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Using a targeted metabolomics approach, we showed that late copepodite stages of the keystone Arctic copepod Calanus glacialis experience important changes in several central energetic pathways following exposure to decreasing pH. These findings shed light on the physiological changes underpinning the effects of OA on fitness related traits such as ingestion rate and metabolic rate previously observed in this species17,18,20.Cellular energy metabolismCellular energy production was altered consistently in both stage CIV and CV, with concentrations of higher energy adenosine phosphates (ATP and ADP) increasing, and concentrations of the lower energy, less-phosphorylated AMP decreasing, with decreasing seawater pH. Moreover, Phospho-L-arginine, which in crustaceans functions as phosphagen in the replenishment of ATP from ADP during transient energy demands32, increased significantly in stage CV. These changes strongly suggest that exposure to low pH affects energy production and expenditure in both developmental stages, although with nuanced differences.NAD+ increased significantly in stage CIV. NAD+ is an essential redox carrier receiving electrons from oxidative processes in the glycolysis, the TCA cycle, and fatty acid oxidation to form NADH. A high NAD+/NADH ratio facilitates higher rates of these reactions and thus potentially higher rates of ATP production (unfortunately, the LC-HRMS could not detect NADH). But most importantly, the produced NADH serves as electron donors to ATP synthesis in the oxidative phosphorylation. For every ATP produced in the oxidative phosphorylation one NADH is oxidised back to NAD+. High rates of ATP production in the oxidative phosphorylation would therefore amass NAD+, as observed in stage CIV. Conversely, ATP production in the glycolysis and TCA cycle consumes NAD+ (9 NAD+ per 4 ATP) and glycolytic ATP production would decrease the NAD+ concentration with decreasing pH.Heterotrophic organisms generally face a trade-off between rate and yield of ATP production. The efficient low rate/high yield production in the TCA cycle/oxidative phosphorylation may prevail under certain circumstances, whereas under other circumstances, the less efficient high rate/low yield production in the glycolysis may predominate33. Because glycolysis and oxidative phosphorylation compete for ADP, the one dominate over the other in terms of rates depending on the substrate being metabolised. In stage CIV copepodites, the TCA cycle pathway was enriched in the MetPA, and metabolites associated with glycolysis and the TCA cycle showed significant changes in their concentrations at decreasing seawater pH. Glucose, the entry point to glycolysis, increased significantly with decreasing pH. High levels of blood glucose (hyperglycemia) have been observed as a general stress response in decapod crustaceans34. Copepods have no circulatory system (although they have a dorsal heart) but might nevertheless react similarly on the cellular level. Along with the significant increase in glucose, lactate decreased significantly with pH in stage CIV. Lactate is an inevitable end product of glycolysis, because lactate dehydrogenase has the highest Vmax of any enzymes in the glycolytic pathway and the Keq for pyruvate to lactate is far in the direction of lactate35. Accordingly, although the glycolysis was not enriched in the MetPA, conceivably because none of its intermediate metabolites were included in the analyses (the protocol did not allow for it), we hypothesise that stage CIV copepodites experience a general down-regulation of glycolysis under decreasing pH. Alternatively, the amassing of glucose and depletion of lactate could also indicate increased gluconeogenesis. Gluconeogenesis occurs during starvation to replenish glycogen stores and ingestion rates did decrease in stage CIV20. But again, we did not target any intermediates in our analyses, and thus cannot firmly conclude on this.Phosphofructokinase-1 is a key regulatory enzyme of glycolysis36. This enzyme is allosterically inhibited by ATP and activated by AMP, and interestingly this regulation is augmented by low pH37,38. Thus, phosphofructokinase-1 could be key to the down-regulation of glycolysis we hypothesise. The fact that we found increasing oxygen consumption with decreasing pH in stage CIV copepodites from the same experiment adds further momentum to this line of thought20. It seems that stage CIV copepodites might experience the so-called Pasteur effect—a decrease in glycolysis at increased levels of oxygen uptake—when exposed to decreasing pH39. Although ATP and AMP were significantly affected also in stage CV, glucose, pyruvate and lactate did not change with decreasing pH, which perhaps indicate absence of the down-regulation of glycolysis we hypothesise for stage CIV. There is, nevertheless, one indication that down-regulation may in fact occur also in this developmental stage. Alpha-glycerophosphate decreased significantly with decreasing pH in stage CV. This molecule is an intermediate in the transfer of electrons from NADH produced by glycolysis in the cytosol to the oxidative phosphorylation in the mitochondria, and decreased concentrations could result from down-regulation of the glycolysis also in stage CV copepodites.The TCA cycle was enriched for stage CIV and most of the measured TCA cycle metabolites (alpha-ketoglutarate, succinate, fumarate, and malate) showed increasing concentrations at decreasing pH. Trigg et al.40 observed a similar increase in concentrations of TCA cycle-related metabolites in the Dungeness crab, Cancer magister (Dana, 1852), at decreased pH and concluded that TCA cycle activity is upregulated under OA. Since NAD+ is the product of the transport of electrons from the TCA cycle to the oxidative phosphorylation in the mitochondria,  the increase in NAD+ concentration we observed in stage CIV could reflect an increase in the flow of electrons from the TCA cycle to the oxidative phosphorylation, and by extension an increase in the energy production by the TCA cycle and the oxidative phosphorylation. There is negative feedback from the TCA cycle to glycolysis through inhibition of phosphofructokinase-1 by citrate, a metabolite of the TCA cycle38. Unfortunately, we did not target citrate in our targeted approach to specifically test this hypothesis, but the amassing of NAD+ do provide additional support to the idea that glycolysis is down-regulated at decreasing pH. Again, there is a less clear picture of how cellular energy metabolism is affected by decreasing pH in stage CV when compared to stage CIV. There was no clear pattern of regulation of TCA metabolites, and the TCA cycle was not enriched in the MetPA. Nevertheless, alpha-ketoglutarate concentrations did increase with decreasing pH in CVs.The glyoxylate/dicarboxylate cycle was also enriched in the pathway analysis, but this is probably also a result of the increases in concentrations of alpha-ketoglutarate, succinate, fumarate, and malate, and we are unable to distinguish it from the TCA cycle based on the set of metabolites analysed.Conclusively, lowered glycolysis due to inhibition of phosphofructokinase-1 and upregulation of the TCA cycle and oxidative phosphorylation at low pH in stage CIV appear plausible causes for the changes in ATP, ADP and AMP concentrations we observed. Alongside these effects, down-regulation of transcription of genes involved in the glycolysis were also present in nauplii of C. glacialis exposed to 35–38 days of low pH conditions16. On the other hand, studies on the acclimatisation and adaptation to OA in another calanoid copepod species, Pseudocalanus acuspes (Giesbrecht, 1881), showed no increase in expression of mitochondrial genes at pHT 7.54, which would have been expected if the TCA cycle or oxidative phosphorylation is upregulated41. Interestingly, De Wit et al.41 also showed natural selection in a large fraction of mitochondrial genes under OA conditions. Even evolutionarily conserved sequences, such as cytochrome oxidase subunit I, were under selection and it was hypothesised that the mitochondrial function of oxidative phosphorylation is a target for natural selection in copepods at low pH41.Besides its role in the transfer of energy from the mitochondria to the cell, ATP is also used to fuel cell homeostasis and active cellular acid–base regulation by activation of ATP-dependent enzymes involved in osmo-ionic- and acid–base regulation. In crustaceans, acid–base status is linked to ion regulation, and is maintained primarily through ion transport mechanisms moving acid and/or base equivalents between the extracellular fluid and the ambient water42. One prominent process in this respect is regulation by Na+/K+-ATPase42,43. While this regulation takes place in the gills of decapod crustaceans43, it is located in the maxillary glands and other specialised organs on the swimming legs of copepods44. Any extensive ATPase mediated pH regulation could have manifested itself by decreasing ATP concentrations, but this is contrary to what we report here. Interestingly, while the pCO2-sensitive isopod Cymodoce truncata (Leach, 1814) is able to maintain its cellular ATP concentration at the expense of the concentration of carbonate anhydrase (an enzyme involved in the cellular transformation of water and CO2 to bicarbonate ions and H+ prior to the ATPase mediated transport of H+ across the cell membrane), the pCO2-tolerant isopod Dynamene bifida (Torelli, 1930) upregulates ATP with no functional compromise to CA concentrations45. Finally, C. glacialis nauplii have shown upregulation of Na+/H+-antiporters independent of ATPase as a response to OA16, which one could hypothesise also may be the case in the copepodites. Arctic populations of the amphipod Gammarus setosus also do not experience increased ATPase activity during OA conditions46. It seems that C. glacialis faces OA without any ATP dependent acid/base regulation activity.Glycolysis is the first step of catabolism of carbohydrates for the production of energy. When down-regulating glycolysis the copepods may be increasingly dedicated to catabolism of amino acids e.g. through oxidative deamination of glutamate and/or catabolism of fatty acids through beta-oxidation to produce the energy they require21. Both lead to the production of molecules entering the TCA cycle and ultimately the oxidative phosphorylation for energy production in the mitochondria.Amino acid metabolismOf the free amino acids which were significantly affected by decreasing pH, the majority decreased in concentration, for both stage CIV and CV copepodites. This could be an indication of changes in protein synthesis at decreasing pH. Supporting this idea, biosynthesis of aminoacyl-tRNA was indicated as significantly enriched in the MetPA in both stage CIV and CV. Aminoacyl-tRNA partakes in the elongation of the protein amino acid chain during protein synthesis and the enrichment was most likely due to the changes in concentration of the many amino acids tested. One probable cause of protein synthesis is the increased demands of enzymes needed to handle stress at low pH, including for example enzymes involved in acid–base- and osmo-regulation or regulation of energy production. Increased protein synthesis caused by OA conditions has been observed in larvae of the purple sea urchin Strongylocentrotus purpuratus (O.F. Müller, 1776), where in vivo rates of protein synthesis and ion transport increased ∼50%47. Costs of protein synthesis are high and have shown to constitute a major part of copepod metabolic demand48 and we did observe significant increases in metabolic rate in copepodite stage CIV from the same experiment20 giving further credit to the idea that protein synthesis was upregulated.An alternate but not mutually exclusive explanation is that the copepods experience increased amino acid catabolism under OA. Glutamate increased in stage CIV accompanied by a significant increase in alpha-ketoglutarate in both stage CIV and CV. Alpha-ketoglutarate is part of the metabolic pathway of glutamine, glutamate and arginine in which glutamate acts as an intermediate in catabolism of these amino acids when it is deaminated to alpha-ketoglutarate to enter the TCA cycle49. Glutamate metabolism (in conjunction with alanine and aspartate metabolism) was significantly enriched in the MetPA in both stage CIV and CV, and these changes could be taken as an indication of a shift towards amino acid catabolism with decreasing pH. The key enzyme catalysing the oxidative deamination of glutamate is glutamate dehydrogenase (GDH), which functions in both directions: deamination of glutamate to form alpha-ketoglutarate or formation of glutamate from alpha-ketoglutarate. Studies on the ribbed mussel, Modiolus dernissus (Dillwyn, 1817), have shown that the balance of this action is strongly pushed towards deamination when pH decreases from 8.0 to 7.550. GDH is activated by ADP, and one could argue that the increase in ADP we observed would work against this shift, but ADP activates GDH mainly in the glutamate forming direction51. The other measured amino acids enter the TCA cycle at different positions we unfortunately could not target in our analyses. Glutamate also partakes in the arginine biosynthesis pathway in which it is transformed to ornithine to enter the urea cycle. Arginine biosynthesis was enriched in the MetPA and it is therefore possible that decreasing pH also changes amino acid catabolism to increase urea excretion. Decreasing pH has a similar depressing effect on amino acid concentration in the gills of the shore crab Carcinus maenas (Linnaeus, 1758) which also has been interpreted as a sign of increased protein catabolism52. Hammer and colleagues52 argued that this increase in catabolism served to buffer H+ by supplying nitrogen to NH4 formation in the cells. All in all, we hypothesise that increased amino acid catabolism, possibly driven by changes in GDH activity, and the down-regulation of glycolysis by inhibition of phosphofructokinase-1 may be major drivers of a shift from carbohydrate metabolism towards catabolism of amino acids.D-glutamine/D-glutamate metabolism was highly enriched in the MetPA in both developmental stages. Several studies show enriched D-glutamine/D-glutamate metabolism in crustaceans [e.g. 53], but they offer no explanation of its function or the reason why it is enriched. While D-glutamate act in neurotransmission, this action is evolutionarily restricted to ctenophores, and biochemical measurements of D-amino acid concentrations have shown absence of D-glutamate in crustaceans54,55.We observed no changes in concentrations of 8-oxy-2-deoxyguanosine, a product of DNA oxidation. Furthermore, regulation of cellular response to oxidative stress is down-regulated in C. glacialis nauplii16, and OA may not induce oxidative stress in C. glacialis.Fatty acid metabolismBesides their importance in energy storage as wax esters, fatty acids are involved in many central processes in cells, most prominently through their function as cell membrane building blocks. Many fatty acids are obtained from the diet but some longer chain fatty acids, such as 20:1n-9 are synthesised de novo in copepods56. Stage CV copepodites experienced increases in most of the targeted free fatty acids (18 of 21) with decreasing pH. Only one of those 18 increased significantly, but since the direction of change were the same in all, we argue that the pattern of change does merit consideration. Conspicuous exceptions were eicosapentaenoic acid (EPA) 20:5n-3 and docosahexaenoic acid (DHA) 22:6n-3, which both decreased significantly. The only other study (to our knowledge) of metabolomic effects of environmental changes in copepods showed the exact same response to starvation in a mix of C. finmarchicus and C. helgolandicus stage CV copepodites, with most fatty acids increasing while EPA and DHA decreased in concentration57. EPA and DHA are key marine polyunsaturated fatty acids (PUFAs) exclusively produced by marine algae. They contribute a major fraction of the fatty acids of cell membrane phospholipids58, and zooplankton reproductive production is highly dependent on especially EPA59. EPA and DHA are key for cell membrane fluidity, which for calanoid copepods is especially important during diapause in the deep during copepodite stage CV60. They have also been linked to diapause buoyancy control, and are selectively metabolized in diapausing copepodites61. The importance of EPA and DHA for cell membrane integrity may be central for the changes we observed. Glycerol-3-phosphate, the precursor for the glycerol backbone of cell membrane phospholipids also decreased significantly and it seems decreasing pH could affect cell membrane turnover.Changing fatty acid concentration could be due to either a change in lipid intake from feeding or increased fatty acid catabolism. While ingestion rates decreased in stage CIV, they were unchanged in stage CV with decreasing pH20. Also, Thalassiosira weissflogii (Grunow) G.Fryxell & Hasle, 1977, the diatom we fed to the copepods, is rich in 16:0, 16:1n-7 and EPA59. The concentrations of 16:0 and 16:1n-7 increased, whereas EPA concentration decreased. If fatty acid concentrations reflected feeding, we would have seen increased concentrations of all three. We therefore believe that the general increases in concentrations of free fatty acids were caused by increasing catabolism of the wax esters stored in stage CV. It may be that due to the metabolic reconfiguration to enter hibernation, stage CV copepodites are already committed to the catabolism of fatty acids through beta-oxidation, and stored wax esters are being hydrolysed to increase the availability of free fatty acids for energy production. Mayor and colleagues57 arrived at the same conclusion. We hypothesise that stress due to low pH increases the organism’s energetic demands, but carbohydrates are not used to accommodate these demands due to the down-regulation of the glycolysis, rather demands are met by hydrolysing and metabolising wax esters in stage CV. The further ramifications of future OA could therefore be a less efficient build-up of wax esters so important for hibernation in this species.Finally, besides their importance for cell membrane fluidity, EPA and DHA are important precursors for eicosanoid endocrine hormones. These hormones are important regulators of, among other processes, ion flux62. As mentioned above, acid base regulation is coupled to osmoregulation in crustaceans42, and the decrease in concentrations of these two specific fatty acids, when all other fatty acid concentrations increased might represent an indication for changing endocrine hormone production to counter adverse whole-organism effects of OA.Changes in metabolite concentrations cannot be directly translated into changes in the rate of the processes they are involved in. However, they do pin-point processes which are affected by the imposed environmental changes. Also, in our analyses we targeted a limited range of molecules. In that respect OA could inflict changes in other important metabolic pathways we did not investigate. The absence of specific biochemical pathways in our analyses and discussion should therefore not be taken as indication that these are not implicated in this species responses to OA.From our previously published study on copepodites from the same incubations, we know that high pCO2/low pH conditions have detrimental effects on the balance between energy input (ingestion) and energy expenditure (metabolism) in stage CIV copepodites but not in stage CV copepodites20. The effects we report here help in this sense to shed light on the metabolic origin of the rather severe effects on energy balance we observed in stage CIV copepodites and the difference in response between stage CIV and CV20. 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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