Modelling cage-level dissolved oxygen variation within salmon farms

Dissolved oxygen (DO) is a critical factor for animal welfare and production performance in Atlantic salmon sea cage farming, but is challenging to monitor and manage in the complex farm environment due to complex interactions between the environmental variation, large fish populations, farm structures, and production activities. Understanding this intra-farm variation in DO is therefore key to improving management and production outcomes. In this study, we combine in-situ environmental measurements and production data with a mathematical model that simulates DO variation at the cage-level. The approach is applied to three commercial sea cage farms to understand production limitations not captured by sensors and to identify key drivers of DO variation using a statistical model. The results show substantial intra-farm variation in DO. The model output indicates more severe conditions than suggested by the in-situ measurements, with estimated production impairment up to 65 percentage points greater at the modelled cage-level. From July to October, model outputs indicate that all sites experienced continuous DO levels below maximum feed intake, for 62-80% of the time, with periods of heightened welfare risks. Environmental factors were identified as the main drivers of variation, while 13-15% was attributed to farm-controlled factors, including cage position, biomass and feed ration. These results demonstrate that integrating in-situ measurements with modelling can reveal intra-farm dynamics not captured by standard monitoring methods. By augmenting local sensors with mathematical and statistical models, a method for aligning operations to environmental restrictions and a greater precision in farm management is offered, without the need for dense sensor networks. Adjusting the number, placement and quality of the sensors, according to where the models have the highest benefit, will further improve the potential of future farm management.

Dissolved oxygen (DO) is central to the welfare and growth of Atlantic salmon (Fry, 1971; Remen et al., 2012, Remen et al., 2013, Remen et al., 2016; Liland et al., 2026), and consequently, suboptimal or harmful variation can impair production performance in sea cage farms (Remen et al., 2014, Remen et al., 2016; Liland et al., 2026). These farms operate in highly dynamic and environmentally heterogeneous marine settings, characterised by large, open volumes where DO levels can fluctuate rapidly and non-uniformly (Solstorm et al., 2018). The drivers of DO variation, such as bathymetry, sea current regimes, thermal stratification, and sea temperature (Berntsson et al., 2025a), are inherently site-specific (Johansson et al., 2007; Burt et al., 2012; Burke et al., 2021; Jeong et al., 2024) and largely beyond operational control. Thus, sea cage farms constitute complex systems where physical, biological, and operational factors interact, creating substantial variability both within and between sites.

The complexity of DO variation poses a fundamental challenge for effective monitoring and management, where precision aquaculture emerges as an opportunity to increase the level of insight farmers have of their farms (Føre et al., 2018; O’Donncha and Grant, 2019). The spatiotemporal variability of DO, driven by interacting environmental and operational processes, makes it difficult to obtain accurate, high-resolution data that reflect the actual conditions experienced by the fish (Solstorm et al., 2018; Burke et al., 2021). As a result, farmers often lack the information necessary to understand the scope of the problem or to diagnose site-specific causes of DO depletion. Addressing this gap requires targeted strategies for collecting high-quality data, developed in alignment with specific analytical and operational applications (Page et al., 2005; Burke et al., 2021; Fu et al., 2024), as well as methods capable of processing and interpreting such data in near real-time. Yet, a recently developed mathematical model simulates DO dynamics across cages using environmental inputs external to the farm, offering insights into the intra-farm variation and potential causes of suboptimal DO conditions (Alver et al., 2022, Alver et al., 2024). The model has been validated both for a large single-unit offshore production unit (Alver et al., 2022) and for a traditional multi-cage farm (Alver et al., 2024). For the multi-cage farm, the model predicted the overall spatial and temporal variations in DO levels well, with average model bias less than 0.1 mg/l and root mean square error on the order of 0.7 mg/l for the best model configuration. Deviations occurred due to a number of known and unknown unmodelled effects, likely including the local flow field in the farm and the variable spatial distribution of the fish. Such models represent a promising approach for understanding variation at the large farms and disentangling the site-specific drivers of harmful DO variation.

Beyond physical monitoring, determining when conditions in commercial sea cages become harmful to the animals’ welfare or production performance is another challenge farmers face (Berntsson et al., 2025a). Reduced DO levels impair metabolic and cardiorespiratory function, activate stress responses and suppress the immune function, impacting feed intake, growth and susceptibility to diseases and mortality (Remen et al., 2013, Remen et al., 2016; Oldham et al., 2019; Liland et al., 2026). At the farm level, this results in reduced production performance, poorer feed conversion efficiency, increased management interventions, and higher economic risk due to potential losses. Although models of physiological limits have been developed (Remen et al., 2013, Remen et al., 2016), these are based primarily on controlled, homogenous tank experiments with small, healthy fish. In contrast, farmed salmon grow large and are subject to multiple co-occurring stressors (Afonso, 2020). Common stressors include various health issues (Moldal et al., 2025), such as gill disease, circulatory issues, and sea lice infections, which reduce oxygen uptake and increase metabolic demands (e.g., Bowden et al., 2022; Hvas and Bui, 2022). Additionally, in the heterogeneous cage environments, the fish may be able to swim in and out of suboptimal or harmful conditions (e.g., Solstorm et al., 2018), but do not necessarily avoid them unless severely stressed (Remen et al., 2012; Oppedal et al., 2011). Ultimately, even if farmers are aware of the presence of harmful or suboptimal conditions, there is an uncertainty of which mitigation strategies are available to improve the DO conditions.

According to the literature, optimisation is theoretically possible if farm operations are aligned with the site-specific environmental conditions. Tailoring variables such as cage configuration, biomass density, and feeding regimes to local environmental limitations may improve conditions that the animals experience in the sea cages (Quiñones et al., 2019; Berntsson et al., 2025a). Short-term adjustments include reducing feed ration or fasting the fish (e.g., Hvas et al., 2020) or adjusting well boat schedules and delaying stressful activities (e.g., Portz et al., 2006) if suboptimal or harmful DO conditions are present in the sea cages. This may reduce stress in the animals and waste in production (Remen et al., 2014; Hvas et al., 2024; Berntsson et al., 2025a). Long-term improvements include altering the farm configuration to optimise water flow-through, Q, or reducing biomass ponding size based on the environmental dynamics. However, such alignment requires knowledge of the environmental drivers and the nature of DO variation at the site in question to ensure the right decisions are made. Given that the drivers differ between farms (e.g., Johansson et al., 2007; Burt et al., 2012; Burke et al., 2021), site-level understanding of these dynamics is essential for implementing effective mitigation and optimisation strategies. Here, access to reliable information about the true conditions in the sea cages during operations can aid farmers in making suitable decisions for reducing stress in the animals, while incorrect information may lead to decisions that harm either animal welfare or production performance (e.g., Haug et al., 2011).

As DO declines with climate change, especially in coastal areas (Diaz and Rosenberg, 2011), and poses a threat to sea-cage farm productivity (Aksnes et al., 2019; Jyoti et al., 2024), effective management of DO variation in these farms grows increasingly urgent. In this study, we investigate DO variation at three Norwegian sites located in a region with elevated sea temperatures during late summer and autumn, with the purpose of understanding the presence and impact on the farm. The company operating these farms has enhanced its environmental monitoring to better understand DO-related risks for its animals and operations. By combining environmental monitoring data with farm inventory records, we investigate what actionable insights can be derived for the farm management from the in-situ observations at the three sites. In addition, we apply the mathematical model developed by Alver et al. (2024) to the same datasets to assess how model integration enhances or refines the understanding of DO variation and its impacts on animal welfare and production performance at Atlantic salmon farms. A central aim of the study is to compare the value of in-situ data alone versus model-informed interpretations in safeguarding animal welfare at farms, by identifying when and where fish are exposed to suboptimal or harmful DO conditions. To understand the impact of environmental and farm factors during production, we apply generalised additive modelling to real and simulated data. This approach allows us to explore not only how DO variation influences production performance and welfare at each site, but also to pinpoint the key drivers behind harmful or suboptimal within-farm variation.

In-situ measurements and company data

The data shared from the farms include datasets on both biological and environmental aspects, as well as site-specific information and pre-production reports. The quantitative data used in this study were exported from the company on January 21 st, 2025. The exported datasets included separate files on inventory, harvest and time series for each environmental variable for all three sites.

Farm configurations

The three sites are denoted A, B and C in the study, and have varying characteristics. Sites A and C are fjord sites: site A is placed some distance into a fjord, and site C is placed at the mouth of a fjord. Site B is a coastal site. The configurations of the cages on the three sites are illustrated in Figure 1, with cage numbering. The top cage circumference is 160 m at all three sites, and the bottom cage circumference is 112 m at a depth of 20 m. At site A, all cages are stocked at some point during the data period, while on site B and C, all cages but one are stocked during the data period.

Environmental monitoring and inventory data

The environmental data is collected from the feeding barge on all three sites, and from cage 3 on site A, cage 8 on site B and cage 6 on site C, as illustrated in Figure 1, for specific periods, as listed in Table 1.

The time series are stored as individual series for each environmental variable, including sea temperature, DO (separate time series for concentration and saturation) and salinity. The cage measurements include 5 m depth only, while the feeding barge measurements contain additional data on 15 m, 30 m and 50 m depth. Salinity measurements are only available for the 5 m depth.

Inventory data is shared as registrations on weight, count and biomass for each cage and fish group (anonymised when shared), including ponding, harvest, and estimated daily open and close values for biomass and mortality. Additionally, daily feed weight is included and calculations on produced biomass and feed conversion ratio, FCR (both biological and economic). It is important to note that only ponding and harvest biomass and count are measured values, and all open and close values are estimated using standard industry formulas. The company notes that these formulas are likely slightly outdated due to developments in Atlantic salmon genetics and growth potential. This introduces a potential bias in biomass and mortality estimation. When comparing the biomass values recorded on the day of harvest with the final estimated biomass, a negative deviation in biomass was observed for all fish groups harvested at the time the data were shared.

Fish health status

The farms shared insights into the health status of the populations, as registered at the individual sites during the production periods.

Site A: Suspected outbreak of Yersinia ruckeri from September 2024 and winter ulcer from January 2025.

Site B: Winter ulcer from April 2024, Mycobacteria from May 2024, gill inflammation from September 2024 and Pasteurella from November 2024.

Site C: Gill inflammation from August 2024, complex gill disease, CGD, from November 2024 and winter ulcer from January 2025.

All three sites further conducted treatments for lice infestation multiple times during the production period, indicating that all populations suffered from parasites.

Exposure thresholds

As the DO limits for welfare and growth recommended by the operational welfare indices (OWIs) are the limiting oxygen saturation, LOS, and the DO level where feed intake in the fish is reduced, DO max FI (Noble et al., 2018), these are used in this study. LOS is the term for the lowest tolerance limit of the fish before the environment becomes harmful to the welfare of the animal. At this level, the animals can no longer uphold routine metabolic rate (Remen et al., 2013). DO max FI is the term for the tolerance limit where feed intake (FI) of the fish begins to decline (Remen et al., 2016). As appetite is affected, it is also likely that welfare begins to be affected at levels below DO max FI (Berntsson et al., 2025a). These limits vary with any factor that increases metabolic rates, including feeding and activity (Remen et al., 2013, Remen et al., 2016). A safety factor of 40% is included to account for the uncertainties of applying the formulas in commercial environments (Remen et al., 2013; Berntsson et al., 2025a).

The threshold formulas used are:

Here, MO 2 is the metabolic oxygen consumption per kg fish (mg O 2 kg -1 h -1) and T is the sea temperature (°C). MO 2 is here calculated using the following formula:

DO levels above DO max FI we classify as optimal levels, whereas between DO max FI and LOS we classify as suboptimal levels and below LOS as harmful levels. These terms are used throughout the paper.

Spatiotemporal limits

Regarding the spatiotemporal limits for hypoxic exposure, in this study, exposure events are only considered significant when more than 50% of the sea cage volume falls below LOS or DO max FI for a continuous duration of minimum 105 minutes. This temporal threshold is based on previous findings that fluctuations of this length have been observed to cause physiological stress and impaired performance in Atlantic salmon (Remen et al., 2012, Remen et al., 2013, Remen et al., 2016), while chronic hypoxic exposure further affects the immune system in Atlantic salmon (Rojas et al., 2025; Liland et al., 2026). Although the fish physiologically acclimatise to chronic hypoxia to some degree, reduced feed intake and lower growth continue in chronic exposure as part of the acclimatisation (Liland et al., 2026). The spatial threshold is set because of the opportunity the fish may have to swim out of harmful environments in the cage.

Oxygen model configuration

In-cage DO concentrations at the three locations were simulated for the period from 1 st of June to 31 st of December 2024 using the model by Alver et al. (2024). The model domain for each location was set to cover the entire site, as illustrated in Figure 1, with a horizontal and vertical grid cell size of 2.5 m. For efficiency, the model domains were aligned with the orientation of each farm. Cages were shaped as cones with a radius of 25.5 m at the surface, narrowing to 17.8 m at 20 m depth, then narrowing to 0 at the bottom tip of 38 m depth. In the model grid, the centre point of each cage was determined, and all cells whose centre’s horizontal distance from the cage centre was less than or equal to the radius at the appropriate depth were counted as inside the cage. All DO statistics for a particular cage were based on the collection of grid cells inside that cage.

Model inputs

The oxygen model (Alver et al., 2024) is based on the advection-diffusion equation with the advection term representing current and the sink term representing the oxygen consumption by the fish in each farm. Boundary conditions are determined by measured ambient DO level, and coefficients for turbulent diffusion have been chosen through earlier studies (Alver et al., 2016, Alver et al., 2024). The oxygen consumption per fish is calculated based on temperature and fish size using a modified version of the empirical model by Grøttum and Sigholt (1998). A simplified fish behaviour model is used to determine the spatial distribution of oxygen consumption, combining a feed distribution model providing estimates of the distribution of feeding fish with a vertical profile estimating the distribution of non-feeding fish. The model thereby combines ambient DO, temperature and the water exchange rate with the oxygen consumption in the farm to estimate the resulting DO levels in individual cages.

Biomass and feeding

One separate model simulation was done for each day of the simulation period for each site. At startup, the inventory data from the site was used to determine the number of fish, average weight and amount of feed added for each cage. The feeding was uniformly distributed over the time interval 0700–1900 daily in the model.

Ambient DO levels

DO measurements at each site’s feeding barge at 5, 15 and 30 m were used to set the ambient DO levels of the model. Measurements were linearly interpolated to 5-minute intervals, and at each update, the measurements at the three depths were linearly interpolated to get a profile covering all vertical layers of the oxygen model. Extrapolation was done by extending the 5 m value up to the surface layer and the 30 m value to all depths below. At model initialisation, all cells at each depth layer in the model were initialised equal to the ambient DO level at that depth.

Current and temperature

Data on current vectors, temperature, salinity and sea surface height (sea surface elevation) were extracted from the NorFjords operational model system with 160 m horizontal resolution (Dalsøren et al., 2020), which uses boundary conditions from Norkyst800 which has an 800 m resolution (Asplin et al., 2020). Data was extracted with one hour time resolution for the entire simulation period at each of the three locations. The vertical profiles were linearly interpolated from the NorFjords model layers into the oxygen model’s vertical layers. Since the oxygen model’s domains are oriented along the length axis of the farms, the modelled layout of each farm is effectively rotated by an angle θ (i), where i represents site A, B or C, compared to the farm’s real orientation. The current vectors were rotated by − θ (i) at each location to compensate. To account for the reduction in current speed caused by the presence of the farm and the fish biomass, current speeds were reduced by 20% from the speed given by the NorFjords model, as was done in Alver et al. (2024), based on previously observed values (Endresen et al., 2013; Klebert et al., 2015).

Oxygen model processing

The oxygen model stored key values for each cage at a time interval of 1 minute: DO level at virtual sensor positions (centre and along outer edge of cage; 5, 10 and 15 m depth), mean DO value over the cage cells (all model cells within the cage volume), 5th percentile DO value in the cage, and distribution of DO values over the cage cells (counts in intervals at a resolution of 0.1 mg/l). The stored DO distributions can be used to calculate the fraction of cells in a cage falling below temperature dependent DO max FI or LOS thresholds at any time in the simulation, to be classified as suboptimal and harmful levels.

When calculating daily values, the initial 60 minutes of each simulation (from midnight to 1 AM) were disregarded to reduce the effect of the model’s initial values. First, the worst-case conditions were found for each cage per day by using the day’s lowest values of the mean and fifth percentile values and the day’s highest fractions of cells below threshold levels. Then, the “best” and “worst” cages were found on each day to highlight the span of conditions seen over the farm.

Periods with doubtful data quality in the input DO data were identified and removed at site C, including the following dates: May 7 th – 10 th, June 2 nd – 4 th, July 20 th – 22 nd, and November 8 th – 10 th.

Model bias

Model bias was tested for the effect of DO sensor position on the oxygen model, alongside the bias between measured and modelled sea temperature values in the current model, to gauge discrepancies. The results are presented in this section.

Sensor placement

The sensor placement influences the model values, and as detailed in Alver et al. (2024), the ideal position for in-situ measurements is without influence from the farm. However, this is typically not the case, as the monitoring equipment is usually set up inside or near a cage or at the feeding barge, where it is most practical to position and maintain. Figure 2 shows the bias of model simulations based on in-situ measurement positions near the barge compared to in a cage. As the figure shows, there is considerably less bias in data from the position by the barge, and consequently, only this data was utilised in the model simulations, to minimise bias in the study results.

Oceanographic model

To assess the accuracy of the data from the oceanographic model (Dalsøren et al., 2020), biases between the measured and simulated temperature values were studied and are visualised in Figure 3. Overall, the simulated values have a high accuracy, with a small negative bias that increases with depth, indicating that the model might underestimate sea temperatures at deeper layers. There can also be deviations and bias in the measured values of individual sensors; however, the overall biases are fairly similar across the three locations, indicating that the bias is likely to be mainly in the simulated values.

Production impairment classification

A production impairment classification table, building on that developed by Jeong et al. (2024), is used to analyse to which degree the animals are exposed to suboptimal or harmful DO levels throughout the analysed periods at the three sites. In this study, we adapt it with the thresholds LOS and DO max FI (Remen et al., 2013, Remen et al., 2016), described in the previous section. Here again, levels below LOS are classified as harmful, levels between LOS and DO max FI are classified as suboptimal, and levels above DO max FI are classified as optimal.

Generalised additive models

To determine site-specific drivers of variation in DO across the sea cages, generalised additive models (GAMs) are used as a diagnostic tool for understanding the contribution to the observed variation by different factors. GAM models extend generalised linear models (GLMs) by allowing non-linear relationships between the response and explanatory variables using smoothing functions (Wood, 2017), typically in the form of splines. Analyses were conducted in R using the mgcv package. We modelled the mean DO from the oxygen model output within cages at 20-minute intervals. The mean DO of the full cage volume was chosen over the minimum DO values in the sea cages, because of the uncertainty of short-term, local minima on animal welfare and growth. Multiple GAMs were fitted to evaluate how environmental and operational factors contributed to DO variability. We modelled the response variable as a function with the general structure:

where y is the mean DO of a cage and s(x i) denotes a smooth function estimated for each continuous predictor. This approach allows for flexible, data-driven estimation of non-linear relationships. We tested interaction effects using different tensor product smooths, cyclic smooths for periodic variables, and modelled cage as a categorical factor. The main model was chosen based on performance and an evaluation of the behaviour of the variable smooths, and was ultimately modelled as follows:

MeanDO ~ te(Temperature 5m, Temperature 15m, Temperature 25m, k = c(3,3,3)) + te(ExternalO2, CurrentSpeed, k=5) + te(SeaSurfaceHeight, CurrentDirection, k = c(3, 3), bs=c(“tp”, “cc”)) + s(Salinity, k=5) + s(Feed, k=5) + s(Biomass, k=10) + s(Hour, bs = “cc”, k=10) + s(Month, k=5) + Cage

where te(x) denotes a tensor product smooth function estimated for interacting variables (including main effects). The k-parameters, controlling the smoothness, in the te- and s-functions are set to the levels in the equation to limit the model’s ability to overfit to the data, and the bs-parameter is set to “cc” for cyclic variables. When bs is not set, “tp” is the default, resulting in a thin plate regression spline basis. Cage-level effects are explored by setting the by-parameter to “Cage.” The importance and contribution of each variable on the mean DO variation in the cages of each farm are evaluated based on hierarchical partitioning in the gam.hp library developed by Lai et al. (2024).

Overview of workflow

Multiple data sources and models were used to produce the results in this study. This section presents an overview of the data flow and models to summarise the complex flow in a visualisation. Figure 4 illustrates how the different data points flow from the data sources, the model data that is added from oceanographic model NorFjords160 (Dalsøren et al., 2020), into the oxygen model, adapted from Alver et al. (2024), and the GAMs.

The multiple-depth DO measurements from the on-site environmental monitoring were used as boundary conditions for the oxygen model, together with the hydrodynamic data on sea current obtained from the NorFjords model to estimate the flow of DO to the cages. Biomass and feed data from the inventory dataset, were used in combination with sea temperature from the NorFjords model, to estimate oxygen consumption in the cages. The data treatment of these variables are detailed in Sections 2.4.1-2.4.3 and 2.5. The oxygen model, described in Sections 2.3 and 2.5, integrates these components to simulate the spatiotemporal variation of DO within each cage volume, resulting in a high-resolution dataset of DO conditions. The outputs were subsequently post-processed in MATLAB (The MathWorks Inc., 2024) to derive aggregated metrics, and analysed according to the exposure thresholds, detailed in Section 2.2, to produce the results in Sections 3.1 and 3.2.1. Finally, the outputs from the model were used as input to the GAMs, described in Section 2.8, which were implemented in R (R Core Team, 2025), to produce the results presented in Section 3.2.2.

DO variation at the sites

Observed and modelled variation at the farms

The measured values show mainly optimal conditions at all three sites for June-December (Figure 5), with few signs of suboptimal or harmful variations, except for a period of suboptimal levels in September. However, when applying the oxygen model to understand in-cage variation, the overview shifts to mostly suboptimal levels during summer and autumn, and even some harmful periods, especially in September and October, with large variation between individual cages.

Spatiotemporal exposure to low DO at the farms

As indicated by the simulations in Figure 5, the cages at the different sites have varying exposure to suboptimal and harmful DO variation. In Figure 6, the average fractions of hypoxic cells, i.e., the volume exposed to hypoxia, are presented for the cages with the greatest and least exposure from June to December. The contrast within and between sites is evident, where site A has the greatest exposure to harmful conditions, while site C has the greatest exposure to suboptimal conditions. In the period August-October, site C shows almost no differences between cages, and all are nearly completely exposed to suboptimal DO in this period.

While the plots in Figure 6 shows almost complete exposure to suboptimal levels in the period between mid-July and mid-October, the production impairment classification, presented in Table 2, shows the average exposure to suboptimal and harmful levels across all cages on the sites, from the start of July until the end of October. According to the model, the three sites were on average exposed to suboptimal conditions for 62–80% of the time in the period from the start of July to end of October and to harmful conditions for up to 4% of the time. In contrast, the in-situ measurements show suboptimal exposure for only 31–43% of the time during this period, with no harmful exposure detected. Overall, modelled and measured data differ substantially in the insights provided regarding the exposure to optimal, suboptimal, and harmful conditions across all sites from July to October.

The worst conditions occur in September, where the model indicates no optimal conditions at the cage level, only harmful and suboptimal exposure, although the measurements show periods of optimal conditions. While September represents the poorest oxygen conditions overall, the greatest discrepancies between modelled and measured values occur in June and August, with differences in exposure ranging from 26 to 65 percentage points. In comparison, differences in September and October are smaller, ranging from 12 to 33 percentage points. In addition, when exploring minimum DO levels, these highlight even greater disparities. For example, at Site B in August, the lowest modelled values differ by 90 percentage points to the in-situ measurements.

In Figure 7, temporal fluctuations from the model output at the sites are shown for the period June to December. Suboptimal episodes above 105 minutes are more frequent than harmful episodes in the analysed period, with some daily periods lasting for 24 h. However, as the data is analysed per day, multiple days with one episode of 24 h indicate a consistent presence of suboptimal levels and chronic exposure to hypoxia across the sites’ cages. During these periods, a reduction in growth and maximum feed intake is expected. During the months with the greatest exposure, sites A and C have more homogenous results across cages, while site B has more variation in suboptimal DO levels between cages. Furthermore, while no harmful episodes above 105 min were observed in site C, sites A and B have periods above 105 min, where more than 50% of the cage are harmful in September, indicating that the animals on these two sites likely experienced harmful conditions. In the worst episode, harmful conditions were present for more than 10 h.

Drivers of suboptimal DO at the farms

Overview of variation in influential parameters

Influential parameters vary at the three sites and indicate potentially different drivers of DO variation, which require different considerations when adapting operations to the environmental restrictions. All three sites are exposed to varying sea temperatures in the vertical profile with quite similar profiles, where the periods with the absolute highest sea temperatures are not concurrent with the largest drops in DO (see Figure 5). The sites have different sea current variation (Figure 8), where site B has a lower average sea current speed, but less variation compared to site A and C, which both have greater maximum speeds compared to site B. This result is unexpected, since sites A and C are fjord sites, and site B is a coastal site. All sites have brief periods of stand-still water, indicating that tidal variation is present at all three sites.

The dominant current direction is northwest on site A and B, and northeast on site C, in this dataset. Not only is the current speed variation different at the three sites, but the flow-through of water, Q, differ as well, as visualised in Figure 9. The combination of different farm configurations, Q and variation in current speed and direction causes different downstream influences between cages at the sites.

The heatmaps in Figure 9 are snapshots in time and exemplify how Q influences cages in the horizontal and vertical space of the three farms at these particular points in time. The animations included in Supplementary Materials 1–3 of this paper show how this influence varies throughout the day at the three sites.

For the point in time included in Figure 9, the variation in mean DO between cages on site A ranges 6.09-6.42 mg/L, while the minimum DO ranges 3.87-5.39 mg/L. Here, the lowest biomass is found in cage 1 and the largest in cage 4, where cage 4 has more than twice as high biomass as cage 1 and is fed twice as much feed. These cages correspond to the highest and lowest DO levels at the site, for the time shown in the heatmap, both in terms of mean and minimum DO, where cage 4 has the lowest values and cage 1 the highest.

On site B, the mean DO values found in the individual cages range 5.90-6.42 mg/L, while the minimum DO levels range 3.32-5.95 mg/L, at the time of the snapshot. The largest biomass is found in cage 3, followed by cage 6, and the lowest biomass is found in cage 2 (excluding the empty cage 5), where cage 3 has four times larger biomass than cage 2. The largest daily feed ration is found in cage 6 and the lowest in cage 8, except for cages 1, 2 and 4, which are not fed this day. The lowest minimum DO levels are found in cage 6 with 3.32 mg/L, followed by cage 3 with 3.54 mg/L, while the highest minimum DO levels are found in cage 4 at 5.95 mg/L, even when including the empty cage 5. The lowest mean DO is found in cage 6, followed by cage 1, and the highest is again found in cage 4, also when including cage 5.

On site C, mean DO ranges 5.73-6.41 mg/L and minimum DO ranges 4.87-5.65 mg/L, where the lowest minimum and mean values are both found in cage 1, placed downstream of the cages, and the highest values are found in cage 12, where the water flow enters the farm. However, cage 1 further corresponds to the cage with the highest biomass, followed by cage 6, while cage 11 has the lowest biomass. The biomass size in cage 1 is nearly 1.5 times larger than that in cage 11. Cage 11 is also fed the smallest amount, nearly half of the largest daily feed ration, which is fed to cage 6.

Drivers of DO variation at the sites

The GAMs identify how individual parameters influence mean DO variation in the sea cages of the farms, and the best performing models explain 86–88% of the variation. The intercept, i.e., the baseline level of DO, is near 7.5 mg/L at all sites. At site A, the largest deviations from the intercept at cage 1 are in cages 3 (0.038) and 5 (-0.038), at site B, in cages 8 (0.026) and 4 (-0.084), and at site C, in cages 12 (0.16) and 4 (-0.082). These deviations indicate that the baseline differs from cage to cage across the period. The p-values for both the intercept and the variables are <2e-16 for the models at each site, indicating highly significant effects, i.e., that the effect on mean DO inside the cages is not random. 12-14% of the variation could not be explained, either because some sources of variation are missing or simply because this variation could not be captured by the smooths, partially caused by the chosen amount of smoothing. The contribution of each individual parameter to the in-cage mean DO variation is visualised in Figure 10.

Although all variables are identified with significant contributions, the interaction of external DO with current speed, and the combined effect of water column temperature at multiple depths, explained the largest portion of the variation at all three sites. These effects were captured using tensor product smooths, allowing the model to flexibly account for how the response changes with combinations of variables, rather than treating them independently. Following these, seasonal variation, represented by the months, and tidal variation, represented by the interaction between sea surface height and sea current direction, also contributed meaningfully. Salinity had a relatively small contribution across the sites. The biomass size had a considerable influence on sites B and C, and slightly less on site A. On site A, however, the daily feed ration contributed more to the mean DO variation compared to the other two sites. The parameters that the farm management has control of include biomass size, daily feed ration and cage position, and are here found to contribute to the overall mean DO variation by 13% at site A, 15% at site B and 14% at site C.

It is important to note that the variables included in the GAMs may interact in ways not fully captured when modelled simultaneously. For example, biomass size, feed ration, and time each partially reflect biomass growth and increasing oxygen consumption, which strongly influences in-cage DO levels. At the same time, temperature also contributes to biomass growth, further complicating these relationships. The same is true for the interaction between external DO, sea current variation and cage position, as these may all represent Q and cage configuration. As a result, the effect attributed to any single variable may partially represent the influence of correlated or interacting factors. The sum of the correlated variables may be more representative than the variables’ individual contributions.

Cage-level analysis using tensor product smooths

While the main model for each site captures most of the variation in mean DO across cages, examining additional models’ smooth functions at both the farm- and cage-level provides additional detail. In Figure 11, an adjustment of the model is made, where a tensor product smooth of external DO and current direction replaces the tensor product smooth of external DO and current speed. Examining the cage-effect of this tensor product smooth shows a consistent interaction effect on cage-level DO at site A. This effect is not included in the main model presented in Figure 10, because other terms jointly explained more of the variation, but highlights how cage-level dynamics can be further explored and understood by adjustments in the GAMs.

Figure 11 shows contour plots of the combined effect of current direction and external DO on internal DO. The contour lines represent areas of equal predicted response, with blue and red areas indicating negative and positive effects, respectively. At the farm scale, negative effects on internal DO are observed across all cages and current directions when external DO levels fall below ~8 mg/L, whereas positive effects occur when DO exceeds this threshold. Currents flowing along the length of the farm, in the -50° to 50° (northwest to northeast) direction, and between 150° and 250° (southeast to southwest) direction, show minimum and maximum effects, from -1 to 1.

At the cage-level, responses differ among the cages at the same site. In cage 1, the response of variation in external DO and current direction on internal mean DO is generally positive, except when external DO is low and the current flows northwest, which is consistent with when the water flows through all the cages of the farm before it reaches cage 1. For this same combination in cage 6, located at the opposite end of the farm, positive effects are observed. Here, the strongest negative effect is observed when current flows east with low external DO, while high external DO produces positive effects in the same direction. In contrast, cage 3, at the midpoint of the farm, shows a reversed response for eastern currents. Similar to cage 1 and the farm-level response, cage 3 shows slightly negative effects in the northwest direction when external DO is low. The magnitude of effects varies between cages, with cage 1 ranging from -1 to 6, cage 3 from -4 to 4, and cage 6 from -1 to 1. These patterns highlight how the effect of different variables changes across the cages of a farm, and the additional detail provided when analysed at the cage- or farm-level.

This study demonstrates how combining environmental and operational data with a mathematical model can reveal DO variation at the cage-level. The following sections discuss the operational potential of this approach and outline key steps needed before implementation.

The potential of augmenting in-situ measurements with mathematical modelling in operational DO management

Combining sensor and inventory data with mathematical modelling can improve spatial understanding of DO conditions and support management decisions.

Enhancing operational understanding of the sea cage environment

The results show that the point measurements at each farm, as captured by the in-situ monitoring by the farms, reflect only the local conditions at the sensor positions and lack the spatial resolution needed to assess variability within and between cages (Page et al., 2005; Johansson et al., 2007; Burt et al., 2012; Solstorm et al., 2018; Burke et al., 2021). In previous studies, the farm itself is identified as the driving force of DO variation (Vigen, 2008; Burke et al., 2021), and it is the combination of environmental variation, farm infrastructure and presence of large fish populations that causes low DO levels, rather than the environment itself. Consequently, scholars argue that one sensor point or one sample per day regime for monitoring variation is insufficient to understand the intra-farm variation (Page et al., 2005; Burke et al., 2021).

To succeed in capturing the spatial variation in DO with in-situ measurements, dense sensor networks are required, as demonstrated by multiple studies, using between six and 23 environmental loggers (e.g., Solstorm et al., 2018; Burke et al., 2021; Alver et al., 2024). While efficient in indicating intra-farm and in-cage variation, they are not necessarily scalable to commercial operation, as maintaining such networks demands substantial investments not only in hardware but also in upkeep and data management (Bittig et al., 2018). To account for these complex dynamics, without relying on dense sensor networks, the mathematical model developed by Alver et al. (2022, Alver et al. 2024) integrates fish physiology and metabolism with hydrodynamic processes and farm structure interactions, and estimates DO variation across the farm effectively. While site-specific validation and further input refinement are still necessary, the findings from this study support its utility as a complementary monitoring method, without the need to implement the dense sensor networks. The low bias of the model demonstrated in previous studies (Alver et al., 2022, Alver et al. 2024) highlights the model’s potential as a resource-effective tool for enhancing environmental monitoring in aquaculture operations.

In the present study, the model displays its ability to reveal fine-scale DO variability across the farm. For example, although measurements near the feeding barge indicated generally acceptable conditions, the model showed significant in-cage DO declines from July to October, suggesting a higher risk to fish health and production performance than monitoring alone would reveal. This suggests that the animals may have been more susceptible to diseases and parasites due to hypoxia than known, especially as the understanding of the combined effects of such stressors has been limited by insufficient access to high-quality data (Afonso, 2020; Oliveira et al., 2021). Discrepancies between observed and model-predicted production impairment reached up to 65 percentage points in certain periods, highlighting the limitations of point-based monitoring alone. These findings align with the observations of the studies using dense sensor networks: Solstorm et al. (2018) found that fish-mounted sensors recorded suboptimal DO conditions in 24–63% of observations, despite adequate reference point values, while Burke et al. (2021) reported DO discrepancies of up to 4 mg/L between cages at the same farm. Consequently, the modelling approach provides a scalable alternative to dense instrumentation, offering cage-level insights without proportional increases in monitoring effort.

Building on the enhanced understanding of intra-farm DO variability, the model presented in this study lays the foundation for cage-level management, enhancing traditional farm-level approaches with a step toward precision fish farming and digital twins (Føre et al., 2018, Føre et al., 2024; O’Donncha and Grant, 2019).

Increased insights enable operational optimisation

In aquaculture farms, access to detailed information for cage-specific optimisation can help farmers adjust production to the environmental restrictions (Quiñones et al., 2019; Berntsson et al., 2025a). Understanding how the variables that influence DO variation interact at the cage-level enables operational adjustments in the variables that operations control to improve welfare, reduce waste, and enhance overall efficiency (Berntsson et al., 2025a). In this study, statistical models are used to identify the contribution of the factors that the farm can and cannot control, where the combination of all these variables contributes to suboptimal or harmful conditions. While the factors that the farm cannot control can be adjusted to, the farm-controlled factors, including cage position, biomass size and daily feed ration, contribute to 13-15% of the in-cage mean DO variation in the present study. This indicates an initial potential of using statistical models as tools to optimise and align operations to the environmental restrictions.

Furthermore, simulations incorporating seasonal forecasts or projected biomass growth can help managers identify high-risk periods in advance. For instance, the present study found that DO risk peaked between July and October across all three sites, with the most critical conditions in September, in alignment with previous studies (e.g., Johansson et al., 2007; Vigen, 2008; Oppedal et al., 2011; Jeong et al., 2024). In contrast, model simulations for the early monitoring period, despite the high bias in in-cage data, indicated stable conditions until June, further supporting the seasonal importance of DO management. While the exact timing may vary by geographic location, farms with similar dynamics should prioritise improved DO management during July–October and explore whether suboptimal and harmful DO levels can be avoided by operational adjustments, and what the effects of that would be.

Combining models with in-situ measurements has proven effective within agriculture. For instance, Monzon et al. (2018) found that a farm with precision agriculture technology for site-specific zone management performed better than neighbouring farms, with a 54% higher farm output, 46% higher gross margin and higher net income, despite increased total costs for the implementation and management of the technology. This echoes previous results in cost and profit estimation of technology adaptation (Schimmelpfennig, 2018), displaying the potential of successful implementation. These parallels suggest the significant potential for precision aquaculture to follow suit, as outlined in detail by previous studies (Føre et al., 2018, Føre et al., 2024; O’Donncha and Grant, 2019).

Proposing specific optimisation actions

Real-time management of DO variation

The oxygen model in combination with the statistical model can help proactively identify cages vulnerable to low DO, particularly during risk periods, such as slack currents, high temperatures, vertical stratification or large biomass sizes (Quiñones et al., 2019; Berntsson et al., 2025a). This supports timely decisions such as adjusting or prioritising feeding or handling schedules to reduce fish stress in exposed cages and production waste (O’Donncha and Grant, 2019). As appetite declines and digestion slows down in the suboptimal levels below the DO max FI threshold, adjusting daily feeding ratio to the maximum feed intake (DFI max) recommended for the specific temperature and DO saturation has the potential of reducing both feed waste and stress in the animals (Remen et al., 2014, Remen et al., 2016; Hvas et al., 2020, Hvas et al., 2024; Nuic et al., 2024). As all three farms in this study are consistently below the threshold for maximum feed intake between July and October, adjusting feeding routines is an action these farms are recommended to explore for this period. Feeding rations are often based on sea temperature and fish size, however, feed intake under hypoxia has been observed to reduce to 60-72% of that under normoxic conditions (Liland et al., 2026), indicating that feeding strategies that do not account for DO conditions may lead to significant overfeeding.

In addition to adjusting feeding routines, farmers should mitigate the impact of low DO episodes by avoiding stressful, crowding-inducing activities during critical periods or by scheduling them when environmental conditions can accommodate the animals’ metabolic demands. For instance, Forsberg (1995) observed handling stress to increase Atlantic salmon biomass density from 51 to 180 kg/m³, raising oxygen consumption by 4-7-fold from resting metabolic rate, equal to maximum metabolic rates in swimming experiments (Brett and Groves, 1979). In Forsberg (1995), the effect of crowding lasted for 3–4 h after the handling event was concluded. Naturally, such activities further impact the variation in cage DO levels (Alver et al., 2024; Berntsson et al., 2025a), and may push suboptimal levels to harmful, if poorly timed. If farmers plan these production activities according to expected environmental variation and expected increase in metabolic requirements in the population by the activity, negative impacts on animal welfare may be avoided or reduced. To our knowledge, no previous studies have investigated this topic. However, the farming partner providing data for this study reports that well-boat operations are aborted due to signs of fish stress, which are typically only detected immediately prior to the initiation of operations.

Long-term adjustments to consistent patterns

Long-term actions such as adjusting biomass density and cage configuration should align with site-specific hydrodynamics and environmental constraints (Quiñones et al., 2019; Berntsson et al., 2025a). The results from the GAM analyses and intra-farm variation in DO show that drivers like current speed, biomass, and sea surface height influence DO variation, in combination, differently across cages and sites. Although these findings must be validated with longer time-series, aligning biomass size with the true carrying capacity of individual cages could improve both welfare and performance (Oppedal et al., 2011; Quiñones et al., 2019). Cage size and placement are also critical: larger cages tend to exhibit lower DO (Oldham et al., 2018; Alver et al., 2023), and cages positioned downstream of the others may be adversely affected if spacing is insufficient (Alver et al., 2024), as indicated by the effect of sea current direction on different cages in Figure 11. While regulatory limits on biomass density may be satisfied by the farms, for the full cage volume [e.g., 25 kg/m³ in Norway (Akvakulturdriftsforskriften § 25, 2018)], in-cage variation in biomass distribution due to temperature preference (Oppedal et al., 2011; Stehfest et al., 2017) or handling activities causing crowding (Forsberg, 1995, Oppedal et al., 2011) may increase the biomass density in subspaces of the cages. Consequently, regulated densities may not be supported at the sites in reality, due to local environment, fish behaviour and farm configurations (Oppedal et al., 2011; Quiñones et al., 2019; Berntsson et al., 2025a). With tools for scenario planning and further development of the oxygen model by Alver et al. (2022, Alver et al. 2024), farm managers and industry administrators can explore whether aligning carrying capacity to the environmental restrictions of a site, rather than a fixed rate per volume unit, is more beneficial to productivity and animal welfare than the current maximum allowances.

Although not yet ready for operational implementation, these findings show that calibrated, site-specific models alongside traditional monitoring can enhance adaptive, efficient, and welfare-oriented management in aquaculture.

Further work

Uncertainty in both the data material and the modelling methods limits the precision and reliability of the results. Before operational application, further development is needed, including improved input data from the farms, refinement of the oxygen model, and more robust exposure thresholds.

Input data

The environmental monitoring

The in-situ measurements of DO and sea temperature generally behaved as expected and appear reliable, except for the excluded periods detailed in Section 2.5. However, validation is not possible because only one measurement was available per depth and time unit, with the exception of an additional sensor at 5 m-depth in cage 8 at site B. Uncertainty is further increased by the absence of in-situ current data, a key input variable for the oxygen model (Alver et al., 2022, Alver et al. 2024). While currents from the NorFjords model are expected to statistically represent conditions reasonably well, they will not capture hour-to-hour variability (Dalsøren et al., 2020; Asplin et al., 2020). As illustrated in Figure 3, sea temperature values aligned reasonably well with observations but showed a consistent negative bias at depth. If farms measured vertical profiles of sea current, in addition to DO, sea temperature and salinity, the performance of NorFjords at each site could be assessed and calibrated for local deviations. Furthermore, although no models of algal dynamics at the fine spatial scale of the present study currently exist, to the knowledge of the authors of this study, this would be a valuable contribution in the future.

Spatiotemporal aspects of data collection

Inconsistencies in spatial coverage, monitoring periods, and temporal resolution reduce the potential for advanced analysis. Model accuracy is particularly sensitive to sensor positioning. In this study, barge-based measurements produced lower bias than in-cage measurements. Upstream sensors are likely to provide more representative input by capturing true inflow conditions (Alver et al., 2022, Alver et al. 2024). However, in-cage sensors could support validation of model outputs and improve understanding of actual fish exposure, provided that they overlap in time with barge-based monitoring. A combined strategy, using upstream buoy-based monitoring for inflow conditions alongside in-cage measurements of exposed cages, could therefore enhance input fidelity while also fulfilling requirements for fish welfare reporting (Oppedal et al., 2011; Noble et al., 2018; Alver et al., 2024).

The short monitoring period also prevents the identification of long-term or cyclic trends. The GAMs could not study cyclic effects for specific months (see Section 2.8), as less than one year of suitable data was available, and consequently, non-cyclic terms were used. Given these data limitations, the GAM-parameterization was intentionally conservative, prioritising robustness and interpretability over exploration of more complex spline formulations. Nevertheless, the GAM framework offers substantial flexibility, and future applications with multi-year observations would allow the use of cyclic smooths and more advanced parameterisations to better resolve seasonal patterns during periods of highest risk. Such analyses would benefit from data collected over multiple years at consistent spatial locations (Cichy and Rass, 2019; Bittig et al., 2018).

Finally, the temporal resolution of certain variables, especially feeding, limits analytical value. Currently, the daily feed ration is reported only as a total per cage and then distributed uniformly across feeding hours (0700–1900) in the model (Sections 2.1 and 2.4.1). In practice, feeding is non-uniform and depends on appetite assessments. Consequently, hourly effects of feeding cannot be evaluated, despite their importance for understanding immediate and delayed metabolic demands (Forsberg, 1997). More precise temporal recording of feeding time and ration would improve subsequent analysis of the impact of this variable.

Biological data

Oxygen consumption by the biomass is a key model input (Alver et al., 2022, Alver et al. 2024), but the operational data on biomass, fish size, and mortality rates are available only as estimates rather than measurements in this study (see Section 2.1). Increasing the accuracy and certainty of these measurements would be beneficial to reduce uncertainty in the model. Improved accuracy in biomass and fish size is a central objective of precision aquaculture, and will likely improve alongside developments in submarine camera technology and machine learning (e.g., Li et al., 2020; Sauphar et al., 2024). Additionally, the data shared on the presence of disease at the farms is high-level and lacks detail at the cage level. More accurate and standardised data collection methods for these parameters would improve the representation of biomass requirements in the management of DO variation.

Oxygen model

Farm structures and fish biomass alter current speeds and directions within and around cages, creating complex flow fields that are difficult to represent accurately (Michelsen et al., 2019; Broch et al., 2020). The oxygen model simplifies these dynamics by assuming uniform, time-varying current speed and direction at each depth and applies a constant 20% reduction to NorFjords’ values. Combined with the uncertainties in input data, this can lead to over- or underestimation of DO levels. In Alver et al. (2024), the full farm model showed a positive bias of about 0.2 mg/L; although the magnitude may differ between sites, the bias is expected to remain relatively small. The assumption of uniform current also reduces the model’s ability to represent differences between cages. In reality, current speeds often decrease toward downstream cages, lowering flow rates and DO levels. The model may therefore underestimate the negative effects on downstream cages, and validation against observed cage-level differences is needed before operational use. Additionally, further exploring the effect of net biofouling on water exchange and the potential of including a dynamic biofouling coefficient could enhance the precision of the model. In Alver et al. (2024), the authors simulated the gradual build-up of moderate biofouling, which reduced the overall bias. If farms share insights on the degree of biofouling on their nets, this effect can be included in the model.

The model currently applies existing growth formulas (Grøttum and Sigholt, 1998). However, to improve precision, Alver et al. (2022) increased the growth rate by 30%, and Alver et al. (2024) by an additional 20%, highlighting the need for updated empirical growth estimations for modern genetics. In addition, the model does not yet incorporate variation in metabolic activity due to digestion (Forsberg, 1997), which implies higher oxygen consumption after feeding. Ongoing work is addressing this variability and analysing its impact on cage DO levels.

Exposure thresholds

The thresholds used to evaluate harmful DO conditions are based on laboratory experiments involving small, unstressed fish (Remen et al., 2012, Remen et al., 2013, Remen et al., 2016). While a 40% safety factor was applied in this study to account for increased sensitivity under commercial conditions, as recommended by the original authors, these thresholds may still underestimate the actual vulnerability of fish in sea cages, where biomass densities are higher and environmental stressors are more complex (Afonso, 2020). Smaller fish are also known to have a greater oxygen consumption rate per weight unit (Berntsson et al., 2025a), compared to larger fish that have a greater total oxygen consumption rate, so the physiological thresholds applied in this study may under- or overestimate the effect on large fish (Remen et al., 2013, Remen et al., 2016). Thresholds for spatial and temporal exposure are also subject to uncertainty. For example, in this study, we identify that suboptimal or harmful conditions are present when 50% of the cage volume falls below a threshold. This limit is arbitrary and lacks empirical validation. In Solstorm et al. (2018), fish were observed to swim in and out of low DO zones within the cage, and the effect of such fluctuation on welfare or growth over time is not known (Oppedal et al., 2011; Berntsson et al., 2025a). Similarly, while the 105-minute threshold for fluctuating hypoxia is supported by laboratory evidence (Remen et al., 2012, Remen et al., 2013, Remen et al., 2016), the applicability of this value in operational environments remains uncertain. While this study presents episodes where the fish are exposed to suboptimal or harmful levels for specific periods of time, it cannot assess the implications of the findings due to limited knowledge on the spatiotemporal exposure limits for welfare and growth. Further research is required to cover these knowledge gaps.

Health status adds further complexity. Diseases affecting gills and heart, as well as parasitic infections such as sea lice, have been observed to reduce tolerance to low DO (Hvas et al., 2017; Oldham et al., 2020; Hvas and Bui, 2022; Bowden et al., 2022). Studies report elevated metabolic demands of 8–13% at 15–19 °C in fish affected by amoebic gill disease, AGD (Bowden et al., 2022), and 26% at 9 °C in fish with severe lice infestations (Hvas and Bui, 2022). In the present study, additional safety margins were not applied due to uncertainty in transferring these findings to complex gill disease, the lack of detail in health records regarding both disease and lice infestation severity, and the difficulty of accounting for multiple diseases simultaneously. Nevertheless, the effect of the diseases in the populations likely affected the tolerance thresholds for DO, compared to those used in this study. Future work should examine the combined effects of large fish size, high biomass density, crowding, complex health challenges, and disease treatments on metabolic requirements, and how such information can be operationalised.

Operational implications and value for industry adoption

The operational implications of applying the methods used in this study are uncertain and require further research. Future studies should assess the feasibility of implementing the oxygen and statistical models in commercial settings, including financial viability and farmer perceptions of their value. While the GAM analyses suggest that key parameters contribute differently to DO variation across cages, it remains unclear whether this information will improve operational decision-making for welfare, performance, or resource efficiency. Clarifying how the model can be integrated into existing workflows will be essential for practical uptake and long-term adoption and may contribute to precision fish farming (Føre et al., 2018; O’Donncha and Grant, 2019). Furthermore, coupling the intra-farm variation model with a fine-scale process-based ecosystem model (Geary et al., 2020) could help understand the dynamics between the external and internal environments. Understanding the feedback loops caused by the effects on the environment by the farm, and subsequent effects on the farm by the environment, would be a valuable contribution in future research.

Finally, only simple GAM analyses were applied in this study, as uncertainty in the input data propagated into the results. Further development of these analyses and optimisation of the GAMs would be valuable. For instance, testing cage-level drivers and examining lagged effects of feeding, handling, temperature, and currents could provide deeper insight, since these factors likely influence DO with a delay rather than immediately (e.g., Elshewey et al., 2023).

This study combined in-situ measurements from sea cage farms with a mathematical model of intra-farm DO variation to assess cage-level variation and animal exposure to suboptimal or harmful conditions. To our knowledge, it is the first to integrate farm data on water quality and inventory, with advanced models of oceanographic and intra-farm DO variation. The results demonstrate that the model can reveal site-specific variations not captured by in-situ measurements and that production-impairing and growth-reducing conditions likely occur more frequently than indicated by in-situ point measurements in the monitoring system alone. The application of an additional layer of statistical model enables a deeper understanding of the drivers of DO variation, which may support improved decision-making to minimise impacts on animal welfare and production performance. Overall, this study represents a first step toward precision aquaculture in DO management for sea cage farms.