معرفی

تحلیل‌های اخیر سناریوهای آب و هوای جهانی نشان می‌دهد که محدود کردن گرمایش به کمتر از 1.5 درجه بالاتر از سطوح قبل از صنعتی شدن، به کاهش زیادی در انتشار گازهای گلخانه‌ای و همچنین حذف ~2.5-13 Gt-CO 2-1 (~0.7-3.6 GtC) نیاز دارد. سال −1 ) تا اواسط قرن 1 ، 2 . برخی از استراتژی‌ها برای کاهش انتشار گازهای گلخانه‌ای شامل ترکیب ماکرو جلبک‌های پرورشی (جلبک دریایی) در رژیم غذایی انسان و حیوان یا تولید سوخت‌های زیستی 6 ، 7 ، 8 است، اگرچه برخی چالش‌ها هنوز تولید کارآمد و استفاده تجاری از جلبک‌های دریایی را محدود می‌کنند . سوخت های زیستی9 . در حالی که همزمان ارائه خدمات اکوسیستم 10 یا پیشبرد اصلاح زیستی آبهای ساحلی 11 ، 12 ، 13 ، 14 ، پرورش جلبک دریایی همچنین می تواند حذف دی اکسید کربن اقیانوس (CDR) را با تثبیت کربن از سطح اقیانوس به زیست توده آلی، که می تواند متعاقباً در معرض آفتاب قرار گیرد، افزایش دهد. اعماق اقیانوس، یا جدا از جو 15 ، 16 ، 17 ، 18. برخلاف زیست توده زمینی، پرورش جلبک دریایی به زمین زراعی یا آب شیرین نیاز ندارد. در واقع، صنعت پرورش جلبک دریایی در حال رشد است: تولید سالانه جلبک دریایی بین سال‌های 2015 تا 2020 به طور متوسط ​​13 درصد افزایش یافته است، با 3.5 میلیون تن وزن خشک (~1 MtC) در سطح جهان در سال 2020 19 . اگرچه امروزه بیشتر کشاورزی در آب‌های ساحلی چین و اندونزی انجام می‌شود، فناوری برای کشاورزی فراساحلی در حال توسعه است 20 ، 21 ، 22 ، 23 ، 24 .

ارزیابی های اولیه از پتانسیل جهانی برای پرورش جلبک دریایی، اگرچه قابل توجه است، اما عموماً از بازده مشاهده شده در مناطق با مواد مغذی بالا 13 ، 15 ، 16 ، 17 ، 25 یا میانگین زیست توده جهانی جلبک های دریایی وحشی 5 ، 26 ، بی توجهی به تغییرات هیدرودینامیکی و فضایی استخراج شده است. شار مواد مغذی، و عدم اطمینان در بهره وری جلبک دریایی و بازده آبزی پروری. در همین حال، مدل‌های پویا رشد جلبک دریایی تحت محدودیت‌های مواد مغذی و محیطی 27 ، 28 ، 29 ، 30 ، 31 اغلب بر روی نسبتاً کوچک (کمتر از 500 کیلومتر مربع ) متمرکز شده‌اند.) مناطق ساحلی و سطوح جذب شدید مواد مغذی مورد نیاز برای تولید زیست توده در مقیاس های مربوط به بودجه جهانی کربن (به عنوان مثال، > 1 GtC) را بررسی نکرده اند. یک مطالعه اخیر، کشت ماکرو جلبک ها را در سراسر جهان مدل کرد، اما بر یک گروه جلبک دریایی متمرکز شد و عدم قطعیت های بیوفیزیکی را بررسی نکرد . در اینجا ما یک مدل جهانی پویا از رشد جلبک دریایی، سیستم مدلسازی جهانی ماکرو جلبک (G-MACMODS)، برای تجزیه و تحلیل پتانسیل کشاورزی جلبک دریایی برای تولید کربن زیست توده در مقیاس Gt تحت مفروضات مکانیسم‌های محدودکننده رشد، توسعه داده و استفاده می‌کنیم. ما بر روی کشت فراساحلی چهار نوع جلبک دریایی تمرکز می کنیم و به طور سیستماتیک حساسیت عملکرد برداشت جلبک دریایی را به طیفی از پارامترهای بیوفیزیکی نامشخص آزمایش می کنیم.

جزئیات G-MACMODS، منابع داده و روش های تحلیلی در روش ها آمده است. به طور خلاصه، مدل (شکل تکمیلی  1 ؛ ارائه شده توسط مدل قبلی کشت ماکرو جلبک 33 ) حل شده فضایی را پیش بینی می کند (1/12th ∘رزولوشن) عملکرد جلبک دریایی را با محدودیت‌هایی از عوامل بیرونی (اجبار محیطی) و درونی (پارامترهای بیولوژیکی؛ به عنوان مثال، نرخ رشد، جذب نیترات، ترشح نیتروژن و مرگ و میر و غیره) کشت می‌کنند. برای آزمایش حساسیت‌ها و ارزیابی عدم قطعیت‌ها، ما 1012-1066 شبیه‌سازی رشد و برداشت ماکرو جلبک را برای هر یک از چهار نوع جلبک دریایی (تعریف شده با استفاده از ویژگی‌های بیوفیزیکی از جنس‌های سرخ و قهوه‌ای معتدل و گرمسیری در حال حاضر پرورش‌دهی شده) انجام دادیم. هر شبیه سازی از توزیع یکنواخت مقادیر پارامتر که طیف کاملی از مقادیر مرتبط گزارش شده در ادبیات را در بر می گیرد نمونه برداری شده است (جدول تکمیلی  1). اجبار محیطی شامل دمای آب، تابش خورشید، سرعت‌های جاری، ارتفاع موج، دوره موج، و غلظت نیترات بود که از ترکیبی از اندازه‌گیری‌های ماهواره‌ای (MODIS) و شبیه‌سازی‌های مدل اقیانوس جهانی (HYCOM و CESM) تهیه شد. اگرچه ما مدل را با داده‌های اجباری از سال‌های مختلف آزمایش کردیم، نتایج گزارش‌شده در اینجا منعکس‌کننده سال 2017 است (سال اخیر بدون ناهنجاری‌های قوی ال نینو/لا نینا؛ شکل‌های تکمیلی 2، 3)  و یک اقلیم شناسی متفاوت فصلی با واسطه فیزیکی. شارهای نیترات (شکل تکمیلی  4). شبیه‌سازی‌هایی که از مقادیر پارامتری استفاده می‌کنند که به بهترین وجه توسط ادبیات پشتیبانی می‌شود یا توسط نویسندگان مناسب‌ترین تشخیص داده می‌شود، اجراهای استاندارد نامیده می‌شوند. کاشت و برداشت برای هر نوع جلبک دریایی بر اساس بازده از این پیکربندی استاندارد بهینه شد. ما اهمیت پارامترهای مدل مختلف را با استفاده از تجزیه و تحلیل طبقه بندی “جنگل تصادفی” ارزیابی می کنیم.

G-MACMODS فرض می کند که نیتروژن ماده غذایی محدود کننده است زیرا تقاضای آن نسبت به سایر مواد مغذی مانند فسفر، اغلب بیشتر از عرضه آن در اقیانوس است . متوسط ​​نسبت N:P در جلبک های بزرگ 38:1 35 است ، با این حال متوسط ​​نسبت N:P در اقیانوس 22:1 36 است . G-MACMODS به طور خاص نیتروژن را به شکل نیترات ترکیب می کند، اگرچه سایر اشکال نیتروژن (به عنوان مثال، آمونیوم و اوره) می توانند به رشد جلبک دریایی در محیط های کم نیترات کمک کنند . فرض اینکه نیتروژن تنها ماده مغذی محدود کننده است، یک نقص بالقوه چارچوب مدل است، اما ما فرض می کنیم که سایر محدودیت های مواد مغذی (مانند کمبود آهن) را می توان با شیوه های کشاورزی غلبه کرد.

ما دو سناریوی نیترات محدود را در نظر می گیریم: (1) یک مورد نیترات محیطی که در آن میانگین غلظت نیترات در 20 متر بالا برای جلبک های دریایی بدون کاهش یا رقابت در دسترس است و (2) یک مورد نیترات محدود که در آن تجمع زیست توده با چیزی که دوباره پر می شود محدود می شود. روزانه از طریق شارهای عمودی طبیعی نیترات در عمق 100 متری (یعنی از طریق اختلاط یا بالا آمدن). سناریوی نیترات محیطی، در حالی که برای تولید فشرده در مقیاس جهانی بدون بالا آمدن مصنوعی خوشبینانه غیرواقعی است، اگر شدت کشاورزی کم باشد و بازخورد قابل توجهی با اصلاح بودجه نیترات منطقه ای ایجاد نکند، نماینده بازده بالقوه در یک منطقه معین است. مورد نیترات محیط برای مزارع کوچک کشت جلبک دریایی مانند مزارع در حال حاضر در اندونزی (<1 هکتار 39) کاربرد دارد.فیلیپین (<3 هکتار 40 )، یا شیلی (<25 هکتار 41 ). در مقابل، سناریوی محدود نیترات ممکن است محدودیت‌ها را در کشاورزی متراکم، مانند مشاهده شده در چین (> 3500 هکتار 42 ) ، یا در شرایط رقابت فیتوپلانکتون‌ها ، بهتر منعکس کند . در سناریوی نیترات محدود، نیترات موجود برای جلبک دریایی را به چیزی که با شارهای عمودی طبیعی دوباره پر می شود، می بندیم، زیرا مزارع متراکم می توانند تامین مواد مغذی از آب های اطراف را با خفه کردن تبادل بین ساحلی محدود کنند .. هم نیترات محیط و هم موارد محدود نیترات سناریوهای ایده آل هستند زیرا اجرای “آفلاین” G-MACMODS به صراحت برای بازخورد چرخه نیترات یا رقابت با فیتوپلانکتون ها توضیح نمی دهد. سناریوهای مختلف برای کمک به سنجش حساسیت رشد جلبک دریایی به محدودیت‌های نیترات در نظر گرفته شده‌اند. تجزیه و تحلیل ما بر تولید دریایی متمرکز است، با این فرض که استفاده های رقابتی از محیط های نزدیک ساحل مانع از گسترش چشمگیر فعالیت های کشت در نزدیکی ساحل می شود.

هدف این کار حمایت از استقرار گسترده مزارع جلبک دریایی در بخش قابل توجهی از اقیانوس های جهانی نیست، زیرا ما انتظار داریم که این امر با مبادلات غیرقابل قبولی برای سلامت اقیانوس ها همراه باشد 32، 45 ، 46 ، بلکه ارزیابی توزیع جغرافیایی و پتانسیل پرورش جلبک دریایی فراساحلی برای تولید زیست توده قابل برداشت در مقیاس های مرتبط با آب و هوا. مطالعه ما تولید بالقوه زیست توده جلبک دریایی در سطح اقیانوس را پیش‌بینی می‌کند و به صراحت سرنوشت این زیست توده پس از برداشت را نشان نمی‌دهد. مطالعه همراه 47از G-MACMODS برای توسعه یک تجزیه و تحلیل فنی اقتصادی استفاده می کند که هزینه های کشت جلبک دریایی برای حذف کربن (مثلاً از طریق غرق شدن) یا اجتناب از انتشار گازهای گلخانه ای (مثلاً استفاده از جلبک دریایی برای غذا، خوراک حیوانات و سوخت های زیستی) را کمیت می کند.

Global seaweed harvested yields

Maps in Fig. 1 show the magnitude and types of seaweed harvested in our standard simulations, including the ambient and limited nitrate scenarios; we assume that the seaweed type with the greatest harvested yield is farmed in each grid cell. Results indicate that seaweed could be grown and harvested over large areas of the surface ocean (~200 million km2 and ~130 million km2 in the ambient and limited nitrate runs, respectively, larger than previous estimates16,32); however, annual harvests vary substantially in space and are vastly different between the two nitrate scenarios. The most productive locations include the equatorial Pacific and upwelling regions (e.g., along coasts or near energetic western-boundary currents). Nitrate limitation precludes substantial productivity in oligotrophic regions; thus, almost no seaweed is harvested within the subtropical gyres (Fig. 1b, c).

Fig. 1: Global seaweed harvest.
شکل 1

Maps of G-MACMODS annual potential harvest per unit area (b, c) of the preferred seaweed group (the type with the largest harvest in each grid cell; f, g). While G-MACMODS estimates biomass, we assume that carbon constitutes 30% of seaweed dry weight. White boxes correspond to regions depicted in Fig. 2. Zonally-averaged annual harvest for the preferred seaweed group, seaweed production of particulate organic carbon (POC) and phytoplankton net primary productivity (NPP) estimated from satellite observations48 are shown in (a, d). Zonally-averaged annual harvests for the four seaweed types are shown in (e, h).

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To provide context for the seaweed harvest distributions simulated by G-MACMODS, we compare seaweed production of particulate organic carbon (POC) to phytoplankton net primary productivity (NPP) estimated from satellite ocean-color observations48 (Fig. 1a, d). Notably, a substantial fraction of phytoplankton NPP is fueled by nitrate recycled in the euphotic zone; it represents an upper bound on a new product or, similarly, net community production (NCP; typically, NCP < phytoplankton NPP49) in the unperturbed natural system. In steady-state, the upper ocean nutrient inventory is set by a balance between biologically-mediated export (e.g., sinking particulate organic matter), equivalent to NCP, and physically-mediated supply; nutrient supply thus comprises an ultimate constraint on the magnitude of NCP.

Macroalgal growth and carbon fixation generally occur at slower rates than in unicellular phytoplankton because the multicellularity and specialized tissues in macroalgae require greater resources50,51,52. However, these specialized structural tissues, including holdfasts and thalli, allow macroalgae to gain access to more persistent light and nutrients at the ocean surface in coastal areas. Moreover, resource storage and mobilization, as well as chemical grazing defenses, permit survival during resource gaps53,54. Combined with higher carbon-to-nitrogen (C:N) ratios than phytoplankton55, these features allow macroalgae to achieve equivalent or greater productivity56,57, and much greater biomass density58, than phytoplankton for a given amount of nutrients.

Assuming that nutrient availability is the only constraint to macroalgal growth (neglecting all other growth and nutrient uptake limitations), we expect macroalgal productivity to be proportional to NCP or, as an upper bound on new production, phytoplankton NPP. Seaweed C:N average ~20:159,60 to ~40:161,62,63. These values are ~3–6 times higher than the ~6.6:1 (Redfield ratio) typical of phytoplankton. If seaweed consumed all the nitrogen available to phytoplankton, then we would expect to see, at most, six times as much seaweed POC as phytoplankton NPP. However, in our ambient nitrate simulations, seaweed POC is 10 to 12 times larger than observed phytoplankton NPP, indicating that the modeled seaweed growth under the assumption of nitrate availability surpasses the constraints imposed by nitrate supply (Fig. 1a). This suggests that the ambient nitrate case greatly overestimates the potential productivity of widespread, intensive farming in the absence of artificial upwelling, but it might provide a reasonable estimate of the localized potential harvests of farming operations small enough in scale (e.g., <25 ha39,40,41) so as to not dramatically alter local nitrate budgets. Indeed, the harvested yields simulated in the ambient nitrate scenario agree well with harvest values reported in the literature for many small farms and a few large farms situated near river mouths where nitrogen is likely more abundant (Supplementary Figs. 5–8). In contrast, zonally-averaged production of particulate carbon by seaweed is less than six times the observed phytoplankton NPP in our limited nitrate simulations (Fig. 1d). The lower harvests estimated in the limited nitrate scenario may, therefore, better reflect production when farming at scales large enough to substantially modify or deplete the surface fixed-nitrate inventory, relying on the influx of new nitrate from below the nutricline (Fig. 1c, d).

The standard simulations of both nitrate scenarios predict that temperate brown and tropical red seaweed out-compete temperate red and tropical brown seaweeds over most of the global ocean (Fig. 1f, g). The zonally-integrated annual harvest of tropical red seaweed is ~4–5 times higher than that for tropical brown seaweed; similarly, the zonally-integrated annual harvest of temperate brown seaweed is ~4–12 times larger than that for the temperate reds (Fig. 1e, h).

At regional scales (e.g., areas enclosed by boxes in Fig. 1b, c), physical processes such as western-boundary currents, coastal upwelling, and frequent eddy activity influence environmental variability and seaweed growth. Within the seaweed growth model, four factors govern seaweed growth rate: water temperature, nitrate availability, light, seaweed density, or crowding (equation (8)). Of these factors, water temperature largely determines the latitudinal distribution of different seaweed types (e.g., tropical seaweeds in the South/East China Sea (Fig. 2, top row) and temperate seaweed in the Norwegian Sea (Fig. 2, third row)). At smaller scales, nitrate availability controls regional patterns of seaweed harvested yield and, as expected, is more important in simulations with limited nitrate than in the ambient nitrate scenario (Fig. 2). Light availability and crowding (e.g., self-shading and sub-grid scale nitrate competition) can become relatively important growth limitation factors in regions with readily available nitrate.

Fig. 2: Regional harvest.
شکل 2

(Maps a–d, i–l) G-MACMODS annual harvested yields for the boxed regions in Fig. 1, assuming that carbon constitutes 30% of seaweed dry weight. (Bars e–h, m–p) The relative influence of growth parameters (equation (7)) in determining regional harvested yield for each seaweed type. (Spark lines) Relative spatially integrated annual harvest for each seaweed type.

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Uncertainty analysis

To assess the sensitivity of our results to uncertainty in the biophysical parameters in G-MACMODS, we conducted a Monte Carlo analysis over a range of literature-based parameter values with uniform distributions (Supplementary Table 1). The standard deviation of Monte Carlo simulations increases in direct proportion to the simulated harvested yield (Fig. 3). For example, regions with larger harvests in our standard simulations also show greater uncertainty in the Monte Carlo results (Fig. 3e, f; Fig. 3a, b as compared to maps in Fig. 1b, c). In the limited nitrate scenario, the average harvested yield in the most productive 10% of the ocean can range from 136–875 tC km−2 year-1 ، بسته به مقادیر پارامترهای مدل بیوفیزیکی.

شکل 3: عدم قطعیت برداشت.
شکل 3

نقشه‌های انحراف استاندارد از نتایج مونت کارلو ( a ، b ) و تابع چگالی احتمال (PDF) عملکرد برداشت سالانه استاندارد ( c ، d )، با این فرض که کربن 30٪ وزن خشک جلبک دریایی را تشکیل می‌دهد. محور y برای تجسم بهتر مقادیر PDF کوچکتر (مرتبط با برداشت های بزرگتر) قطع شده است. میانگین بن آمار مونت کارلو به عنوان تابعی از نتایج اجرای استاندارد نشان داده شده است ( e , f). میانگین برداشت به صورت یک خط ثابت نشان داده شده است. سایه تاریک و روشن به ترتیب مقادیر بین صدک 25 و 75 و صدک 5 و 95 را نشان می دهد. خط شکسته 1:1 نشان می دهد که اگر با برداشت استاندارد برابر باشد، میانگین برداشت کجا خواهد بود. اهمیت نسبی پارامترهای بیولوژیکی در جدول تکمیلی  1 ، همانطور که با تجزیه و تحلیل تصادفی جنگل تعیین شده است، در ( g ، h ) نشان داده شده است. V [μmol-N m -2  h -1 ] حاصل ضرب حداکثر سرعت جذب است (V{}_{\max }^{* } {}_{\max }) و نسبت زیست توده به سطح (B:SA). پارامترهای بیولوژیکی که به صراحت نامگذاری نشده اند در دسته “سایر” گروه بندی می شوند (تصویر تکمیلی  9) .

تصویر در اندازه کامل

بر اساس تجزیه و تحلیل تصادفی جنگل نتایج مونت کارلو، پارامترهای بیولوژیکی که به طور مداوم بر عملکرد جلبک دریایی در هر دو سناریو نیترات حاکم است، نرخ مرگ و میر ثابت (نه به دلیل امواج) و فاکتور موج (به طور خاص با مرگ و میر امواج مرتبط است)، همانطور که مشاهده می شود. در شکل  3 g, h. شبیه سازی مونت کارلو ما نرخ مرگ و میر ثابت را از 0.003 روز -1 -0.017 روز -1 ارزیابی می کند . برخی از مدل‌های قبلی از مقادیر مشابه یا کمی پایین‌تر استفاده کرده‌اند (0.001 روز -1 -0.01 روز -1 ) 29 ، 30 ، 64 ، 65. به طور مشابه، ضریب موج از 0.3 تا 1.7 تغییر می‌کند، که تأثیر رابطه مرگ و میر امواج را کاهش یا افزایش می‌دهد (معادله ( 12 )) تا عدم قطعیت‌های پیرامون از دست دادن زیست توده ماکرو جلبکی ناشی از موج را برطرف کند.

حداکثر نرخ رشد به طور قابل‌توجهی بر عملکرد برداشت در مناطق کم‌مولد تأثیر می‌گذارد، مانند مناطقی که کمتر از 250 tC km -2 year -1 قابل برداشت است (به ترتیب 40% و 93% سلول‌های شبکه در شبیه‌سازی نیترات محیطی و محدود). شکل  3 ج، د). از آنجایی که جلبک دریایی فقط زمانی برداشت می شود که به وزن مورد نظر برسد (به روش ها مراجعه کنید)، حداکثر نرخ رشد تعیین می کند که آیا جلبک دریایی به شرایط قابل برداشت برسد یا خیر.

تولید مقیاس در مناطق EEZ

The maps in Fig. 4 show the area of exclusive economic zones (EEZs) that would be required to harvest seaweed biomass of 1, 2, and 3 GtC year−1 in our standard, limited nitrate simulation, assuming that seaweed carbon content is 30% of its dry weight. Figure 4b–d provides examples of productive regions, highlighting local variability. Cumulative distribution functions of annual harvest derived from the limited nitrate simulations as a function of EEZ area (sorted by harvested yield, such that the areas with the largest harvests are cultivated first; Fig. 4e) show diminishing returns from farming more than ~15% of EEZs (locations scattered across the world), with harvests approaching a limit of ~3.5 GtC year−1 at ~25% of EEZs (Fig. 4e). In the standard, limited nitrate simulation, the most productive ~0.8% of EEZs (1 million km2; located in the equatorial Pacific; Fig. 4a, c) is enough to harvest 1 GtC year−1, with a range of 0.35 to 1.6 GtC year−1 at the 5th to 95th percentiles of the Monte Carlo simulations– less than half the 2.2 GtC year−1 harvested in the standard, ambient nitrate simulation (Fig. 4f). Assuming that macroalgal carbon content could constitute as low as 20% or as high as 40% of its dry weight35, then the area required to harvest 1 GtC year−1 would be ~2 million km2یا 0.8 میلیون کیلومتر مربع ، به ترتیب، با عدم قطعیت متناظر 0.3-1.8 GtC سال -1 و 0.4-1.6 GtC سال -1 در صدک 5 و 95.

شکل 4: کل برداشت بالقوه در مناطق EEZ.
شکل 4

a – d مناطق مناطق انحصاری اقتصادی (EEZs) مورد نیاز برای برداشت 1، 2، و 3 GtC سال -1 از زیست توده جلبک دریایی در شبیه‌سازی‌های استاندارد و محدود نیترات، طبقه‌بندی شده بر اساس عملکرد برداشت شده (یعنی اولویت‌بندی مناطق پربار). جعبه های سفید در ( a ) با مکان های نشان داده شده در ( b – d ) مطابقت دارد. e ، fتوابع توزیع تجمعی کل کربن جلبک دریایی برداشت شده نسبت به سهم EEZ های جهانی پرورشی. نتایج حاصل از اجرای استاندارد نیترات محیطی و محدود به صورت خطوط چین نشان داده شده است. خط سبز جامد و سایه‌های اطراف، محدوده برداشت مونت کارلو، شبیه‌سازی‌های محدود نیترات را نشان می‌دهد. در حالی که G-MACMODS زیست توده را تخمین می زند، ما فرض می کنیم که کربن 30 درصد وزن خشک جلبک دریایی را تشکیل می دهد.

تصویر در اندازه کامل

بحث و نتیجه گیری

این کار نسبت به تخمین های قبلی بهره وری جلبک دریایی و زیست توده قابل برداشت بهبود یافته است زیرا از یک مدل رشد پویا (G-MACMODS) برای شبیه سازی کشت جلبک دریایی تحت دو سناریو مواد مغذی مرزی استفاده می کند و حساسیت های پارامتریک را ارزیابی می کند. در حالی که برخی از بازخوردهای اکوسیستم را حذف می‌کنند، این شبیه‌سازی‌ها مرزهای بالایی خوش‌بینانه را در تولید و برداشت جلبک دریایی بر اساس نرخ‌های بیولوژیکی مشاهده‌شده، شیوه‌های کشاورزی فعلی و فیزیک اقیانوس نشان می‌دهند. نتایج مدل شبیه‌سازی استاندارد در مقایسه با مقادیر منتشر شده موجود و مرتبط عملکرد برداشت شده جلبک‌های دریایی مزرعه‌ای و وحشی ارزیابی شده است (شکل‌های تکمیلی  5-8 و جداول  تکمیلی 2-5 ). سناریوی نیترات محیطی، که فرض می‌کند غلظت نیترات تحت تأثیر مزارع جلبک دریایی قرار نمی‌گیرد، نشان‌دهنده یک برون‌یابی جهانی از کشاورزی غیرفشرده جلبک دریایی است، مشابه بسیاری از تلاش‌های فعلی در مناطق ساحلی 39 ، 40 ، 41 . با این حال، در کشاورزی فشرده با چگالی بالا، واضح است که نیترات ضعیف شده را نمی توان از طریق حمل و نقل از محیط اطراف بدون فشار سریع موجودی مواد مغذی اقیانوس نزدیک به سطح و اختلال در پمپ کربن بیولوژیکی طبیعی جایگزین کرد 32 . بنابراین، حفظ سطوح تولید شبیه‌سازی‌شده در سناریوی نیترات محیطی در مناطق بزرگ، به نوعی اصلاحات نیترات نیاز دارد (به عنوان مثال، بالا آمدن مصنوعی یا چرخش عمقی 23) .) که به نوبه خود هزینه های اضافی و پیامدهای زیست محیطی را در پی خواهد داشت. شبیه‌سازی‌های محدود نیترات ما منعکس‌کننده مرزهای بالایی خوش‌بینانه تولید جلبک دریایی است که ممکن است تنها با استفاده از نیتروژن جدیدی که به‌طور طبیعی از اعماق اقیانوس دوباره پر می‌شود (از طریق بالا آمدن طبیعی و فرآیندهای اختلاط به سمت بالا در سطح 100 متری از طریق بالا آمدن طبیعی و فرآیندهای اختلاط حرکت می‌کند و به طور مصنوعی بالا نمی‌رود، پشتیبانی می‌شود. ). نسبت به سناریوی محیطی، شبیه‌سازی‌های محدود نیترات، برداشت بالقوه جلبک دریایی در سراسر جهان را به طور متوسط ​​90 درصد کاهش می‌دهد.

Recent studies on macroalgae farming highlight this industry’s potential to offset greenhouse gas emissions5,15,16,17 without addressing geographical variability in seaweed productivity. In this study, using the limited nitrate simulations, we estimate that a climate-relevant mass of carbon (e.g., 1 GtC year−1) could be harvested by farming seaweed in the most productive 0.8% of EEZs worldwide (Fig. 4f; ~1 million km2), representing a ~370-fold increase in the area where seaweed is currently farmed (~2500 km2 66,67). For comparison, the area occupied by all agricultural cropland in the United States is ~1.6 million km2 68. The US National Academy of Sciences, Engineering, and Medicine suggests that, as one of several CDR strategies, seaweed cultivation could play a meaningful role in atmospheric CO2 reduction at an extraction level of ~0.03 GtC year−115; however, even this target requires increasing the current seaweed cultivation area by over tenfold, sustaining high yields in the most productive regions of the ocean, and ensuring that harvested biomass is sequestered. Reaching climate-relevant carbon targets is even more challenging when cultivating seaweed outside of the most productive areas of the EEZs (the equatorial Pacific). Harvesting 0.1–1 GtC year−1 outside of the most productive 1 or 5% of the EEZs, would require growing macroalgae over 200,000–3 million km2 or 1 million–24 million km2, respectively, according to our standard runs. This is similar in magnitude to existing estimates15,69 yet beyond the capacity of the current seaweed-farming industry. When entertaining such massive changes to the ocean for offsetting greenhouse gas emissions, we must also consider technoeconomic challenges47, as well as limits to CO2 removal due to time scales of air-sea carbon fluxes, and disruptions to the natural biological carbon pump32,70,71.

As indicated by the spread across the Monte Carlo simulations, the largest uncertainties in our estimates of seaweed harvest correspond to biophysical parameters related to seaweed mortality, which we divide into a wave-related erosion term, and a constant loss term, set at 1% per day, that accounts for senescence, dislodgement, disease, epiphytic infestation, grazing, and other loss processes. The wave-loss term (dw, equations (12, 13)) varies with significant wave height (Hs) and wave period (Tw). As an example of its magnitude, for Hs = 1 m and Tw = 12 s, the wave-loss term would reach dw = 0.3% per day. Existing models and observations span both lower29,30,32,65,72 and higher mortality rates59,73,74, yet these sources, which primarily consider nearshore farms, often do not distinguish between wave-related mortality and other sources of loss, and may have limited applicability to mortality on open ocean farms. Moreover, real mortality might be episodic and associated with disturbance events like storms or disease outbreaks. Our results thus highlight the importance of further research to constrain seaweed mortality under the conditions faced during cultivation to improve harvest predictions.

Using the dynamic biophysical seaweed growth model, G-MACMODS, we estimate the global potential for seaweed farming in detail. Our results suggest that biophysical ocean limits may support annually harvested seaweed containing 1 GtC year−1 from intensive farming in ~1 million km2 of the most productive ocean areas. However, practical, but different assumptions about the geographical location of farms, farming intensity, and the optimization of seeding and harvesting can cause the estimates of the area required to reach the same 1 GtC year−1 goal to increase substantially. In addition to narrowing uncertainties and accounting for the effects of climate change, future work must further assess the economic and political feasibility of farming seaweed over large areas that may have other uses or protections (e.g., fishing, shipping traffic, and marine protected areas). Similarly, if the purpose of harvesting such large quantities of seaweed is to sink it into the deep ocean and thereby sequester carbon, the effects on abyssal ecosystems75,76,77 and the possibility of increasing the extent of hypoxic regions78,79 deserve more investigation80. Given that there remain many unknowns and hurdles for large-scale seaweed farming, our analysis suggests that refinement of the global seaweed cultivation potential warrants investment in future research.

Methods

G-MACMODS overview

The Global MacroAlgae Cultivation MODeling System (G-MACMODS) used in this study draws on recent work on within-farm biophysics33, using elements from previously published research27,28,29. The state variables in the model are seaweed biomass (B; g-DW m−2; where DW is dry weight) and nitrogen cell quota (Q; mg-N g-DW−181). Nitrogen in the form of nitrate is the limiting macronutrient in G-MACMODS, although other forms of nitrogen (e.g., ammonium and urea) can contribute to seaweed growth in low-nitrate environments37,38. We recognize that other macronutrients and micronutrients could further limit our results in, for example, high-nitrogen, low chlorophyll environments82. G-MACMODS estimates seaweed biomass in units of dry weight; biomass is converted to units of carbon by assuming that carbon constitutes 30% of the seaweed dry weight for all seaweed groups35,83,84, though carbon content may vary across time, space, and genus35,62. We address how other carbon-content assumptions affect our conclusions under the section Scaling Production in the EEZs.

A diagram of the conceptual model is presented in Supplementary Fig. 1. The model has a daily time step and considers macroalgae to be grown at 2 m depth below the surface for the purposes of light attenuation. Seaweed biomass is depth-integrated across the top 20 m of the water column to account for the depth of kelp cultivation.

G-MACMODS state variables

Temporal changes in the state variables (B and Q) can be described with the following equations:

dQ=Vdt+Q\left(\frac{1}{1+\mu dt}-1\right)-E(Q-{Q}_{\min })dt،

(1)

and

dB=\mu Bdt-{d}_{{{{{{{{\rm{M}}}}}}}}Bdt،

(2)

where V is the nitrogen uptake rate [μmol-N (g-DW h)−1], E is a fractional exudation rate (day−1; Supplementary Table 1), μ is the fractional growth rate (day−1; equation (7)), and dM is the total fractional death rate (day−1; equation (12)).

G-MACMODS nitrogen uptake

The rate of nitrogen uptake by seaweed is determined by extrinsic (environmental) and intrinsic (biological) limiting factors:

V={V}_{\max }\ f(Q)\ f(| {{{\bf{u}}}}|،{{T}}_{{{{{{{w}}}} }}}،{{C}})،

(3)

where {V}_{\max} is the maximum uptake rate (Supplementary Table 1), f(Q) represents a dynamic nitrogen cell quota which allows for luxury uptake of nitrogen, and f(∣u∣, Tw, C) represents both kinetic and mass-transfer limitations on nitrogen uptake. We use a linear nitrogen cell quota33:

f(Q)=\frac{{Q}_{\max }-Q}{{Q}_{\max}-{Q}_{\min }}،

(4)

where {Q}_{\min } is the minimum amount of nitrogen that should be found in a seaweed cell (structural nitrogen), {Q}_{\max} is the maximum amount of nitrogen stored internally, such that uptake decreases as the internal nitrogen concentration increases, and f(Q) is a unitless coefficient between 0 and 1. The parameter f(∣u∣, Tw, C) in equation (3) is a limit on uptake based on a combination of Michaelis–Menten kinetics and mass-transfer limitation regulated by the surrounding waves and currents85,86,87 :

f(| {{{{{{\bf{u}}}}}}}}|،{T}_{{{{{{{{\rm{w}}}}}}}}}، ج)=\frac{C}{{K}_{{{{{{{{\rm{m}}}}}}}}}\left(\frac{C}{{K}_{{{ {{{{\rm{m}}}}}}}}}+\frac{1}{2}\left(\gamma +\sqrt{{\gamma }^{2}+4\frac{ C}{{K}_{{{{{{{{\rm{m}}}}}}}}}}\right)\right)}،

(5)

where \gamma =1+\left({V}_{\max }/\beta {K}_{{{{{{{\rm{m}}}}}}}}}\راست)-\چپ (C/{K}_{{{{{{{{\rm{m}}}}}}}}}\راست), Km is the half-saturation constant (Supplementary Table 1), C is the external concentration of nitrogen, and

\beta =\frac{D}{{\delta }_{{{{{{{{\rm{D}}}}}}}}}}+\frac{4{\delta }_{{{{{{{{\rm{D}}}}}}}}}}{{T}_{{{{{{{{\rm{w}}}}}}}}}}\mathop{\sum }\limits_{n=1}^{\infty }\left(\frac{1-\exp \left(\frac{-D{n}^{2}{\pi }^{2}{T}_{{{{{{{{\rm{w}}}}}}}}}}{2{\delta }_{{{{{{{{\rm{D}}}}}}}}}^{2}}\right)}{{n}^{2}{\pi }^{2}}\right)

(6)

with units of m s−1. In equation (6), D is the molecular diffusivity of nitrate at 18∘ C (7.3 × 10−10 m2 s−1)33,88, Tw is wave period, and δD is the thickness of the diffusive boundary layer, defined using the thickness of the viscous boundary layer {\delta }_{{{{{{{{\rm{D}}}}}}}}}={\delta }_{\nu }=10\nu /(\sqrt{{C}_{{{{{{{{\rm{D}}}}}}}}}}| {{{{{{{\bf{u}}}}}}}}| ) where ν is the molecular kinematic viscosity (10−6 m2 s−1) and CD is the drag coefficient87 (Supplementary Table 1). The parameter f(∣u∣, Tw, C) is unitless and varies between 0 and 1. Note that this nitrogen uptake model assumes that (a) the diffusive boundary layer is completely stripped away every half a wave period, regardless of the size of the wave, (b) the thickness of the diffusive boundary layer (δD) can be parameterized with the thickness of the viscous boundary layer (δν), and (c) that we can ignore near-boundary turbulent transport (i.e., assume the blade is smooth)87, though this has been shown to enhance exchange rates89. We do not consider within-canopy flow reduction, which negatively affects uptake33,90. We assume that wave height has a negligible effect on uptake, since renewal of the diffusive boundary layer (and, hence, enhanced nitrate uptake) can occur through blade flapping in a low-flow environment91. Thus, equation (3) is used to estimate the amount of nitrogen that the seaweed could, theoretically, take up from the environment (dN).

Two nitrate scenarios are tested in this study: (1) a case where nitrate concentrations from a global ocean model (CESM) are averaged over the top 20 m of each grid cell and are available to seaweed without depletion or competition is referred to as the ambient nitrate scenario and (2) a case where the amount of nitrate available for uptake is capped by the nitrogen that is naturally fluxed upward through the 100-m depth plane (Nnew), referred to as the limited nitrate scenario. In the limited nitrate scenario, the nitrogen uptake rate (equation (3)) is still determined by the ambient (average of top 20 m) nitrate concentration, but if the amount of nitrogen that would be theoretically taken up by seaweed at a given time is greater than that fluxed upward at 100 m depth, dN > Nnew, then uptake (V in equation (1)) is capped using dN = Nnew. Additional simulations were performed to test an alternate depth for estimating Nnew—at the annual maximum mixed-layer depth at each grid cell—but resulting harvested yield differences were relatively small compared to other uncertainties presented in the Uncertainty Analysis section (median increase of 6% in the annual harvest).

G-MACMODS growth

Similar to the nitrogen uptake rate, growth rate (μ) is also constrained by extrinsic and intrinsic limiting factors:

\mu ={\mu }_{\max }\ g(k)\ g(Q)\ g(T)\ g(E).

(7)

The maximum growth rate allowed under ideal conditions ({\mu }_{\max }) is constrained by crowding effects that account for self-shading and sub-gridscale nutrient limitations [g(k)], internal nitrogen reserves [g(Q)], water temperature [g(T)], and light [g(E)], all of which are represented by unitless coefficients, varying between 0 and 1.

The growth rate limitation imposed by crowding in the seaweed canopy [g(k)] embodies the general idea that less-dense seaweed can grow faster, or

g(k)=\frac{{k}_{{{{{{{{\rm{R}}}}}}}}}}{{\mu }_{\max }}\ {\left(\frac{B}{{B}_{{{{{{{{\rm{cap}}}}}}}}}}\right)}^{-0.75},

(8)

where Bcap (g-DW m−2) is the biomass density at which seaweed grows by a fraction kR = 0.05 day−1 under ideal conditions. We tuned Bcap to match field observations from the literature (see Model-Field Data Comparison). The power law in equation (8) was derived by re-fitting data from a comprehensive meta-analysis92. Our fit was applied to the data in ref. 92 and binned to 0.01-width bins from 0–1 g L−1 and 0.1-width bins for 1–60 g L−1 seaweed density, weighted by the number of observations in each bin (with a minimum weight of eight observations). Our fit excluded data corresponding to total-nitrogen (NO3 + NH4) conditions not likely to be found in the surface ocean (values above 20 μM). Although according to equation (8), g(k) → ∞ as B → 0, we cap g(k) at 1.

The nitrogen quota limitation g(Q) in equation (7) is a modified form of the Droop model81:

g(Q)=\frac{Q-{Q}_{\min }}{Q}\frac{{Q}_{\max }}{{Q}_{\max }-{Q}_{\min }}.

(9)

where Q{}_{\min } and Q{}_{\max } are set per seaweed type (Supplementary Table 1). The temperature limitation term in Equation (7) is similar to a Gaussian probability curve93:

g(T)=\exp (-{\beta }_{1}{(T-{T}_{{{{{{{{\rm{opt}}}}}}}}})}^{2}),T \, < \, {T}_{{{{{{{{\rm{opt}}}}}}}}}\\ g(T)=\exp \left(-{\beta }_{2}{(T-{T}_{{{{{{{{\rm{opt}}}}}}}}})}^{2}\right),T \, > \, {T}_{{{{{{{{\rm{opt}}}}}}}}}\\ g(T)=1,T ={T}_{{{{{{{{\rm{opt}}}}}}}}},

(10)

where Topt is a 5∘ optimal temperature range for each seaweed group (Supplementary Table 6), T is the daily temperature, and the β1 and β2 coefficients are adjusted to reach zero near the lower- and upper-temperature limits, respectively.

The light limitation in equation (7) is largely informed by phytoplankton studies94:

g(E)=f\frac{I-{I}_{{{{{{{{\rm{c}}}}}}}}}}{{I}_{{{{{{{{\rm{s}}}}}}}}}-{I}_{{{{{{{{\rm{c}}}}}}}}}}\exp \left(-\frac{I-{I}_{{{{{{{{\rm{c}}}}}}}}}}{{I}_{{{{{{{{\rm{s}}}}}}}}}-{I}_{{{{{{{{\rm{c}}}}}}}}}}+1\right),

(11)

where Is and Ic are the daily-averaged saturating and compensating irradiance (W m−2), f is the fraction of daylight that is implemented to account for periods of darkness, and I is the irradiance reaching an underwater depth of 2 m. The irradiance is attenuated following the implementation in the Marine Biogeochemistry Library (MARBL)95,96.

G-MACMODS mortality

The total mortality rate, dM in equation (2), is the sum of a constant daily mortality rate that is meant to incorporate grazing, aging, and disease (d; Supplementary Table 1) and a term that accounts for breakage from waves (dw), such that

{d}_{{{{{{{{\rm{M}}}}}}}}}=d+{{\Pi }}{d}_{{{{{{{{\rm{w}}}}}}}}}.

(12)

The dw term is dependent on wave power and, as such, is variable in both time and space97:

{d}_{{{{{{{{\rm{w}}}}}}}}}=(2.3\times 1{0}^{-4})(P\times 1{0}^{-3})+2.2\times 1{0}^{-3},

(13)

where P is wave power in Watts:

P=\frac{\rho {g}^{2}}{64\pi }{H}_{{{{{{{{\rm{s}}}}}}}}}^{2}{T}_{{{{{{{{\rm{w}}}}}}}}}

(14)

where ρ is the density, Hs is the significant wave height, and Tw is the wave period. Ref. 98 offers a different macroalgal wave mortality equation, but the one we implement penalizes seaweed growth to a lesser degree. However, in equation (12), Π (Supplementary Table 1) is a wave factor that accounts for the uncertainty surrounding the use of a single equation to represent wave mortality across all seaweed types. For our standard runs, Π = 1 and dM = d + dw.

Environmental data

The environmental inputs applied to our model (water temperature, solar irradiance, current velocities, wave height, wave period, and nitrate concentrations) stem from a combination of satellite measurements and global ocean model outputs spanning multiple years. For the purposes of this manuscript, we explore a suite of simulations using inputs from 2017, the most recent year with available data that is also not identified as having a strong ENSO index. Input data from 2003–2019 were used in simulations examining interannual differences in estimated seaweed growth (Supplementary Fig. 11); however, regional interannual variability was comparatively small with respect to parameter uncertainty and is therefore not the focus of this study.

Sea surface temperature (SST) and surface photosynthetically active radiation (PAR) are used as a proxy for in situ temperature and irradiance, respectively, over the depth of macroalgal growth. SST and PAR used in this study are 8-day averages from the Moderate Resolution Imaging Spectroradiometer (MODIS; R2018), on the NASA Earth Observing System, with a spatial resolution of 1/12∘. Net oceanic primary productivity (NPP) was estimated from MODIS chlorophyll measurements using the Vertically Generalized Production Model (VGPM)48. SST, PAR, and NPP were downloaded from the Ocean Productivity website99,100.

Zonal and meridional current velocities were extracted from the HYbrid-Coordinate Ocean Model (HYCOM101) Global Ocean Forecasting System (GOFS) 3.1102. HYCOM is a global data-assimilating model103 with 1/12∘ horizontal resolution and 41 depth levels, of which we use the surface velocities.

Significant wave height and wave period were taken from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5104 atmospheric reanalysis produced by the Copernicus Climate Change Service105. ERA5 provides hourly significant wave height of combined wind waves and swell, and mean wave period with a 1/2∘ horizontal resolution. The data were averaged in 8-day time intervals.

Nitrate information is taken from a high-resolution biogeochemical simulation led by the National Center for Atmospheric Research (NCAR) and run in the Community Earth System Model (CESM) framework106,107,108. The biogeochemical model has a 1/10th ∘ horizontal resolution and 62 depth levels. Fields used in this study include 5-day mean nitrate concentrations averaged over the upper 20 m, and vertical fluxes of nitrate across the 100-m depth plane were calculated to provide an estimate of fluxes of new nitrogen into the euphotic zone.

Although G-MACMODS steps forward with a daily time step, we apply the 8-day environmental inputs that best correspond to the G-MACMODS time stamp. All environmental inputs were spatially interpolated onto a 1/12 ∘ global grid, using linear interpolation if the input data were of higher resolution, or nearest-neighbor if the input data were of lower resolution.

Seaweed groups

Here, we focus on four seaweed groups containing seaweed genera that are among the world’s ten most cultivated by weight109: tropical reds (e.g., Eucheuma, Kappaphycus), tropical browns (e.g., Sargassum), temperate reds (e.g., Pyropia), and temperate browns (e.g., Saccharina, Laminaria, and Macrocystis). Values of parameters required by G-MACMODS were gathered from available literature for a few representative seaweed genera (Supplementary Table 1); standard runs were defined using average (when multiple parameter estimates were available) or speculated values (based on information from other genera when there were few or no published values), though we modify some of the values implemented in the standard runs to improve comparison with the field data (see the section on Model-Field Data Comparison). We define the temperature parameters in equation (10) similarly, using available information for representative genera (Supplementary Table 6). The optimal temperature range in equation (10) is extended to a 5∘ width, rather than a single number, to account for variations within a seaweed genus.

The standard runs were spun up for 1 year, and the seeding was optimized by choosing the run initialization date that yielded the largest yearly biomass harvest (averaged across 2003–2019) for every grid point. Tropical and temperate brown seaweed runs were seeded with 50 g-DW m−2. Tropical and temperate red seaweed runs were seeded with 200 g-DW m−2 and 10 g-DW m−2, respectively, following examples in the literature (see Supplementary Tables 2–5). Seaweed are seeded with an initial nitrogen cell quota (Q0), such that

{Q}_{0}={Q}_{\min }+\frac{N}{35}\left({Q}_{\max }-{Q}_{\min }\right),

(15)

where N/35 is the ratio of the ambient nitrogen concentration at the time of seeding to the a representative N concentration below the nutricline (35 μM).

Model-field data comparison

To test our choice of standard parameters (Supplementary Table 1) and calibrate Bcap (equation (8)), we compared biomass from our G-MACMODS standard runs to published observations of seaweed mariculture and wild seaweed standing stock surveys. Only farmed values published after the year 2000 are included in this comparison to account for changes in technology and methods across the years, whereas we include wild stock values from literature published as far back as 1990. Overall, G-MACMODS produces a range of biomass that agrees with what has been observed in published field studies (Supplementary Figs. 5–8). We carried out further detailed comparisons to examine the performance of G-MACMODS at the locations specified in the published studies. To do so, we applied the following protocols to our analysis:

  • If the published manuscript mentioned specific coordinates or a coordinate range, we found the spatial mean of our variable of interest within a 50 km radius of the specified coordinates or within the specified coordinate range, respectively. If the manuscript included a map with sampling locations (no specific coordinates) or enough geographic information to narrow down a location to a single point, we found the most representative coordinates of that location and calculated the spatial mean of our variable of interest within a 50 km radius of those representative coordinates. However, if the manuscript did not provide enough information to narrow down a location to a specific point, then we estimated the spatial mean of our variable of interest within a 3∘ × 3∘ box in the general region of the published study.
  • If the published manuscript reported biomass, rather than harvest weight, we compared the article’s maximum attained biomass to the maximum biomass grown in G-MACMODS over the course of the specified harvest cycle at the corresponding location.
  • Any biomass reported in fresh weight is converted to dry weight using a 10:1 ratio.
  • Unless otherwise specified, these G-MACMODS simulations use the 2017 temperature, PAR, current velocity, and wave fields typical of our standard runs.

We applied some additional protocols that vary across seaweed types:

  1. 1.Tropical red seaweed: The G-MACMODS simulations were seeded with a biomass density equivalent to that used in the referenced publications; the biomass was harvested back to seed weight at the corresponding harvest period (Supplementary Table 2). If the referenced publications did not provide seed or harvest period information, then we assumed a seed density of 200 g-DW m−2 and a 45-day harvest period, which was the most common farming configuration. The validations were run with a constant nitrate concentration comparable to the maximum nitrate concentration reported for each field experiment; if no nitrate information was available, we used the CESM nitrate field previously described under the Environmental Data subsection of the Methods. We compared the temporal maximum of the G-MACMODS harvested biomass to the mean harvest yield reported in the corresponding literature to examine whether G-MACMODS could approximate the values observed in the field, notwithstanding the lack of information from the published field studies. The G-MACMODS runs for these comparisons did not include wave energy, since most tropical red seaweed cultivation takes place in shallow sheltered areas.
  2. 2.Tropical brown seaweed: Given that the published studies that we reference report wild seaweed standing stock (Supplementary Table 3), we did not include harvesting in the G-MACMODS comparison simulations. The seeding process, however, followed the protocol established for our standard runs. In addition, these G-MACMODS simulations did not include wave energy and used the CESM nitrate field previously described under the Environmental Data subsection of the Methods.
  3. 3.Temperate red seaweed: We simulated temperate red macroalgae cultivation across the same time period as specified in the published literature (Supplementary Table 4) using an identical harvest scheme and seed density to that applied in our standard runs. When reported, we applied the mean NO3 concentration in the field studies to the G-MACMODS simulations. As a metric of model performance, we compared the harvest yield from the G-MACMODS simulations to the mean harvested biomass from the literature.
  4. 4.Temperate brown seaweed: We simulated temperate brown seaweed cultivation across the same time period as specified in the published literature (Supplementary Table 5), assuming a biomass density of 50 g-DW m−2 after 30 days of cultivation, with only one harvest at the end of the cultivation period, when applicable. We did not include harvesting in the G-MACMODS simulations that try to reproduce field studies of macroalgal standing stock. If reported, we applied the mean NO3 concentration in the field studies to the G-MACMODS simulations. When relevant, we compared the harvest yield from the G-MACMODS simulations to the mean harvested biomass from the literature using units of g-DW m−1, assuming a 1-m line separation in the G-MACMODS simulations. Waves were included in these G-MACMODS simulations.

Overall, G-MACMODS has the capacity to produce biomass at the levels observed in published field studies (Supplementary Figs. 5–8, panel b). Some of the more specific comparisons do not agree with each other (Supplementary Figs. 5–8, panel c); however, we expected some disagreement since, in many cases, we lacked the information to adequately reproduce individual studies’ field conditions. For example, many studies did not include any nitrate information (Supplementary Tables 2–5). While the CESM nitrate fields were, at times, enough to replicate the conditions in the published studies, the CESM NO3 cannot account for farming practices that include nitrate fertilization110 or the placement of seaweed farms downstream of a substantial nitrate source (e.g., fish farm, river outlet, or other coastal feature). Given those exceptions, we find G-MACMODS to perform adequately when compared to field data.

Harvest

Harvest schemes were based on available information of current farming practices20,32,39,40,41,111,112 and optimized for each seaweed group to achieve maximal biomass per harvest based on standard run tests of three harvest schemes: periodic harvesting, periodic harvesting with a biomass threshold, and conditional harvesting (with dual criteria of a target weight or when death exceeds growth). The test runs also allowed for optimization of the target weight to initiate harvest (10, 20, 30, 40, 50, or 80% of Bcap), as well as the percent of biomass removed at each harvest (40, 60, or 80%). Finally, the number of harvests per year were limited based on documented cultivation practices. The temperate brown and red algae are commonly harvested twice20 and six times a year111, respectively, while the tropical brown and red algae are harvested up to eight times a year40,113. Temperate brown seaweeds were allowed to grow without consideration for harvest for at least 60 days after seeding. Considering the above factors, the harvesting schemes that produced the highest harvested yields for each seaweed group are as follows:

  1. 1.Tropical red and brown seaweeds: Harvest occurs every 45 days only if the seaweed biomass has reached the target weight of 800 g-DW m−2 (40% of Bcap) for tropical reds and 400 g-DW m−2 (80% of Bcap) for tropical browns. If 45 days elapse and the seaweed does not reach its target weight, another 45-day period must transpire before re-evaluating the biomass. If the biomass has reached its target weight, then 80% of the biomass is harvested.
  2. 2.Temperate red seaweeds: Harvest is initiated whenever the biomass reaches the target weight (80 g-DW m−2, 64% of the Bcap) within 150 days after seeding or if the death exceeds growth for 7 days. If the biomass has reached its target weight, then it is harvested down to 60 g-DW m−2. If the death exceeds growth for >7 days or the final harvest period is reached, 99% of the biomass is harvested (1% loss rate assumed in the final total harvest).
  3. 3.Temperate brown seaweeds: Harvest occurs when the biomass reaches the target weight (1350 g-DW m−2, 68% of the Bcap) within 220 days after seeding or if death exceeds growth for 7 days. If the biomass has reached its target weight, then 80% of the biomass is harvested; if the death exceeds growth for >7 days or the end of 220 days is reached, 99% of the biomass is harvested (1 % loss rate assumed in final total harvest).

Monte Carlo simulations

We used Monte Carlo methods to estimate the uncertainty surrounding our standard run harvest amounts. We performed between 497–534 Monte Carlo simulations for each seaweed group and nutrient scenario (ambient vs. limited nitrate). Each Monte Carlo simulation chose the value of the seaweed biological parameters using a uniform probability distribution bounded by the magnitudes in Supplementary Table 1. When possible, these bounds are 25% greater (lower) than the maximum (minimum) biological parameter values found in the literature. However, we prioritized having symmetric bounds over bounds that cover the range of values in the literature to aid the interpretation of the results. The mean, median, standard deviation, and percentiles (5th, 25th, 75th, and 95th) of annual harvested yields resulting from these Monte Carlo simulations were calculated across each model grid cell. The relative importance of each Monte Carlo parameter value upon harvested biomass was evaluated using random forest analysis.

Model limitations

G-MACMODS and our scenarios are subject to a number of important limitations and caveats. First, operating farms will not have the benefit of hindsight that our model uses to optimize seeding and harvest schedules, and the model assumptions are optimistic with regard to micronutrient fertilization and environment/strain optimization in cultivars. Second, neither of the implemented nutrient scenarios considers how seaweed farms affect the surrounding hydrodynamics, which can substantially affect nitrate uptake and yields33 but are challenging to resolve in a global-scale model. We expect that densely-packed farms would impede thinning of the diffusive boundary layer, thus reducing macroalgae’s ability to take up nitrate. Third, the nitrate data (from CESM simulations) do not resolve nitrate runoff in coastal areas114, sources of nitrogen other than nitrate (e.g., ammonium or urea), nor consider other limiting macronutrients such as phosphate. However, standard ambient nitrate runs using a second set of nitrate inputs from a biogeochemical hindcast model that incorporates riverine nutrients (produced at Mercator-Ocean and distributed by E.U. Copernicus Marine Service Information; DOI:10.48670/moi-00019) suggests that the uncertainty associated with the source of nutrients is within the range of uncertainty related to the biological parameters in our model (Supplementary Fig. 10).

G-MACMODS would also benefit from a more refined expression of seaweed mortality that could account for episodic events (e.g., storms, diseases) and nonlinear grazing pressure, among other factors, as well as an improved understanding of wave mortality for different genera. Moreover, we do not explicitly model the effects of climate change and projected changes in ocean conditions that can stress growing seaweeds, shift their geographical distribution, increase the frequency and severity of storms, decrease nitrate fluxes by enhanced stratification, and make diseases and epiphytes more prevalent115,116. These are important areas for future research. Although certainly not a proxy for the many effects of climate change, we note that interannual variability in environmental forcing (2003–2019) affects our harvest estimates less than the uncertainties related to biological parameters (Supplementary Fig. 11).