- Fig. 3. Coarsening bracket (ACC): permanent subduction versus model resolution (2/25/50/100 km), with the atlas GCM resolution (~1°) shaded; the resolved subduction collapses to ~0 at atlas resolution. (fig_coarsen_bracket.png)
- Fig. 4. ACC window-length convergence: native vs coarse f_perm and the native/coarse ratio versus integration window, converging to the ~1.5× net enhancement of Balwada et al. (2018). (fig_acc_window_sweep.png)
- Fig. 5. Global regime map: Zhou atlas efficiency | submesoscale-subduction penalty | corrected near-term efficiency. (fig_e4_global_penalty.png)
- Fig. S1. Predictor scatter: measured f_perm vs winter MLD, |∇b|, and EKE (all weak; the process is unparameterizable from coarse fields). (fig_e4_calibration.png)
- Fig. S2. Independent-model validation: submesoscale vertical-exchange enhancement in NEMO eNATL60 vs MITgcm LLC4320. (enatl_check.csv)
References
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Table 1. Measured permanent submesoscale subduction fraction (native 2 km) by region and regime. See outputs/e_campaign_global.csv. All figure source files in gs://airloom-marine-cdr/outputs.