Modelling emerging patterns in bird migration across Western Europe

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Modelling emerging patterns in bird

migration across Western Europe

Walter van Dijk

Bsc Thesis

July 2018, Amsterdam

Starlings (Sturnus vulgaris) in Germany. Wikimedia Commons.

Supervisors: - Willem Bouten - Maja Bradaric

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Abstract

Gaining insight in bird migration patterns is vital for preventing casualties under birds due to collisions with man-made constructions like wind turbines or airplanes. In this research the relation between weather and migratory routes of birds in western Europe is analysed. The main objective is to gain insight in the influence of environmental conditions on patterns that emerge in bird migration. To accomplish this an agent-based model that simulates a large quantity of individual nocturnally migrating birds is created. According to a set of rules and parameters the routes that the birds follow are shaped. Model development consisted of adding elements to the model step by step. The modelled aspects include: 1. setting up the model in a homogenous landscape; 2. differentiating between land and water; 3. integrating weather data; 4. adding take-off decisions; 5. Compensation in flight behaviour. The model was evaluated with varying configurations. This showed the influence of model elements on pattern formation. Wind was found to be very influential in shaping migration routes, especially in the full wind drift scenario. Both compensation of flight and take-off decisions reduced this effect. Clustering of birds was mainly the result of birds resting after passing a large water body and take-off decisions. Total compensation against wind appeared to be a suboptimal migration strategy when implemented as only wind compensation because this caused migration speed to

decrease substantially. Modelling bird migration provides insight in the migration system. This insight can be used to improve strategies to mitigate bird-wind turbine collisions. Therefore, this research contributes to limiting the impact of human society on the natural world while enabling the expansion of sustainable energy.

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Introduction

It is becoming increasingly apparent that anthropogenic greenhouse gas emissions are related to climate change (Solomon et al., 2007). Consequently, Dutch policy to reduce

greenhouse gas emissions in energy production is implemented (Kern & Smith, 2008). To increase the production of renewable energy in the Netherlands, in the coming years more wind turbines will be placed (Rijksoverheid). The Netherlands is located in an important area for migratory birds. As wind turbines can provide a risk of collision for birds, collisions between migratory birds and wind turbines are prone to increase (Drewitt & Langston, 2006).

Krijgsveld et al. (2016) indicated that turning off wind turbines for only a few carefully planned nights per year can significantly reduce casualties under migratory birds. Because the loss of power from turning off wind turbines needs to be compensated with energy from elsewhere, the amount of time between making the decision to turn off a wind turbine and actually turning it off is of economic importance (Blanco, 2009). Buying in energy becomes more expensive when it is needed in the more recent future (Heier, 2014). It is therefore valuable to be able to predict bird migration so the impact of the expansion of wind energy on birds can be decreased without making wind energy unprofitable.

Especially for important aspects including: where the birds will migrate in space and time, where their stopover locations are and when they arrive there or take off, it is crucial to make a model to predict when the wind turbines need to be turned off. For the prevention of collisions with wind turbines, stopover locations are exceptionally important because birds will fly at dangerous altitudes when they are in close proximity to their resting areas (Richardson, 1998). All of these aspects are influenced by weather (Able, 1973; Alerstam, 2011). Wind direction can influence the route birds follow when they migrate and they can consequently pass through different areas (Liechti, 2006). Bad weather can also influence the decision of birds when to take flight (van Belle et al., 2007).

Recent research of Liechti et al. (2013) investigated similar dynamics in Switzerland. In that study, altitude was an important component. The modelling resulted in a sensitivity map for the potential collision rates of migrating birds with wind turbines. This allows to quantify the collision risk with respect to topography.

Compared to the model of Liechti et al. (2013), in this research altitude is not taken into consideration. Instead, the relation between weather and migratory routes of birds has a more central role. The whole of Western Europe is analysed by means of a theoretical model. The model is agent-based and simulates a large quantity of individual birds. According to a set of rules and parameters the routes that the birds follow are shaped. There is no interaction between agents.

Migrating bird species in the area can be divided in two groups. First there are the species that migrate during the day. The updrafts caused by the warming of the land through solar radiation allow them to soar and glide to save energy. The other group consists of species that migrate during the night. These species use this strategy to save daytime for gathering food. The majority of migratory birds in the area are nocturnally migrating (Libby, 1899), therefore the focus of the model will be on this group.

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Due to limited time availability choices had to be made regarding the modelled aspects. The full complexity of bird migration is not simulated in this research. Firstly a relatively simple model was made, which formed a simple method to simulate bird migration. When this was in place various elements that increase the complexity were added.

The goal of this research is to obtain insight in the influence of environmental conditions on patterns that emerge in bird migration. Because the model was analysed with various

configurations of environmental conditions, the patterns that emerge can be linked to environmental influences. Additionally, the model can be used to test statistical models. The amount of artificial data that can be generated with this theoretical model is more extensive than the available measurements in the real world. Therefore it can give insight in whether statistical analysis that are conducted on the real measurements apply on the scale that can be modelled.

Methods

This research consisted of creating a model to analyse bird migration in Western Europe. The birds that were included in the modelling consist of the nocturnally migrating species that fly along the East Atlantic Flyway (Boere & Stroud, 2006). Nocturnally migrating species were chosen because they make up the largest part of migrating birds (Libby, 1899). The constructed model consisted of a migration model with difference between land and open water as the only landscape variation, integrated with wind data.

The modelling was conducted in Matlab. Model development consisted of increasing the complexity stepwise, i.e. adding elements to the model part by part. The basis was relatively simple, however as more features were added the complexity increased. Parameter values were chosen in accordance with literature (Liechti, 1993; Liechti et al., 2013; McLaren et al., 2013).

Because time for model development has been limited, a selection had to be made regarding the environmental features that were to be modelled. The different parts of the model are described below. First the essential elements to simulate migration behaviour and wind influence are described. Afterwards additional elements that are integrated to increase the realism of the model are explained. The model was analysed by investigating various simulations with different configurations of the elements that are described here.

Basic model

1 Homogenous landscape

To start, birds were introduced as agents in the model. They moved through a grid which only resembled distance. There were no landscape features and there was no difference between land and water. At this stage the dimensions of the model were determined and

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longitude and latitude were introduced. The birds all departed at the same time, flew in their endogenous direction (Erni et al., 2003) and rested at the same intervals. Departing times were set to be at sunset and arrival times were set at sunrise. The birds flew with a constant airspeed, being 10 m s-1_.

At this stage the direction the birds travel was completely determined by their energy expense. The preferred direction for every individual bird was calculated when the birds started to fly, after which it remained constant throughout the night. The method of calculation

consisted of finding the initial heading on a great circle path (Loomis et al., 1999) from the locations where the birds were located, to their destination. This was done by solving for a spherical triangle (formula 1). The atan2 function was used to obtain the direction in degrees. In the resulting flight direction some randomness was introduced to simulate inaccuracy in the bird’s method to determine direction.

Formula 1. Initial heading on a great circle path. ɑ = angle of initial heading; φ = latitude; λ = longitude; 1 & 2 resemble the departing and destination location, respectively.

2 Land and water

In the next step the landscape has taken shape. A shapefile which resembles the coastline of Europe was introduced in the model. This allowed for the prevention of birds landing on or taking off from water. After the birds have been flying for a whole night it was checked whether they were above land. If they were above land the birds could stop flying and rest at this location during the day. If a bird was not above land they have to keep flying until land was reached. This could lead to very lengthy travel times. When the consecutive flight time of a bird exceeded 36 hours, this bird would have died from exhaustion.

When the difference between land and water was implemented in this manner, the birds that could not have landed because they were above sea continued flying for longer than the birds that were able to land. Therefore, to keep the travel speed differences between birds realistic, a simple form of an energy balance had to be implemented. More energy spent by flying longer should be compensated for by a longer refuelling period. In the model extra time spent flying after a bird would normally have stopped was taken away from the flight time the next day. This could have led to some birds not taking flight at all.

3 Weather

This section introduces wind data. The dataset that was used in this model consisted of ECMWF reanalysis data of a large part of Europe from August until October 2013. This dataset originally had a resolution of 0.25 degrees. However, in this research a simplified 0.75 degrees resolution version was used. For the purpose of this research this was an adequate accuracy which helped to reduce calculation times.

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The data was available in the form of two values per grid cell that describe wind speed. These values consisted of speed in longitudinal (Vw) and latitudinal (Uw) direction in m s-1_{. The} preferred direction of the birds, here referred to as airspeed, was quantified in the same

metrics, also having a longitudinal (Va) and latitudinal (Ua) component. These components were summed together with the wind data to obtain three values for groundspeed: speed in longitudinal direction, speed in latitudinal direction and summed speed (Vg, Ug & GS). The method used can be seen in formula 2 and is visualized in figure 1. This situation is comparable to full wind drift as described by Kemp et al. (2012).

Vg = Vw + Va [m s-1_] Ug = Uw + Ua [m s-1_]

GS =√ [m s-1_]

Formula 2. Combining wind and flight components. Names are composed of prefix V or U relating to longitude or latitude, respectively, along with subscripts indicating of groundspeed, wind speed or airspeed. GS resembles groundspeed.

Figure 1. Combining latitudinal and longitudinal components of wind speed and airspeed to obtain groundspeed. Green lines resemble airspeed, blue resembles wind speed and red is used for groundspeed. In the model the dashed lines are used for calculations. In this figure it can be seen that summing both dashed lines produces the same result as summing the solid lines.

Additional elements

4 Take-off decisions

There are myriad influences on the decision of birds when to take flight (Åkesson & Hedenström, 2000). In van Belle et al. (2007) the decision of taking flight was influenced by a parameter regarding unfavourable weather. This parameter was constructed by combining data regarding unfavourable wind and rain. The effect of these variables was adopted from Erni et al. (2002), where an accumulation effect was used to transcribe unfavourable weather into

accumulation of birds. This effect also took into account the amount of accumulation that was already present.

Vw

Uw

Va

Ua

Vg

Ug

=

+

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In the model of this research however, the decision of taking flight was simpler. Here wind was the only variable indicating bad weather. It was divided in two values: the angle and the strength. Both were checked to see if the weather was bad. For the angle the difference in degrees between the wind direction and the preferred direction of the bird was calculated. If the wind direction would differ more than a set amount of degrees from the preferred direction of the birds, this indicated bad weather. Additionally, it was checked whether the wind strength was above a threshold. This threshold consisted of the minimum wind strength to have influence on the decision making process of birds. Both of these parameters can easily be changed in the initialization part of the model. For the simulations here, the angle was set to a maximum of 25 degrees difference between preferred direction and wind direction and the threshold was set to half the airspeed of the birds.

At all bird locations it was checked whether the wind strength was above the threshold and had a direction more than the determined angle away from the preferred direction of the bird. If both were true for the largest part of two hours before take-off, the bird did not fly in the model. This decision was only made at the beginning of the flight period. If a bird decided to fly, but the weather became bad after taking off, the bird still kept flying.

5 Compensation of flight

To further capture reality in the model, birds should be able to change their flight behaviour in response to the wind (McLaren et al., 2012). In Kemp et al. (2012) methods of quantifying the effect of wind on trajectories of organisms are described. The formula of partial compensation (formula 3) of trajectory that is discussed in this study was adapted in the model. In this situation the birds had a fixed airspeed, but could alter their flight direction to offset the effect of wind. A parameter indicating the proportion of compensation was introduced here. If it was set to 1 the birds totally compensate for the wind, if set to 0 the birds do not compensate, a value between 0 and 1 results in partial compensation. When the proportion of compensation is not 0, the equation cannot produce a real solution under some wind conditions. This is when the wind would be too strong for the birds to compensate for.

Formula 3. Partial compensation of flow assistance. FA = flow assistance; y = speed of wind; θ = degrees difference between preferred direction and wind direction; z = speed relative to wind; f = proportion of compensation. From Kemp et al. (2012).

The method of quantifying flow assistance in the model was similar to the method in Kemp et al. (2012), but some key concepts differed. The starting parameters also consisted of: the difference between preferred direction and wind direction, airspeed, wind speed and proportion of compensation. However, in the model the calculations resulted in the degrees change in flight direction needed to keep flying along the preferred direction.

In formula 4 the quantification of flight compensation that was used in the model is described. This formula resulted in degrees change from the preferred direction. A separate

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algorithm was used to find out whether the change is positive or negative. When the formula would not be able to provide a real solution, i.e. when the birds were not able to completely compensate for the wind, the compensation was set to a predetermined maximum

compensation amount. Also, when this maximum amount would be exceeded the compensation is set to the maximum amount. The maximum amount was set to 90 degrees when there was total compensation. When there was partial compensation the maximum amount would change according to the proportion of compensation. For example, a proportion of 0.5 would result in a maximum compensation angle of 45 degrees.

(

| |

)

Formula 4. Compensation of flight. C = Compensation in degrees defiance from the preferred direction; y = speed of wind; θ = degrees difference between preferred direction and wind direction; A = airspeed; f = proportion of compensation.

Results & Discussion

The emergent behaviour of the model changed when environmental features were added, removed or changed. Therefore, the behaviour of the model with various configurations is shown and discussed here. The figures displayed here represent one day in a simulation. For a better impression of the characteristics of the simulation, videos were made available in the digital appendix. These videos show a 30-day visualisation of the simulation.

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No wind

Figure 2. The model at day 241 without the influence of wind.

Without wind, the flight direction of the birds is determined by their preferred direction. This results in a great circle arc (formula 1) from the starting location to the destination

location. The effect of water bodies can be seen in figure 2. Coastlines where birds arrive generally have a larger density of birds. An area with a relatively low density of birds above parts of Germany is also visible in figure 2. These dynamics are due to the starting locations of birds being exclusively on land. What can be seen above Germany is the projection of the Baltic Sea. If the model would be expanded to the north this behaviour might be different.

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Total wind drift

Figure 3. The model at day 241 with the wind data integrated. This situation is comparable to full drift as described by Kemp et al. (2012).

When wind influence was added the behaviour of the model changed considerably. In figure 3 it can be observed that wind has a very large infuence on the flight direction of birds when no other control parameters are in place. This becomes even more apparent in the related video in the digital appendix. In this simulation the airspeed of the birds was set at 10 m s-1_{. If} the airspeed would be set higher, the influence of wind becomes smaller. Nevertheless it can be concluded that wind was very influential on the flight direction.

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Take-off decisions

Figure 4. The model at day 241 with the wind data and a decision making process for taking off integrated.

In order to reduce some influence of wind, birds should be able to decide to only take off when the weather was beneficial. The combination of weather dynamics and take-off decisions results in clustering of birds, as can be seen in figure 4. Birds accumulated at locations where weather prevented take-off. The birds started clustering because they could arrive at a location with bad weather, but not depart. In this simulation the take-off decision parameters were set to an angle of 25 degrees and a threshold of half the airspeed, which resulted in 5 m s-1_{. The birds} would therefore not take off if the direction of the wind differs more than 25 degrees from their preferred direction and is stronger than 5 m s-1_.

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Total compensation

Figure 5. The model at day 241 with the wind data and total compensation of flight.

In this simulation the take-off decision was removed and compensation in flight behaviour was added. Similar to the first two simulations, the birds departed every day. However, instead of fully drifting in the wind the birds would change their flight direction to remain on the path of their preferred direction. In figure 5 it becomes appearant that this was not always managed. Often the influence of wind was too strong to compensate for. Additionally the distance travelled in one night could become smaller. This was the result of birds spending energy to cancel out some energy of the wind. In this simulation the amount of birds that ended in sea and drowned due to exhaustion became notably larger. This was likely the result of the shortening of some tracks due to birds using energy to offset wind drift. The speed above sea became subtantially small, resulting in birds dying from exhaustion before they had reached land.

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Partial compensation and take-off decision

Figure 6. The model at day 241 with the wind data, a decision making process for taking off and partial compensation of flight.

In this final simulation the take-off decision making process is utilized together with partial compensation of flight diraction. The resulting figure (figure 6) is very similar to the figure of the simulation without compensation in flight behaviour (figure 4). The tracks do follow a more direct path to the destination, but distance travelled per day is shorter.

Compensation in flight direction might therefore have an effect on the average migration time. With these rules in place the clustering of simulated birds became very pronounced. This behaviour can best be observed in a visualisation which includes a time element. In figure 7 a sequence of 9 days is displayed. A longer time series in the form of a video can be found in the digital appendix. This pulsating behaviour is the result of the rules that are implemented, there is no interaction between agents.

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Figure 7. A sequence of visualizations of the model starting at day 241. Here the model is run with the wind data, a decision making process for taking off and partial compensation of flight.

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Conclusion

In a homogenous landscape without wind birds can fly to their destination in a straight line. This line will have the same angle as their preferred direction. However, when ecological barriers like open water are encountered the density of birds is likely to be larger before and after the barrier. This is because the birds will have to prepare before they cross the barrier and refuel after having used a lot of energy to cross the barrier (Shamoun-Baranes & van Gasteren, 2011). Similarly, other environmental influences shape the patterns that appear in the bird migration routes.

In the simulations it can be seen that the effect of wind is very pronounced (figure 3), especially when there is no component reducing its influence. When take-off decisions are added dynamics of the simulation change substantially (figure 4). Birds start to cluster when bad weather prevents departure. Besides take-off decisions, compensation in flight behaviour produces interesting patterns as well. In figure 5 it can be observed that total compensation of flight can result in a shorter distance travelled daily. As a consequence, it can take longer to cross water bodies and more birds die from exhaustion above sea. This makes total

compensation alone seem like a suboptimal migration strategy.

Of the two elements that were added to control the influence of wind, take-off decisions and compensation of flight, take-off decisions seems to have the largest effect. This can be seen by comparing figure 6 with figure 4. These figures are very similar, indicating that the effect of take-off decisions is dominant. It would be logical that take-off decisions have more influence than compensation of flight because the difference between not flying and flying is greater than the difference between fully drifting in the wind and compensating for wind. Moreover, the days when a bird would choose not to fly are the days with the least favourable wind. Therefore take-off decisions decrease the drift from the preferred direction as well.

In figure 7 clustering through time can be observed. This shows that the simple rules that make up this model can manifest in large-scale patterns. These large-scale patterns through time change according to the model configuration, as can be seen in the digital appendix.

Further research

This model is a very simplified representation of reality. This can be seen as a strength or weakness, depending on where it is used for. When exact locations of birds need to be predicted a model should be as close to the real situation as possible. However, when the influence of the environment on general patterns in bird migration is analysed, a simpler model might more robust. Some aspects the influence of the environment can be tested on include: survival rate, migration speed and clustering.

Adding elements to the model can make it more realistic. However it can also result in losing the simplistic nature. Some aspects of this model that can be made more realistic without sacrificing too much simplicity are described below. The ultimate goal of the model should

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always be considered when implementing additional elements, to prevent unnecessary complication of the model.

6. Heterogeneity of landscape

The landscape throughout Europe has a lot of variation, which influences the migration patterns of birds. Ecological barriers influence the migratory route of birds (La Sorte & Fink, 2017). In Europe, besides seas, the Alps and the Pyrenees form large ecological barriers and should be avoided by the birds. Additionally, there is a difference in food availability in nature reserves compared to agricultural fields and cities. This can be incorporated in the model by using a grid in which Natura 2000 sites have a different value. These areas can subsequently be assigned to improve the rate of fuel recovery when birds rest here, which relates to the next section.

7. Fuel, energy loss and recovering at resting sites

Instead of flying every night, it is more realistic that the birds take some days to regenerate their energy after they have flown a night. Additionally, quality of habitat can influence the accumulation rate of energy. McLaren et al. (2013) studied the decision making process regarding finding a resting site and how this influences the energy balance of migratory birds. Parameters from this study can be incorporated in the model to make the energy balance more realistic.

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Modelling emerging patterns in bird migration across Western Europe