## Main

Reaching net-zero CO2 emissions will entail drastically reducing fossil fuel emissions and offsetting any residual emissions by removing carbon from the atmosphere (that is, negative emissions)1,2,3,4,5. Biomass-based technologies may help in both fronts by supplying carbon-neutral alternatives to fossil fuels6,7 and providing negative emissions via enhancement of natural sinks8 and/or bioenergy with carbon capture and storage9. However, numerous studies have questioned whether terrestrial biomass can provide either energy or negative emissions at the scales required in many climate mitigation scenarios, often owing to limited land and water resources10,11,12. This has driven surging interest in ocean-based carbon dioxide removal, including via cultivated macroalgae (seaweed), which would not require inputs of land or freshwater and might have environmental co-benefits (for example, see refs. 13,14,15,16,17,18,19,20,21). Seaweed products might also help to lower greenhouse gas emissions, for example by reducing methane emissions from ruminants22, and replacing fossil fuels23 and emissions-intensive agricultural products24.

Seaweed has been successfully farmed in some places for centuries, and used for food, animal feed, and in more modern times, cosmetics, medicine, fertilizer and biofuels25,26,27,28. Production of seaweed for food increased 6% per year in 2000–201829 and harvest totalled ~1 million tons of carbon worldwide in 201829. In comparison, climate scenarios that limit warming to 1.5 ° or 2 °C generally require more than 1 gigaton of carbon (that is >3.67 GtCO2) to be removed annually from the atmosphere in the year CO2 emissions reach net-zero3. To contribute to such climate goals, seaweed farming must therefore expand tremendously, and in turn contend with large uncertainties in the productivity of different types of seaweed in different places, the net costs of farming, the magnitude of emissions avoided or carbon sequestered, and the potential for undesirable ecological impacts. Recent studies of seaweed farming have examined localized opportunities and dynamics in particular regions15,16,30, made rough estimates of the global potential13,14,31,32 and modelled the Earth system response to gigaton-scale production19. Yet the productivity, costs and potential climate benefits of such farming are spatially heterogeneous and scale-dependent, and the key sensitivities and trade-offs important to investors and decision-makers have not been comprehensively evaluated. Here we use coupled biophysical and technoeconomic models to systematically assess the economic costs and potential climate benefits of seaweed farming, testing their sensitivity across large ranges in individual variables and comparing different product pathways.

Details of our analytic approach are described in Methods. In summary, we use outputs from a newly developed biophysical model (G-MACMODS)33,34 to estimate potential harvest of four different seaweed types (tropical red, tropical brown, temperate red and temperate brown; Supplementary Fig. 1) at a resolution of 1/12° (~9 km at the equator) globally. Nutrients are a key constraint on seaweed growth. G-MACMODS assumes that nitrogen is the limiting nutrient and we model two idealized scenarios: an ‘ambient’ nutrient scenario that computes growth on the basis of observed climatological surface nitrate concentrations, and a ‘limited nutrient’ scenario that computes growth rate on the basis of ambient nitrate concentrations but limits algal biomass increases so as not to exceed the magnitude of local natural (upward) nitrate supply as estimated by a high-resolution simulation of the Community Earth System Model35. On the basis of the simulated yields, we then calculate spatially explicit costs per ton of seaweed harvested and either costs per ton of greenhouse gas (GHG) emissions avoided (when used as food, feed or for biofuels) or costs per ton of carbon removed from the atmosphere as a carbon dioxide removal (CDR) strategy. Given the large uncertainty in technoeconomic parameters, we perform a Monte Carlo simulation with n = 5,000 for each nutrient scenario, assuming uniform distributions of each variable. Technoeconomic variables include (1) farming costs (for example, capital cost, harvest costs), (2) for carbon sequestration, the fraction of sunk seaweed carbon sequestered for >100 yr in the deep sea and (3) for GHG emissions mitigation, the net cost and net emissions of seaweed transported and converted into a product (Table 1; see Supplementary Tables 1 and 2 for listings of all variables and relevant sources). We test model sensitivity to seaweed yield by sampling from a normal distribution of seaweed yield uncertainty for each Monte Carlo simulation. Additionally, because seaweed draws carbon from the surface ocean dissolved inorganic carbon pool (which does not maintain instantaneous equilibrium with the atmosphere) and because large-scale seaweed farming can reduce natural carbon uptake by phytoplankton via nutrient competition, we include a variable representing the net efficiency of seaweed growth in reducing atmospheric CO2 (‘atmospheric removal fraction’; Supplementary Table 1). Our approach is predicated on large uncertainties associated with most of the variables we analyse, not only in the future but also the present (the relatively few costs reported in the literature are location- and/or species-specific), as well as our primary goal of informing future research by identifying relative differences, sensitivities and trade-offs that are robust across our simulations.

## Results

### Seaweed production cost

The maps in Fig. 1 show the range of modelled seaweed production costs (that is, US$per ton of harvested dry weight (DW) before transport) in different regions under the ambient-nutrient scenario and assuming the most productive type of seaweed is grown in each grid cell (Supplementary Fig. 2 shows analogous costs for a limited-nutrient scenario). Minimum modelled costs (Fig. 1a,d) thus reflect high levels of seaweed growth (ambient nutrients) and very low assumed costs of farming, whereas the maximum costs in Supplementary Fig. 2c,f reflect lower levels of seaweed growth in most areas (limited nutrients) and high-end cost assumptions. Since our ability to accurately assess the role of nutrient constraints as a determinant of yield is a major driver of total uncertainty in cost, our results are thereby likely to encompass a wide range of outlooks, including substantial future reductions in farming costs related to technological breakthroughs, returns to scale and boosted productivity (for example, autonomous farms, depth cycling, artificial upwelling and offshore integrated multitrophic aquaculture36,37). Although the spread in average cost in the 1% of ocean area where costs are lowest (labels beneath each panel) ranges from$190 to $2,790 per ton of dry weight (tDW) seaweed yield, regional patterns of production costs are relatively consistent across cost simulations (Fig. 1). For example, the equatorial Pacific, Gulf of Alaska and southeastern edge of South America are consistently among the lowest cost areas to produce seaweed (yellow and green shading in Fig. 1), and there are large swaths of ocean that cannot produce seaweed for <$2,000 tDW−1 in any case (areas shaded blue in Fig. 1). These patterns reflect the combination of seaweed productivity and the associated number of harvests (Supplementary Figs. 3 and 4, respectively). Higher harvest costs can erode the cost advantage of highly productive areas: for example, despite having much lower seaweed yields per unit area, the North Pacific’s lower harvest costs lead to production costs that are often similar to those in the Equatorial Pacific (Fig. 1 and Supplementary Fig. 3). Moreover, because transportation of harvested seaweed is not included in the at-farm production costs but rather in the post-cultivation costs (Methods), some areas of open ocean far from ports have low at-farm production costs. On average, the costs of seeded line, total harvest costs and capital costs (including mooring costs) dominate total production costs, representing 56 (32–92)%, 19 (4–38)% and 17(3–33)% across seaweed types, respectively (Supplementary Fig. 5).

Finally, since global seaweed yield is reduced in simulations that limit nutrient availability to natural vertical nutrient fluxes, the production costs in the 1% of ocean area with the lowest cost are much higher ($350–$7,150 tDW−1; Supplementary Fig. 2) than in simulations in which seaweed is allowed to use all ambient nutrients. This suggests that without methods to enhance nutrient availability (for example, depth cycling, artificial upwelling, or offshore integrated multitrophic aquaculture36,37), limiting seaweed yields to maintain surface ocean nutrient levels might be cost-prohibitive except in the most optimistic technoeconomic scenarios.

### Net cost of climate benefits

The maps in Fig. 2 show net costs of different climate benefits from farmed seaweed. We choose to show costs when propagating the most optimistic assumptions (5th percentile costs) from ambient-nutrient simulations to reflect low-cost results that might be achieved with economies of scale (Supplementary Figs. 6 and 7 show results under limited nutrients and for median net costs, respectively). We define the cost to sequester carbon via sinking seaweed as the $per tCO2 removed from the atmosphere for at least 100 yr, assuming no other economic value. In contrast, costs of emissions avoided by using produced seaweed for food, feed or biofuel are given in units of$ per tCO2-eq and in each case reflect seaweed production, transportation and conversion costs, and the product’s market value as well as the CO2-equivalent GHG emissions (CH4 and N2O assuming Global Warming Potential (GWP)100) displaced by the product net of any emissions related to transportation and processing (Methods). When calculating GHG emissions avoided, we assume that products made from seaweed can directly replace conventional food (pulses, vegetables, fruits, oil crops and cereals), feed (oil crops and cereals) and fuels, thereby avoiding GHG emissions from industrial agriculture practices or CO2 emissions from fossil fuel combustion24. For example, if seaweed is used for food and replaces some amount of vegetables in a person’s diet, then the GHG emissions associated with the production of those vegetables that the seaweed replaces are counted as avoided emissions.

In the lowest-cost 1% ocean areas, the average cost is much higher per ton of carbon sequestered by sinking seaweed ($540 per tCO2) than per ton of CO2-eq emissions avoided, regardless of whether the seaweed is used for food ($20 per tCO2-eq), animal feed ($140 per tCO2-eq) or biofuel ($320 per tCO2-eq). The substantial cost difference between sequestration by sinking and emissions avoided by products is most influenced by the products’ market value and the potential to avoid non-CO2 GHGs, despite the higher cost and emissions required to transport harvested seaweed to port.

In particular, the non-CO2 GHG emissions that could be avoided by using seaweed for either food consumed by humans or feed consumed by animals effectively multiply the potential climate benefits of a ton of seaweed carbon, whereas the climate benefits of either sinking or converting seaweed to biofuels are constrained by the carbon present in the seaweed itself. Yet carbon sequestration is nonetheless favoured in some locations given the high costs of transporting seaweed back to the nearest port (for example, areas of the equatorial Pacific that are shaded yellow and green in Fig. 2a and blue in Fig. 2c; see also Supplementary Fig. 8).

### Key sensitivities

Figure 3 shows the relative importance of all variables in generating spread in our Monte Carlo estimates of production costs and net costs of climate benefits, focusing on the lowest-cost areas (Supplementary Fig. 9 shows the same results for limited-nutrient simulations). These results emphasize which variables are most important to achieving very low costs. Low production costs are most sensitive to seaweed yields, followed by the cost of seeded line (secondary line with seaweed seedlings that is wrapped around a structural rope, or nets for some temperate red seaweeds; yellow in Fig. 3a) and capital costs (for example, boats, harvest machines, buoys, anchors and other lines; green in Fig. 3a). Together, seaweed yield and seeded line cost account for >89% of the uncertainty in production costs in the places where costs are lowest, and costs are never below $400 tDW−1 in simulations where seeded line is assumed to cost >$1 m−1.

Costs of carbon sequestered are quite sensitive to production costs (including all parameters shown in Fig. 3a), but the most important parameter aside from production costs and yield is the fraction of the seaweed carbon that corresponds to equivalent carbon removal from the atmosphere (light green in Fig. 3b). Although this fraction has generally been assumed to be 1, recent studies have shown that air–sea fluxes of CO2 may not keep pace with carbon uptake by growing seaweed and, among other mechanisms that reduce efficiency, nutrient competition from farmed seaweed may diminish natural carbon uptake and export accomplished by phytoplankton15,19. The atmospheric removal fraction accounts for >24% of the variation in sequestration costs in the places where costs are lowest, and costs are never below $400 per tCO2 sequestered unless the removal fraction is assumed to be >0.6 (Fig. 3b,e). Our estimates of cost per GHG emissions avoided are most sensitive to the assumed magnitude of CO2-equivalent emissions avoided by a seaweed product (light blue in Fig. 3c). The product-avoided emissions account for >38% of the variation in costs per emissions avoided in the places where costs are lowest, and costs are never more than$700 per tCO2-eq avoided in simulations where the product-avoided emissions are assumed to be >4.25 tCO2-eq tDW−1 seaweed (Fig. 3c,f). Yet production costs remain important, and low costs of emissions avoided (<$200 per tCO2-eq) can be achieved even when the avoided emissions are <1 tCO2-eq tDW−1 if seaweed production costs are very low (Fig. 3c,f). ### Costs and benefits of large-scale seaweed farming Figure 4 shows the cumulative potential of GHG emissions avoided or carbon sequestered in the 1% of ocean areas with the lowest costs, shaded with costs per ton on the basis of the 5th percentile of 5,000 ambient nutrient–cost simulations (that is, reflecting optimistically high seaweed yield, low farming costs and large climate benefits from replacement of agricultural products; Supplementary Figs. 10 and 11 show results for median costs and limited-nutrient scenario). No matter the scenario or percentile, in the 1% of areas with the lowest costs, the costs per ton of CO2 sequestered are always higher than the costs per ton of CO2-eq emissions avoided. In the optimistic case depicted in Fig. 4, 1 Gt of CO2-eq emissions might be avoided or 1 Gt of CO2 sequestered by farming 0.025% and 0.110% of lowest-cost ocean areas, respectively (roughly 90,000 km2 and 400,000 km2 or close to the areas of Portugal and Zimbabwe, respectively), at an average profit of$50 per tCO2-eq emissions avoided or at an average cost of $480 per tCO2 sequestered. In limited-nutrient simulations with optimistic cost assumptions (Supplementary Fig. 11a,b), the lowest-cost ocean area that might be required to reach 1 GtCO2-eq avoided emissions or 1 GtCO2 sequestered annually is 0.035% and 0.100% for avoided emissions and sequestration, respectively, or roughly 130,000 km2 and 360,000 km2, with associated costs of$30 per tCO2-eq avoided and $830 per tCO2 sequestered. Average costs at the median of Monte Carlo simulations for both nutrient scenarios rise substantially to$110–310 per tCO2-eq emissions avoided or $1,120–$2,090 per tCO2 sequestered, respectively (Supplementary Figs. 10 and 11a,b). These costs increase to $140–420 per tCO2-eq at 3 GtCO2-eq avoided and to$1,190–2,280 per tCO2 at 3 GtCO2 sequestered annually, requiring ocean areas of 0.085–0.100% and 0.285–0.410% for avoided emissions and sequestration, respectively (roughly 310,000–360,000 km2 and 1,030,000–1,480,000 km2). Moreover, climate benefits increase approximately linearly with area up to 1% of ocean area, reaching totals of >29 GtCO2-eq avoided or >9 GtCO2 sequestered annually in the ambient-nutrient simulations and >19 GtCO2-eq avoided or >8 GtCO2 sequestered annually in the limited-nutrient simulations.

Supplementary Fig. 12 shows the locations of the lowest cost areas in Fig. 4, which, for sequestration, are concentrated in the equatorial Pacific and Gulf of Alaska, and for avoided emissions products include additional areas offshore of Argentina, the Korean Peninsula and New Zealand as well as areas of the North and Norwegian Seas. Importantly, we estimate that perhaps 10–15% of lowest cost areas for sequestration and 40–45% of lowest cost areas for avoided emissions are either in highly trafficked shipping lanes or part of existing marine protected areas (Methods), which could present challenges for seaweed farming in these areas.

Despite being a small percentage of global ocean area, farming 0.025% of the global ocean area (~90,000 km2) would represent over a 30-fold increase in the area of current seaweed farming (~2,700 km2; refs. 29, 38, 39). Thus, producing seaweed in the lowest cost areas to reach 1 GtCO2-eq of emissions avoided or 1 GtCO2 sequestered by 2050 would entail increasing the area farmed by roughly 12% or 18% per year, respectively, compared with the 2000–2018 seaweed farming industrial growth rate of 6%29. Achieving the same level of climate benefits from seaweed by 2030 increases the implied expansion rate of farms to roughly 42% or 64% per year for emissions avoided or carbon sequestered, respectively. Note that these areas and industry growth rates reflect the minimum that might be required for gigaton-scale climate impact, since the ambient-nutrient scenario assumes that all surface ocean nutrients are available for seaweed growth. In the limited-nutrient scenario, reaching 1 GtCO2-eq of emissions avoided in the lowest-cost areas by 2050 might require ~130,000 km2, which would represent a nearly 50-fold increase in the area currently farmed and would entail a 14% annual growth rate.

## Discussion

Our results suggest that it might be possible to sequester >1 GtCO2 at costs as low as $480 per tCO2 if nearly all seaweed carbon corresponds directly to an amount of CO2 removed from the atmosphere, production costs are reduced to near the lowest published costs40,41 (for example, seeded line and capital costs of <$0.40 m−1 and $3,300 ha−1, respectively), and/or seaweed yields are high (for example, >6,000 tDW km−2 for tropical reds and >2,000 tDW km−2 for temperate browns). Nonetheless,$480 per tCO2 is comparable to the $500–600 t per CO2 costs of direct air capture (DAC) reported by the company Climeworks42 (but much more than the$94–$232 DAC costs estimated in ref. 43). Sequestration costs also rise sharply if the assumed atmospheric removal fraction or seaweed yield decreases or if production costs increase (Supplementary Figs. 7 and 10, and Fig. 3e). In comparison, >1 GtCO2-eq emissions might be avoided at a profit of$50 per tCO2-eq if similarly low production costs are achieved and seaweed products avoid emissions of >3 tCO2-eq tDW−1 (for example, by displacing vegetables, legumes, or soy from some regions). Although the cost per emission avoided is typically higher if seaweed is instead used for biofuels (Fig. 2, and Supplementary Figs. 6 and 7), such fuels may command a substantial ‘green premium’ as countries seek to decarbonize aviation and long-distance transportation of freight4,7,44,45.

Although it is thus conceivable that farmed seaweed could feasibly deliver globally relevant climate benefits, our modelling and cost estimates are subject to important caveats and limitations. First, modelled economic parameter ranges are broad, spanning a relatively small number of divergent data points from publicly available datasets and scientific literature. In some cases, these ranges were extended downward to reflect potential future cost reductions that were not represented by existing data. Better constraining these cost ranges for both current and future scenarios would improve the model and reduce uncertainty. Similarly, future work could analyse in greater detail the specific types and scale of agricultural or energy product that might be displaced by seaweed and their GHG emissions. Although the relative benefits of avoiding different GHG emissions versus sequestering carbon for different periods of time are beyond the scope of our analysis, they may be important to investors and decision-makers. For example, in many potentially low-cost seaweed production regions, the time scale of sunk carbon that remains ‘sequestered’ in the deep ocean is less than 100 yr8; if CDR accounting requires multi-century sequestration, the cost of seaweed-based CDR may become prohibitively high.

There are also large sources of uncertainty that deserve further exploration in the future. For example, we find that estimated costs per ton of CO2-eq emissions avoided or CO2 sequestered are highly sensitive to both the nutrient scenario (ambient vs. limited nutrients, Fig. 2 and Supplementary Fig. 6) and yield uncertainty within each nutrient scenario. Nutrient reallocation from competition between farmed seaweed and phytoplankton is also a critical dynamic that warrants analysis in the context of a fully coupled earth system model, since farming seaweed at gigaton scales would probably diminish natural carbon uptake by phytoplankton and therefore reduce the net drawdown of atmospheric CO246. Moreover, our climate benefit calculations do not include particulate seaweed biomass that may be exported to the deep sea before harvest (analogous to sinking ~5% of the harvested biomass21), and we also do not consider any potential non-CO2 GHG emissions from the seaweed cultivation process. The G-MACMODS model also assumes that nitrogen is the limiting macronutrient for seaweed growth (and micronutrients are supplemented by farming techniques), and while nitrogen limits production in large parts of the ocean, phosphorus might be more limiting in some regions. Finally, we must continue to evaluate potential consequences to ocean ecosystems and biogeochemical cycles before seriously considering farming and/or sinking gigatons of seaweed19.

Despite these uncertainties and limitations, our analysis supports continued research, development and demonstration of the potential for seaweed farming to produce meaningful climate benefits. Specifically, our model highlights the most important targets for research and innovation. Biophysical factors such as death (including disease, pests, weather events) and exudation rates are not well-established and may substantially alter projected seaweed yields33; regional biogeochemical and Earth system feedbacks could similarly undermine the efficacy of sinking seaweed carbon; and low or narrow demand for seaweed products could limit the potential to offset land-use and fossil GHG emissions. Finally, although some seaweed innovators are focused on farm designs that reduce labour and transportation costs, our results suggest that the keys to maximizing yield with low production costs are seeded line and basic farm equipment such as boats, buoys and anchors. However, even if seed and capital costs are minimized, seaweed CDR seems likely to be more expensive than alternatives such as direct air capture, and it is not clear that there are viable and large markets for seaweed products. These factors, combined with the challenges inherent in verification and monitoring as well as the potential for ecosystem disruption, suggest that expansion of seaweed cultivation should be approached with caution. The outlook for a massive scale-up of seaweed climate benefits is thus decidedly murky, but our findings can help direct research, investments and decision making to clear the waters.

## Methods

### Monte Carlo analysis

Seaweed production costs and net costs of climate benefits were estimated on the basis of outputs of the biophysical and technoeconomic models described below. The associated uncertainties and sensitivities were quantified by repeatedly sampling from uniform distributions of plausible values for each cost and economic parameter (n = 5,000 for each nutrient scenario from the biophysical model, for a total of n = 10,000 simulations; see Supplementary Figs. 14 and 15)47,48,49,50,51,52. Parameter importance across Monte Carlo simulations (Fig. 3 and Supplementary Fig. 9) was determined using decision trees in LightGBM, a gradient-boosting machine learning framework.

### Biophysical model

G-MACMODS is a nutrient-constrained, biophysical macroalgal growth model with inputs of temperature, nitrogen, light, flow, wave conditions and amount of seeded biomass30,53, that we used to estimate annual seaweed yield per area (either in tons of carbon or tons of dry weight biomass per km2 per year)33,34. In the model, seaweed takes up nitrogen from seawater, and that nitrogen is held in a stored pool before being converted to structural biomass via growth54. Seaweed biomass is then lost via mortality, which includes breakage from variable ocean wave intensity. The conversion from stored nitrogen to biomass is based on the minimum internal nitrogen requirements of macroalgae, and the conversion from biomass to units of carbon is based on an average carbon content of macroalgal dry weight (~30%)55. The model accounts for farming intensity (sub-grid-scale crowding) and employs a conditional harvest scheme, where harvest is optimized on the basis of growth rate and standing biomass33.

The G-MACMODS model is parameterized for four types of macroalgae: temperate brown, temperate red, tropical brown and tropical red. These types employed biophysical parameters from genera that represent over 99.5% of present-day farmed macroalgae (Eucheuma, Gracilaria, Kappahycus, Sargassum, Porphyra, Saccharina, Laminaria, Macrocystis)39. Environmental inputs were derived from satellite-based and climatological model output mapped to 1/12-degree global resolution, which resolves continental shelf regions. Nutrient distributions were derived from a 1/10-degree resolution biogeochemical simulation led by the National Center for Atmospheric Research (NCAR) and run in the Community Earth System Model (CESM) framework35.

Two nutrient scenarios were simulated with G-MACMODS and evaluated using the technoeconomic model analyses described below: the ‘ambient nutrient’ scenario where seaweed growth was computed using surface nutrient concentrations without depletion or competition, and ‘limited nutrient’ simulations where seaweed growth was limited by an estimation of the nutrient supply to surface waters (computed as the flux of deep-water nitrate through a 100 m depth horizon). For each Monte Carlo simulation in the economic analysis, the technoeconomic model randomly selects either the 5th, 25th, 50th, 75th or 95th percentile G-MACMODS seaweed yield map from a normal distribution to use as the yield map for that simulation. Figures and numbers reported in the main text are based on the ambient-nutrient scenario; results based on the limited-nutrient scenario are shown in Supplementary Figures.

### Technoeconomic model

An interactive web tool of the technoeconomic model is available at https://carbonplan.org/research/seaweed-farming.

We estimated the net cost of seaweed-related climate benefits by first estimating all costs and emissions related to seaweed farming, up to and including the point of harvest at the farm location, then estimating costs and emissions related to the transportation and processing of harvested seaweed, and finally estimating the market value of seaweed products and either carbon sequestered or GHG emissions avoided.

#### Production costs and emissions

Spatially explicit costs of seaweed production ($tDW−1) and production-related emissions (tCO2 tDW−1) were calculated on the basis of ranges of capital costs ($ km−2), operating costs (including labour, $km−2), harvest costs ($ km−2) and transport emissions per distance travelled (tCO2 km−1) in the literature (Table 1, Supplementary Tables 1 and 2); annual seaweed biomass (tDW km−2, for the preferred seaweed type in each grid cell), line spacing and number of harvests (species-dependent) from the biophysical model; as well as datasets of distances to the nearest port (km), ocean depth (m) and significant wave height (m).

Capital costs were calculated as:

$$c_{cap} = c_{capbase} + \left( {c_{capbase} \times \left( {k_d + k_w} \right)} \right) + c_{sl}$$
(1)

where ccap is the total annualized capital costs per km2, ccapbase is the annualized capital cost per km2 (for example, cost of buoys, anchors, boats, structural rope) before applying depth and wave impacts, kd and kw are the impacts of depth and waviness on capital cost, respectively, each expressed as a multiplier between 0 and 1 modelled using our Monte Carlo method and applied only to grid cells with depth >500 m and/or significant wave height >3 m, respectively, and csl is the total annual cost of seeded line calculated as:

$$c_{sl} = c_{slbase} \times p_{sline}$$
(2)

where cslbase is the cost per metre of seeded line, and psline is the total length of line per km2, based on the optimal seaweed type grown in each grid cell.

Operating and maintenance costs were calculated as:

$$c_{op} = c_{ins} + c_{lic} + c_{lab} + c_{opbase}$$
(3)

where cop is the total annualized operating and maintenance costs per km2, cins is the annual insurance cost per km2, clic is the annual cost of a seaweed aquaculture license per km2, clab is the annual cost of labour excluding harvest labour, and copbase is all other operating and maintenance costs.

Harvest costs were calculated as:

$$c_{harv} = c_{harvbase} \times n_{harv}$$
(4)

where charv is the total annual costs associated with harvesting seaweed per km2, charvbase is the cost per harvest per km2 (including harvest labour but excluding harvest transport), and nharv is the total number of harvests per year.

Costs associated with transporting equipment to the farming location were calculated as:

$$c_{eqtrans} = c_{transbase} \times m_{eq} \times d_{port}$$
(5)

where ceqtrans is total annualized cost of transporting equipment, ctransbase is the cost to transport 1 ton of material 1 km on a barge, meq is the annualized equipment mass in tons and dport is the ocean distance to the nearest port in km.

The total production cost of growing and harvesting seaweed was therefore calculated as:

$$c_{prod} = \frac{{\left( {c_{cap}} \right) + \left( {c_{op}} \right) + \left( {c_{harv}} \right) + (c_{eqtrans})}}{{s_{dw}}}$$
(6)

where cprod is total annual cost of seaweed production (growth + harvesting), ccap is as calculated in equation (1), cop is as calculated in equation (3), charv is as calculated in equation (4), ceqtrans is as calculated in equation (5) and sdw is the DW of seaweed harvested annually per km2.

Emissions associated with transporting equipment to the farming location were calculated as:

$$e_{eqtrans} = e_{transbase} \times m_{eq} \times d_{port}$$
(7)

where eeqtrans is the total annualized CO2 emissions in tons from transporting equipment, etransbase is the CO2 emissions from transporting 1 ton of material 1 km on a barge, meq is the annualized equipment mass in tons and dport is the ocean distance to the nearest port in km.

Emissions from maintenance trips to/from the seaweed farm were calculated as:

$$e_{mnt} = \left( {\left( {2 \times d_{port}} \right) \times e_{mntbase} \times \left( {\frac{{n_{mnt}}}{{a_{mnt}}}} \right)} \right) + (e_{mntbase} \times d_{mnt})$$
(8)

where emnt is total annual CO2 emissions from farm maintenance, dport is the ocean distance to the nearest port in km, nmnt is the number of maintenance trips per km2 per year, amnt is the area tended to per trip, dmnt is the distance travelled around each km2 for maintenance and emntbase is the CO2 emissions from travelling 1 km on a typical fishing maintenance vessel (for example, a 14 m Marinnor vessel with 2 × 310 hp engines) at an average speed of 9 knots (16.67 km h−1), resulting in maintenance vessel fuel consumption of 0.88 l km−1 (refs. 28, 56).

Total emissions from growing and harvesting seaweed were therefore calculated as:

$$e_{prod} = \frac{{(e_{eqtrans}) + (e_{mnt})}}{{s_{dw}}}$$
(9)

where eprod is total annual emissions from seaweed production (growth + harvesting), eeqtrans is as calculated in equation (7), emnt is as calculated in equation (8) and sdw is the DW of seaweed harvested annually per km2.

#### Market value and climate benefits of seaweed

Further transportation and processing costs, economic value and net emissions of either sinking seaweed in the deep ocean for carbon sequestration or converting seaweed into usable products (biofuel, animal feed, pulses, vegetables, fruits, oil crops and cereals) were calculated on the basis of ranges of transport costs ($tDW−1 km−1), transport emissions (tCO2-eq t−1 km−1), conversion cost ($ tDW−1), conversion emissions (tCO2-eq tDW−1), market value of product ($tDW−1) and the emissions avoided by product (tCO2-eq tDW−1) in the literature (Table 1). Market value was treated as globally homogeneous and does not vary by region. Emissions avoided by products were determined by comparing estimated emissions related to seaweed production to emissions from non-seaweed products that could potentially be replaced by seaweed (including non-CO2 greenhouse gas emissions from land use)24. Other parameters used are distance to nearest port (km), water depth (m), spatially explicit sequestration fraction (%)57 and distance to optimal sinking location (km; cost-optimized for maximum emissions benefit considering transport emissions combined with spatially explicit sequestration fraction; see ‘Distance to sinking point calculation’ below). Each Monte Carlo simulation calculated the cost of both CDR via sinking seaweed and GHG emissions mitigation via seaweed products. For seaweed CDR, after the seaweed is harvested, it can either be sunk in the same location that it was grown, or be transported to a more economically favourable sinking location where more of the seaweed carbon would remain sequestered for 100 yr (see ‘Distance to optimal sinking point’ below). Immediately post-harvest, the seaweed still contains a large amount of water, requiring a conversion from dry mass to wet mass for subsequent calculations33: $$s_{ww} = \frac{{s_{dw}}}{{0.1}}$$ (10) where sww is the annual wet weight of seaweed harvested per km2 and sdw is the annual DW of seaweed harvested per km2. The cost to transport harvested seaweed to the optimal sinking location was calculated as: $$c_{swtsink} = c_{transbase} \times d_{sink} \times s_{ww}$$ (11) where cswtsink is the total annual cost to transport harvested seaweed to the optimal sinking location, ctransbase is the cost to transport 1 ton of material 1 km on a barge, dsink is the distance in km to the economically optimized sinking location and sww is the annually harvested seaweed wet weight in t km−2 as in equation (10). The costs associated with transporting replacement equipment (for example, lines, buoys, anchors) to the farming location and hauling back used equipment at the end of its assumed lifetime (1 yr for seeded line, 5–20 yr for capital equipment by equipment type) in the sinking CDR pathway were calculated as: $$c_{eqtsink} = \left( {c_{transbase} \times \left( {2 \times d_{sink}} \right) \times m_{eq}} \right) + (c_{transbase} \times d_{port} \times m_{eq})$$ (12) where ceqtsink is the total annualized cost to transport both used and replacement equipment, ctransbase is the cost to transport 1 ton of material 1 km on a barge, meq is the annualized equipment mass in tons, dsink is the distance in km to the economically optimized sinking location and dport is the ocean distance to the nearest port in km. We assumed that the harvesting barge travels from the farming location directly to the optimal sinking location with harvested seaweed and replaced (used) equipment in tow (including used seeded line and annualized mass of used capital equipment), sinks the harvested seaweed, returns to the farm location and then returns to the nearest port (see Supplementary Fig. 16). These calculations assumed the shortest sea-route distance (see Distance to optimal sinking point). The total value of seaweed that is sunk for CDR was therefore calculated as: $$v_{sink} = \frac{{\left( {v_{cprice} - \left( {c_{swtsink} + c_{eqtsink}} \right)} \right)}}{{s_{dw}}}$$ (13) where vsink is the total value (cost, if negative) of seaweed farmed for CDR in$ tDW−1, vcprice is a theoretical carbon price, cswtsink is as calculated in equation (11), ceqtsink is as calculated in equation (12) and sdw is the annually harvested seaweed DW in t km−2. We did not assume any carbon price in our Monte Carlo simulations (vcprice is equal to zero), making vsink negative and thus representing a net cost.

To calculate net carbon impacts, our model included uncertainty in the efficiency of using the growth and subsequent deep-sea deposition of seaweed as a CDR method. The uncertainty is expected to include the effects of reduced phytoplankton growth from nutrient competition, the relationship between air–sea gas exchange and overturning circulation (hereafter collectively referred to as the ‘atmospheric removal fraction’) and the fraction of deposited seaweed carbon that remains sequestered for at least 100 yr. The total amount of atmospheric CO2 removed by sinking seaweed was calculated as:

$$e_{seqsink} = k_{atm} \times k_{fseq} \times \frac{{tC}}{{tDW}} \times \frac{{tCO_2}}{{tC}}$$
(14)

where eseqsink is net atmospheric CO2 sequestered annually in t km−2, katm is the atmospheric removal fraction and kfseq is the spatially explicit fraction of sunk seaweed carbon that remains sequestered for at least 100 yr (see ref. 57).

The emissions from transporting harvested seaweed to the optimal sinking location were calculated as:

$$e_{swtsink} = e_{transbase} \times d_{sink} \times s_{ww}$$
(15)

where eswtsink is the total annual CO2 emissions from transporting harvested seaweed to the optimal sinking location in tCO2 km−2, etransbase is the CO2 emissions (tons) from transporting 1 ton of material 1 km on a barge (tCO2 per t-km), dsink is the distance in km to the economically optimized sinking location and sww is the annually harvested seaweed wet weight in t km−2 as in equation (10). Since the unit for etransbase is tCO2 per t-km, the emissions from transporting seaweed to the optimal sinking location are equal to $$e_{\mathrm{transbase}} \times d_{\mathrm{sink}} \times s_{\mathrm{ww}}$$, and the emissions from transporting seaweed from the optimal sinking location back to the farm are equal to 0 (since the seaweed has already been deposited, the seaweed mass to transport is now 0). Note that this does not yet include transport emissions from transport of equipment post-seaweed-deposition (see equation 16 below and Supplementary Fig. 16).

The emissions associated with transporting replacement equipment (for example, lines, buoys, anchors) to the farming location and hauling back used equipment at the end of its assumed lifetime (1 yr for seeded line, 5–20 yr for capital equipment by equipment type)28,41 in the sinking CDR pathway were calculated as:

$$e_{eqtsink} = \left( {e_{transbase} \times \left( {2 \times d_{sink}} \right) \times m_{eq}} \right) + (e_{transbase} \times d_{port} \times m_{eq})$$
(16)

where eeqtsink is the total annualized CO2 emissions in tons from transporting both used and replacement equipment, etransbase is the CO2 emissions from transporting 1 ton of material 1 km on a barge, meq is the annualized equipment mass in tons, dsink is the distance in km to the economically optimized sinking location and dport is the ocean distance to the nearest port in km. We assumed that the harvesting barge travels from the farming location directly to the optimal sinking location with harvested seaweed and replaced (used) equipment in tow (including used seeded line and annualized mass of used capital equipment), sinks the harvested seaweed, returns to the farm location and then returns to the nearest port. These calculations assumed the shortest sea-route distance (see Distance to optimal sinking point).

Net CO2 emissions removed from the atmosphere by sinking seaweed were thus calculated as:

$$e_{remsink} = \frac{{\left( {e_{seqsink} - \left( {e_{swtsink} + e_{eqtsink}} \right)} \right)}}{{s_{dw}}}$$
(17)

where eremsink is the net atmospheric CO2 removed per ton of seaweed DW, eseqsink is as calculated in equation (14), eswtsink is as calculated in equation (15), eeqtsink is as calculated in equation (16) and sdw is the annually harvested seaweed DW in t km−2.

### Net cost of climate benefits

#### Sinking

To calculate the total net cost and emissions from the production, harvesting and transport of seaweed for CDR, we combined the cost and emissions from the sinking-pathway cost and value modules. The total net cost of seaweed CDR per DW ton of seaweed was calculated as:

$$c_{sinknet} = c_{prod} - v_{sink}$$
(18)

where csinknet is the total net cost of seaweed for CDR per DW ton harvested, cprod is the net production cost per DW ton as calculated in equation (6) and vsink is the net value (or cost, if negative) per ton seaweed DW as calculated in equation (13).

The total net CO2 emissions removed per DW ton of seaweed were calculated as:

$$e_{sinknet} = e_{remsink} - e_{prod}$$
(19)

where esinknet is the total net atmospheric CO2 removed per DW ton of seaweed harvested annually (tCO2 tDW−1 yr−1), eremsink is the net atmospheric CO2 removed via seaweed sinking annually as calculated in equation (17) and eprod is the net CO2 emitted from production and harvesting of seaweed annually as calculated in equation (9). For each Monte Carlo simulation, locations where esinknet is negative (that is, net emissions rather than net removal) were not included in subsequent calculations since they would not be contributing to CDR in that location under the given scenario. Note that these net emissions cases only occur in areas far from port in specific high-emissions scenarios. Even in such cases, most areas still contribute to CO2 removal (negative emissions), hence costs from locations with net removal were included.

Total net cost was then divided by total net emissions to get a final value for cost per ton of atmospheric CO2 removed:

$$c_{pertonsink} = \frac{{c_{sinknet}}}{{e_{sinknet}}}$$
(20)

where cpertonsink is the total net cost per ton of atmospheric CO2 removed via seaweed sinking ($per tCO2 removed), csinknet is total net cost per ton seaweed DW harvested as calculated in equation (18) ($ tDW−1) and esinknet is the total net atmospheric CO2 removed per ton seaweed DW harvested as calculated in equation (19) (tCO2 tDW−1).

#### GHG emissions mitigation

Instead of sinking seaweed for CDR, seaweed can be used to make products (including but not limited to food, animal feed and biofuels). Replacing convention products with seaweed-based products can result in ‘avoided emissions’ if the emissions from growing, harvesting, transporting and converting seaweed into products are less than the total greenhouse gas emissions (including non-CO2 GHGs) embodied in conventional products that seaweed-based products replace.

When seaweed is used to make products, we assumed it is transported back to the nearest port immediately after being harvested. The annualized cost to transport the harvested seaweed and replacement equipment (for example, lines, buoys, anchors) was calculated as:

$$c_{transprod} = \frac{{\left( {c_{transbase} \times d_{port} \times \left( {s_{ww} + m_{eq}} \right)} \right)}}{{s_{dw}}}$$
(21)

where ctransprod is the annualized cost per ton seaweed DW to transport seaweed and equipment back to port from the farm location, ctransbase is the cost to transport 1 ton of material 1 km on a barge, meq is the annualized equipment mass in tons, dport is the ocean distance to the nearest port in km, sww is the annual wet weight of seaweed harvested per km2 as calculated in equation (10) and sdw is the annual DW of seaweed harvested per km2.

The total value of seaweed that is used for seaweed-based products was calculated as:

$$v_{product} = v_{mkt} - \left( {c_{transprod} + c_{conv}} \right)$$
(22)

### Distance to optimal sinking point

Distance to the optimal sinking point was calculated using a weighted distance transform (path-finding algorithm, modified from code in ref. 60) that finds the shortest ocean distance from each seaweed growth pixel to the location at which the net CO2 removed is maximized (including impacts of both increased sequestration fraction and transport emissions for different potential sinking locations) and the net cost is minimized. This is not necessarily the location in which the seaweed was grown, since the fraction of sunk carbon that remains sequestered for 100 yr is spatially heterogeneous (see ref. 57). For each ocean grid cell, we determined the cost-optimal sinking point by iteratively calculating equations (1120) and assigning dsink as the distance calculated by weighted distance transform to each potential sequestration fraction (0.01–1.00) in increments of 0.01. Except for transport emissions, the economic parameter values used for these calculations were the averages of unrounded literature value ranges; we assumed that the maximum literature value reflected the 95th percentile and the minimum literature value represented the 5th percentile of potential costs or emissions, or for parameters with only one literature value, we added ±50% to the literature value to represent greater uncertainty within the modelled parameter range. For transport and maintenance transport emissions, we extended the minimum values of the literature ranges to zero to reflect potential net-zero emissions transport options and used the mean values of the resulting ranges. The dsink that resulted in minimum net cost per ton CO2 for each ocean grid cell was saved as the final dsink map, and the associated sequestration fraction value that the seaweed is transported to via dsink was assigned to the original cell where the seaweed was farmed and harvested (Supplementary Fig. 19). If the cost-optimal location to sink using this method was the same cell where the seaweed was harvested, then dsink was 0 km and the sequestration fraction was not modified from its original value (Supplementary Fig. 18).

### Comparison of gigaton-scale sequestration area to previous estimates

Previous related work estimating the ocean area suitable for macroalgae cultivation13 and/or the area that might be required to reach gigaton-scale carbon removal via macroalgae cultivation13,19,36 has yielded a wide range of results, primarily due to differences in modelling methods. For example, Gao et al. (2022)36 estimate that 1.15 million km2 would be required to sequester 1 GtCO2 annually when considering carbon lost from seaweed biomass/sequestered as particulate organic carbon (POC) and refractory dissolved organic carbon (rDOC), and assume that the harvested seaweed is sold as food such that the carbon in the harvested seaweed is not sequestered. The area (0.4 million km2) required to sequester 1 GtCO2 in our study assumes that all harvested seaweed is sunk to the deep ocean to sequester carbon.

Additionally, Wu et al.19 estimates that roughly 12 GtCO2 could be sequestered annually via macroalgae cultivation in approximately 20% of the world ocean area (that is, 1.67% ocean area per GtCO2), which is a much larger area per GtCO2 than our estimate of 0.110% ocean area. This notable difference arises for several reasons (including differences in yields, which in Wu et al. are around 500 tDW yr−1 in the highest-yield areas, whereas yields in our cheapest sequestration areas from G-MACMODS average 3,400 tDW km−2 yr−1) that arise from differences in model methodology. First, Wu et al. model temperate brown seaweeds, while our study considers different seaweed types, many of which have higher growth rates, and uses the most productive seaweed type for each ocean grid cell. The G-MACMODS seaweed growth model we use also has a highly optimized harvest schedule, includes luxury nutrient uptake (a key feature of macroalgal nutrient physiology) and does not directly model competition with phytoplankton during seaweed growth. Finally, tropical red seaweeds (the seaweed type in our cheapest sequestration areas) grow year-round, while others, such as the temperate brown seaweeds modelled by Wu et al., only grow seasonally. These differences all contribute to higher productivity in our model, leading to a smaller area required for gigaton-scale CO2 sequestration compared with Wu et al.

Conversely, the ocean areas we model for seaweed-based CO2 sequestration or GHG emissions avoided are much larger than the 48 million km2 that Froehlich et al.13 estimate to be suitable for macroalgae farming globally. Although our maps show productivity and costs everywhere, the purpose of our modelling was to evaluate where different types of seaweed grow best and how production costs and product values vary over space, to highlight the lowest-cost areas (which are often the highest-producing areas) under various technoeconomic assumptions.

### Comparison of seaweed production costs to previous estimates

Although there are not many estimates of seaweed production costs in the scientific literature, our estimates for the lowest-cost 1% area of the ocean ($190–$2,790 tDW−1) are broadly consistent with previously published results: seaweed production costs reported in the literature range from $120 to$1,710 tDW−1 (refs. 40, 41, 61, 62), but are highly dependent on assumed seaweed yields. For example, Camus et al.41 calculate a cost of $870 tDW−1 assuming a minimum yield of 12.4 kgDW m−1 of cultivation line (equivalent to 8.3 kgDW m−2 using 1.5 m spacing between lines). Using the economic values from Camus et al. but with our estimates of average yield for the cheapest 1% production cost areas (2.6 kgDW m−2) gives a much higher average cost of$2,730 tDW−1. Contrarily, van den Burg et al.40 calculate a cost of $1,710 tDW−1 using a yield of 20 tDW ha−1 (that is, 2.0 kg m−2). Instead assuming the average yield to be that from our lowest-cost areas (that is, 2.6 kgDW m−2 or 26 tDW ha−1) would decrease the cost estimated by van den Burg et al. (2016) to$1,290 tDW−1. Most recently, Capron et al.62 calculate an optimistic scenario cost of $120 tDW−1 on the basis of an estimated yield of 120 tDW ha−1 (12 kg m−2; over 4.5 times higher than the average yield in our lowest-cost areas). Again, instead assuming the average yield to be that in our lowest-cost areas would raise Capron et al.’s production cost to$540 tDW−1 (between the $190–$880 tDW−1 minimum to median production costs in the cheapest 1% areas from our model; Fig. 1a,b).

### Data sources

#### Seaweed biomass harvested

We used spatially explicit data for seaweed harvested globally under both ambient and limited-nutrient scenarios from the G-MACMODS seaweed growth model33.

#### Fraction of deposited carbon sequestered for 100 yr

We used data from ref. 57 interpolated to our 1/12-degree grid resolution.

#### Distance to the nearest port

We used the Distance from Port V1 dataset from Global Fishing Watch (https://globalfishingwatch.org/data-download/datasets/public-distance-from-port-v1) interpolated to our 1/12-degree grid resolution.

#### Significant wave height

We used data for annually averaged significant wave height from the European Center for Medium-range Weather Forecasts (ECMWF) interpolated to our 1/12-degree grid resolution.

#### Ocean depth

We used data from the General Bathymetric Chart of the Oceans (GEBCO).

#### Shipping lanes

We used data of Automatic Identification System (AIS) signal count per ocean grid cell, interpolated to our 1/12-degree grid resolution. We defined a major shipping lane grid cell as any cell with >2.25 × 108 AIS signals, a threshold that encompasses most major trans-Pacific and trans-Atlantic shipping lanes as well as major shipping lanes in the Indian Ocean, the North Sea, and coastal routes worldwide.

#### Marine protected areas (MPAs)

We used data from the World Database on Protected Areas (WDPA) and defined an MPA as any ocean MPA >20 km2.

### Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.