The 3 dimensional model framework SINMOD (Slagstad and McClimans, 2005) was used for the simulations. The hydrodynamic component solves the primitive Navier-Stokes equations using a finite difference scheme on an Arakawa C-grid (Aarakawa and Lamb, 1977). In the present simulations, z-layers were used (i.e., each vertical layer had a fixed thickness except the surface and bottom layers) and a hydrostatic assumption was applied (Slagstad and McClimans, 2005).

A model domain of 160 m horizontal resolution was used (Figure 1). Boundary conditions were produced in a 3 step nesting procedure, running models of successively finer grids from 20,000 m, to 4,000, to 800 m and finally to 160 m resolution, e.g., Broch et al. (2019, 2020). The model setup in 160 m horizontal resolution used here had depth layer thicknesses ranging from 1 to 5 m for the upper 25 m, followed by 25 m thick layers down to 650 m depth. The simulation time step for the 160 m model was 30 s.

Atmospheric forcing was applied using ECWMF's ERA-Interim data (Dee et al., 2011). Forcing by freshwater from rivers and land was implemented by using data from the Norwegian Water Resources and Energy Directorate (www.nve.no) generated by a version of the HBV-model (Beldring et al., 2003).

Previous studies have shown that the model system is able to approximate the local current system at and around aquaculture sites in a realistic manner (Broch et al., 2020). On a larger scale, the model has been shown to reproduce the circulation dynamics at the Norwegian Shelf outside Northern Norway (Skardhamar and Svendsen, 2005).

A conceptual diagram of the deposition model is presented in Figure 2. An Eulerian approach was taken in the transport simulations. This entails the calculation of concentration fields of suspended or sedimented POM. A summary of all the parameters and variables of the transport model, including choices of numerical values where applicable, is given in Table 1.

Four model compartments (D₁,D₂,D₃,D₄) representing the concentrations of kelp POM (unit: gC m⁻³) of different sinking speeds were used (Table 1). The concentration D_j of component number j is calculated according to the following equation (Wassmann et al., 2006):

Here, Adv and Diff are the 3 dimensional advection and diffusion operators, respectively, while the source term G_j represents release of POM from the cultivation sites (Slagstad and McClimans, 2005). It is tacitly assumed that all expressions and equations are valuated in spatial position (x, y, z). A Richardson scheme for vertical mixing is used (Sundfjord et al., 2008).

The sea floor concentration of deposited POM from compartment j (unit: gC m⁻²) is denoted by S_j, and the concentration of kelp POM in compartment j in the model's bottom layer by D_j,bot. The fluxes and inter-actions between D_j,bot and S_j are given by the equations:

and

for j = 1, 2, 3, 4. Here r = r(x, y) is the amount of POM resuspended and s = s(x, y) is the fraction deposited in position (x, y); Δz_bot is the thickness of the bottom layer (Figure 2).

The resuspension and advection of POM from the bottom is calculated as follows. Let u = (u_x, u_y) denote the current velocity in the middle of the bottom grid cell. The shear velocity u_* is calculated using a logarithmic law (Kuhrts et al., 2004; Warner et al., 2008),

where κ = 0.41 is the universal von Kármán constant, z is the distance from the bottom to the middle of the D_j,bot grid cell, and z₀ is the roughness height: the height above the bottom at which the current speed |u| tends to 0 (Figure 2, Table 1). Whether the POM is sedimented, remains neutral, or is resuspended from the sediment, i.e., the values of s and r in Equations (2) and (3), depends on the value of u_* relative to the critical shear velocity for reuspension u_*,R, thus:

where v_j denote the sinking speed of compartment j and

where ρ is the density of sea water and M is a parameter depending on the properties of the matter (Kuhrts et al., 2004). The interactions of sinking and resuspension with horizontal and vertical advection leads to the possibility of aggregation of POM, in contrast to passive tracers.

The sinking speeds v_j used for POM compartments j are recorded in Table 1. The sinking speed of D₂ to D₄ are based on the lower end of the range of values published in Wernberg and Filbee-Dexter (2018). They are sinking speeds for whole fronds, frond fragments, and of sea urchin fecal particles (shredded kelp) for Laminaria hyperborea. The sinking speed of D₁ is about an order of magnitude lower than the lowest ones recorded in Wernberg and Filbee-Dexter (2018). Consequently, a wide range of sinking speeds are covered.

The transport of POM from the beginning of April until the end of June was considered, assuming deployment of the kelp cultures in January-February (Boreal winter). Before this period, the absolute biomass, and biomass export of a farm is low, even if the size and biomass specific growth rates usually are high (Forbord et al., 2020; Fieler et al., 2021).

It was assumed that 10% of the total amount of POM was released in April, 20% in May, and 70% in June (Fieler et al., 2021). The release was assumed to be constant over each month, i.e., the same amount of matter was released for every model time step within each month.

One simulation was run for each of three types of farm locations (Figure 1):

For more information in the prevailing currents along the Norwegian coast cf. (Sætre, 2007). The sheltered farm site is an actual kelp cultivation location with a permit for kelp cultivation of 30 ha. The other two (hypothetical) farms are assumed to cover an area of 125 ha (7 × 7 model grid cells). Although the concepts of “sheltered,” “exposed,” and “offshore” may sometimes be used differently, the words serve to distinguish easily between the sites in the present case.

The generic dispersal simulation results were translated into estimates for organic loading from sugar kelp (Saccharina latissima) aquaculture. While the conditions are suitable for S. latissima cultivation along most parts the Norwegian coast (Forbord et al., 2020), the full cultivation potential is not yet known. Simulation model results indicate an average potential for S. latissima cultivation in Norwegian coastal waters inside the maritime baseline (Harsson and Preiss, 2012) of around 75 t ha⁻¹ year⁻¹ (February-June), though with substantial spatial variability and a maximum potential close to 200 t ha⁻¹ near shore and even higher offshore (Broch et al., 2019).

According to Fieler et al. (2021), 8 to 13% of the S. latissima NPP in culture from January/February until June in Central Norway is lost as POM through frond erosion and plant dislodgement. This translates into the losses by harvest time recorded in Table 2. The results form the dispersal simulations were up-scaled accordingly.

The sensitivity of POM loading to variations in the loss fraction and production intensity was calculated as follows. We consider only the carbon (C) fraction released. Assuming a harvested WW biomass of B_harvest t WW ha⁻¹ and a loss of a fraction p of the NPP B_NPP t WW ha⁻¹ (that is, the biomass had no POM been lost), we have that

with the unit g C m⁻², that is: g C per unit of the farmed area. The factor k_C converts from t WW to g C (Table 2). The maximum loadings (i.e., the loading in the model grid cell/location with the highest carbon loading) from each of the simulations described above for a loss fraction of q = 0.08 (equivalent to 8%), normalized to the unit g C m⁻² (t ha⁻¹)⁻¹ is denoted by S_max(q). This was scaled from the results for q = 0.08 to a production scenario of C_harvest t ha⁻¹ and a loss fraction of p as

again of the unit g C m⁻². In summary

We consider two main dispersal and organic loading scenarios with different distribution of the organic matter between different sinking speeds:

The average (standard deviation, maximum) simulated current speeds (hourly data April, May, and June) at the middle of the sheltered, exposed and offshore sites were 0.078(0.048, 0.443), 0.166(0.091, 0.8530), and 0.219(0.125, 0.681) ms⁻¹, respectively.

The dispersal distances and patterns of POM differed between the three release sites (Figure 3). The least dispersive site was the sheltered one, while the offshore location was the most dispersive one in the sense that the 90% of the POM deposited within a much grater region at the offshore site than at the sheltered one (Figures 3, 4). A higher proportion of faster sinking POM lead to less dispersal, but did not change the ranking between the sites. Almost 80% of the sedimented POM released from the sheltered site was transported less than 1 km away from the center of the release site, and thus sedimented within the farm itself in Scenario A. By contrast, around 60% of the POM released from the offshore site was transported at least 2 km from the center of the release site in Scenario A, and more than 20% of the POM was transported more than 16 km away from the offshore site.

Matter in the slowest sinking POM compartment D₁ was transported relatively far for all release sites. In particular at the offshore location, there was a potential for transport of around 40% of the POM more than 60 km away (Figure 4). In contrast, the fastest sinking POM (compartment D₄) released from the sheltered and exposed sites, never moved more than 2 km, thus in practice remaining within the near zone. At the offshore site, around 30% the D₄ POM was transported more than 4 km away before depositing.

The average deposition depths of the POM varied according to the location, reflecting the bottom depth in the region around the release sites (Figures 1, 5). POM released from the offshore location deposited significantly deeper than that released from both the sheltered and exposed sites for all POM compartments D₁ to D₄ (see confidence intervals in Figure 5). In this case, the deposition depth varied significantly between POM compartments as well, except between D₃ and D₄. The D₁ POM deposited shallower than the other compartments probably because the settling velocity allowed for transport out into deeper waters, and then toward the shallow watered archipelago to the East of the offshore site and directly South West and East of the exposed site (Figure 3). For each POM component D_j the median deposition depth was shallower when released from the sheltered than the exposed site. Between POM compartments, there were significant differences in the median deposition depths between D₁ and D₄ only.

The time to settlement of the released POM was estimated based on the median deposition depths δ_j (Figure 5) and the sinking velocities (Table 1) of POM compartments j = 1, 2, 3, 4:

The fastest sinking POM compartments (D₃, D₄) deposited within a few hours at all the locations (Table 3). The slower sinking compartments spent, on average (median) up to 3(D₂) and 20 days (D₁) in suspension.

The dispersal results were translated into maximum organic loading through (8) and visualized as a function of harvested kelp biomass (t ha⁻¹) and biomass loss [in percentages of the NPP, Equation (7); Figure 6]. The carbon loading at the seafloor was greatest at the sheltered site, in line with the distribution pattern (Figure 3). The partitioning of the biomass between the different POM compartments impacted significantly on the magnitude of the organic carbon loading. Thus, the increase in the maximum carbon loading from scenario A (slow sinking) to B (fast sinking) was 65% for the sheltered location, 58% for the exposed location, and 56% for the offshore location, as POM accumulated over a smaller area.

The maximum carbon loading relative to the average (= max) carbon loading in a situation where the POM sinks straight down (no horizontal advection) is expressed by the quotient of Equation (8) to (7):

This quotient is independent of the cultivation volume and the fraction of matter deposited. A value below 1 means that the matter is dispersed more than in the passive (no horizontal advection) scenario, while a value above 1 indicates that aggregation of matter contributes to the maximum carbon loading (Figure 2). The average loading rates should be the same, assuming no degradation or consumption. The fractions (rounded to one decimal place) for the Sheltered location were 0.8 and 1.2 for Scenarios A and B, respectively. For the exposed location the fractions were 0.7 and 1.2. For the offshore location, the fractions were 0.1 and 0.2.

The deposition area and transport distance from the release point(s) depended substantially on the sinking rates used in the simulations.

The export transport distance and thus the ecological impact area is closely linked to fraction size and particulate sinking rates. Smaller detritus fractions have lower sinking rates and potentially travel further (Wernberg and Filbee-Dexter, 2018). This leads to larger impact areas of kelp farming but with potentially a lower organic loading and following ecological impact (Sweetman et al., 2014). Conversely, larger POM fractions (with greater sinking speeds),will deposit over a smaller area, with potentially greater local effects.

Even the fast sinking POM components (D₃,D₄) were transported far relative to fecal and feed particles from fin fish farming (Broch et al., 2017). This can be explained by two factors. Firstly, the sinking rates even of D₃ and D₄ were low relative to those used in deposition studies for fin fish farming. Settling velocities used in Chang et al. (2014) were a mean of 3.2 × 10⁻² ms⁻¹ for fecal and 11.0×10⁻² ms⁻¹ for feed particles). Secondly, the waters around the exposed and offshore release locations were deep relative to typical coastal fin fish farming locations (Chang et al., 2014; Broch et al., 2017).

Sinking speeds ranging 3 orders of magnitude were considered, allowing for interpretation of the results in the context of a wide range of possible distributions of the biomass between different sinking speeds. In particular, sinking speeds for blade fragments of S. latissima have not been properly established. In Wernberg and Filbee-Dexter (2018), the seaweed POM was correlated to the size and mass of L. hyperborea particles. The weight per unit area of frond tissue in cultivated S. latissima seems to be a lot lower than in naturally growing L. hyperborea (Foldal, 2018; Wernberg and Filbee-Dexter, 2018). This indicates that the sinking speeds of S. latissima POM may be lower than for, e.g., L. hyperborea. On the other hand the average density of L. hyperborea blade tissue fragments reported by Wernberg and Filbee-Dexter (2018) was 1064±96kg m⁻³. Corresponding values for S. latissima blade fragments are 1092±91 (Vettori and Nikora, 2017) and 1120±130 (Norvik, 2017).

Many deposition and transport models employ Lagrangian (i.e., particle based) rather than Eulerian (i.e., concentration fields) approaches (Cromey et al., 2002). One advantage of Eulerian models, used in the present study, is that there is no need to convert from particles representing various parts of the released organic mass to concentration fields. On the other hand, it is possible to track the history of single particles in Lagrangian approaches, and to include many properties of the particles (size, sinking rates, composition) without increasing the computational costs unduly.

There is evidence that the bottom type may impact on the resuspension (Carvajalino-Fernández et al., 2020), though we have not explicitly taken this into consideration here. The effects of resuspension are probably not underestimated since we have used a critical shear velocity for resuspension very close to the parameter used by Kuhrts et al. (2004) for the “fluff” layer of fine matter.

Degradation of kelp POM may take several weeks or even months (de Bettignies et al., 2020b; Smale et al., 2022), with the photosynthetic capacity still partially intact (Frontier et al., 2021). This impacts on the potential for large-scale and long-term transport, and for how long the POM is left on the sea floor has bearing on the degradation rates and the associated bacterial community (Brunet et al., 2021). Therefore, a number of coupled inter-actions between physical transport and biological degradation determine where and in what state kelp POM settles on the sea floor. This should be addressed in more detail in future studies.

The organic loading rates were presented in terms of g C m⁻² per t WW harvested biomass. While a somewhat unorthodox unit, it allows for interpretation of the results both in terms of cultivation intensities and for farm-size independent assessments and generalized appraisals. Thus, the maximum organic loading on the seafloor can be visualized as a function of the production density and the biomass loss (Figure 6). For instance, the organic loading from a farm at a sheltered site with an export of fast sinking (“large”) POM producing 150 t WW ha⁻¹ and having a loss rate of 11% of the gross production [defined in this context by Equation (7)] will result in an added organic loading of 60–80 gC m⁻² y⁻¹, equivalent to the average net pelagic primary production in the Norwegian sea, estimated at 65–79 gC m⁻² y⁻¹ (Skogen et al., 2007; Hansen and Samuelsen, 2009). Thus, the potential for organic input to the sea floor per unit area doubles in this case, assuming that neither kelp nor phytoplankton POM is grazed of remineralized in the water column before depositing on the sea floor. This leads to a conservative estimate for the relative contribution of kelp organic loading, as phytoplankton is largely consumed by secondary producers (e.g., zooplankton) or remineralized in the water column. The present results may be used as a starting point to estimate loading for used in risk management (upper estimates, max loading) until further, more detailed data from large scale operations become available.

Kelp POM deposition on the seafloor also potentially contributes to carbon sequestration through sedimentation and long-term storage of carbon in seafloor sediments or deep water layers (Duarte et al., 2017, 2021). This implies that kelp organic matter is escaping faunal digestion and microbial degradation on the sea floor and is locked away by sedimentation at climatically significant time scales of decades to centuries (IPCC, 2019).

Our simulation results indicate that none of the matter released from any of the 3 locations considered here would reach far and deep enough to move into the North Atlantic thermohaline circulation. A large fraction of the D₁ compartment had not deposited by the end of the simulation, and was even transported out of the model domain, leaving deposition in deep waters outside the continental shelf an open question.

The carbon sequestration potential is, ultimately, dependent on how POM released from kelp farming degrades. This, in turn, depends not only on the composition of the matter, but on the size fraction and sinking rates, as well as oxygen, temperature, and the bacterial community (Wernberg and Filbee-Dexter, 2018; Brunet et al., 2021; Filbee-Dexter et al., 2021). As the time in suspension is strongly affected by sinking rates, we see that the degradation of kelp POM in the water column thus depends on the size of the particles; the average suspension time for the slowest sinking POM (model compartment D₁) was more than 100 times as long as that of the fastest sinking POM (model compartment D₄). This relates well to the difference in sinking speeds applied. However, the model has not included a compartment for burial of POM, so that, in principle, all the deposited matter was available for resuspension. This may have contributed to increasing the average suspension time.

The issue of transport and deposition is basically simple: The horizontal dispersal distance increases with water depth and decreases with increasing sinking rates. Thus, while a specific model setup has been applied in the present study, the simulation scenarios link general features of the released matter (sinking speeds) to water currents and depth, and the results can thus be applied generally. The results are scalable to any farm size and actual release rates from seaweed farming.

This study underscores the importance of constraining the dispersal and deposition of detritus from kelp cultivation in order to better understand and quantify the associated environmental risks (the effects of organic loading), and to explore the potential for seaweed farming as a climate mitigation solution through sediment carbon sequestration. This is becoming increasingly important with the global increase of the seaweed farming industry, and the urgent needs for decreasing the atmospheric and marine CO₂ concentrations.

We suggest that further research includes focus on the size distribution and sinking velocity of POM from seaweed farms, spanning the range of cultivated species and their physical properties and physiological conditions when detached from the farm. Also, the distribution of detritus between size fractions should be further investigated. Finally, the degradation dynamics, and how this interacts with the size spectrum and transport, should be given attention.