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Quantifying year-round nocturnal bird migration with a fluid dynamics model

Abstract and Figures

The movements of migratory birds constitute huge biomass flows that influence ecosystems and human economy, agriculture and health through the transport of energy, nutrients, seeds, and parasites. To better understand the influence on ecosystems and the corresponding services and disservices, we need to characterize and quantify the migratory movements at various spatial and temporal scales. Representing the flow of birds in the air as a fluid, we applied a flow model to interpolated maps of bird density and velocity retrieved from the European weather radar network, covering almost a full year. Using this model, we quantified how many birds take-off, fly, and land across Western Europe, (1) to track waves of bird migration between nights, (2) cumulate the number of bird on the ground and (3) quantify the seasonal flow into and out of the study area through several regional transects. Our results show that up to 188 million (M) birds take-off over a single night. Exemplarily, we tracked a migration wave in spring, in which birds crossed the study area in 4 days with nocturnal flights of approximately 300 km. Over the course of a season, we estimated that 494 million (M) birds entered through the southern transects and, at the same time, 251 M left in the northern transects, creating a surplus of 243 M birds within the study area. Similarly, in autumn, 544 M more birds departed than arrived: 314 M birds entered through the northern transects while 858 M left through the southern transects. Our study show-cases the potential of combining interdisciplinary data and methods to elucidate the dynamics of avian migration from nightly to seasonal and yearly time-scales and from regional to continental spatial scales.
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Quantifying year-round nocturnal bird migration with a fluid dynamics
model
Rapha¨el Nussbaumer1,2,* , Silke Bauer1, Lionel Benoit2, Gr´egoire Mariethoz2, Felix Liechti1&
Baptiste Schmid1
1 Swiss Ornithological Institute, Sempach, Switzerland
2 Institute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerland
* raphael.nussbaumer@vogelwarte.ch
Abstract
The movements of migratory birds constitute huge biomass flows that influence ecosystems and human
economy, agriculture and health through the transport of energy, nutrients, seeds, and parasites. To better
understand the influence on ecosystems and the corresponding services and disservices, we need to
characterize and quantify the migratory movements at various spatial and temporal scales.
Representing the flow of birds in the air as a fluid, we applied a flow model to interpolated maps of bird
density and velocity retrieved from the European weather radar network, covering almost a full year. Using
this model, we quantified how many birds take-off, fly, and land across Western Europe, (1) to track waves of
bird migration between nights, (2) cumulate the number of bird on the ground and (3) quantify the seasonal
flow into and out of the study area through several regional transects.
Our results show that up to 188 million (M) birds take-off over a single night. Exemplarily, we tracked a
migration wave in spring, in which birds crossed the study area in 4 days with nocturnal flights of
approximately 300 km. Over the course of a season, we estimated that 494 million (M) birds entered through
the southern transects and, at the same time, 251 M left in the northern transects, creating a surplus of 243
M birds within the study area. Similarly, in autumn, 544 M more birds departed than arrived: 314 M birds
entered through the northern transects while 858 M left through the southern transects.
Our study show-cases the potential of combining interdisciplinary data and methods to elucidate the
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dynamics of avian migration from nightly to seasonal and yearly time-scales and from regional to continental
spatial scales.
Keywords
biomass flow, weather radar, migration ecology, ornithology, fluid dynamics, interactive visualisation,
ecological modelling.
1 Background 1
The sheer numbers of migratory birds create huge biomass flows (Alerstam, 1993; Dokter et al., 2018; Hahn,
2
Bauer, & Liechti, 2009) that impact ecosystem functions and human economy, agriculture and health 3
through the transport of energy, nutrients, seeds, and parasites (Bauer & Hoye, 2014). To understand these
4
influences on ecosystems and make use of, or avoid, the resulting services and disservices, we need year-round
5
and continental-wide monitoring of migratory fluxes and their quantification at various spatial and temporal
6
scales. Continental networks of weather radars are increasingly becoming essential tools for monitoring 7
large-scale migratory movements (Bauer et al., 2019). However, most studies so far have focused on specific
8
stages of the migration journey: migratory flights (e.g., Dokter et al., 2018; Horton et al., 2020; Nilsson et al.,
9
2019; Nussbaumer et al., 2019; Van Doren & Horton, 2018), or stop-overs (e.g., Buler et al., 2017; Cohen et
10
al., 2020; McLaren et al., 2018). Yet, none have explicitly considered and differentiated between the three 11
successive stages of take-off, flight and landing, and we therefore lack a comprehensive model of the entire 12
migratory journey. 13
To integrate migratory take-off, flight and landing into a single framework, we adopted a methodology 14
from fluid mechanics. While novel in aeroecology, fluid mechanics methods have been applied in ecology 15
before, for instance, the concept of permeability from Darcy’s Law to calculate species movement rates 16
(Jones, Watts, & Whytock, 2018) or a hydrological residence time model to estimate the stop-over duration
17
of migratory birds (Drever & Hrachowitz, 2017). 18
Here, we treat the nocturnal broad-fronted migration as a fluid and model bird density as a conservative
19
quantity using the continuity equation (e.g., Pedlosky, 1987). More specifically, we combine interpolated 20
maps of bird density and velocity into a discretised flow model (Figure 1). Since we assume that the biomass
21
of birds moving from one grid cell to another is conserved, any change of bird density (in the air) must be 22
explained by movements to and from the ground. Thus, we can quantify how many birds take-off, fly, and 23
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land at any given time and location. In subsequent steps, we use the resulting maps of take-off and landing
24
to (1) track waves of bird migration between nights across Europe, (2) estimate the accumulation (i.e. 25
changes in numbers) of birds on the ground throughout the year and (3) quantify the seasonal flow in and 26
out of the study domain through several transects. 27
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Figure 1.
Overview of the methodology for modeling nocturnal bird migration as a fluid flow at the
continental scale.
1. Interpolation and Simulation
(section 2.2). First, we interpolate vertical profile time series of bird
density and velocity field measured by weather radar data into continuous spatio-temporal maps following
Nussbaumer et al. (2019).
2. Flow model
(section 2.3) Then, using the interpolated data in a flow model allows us to estimate the
number of birds entering, leaving, taking off from and landing in each grid cell at each time step.
3. Migration Processes
(section 2.4) The resulting maps of take-off and landing birds allow us to investigate
the spatio-temporal variation of stop-over, the accumulation of birds on the ground, and the geographic
variation in the seasonal fluxes of migrating birds.
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2 Methodology 28
2.1 Data 29
We used the data from 37 weather radars in France, Germany, the Netherlands and Belgium operating 30
between 13 February 2018 and 1 January 2019. This dataset is currently the longest available time series 31
over a large part of Western Europe. It consists of vertical profiles of bird density [birds/km3], flight speed 32
[m/s] and flight direction [] which were generated with the vol2bird software (Dokter et al., 2011) and are 33
available on the ENRAM repository (ENRAM, 2020) at a 5 min x 200 m (0-5000m a.s.l.) resolution. Similar
34
to previous studies (Nilsson et al., 2019; Nussbaumer et al., 2019), the vertical profiles were cleaned as 35
follows (supplementary material 1.2). First, we eliminated high-reflectivity contamination (e.g. rain and 36
ground scatter) using a dedicated graphical user interface. Then, we removed contamination from slow 37
moving targets with low-reflectivitiy such as insects or snow based on standard deviation of radial velocity 38
and air speed (Nussbaumer, Schmid, Bauer, & Liechti, 2021). Finally, we vertically integrated bird density 39
and flight speed (i.e. volumetric to areal) while (1) accounting for the impact of local topography on the 40
surveyed volume, and (2) simulating bird density in the volume of air below the altitude surveyed 41
(supplementary material 1.3). 42
2.2 Interpolation and Simulation 43
Since the radars provide point observations (averaged over a 5-25 km radius around the radar location), we
44
interpolated bird density [birds/km2] into a spatio-temporal grid using the methodology developed in 45
(Nussbaumer et al., 2019). The bird velocity field (i.e. the vector field of birds’ flight speed and direction) 46
was interpolated for the two N-S and E-W components separately using a similar methodology. Adjustments
47
of the interpolation method to a year-round dataset and to a velocity field are detailed in supplementary 48
material 2. 49
The interpolation grid was defined between latitudes 43and 55and longitudes -5and 16, with a 50
resolution of 0.25and between 13 February 2018 and 1 January 2019 with a resolution of 15 min in time. 51
Similarly to Nussbaumer et al. (2019), grid cells were excluded if (1) they were located over a water body or
52
above 2000 m a.s.l, (2) they were more than 150 km away from a weather radar, (3) they spanned over day
53
time (i.e., from sunrise to sunset), or (4) rain intensity exceeded 1mm/hr (interpolated from ERA5 dataset 54
from Copernicus Climate Change Service (C3S) (2017)). Nights without data were excluded from the 55
interpolation (5 nights in early April, and 34 nights in July-August). The resulting interpolation maps can 56
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be visually explored at www.birdmigrationmap.vogelwarte.ch/2018.57
To correctly calculate aggregated measures (e.g. average bird density or sum of birds take-off) and their
58
uncertainties, we generated 500 geostatistical simulations of bird density (Lantu´ejoul, 2002; Nussbaumer et 59
al., 2019). 60
2.3 Flow Model 61
Based on the principle of mass conservation, the continuity equation (Equation 1) describes the transport of
62
a conserved quantity (e.g., bird density): the rate of change of this quantity is equal to its flux into and out
63
of a given volume (e.g. sky). The equation can also include a source/sink term, which accounts for the 64
appearance (and disappearance) of the quantity (e.g., take-off and landing). The differential form of the 65
continuity equation for bird density ρ[birds/km2] is 66
∂ρ
∂t =−∇ · (ρv) + W, (1) 67
where v= [vlon, vlat ] is the bird’s velocity field [km/hr] along latitude and longitude and Wis the 68
source/sink term [birds/hr/km2] and denotes the vector differential operator. The continuity equation is 69
discretised with a Forward Time Centered Space (FTCS) scheme (Roache, 1972). The source/sink term can
70
be computed for each cell (i, j, t) with 71
Wtt+1
i,j =ρt+1
i,j ρt
i,j
t1
2∆lat Φlat|t
i+1,j Φlat|t
i1,j,t+1
2∆lon Φlon|t
i,j+1 Φlon |t
i,j1,(2) 72
where
Φ
=
ρv
=
lon,Φlat ]
is the flux term expressed in [birds/km/h] and discretised in longitude, latitude
73
and time with the indexes i, j, t respectively. ∆lon, ∆lat and ∆t are the grid resolution in time, longitude 74
and latitude respectively. 75
We applied this model to bird migration by using the spatio-temporal maps of bird density (
ρ
) and flight
76
speed vector (v) derived from geostatistical simulations (Section 2.2). The local fluxes were computed for 77
each grid-cell by multiplying the density with the flight vector and then linearly interpolated to the grid cells’
78
boundaries for both the longitudinal and latitudinal components. As the grid was defined in equal latitude 79
and longitude intervals, the resolution ∆
lon
in km varied along the latitude axis. Finally, using Equation 2,
80
the source/sink term was computed for each grid cell at each time step as the change of bird density over 81
time minus the spatial difference of fluxes. The source/sink term Wwas composed of birds taking-off and 82
landing (within the study area) which can be separated according to the sign of
W
. Indeed, as the reference
83
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of the mass balance was the sky, positive values of Wcorrespond to birds taking-off while negative values 84
correspond to landing. Additionally, the values of the fluxes at the study area’s boundaries were extracted as
85
the number of birds entering (positive) and leaving (negative) the study area. We uses the 500 simulations to
86
produce space-time maps of (1) take-off and landing [birds/ km2] and (2) fluxes in lat-lon [birds/hr/km] at 87
the boundaries of the study area. 88
2.4 Migratory Processes 89
The resulting maps were processed to address specific ecological questions. We were particularly interested in
90
characterizing and quantifying nightly migration pulses and stopovers, the accumulation of birds on the 91
ground, and the seasonal migration flows. To achieve this, we processed each of the 500 realisations as follows:
92
The nightly migratory pulses and stopovers were calculated by summing the take-off and 93
landing movements separately over each night, and by visually comparing the maps of landing in the 94
morning with those of take-off the following evening. 95
The year-round accumulation of migratory birds on the ground was quantified by first 96
aggregating the four fluxes (take-off, landing, entering, leaving) over the whole study area and for each
97
night. Then, the nightly change in the number of birds on the ground was computed as the difference
98
between landing and take-off, or equivalently, between entering and leaving. The cumulative sum of 99
these daily changes corresponds to the number of birds that remained on the ground. We arbitrarily 100
set the starting value of the accumulation to zero because the initial number of (resident and/or 101
wintering) birds on the ground is unknown. 102
The seasonal flow of bird migration is quantified by summing the fluxes of birds entering and 103
leaving the study area over spring (February-June) and autumn (August-December). To capture the 104
variability of movements across Europe, we defined six transects along the boundary of the study area
105
according to the major flyways: United Kingdom, the North, the East, the Alps, Spain and the 106
Atlantic (Figure 4). 107
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3 Results 108
3.1 Nightly migratory pulses and stopovers 109
For illustration purposes, we selected a well-defined migration wave spanning from 6 to 10 April, during 110
which birds moved from south-western France to north-eastern Germany (Figure 2). The nightly averaged 111
bird density and flight speed was highest between the main take-off and landing areas. More importantly, 112
one night’s landing and the following night’s take-off were in good agreement, demonstrating that the data 113
and proposed methodology can accurately track a wave of migration over several days. This agreement was
114
particularly striking in this example because birds did not stopped over, migrating every nights. The crossing
115
of the study area in approximately 4 nights corresponds to nightly migratory bouts of around 300 km. On 116
April 10, one radar in south-west France detected a new wave arriving. 117
Figure 2.
Consecutive phases of take-off (top row), flight (middle row) and landing (bottom row) of bird
migration between 6 and 10 April 2018. Take-off and landing maps show the sum of take-off and landing
over the entire night, respectively, while the density and flight speed maps show the average over the night.
3.2 Year-round accumulation of migratory birds on the ground 118
Summing the flow at the daily (or nightly) scale allows us to characterize the year-round changes in numbers
119
of migratory birds on the ground (Figure 3, a seasonal sum of the bird movements (take-off, landing, 120
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entering, and leaving) is provided in the supplementary material Figure 3.1). The number of birds on the 121
ground rises steeply in March with almost 200 million more birds entering in the study area than leaving it,
122
e.g., to migrate further North or East. Numbers are declining from August onwards, and plummeted in 123
mid-October. The number of bird on the ground became negative in autumn because our methods did not 124
explicitly account for reproduction and mortality, therefore the birds leaving the area in autumn included the
125
new generation. The spring migration period was shorter and more condensed (March - May) than the 126
autumn migration (August to mid-November) (Figure 3), with 50% of all take-offs taking place during 19 127
nights in spring and 29 nights in autumn. At peak migration, we estimated 118 (Q5-Q95: 99-137) million 128
birds taking off in a single night in spring (30 March – 1 April) and 148 (133-164) million in autumn (17-18
129
October). Prior to these two peak migration events, we observed that the accumulation curve of bird on the
130
ground flattened, indicating a temporarily reduced migratory traffic possibly due to unfavorable weather 131
conditions (”Zugstau”). 132
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Figure 3.
Time series of the daily number of birds taking-off (blue) and landing (red), and entering (purple)
and leaving (orange) the study area. The changes in the number of birds on the ground and their cumulative
sum (brown line) is calculated as the difference between the number of birds landing in, and taking-off, from
the study area. The uncertainties (Q5-Q95) are illustrated with fine black line on the bar plots and with
shaded area for the cumulative time series. The dotted lines denote absence of data.
3.3 Seasonal Flow 133
The bird migration in the study area (both in spring and in autumn) was mainly directed between Spain and
134
Eastern Germany (Figure 4). Indeed, even the migration through the Atlantic transect mostly comprises 135
birds crossing the Bay of Biscay from/to Spain. 136
In spring, 494 (Q5-Q95: 453-540) million birds entered the study area through the southern transects 137
(Alps, Spain and Atlantic) and, at the same time, 251 (Q5-Q95:228-273) million left it in the northern 138
transects (UK, North and East), thus creating a surplus of 243 (Q5-Q95:200-290) million birds that remained
139
within the study area (Figure 4). Similarly, in autumn, 544 (Q5-Q95:480-610) million more birds departed 140
than arrived: 314 (Q5-Q95:284-344) million birds entered through the northern transects while 858 141
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(Q5-Q95:797-917) left through the southern transects. The ratio of the autumn deficit to the spring surplus
142
is 2.2 (Q5-Q95:1.8-2.8), meaning that for one bird staying in spring, two birds left the ground in autumn. 143
Compared to spring, birds took a more easterly route in autumn, with proportionally more birds flying 144
through the Alps transect (autumn/spring = 114/53 = 2.15) than through the Atlantic transect 145
(233
/
168 = 1
.
4). Moreover, nearly the same number of birds crossed the East transect in autumn and spring
146
(150
/
138 = 1
.
1). Overall, this pattern could be indicative of a clockwise loop migration where birds migrate
147
to their breeding areas via the Iberian Peninsula in spring and fly to their non-breeding areas further East in
148
autumn. 149
The seasonal fluxes per transect summarise the number of birds entering and leaving and can therefore 150
cover some fine scale features of migration. Firstly, some transects showed a more unidirectional flow of 151
migrants whereas the entering and leaving fluxes were more balanced for other transects. For instance, 91%
152
of all movements across the Spanish transect are in-movements in spring, i.e. most birds enter the study area
153
rather than leave it, and similarly, 90% of all movements in autumn are out-movements of birds leaving the
154
study area. In contrast, movements across, e.g., the Alps transect were less uni-directional in both seasons 155
with only 63% of all movements in spring being movements into the study area (entering) and similarly, 72%
156
of all movements in autumn were movements out of the study area (leaving) (Figure supplementary material
157
3.2). Secondly, the timing of migration differs between transects (Figure supplementary material 3.2), with,
158
e.g. Spain and Atlantic transects seeing more than half of its migration before mid-March, while only 20-30%
159
of birds have crossed the East and North transects at that time. 160
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Figure 4.
Bird migration flows (in millions of birds) in spring and autumn were aggregated along six
transects representing the major flyways. The direction of movement, i.e. into or out of the area, is indicated
by the arrows and the sign (+/-) of the mean numbers (bold). The accumulation within the study area results
from summing all inward and outward fluxes. Uncertainty for all estimates is provided by their Q5-Q95
ranges.
4 Discussion 161
In this study, we presented a novel methodology inspired from fluid dynamics to model the flow of nocturnal
162
migrants, from take-off, during nocturnal flight, to landing. The model produces high-resolution maps that 163
allow investigating the dynamics of migratory movements at various spatial and temporal scales. We used 164
the largest dataset available on the ENRAM data repository to characterize and quantify nightly, seasonal 165
and year-round migration patterns over most of Western Europe. 166
4.1 Model 167
The model presented in this study builds on the methodology developed in (Nussbaumer et al., 2019), which
168
interpolates point observations of bird densities measured by weather radars into continuous maps. We used
169
these maps as the input for a flow model by considering bird migration as a fluid. This allows us to extract
170
more dynamic information about bird movements and, in particular, their take-off and landing. 171
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The approach used in this study models bird flow (i.e. average bird movement) rather than individual 172
birds. Indeed, the weather radar data consist of bird density and flight speed averaged over a 25km radius. 173
Therefore, the estimated flows cannot capture the properties or behaviour of individual birds. For instance, 174
individual speed are typically be higher than the speed of the flow and the movement directions of individual
175
birds is more variable than the direction of the flow. Similarly, the modeled flow is unable to track separately
176
multiple bird populations simultaneously migrating in different direction. 177
Throughout the methodology, we identified the sources of errors and tracked the corresponding 178
uncertainties to reliably estimate the ranges of the model outputs. Despite our best efforts to clean the data
179
(supplementary material 1.2), there is an inherent uncertainty in the weather radar data (e.g. ground 180
scattering, measurement errors, radar biases). We partially accounted for the data uncertainty at low altitude
181
when we generated uncertainty range in the vertical integration (see supplementary material 1.3). For more
182
details on the data quality of weather radar, we refers the readers to the assessment and comparison found in
183
Liechti et al. (2019); Nilsson et al. (2018); Nussbaumer et al. (2019). We handle these unknown errors in the
184
geostatical framework (i.e. interpolation) by fitting a nugget effect in the spatio-temporal model (more 185
detailed in supplementary material 2). The nugget effect essentially fits a random noise to the data (e.g., 186
corresponding to the data error), which then, permits the interpolated value to diverge from a datapoint. In
187
addition to the data error (i.e., difference between ’true’ passage and measured passage), the nugget effect 188
also models small-scale variability/discontinuity in bird density not covered by the dataset (<50-100km) 189
caused by, e.g., geographical features (mountains, rivers, sea), weather conditions (e.g. rain). We percolated
190
these uncertainties throughout our methodology by generating 500 simulation of bird density representing 191
the range of possible values (section 2.2), run in the flow model on each of them, and finally are able to 192
provide for each output (e.g. number of bird on the ground) a distribution of the possible value. 193
4.2 Stopover 194
In this study, we demonstrated how waves of bird migration at the regional scale can be tracked over 195
multiple nights (Figure 2). Our flow model links birds on the ground with birds in the air and can thus 196
quantify the fluxes of take-off, flight and landing. Looking ahead, this example suggests that a forecast 197
system based on a flow model of bird migration could accurately predict bird landings during the night, and
198
perhaps, on a longer term, take-off and landing over a few days. 199
Our method can compute the rates of both take-off and landing in higher spatial and temporal resolution
200
than earlier approaches (e.g. 3hrs after sunset in Buler and Diehl (2009), interpolation at civil twilight in 201
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Buler and Dawson (2014); Buler et al. (2012) or at maximum density within two hours after sunset in 202
Aurbach, Schmid, Liechti, Chokani, and Abhari (2020)) - a feature that will be particularly useful in follow 203
up studies that link movements and stop-overs to geographical features or short, intense weather events. 204
Although our model can identify the places and times where birds stop-over, other aspects of stopover 205
dynamics such as stopover duration or survival remain to be tackled in future multidisciplinary studies. The
206
main obstacle to addressing stopover dynamics is the inability to track birds during the day, i.e. which of the
207
birds landing one day are the ones taking-off the following day(s). A similar problem appears at the seasonal
208
scale, where we cannot differentiate birds that are wintering, breeding or passing from the birds landing or 209
taking-off. A potential solution would be to explicitly model stop-over duration with a residence time model
210
(Drever & Hrachowitz, 2017). 211
4.3 Accumulation and seasonal flow 212
Using our novel methodology and an almost continuous one-year dataset, we assessed the relative changes in
213
the number of birds on the ground. We estimated that in autumn 2018, 858 million birds (Q5-Q95: 797-917)
214
migrated southward through Spain and over the Alps (incl. the Atlantic transect) (Figure 4). The only 215
previous quantification of migrant bird population estimated that between 1.52 and 2.91 billion long-distance
216
migrants leave the entire European continent in autumn (Hahn et al., 2009). Our estimation agrees with 217
these numbers if we consider that our study area (from the British islands to Scandinavia, Finland to Poland,
218
and our study area) corresponds to roughly one third of the European continent as compared to the entire 219
continent in (Hahn et al., 2009). In North America, the number of birds migrating out of the US in autumn
220
was estimated to around 4.72 billion birds (Dokter et al., 2018), which corresponds to an average density of
221
236 birds/km2(for an area of 19.8 million km2). Despite the differences of scale and ecological context, we 222
found a comparable average density of 286 birds/km2when we again assume that a third of the European 223
bird population migrates through the southern transect. 224
The ratio between autumn and spring fluxes can be used to estimate an index of net recruitment, 225
accounting for both reproduction and mortality (Dokter et al., 2018). For the US, Dokter et al. (2018) 226
estimated a ratio of 1.36 for a transect along the southern border and 1.60 for a transect along the northern
227
border. In our study area in Europe, the resulting indices are 1.74 (Q5-Q95: 1.55-1.94) in the southern 228
transects (Alps, Spain and Atlantic, Figure 4) and 1.26 (1.09-1.42) in the northern transects (UK, North and
229
East, Figure 4). However, such derived values like recruitment critically depend on birds taking similar 230
migration routes in both spring and autumn. If migration routes vary between seasons, e.g. when birds take
231
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a more easterly route in autumn, recruitment numbers become distorted. Instead of computing the ratio of
232
migratory birds flying across non-representative transects, we can take advantage of the flow model to 233
estimate a ratio of migratory birds entering and leaving an area of interest, and thereby relate the 234
recruitment index computed over this area to environmental characteristics. For the entire study area, a 235
recruitment index of 2.26 (1.80-2.81) resulted from the ratio between the relative number of birds that have
236
left in autumn (i.e., leaving minus entering) (544 M, Figure 3) and the relative number that have arrived in
237
spring (i.e., entering minus leaving) (243 M, Figure 3). However, as the fluxes of wintering and breeding bird
238
populations cannot be distinguished (see discussion on stopover), this recruitment index also depends on the
239
number of wintering birds that leave the study area in spring and return in autumn with offspring. 240
Therefore, while this recruitment index can characterize the migratory bird population growth, it cannot 241
separate the influence of breeding and wintering populations. A possible avenue to address this challenge is
242
to combine breeding and/or wintering bird atlas data with our accumulation of birds on the ground. This 243
approach could provide absolute numbers of breeding, passing and wintering birds along with their 244
corresponding recruitment indices. 245
Acknowledgements 246
We thank Pietro De Anna for initial discussion about applicability of a flow model framework to bird 247
migration, and Mathieu Gravey for the assistance in implementing the Multi-Point Statistics simulation. 248
This study contains modified Copernicus Climate Change Service Information 2019. Neither the 249
European Commission nor ECMWF is responsible for any use that may be made of the Copernicus 250
Information or Data it contains. 251
We acknowledge the European Operational Program for Exchange of Weather Radar Information 252
(EUMETNET/OPERA) for providing access to European radar data, facilitated through a research-only 253
license agreement between EUMETNET/OPERA members and ENRAM (European Network for Radar 254
surveillance of Animal Movements). 255
We acknowledge the financial support from the Globam project funded by BioDIVERSA, including the 256
Swiss National Science Foundation (31BD30 184120), Netherlands Organisation for Scientific Research 257
(NWO E10008), Academy of Finland (aka 326315), Belgian Federal Science Policy Office (BelSPO 258
BR/185/A1/GloBAM-BE) and National Science Foundation (NSF 1927743). 259
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Authors’ contributions 260
RN, FL, BS and SB conceived the study, RN, LB, GM designed the flow model, RN implemented the 261
computational framework and performed the analyses, RN, BS and SB wrote the manuscript, with 262
substantial contributions from all authors. 263
Data Accessibility 264
The Github page of the project (
https://rafnuss-postdoc.github.io/BMM/2018/
) provides links to
265
the MATLAB files (script and livescript) used for preprocessing, interpolation, flow model and creation
266
of the figures. 267
The raw weather radar data were available on the ENRAM repository (ENRAM, 2020) 268
(https://github.com/enram/data-repository). 269
The cleaned vertical time series profile are available on Zenodo (Nussbaumer, 2020) 270
(https://doi.org/10.5281/zenodo.3610184)271
The code of the website (https://bmm.raphaelnussbaumer.com/2018) are available on the Github 272
(https://github.com/Rafnuss-PostDoc/BMM-web-2018)273
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... Each spring and fall, billions of birds migrate between breeding and non-breeding ranges all over the globe (Dokter et al., 2018;Nussbaumer et al., 2020). During their migratory movements, birds encounter diverse anthropogenic activities that have direct consequences for migrants and humans. ...
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