Can the ocean cash the check? An air–water equilibration filter for marine and aquatic carbon-removal investment

Working manuscript (v2, post-review corrections). Steps Ventures. Target: One Earth / Environmental Research Letters; Nature Climate Change if the corrected global result holds. All quantitative claims traced to sources; external facts passed an independent grounded adversarial check (Appendix H).

Abstract

Marine and aquatic carbon dioxide removal (CDR) realize atmospheric removal only through air–water CO₂ gas exchange, a flux that is rate-limited and strongly location-dependent. We build a physics-based due-diligence filter for CDR investment by overlaying the real deployment geographies of companies and national exclusive economic zones (EEZs) onto the first published global atlas of ocean-alkalinity-enhancement efficiency, coupled to a reduced-form Monte-Carlo investability screen. We separate two questions that the sector routinely conflates. First, where does the physics allow removal, and at what cost, if measurement succeeds? Conditional on verification, the corrected model finds mineral ocean alkalinity enhancement (OAE) is broadly viable across most of the open ocean above roughly US$150–250 per tonne, electrochemical OAE above roughly US$250, and marine biomass sinking and iron fertilization uninvestable at any price to US$500 per tonne because their realized-removal efficiency (about 25% and 2% of gross, respectively) and costs overwhelm any siting advantage. These estimates carry wide uncertainty dominated by cost and lifecycle priors. Second, will a project actually be paid? Here the binding near-term constraint is neither physics nor cost but verification: only one marine-CDR project has ever had credits issued, about 0.3% of contracted volume has been issued, and near-term issuance probability is roughly 5–15% for OAE and under a few percent for other pathways. On an unconditional basis every pathway has a low-single-digit-percent chance of being paid today. Physics and cost determine where it works if measurement is solved; verification risk determines whether anyone is paid now. Several nations with active programs, most sharply Chile (mean EEZ efficiency 0.32), invest where their own waters are least favorable. Extending the analysis globally, we show that the three physical controls on realization — air–sea equilibration time, surface-water flushing time, and carbonate buffering capacity — are spatially decorrelated (pairwise |r| ≤ 0.15 in a native, eddy-resolving recomputation), so no single ocean property identifies viable sites; surface flushing in particular is near-uniformly fast at the deployment footprint (a treated patch leaves its origin almost everywhere within a year), so local verification is a near-universal constraint rather than a siting lever. The surface currents underlying these results are validated against Global Drifter Program observations (r = 0.78). Cast in registry data, the gap is stark: of roughly 578,000 t contracted, applying the equilibration lag leaves on the order of 0.5% physically realized by the atmosphere to date. We argue the filter is a necessary, not sufficient, screen for public and private capital.

Note added in revision — companion measurement. A companion study (German, in prep.) measures, in two independent submesoscale-resolving ocean models (MITgcm LLC4320 and NEMO eNATL60), that at open-ocean fronts and deep-convection sites 16 to 38 percent of treated surface water is subducted below the winter mixed layer faster than it can equilibrate — a process the roughly 1° efficiency atlas used here cannot resolve. Applied as a regime map, this implies the atlas over-counts near-term OAE efficiency by of order 10 to 20 percent in the global mean, and up to about 40 percent in the subpolar North Atlantic and Pacific, the Nordic Seas, and the Southern Ocean, the deep-mixed-layer regions this paper flags as most proposed for deployment (a resolution-bounded regime estimate, not a calibrated correction). Three consequences for the results below. (i) The atlas f_kin used here is a near-term upper bound at deep-mixed-layer fronts, so the conditional viability thresholds are optimistic there, and the near-term efficiency at those fronts is over-stated rather than conservative. (ii) The agreement between the atlas and our coarse offline Lagrangian tracer (Appendix A.6) reflects a shared coarse-resolution blind spot, not independent validation of near-front near-term efficiency. (iii) The sign of vertical export is method-dependent: subduction is a near-term penalty for equilibration-dependent methods (OAE, direct ocean capture) but an export aid for biological methods (iron and nutrient fertilization, macroalgae cultivation and sinking, artificial upwelling), where permanence is set by export depth rather than air–sea exchange. The companion result strengthens rather than overturns this paper's central conclusion, that realized near-term removal sits below credited removal and that verification is the binding near-term gate.


1. Capital is moving ahead of the physics — and ahead of verification

Money is flowing into marine and aquatic carbon dioxide removal (CDR) faster than the physics that governs whether it works and faster than the measurement that governs whether it can be sold. Advance-market commitments exceed US$1 billion, national governments in Canada, the United Kingdom, Norway and elsewhere fund programs in their own waters, and offtake agreements underwrite hundreds of thousands of tonnes of future removal. Yet nearly every one of these approaches shares a single physical bottleneck that is rarely applied as an investment filter: atmospheric CO₂ removal happens only when a CO₂ deficit created in surface water is refilled by a net flux from the atmosphere, and that flux is slow.

The gap between commitment and delivery is stark. As of 2025–2026, one marine-CDR project has publicly had credits independently issued (Planetary Technologies, 625.6 tonnes in June 2025 and a further ~1,190 in October 2025, via the Isometric registry), and roughly 0.3% of the ~578,000 tonnes secured through offtake agreements has been formally issued. Two further first-of-a-kind issuances span other water bodies: wastewater alkalinity enhancement (CREW Carbon, ~104 tonnes) and river alkalinity enhancement (CarbonRun, Kvina River, Norway, ~77 tonnes). Part of this shortfall is the ordinary immaturity of a young sector. Part is two unpriced constraints, physical and evidentiary, that we quantify here.

The physics is settled and its location-dependence has been mapped. What has not been done, and what we do here, is the empirical join: we overlay the actual deployment geographies of companies and nations onto the published global efficiency field and ask, deployment by deployment, whether the ocean at that location can realize the removal on a policy-relevant timescale, at a plausible price, and with a plausible chance of certification. Recent work established air–sea equilibration as a cross-cutting constraint conceptually (Oschlies et al. 2025) and defined efficiency metrics for OAE versus direct air capture (Yamamoto et al. 2024); the first global, time-resolved atlas of that efficiency now exists (Zhou et al. 2024). We convert those advances into an investment due-diligence layer, extend the lens across the full pathway set with pathway-specific efficiency, add a verification-risk gate, and organize the field by atmospheric coupling and by water body.

2. The air–water equilibration filter: cashed versus stranded

In plain terms (Fig. 1). Almost every ocean carbon-removal method works by making a patch of surface seawater hungry for CO₂, either by adding alkalinity or by stripping carbon out of the water. That hunger is only satisfied when CO₂ crosses from the air into the sea, and that crossing is slow, taking months to about a year. If the treated water stays at the surface in contact with the air, the atmosphere gradually refills the deficit and the removal is real — the check is cashed. If ocean currents pull that water down below the surface layer before the exchange finishes, the hunger is carried into the deep ocean and the removal is stranded for years to centuries. A common worry is that turbulence dilutes the treated patch and erases the effect. It does not: mixing spreads the deficit over a wider area but conserves the total amount of CO₂ the ocean will eventually take up, so horizontal dilution is not the enemy. Vertical export — subduction — is. Every number in this paper is, at bottom, an estimate of what fraction of the intervention is cashed before it is stranded.

The characteristic e-folding time of this relaxation is τ_eq = (h / k) × (R_ion / R_f), where h is the mixed-layer depth, k the gas-transfer velocity, R_ion the ionization fraction (dissolved inorganic carbon over aqueous CO₂, of order 100–200) and R_f the Revelle buffer factor (of order 8–15) (Jones et al. 2014). The Revelle factor is in the denominator: a higher R_f drives the flux harder and speeds equilibration, so the net slowdown of CO₂ relative to an inert gas is the ratio R_ion/R_f, roughly a factor of 10–20. The global-median τ_eq is 4.1 months, ranging from under a month in high-wind seas to about two years in quiescent subtropical gyres (Jones et al. 2014).

Box 1 — Cashed versus stranded. The alkalinity (or dissolved-inorganic-carbon) anomaly is a conserved tracer. When it mixes horizontally into surrounding surface water the local driving force Δp falls, but the anomaly spreads over a proportionally larger area, and because air–sea flux scales as k·Δp·area, the basin-integrated uptake is conserved; τ_eq is a property of the water column, not of the anomaly's concentration, so dilution does not slow the relaxation. The genuine loss is vertical: if the deficit-bearing water is subducted below the mixed layer before τ_eq completes, its uncashed potential is stranded until that water re-ventilates. The binding competition is τ_eq against the surface-residence time before vertical export. A secondary chemical loss runs the other way: dosing alkalinity too concentrated pushes the aragonite saturation state past a runaway threshold and precipitates CaCO₃, releasing CO₂, so some dilution is protective.

This is why gas exchange alone does not predict success. Near-coast OAE modeling shows realized uptake efficiency (η_CO₂ = ΔDIC/ΔAlk) after one year spans 0.2–0.85 and plateaus at 0.6–0.8 after three to four years (He & Tyka 2023). High-latitude, high-wind sites equilibrate quickly, subtropical sites such as Hawaiʻi take 8–10 years, and North Atlantic deep-water-formation zones stall near 0.4 even after 20 years because the water subducts before it equilibrates despite excellent wind-driven gas transfer (He & Tyka 2023; Nowicki et al. 2024). Regional modeling confirms the corollary that cold, carbon-rich high-latitude water can realize very high efficiency, exceeding 96% in the Bering Sea (Wang et al. 2023) and favoring the Southern Ocean (Burt et al. 2021). We take the fraction of a nominal perturbation cashed before it is stranded, over a stated horizon, as the efficiency variable f_kin; the global atlas maps it for the open ocean by embedding the three-dimensional circulation directly (Zhou et al. 2024).

3. A taxonomy of aquatic carbon removal

Two axes organize the field. The first is atmospheric coupling. Atmosphere-coupled pathways (OAE, direct ocean capture, marine-grown biomass sinking, iron fertilization) create a seawater carbon deficit the atmosphere must refill, so they are gated by realized air–water efficiency. Storage-only pathways sink carbon already fixed from the air elsewhere — most clearly terrestrial biomass sunk into the sea — and are not gated by air–sea exchange; they are the natural control. The coupling penalty is severe for biology: after accounting for air–sea equilibration and remineralization, marine-grown biomass realizes only a fraction of its sunk-carbon value, with model-based central estimates near 25% and a plausible range of roughly 5–40% (Bach et al. 2021; DeAngelo et al. 2023; Gao & Taylor 2024; the qualitative point is also made by Hurd et al. 2024). Iron fertilization is lower still, durably sequestering roughly 2% of stimulated production (0.5–5%; Ward et al. 2025; NASEM 2022).

The second axis is water body. The global atlas resolves air–sea exchange only in the open ocean on a 1° grid (Zhou et al. 2024). It does not resolve marginal and semi-enclosed seas, estuaries and coastal zones, freshwater lakes, rivers, wastewater outfalls, or aquifers and mine pit lakes. The filter still operates there but its value is a known-unknown, frequently worse: marginal seas (Baltic, Black Sea) have restricted exchange and stratified lids; freshwater has low, variable buffering that caps storage; river alkalinity enhancement loses a further 16–27% to in-river carbonate precipitation and outgassing before reaching the sea (UK modeling). The three verified issuances to date span three different water bodies, each requiring a bespoke high-resolution model, which is precisely why a single global atlas cannot serve as investment-grade diligence across the field.

4. Results I — where the physics allows removal, conditional on verification

We treat f_kin as a physical discount on gross performance. The realized creditable fraction of a nominal design tonne is E = eff × (1 − λ_LCA), where eff is the atlas f_kin for OAE (which already embeds the ~0.8 carbonate ceiling — we do not apply a separate chemistry-yield term, correcting an earlier double-count), a pathway-specific efficiency for biological and iron pathways, or 1 for physics-exempt direct ocean capture and terrestrial burial; λ_LCA is the lifecycle-emissions penalty. Net cost is cost_gross/E, evaluated by Monte Carlo over correlated cost and lifecycle priors (Appendix B). All results in this section are conditional on successful measurement (issuance risk is treated separately in Section 5).

Physics breakeven and global area (Fig. 2, Fig. 3). After correcting the ceiling double-count and adding uncertainty, mineral OAE requires a local atlas efficiency of about 0.35 (10–90 range 0.16–0.72) to clear US$200 per tonne, and about 0.21 at US$350. Because most of the open ocean has 5-year efficiency in the 0.4–0.8 band, mineral OAE is investable across roughly 90–100% of the ocean at the median above US$150–200, though the 10–90 band is wide (0 to 100%), reflecting that the answer is dominated by cost and lifecycle uncertainty rather than by physics alone. Electrochemical OAE, being more expensive, requires efficiency near 0.55 at US$200 and clears a median ~78% of the ocean there, rising to near-universal above US$300. Marine biomass sinking and iron fertilization are uninvestable across 100% of the ocean at every price to US$500, because their pathway efficiency (about 25% and 2%) and gross costs (medians about US$1,090 and US$460 per tonne) overwhelm any location advantage. Direct ocean capture and terrestrial burial are physics-exempt and gated only by price.

Company overlay (Fig. 2). Overlaying real deployments on their local efficiency reproduces the observed record. Conditional on verification, OAE projects at good sites clear comfortably at US$350 (Ebb 0.96, Vesta 0.92, Planetary 0.86 probability of clearing cost) and more marginally at US$200 (0.51–0.73). The now-defunct Running Tide operated off Iceland at f_kin 0.47 with a method that never clears on cost; Gigablue targets a South Pacific region with an iron pathway that likewise never clears. Direct ocean capture (Captura, Equatic, SeaO2) is physics-exempt but cost-limited (~0.73 at US$350). These conditional verdicts are the physics-and-cost half of the story.

5. Results II — the binding near-term gate is verification, not physics

The conditional results above assume a project can prove and certify its removal. Most cannot, yet. Only one marine-CDR project has ever had credits issued; about 0.3% of contracted volume has been issued; measurement, reporting and verification can exceed half of project cost; and the reasons for failure — unverifiable far-field uptake, model dependence, unproven additionality and permanence, and immature methodologies — are structural, not transitional (Appendix H; literature synthesis). We therefore model issuance as a binary probability that a project is paid at all, from the recent record (Fig. 4): roughly 5–15% for mineral OAE, 3–12% for electrochemical OAE, 1–5% for direct ocean capture, under 2% for biomass sinking and iron fertilization, and 5–25% for terrestrial burial.

The consequence is decisive. On an unconditional basis — clearing both the physics-and-cost hurdle and being certified — every pathway has a low-single-digit-percent chance of being paid in the near term: mineral OAE at a good site about 9%, electrochemical OAE 6–7%, direct ocean capture ~2%, biomass and iron ~0%, terrestrial burial ~15%. Verification risk is larger than physics and cost combined. This reframes the entire due-diligence question: the physics filter tells an investor where a technology can work once measurement is solved, but the near-term expected value is set almost entirely by whether the project can be certified. It also explains the market's own record: the durable survivors are exactly the pathways with the shortest measurement path (near-field, engineered, or mass-measured), and the collapses (Running Tide) and disputes (Gigablue) cluster where far-field verification is hardest.

6. Results III — national investment overlooks equilibration geography

National strategies direct capital toward coastline length and nominal capture potential rather than toward waters where removal can be realized. Aggregating five-year f_kin across each EEZ exposes a systematic misalignment (Fig. 5). Canada, the United Kingdom, Norway and the Netherlands invest and hold favorable waters (mean EEZ efficiencies 0.71, 0.69, 0.68, 0.68); the United States sits at 0.62 (from few resolved cells; treat as indicative). Chile, an active investor, holds the least favorable waters of any investor at 0.32, its coast dominated by the Humboldt upwelling, which brings CO₂-rich water to the surface and creates a high-background, outgassing-prone environment an intervention must first overcome. The best-endowed waters are largely uninvested (Guyana and Barbados near 0.83, Uruguay 0.80, on small samples). The US national marine-CDR research strategy does not treat air–sea equilibration as a gating factor. Physics is necessary, not sufficient: legal and social license gate independently, as when New Zealand rejected the Oceaneos iron-fertilization proposal as prohibited dumping. Small-sample EEZ means (United States, Netherlands, Guyana, Barbados) are indicative only, given the atlas's 1° resolution near coasts.

Guidance, nation by nation. The efficiency ranking becomes actionable when fed into a national public-investment optimizer that allocates a budget between deploying the best-fit pathway and funding measurement (Appendix E, expanded). The result is uncomfortable for national OAE programs: for every nation the physics-exempt storage baseline (terrestrial burial, direct ocean capture) delivers roughly two-to-five times more verified removal per public dollar than ocean OAE — the OAE-versus-exempt ratio runs from 0.46 in the best-endowed waters (Guyana) down to 0.18 for Chile — and the optimizer sends about 31% of budget to measurement rather than deployment regardless of water quality. Even a well-sited nation gets less than half the verified removal per dollar from ocean alkalinity enhancement than from storage or near-field capture; a poorly-sited active investor like Chile gets one-fifth. Two of the most active national investors, Japan and New Zealand, cannot be scored from the atlas at all — it has zero resolved cells in their exclusive economic zones — and our offline tracer, built for exactly this coastal gap, estimates within-EEZ physical retention at roughly 0.50 (Japan) and 0.84 (New Zealand, favorable but socially contested after the Oceaneos rejection). The first-pass national message is consistent across methods: fund measurement and the physics-exempt baseline before subsidizing ocean-OAE deployment, and never subsidize deployment where the water cannot deliver.

7. Durability and the horizon choice

The efficiency we report is realized atmospheric uptake, not permanence. We report f_kin at 1, 5, 10 and 15 years (the atlas limit); OAE efficiency generally rises with horizon as subducted alkalinity partly re-emerges, so 5-year values are conservative for slow sites and near-complete for fast ones. Durability beyond 15 years is a separate question governed by re-ventilation timescales (years to millennia; Siegel et al. 2021) and, for stored-carbon pathways, by preservation. Bicarbonate from OAE is stable for 10⁴–10⁵ years if it does not re-precipitate; sunk biomass can re-mineralize and outgas within 100–150 years; anoxic-basin terrestrial burial (the control) is preservation-limited, not equilibration-limited, and carries its own methane risk. We adopt 5 years as the policy-relevant crediting horizon and show the full curve in Appendix F.

8. Implications for investment, verification and governance

For capital, the filter draws hard boundaries: it flags whole pathways (biomass sinking, iron fertilization) that do not close on cost at any plausible price even before verification, and it shows that among viable pathways the near-term expected value is set by issuance risk, not siting. The rational near-term portfolio favors short-measurement-path pathways (engineered, near-field, mass-measured) and treats far-field open-ocean removal as an option on future measurement science. For verification, the atlas supplies global context for the site-specific models registries require, and names the frontier risk: the fastest-growing categories (coastal, wastewater, river, freshwater) operate where the global atlas does not reach. For governance, the EEZ atlas gives nations a first-pass reading of their own physical potential and a warning against subsidizing deployment where the water cannot deliver. Air–sea gas exchange and independent verification are the two non-negotiable constraints every atmosphere-coupled pathway must pay; pricing them, geographically and per pathway, is the missing due-diligence layer for a sector now allocating billions.

A playbook for private capital. Treated as an options problem rather than a siting problem, the near-term picture is stark (Appendix J). At US$350 per tonne and today's issuance probabilities, diversified expected value is negative for every ocean pathway and positive only for physics-exempt terrestrial burial (+0.77 in relative units). Mineral OAE is −0.65 today but +1.07 if issuance matures toward 60% — a real option worth waiting on: commit in roughly four years, when issuance clears its ~29% breakeven or the credit price reaches ~US$177. Electrochemical OAE is a ~seven-year wait; biomass sinking and iron fertilization never reach positive value even with mature measurement. Four rules follow. (i) Triage by measurement path — fund near-field, engineered, mass-measured methods now; avoid biomass and iron at any price; hold far-field OAE as a dated option. (ii) The highest-return near-term capital is MRV infrastructure, because it moves the issuance probability that dominates every pathway's value. (iii) Diversify — because sites' interannual delivery variability is only partly correlated, a multi-site portfolio cuts delivery variance by ~73% at equal expected removal (Appendix I.7). (iv) Stage commitments against issuance maturity; the option value of waiting is large while issuance sits below ~15%.

9. Methods (summary; full detail in Appendix A)

We generate no new climate simulations. We sample the published Zhou et al. (2024) global OAE efficiency atlas at the exact coordinates of each deployment, snapping coastal points to the nearest resolved ocean cell and recording the snap distance. Uncertainty in f_kin is taken from the four-season spread plus a ~10% model term. The investability screen is a reduced-form Monte Carlo over literature-anchored, correlated cost and lifecycle priors and pathway-specific efficiency priors (Appendix B); it is not a bankable techno-economic analysis, and air–sea efficiency is a necessary not sufficient condition. Issuance probability is modeled as a binary near-term gate from the recent issuance record. A transparent reduced-complexity emulator (Wanninkhof 2014 gas transfer; PyCO2SYS carbonate chemistry) is used only as a first consistency check; it reproduces the published site ordering but shares physical inputs with the atlas. As a stronger, independent check we also ran an offline three-dimensional Lagrangian tracer model forced by GLORYS12 reanalysis currents and CMEMS wind-stress (Ekman pumping) — data independent of the atlas's CESM — with bathymetry-aware shelf ventilation; it reproduces the atlas f_kin across temperate, coastal, subpolar and shelf regimes within ≈0.05 and clarifies which coastal and shelf waters the 1° atlas cannot resolve, under-counting only the subtropical gyre where re-emergence is decadal (Appendix A.6). National aggregation area-weights f_kin over EEZ polygons (Marine Regions). Key correction from an earlier draft: the atlas f_kin already includes the carbonate-chemistry ceiling, so it is the sole location-efficiency term for OAE (no separate yield multiplier), and biological/iron pathways use their own efficiency rather than the OAE atlas.

Competing interests

The author is affiliated with Steps Ventures, an advisory firm with a potential interest in marine-CDR outcomes, and maintains a public interactive tool derived from this analysis. The analysis reuses third-party published data and code and reports uncertainty transparently; readers are directed to the released repository to inspect all priors and reproduce every figure.

Data and code availability

Efficiency field: Zhou et al. 2024 / [C]Worthy Global OAE Efficiency Atlas (source.coop/cworthy/oae-efficiency-atlas). EEZ boundaries: Marine Regions (VLIZ). The deployment-geography dataset compiled here, all Monte-Carlo priors, and the analysis and figure code are released at https://github.com/steps-re/marine-cdr-investability (MIT/CC-BY). Author contributions: sole author (co-authorship with an oceanographic collaborator to be added before submission).


Figures

Figure 1. The cashed-versus-stranded mechanism, in plain terms. A carbon-removal intervention makes surface seawater hungry for CO2; that hunger is satisfied only as CO2 crosses from air to sea over months to a year. If the treated water stays at the surface it is refilled by the atmosphere (cashed, left, green); if currents subduct it below the mixed layer first, the deficit is stranded in the deep ocean for years to centuries (right, red). Horizontal mixing spreads the signal but conserves the total, so dilution is not the loss; vertical export is. Right panel: realized removal (f_kin) rises toward the chemistry ceiling if equilibration outruns subduction, or freezes low if it does not.
Figure 2 (corrected). Net cost per creditable tonne versus atlas efficiency, conditional on verification, after removing the double-counted chemistry ceiling. OAE deployments plotted at their atlas f_kin; DOC and terrestrial burial are physics-exempt (flat); biomass and iron sit far above the market band.
Figure 3 (corrected). Fraction of the open ocean investable per method versus credit price, CONDITIONAL ON VERIFICATION, with 10-90 uncertainty bands. Mineral OAE clears most of the ocean above ~$150-200 (median) but with wide bands; biomass and iron are 0% everywhere.
Figure 4. The dominant near-term gate: probability a project actually gets credits issued, by pathway. Only Planetary has ever issued mCDR credits; ~0.3% of contracted volume issued. This multiplies conditional investability down to low-single-digit unconditional probabilities.
Figure 5. National EEZ mean 5-yr efficiency, colored by investment level. Chile (0.32) invests where its waters are least favorable; the best-endowed EEZs are largely uninvested. Small-sample EEZs are indicative only.
Figure 5b. Global choropleth of EEZ mean efficiency with engineered-mCDR investors marked.
Figure 6. Carbonate ceiling and safe-dose envelope per site (Appendix A.7 i). Left: the attainable-efficiency ceiling eta_max, higher in cold water. Right: aragonite saturation versus instantaneous alkalinity dose; the steeper warm-water curves hit the runaway threshold (Omega=5) far sooner, capping the per-deployment dose.
Figure 7. Delivery-risk: mean realized removal with its interannual P10-P90 spread across forcing years 2011-2020 (Appendix A.7 ii). Wide bars / high CV mark sites whose year-to-year delivery an offtaker must underwrite; absolute levels are monthly-forced and biased low, so the spread is the signal.
Figure 8. Site-level MRV verifiability from the real dispersing plume (Appendix A.7 iii): detectable window x containment -> implied issuance probability. Low everywhere, marginally best in contained settings; verification is the binding gate at site resolution.
Figure 9. Deployment-timing sweep (Appendix A.7 iv): realized removal by release quarter. Large seasonal swings at some sites (dose into the deep winter mixed layer, not the summer lid), negligible at deep-mixing sites.
Figure 10. First-order equilibration efficiency for water bodies outside the open-ocean atlas domain (Appendix I.1). The binding constraint changes by class: enclosed seas equilibrate fully (limit is source/durability), rivers and engineered outfalls are flushing/re-evasion-limited. Freshwater buffering recomputed per body.
Figure 11. The crediting-versus-realization gap (Appendix I.2, log scale). ~578,000 t contracted -> ~5,000 t issued -> ~2,800 t (~0.5%) physically realized once the equilibration lag is applied. Registry-verified data (Isometric, mid-2026).
Figure 12. Interannual efficiency anomaly versus climate modes (Appendix I.3). Variability is real (~10-20% CV) but only weakly predictable: best correlations are a modest NAO signal at North Atlantic coastal sites; presented as a largely irreducible delivery risk, not forecastable skill.
Figure 13. Site flushing time from Lagrangian survival (Appendix I.4), 0.9-159 yr. It is set by flow geometry, not current speed: Duck NC has the fastest current yet moderate flushing (recirculating), the North Sea the fastest flushing (through-flow).
Figure 14. Global surface current speed, equilibration time tau_eq, and Lagrangian flushing time. The three controls are spatially decorrelated (speed-flushing r=-0.04, tau_eq-flushing r=0.06): no single ocean property identifies viable sites (Appendix I.4).
Figure 15. Independent validation against the NOAA Global Drifter Program climatology (Laurindo et al. 2017): modeled surface speed vs observed drifter speed, r=0.78 (Appendix I.5).
Figure 16. Global verifiable-realization potential V = [tau_flush/(tau_flush+tau_eq)] x eta_max (Appendix I.6): where the ocean cashes the check where it can be seen. Triangles = real deployments.
Figure 17. Integrated 0-100 investability score by deployment, fusing realization, verifiability, capacity, reliability and retention (Appendix I.7). ~13% of announced contracted volume sits in below-median-score waters.
Figure 18. CDR siting as a risk-return portfolio (Appendix I.7). Because sites' interannual variability is only partly correlated, a diversified portfolio cuts delivery variance ~73% at similar expected verified removal versus the single best site.
Figure 19. National public-investment optimizer (Appendix E): verified tonnes of removal delivered per US$1M of ocean-OAE spend, by nation and investment level. A physics-exempt storage baseline delivers 2-5x more per dollar for every nation; optimal MRV budget share ~31%.
Figure 20. Private-investor real-options view (Appendix J): diversified expected return per pathway now versus if measurement matures, with commit-vs-wait timing. Only physics-exempt burial is positive today; mineral OAE is a ~4-year option; biomass and iron never clear.

Figure captions

Appendices

See APPENDICES.md (A methods; B priors incl. pathway efficiency and issuance; C water-body taxonomy; D deployment overlay; E national EEZ; F global area + horizons; G screener; H adversarial check) and REFERENCES.md (references with DOIs).


Appendices

Appendix A — Methods in full

A.1 Air–sea efficiency field. We use the published global atlas of ocean-alkalinity-enhancement (OAE) efficiency (Zhou et al. 2024; open data at source.coop/cworthy/oae-efficiency-atlas), a CESM ocean–biogeochemistry ensemble of 690 alkalinity-release regions × 4 injection seasons, integrated 15 years. The archived field OAE_efficiency(season, month, nlat, nlon) is the cumulative atmospheric CO₂ uptake divided by alkalinity added, i.e. f_kin, on the model's curvilinear grid. We take the season mean at month 60 as the 5-year f_kin (and months 12, 120 for the 1- and 10-year horizons).

A.2 Sampling at deployment coordinates. For each project we find the nearest grid cell with a defined efficiency value (snapping coastal points to the nearest resolved ocean cell) and record the snap distance in degrees; snaps beyond ~1° are flagged as coarse. Validation sites reproduce He & Tyka (2023): Peru/Tasmania/Patagonia/Brazil 0.70–0.79 at 5 yr (fast); Hawaiʻi 0.59→0.72 (1→10 yr, slow-recovers); North Atlantic deep-water 0.50→0.52 (stalls).

A.3 Reduced-complexity emulator (cross-check). An independent box model computes τ_eq = (h/k)(R_ion/R_f) with k from Wanninkhof (2014) and R_f, R_ion from PyCO2SYS (Humphreys et al. 2022), and realized kinetic efficiency from the competition between τ_eq and a surface-residence prior. It reproduces the atlas/He–Tyka ordering (Fig. A1) and is used only as a transparent audit and to reason about unresolved water bodies. Planetary/Halifax lands at 0.62–0.64 (emulator and atlas), consistent with the published ~0.515 realized fraction for Halifax Harbour.

A.4 Investability identity. cost_net = cost_gross / (f_kin · η_yield · (1 − λ_LCA) · ν_MRV). For physics-exempt methods f_kin ≡ 1. The physics breakeven at price P is the minimum f_kin with P(cost_net < P) ≥ 0.5 under the Monte-Carlo priors (Appendix B), 8,000–20,000 draws.

A.5 National aggregation. We area-weight (cos φ) the 5-year f_kin over all resolved ocean cells within each sovereign EEZ (Marine Regions polygons, made valid and simplified to 0.1°), reporting means for EEZs with ≥20 cells. The 1° atlas resolves narrow coastal EEZs poorly (e.g. the United States retains only ~47 cells); small-sample means are flagged.

A.6 Independent circulation cross-check (offline Lagrangian tracer). To test whether our reading of the atlas is physically sound with independent inputs, we ran an offline three-dimensional tracer-transport model on a different data source than the atlas's embedded CESM: daily GLORYS12 reanalysis currents and mixed-layer depth (Copernicus Marine, 1/12°) plus CMEMS L4 wind-stress for Ekman pumping. Neutrally-buoyant parcels are advected in 3-D (OceanParcels, RK4); while a parcel is in the mixed layer it relaxes its CO₂ deficit at the local air–sea rate k·R_f/R_ion, and it is carried below by the resolved vertical velocity — continuity divergence plus Ekman pumping w_ek = −curl(τ/ρf). Permanent stranding is emergent, not imposed: a parcel that subducts below the winter-maximum mixed layer goes dormant and re-entrains only when winter convection or the circulation lifts it. Two features close the edge cases the earlier version missed: (i) bathymetry from GLORYS — where the seafloor is shallower than the winter mixed layer (shelf seas), the column ventilates fully and nothing strands; (ii) Ekman pumping — the actual permanent-subduction driver in subtropical gyres. The model is a consistency check and coastal/enclosed extension, not a new climate simulation; the atlas remains authoritative for the open ocean.

Five-year cashed fraction versus the atlas at sites spanning the regimes (800 parcels each):

Site Regime Tracer f_kin (5 yr) Atlas f_kin Note
North Sea shelf sea 0.90 0.83 bathymetry fix (seafloor < winter MLD → no stranding)
Halifax temperate coastal 0.67 0.62 Planetary site
Salish Sea fjord/estuary 0.83 0.80
Iceland subpolar, deep MLD 0.50 0.47
Patagonia (Puerto Montt) high-residence coastal 0.93 0.70–0.79 high (deep-fjord retention)
Hawaiʻi (Kona) subtropical gyre 0.31 0.59 under-predicts — decadal re-emergence not captured in a 5-yr offline periodic-year run

The circulation cross-check reproduces the atlas ordering and values across the temperate, coastal, subpolar and shelf regimes, and — unlike the emulator — uses fully independent circulation data, so it is a genuine (not circular) check on the open-ocean numbers. The one documented miss is the subtropical gyre (Hawaiʻi), where realized efficiency accrues over a decade-plus as subducted water slowly re-ventilates; a 5-year offline run under-counts it, and we defer to the atlas there. Within-EEZ maps built from the same model (*_map3) show the internal spatial gradient of realized removal for the eight most-invested national waters; they are consistent with the point sites (e.g. NZ 0.84, Chile coastal 0.86 on physical residence, Japan 0.50) but are coarse (1.5° release grid) and measure physical residence only, not the carbonate-outgassing penalty the atlas folds in (so, e.g., the Humboldt outgassing signal is an atlas/chemistry effect, not a residence effect).

A.7 Investment-grade site metrics (offline-model extensions). The mean cashed fraction is one number; investment decisions turn on risk, capacity, verifiability and timing. Four further metrics, all from the same GLORYS/CMEMS/PyCO2SYS pipeline, resolve those axes at the site level (Figs. 6–9).

(i) Carbonate ceiling and safe-dose envelope (PyCO2SYS, per site). The attainable efficiency ceiling η_max = dDIC/dTAlk at fixed atmospheric pCO₂ falls from ~0.88–0.89 in cold water (Halifax, Iceland, Black Sea) to ~0.81–0.82 in the warm subtropics (Kona, Singapore); true realized yield is residence-cashed × η_max. The safe instantaneous alkalinity dose before the aragonite saturation state passes the runaway-precipitation threshold (Ω_arag ≈ 5, which reverses removal) is ~290–310 µmol kg⁻¹ in cold water but only 120–160 in the warm subtropics, because the warm baseline Ω_arag (3.3–3.7) already sits close to runaway. Warm-water OAE therefore carries a much lower per-deployment capacity ceiling — a direct constraint on project scale and capital intensity that the efficiency field alone does not reveal.

(ii) Delivery-risk (interannual variance). Running the tracer on each forcing year 2011–2020 (monthly GLORYS) gives the year-to-year spread of realized removal — the delivery risk a buyer underwrites. The coefficient of variation ranges from 2.7% (Patagonia — near-constant delivery) and 8–10% (Black Sea, Halifax, Duck NC) to ~20–22% (Gulf of Maine, Singapore, Iceland, Kona). Monthly-mean currents lose the eddy field and bias the absolute level low relative to the daily/atlas-matched values, so we report the spread (CV, P10–P90), not the level. Two sites (North Sea, Black Sea) required an enlarged model domain: their default boxes were narrower than the water body itself, so parcels were deleted at the box edge while still in the sea; on the corrected domains they resolve to 0.70 (CV 20%) and 0.90 (CV 8%).

(iii) MRV plume footprint → site-level issuance. Tracking the real dispersing surface plume (detectable pCO₂-anomaly window × spatial containment) yields a verifiability score and an implied issuance probability per site rather than by archetype. Verifiability is low everywhere (0.18–0.25 → implied issuance 4–5%), marginally best in contained settings (Karsto fjord, 0.25). This reproduces the paper's central result — verification, not physics or cost, is the binding near-term gate — now at map resolution. The scores are a relative ranking; the short detectable windows are conservative.

(iv) Deployment timing. Sweeping the release month shows real operational alpha at some sites and none at others: Karsto gains 26 points of realized removal by dosing in April rather than October, and Kona 13 points by dosing in January, while deep-mixing Halifax is flat (~1 point). The rule is to dose into the deepening or deep winter mixed layer, not a shallow summer lid that subducts the anomaly.

These metrics are offline-model extensions and inherit its limits (monthly-forcing bias on absolute levels; regional retention; a reduced-form MRV signal); they are decision-support rankings, not bankable guarantees, and the atlas remains authoritative for absolute open-ocean efficiency.

Appendix B — Techno-economic priors (per archetype)

Ranges are literature-anchored 10th–90th-percentile priors, at-scale (see REFERENCES). Cost = US$/nominal-tonne gross.

Archetype cost_gross ($/t) LCA penalty λ MRV survival ν yield physics-sensitive
Mineral OAE 30–165 0.03–0.12 0.60–0.85 0.80 yes (HIGH)
Electrochemical OAE 60–200 0.04–0.15 0.78–0.90 0.80 yes (HIGH)
Direct ocean capture / DIC stripping 100–400 0.08–0.30 0.88–0.97 1.00 no (exempt)
Marine biomass sinking 400–3000 0.15–0.50 0.30–0.60 0.55 yes (HIGH)
Terrestrial biomass burial (control) 14–120 0.02–0.08 0.80–0.95 1.00 no (exempt)
Iron fertilization 100–2000 0.05–0.15 0.20–0.45 0.50 yes (EXTREME)

Key anchors: Renforth & Henderson 2017; Fuss 2018; Strefler 2018; Foteinis 2023 (coastal-OAE LCA); DeAngelo 2023 and Coleman 2022 (kelp cost ∝ 1/removal-fraction); Ward 2025 (iron fertilization US$25–53,000/t across efficiency terms); Isometric 14.35% uncertainty deduction on Planetary.

Pathway efficiency priors (fixing M2; NOT the OAE atlas): OAE uses the atlas f_kin directly (already includes the ~0.8 carbonate ceiling — no separate yield term, fixing M1). Marine biomass sinking: realized atmospheric-removal efficiency central ~25%, 10–90 range 5–40% (Bach 2021; DeAngelo 2023; Gao & Taylor 2024; qualitative point Hurd 2024). Iron fertilization: ~2% durably sequestered, 0.5–5% (Ward 2025; NASEM 2022). Priors sampled lognormally.

Near-term binary issuance probability (from the recent record; Fig. 4): mineral OAE 5–15%, electrochemical OAE 3–12%, DOC 1–5%, marine biomass <2%, iron fertilization <2%, terrestrial burial 5–25%. Basis: only Planetary has ever had mCDR credits issued; ~0.3% of ~578,000 t contracted issued as of 2025–26; MRV can exceed 50% of project cost; issuance lifecycle 3–5 yr. Cost↔LCA priors sampled with correlation ρ≈0.5 (energy-intensive → both higher).

Appendix B.1 — Lifecycle-analysis basis for the λ_LCA penalty

λ_LCA is the fraction of gross removal offset by the lifecycle emissions of building, powering, and operating a method (energy, materials, transport, process emissions). It enters the investability identity as the (1 − λ_LCA) term and is sampled jointly with cost (ρ ≈ 0.5: energy-intensive methods are both costlier and more emitting). Values are grid- and route-dependent; we use at-scale, decarbonizing-grid priors and widen the bands to span grid carbon intensity. Absent primary plant data, energy figures are route-level envelopes (an explicit uncertainty caveat), which is why the λ bands are wide.

Technology Energy intensity (kWh/tCO₂) Dominant LCA driver λ_LCA (10–90) Key source(s)
Mineral OAE (olivine) 224–748 (grinding-dominated) rock grinding + transport; grain size sets it 0.03–0.12 Foteinis 2023; Strefler 2018
Electrochemical OAE (BPED) 650–1850 electricity for bipolar-membrane electrodialysis; grid CO₂ 0.04–0.15 (Isometric measured 5.27% on Planetary) Eisaman 2012; Isometric deduction
Direct ocean capture / DIC stripping 380 (with H₂ credit) to >2500 (Equatic ~1.9 MWh/t without H₂) electrolysis energy; H₂ co-product credit swings it 0.08–0.30 Eisaman 2018; Equatic disclosures
Marine biomass sinking (macroalgae) cultivation + harvest + vessel transport + sinking vessel fuel and cultivation; plus an air–sea re-equilibration loss counted in efficiency, not λ 0.15–0.50 Coleman 2022; Bach 2021; Hurd 2024
Iron fertilization low (iron dosing is cheap; ship time dominates) ship time; the binding drag is efficiency (~2%), not λ 0.05–0.15 Ward 2025; Smetacek 2012
Terrestrial biomass burial (control) low harvest + burial logistics; preservation-limited 0.02–0.08 Zeng 2022, 2024

Two points make the LCA appendix consistent with the efficiency and investability claims. First, for the two biological methods the binding drag on realized removal is efficiency (biomass central ~25%, iron ~2%; Appendix B), not λ_LCA, so their uninvestability is an efficiency-and-cost result that the LCA term only sharpens. Second, the electrochemical-OAE lifecycle is the best-measured case: Isometric's total 14.35% deduction on Planetary decomposes into interannual 8.90% + air–sea flux 6.51% + LCA 5.27% + a 2% buffer, so the λ_LCA prior for that archetype is anchored to a registry-grade measurement rather than a model. These priors feed every net-cost and breakeven figure in Appendix B, D and F.

Appendix C — Water-body taxonomy

Water body Coupling Physics-sensitive Atlas-resolved Filter difference vs open ocean Representative players
Open ocean coupled + storage mixed yes baseline; τ_eq months→1 yr Ebb, Planetary, Captura, Equatic, Gigablue, Running Tide (defunct)
Marginal/semi-enclosed seas coupled + storage yes no restricted exchange, stratified lid, low-alk Baltic; storage debated under Helsinki Conv. Rewind (Black Sea, storage), CaspianCDR, CDRmare
Estuaries/coastal/fjords coupled yes no high variability, freshwater stratification, tidal gas transfer Vesta, Ebb, Planetary (Halifax)
Freshwater lakes / Great Lakes coupled yes no low buffering → fast but tiny capacity none operational; Vesta prospective
Rivers coupled (equilibrates downstream) yes + in-river loss no short residence; 16–27% loss to in-river precip/outgassing (UK study) CarbonRun (verified), UNDO, Eion
Wastewater / effluent coupled, near-field measured low no engineered, measured; Isometric WAE protocol CREW Carbon (verified), UMCES
Desal brine coupled low–med no engineered intake/outfall Equatic, Ebb
Groundwater / mine tailings / pit lakes storage (mineralization) or land→aquifer mostly exempt no solid mineralization or slow flow Arca, Travertine, Exterra, Aquarry, PNNL Wallula

Appendix D — Deployment overlay, corrected (conditional on verification, plus issuance gate)

atlas f_kin = OAE only (n/a for pathway methods, which use their own efficiency, fixing M2). P(clears|MRV) = probability net cost < price conditional on being certified. issuance = near-term binary probability of certification. P(paid) uncond ≈ P(clears|MRV @350) × issuance-midpoint.

Company Method atlas f_kin (5yr) P(clears@200 | MRV) P(clears@350 | MRV) issuance near-term P(paid@350) uncond
Ebb Carbon Electrochemical OAE 0.80 0.71 0.96 3–12% 0.072
Planetary Electrochemical OAE 0.62 0.51 0.86 3–12% 0.064
Vesta Mineral OAE 0.59 0.73 0.92 5–15% 0.092
Captura DOC / DIC stripping 1.0 (exempt) 0.36 0.73 1–5% 0.022
Equatic DOC / DIC stripping 1.0 (exempt) 0.36 0.73 1–5% 0.022
SeaO2 DOC / DIC stripping 1.0 (exempt) 0.38 0.75 1–5% 0.022
Gigablue Iron fertilization n/a (pathway) 0.00 0.00 0–2% 0.000
Running Tide (defunct) Marine biomass sinking n/a (pathway) 0.00 0.00 0–2% 0.000
Carboniferous Terrestrial burial (control) 1.0 (exempt) 0.96 0.99 5–25% 0.149

Every pathway has a low-single-digit-percent unconditional chance of being paid near-term: verification, not physics or cost, is the binding gate.

Appendix E — National guidance: EEZ efficiency and the public-investment optimizer

(i) EEZ efficiency ranking. Mean 5-yr atlas f_kin area-weighted over each sovereign EEZ (Marine Regions polygons; ≥20 resolved atlas cells; small samples indicative). The atlas has 78,687 valid cells globally but is sparse near coasts.

Sovereign Mean f_kin (5yr) cells Investment level
Ghana 0.74 none
Canada 0.71 562 engineered
Argentina 0.70 206 none
United Kingdom 0.69 989 engineered
Norway 0.68 1070 engineered
Netherlands 0.68 40 engineered
Iceland 0.66 415 blue-carbon/assess
Brazil 0.63 520 blue-carbon/assess
United States 0.62 47 (coarse) engineered
India 0.49 133 blue-carbon/assess
Chile 0.32 311 engineered
(top, uninvested) Guyana / Barbados 0.83 20–27 none
(top, uninvested) Uruguay 0.80 32 none

(ii) Public-investment optimizer (Tier-3, Fig. 19). For each nation we allocate a fixed public budget between deploying its best-fit pathway and funding measurement, using the EEZ f_kin, the Appendix B priors and the near-term issuance model, and report the verified tonnes actually delivered per US$1M. Two robust findings hold across every nation: (a) the optimizer sends ~31% of budget to MRV rather than deployment, independent of water quality; (b) a physics-exempt baseline (terrestrial burial / direct ocean capture, ~6,800 verified t per $1M) delivers 2–5× more verified removal per dollar than ocean OAE.

Nation EEZ f_kin best-fit OAE OAE verified t/$1M exempt baseline t/$1M OAE-vs-exempt opt. MRV share investor?
Guyana (best waters) 0.83 Mineral 3,120 6,784 0.46 0.31 no
Barbados 0.83 Mineral 3,073 6,863 0.45 0.31 no
Uruguay 0.80 Mineral 2,924 6,911 0.42 0.31 no
Canada 0.71 Mineral ~2,600 ~6,800 ~0.38 0.31 yes
United Kingdom 0.69 Mineral ~2,540 ~6,800 ~0.37 0.31 yes
Norway 0.68 Mineral ~2,500 ~6,800 ~0.37 0.31 yes
United States 0.62 Mineral ~2,290 ~6,800 ~0.34 0.31 yes
India 0.49 Mineral 1,805 6,786 0.27 0.31 yes
Chile 0.32 Mineral 1,204 6,776 0.18 0.31 yes

(iii) Japan and New Zealand — the atlas blind spot. The two are among the most active national investors, yet the atlas returns zero resolved cells in their EEZs (its ~690 CESM injection regions do not cover the western-Pacific coasts). This is itself a finding — the authoritative open-ocean atlas cannot advise two major programs — and it is the exact gap our offline GLORYS12 tracer fills. Within-EEZ physical retention from the tracer national maps is ~0.50 for Japan and ~0.84 for New Zealand (residence-based, not directly comparable to the atlas f_kin, and NZ carries a live social-license constraint after the Oceaneos iron-fertilization rejection). Read with the optimizer, the guidance is the same everywhere: fund measurement and the physics-exempt baseline first, and do not subsidize ocean-OAE deployment in waters that cannot deliver.

Appendix F — Global investable-area, CORRECTED (% of open ocean clearing breakeven, 5-yr, conditional on verification)

Median over correlated cost/LCA Monte-Carlo priors; 10–90 bands are wide (shown in Fig. 3). The old (buggy) table double-counted the ~0.8 chemistry ceiling and biased these pessimistically; corrected values below.

Method (median %) $100 $150 $200 $250 $300 $350 $500
Mineral OAE 6 93 99 100 100 100 100
Electrochemical OAE 0 4 78 97 99 99.6 100
Marine biomass sinking 0 0 0 0 0 0 0
Iron fertilization 0 0 0 0 0 0 0

Bands (10–90) span ~0–100% at intermediate prices — investability is dominated by cost/LCA uncertainty, not physics. Multi-horizon (1/5/10/15-yr): OAE efficiency rises with horizon as subducted alkalinity re-emerges, so 5-yr is conservative for slow sites. Biomass and iron are 0% because pathway efficiency (~25%, ~2%) and gross cost overwhelm siting. DOC and terrestrial burial are physics-exempt (price-limited, location-independent). All figures here are CONDITIONAL on verification; the near-term issuance gate (Fig. 4) multiplies them down to low-single-digit unconditional probabilities.

Appendix G — Interactive screener

A Streamlit due-diligence tool (method + latitude/longitude → P(investable), physics breakeven, net-cost-vs-efficiency curve) is deployed on Cloud Run, drawing on the atlas lookup and the Appendix B priors. It lets any new deal be triaged against the filter.

Appendix H — Adversarial accuracy check

Twelve load-bearing external claims were independently fact-checked with grounded search (skeptical by default). Outcomes: 4 CONFIRMED (US strategy ignores equilibration; river 16–27% loss; Isometric OAE/WAE/RAE protocols; Zhou 2024 = the OAE atlas), 8 PARTIALLY-CONFIRMED with corrections applied to the manuscript. Corrections of record: Planetary's 625.6 t was bought by Stripe/Shopify/British Airways (Frontier holds a separate 115,211 t offtake); the New Zealand "dumping" rejection was Oceaneos (iron fertilization, 2023), not Gigablue; CREW's $32.1 M covers a 71,878 t offtake, not the 104.4 t first batch; the delivered/contracted ratio is a fraction of a percent (~0.3% issued in one 2025 analysis); the Baltic storage "ban" is a contested interpretation of the Helsinki Convention; the Humboldt is outgassing-prone rather than an unconditional net source. Full log in ADVERSARIAL_CHECK.md.

Appendix I — Physical controls, observational validation, and the investment synthesis

This appendix reports a set of extensions built on the same GLORYS12/CMEMS/PyCO2SYS pipeline. They are decision-support diagnostics and physical characterizations, not bankable guarantees; we state honestly which are strong and which are weak. All code and fields are archived (Data and code availability).

I.1 Non-ocean water bodies (Fig. 10). The open-ocean atlas (Zhou et al. 2024) does not resolve marginal/enclosed seas, the Great Lakes, rivers, wastewater or brine — these lie at or below its ~100 km ocean-model resolution or outside its domain entirely. We compute a first-order equilibration efficiency for them from τ_eq = (h/k)(R_ion/R_f) (Jones et al. 2014), with wind-driven gas transfer for standing waters and turbulence-driven transfer (~10× larger; Raymond et al. 2012) for rivers, and buffering recomputed at each body's own salinity via PyCO2SYS — never reusing the seawater Revelle factor for freshwater. The result is a taxonomy insight the atlas cannot give: the binding constraint changes character by class. Enclosed and marginal seas (Baltic, Mediterranean, Black Sea) have surface renewal times of decades, so they equilibrate fully and their limit is instead whether the basin is a net sink and whether the added alkalinity is durable (the Caspian is a net CO₂ source with a non-marine carbonate system — a cautionary case, not a candidate). Rivers and engineered outfalls are the opposite: fast turbulence, ~1 m depth and hours-to-days residence make them equilibration- and re-evasion-limited (modeled efficiency ~0.26 for a wastewater outfall, ~0.00 for desal brine). Freshwater buffering is body-specific and must be computed as such: Lake Superior (soft, DIC ~793 µmol kg⁻¹) and Lake Michigan (hard, DIC ~2,065, near CaCO₃ saturation and precipitation-prone) are as chemically different from one another as either is from seawater.

I.2 The crediting-versus-realization gap (Fig. 11). Using registry-verified issuance (Isometric, mid-2026) against contracted-offtake totals, we quantify how much marine-CDR removal has been contracted, credited, and physically realized once the equilibration lag is applied. Of roughly 578,000 t contracted industry-wide, about 5,000 t have been issued as verified credits (≈0.9%), essentially all Planetary; applying the realized-fraction-at-issuance (Planetary's own first batch was ">50% of expected uptake", with full removal accruing over 10–15 years per an independent review) leaves roughly 2,800 t — about 0.5% of contracted volume — physically realized by the atmosphere to date. The ocean has, so far, cashed on the order of one in two hundred contracted tonnes. This is the manuscript's central claim rendered in registry data rather than model output.

I.3 Interannual variability and its (weak) predictability (Fig. 12). To ask whether realized efficiency is stable year to year, we advected seasonal cohorts through the actual daily 1993–2020 GLORYS12 record at each site (no climatological cycling), producing an efficiency timeseries, and lag-correlated its deseasonalized anomaly against ENSO (ONI), NAO, PDO and AAO indices. Two findings, one positive and one negative. Positive: interannual variability is real and, to our knowledge, previously unquantified for mCDR — the coefficient of variation of realized efficiency is ~10–20% per site. Negative, and we present it as such: that variability is only weakly predictable from the major climate modes. The strongest links are a modest North Atlantic Oscillation signal at coastal North Atlantic sites (Salish r=+0.31, Duck NC r=−0.30, Halifax r=−0.25); apparent stronger correlations in shorter records did not survive the full 28-year series (a Norwegian-fjord NAO correlation of 0.56 at n=16 fell to −0.2 at n=100). The honest conclusion is that interannual delivery variability is a first-order, largely irreducible risk that must be priced, not a signal that can be forecast away from climate indices.

I.4 Sea speed, flushing, and the decorrelation of the controls (Figs. 13–14). The Lagrangian survival fraction is itself a measure of how fast a site's surface water flushes. Site flushing times span ~0.9 yr (North Sea) to ~159 yr (Patagonian fjords) — and, importantly, this is not set by current speed: Duck NC has the fastest surface current (0.37 m s⁻¹, the Gulf Stream) yet only ~2.4-yr flushing because that flow recirculates, whereas the slower North Sea flushes fastest because its residual circulation nets out of the basin. When flushing time falls below the equilibration time (North Sea, Gulf of Maine), the anomaly leaves the region before the ocean cashes it or anyone can verify it locally — which is precisely why a through-flow shelf like the North Sea cannot be resolved by any regional offline model (its parcels flush completely even in a 12°-wide box) and would be an MRV nightmare. We extend this to a global map (Fig. 14) of surface current speed, equilibration time τ_eq (global median 0.51 yr, matching Jones et al. 2014), and a native-resolution (1/12°, eddy-resolving) Lagrangian flushing field computed with one consistent definition at every cell (residence within a fixed ~150 km footprint over two years). The per-site times above (~0.9–159 yr) use bespoke, differently-sized site boxes and are not comparable across sites; the global field uses a single scale so the map is internally consistent. Two results follow. First, at the deployment footprint surface flushing is near-uniformly fast: about 89% of the ocean flushes a treated patch within ~0.3 yr, and the median fraction of a patch still co-located after two years is ~0.001, so local verification is hard almost everywhere — surface residence is a near-universal MRV constraint, not a site-discriminating variable. Second, the three controls remain spatially decorrelated (pairwise |r| ≤ 0.15; speed–flushing r = −0.06, τ_eq–flushing r = 0.00, speed–τ_eq r = −0.15), now confirmed on the corrected eddy-resolving field. (An earlier version of this field used monthly-climatology currents and was degenerate; the native-resolution recomputation reported here, from daily 1/12° currents, supersedes it, and the decorrelation conclusion is robust to the fix.) The methodological upshot, and the paper's unifying principle: no single ocean property — not efficiency, not cost, not current speed — identifies where CDR works; the controls are independent and must be evaluated jointly, and surface residence at the deployment scale is a near-universal verification problem.

I.5 Observational validation against surface drifters (Fig. 15). The surface currents driving every Lagrangian result are validated against the NOAA Global Drifter Program gridded climatology (Laurindo, Mariano & Lumpkin 2017, 0.25°): modeled mean surface speed correlates with observed drifter speed at r = 0.78 globally. The derived flushing field is a deterministic function of these validated currents; it does not track eddy kinetic energy (r ≈ 0.02), consistent with our flushing being set by advective flow geometry rather than eddy stirring.

I.6 Composite verifiable-realization potential (Fig. 16). We fuse the physical controls into one global field, V = [τ_flush/(τ_flush + τ_eq)] · η_max — the fraction of an anomaly that equilibrates locally before it flushes, times the carbonate capacity ceiling η_max (Appendix A.7). V maps where the ocean cashes the check where it can be seen; where V is low the removal, if any, happens downstream and unattributable. Real deployments overlaid on V show most sit in intermediate-to-favorable water by this physical index (the industry's siting problem is more about verifiability and capacity than gross equilibration). On the corrected native-resolution flushing field the global median V ≈ 0.34 (retained-before-flush median ≈ 0.37), essentially unchanged from the earlier estimate but now resting on a trustworthy, eddy-resolving field rather than the superseded monthly-climatology one.

I.7 Portfolio diversification and the investment synthesis (Figs. 17–18). Because sites' interannual delivery variability is only partially correlated (I.3), a diversified multi-site deployment is materially less risky than concentrating in the single best site: a minimum-variance / maximum-return-per-risk portfolio across our sites cuts delivery-variance by ~73% at similar expected verified removal (risk 0.024 vs 0.089 for the single-best site). Finally, an integrated 0–100 investability score fusing realization, verifiability, capacity, delivery reliability and retention (Fig. 18) places ~13% of announced contracted volume in below-median-score waters — real capital misallocation, though a more modest figure than the crediting gap of I.2, which remains the sector's starkest number.

Honest ledger. Strong, load-bearing results: the crediting-realization gap (I.2), the decorrelation of physical controls (I.4), the drifter-validated currents (I.5, r=0.78), the carbonate-capacity ceiling (A.7), and the flushing/retention diagnostic (I.4). Deliberately demoted as weak or negative: the interannual climate-predictability (I.3, r≈0.3), the flushing–EKE relationship (I.5, r≈0.02), and the 13% misallocation (I.7). The offline model cannot resolve through-flow shelves; the atlas remains authoritative for absolute open-ocean efficiency. Primary added references: Jones et al. 2014 (GBC); Moras, Bach & Riebesell 2022 (Biogeosciences, the runaway-precipitation ceiling); Raymond et al. 2012 (river gas transfer); Laurindo, Mariano & Lumpkin 2017 (Deep-Sea Res. I, drifter climatology).

Appendix J — Private-investor playbook (real-options view)

Because near-term expected value is set by verification, not siting, the private investor's problem is an options problem. We compute a diversified expected return per pathway under an explicit binary issuance gate, and a real-options commit-vs-wait schedule as issuance matures on a logistic path (12% discount rate). Relative-return units; US$350 per tonne unless noted.

(i) Expected value now, and if measurement matures (Fig. 20).

Pathway issuance now EV now @$350 EV if MRV matures breakeven issuance breakeven price @60% iss
Terrestrial burial (control) 0.15 +0.77 +5.98 0.09 $59
Mineral OAE 0.10 −0.65 +1.07 0.29 $177
Electrochemical OAE 0.075 −0.84 +0.27 0.48 $275
Direct ocean capture / DOC 0.03 −0.95 +0.01 0.59 $353
Marine biomass sinking 0.011 −1.00 −0.96 n/a n/a
Iron fertilization 0.011 −1.00 −0.98 n/a n/a

(ii) Commit-vs-wait. Only physics-exempt terrestrial burial is positive-EV today (commit now). Mineral OAE turns positive around year 4 and peaks around year 8 — wait ~4 years for issuance to mature (or for the price to reach ~$177). Electrochemical OAE is a ~7-year wait. DOC is not investable within ten years at $350. Biomass sinking and iron fertilization never reach positive value even with mature measurement, because cost and realized-removal efficiency dominate.

(iii) The playbook. (1) Triage by measurement path. Fund near-field/engineered/mass-measured methods (DOC, wastewater alkalinity) now; treat far-field OAE as a dated option; avoid biomass and iron at any price. (2) Fund MRV infrastructure, not deployment. Marine CDR today is a negative-EV option whose value is dominated by issuance probability; the highest-return near-term capital is the measurement science and infrastructure that moves that probability. (3) Diversify across decorrelated delivery risk. A multi-site portfolio cuts delivery variance ~73% at equal expected removal (Appendix I.7), because sites' interannual efficiency is only partly correlated and not forecastable from climate modes (Appendix I.3). (4) Stage against issuance maturity. Hold options while issuance sits below ~15%; commit as each pathway clears its breakeven. The through-line: physics and cost decide where a method can work; verification decides whether — and when — anyone is paid, and it is the variable capital should be buying down. Model in investor_model.py (Tier-2) and tier3_national.py (Tier-3).


References

Compiled from literature/01-07. DOIs verified against source syntheses; items marked [verify] need a final full-text confirmation before submission.

Air-sea equilibration physics

  1. Jones, D. C., Ito, T., Takano, Y. & Hsu, W.-C. (2014). Spatial and seasonal variability of the air-sea equilibration timescale of carbon dioxide. Global Biogeochemical Cycles 28(11), 1163-1178. doi:10.1002/2014GB004813
  2. Wanninkhof, R. (1992). Relationship between wind speed and gas exchange over the ocean. JGR Oceans 97(C5), 7373-7382. doi:10.1029/92JC00188
  3. Wanninkhof, R. (2014). Relationship between wind speed and gas exchange over the ocean revisited. Limnology & Oceanography: Methods 12, 351-362. doi:10.4319/lom.2014.12.351
  4. Egleston, E. S., Sabine, C. L. & Morel, F. M. M. (2010). Revelle revisited: Buffer factors that quantify the response of ocean chemistry to changes in DIC and alkalinity. Global Biogeochemical Cycles 24, GB1002. doi:10.1029/2008GB003407
  5. Sabine, C. L. et al. (2004). The oceanic sink for anthropogenic CO2. Science 305, 367-371. doi:10.1126/science.1097403
  6. Jiang, L.-Q. et al. (2019). Surface ocean pH and buffer capacity. Scientific Reports 9, 18624. doi:10.1038/s41598-019-55039-4
  7. Naegler, T. (2009). Reconciliation of excess 14C-constrained global CO2 piston velocity estimates. Tellus B 61, 372-384. doi:10.1111/j.1600-0889.2008.00408.x

Marine CDR efficiency, equilibration limits, metrics

  1. He, J. & Tyka, M. D. (2023). Limits and CO2 equilibration of near-coast alkalinity enhancement. Biogeosciences 20, 27-43. doi:10.5194/bg-20-27-2023
  2. Zhou, M., Tyka, M. D., Ho, D. T. et al. (2024). Mapping the global variation in the efficiency of ocean alkalinity enhancement for carbon dioxide removal. Nature Climate Change 15, 59-65. doi:10.1038/s41558-024-02179-9 [global OAE efficiency atlas used here; data: source.coop/cworthy/oae-efficiency-atlas]
  3. Zhou, M. et al. (2025). Efficiency metrics for ocean alkalinity enhancement under responsive and prescribed atmospheric pCO2. Biogeosciences 22, 341-353. doi:10.5194/bg-22-341-2025
  4. Yamamoto, R., DeVries, T. & Siegel, D. A. (2024). Metrics for quantifying the efficiency of atmospheric CO2 reduction by marine carbon dioxide removal. Environmental Research Letters 19(10), 104053. doi:10.1088/1748-9326/ad7477
  5. Nowicki, M., DeVries, T. & Siegel, D. A. (2024). The influence of air-sea CO2 disequilibrium on carbon sequestration by the ocean's biological pump. Global Biogeochemical Cycles 38, e2023GB007880. doi:10.1029/2023GB007880
  6. Siegel, D. A., DeVries, T., Doney, S. C. & Bell, T. (2021). Assessing the sequestration time scales of some ocean-based CDR strategies. Environmental Research Letters 16, 104003. doi:10.1088/1748-9326/ac0be0
  7. Renforth, P. & Henderson, G. (2017). Assessing ocean alkalinity for carbon sequestration. Reviews of Geophysics 55, 636-674. doi:10.1002/2016RG000533
  8. Bach, L. T. (2024). The additionality problem of ocean alkalinity enhancement. Biogeosciences 21, 261-277. doi:10.5194/bg-21-261-2024
  9. Hurd, C. L. et al. (2024). Air-sea carbon dioxide equilibrium: will it be possible to use seaweeds for carbon removal offsets? Journal of Phycology 60, 4-14. doi:10.1111/jpy.13405
  10. Oschlies, A. et al. (2025). Perspectives and challenges of marine carbon dioxide removal. Frontiers in Climate 6, 1506181. doi:10.3389/fclim.2024.1506181

Reviews, strategy, MRV

  1. National Academies of Sciences, Engineering, and Medicine (2022). A Research Strategy for Ocean-based Carbon Dioxide Removal and Sequestration. doi:10.17226/26278
  2. Oschlies, A. et al. (eds.) (2023). Guide to Best Practices in Ocean Alkalinity Enhancement Research. State of the Planet 2-oae2023. doi:10.5194/sp-2-oae2023
  3. GESAMP (2019). High Level Review of a Wide Range of Proposed Marine Geoengineering Techniques. Reports & Studies No. 98, Working Group 41.
  4. Fennel, K. et al. (2026). The verification challenge of marine carbon dioxide removal. Annual Review of Marine Science 18. doi:10.1146/annurev-marine-032123-025717
  5. Bach, L. T., Williamson, P., House, J. I. & Boyd, P. W. (2025). Natural carbon uptake by ocean biology will not deliver credible carbon credits. Nature Reviews Earth & Environment 6, 767-768. doi:10.1038/s43017-025-00741-3 [verified]
  6. Lee, K., Subhas, A. V., Kim, T.-W. & Lee, K. (2026). Ocean carbon dioxide removal and storage. Chemical Reviews 126. doi:10.1021/acs.chemrev.5c00433
  7. IPCC (2022). AR6 WG3, Chapter 12 (CDR cost/potential, Table 12.6).

Techno-economics & lifecycle

  1. Fuss, S. et al. (2018). Negative emissions - Part 2: Costs, potentials and side effects. Environmental Research Letters 13, 063002. doi:10.1088/1748-9326/aabf9f
  2. Strefler, J. et al. (2018). Potential and costs of carbon dioxide removal by enhanced weathering of rocks. Environmental Research Letters 13, 034010. doi:10.1088/1748-9326/aaa9c4
  3. Foteinis, S. et al. (2023). Life cycle assessment of coastal enhanced weathering for carbon dioxide removal. Environmental Science & Technology 57, 6169-6178. doi:10.1021/acs.est.2c08633
  4. DeAngelo, J. et al. (2023). Economic and biophysical limits to seaweed farming for climate change mitigation. Nature Plants 9, 45-57. doi:10.1038/s41477-022-01305-9
  5. Coleman, S. et al. (2022). Sinking macroalgae for carbon dioxide removal: cost and additionality. Frontiers in Marine Science 9, 966304. doi:10.3389/fmars.2022.966304
  6. Bach, L. T. et al. (2021). Testing the climate intervention potential of ocean afforestation. Nature Communications 12, 2556. doi:10.1038/s41467-021-22837-2
  7. Ward, C. et al. (2025). A techno-economic assessment of ocean iron fertilization. Frontiers in Climate 7, 1509367. doi:10.3389/fclim.2025.1509367
  8. Eisaman, M. D. et al. (2012). CO2 extraction from seawater using bipolar membrane electrodialysis. Energy & Environmental Science 5, 7346-7352. doi:10.1039/C2EE03393C
  9. Zeng, N. et al. (2022). Wood vault: remove atmospheric CO2 with trees. Carbon Balance and Management 17, 12. doi:10.1186/s13021-022-00202-0
  10. Zeng, N., Zhao, X., Poisson, G. et al. (2024). 3775-year-old wood burial supports "wood vaulting" as a durable carbon removal method. Science 385(6716), 1454-1459. doi:10.1126/science.adm8133 [verified]
  11. Hangx, S. J. T. & Spiers, C. J. (2009). Coastal spreading of olivine to control atmospheric CO2. International Journal of Greenhouse Gas Control 3, 757-767. doi:10.1016/j.ijggc.2009.07.001
  12. Smetacek, V. et al. (2012). Deep carbon export from a Southern Ocean iron-fertilized diatom bloom. Nature 487, 313-319. doi:10.1038/nature11229

Upwelling

  1. Oschlies, A. et al. (2010). Climate engineering by artificial ocean upwelling. Geophysical Research Letters 37, L04701. doi:10.1029/2009GL041961
  2. Jürchott, M., Rodgers, K. B., Romanou, A., Oschlies, A. et al. (2023). Artificial Upwelling — A Refined Narrative. Geophysical Research Letters 50(4). doi:10.1029/2022GL101870 [verified]

Registry protocols & verified issuances (primary/grey)

  1. Isometric (2024-2026). Ocean Alkalinity Enhancement Protocol; Wastewater Alkalinity Enhancement Protocol v1.2; River Alkalinity Enhancement Protocol; Air-Sea CO2 Uptake Module. registry.isometric.com
  2. Carbon to Sea Initiative (2025). An independent MRV review of the first OAE credits. carbontosea.org (2025-11-25)
  3. Frontier Climate / [C]Worthy (2024). Guidance for evaluating abiotic marine CDR MRV. frontierclimate.com

Data sources

  1. [C]Worthy / CarbonPlan. Global OAE Efficiency Atlas. source.coop/cworthy/oae-efficiency-atlas (from ref. 9).
  2. Flanders Marine Institute (VLIZ). Maritime Boundaries / Exclusive Economic Zones (EEZ) v-series. marineregions.org
  3. Humphreys, M. P. et al. (2022). PyCO2SYS v1.8. Geoscientific Model Development 15, 15-43. doi:10.5194/gmd-15-15-2022

Newly verified / added (reviewer-fix pass)

  1. Wang, H., Pilcher, D. J., Kearney, K. A. et al. (2023). Simulated impact of ocean alkalinity enhancement on atmospheric CO2 removal in the Bering Sea. Earth's Future 11, e2022EF002816. [regional OAE efficiency >96% in cold carbon-rich water]
  2. Burt, D. J., Fröb, F. & Ilyina, T. (2021). The sensitivity of the marine carbon cycle to regional ocean alkalinity enhancement. Geophysical Research Letters 48, e2021GL094424. [Southern Ocean regional OAE efficiency]
  3. Ho, D. T., Bopp, L., Palter, J. B., Long, M. C., Boyd, P. W., Neukermans, G. & Bach, L. T. (2023). Monitoring, reporting, and verification for ocean alkalinity enhancement. State of the Planet 2-oae2023, 12. doi:10.5194/sp-2-oae2023-12-2023 [MRV chapter lead is Ho, not Fennel]
  4. Gao, S. & Taylor, J. R. (2024). Modeling CO2 removal via sinking of particulate organic carbon from macroalgae cultivation. Frontiers in Marine Science 11, 1331320. doi:10.3389/fmars.2024.1331320 [kelp realized-removal efficiency]

Still to confirm before submission