Biophysical potential and uncertainties of global seaweed farming

International climate goals require over 5 gigatons/year (Gt/year) of CO2 to be removed from the atmosphere by midcentury. Macroalgae mariculture has been proposed as a strategy for such carbon dioxide removal (CDR). However, the global potential for seaweed cultivation has not been assessed in detail. Here, we develop and use a dynamic seaweed growth model, the Global MacroAlgae Cultivation MODeling System (G-MACMODS), to estimate potential yields of four different types of seaweed worldwide, and test the sensitivity of these estimates to uncertain biophysical parameters under two nutrient scenarios (one in which the surface ocean nutrient budget is unaltered by the presence of seaweed farms, and another in which seaweed harvest is limited by nutrients that are resupplied by vertical transport). We find that 1 Gt of seaweed carbon could be harvested in 0.8% of global exclusive economic zones (EEZs; equivalent to ∼1 million km2) if farms were located in the most productive areas, but potential harvest estimates are highly uncertain due to ill-constrained seaweed mortality and nitrogen exudation rates. Our results suggest that seaweed farming could produce climate-relevant quantities of biomass carbon and highlight key uncertainties to be resolved by future research. Recent analysis of global climate scenarios suggests that limiting warming to < 1.5◦ above pre-industrial levels will require 1 large reductions in CO2 emissions as well as the removal of 4-14 Gt-CO2/year by midcentury1, 2. The ocean operates as a 2 natural sink for CO2, having absorbed 26% of anthropogenic CO2 emitted in the last century3, 4. There is increasing interest in 3 enhancing ocean carbon dioxide removal (CDR) through seaweed farming where surface carbon, fixed in seaweed biomass, is 4 sunk and sequestered in the deep ocean5–7. In contrast to terrestrial biomass, seaweed farming does not require arable land 5 or freshwater. Moreover, farmed seaweed may be used for biofuel production8–10, animal feed11, 12, and bioremediation13–16, 6 while also providing ecosystem services17. Annual production of seaweed increased by an average of 50% between 2010 and 7 2015, with 3.2 Mt of dry weight (∼1 MtC) harvested globally in 201818. Although most farming today occurs in coastal areas 8 of China and Indonesia, technology to farm offshore is quickly evolving19–23. 9 10 Previous assessments of the global potential of farmed seaweed to remove carbon, though noteworthy, have generally extrapo11 lated from observed yields in high-nutrient regions5–7, 15, 24 or average global productivity of wild seaweeds25, disregarding 12 spatial variations in hydrodynamics, nutrient fluxes, and parameter uncertainty. Meanwhile, dynamic models of seaweed growth 13 under nutrient and other environmental limitations26–30 have often focused on relatively small (< 500 km2) coastal areas and 14 have not examined the levels of intensive nutrient uptake required to produce biomass at scales relevant to the global carbon 15 budget (e.g., > 1 GtC). A recent global study provides improved estimates of seaweed cultivation and carbon sequestration 16 potential31, but it is limited to one seaweed group and does not elaborate on uncertainties. Here we develop and use a global 17 dynamic model of seaweed growth, the Global MacroAlgae Cultivation MODelling System (G-MACMODS), to analyze the 18 potential of seaweed farming to produce Gt-scale biomass carbon under the assumptions of bottom-up limitation mechanisms. 19 We focus on the cultivation of four seaweed types and systematically test the sensitivity of seaweed production to a range of 20 uncertain biophysical parameters. 21 22 Details of G-MACMODS, data sources, and analytical methods are in Methods. In summary, the model32(Supplementary 23 Fig. 1) predicts spatially-resolved (1/12th◦ resolution) seaweed cultivation with constraints from both extrinsic (environmental 24 This is a non-peer reviewed preprint submitted to EarthArXiv. forcing) and intrinsic factors (biological parameters; e.g., growth rates, nutrient uptake and storage, exudation, and mortality, 25 among others). To test sensitivities and evaluate uncertainties, we performed ∼ 800 simulations of global growth and harvest for 26 four seaweed types (using biophysical characteristics based on currently-farmed temperate and tropical red and brown genera). 27 Each simulation sampled from a uniform distribution of parameter values spanning the full range of relevant values reported in 28 the literature (Table 1), and was forced with temperature, solar irradiance, current velocities, wave height, wave period, and 29 nutrient data sourced from a combination of satellite measurements (MODIS) and global ocean model simulations (HYCOM 30 and CESM). Although we tested the model with forcing data from different years, results reported here reflect the year 2017 (a 31 recent year without strong El Niño/La Niña anomalies; Supplementary Figs. 2-3), and a seasonally-variant climatology of 32 nutrient inputs (Supplementary Fig. 4). Simulations that use parameter values best supported by literature are termed "standard 33 runs." Seeding and harvesting for each seaweed type were optimized based on the standard runs. We also assess the importance 34 of different model parameters via Monte Carlo methods and “random forest” classification analysis. 35 36 G-MACMODS assumes nitrogen is the limiting nutrient (i.e. implying that micronutrient constraints could be overcome by 37 farming practices). The 800 simulations of each seaweed type were split between two bounding nutrient scenarios: (1) an 38 "ambient nutrient" case in which average nitrate concentrations within the top 20 m are available to seaweed without depletion 39 or competition, and (2) a "flux-limited" case where only the mass of nitrate replenished through vertical flux across 100-m 40 depth is available to seaweed. The ambient scenario, while unrealistically optimistic for intensive production on a global 41 scale without artificial upwelling, is illustrative of farming at a scale that does not generate substantial feedback modifying 42 regional nutrient budgets. In contrast, the flux-limited scenario may better reflect nutrients in a situation of dense farming or 43 nutrient competition from phytoplankton31, 33. However, both are idealized scenarios because the “offline” implementation of 44 G-MACMODS cannot explicitly account for feedback to nutrient cycling; the different scenarios are intended to help gauge the 45 sensitivity of seaweed production to nutrient constraints. Our analysis focuses on offshore production, as competing uses and 46 poor resolution of coastal nutrient inputs limit model fidelity in the nearshore. The purpose of this work is not to advocate for 47 the widespread deployment of seaweed farms over a significant fraction of the global oceans, as we expect this would come 48 with unacceptable trade-offs to ocean health, but rather to assess the geographic distribution and potential of offshore seaweed 49 farming to produce biomass at climate-relevant scales. 50 51 Global Seaweed Yields 52 Maps in Figure 1 show the magnitude and types of seaweed harvested in our standard simulations of the ambient and flux-limited 53 nutrient scenarios (where the seaweed type that produces the largest harvest in each grid cell is farmed). Seaweed could be 54 harvested over large areas of the ocean (208 million km2 and 132 million km2 in the ambient and flux-limited runs, respectively; 55 cf. 6, 31); however, yields vary substantially in space, and annual harvests are vastly different in the two nutrient scenarios. The 56 most productive locations include the equatorial Pacific and upwelling regions (e.g., along coasts or near energetic western 57 boundary currents). Almost no seaweed is harvested in either nutrient scenario in the oligotrophic regimes characteristic of the 58 center of the subtropical oceanic gyres (Figs. 1b and 1c). 59 60 Although G-MACMODS does not dynamically represent the interaction between farmed seaweed and phytoplankton, we 61 compare the modeled rates of carbon fixation by seaweed (seaweed net primary productivity (NPP)) with phytoplankton NPP 62 estimated from satellite ocean-color observations34 (Fig. 1a and Figure 1d). While phytoplankton NPP includes a significant 63 component fueled by recycled nutrients in the euphotic zone, it represents an upper bound on new production or, similarly, 64 net community production (NCP; typically, ∼ 10-20 % of phytoplankton NPP35). Seaweed have average carbon-to-nitrogen 65 ratios (C:N) of ∼ 20:1 in temperate regions36, 37 and ∼ 40:1 in tropical regions38–40, which are much higher than the ∼ 6.6:1 66 (Redfield ratio) typical of phytoplankton. For the same amount of nitrogen, therefore, seaweed can fix 3-6 times as much carbon. 67 However, in our ambient nutrient simulations, seaweed NPP is 7 and 14 times larger than observed phytoplankton NPP (∼ 35 68 and 70 times larger than phytoplankton NCP) near the temperate and tropical regions, respectively, implying that the modeled 69 seaweed growth consumes more than 10 times the nitrogen that is taken up by phytoplankton NCP (Fig. 1a). This suggests that 70 the ambient nutrient case does not provide a sound basis for estimating potential productivity of widespread, intensive farming 71 in the absence of artificial upwelling, but it might provide a reasonable estimate of the potential harvests of operations small 72 enough in scale so as to not radically alter local nutrient budgets. Indeed, the yields simulated in the ambient nutrient scenario 73 results agree well with harvest values reported in the literature for many small farms and a few large farms situated near nutrient 74 outflows (Supplementary Figs. 5-8). In contrast, zonally-averaged seaweed NPP is less than observed phytoplankton NPP in 75 our flux-limited simulations, except in equatorial regions where phytoplankton growth is iron-limited41, 42 (Fig. 1d), consistent 76 with our NCP constraint. The lower harvests estimated in the flux-limited scenario may therefore better reflect production 77 when farming at scales large enough to significantly deplete the surface fixed-nitrogen inventory, relying on the influx of "new" 78

primarily consider nearshore farms, may have limited applicability to mortality on open ocean farms. Like mortality, nitrogen 157 exudation by seaweeds is understudied, despite its importance in modeling productivity in nutrient-limited waters. Nitrogen 158 exudation rates between 0.002/day 36 and 0.2/day 51 have been reported. We assume a constant rate of nitrogen exudation 159 (0.05/day in the standard simulations), but the rate is likely to fluctuate in time with environmental conditions [52][53][54] and ratios of 160 nutrients in the seaweed (as observed for carbon exudation) [54][55][56][57] . Although not represented in our model, exudation rates may 161 be related to seaweed growth rates 51 , and mortality rates 58 . Maximum growth rate, maximum uptake rate, and half saturation 162 constant also affect estimated harvests to varying but lesser degrees (Fig. 3). Maximum growth rate cannot be easily parsed 163 from observations of relative growth rate, and existing maximum uptake rate and half saturation constants may not have been 164 estimated using standardize environmental conditions. Our results thus highlight the importance of further research to narrow 165 uncertainties related to mortality and exudation rates under real-world conditions expected during cultivation and thereby 166 narrow the uncertainty bounds around our harvest estimates.  in G-MACMODS. Though we recognize that other macronutrients and micronutrients could further limit our results in, for 185 example, high-nitrogen low chlorophyll environments 42 , we assume that the aquaculture industry has implemented micronutri-186 ent fertilization. G-MACMODS estimates seaweed biomass in units of dry weight; biomass is converted to units of carbon 187 by assuming that carbon constitutes 30% of the seaweed dry weight for all seaweed groups 65, 66 , though carbon content may 188 actually be lower for tropical red seaweed 39 .  Model structure 194 Temporal changes in the state variables (B and Q) can be described with the following equations: and where V is the nitrogen uptake rate [µmol-N/(g-DW h)], E is a fractional exudation rate (1/day), µ is the fractional growth rate 197 (1/day), and d M is the fractional death rate (1/day).

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This is a non-peer reviewed preprint submitted to EarthArXiv.
Nitrogen Uptake 199 The rate of nitrogen uptake by seaweed is determined by extrinsic (environmental) and intrinsic(biological) limiting factors: where V max is the maximum uptake rate (Table 1), f (Q) represents a dynamic nutrient cell quota which allows for luxury uptake 201 of nutrients, and f (|⃗ v|, T w ,C) represents both kinetic and mass-transfer limitations on nitrogen uptake. We use a linear nutrient 202 cell quota 32 : where Q min is the minimum amount of nitrogen that should be found in a seaweed cell (structural nitrogen), Q max is the 204 maximum amount of nitrogen stored internally, such that uptake decreases as the internal nitrogen concentration increases, 205 and f (Q) is a unitless coefficient between 0 and 1. The parameter f (|⃗ v|, T w ,C) in equation (3) is a limit on uptake based on a 206 combination of Michaelis-Menten kinetics and mass-transfer limitation regulated by the surrounding waves and currents 67-69 : where (Table 1), C is the external concentration of nitrogen, with units of m/s. In equation (6), D is the molecular diffusivity of nitrate at 18 • C (7.3 × 10 −10 m 2 /s) 32,70 , T w is wave 210 period, and δ D is the thickness of the diffusive boundary layer, defined using the thickness of the viscous boundary layer where ν is the molecular kinematic viscosity (10 −6 m 2 /s) and C D is the drag coefficient 69 (Table   212   1). The parameter f (|⃗ v|, T w ,C) is unitless and varies between 0 and 1. Note that this nitrogen uptake model assumes that (a) 213 the diffusion boundary layer is completely stripped away every half a wave period, regardless of the size of the wave, (b) the 214 thickness of the diffusive boundary layer (δ D ) can be parameterized with the thickness of the viscous boundary layer (δ ν ), and 215 (c) that we can ignore near-boundary turbulent transport (i.e. assume the blade is smooth) 69 , though this has been shown to 216 enhance exchange rates 71 . We do not consider within-canopy flow reduction, which negatively affects uptake 32 N new -at the annual maximum mixed-layer depth at each grid cell -but resulting productivity differences were relatively small 229 compared to other uncertainties presented in the Uncertainty Analysis section (median increase of 5% in the annual harvest 230 yield).
where µg(k) (1/day) is the maximum growth rate at a given seaweed density, accounting for the crowding effects of self-shading 234 and within-farm (sub-gridscale) nutrient limitation. The maximum growth rate is further constrained by the internal nitrogen 235 cell quota g(Q), water temperature g(T ), and light g(E), all of which are unitless coefficients, varying between 0 and 1.

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The growth rate limitation imposed by crowding in the seaweed canopy embodies the general idea that less-dense seaweed can 238 grow faster, described as where A [(1/d)/(g-DW/m)] is a factor that represents the growth rate at the maximum allowable biomass density. Strictly defined,   (Table   247 1), such that µg(k) → µ max as B → B seed , where B seed is the seed weight.

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The nitrogen quota limitation g(Q) in equation (7) follows the Droop model 64 : where Q min is set per species type ( Table 1). The temperature limitation term in Equation (7) is similar to a Gaussian probability 251 curve 75 : where T opt is a 5 • optimal temperature range for each seaweed group that we are examining, T is the daily temperature, and the 253 β 1 and β 2 coefficients are adjusted to reach zero near the lower and upper temperature limits, respectively.

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The light-limitation in equation (7) is largely informed by phytoplankton studies 76 : where I s and I c are the daily-averaged saturating and compensating irradiance (W/m 2 ), f is the fraction of daylight that is 257 implemented to account for periods of darkness, and I is the irradiance reaching an underwater depth of 2 m. The irradiance is 258 attenuated following the implementation in the Marine Biogeochemistry Library (MRBL) 77, 78 .

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The mortality rate, d M in equation (2), is the sum of a constant daily mortality rate that is meant to incorporate grazing, aging, 261 and disease (d; Table 1) and a term that accounts for breakage from waves (d w ), such that d M = d + d w . The d w term is 262 dependent on wave power and, as such, is variable in both time and space 79 : where ρ is the density, H s is the significant wave height, and T w is the wave period.

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Environmental data 266 The environmental inputs applied to our model (water temperature, solar irradiance, current velocities, wave height, wave period, year with available data that is also not identified with having a strong ENSO index. Input data from 2003-2019 were using in 270 simulations examining inter-annual differences in estimated seaweed productivity ( Supplementary Fig. 10), however, regional 271 inter-annual variability was comparatively small with respect to parameter uncertainty and is therefore not the focus of this study.  Although G-MACMODS steps forward with a daily time step, we apply the 8-day environmental inputs that best correspond to 298 the G-MACMODS time stamp. All environmental inputs were spatially interpolated onto a 1/12 • global grid, using linear 299 interpolation if the input data were of higher resolution, or nearest-neighbor if the input data were of lower resolution.

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Seaweed groups 301 Here, we focus on four seaweed groups containing seaweed species that are among the world's ten most cultivated by weight 86  representative genera ( Table 2). The optimal temperature range in equation 6 is extended to a 5 • width, rather than a single 308 number, to account for variations within a seaweed genus.

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The standard runs were spun up for one year, and the seeding was optimized by choosing the run initialization date that with an initial nitrogen cell quota (Q 0 ), such that where N/35 is the ratio of the ambient nitrogen concentration at the time of seeding to the a representative N concentration 316 below the nutricline (35 µM).

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To test our choice of standard parameters (Table 1)   Temperate brown seaweeds were allowed to grow without consideration for harvest for at least 60 days after seeding. Consid-345 ering the above factors, the harvesting schemes that produced the highest harvested yields for each seaweed group are as follows:                           Values reported in fresh weight were converted to dry weight by assuming a dry-to-wet biomass ratio of 1:10. Pink triangles indicate the mean harvest value in the literature articles referenced above. Values reported in fresh weight were converted to dry weight by assuming a dry-to-wet biomass ratio of 1:10.

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This is a non-peer reviewed preprint submitted to EarthArXiv. Values reported in fresh weight were converted to dry weight by assuming a dry-to-wet biomass ratio of 1:10.