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Monte Carlo analysisSeaweed 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 modelG-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 modelAn 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 emissionsSpatially 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 seaweedFurther 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 benefitsSinkingTo 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 mitigationInstead 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)
where vproduct is the total value (cost, if negative) of seaweed used for products ($ tDW−1), vmkt is how much each ton of seaweed would sell for, given the current market price of conventional products that seaweed-based products replace ($ tDW−1), ctransprod is as calculated in equation (21) and cconv is the cost to convert each ton of seaweed to a usable product ($ tDW−1).The annualized CO2 emissions from transporting harvested seaweed and equipment back to port were calculated as:$$e_{transprod} = frac{{left( {e_{transbase} times d_{port} times left( {s_{ww} + m_{eq}} right)} right)}}{{s_{dw}}}$$
(23)
where etransprod is the annualized CO2 emissions per ton seaweed DW to transport seaweed and equipment back to port from the farm location, etransbase is the CO2 emissions from transporting 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.Total emissions avoided by each ton of harvested seaweed DW were calculated as:$$e_{avprod} = e_{subprod} – left( {e_{transprod} + e_{conv}} right)$$
(24)
where eavprod is total CO2-eq emissions avoided per ton of seaweed DW per year (including non-CO2 GHGs using a GWP time period of 100 yr), esubprod is the annual CO2-eq emissions avoided per ton seaweed DW by replacing a conventional product with a seaweed-based product, etransprod is as calculated in equation (23) and econv is the annual CO2 emissions per ton seaweed DW from converting seaweed into usable products. esubprod was calculated by converting seaweed DW to caloric content58 for food/feed and comparing emissions intensity per kcal to agricultural products24, or by converting seaweed DW into equivalent biofuel content with a yield of 0.25 tons biofuel per ton DW59 and dividing the CO2 emissions per ton fossil fuel by the seaweed biofuel yield.To calculate the total net cost and emissions from the production, harvesting, transport and conversion of seaweed for products, we combined the cost and emissions from the product-pathway cost and value modules. The total net cost of seaweed for products per ton DW was calculated as:$$c_{prodnet} = c_{prod} – v_{product}$$
(25)
where cprodnet is the total net cost per ton DW of seaweed harvested for use in products, cprod is the net production cost per ton DW as calculated in equation (6) and vproduct is the net value (or cost, if negative) per ton DW as calculated in equation (22).The total net CO2-eq emissions avoided per ton DW of seaweed used in products were calculated as:$$e_{prodnet} = e_{avprod} – e_{prod}$$
(26)
where eprodnet is the total net CO2-eq emissions avoided per ton DW of seaweed harvested annually (tCO2 tDW−1 yr−1), eavprod is the net CO2-eq emissions avoided by seaweed products annually as calculated in equation (24) 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 eprodnet is negative (that is, net emissions rather than net emissions avoided) were not included in subsequent calculations since they would not be avoiding any emissions in that scenario.Total net cost was then divided by total net emissions avoided to get a final value for cost per ton of CO2-eq emissions avoided:$$c_{pertonprod} = frac{{c_{prodnet}}}{{e_{prodnet}}}$$
(27)
where cpertonprod is the total net cost per ton of CO2-eq emissions avoided by seaweed products ($ per tCO2-eq avoided), cprodnet is total net cost per ton seaweed DW harvested for products as calculated in equation (25) ($ tDW−1) and eprodnet is total net CO2-eq emissions avoided per ton seaweed DW harvested for products as calculated in equation (26) (tCO2 tDW−1).Parameter ranges for Monte Carlo simulationsFor technoeconomic parameters with two or more literature values (see Supplementary Table 1), 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. For parameters with only one literature value, we added ±50% to the literature value to represent greater uncertainty within the modelled parameter range. Values at each end of parameter ranges were then rounded before Monte Carlo simulations as follows: capital costs, operating costs and harvest costs to the nearest $10,000 km−2, labour costs and insurance costs to the nearest $1,000 km−2, line costs to the nearest $0.05 m−1, transport costs to the nearest $0.05 t−1 km−1, transport emissions to the nearest 0.000005 tCO2 t−1 km−1, maintenance transport emissions to the nearest 0.0005 tCO2 km−1, product-avoided emissions to the nearest 0.1 tCO2-eq tDW−1, conversion cost down to the nearest $10 tDW−1 on the low end of the range and up to the nearest $10 tDW−1 on the high end of the range, and conversion emissions to the nearest 0.01 tCO2 tDW−1.We extended the minimum range values of capital costs to $10,000 km−2 and transport emissions to 0 to reflect potential future innovations, such as autonomous floating farm setups that would lower capital costs and net-zero emissions boats that would result in 0 transport emissions. To calculate the minimum value of $10,000 km−2 for a potential autonomous floating farm, we assumed that the bulk of capital costs for such a system would be from structural lines and flotation devices, and we therefore used the annualized structural line (system rope) and buoy costs from ref. 41 rounded down to the nearest $5,000 km−2. The full ranges used for our Monte Carlo simulations and associated literature values are shown in Supplementary Table 1.Distance to optimal sinking pointDistance 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 (11–20) 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 estimatesPrevious 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 (0.31 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 0.085% 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 estimatesAlthough 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 sourcesSeaweed biomass harvestedWe 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 yrWe used data from ref. 57 interpolated to our 1/12-degree grid resolution.Distance to the nearest portWe 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 heightWe 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 depthWe used data from the General Bathymetric Chart of the Oceans (GEBCO).Shipping lanesWe 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 summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article. More

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