The impact of global warming on the small Scottish Fishing Company

Seawater temperatures rise due to global warming, which has an impact on marine life and their habitat [1]. For example, the lobsters in Maine have been gradually moving towards the cooler Arctic to maintain their habitat [2]. In Scotland, small fishing companies and small fishery vessels hold a huge investment in the fishing industry [3], and they usually rely on herrings and mackerels that are sensitive to water temperature [4]. Thus, like the lobster of Maine, these fish will migrate to areas with more suitable temperatures as sea temperatures rise. In the work presented here, the impact of this migration on the Scottish fishery is reported, and in particular on small fishing companies, and propose solutions to mitigate the impact on that fishery.

The sea surface temperature (SST) data supporting the mathematics model used here are from previously reported studies and datasets. The data are available at the Met Office Hadley Centre. (Met Office Hadley Centre observations datasets: Hadley Centre Sea Ice and Sea Surface Temperature data set [HadISST]). Since the area of the habitat for the fish covers an area of >10000 km² [5], sharing the same order of magnitude with the area of 1° (longitude) × 1° (latitude), the centre of this lattice is used as a sampling point. The temperature change at the sampling point represents the water temperature change in the whole lattice. The time span is 1991–2019.

The distribution of landings data supporting the mathematics model used herein are from previously reported studies and datasets, which reflects where and how much mackerels and herrings can be caught in 2013. The resolution is 1° (longitude) × 0.5° (latitude). Compared to the distribution of landing in 2011, the distribution trend can be considered stable. The data are available (Fish and Shellfish Stocks: 2015 Edition, https://www.gov.scot/publications/fish-shellfish-stocks-2015-edition/pages/1/).

The following details were used in our analyses:

Small fishing companies are defined as those that have limited or very limited financial resources to invest in new equipment/vessels, which engage in commercial fishing, and that they have only small fishing vessels without onboard refrigeration to harvest and deliver fresh fish to markets in Scottish fishing ports.

Only concerned with the distribution of fish that can be caught (i.e. the habitat for fish extends beyond the range that is economical for small Scottish fishing companies, but for variable quantity control, these will not be considered). Therefore, in this study, fish positions are those where fish stocks can be caught (i.e. Figure 1). So, according to the 2015 official mackerel and herring fishing report [10], in 2013, the main populations gathered in the North Sea, and thus fishers also mainly captured mackerel from the northern part of the North Sea. Herring fish are distributed in two areas near Scotland: in the Atlantic, with a habitat in the northwest and north of Scotland, and in the North Sea, with a habitat in the central and northern North Sea.

Fig. 1

If the temperature of their habitat in 2013 is known, the suitable temperature for their habitat can be inferred. Herring and mackerel generally move near the sea surface, but herring sometimes have a deeper home range [11]. Since the water temperature has the same changing pattern as a function of depth [12], SSTs are used to track the seawater temperature of the habitats of herring and mackerel. The movement of the habitat of the fish is extremely slow; changes are only noticeable over years. To simplify the calculation, the monthly average water temperature is used to represent the water temperature of the whole month, without compromising precision. Using published SSTs [13], the temperature distribution map for all of 2013 is plotted. From the data, temperatures in April–June can be considered to reflect the year average temperature (i.e. Figure 2), and, since this period is also the time for spawning and fishery for mackerel and herring [14], and the SSTs in April–June is the suitable temperature for these fishes. Combining the distribution of landing of mackerel and herring, the SSTs of the habitats of mackerel and herring are known, which range from 6.5°C to 10.5°C, and thus take 8.5°C as the suitable survival temperature for these two fish species.

Fig. 2

Seawater temperatures are the most significant factors affecting the survival of fish [1], with the relationship between fish population and temperature satisfying a normal distribution function [15]. Fish populations are mainly distributed in waters with the most suitable temperature. Thus, the key to predicting the future habitats of herring and mackerel is predicting the trend in water temperature. In addition to the fact that global warming has caused sea temperatures to rise in general, multiple factors may affect seawater temperatures at a given location, such as ocean currents, the depth of the sea, tides, seasons, Sun-Earth distance and so on [16]. While it is difficult to understand precisely each factor's influence on water temperature, it is possible to summarise the patterns from years of records on seawater temperature since recorded temperatures are all quantities linked to nature's movements.

Considering the SST data from 1991 to 2019, the SST has risen, but in fluctuations, it complicates our effort to find a model to accurately describe the behaviour. Therefore, two fitting models are proposed, and they are compared to find the better one.

Model 2: Monthly linear combination of cosine squared and linear terms

As per the regularity of nature, the influencing factors of water temperature for each month are similar, and seasonal changes have the greatest impact on water temperature. Therefore, in this model, the temperature data for the same month in different years is fitted (i.e. 12 curves were fitted). From the SST data, the monthly temperature fluctuates year by year, and the fluctuation is still like a radio signal, so a linear combination of cosine squared and linear terms are still used here.

Fitting result: (2) Tijk=aijk⋅cos2(πx)+kijkx+bijki=1,2,…,12,k=19.5∘W,18.5∘W,…,0.5∘W,0.5∘E, 1.5∘E,…,6.5∘E \matrix{{{T_{ijk}}} \hfill & {= {a_{ijk}} \cdot \mathop {\cos}\nolimits^2 \left({\pi x} \right) + {k_{ijk}}x + {b_{ijk}}} \hfill \cr \quad i \hfill & {= 1,2, \ldots,12,} \hfill \cr \quad k \hfill & {= {{19.5}^ \circ}W,{{18.5}^ \circ}W, \ldots,{{0.5}^ \circ}W,{{0.5}^ \circ}E,\;{{1.5}^ \circ}E, \ldots,{{6.5}^ \circ}E} \hfill \cr}

Test: Comparing the predicted data and actual data for every sampling point, the average root mean squared error is arrived: RMSE₂ = 0.363127.

In the past, it took approximately 20 years for the yearly average SSTs to increase by 1°C. By comparing the RMSEs of the two functions, RMSE₂ < RMSE₁ is obvious, and the RMSE for Model 1 is approximately 1°C, which means the error is about 20 years, which is too large for a 50-year prediction, and so the function from Model 2 is used as the function for predicting the future SSTs. By calculation, a map of SST changes (e.g. Figure 3) is obtained for each North Atlantic sampling point, from which an isotherm plot for each month is derived (e.g. Figure 4). Through observation of the change of the 8.5C isotherm lines over time (e.g. Figure 4), combined with the distribution of herring and mackerel populations and the suitable temperatures for their habitats, the future migration direction is inferred (i.e. Figure 5).

Fig. 3

Fig. 4

Fig. 5

In general, without refrigeration, the freshness of fish declines soon after they are caught (i.e. 1 day or less). Since, after landing, fish are typically delivered to customers, requiring 0–0.5 days, fishers who are not equipped with refrigeration must deliver their catch to port within 0.5 days of catching them so that their entire journey is restricted to 1 day. Therefore, it must be determined whether the mackerel or herring are located within a region that is practical for delivery for small vessels without refrigeration. Here, it is only considered whether fish can be caught, ignoring for the moment the economic problem. The design speed of fishing vessels is generally: v ≈ 10 knots (i.e. ≈ 18 km/h) (Bo, 2007), so that a fishing vessel can travel 216 km in 12 h. Thus 216 km is an upper limit, but in practice, they must return to port within the 12 h of the start of fishing to stay within the constraints outlined above so that their range is significantly less.

To minimise the errors in our predictions, a range of years instead of a certain year will be given. For this reason, the worst case, the best case, and the most likely case are considered, and then a range of years that the small vessel starts without catching fish is inferred from that three cases.

There are many fishing ports in Scotland. Different ports have different distances from fish habitats, which affects fishing production. As the habitat moves towards the northeast of Scotland, the port in the northeast corner of Scotland is set as the best case. The small fishing boats' ports that hunt for mackerel and herring are considered to be located in the east of Scotland, the port in the worst case is set to the southeast corner of Scotland; Peterhead is Scotland's largest fishing port [18], where lots of small companies are gathered, so Peterhead is set as the port for the most likely circumstance.

The rising sea temperature has caused herrings and mackerels to gradually migrate away from Scotland towards the coasts of Norway and Iceland where the temperature is lower. The faster the ocean temperature rises, the faster fish schools move away from Scotland, and the more difficult it is for fishing boats to catch fish near Scotland. Therefore, in terms of temperature change, where the temperature rises fast or slow, it is considered as the worst and best cases, respectively. The prediction in the migration route is based on the data for the past 29 years. The huge amount of data can minimise the error caused by occasionality. So, this is the most likely situation for temperature changes, but this situation may underestimate the impact of climate change since humans may emit more greenhouse gases in the future.

Here the best and worst cases are first considered. Regarding temperature, from the past data for a fixed reference point, the temperature increases faster in some time periods and slower in others. The worst-case prediction is that when the temperature-change rate in all future years is set to the most rapid temperature increment rate in the past years; and the best-case prediction is that when these changes are least rapid. To reduce the error when calculating the temperature increase rate of the past years in various time periods, the data contained in the time period cannot be too small, and the number of time periods cannot be too small. The appropriate time period selection scheme was determined by dividing these periods into different parts under the following three schemes:

5 years as a time period, and the data of each reference point over the past 29 years are divided into 1991–1995, 1996–2000, 2001–2005, 2006–2010, 2011–2015, 2016–2019.

Trial process: Since predictions are made based on a monthly linear model, in this model, the temperature-year relation of the same month satisfies: (3) Tjk=ajk⋅cos2(πx)+kjkx+bjk {T_{jk}} = {a_{jk}} \cdot \mathop {\cos}\nolimits^2 \left({\pi x} \right) + {k_{jk}}x + {b_{jk}}

The a mount representing temperature increase in this model is k, so the worst and best cases (maximum and minimum k, respectively) need to be found. MATLAB is used to fit data from previous years, and it uses a linear function to fit the data in a time period to eliminate temperature fluctuations caused by factors such as seasons. The slope of the linear function is the value of k. In different cases, the future temperatures are predicted separately. After comparison, in the first scheme, k of some reference points has negative values, and the error is large; in the third scheme, the k of some reference points is high, and the temperature change exceeds the most likely situation. Therefore, the result of the second scheme for predictions is chosen, since the temperature fluctuation is eliminated and the water temperature changes linearly. To facilitate observation and calculation, the predicted annual temperature change in April of each year is used and plotted.

For the best case, the northeast corner of Scotland is taken as the centre and a 216 km straight line is drawn on the isotherm. Because the Earth is spherical, the distance between the two meridians is different at different latitudes. The actual distance between the two latitudes is 108 km, and the actual distance between the two longitudes is 108 km × cos θ, where θ is the latitude and that the distance between two longitudes is measured. The end points of these straight lines form an oval shape (i.e. Figure 6). Calculating the intersection between the 8°C isotherm and this shape, researchers find that since there is still an 8°C isotherm inside the ellipsoid until 2069, fishing boats can catch fish for the next 50 years (i.e. Figure 6a). For the worst case, the ellipsoid is placed with the southwest corner of Scotland as the centre. It is obvious that it is impossible to catch herring or mackerel by approximately 2024 (i.e. Figure 6b). For the most likely case, the above ellipsoid is made with Peterhead as the centre. It is obvious that it is impossible to catch herring or mackerel by approximately the year 2054.

Fig. 6

For small fishery companies, the most important factor is the economic benefit, and thus this will be the main factor in our assessment of the impact of global warming, which will determine when companies are no longer viable or whether companies need to change their operating strategy and how to change it. Various factors affect the economy of a commercial fishing company. The three main factors are: sales of fish E, the salary of personnel F, use fees for the fishing boat G. The total income is thus: (4) Y=E−F−G (unit:£) Y = E - F - G\quad \left({{\rm{unit}}:{\rm{\pounds}}} \right)

Use fees are mainly due to the fuel consumption of the fishing vessels [19], and the fuel consumption is related to the vessel type and fuel price. According to relevant data, the fuel consumption for the improved diesel engines of fishing boats is about 230 ml/kWh [20]. Small fishery company operates mostly small fishing boats whose lengths are <15 m [21]. To consider long-distance navigation, it is assumed that all fishing boats for this company are 12 metres long, with a speed of 10 knots and a maximum fish transport capacity of 10 t (large enough), a diesel engine power is 110 kW, carrying three people [22]. Diesel fuel prices often fluctuate and are affected by many factors; thus it is difficult to predict diesel fuel prices (or the prices of other commodities) [23]. The average price in recent years is used as a predictor of future fuel prices. In recent years, diesel fuel average price has been approximately 0.75 £/L [25]. It is assumed that over the long term, prices will follow the annual inflation rate. To sum up, for a vessel: (5) G=110×230×t×0.751000=18.975t G = {{110 \times 230 \times t \times 0.75} \over {1000}} = 18.975t

It is assumed that the fishers are all skilled workers over the age of 25. They are paid when they go out to the sea but otherwise are not paid. It is assumed that there are no vacations during the fishing season. The average daily wage of fishermen in 2015 was about 56 £, about 8 times the minimum daily wage of 6.7 £/ [5]. It is assumed that this relative relationship will not change in the future. According to the British minimum wage change table [5], the fitted curve shows that the minimum hourly wage satisfies the following functional relationship: (6) f(y)=0.2557y−508.3 f\left(y \right) = 0.2557y - 508.3

Here y is the year (i.e. 2020 years mean y = 2020). To sum up, for a vessel a day: (7) F=3×8f(y)=24f(y) F = 3 \times 8f\left(y \right) = 24f\left(y \right)

For the fish sales model, the two quantities that affect sales are the price e. the fish and the hourly catch Z. the fish, that is, E = eZt.

The selling price of fish and the number of fish caught is considered separately.

In 2018, the price of herring was 0.38 £/kg, and the price of mackerel is 1.07 £/kg [25]. Due to the growing economy, the price of fish has increased year by year. In the long term, the increase in price for fish to reflect the overall UK Consumer Price Index (CPI) [26]. Because the CPI has not changed significantly in recent years, for calculation simplicity, the average value of these years is used as the proportion of the annual increase in fish price (+2.7%/year) in the forecast, that is: (8) ei(y)=1.027y−2018×ei(2018)herring: e1(2018)=0.38mackerel: e2(2018)=1.07 \matrix{{{e_i}\left(y \right){{= 1.027}^{y - 2018}} \times {e_i}\left({2018} \right)} \hfill \cr {herring:\;{e_1}\left({2018} \right) = 0.38} \hfill \cr {mackerel:\;{e_2}\left({2018} \right) = 1.07} \hfill \cr}

From experience, a fishing boat generally catches 20–110 kg/h [27], which is not only a wide range but also inaccurate for science, and due to the temperature, the density of the fish will change, which will also affect the catch. To refine the fishing volume of fishing vessels, a model is built to estimate the fishing volume of fishing vessels.

Due to the different starting points for fishing vessels, the sailing distances to the same area vary. As an example, a relatively common port, for example, the Aberdeen port is chosen as the port of departure of the ship for calculation. From Marine Scotland Science Fish and Shellfish Stocks [10], the distribution of the mackerel and herring catch in 2013 can be known (i.e. Figure 1). Since the catch distribution, the school density and catches per hour are closely related, the change rate of the catch distribution at different positions is used to assess the change rate of fish density and catch per hour. From Figure 1, it is found that the distribution of the North Sea herring is generally decreasing on either side of the ocean centreline, while the distribution of the herring north of Scotland is approximately a fixed value, and the North Sea mackerel distribution is changing approximately along the North Sea to the northeast direction, first a constant, and then in increments. Based on these observations, the rules of the hourly capture volume is quantified (i.e. Figure 7) in different regions based on the following models:

Herring distribution model (i.e. Figure 7a). Point a: 58.62N, 4.98W; Point b: 62.15N, 5.11E; Point c: 59.88N, 1.05W; Point d: 52.48N, 5.09E. In Regions A and B, the hourly average catch decreases evenly from both sides of the line cd at Δm₁kg/(h*km), and the catch at Aberdeen port is m1 kg/h, at cd it is about (m₁ + 200 * Δm₁) kg/h. In region C, the average value is used, so the hourly catch is (m₁ + m₁ + 200 * Δm₁)/2 kg/h. Here, m₁ is the weight of fish caught per hour. (20 ≤ m₁ ≤ 110, 20 ≤ (m₁ + 200 * Δm₁) ≤ 110).

Fig. 7

The number of fish populations has a normal distribution relationship with temperature [15], so the hourly volume and temperature also have a normal distribution function. The normal distribution function is fitted with two linear functions, which only consider the area of two standard deviations near the average density (i.e. according to the property of normal distribution function, since this area contains >95% of fish, there are no significant fish populations out of this area). From the calculation, the volume will decrease by 53 kg/h for each 1°C increase in temperature. Using the water temperature prediction model, the average growth rate of the North Atlantic water temperature (0.018°C/year) is calculated; that is, the decline in fishing is 0.9 kg per year. Taking 2013 as the base year and assuming that the vessel is not engaged in fishing during the voyage, and that the fishing vessel sails in a straight line after leaving the port, the catch going forward can be projected. The relationship between the hourly catch and the distance travelled by the vessel is: Herring: Z1={region A110∑n=09[m1+Δm1nlcos(πn20)]−0.954(y−2013)region Cm1+200*Δm1n−0.954(y−2013)Mackerel: Z2={region C m2−0.954(y−2013)region B110∑n=09[m2+Δm2nlsin(πn20)]−0.954(y−2013)region Am2+200*Δm2n−0.954(y−2013) \matrix{{Herring:{\kern 1pt} {Z_1} = \left\{{\matrix{{{\rm{region}}\;A{1 \over {10}}\mathop {\sum\limits_{n = 0}^9}\left[{{m_1} + \Delta {m_{1n}}l\cos \left({{{\pi n} \over {20}}} \right)} \right]} \hfill \cr {- 0.954\left({y - 2013} \right)} \hfill \cr {{\rm{region}}{\kern 1pt} {\rm{C}}{m_1} + 200*\Delta {m_{1n}} - 0.954\left({y - 2013} \right)} \hfill \cr}} \right.} \hfill \cr {Mackerel:{\kern 1pt} {Z_2} = \left\{{\matrix{{{\rm{region}}\;{\rm{C}}\;{m_2} - 0.954\left({y - 2013} \right)} \hfill \cr {{\rm{region}}\;B{1 \over {10}}\mathop {\sum\limits_{n = 0}^9} [{m_2} + \Delta {m_{2n}}l\sin \left({{{\pi n} \over {20}}} \right)]} \hfill \cr {- 0.954\left({y - 2013} \right)} \hfill \cr {{\rm{region}}\;{\rm{A}}{m_2} + 200*\Delta {m_{2n}} - 0.954\left({y - 2013} \right)} \hfill \cr}} \right.} \hfill \cr}

For mackerel, the hourly volume is different in different places in Region B, as it is for herring in Region A. To determine the average hourly volume, the Aberdeen port is taken as the centre, and a line is drawn every ten degrees to calculate the volume for ships travelling along each line and the average taken as the first part in the equation. Then the earnings of a vessel are used to represent the earnings of the entire company (i.e. the small company consists of several vessels). Then, (9) Yi=2(t−l18)Ziei(y)−24f(y)−18.9752t (i=1,2) {Y_i} = 2\left({t - {l \over {18}}} \right){Z_i}{e_i}\left(y \right) - 24f\left(y \right) - 18.9752t\quad \left({i = 1,2} \right)

According to the company's current operating strategy, the vessel can sail for a maximum of 1 day (i.e. t = 12 h), since small vessels can only navigate 216 km in 12 h (i.e. vessels have no time to catch fishes in this distance, so, this distance is the upper bound). So, for small fishery vessels, herring Region B, C is too far away from the Aberdeen port, and likewise, for mackerel in Region A. Thus, Region A for herring and Regions B and C for mackerel are only considered. Unfortunately, a reliable source of Δm₁ and Δm₂ cannot be found, and these may be different in different places since not only the SSTs but also fishery intensities affect them. In some locations, the temperatures only make a small difference in hourly capture volume, but the real landing volume has several time differences. Unless there are a large number of samples for different locations, it is difficult to determine accurate values for Δm₁ and Δm₂. To see the tendency as the year changes, let Δm_1n = 0.35, Δm_2n = 0.3, and l = 100. Then the ranges of m₁ and m₂ are known, 20 ≤ m₁ ≤ 40, 20 ≤ m₂ ≤ 50. With these assumptions, it is found that small fishing vessels' earnings in these three areas will gradually decrease in the future, and that there will be a sharp decline to <0£ in the next 50 years (i.e. Figure 8).

Fig. 8

Our research team, based on historical ocean temperature data collected by satellite and ocean buoys, conclude that, over time, the water temperature in the North Atlantic will continue to rise in the next 50 years, and that this will have a dramatic impact on the fishery in Scotland. Two major commercial fish species in Scotland, herring and mackerel, are suitable for seawater around 8.5°C; as the temperature rises in the next 50 years, these fish will move to cooler waters near Iceland and Norway. It will be more and more difficult for fishermen to catch these two fishes off Scotland, and this will cause small fishing company going bankrupt in the next 50 years. In the future, when the temperature of seawater increases and it is difficult to catch fish near the fishing ports, fishers who own ocean-going fishing vessels may be minimally impacted, but fishers operating near their home ports will find it uneconomical to continue.