Estimating growth, loss and potential carbon sequestration of farmed kelp: a case study of Saccharina latissima at Strangford Lough, Northern Ireland

ABSTRACT Many governments are evaluating marine carbon sequestration processes for their capacity to mitigate the adverse impacts of climate change. This includes the cultivation of macroalgae to sequester carbon dioxide from the atmosphere, which requires accurate estimates from the field. This study estimated the potential rates of carbon sequestration of cultivated macroalgae by quantifying the amount of biomass released into the environment from a kelp, Saccharina latissima, farm in Strangford Lough, Northern Ireland (54.4° N, 5.58° W). We estimated that a mean of 41% of net primary productivity (NPP) of the cultivated kelp was lost prior to harvest following blade fall-off, equivalent to a mean of 7.4 kg of carbon sequestered per 100 m longline at the site during the cultivation period. Coarse estimates requiring verification predicted that a further 43.2% of NPP may have been lost through chronic erosion and exudation of organic carbon. This rate of sequestration is similar to that of several government-funded agroforestry schemes. There is potential, therefore, that this quantified ecosystem service could be subsidized to incentivize the sustainable development of the macroalgae industry. These findings are essential for those promoting the sustainable development of the macroalgae cultivation industry and are highly relevant for implementation of UN Sustainable Development Goal 13 (Climate action) and Goal 14 (Life below water: “Conserve and sustainably use the oceans, seas and marine resources for sustainable development”).


Introduction
Given the urgent need to limit global greenhouse gas (GHG) emissions, many governments are now reevaluating proprietary carbon sinks, with a novel focus on aquatic plants and macroalgae (Gundersen et al., 2010;Jiao et al., 2018;Muraoka, 2004;Sondak & Chung, 2015). In the last two decades, and particularly since the publication of the UN report, "Blue Carbon: A Rapid Response Assessment" (Nellemann et al., 2009), attempts to quantify CO 2 sequestration by marine macrophytes have increased. This report introduced the concept of "Blue Carbon" and highlighted its importance by estimating that marine macrophytes perform at least 50% and up to 70% of carbon sequestration in ocean sediments.
Macroalgae, particularly the Phaeophyceae (brown algae including kelp), have very high rates of primary productivity, although this varies according to the temperature and other environmental conditions (Mann, 1973;Smale et al., 2020). Cultivated macroalgae absorb large amounts of inorganic carbon in the water column for photosynthesis, which subsequently reduces the partial pressure of CO 2 in the water (Jiang, Fang, Mao, Han, & Wang, 2013;Lin et al., 2019). This increases the gas transfer velocity of atmospheric CO 2 across the air-sea boundary layer into the ocean relative to adjacent sites without macroalgae present (Delille, Borges, & Delille, 2009;Jiang et al., 2015;Zhang et al., 2012). The magnitude of this increase will depend heavily, however, on airsea equilibration timescales and the residence time of CO 2 -depleted seawater in the surface mixed layer (Bach et al., 2021;Jones, Ito, Takano, & Hsu, 2014). It is for this reason that efforts are being made to test cultivated macroalgae as a measure to offset carbon emissions at global and national scales (e.g., Oceans 2050Foundation, 2019). Much consideration has been given to the possibility that macroalgae can be grown for "carbon credits", which businesses or institutions may purchase to offset their carbon emissions (Collins, Mediboyina, Cerca, Vance, & Murphy, 2022;Hurd et al., 2022). The 26th Conference of Parties of the United Nations Framework Convention on Climate Change endorsed the voluntary carbon credit market by permitting parties to purchase carbon offsets to achieve carbon neutrality. This provokes concern that the nascent field of carbon sequestration by macroalgae will be prematurely capitalized upon by opportunistic carbon credit trading schemes and mechanisms. This risks carbon storage being recorded inappropriately, permitting the emission of CO 2 elsewhere, and resulting in a net increase in carbon emissions. A less risky approach to reward and incentivize carbon sequestration by macroalgae may be by providing government subsidies for the expansion of commercial macroalgal farms. Such incentivized farms would be planted with the specific aim of carbon sequestration or carbon trading which would require a thorough life-cycle-type assessment (Collins et al., 2022;Hurd et al., 2022).
Thus far, the majority of studies that have investigated the potential of macroalgae farms as carbon sinks have focused on the "removable" carbon, that is the carbon in biomass harvested from the farm (Turan & Neori, 2007;Chung, Beardall, Mehta, Sahoo, & Stojkovic, 2011;Jiao et al., 2018;Tang, Zhang, & Fang, 2011;Zhang et al., 2017). The macroalgal carbon removed during harvesting, however, will probably return to the atmosphere through respiration and in waste streams. Life cycle assessments of macroalgal cultivation, refinery and usage of products indicate that for every dry ton of macroalgae cultivated, there is an overall sequestration of 0.13 tons of atmospheric CO 2 over a 100-year period (Seghetta, Marchi, Thomsen, Bjerre, & Bastianoni, 2016). Alternatively, comparative studies have been conducted that compared the sediment beneath intensive macroalgal cultivation zones to control sites (Juanjuan, Jihong, Jeffrey, & Fan, 2019;Pan et al., 2019;Ren et al., 2014). It is important to note, however, that this approach may underestimate carbon sequestration, as macroalgal detritus is known to travel across community boundaries for kilometres over the space of several days (e.g., Dierssen, Zimmerman, Drake, & Burdige, 2009;Filbee-Dexter & Scheibling, 2012Filbee-Dexter, Wernberg, Norderhaug, Ramirez-Llodra, & Pedersen, 2018;Queirós et al., 2019). For this reason, localized assessments of the sediments beneath the site of photosynthetic capture of CO 2 may not be the most effective measure of carbon sequestration. A recent simulation of the dispersal and deposition of particulate organic matter from cultivated Saccharina latissima (Linnaeus) in Norway predicted that organic matter may be transported and deposited hundreds to a thousand metres away from the release site, dependent on the sinking rates, time of release and the location of cultivation (Broch, Hancke, & Ellingsen, 2022).
Assessing carbon sequestration by cultivated macroalgae through local sediment samples may also lead to underestimation because it does not account for the carbon stored in the water column as recalcitrant dissolved organic carbon (RDOC). Carbon may be released from macroalgae as dissolved organic matter or carbon (DOM/DOC) through processes of erosion and exudation or particulate organic matter or carbon (POM/POC) because whole individuals fall away from the cultivation platforms by the holdfast or lower parts of the tissue break off before they are harvested (Fieler et al., 2021). The distinction among DOC, POC and POM is useful for calculation purposes, but in reality, released macroalgal organic carbon occupies a molecular-size continuum (Jiao et al., 2010). When DOC is released from macroalgae, it may be converted to recalcitrant DOC (RDOC) by bacterial activity. This means it is very stable and increases the likelihood of this carbon being stored in deeper waters. Macroalgal carbon storage as refractory inert organic carbon in the water column is an overlooked but appropriate method of carbon sequestration, as DOC represents ~70% of all organic carbon in the ocean, and the majority of this is at depths greater than 1000 m with an average age of 4000-6000 years (Santos et al., 2021). For this reason, we recommend considering the carbon released from cultivated macroalgae in estimates of carbon sequestration.
There is currently a lack of quantitative data characterizing the loss of biomass from cultivated macroalgae, particularly in the NE Atlantic region. Research on the environmental impacts of macroalgal cultivation has been dominated by several Asian-Pacific countries, which make up the vast majority of global production , but see Walls, Kennedy, Edwards, & Johnson, 2017Visch, Kononets, Hall, Nylund, & Pavia, 2020). Carbon loss from a Saccharina japonica farm in China has been estimated as >60% of gross biomass production (Zhang et al., 2012). More recently, seafloor investigations under the KELPPRO (2017-2020) project in Norway showed that annually 8-13% of the harvested S. latissima (Lane, Mayes, Druehl, & Saunders, 2006) biomass is released to the environment from the cultivation site, equivalent to 630-880 kg C ha -1 yr -1 (63-88 g C m -2 yr -1 ). This loss increases to 49.4% of the harvested biomass if the harvest is conducted in August (Fieler et al., 2021). The subsequent fate of these different forms of carbon released to the environment remains understood poorly (Dolliver & O'Connor, 2022;Troell, Henriksson, Buschmann, Chopin, & Quahe, 2022). More accurate predictions of the expected loss of biomass from cultivated macroalgae are also needed to efficiently grow the required harvest to meet market demand. The aim of this study was to (1) quantify the growth of sugar kelp, S. latissima, on a kelp farm in the NE Atlantic using a typical longline cultivation method; (2) quantify the proportion of net primary productivity (NPP) lost from the harvest and released to the environment through processes of erosion, exudation and dislodgement of entire individuals during kelp cultivation periods and (3) estimate the carbon sink that this released biomass represents. Robust estimates, such as these, are required to quantify the current contribution of cultivated macroalgae to the carbon sink and to build accurate predictive models as this sector expands rapidly. The focus of this study was on the kelp growth and loss, and as such, an assessment of the carbon emissions associated with cultivation in this experiment is not currently included.
Definitions of carbon sequestration vary according to different opinions on the necessary retention time of carbon to be considered as a "sink" (Herzog, Caldeira, & Reilly, 2003;Marland, Fruit, & Sedjo, 2001;Olson, Al-Kaisi, Lal, & Lowery, 2014). Here we consider carbon sequestration as the effective removal of atmospheric carbon dioxide with little risk of it being re-released for >100 years (

Study site
To quantify the amount of NPP released to the environment during two cultivation periods of S. latissima, data were analysed which were collected as part of the SeaGas project (BBSRC: SeaGas) at an experimental kelp farm at Queen's University Belfast Marine Laboratory, Portaferry. S. latissima is a subtidal phaeophyte (kelp) with a large undivided blade and a rubbery texture. It attaches to the benthos or cultivation infrastructure using a holdfast and stipe. The cultivation site is located within the semi-enclosed, fully saline Strangford Lough, Co. Down, Northern Ireland (54.4° N, 5.58° W; Fig. 1). The Lough is approximately 130 km 2 in size, 31 km in length and 4-7 km wide and is connected to the Irish Sea via the Strangford Narrows (Boyd, 1973). The farm site is over waters 2-11 m deep off the southern shore and is relatively sheltered with an average current speed of 0.3 m s -1 which runs predominantly west to east (Mooney-McAuley, Edwards, Champenois, & Gorman, 2016). The SeaGas project was designed to optimize the cultivation methods of macroalgae for use as a feedstock for biogas generation through anaerobic digestion; thus, the aim of the production method was to enhance biomass production during the optimal growth period.

Sporophyte growth (hatchery cultivation)
Reproductive material was collected from a local shore or crossed in the laboratory from previously cultured strains. Reproductive sori were stress-induced to release zoospores which were grown to gametophytes. Gametophytes developed for 3-5 months and were then sprayed onto the culture twine which was wrapped around plastic racks (collectors). These collectors were further cultivated for 4-6 weeks until the sporophytes attached were sufficiently mature to survive deployment at sea and when weather conditions were deemed suitable.

Longline deployment at sea
Longlines (100 m) were deployed into the adjacent Strangford Lough, which consisted of header ropes buoyed at about 0.5 m-1 m beneath the surface of the water, attached to anchor blocks at each side. The twine with attached juvenile sporophytes was wound around the header rope during deployment. The first cultivation period spanned 6 months from January 2016 to June 2016, for which 12 longlines were deployed. The second cultivation period spanned 11 months from October 2016 to September 2017, for which 21 longlines were deployed. Data from both cultivation periods were compared by standardized "days of cultivation", although growth conditions varied considerably with season.

Sampling to quantify algal production
The growth and blade morphology of the cultivated S. latissima were monitored throughout each cultivation period. Five replicated samples of 30 cm culture line were selected randomly from each of the deployed 100 m longlines each month during the growing period. In the first cultivation period, six longlines were sampled, and in the second cultivation period, four longlines were sampled. Randomly selected 30 cm samples, which had previously been sampled, were excluded (to ensure independent data collection). All biomass within each 30 cm sample was removed, and the number of individuals present was counted. The 12 largest individuals from each 30-cm sample were selected for measurement because these generally formed the majority of the biomass. The remainder of the biomass from each of the 30-cm sample was weighed. The maximum length and width of individual blades, blade wet and dry biomass and stipe length were all measured. At the end of each cultivation period, all the biomass was removed from the longlines and weighed. Throughout the two cultivation periods, environmental conditions of light intensity, nutrient concentrations (nitrate, nitrite, and phosphate) and water surface temperature were recorded at the experimental site.

Data analysis
The organic carbon released from the macroalgal farm was assumed to be a combination of blade fall-off and loss of carbon through erosion and exudation. Blade fall-off was measured directly; however, loss of organic carbon through erosion and exudation was estimated using blade area and published rates of erosion and exudation from the same species in the same temperate climatic zone. Therefore, the estimates of carbon released through exudation and erosion are presented with caution and will require further experimental manipulation to be verified.
The net growth rate of individual sporophytes was obtained by applying the formula: Net growth rate in weight g day À 1 À Where M f and M i represent the wet biomass of the sporophyte at the present time of measurement T f and at the last time of measurement T i , respectively. The number of blades lost per sampling interval was determined by comparing the blade density between sampling dates. The biomass and carbon content of the blades lost were calculated based on the mean size of the blades between the sampling dates and using the published ratio of 0.18 g of carbon per 1 g of dry structural biomass in S. latissima (Broch & Slagstad, 2012). The amount of carbon in blades lost for the entire cultivation period was the sum of the blades lost across each sampling interval. Release of organic carbon, either through erosion or exudation, was estimated following methods described by Broch & Slagstad (2012), who estimated the productivity, growth and nutrient contents of S. latissima. More recent models exist, which describe the energy and growth of S. latissima; however, these do not detail the carbon contents nor the amount of biomass lost through erosion or exudation (e.g. Vondolia, Chen, Armstrong, & Norling, 2020). For each sampling interval lasting approximately 30 days, the amount of organic carbon released through erosion and exudation was estimated. These values were summed to describe the overall cultivation periods. As erosion and exudation are modelled values, these results should be interpreted with discretion. The release of organic carbon from macroalgae, either through erosion or exudation, varies considerably depending on the nutrient availability and temperature (Xu et al., 2021), and DOC exudation is also reported to increase under conditions of desiccation, excess irradiance, high or low salinity and elevated dissolved carbon dioxide (CO 2 ) concentrations (Paine, Schmid, Boyd, Diaz-Pulido, & Hurd, 2021).
The frond of S. latissima is constantly being eroded at the apex, and erosion increases with increased tissue age and water motion (Fieler et al., 2021;Pedersen et al., 2020;Sjøtun, 1993). The model for erosion applied to the data was in terms of blade area lost, which was subsequently converted to wet and dry biomass using scaling relationships from the data and to carbon using the ratio of 0.18 g of carbon per 1 g of dry structural biomass (Broch & Slagstad, 2012). Erosion was estimated as v A ð Þ ¼ 10 À 6 exp εA ð Þ 1 þ 10 À 6 exp εA ð Þ À 1 ð Þ ð Þ

� �
Where ε is the frond erosion parameter. A model was built using scaled digitized herbaria samples from the "Macroalgal Digitization Project" (Macroalgal Digitization Project, 2021) to describe frond area using length and width as inputs. One hundred and four specimens were analyzed using ImageJ for this purpose, and care was taken to ensure that representative specimens of varying maturity and diverse morphologies were included.
Similar to many other macroalgal species, the morphology of S. latissima is highly variable depending on the environmental conditions of its growth. Most specimens of S. latissima are much longer than they are wide, but occasional individuals are almost circular. Specimens also have varying degrees of ruffling along the lateral edges of the blades. Although this is not addressed here, it does increase the surface area of the blade in sheltered localities to provide a larger area for nutrient uptake (Sjøtun, 1993). This diversity of form was the reason that a model of generalized dimensions as described by Peteiro & Freire (2013) was not applied.
The model for exudation is in terms of carbon and describes both actively excreted compounds, such as laminarin and mannitol, and leaked carbohydrates (Becker et al., 2020;Sharma et al., 2018;Wada et al., 2007). Exudation was estimated as Where parameter γ controls the rate at which carbohydrates are exuded and is set to γ = 0.5, C min is the minimal reserve carbon pool and C is the total carbon in the kelp at the time (Broch & Slagstad, 2012).
Once the amount of carbon lost through break-off of whole blades (macroalgal detritus) or through erosion and exudation was determined, the carbon sink which this biomass represents was approximated according to estimates described in Krause-Jensen & Duarte (2016). The carbon lost (i.e., released to the environment) was compared to the carbon harvested at the end of the cultivation periods. The carbon entering the biological cycle through net primary production was assumed to be equal to the sum of carbon released to the environment and the carbon harvested.

Results
Daily growth rates initially increased linearly in both cultivation periods despite the different times of year (figure 2). The mean of individual daily growth rates across both cultivation periods ranged between −0.75 g and 7.54 g wet biomass day -1 . If erosion outstrips growth, then the growth rate will have a negative value. Growth rates plateaued during the late stages of the second cultivation period because the individuals reached their maximum size (300 g wet biomass and 313 cm blade length (Fig. 2).
In both growth trials, there was a logarithmic relationship between maximum blade length (cm) and wet biomass (g; Fig. 3). The mean amount of carbon harvested per 100 m longline across both cultivation periods was 9.5 kg, although this varied considerably between a minimum of 1 kg and a maximum of 19.9 kg.

Area relationship
Multiple linear regression with an interaction effect was the most suitable model to describe the relationship between the area of an S. latissima blade and the maximum length and maximum width of that same blade (R 2 = 0.97). Blade area was estimated as  Where ML represents maximum length and MW represents maximum width.

Blade fall-off
The density of individuals per 30 cm was highly variable and ranged from 3050 to 0 individuals across both cultivation periods. An initial high density of juveniles dropped over the course of both cultivation periods as a result of competition for space (Fig. 4). A mean of 41% of NPP was lost as blade fall-off per 100 m longline across both cultivation periods (Fig. 5). There was a positive linear relationship between NPP and the proportion of NPP lost to blade fall-off (R 2 = 0.78; Fig. 6). The most productive longline converted 360 kg of inorganic carbon to organic carbon over 291 days, and 62% of this was lost to blade falloff. The minimum amount of NPP lost as fall-off per longline was 24%. There was a logarithmic relationship between the amount of carbon lost through blade fall-off and the amount of carbon harvested across both cultivation periods (R 2 = 0.75). The least productive longlines lost approximately the same amount of carbon to fall-off as the amount of carbon harvested (Fig. 5).

Exudation
The estimated mean loss of NPP through exudation of organic carbon per longline, across both cultivation periods, was 43% and varied from 33% to 58% (Fig. 5). There was a positive linear relationship between the amount of carbon released to the environment through exudation and the amount of carbon harvested (R 2 = 0.80). There seemed to be a negative relationship between productivity and proportional exudation (Fig. 6) although more replicates across a greater and more even range of productivities would be required to investigate this further. There was a strong positive relationship between the daily growth rate and the daily carbon exudation rate of individual blades (Fig. 7).

Erosion
Across both cultivation periods, the amount of carbon which was lost through erosion was lower by orders of magnitude in comparison to the amount lost through

Discussion
Our results show that the longlines of cultivated kelp which were relatively the most productive during the cultivation period also released macroalgal carbon to the environment predominantly through blade fall-off. This is in contrast to the findings of a previous study of S. japonica in China (Zhang et al., 2012), which described blade fall-off as a relatively unimportant process, only contributing to the loss of 4% of gross production at their cultivation site. This high blade fall-off may be attributable to the fact that S. latissima is a coldwater species, which has reduced tissue strength when exposed to 14°C for 3 weeks (Simonson, Scheibling, & Metaxas, 2015). Temperatures were recorded in four locations every 10 minutes throughout this study and rose above 14°C by May in both 2016 and 2017, with the highest temperature recorded during the study period reaching 25.5°C. Our findings show that the less productive longlines appeared to lose carbon predominantly through exudation, which is in line with the estimated rates of DOC exudation from wild macroalgae populations (Broch & Slagstad, 2012;Hatcher, Chapman, & Mann, 1977;Khailov & Burlakova, 1969;Wada et al., 2007). Given the caveats of the erosion and exudation modelling used in the current study, we recommend that future studies should implement direct measurements of erosion and exudation of organic matter using the hole punch method (Mann, 1972), welldesigned incubation experiments (e.g., Weigel & Pfister, 2020) or the use of some traceable reporter molecule (Wada & Hama, 2013;Watanabe et al., 2020). Excluding the estimates of erosion and exudation, the release of carbon from cultivated macroalgae to the environment was a considerable mean of 41% of NPP per 100 m longline.
The rates of erosion derived from the Broch & Slagstad (2012) model never exceeded 1% of NPP, and it is acknowledged that there are some limitations with this current model's erosion estimates. These calculated erosion rates were very low in comparison to previously reported rates of erosion in both cultivated and wild macroalgae (de Bettignies, Wernberg, Lavery, Vanderklift, & Mohring, 2013;Pedersen et al., 2020;Pessarrodona, Moore, Sayer, & Smale, 2018;Zhang et al., 2012). The model may have previously been adjusted against a population in which the majority of individuals were juvenile or showed few signs of erosion for other reasons, such as the absence of wave action, temperature stress or mechanical stress (Krumhansl, J-S, & Scheibling, 2014; Krumhansl & Scheibling, 2011). Additionally, recent work demonstrated that there is a significant difference in the length-to-dry weight relationship for different sections of the algal blade, meaning an areacarbon content relationship derived from the whole blade could bias the value of eroded carbon calculated using area (Fieler et al., 2021). Another study of a cultivated kelp, Undaria pinnatifida, in Japan estimated that erosion of DOC was 30-40% of biomass production in March and >80% of production in April (Yoshikawa, Takeuchi, & Furuya, 2001). In comparison, the greatest rate of erosion calculated for any of the lines sampled in the current study in either the first or second cultivation period was 0.8% of NPP.
Previously described methods to estimate macroalgal carbon sequestration (Krause-Jensen & Duarte, 2016) were applied to estimate the amount of released organic carbon from this cultivation site which could be considered sequestered. It is acknowledged that this simple method is based on a limited sample size and has documented limitations to its application (Gallagher, Shelamoff & Layton, 2022); however, in the context of the current study, it is sufficient to approximate possible carbon sequestration. With regards to blade fall-off, 4% of the carbon in the blades which fell from the rope can be considered sequestered in continental shelf sediments and 10% of this carbon can be considered sequestered in the deep sea (Krause-Jensen & Duarte, 2016). This corresponds to a mean of 2 kg of carbon buried in the continental shelf per longline and 5.4 kg buried in the deep sea per longline over one growth period at this experimental farm.
Local burial of detritus is rare in naturally occurring macroalgal forests (0.4% of primary productivity) because they attach to hard substratum (bedrock). Local burial may be more common in cultivated macroalgae systems, however, because they are often grown over sedimentary seafloors. At Strangford Lough, burial of detritus in underlying sediment is assumed to be zero because blades and detritus have been noted not to accumulate beneath the cultivation infrastructure, most likely because of the tidal currents in the area. In future studies, it would be valuable for macroalgal blades or artificial blade fragments to be marked at the cultivated site, released and tracked in order to determine where they may be deposited and whether they are subsequently buried beneath a depth of remineralization.
If we were to include the organic carbon released from macroalgae through erosion and exudation, approximately 33% can be considered sequestered because this carbon is exported below the mixed layer in the water column and removed from interaction with the atmosphere for thousands of years (Krause-Jensen & Duarte, 2016). In our study system, this would equate to a mean of 12 kg of organic carbon burial per 100 m kelp longline over one growth period. One experiment estimated the loss of DOC from the phaeophyte Sargassum horneri in Japan and determined the proportion released DOC which was recalcitrant in the water column (Watanabe et al., 2020). The net release of DOC from the S. horneri sampled was equivalent to 35% of net community productivity, 56% of which was recalcitrant, that is humic and not remineralized 150 days after release. In this example and others (e.g., Li et al., 2018;Weigel & Pfister, 2020;Zhang et al., 2017), it is clear that the DOC released from cultivated macroalgae should not be disregarded as a potential sequestration process.
This study explores how carbon sequestration, a key ecosystem service, provided by cultivated macroalgae may be monitored and assessed. In addition to the previously stated caveats, the amount of carbon lost through both exudation and erosion may be slightly overestimated as the mean blade size at any given time was derived from the 12 largest blades per destructive sample. Additionally, the method for estimating carbon burial and sequestration from different pools must be improved and adapted to local conditions by in situ empirical studies (Krumhansl & Scheibling, 2012). Despite these shortcomings, we recommend this approach over previous studies (e.g., Zhang et al., 2017), in which the carbon sink of national cultivated macroalgae is estimated based on published rates of exudation, erosion and the export of large detritus particles from naturally occurring macroalgal forests. Previous approaches may be inaccurate because the suspension of blades from a cultivation platform is physically distinct from the growth of blades up from holdfasts on the ocean floor. Blade dislodgement or loss in a mariculture system may be more common owing to the smaller area of attachment or the greater physical disturbance in the surface waters. A macroalgal farm is not entirely comparable to a naturally occurring macroalgae forest, which contains a mixture of species at different stages of maturity in a more heterogenous environment (Wood, Capuzzo, Kirby, Mooney-McAuley, & Kerrison, 2017). The direct measurement of the loss of carbon from a macroalgal farm in this study highlights the importance of empirically assessing ecosystem services instead of assuming them.
There is an argument to be made that macroalgae farmers should be compensated for facilitating carbon sequestration, for example as European farmers are subsidized for adopting climate-friendly farming practices (Alliance Environnement, E. E. I. G., The Thünen Institute and European Commission, 2017). With the development of the approach outlined in this study, a roadmap could be established for macroalgal farms operating commercially to estimate their potential carbon sequestration. It is reasonable and appropriate to compare the amount of estimated carbon sequestered in this case study to a typical agroforestry scheme, such as the Afforestation Scheme provided to landowners by the Irish Department of Agriculture, Food and the Marine from 2014 to 2020. Under this scheme, financial support of €6,220 is provided to establish a tree plantation on land being used for farming, and an annual premium of up to €680 ha −1 is paid. Under this scheme, for example, an established forest of 1 hectare planted with silver birch (Betula pendula Roth) would receive a premium of €575 ha −1 as a broadleaf plantation other than oak or beech. Under the terms of the scheme, the biomass may be harvested and combusted, releasing the carbon stored in above ground biomass (Department of Agriculture Food and the Marine, 2015). The amount of carbon sequestered in birch soil can be negligible over time (Friggens et al., 2020;Uri et al., 2012); thus, a generous estimation of the rate of carbon flux from young trees through plant litter is 1.2 t −1 ha −1 (Uri et al., 2012), assuming that this litter is buried and not remineralized. Thus, the landowner receives €575 in a year in exchange for the carbon sequestration of 1.2 tonnes of carbon. If 100 longlines of cultivated S. latissima such as those described in our study covering an area of 6 ha (spacing the 100 m longlines out by 6 m and including exudation and erosion) were deployed, they would capture nearly two tonnes of carbon each growing period. A recent study estimated the full life cycle cost and indicated that a model macroalgal farm in Ireland is economically achievable over 20 years but that income from the voluntary carbon offset market would be minimal, only 5% of the project's total revenue (Collins et al., 2022). Thus, the ecosystem service of macroalgal carbon sequestration may be best incentivized by rewarding pre-existing macroalgal farms or commercial farms as opposed to farms purpose-built to be carbon sinks, particularly at this early stage of research. A system may be designed in which a farmer either harvests their crop before the net growth rate plateaus or continues to let it grow in favour of increasing carbon sequestration and potential financial incentives.
As a note of caution, it should not be assumed that cultivated macroalgal installations are environmentally beneficial in all circumstances. The construction and maintenance of macroalgal cultivation infrastructure will create CO 2 emissions, as will the harvesting, processing and distribution of macroalgal products. For example, some large-scale cultivation sites that have been utilized continuously for many subsequent years are now depleted in nitrogen (Wang, Cao, Micheli, Naylor, & Fringer, 2018). The extent of large-scale cultivation may slow the supply of nutrients entering the upper layer of the cultivation area by weakening hydrodynamic forces (Li et al., 2017). This then requires fertilization or artificial upwelling interventions in order to continue cultivating macroalgae at the site, which negates the regulating ecosystem service that the installation might have previously provided. Additionally, there is a low but non-zero risk that cultivated macroalgae may interact with and disrupt the natural genetic structuring of wild populations . If macroalgae cultivation is to be intensified and expanded, then the environmental impacts must be carefully monitored. Although the industry has many associated ecosystem benefits, any form of large commercial activity risks negatively, affecting the natural habitat (Campbell et al., 2019). As cautioned by Gallagher et al. (2022), cultivated macroalgae will have a net carbon sequestration effect unless their introduction ecologically displaces a more efficient carbon sink community, such as phytoplankton, or if the emissions associated with deploying, maintaining or harvesting macroalgae are in excess of the net ecosystem productivity.
In conclusion, this study explores how the carbon sequestration ecosystem service provided by farmed macroalgae might be assessed and remunerated. Future studies should also quantify erosion and exudation directly and track displaced blades below the deployed cultivation platform to estimate detrital inputs directly (Ren et al., 2014). Subsidizing this ecosystem service in order to incentivize farmers and entrepreneurs to develop the macroalgae industry sustainably should be considered by government and regulatory agencies (Duarte, Bruhn, & Krause-Jensen, 2022;Mc Monagle & Morrison, 2020). Ashton, Brendan McNamara and Emma Gorman for their work on the SeaGas project. We also would like to thank the Macroalgae Digitization Project funded by the United States of America's National Science Foundation for making a wealth of macroalgal herbaria samples publicly available.

Authors' contributions
According to the CRediT scheme of accreditation, Dolliver contributed to Formal analysis, Software, Validation, Visualization and Writing the original draft. O'Connor contributed to Data curation, Investigation, Resources and Supervision. Both authors contributed to Conceptualization, Funding Acquisition, Methodology, Project Administration and Reviewing and Editing.

Code availability
R code used to generate figures is available upon request from the corresponding author.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
The SeaGas project was funded by Innovate UK for industrial partners (grant number 102298) and by UK Research and Innovation for academic partners (grant number BB/ M028690/1; BBSRC). This research was supported by the Trinity CollegeDublin Postgraduate Research Studentship.

Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.