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remote sensing

Article

A Geostatistical Approach to Estimate High

Resolution Nocturnal Bird Migration Densities

from a Weather Radar Network

Raphaël Nussbaumer 1,2,* , Lionel Benoit 2, Grégoire Mariethoz 2, Felix Liechti 1,

Silke Bauer 1and Baptiste Schmid 1

1Swiss Ornithological Institute, 6204 Sempach , Switzerland; Felix.Liechti@vogelwarte.ch (F.L.);

Silke.Bauer@vogelwarte.ch (S.B.); Baptiste.Schmid@vogelwarte.ch (B.S.)

2Institute of Earth Surface Dynamics, University of Lausanne, 1015 Lausanne, Switzerland;

Lionel.Benoit@unil.ch (L.B.); Gregoire.Mariethoz@unil.ch (G.M.)

*Correspondence: raphael.nussbaumer@vogelwarte.ch

Received: 25 July 2019; Accepted: 19 September 2019; Published: 25 September 2019

Abstract:

Quantifying nocturnal bird migration at high resolution is essential for (1) understanding

the phenology of migration and its drivers, (2) identifying critical spatio-temporal protection zones

for migratory birds, and (3) assessing the risk of collision with artiﬁcial structures. We propose a

tailored geostatistical model to interpolate migration intensity monitored by a network of weather

radars. The model is applied to data collected in autumn 2016 from 69 European weather radars.

To validate the model, we performed a cross-validation and also compared our interpolation results

with independent measurements of two bird radars. Our model estimated bird densities at high

resolution (0.2

◦

latitude–longitude, 15 min) and assessed the associated uncertainty. Within the area

covered by the radar network, we estimated that around 120 million birds were simultaneously in

ﬂight (10–90 quantiles: 107–134). Local estimations can be easily visualized and retrieved from a

dedicated interactive website. This proof-of-concept study demonstrates that a network of weather

radar is able to quantify bird migration at high resolution and accuracy. The model presented has

the ability to monitor population of migratory birds at scales ranging from regional to continental in

space and daily to yearly in time. Near-real-time estimation should soon be possible with an update

of the infrastructure and processing software.

Keywords:

aeroecology; bird migration; geostatistical modeling; interactive visualization; kriging;

radar network; spatio-temporal interpolation map; weather radar

1. Introduction

Every year, several billions of birds undergo migratory journeys between their breeding and

non-breeding grounds [

1

,

2

]. These migratory movements link ecosystems and biodiversity on a global

scale [

3

], and their understanding and protection require international efforts [

4

]. Indeed, declines in

many migratory bird populations [

5

,

6

] resulted from the rapid changes in their habitats, including

the aerosphere [

7

]. Changes in aerial habitats are diverse, and their consequences still poorly known.

Climate change may alter global wind patterns and consequently the wind assistance provided to

migrants [

8

]. Likely to be more severe, the impact of direct anthropogenic changes, including light

pollution that reroutes migrants [

9

], buildings [

10

], wind energy production [

11

], and aviation [

12

],

causes billions of fatalities every year [13].

In the face of these threats and to set up efﬁcient management actions, we need to quantify bird

migration at various spatial and temporal scales. Fine-scale monitoring is crucial for understanding

the phenology of migration and its drivers, identifying critical spatio-temporal protection zones to

Remote Sens. 2019,11, 2233; doi:10.3390/rs11192233 www.mdpi.com/journal/remotesensing

Remote Sens. 2019,11, 2233 2 of 24

support conservation actions, and assessing collision risks with artiﬁcial structures and aviation to

inform stakeholders. However, the great majority of migratory landbirds ﬂy at night [

14

], rendering

the quantiﬁcation of the sheer scale of bird migration a challenging exercise.

Radar monitoring has the potential to quantify birds’ migratory movements at the continental

scale [

15

]. Initially limited to single dedicated short-range radars, radar aeroecology truly took off

when it was able to leverage existing weather radar networks, thus providing continuous monitoring

over large geographical areas such as Europe or North America [

2

,

16

–

19

]. One important challenge

in using networks of weather radars is the interpolation of their signals in space and time. Recent

studies [

2

,

19

] have used relatively simple interpolation methods as they targeted patterns at coarse

spatial and temporal scales. However, these methods are insufﬁcient if higher spatial or temporal

resolution is needed, such as for the fundamental and applied challenges outlined above.

To achieve a high-resolution interpolation of migration intensity derived from weather radars

( 20 km–15 min), we propose a tailored geostatistical framework able to model the spatio-temporal

patterns of bird migration. Starting from time series of bird densities measured by a radar network,

our geostatistical model produces a continuous map of bird densities over time and space. A major

strength of this method is its ability to provide the full range of uncertainty and thus to evaluate

complex statistics, for instance, the probability that bird densities reach a given threshold. In addition

to the estimation map, the method also produces simulation maps which are essential for several

applications such as quantiﬁcation of the total number of birds.

As a proof-of-concept, we applied our geostatistical model to a three-weeks dataset from the

European Network of weather radars [

20

] and validated the results with independent dedicated bird

radars. In addition to insights into the spatio-temporal scales of broad-front migration, our approach

provides high-resolution (0.2

◦

latitude and longitude, 15 min) interactive maps of the densities of

migratory birds.

2. Materials and Methods

2.1. Weather Radar Dataset

Our dataset originates from measurements of 69 European weather radars, spread from Finland to

the Pyrenees (eight countries) and covering the period from 19 September to 10 October 2016 (Figure 1).

It thus encompasses a large part of the Western European ﬂyway during fall migration 2016.

Based on the reﬂectivity measurements of these weather radars, we used the bird densities as

calculated and stored on the repository of the European Network for the Radar surveillance of Animal

Movement (ENRAM) (https://github.com/enram/data-repository) ([

21

] for details on the conversion

procedure). We inspected the vertical proﬁles and manually cleaned the bird densities data (see

detailed procedure in Appendix Aand resulting vertical proﬁles in Supplementary Material S1).

As we targeted a 2D model, we vertically integrated the cleaned bird densities from the

radar elevation to 5000 m above sea level. Because we aimed at quantifying nocturnal migration,

we restricted our data to night-time, between local dusk and dawn (civil twilight, sun 6

◦

below

horizon). Furthermore, as rain could contaminate and distort the bird densities calculated from radar

data, a mask for rain was created when the total column of rain water exceeds a threshold of 1 mm/h

(ERA5 dataset from [22]). In the end, the resulting dataset consisted of a time series of nocturnal bird

densities [bird/km2] at each radar site with a resolution of 15 min (Figure 2).

Remote Sens. 2019,11, 2233 3 of 24

15min

Temporal resolution

69

Radars

09/09 - 10/10/2016

Period

143 km

closest radar

25km(64) - 40km(5)

Radar range

50°N

60°N

0°E

10°E

20°E

30°E

Figure 1.

(

Left

) Locations of weather radars of the European Network for the Radar surveillance of

Animal Movement (ENRAM) network, whose fall 2016-data were used in this study (yellow dots) and

the two dedicated bird radars for validation (red dots). (

Right

) Key characteristics of the dataset used.

100

20

30

40

50 (a)

(c)

(d)

Sep 27 Sep 28

Bird densities [bird/km2]

0

50

100

50

10

Sep 22 Sep 28 Oct 04 Oct 10

2016

(f)

(g)

Date

100

200

0

100

200

200

0

0

100

(b)

0

10

20

(e)

30

Bird densities [bird/km2]

0

Figure 2. Illustration of the spatio-temporal variability of bird densities measured by a weather radar

network. (

a

) Average bird densities measured by each radar over the whole study period. (

b

–

d

) Time

series of bird densities measured by the radar with the corresponding outer ring color in panel (

a

).

(

e

–

g

) Zoom on a two-days period. A strong continental trend appears in panel (

a

) as well as a correlation

at the multi-night scale when comparing (

b

)–(

d

). These spatial correlations are even stronger at the

regional scale when comparing within a subplot (

f

). The intra-night scale shows an obvious bell-shape

curve pattern during each night (g).

2.2. Interpolation Approach

Bird densities are strongly correlated spatially (Figure 2a) and temporally at both nightly

(Figure 2b–d) and sub-nightly scales (Figure 2e–g). These strong spatio-temporal correlations motivated

the use of a Gaussian process regression to interpolate bird densities measured by weather radars at

high temporal resolution. In this framework, the spatio-temporal structure of bird migration is ﬁrst

Remote Sens. 2019,11, 2233 4 of 24

learned from the punctual radar measurements. This model is then combined with the measurements

to estimate bird densities at any location in space and time. In this paper, we adopt the terminology

and notations of Geostatistics [

23

,

24

], and mention its correspondence with Gaussian processes in the

ﬁeld in machine learning [25].

Because of the multi-scale temporal structure of bird migration (Figure 2), we consider here an

additive model combining two temporal scales: ﬁrst, a multi-night process that models bird density

averaged over the night and, second, an intra-night process that models variations within each night.

Subsequently, each scale-speciﬁc process is further split into two terms: a smoothly-varying (in space

time) deterministic trend and a stationary Gaussian process.

2.3. Geostatistical Model

The bird density B(s,t)observed at location sand at time tis modeled by

B(s,t)p=µ(s) + M(s,d(t))

| {z }

Multi-night scale

+ι(s,t) + I(s,t)

| {z }

Intra-night scale

, (1)

where

µ

and

ι

are deterministic trends at the multi-night and intra-night resolution, respectively,

and

M

and

I

are random effects at the multi-night and intra-night resolution, respectively;

d(t)

is

a step function that maps the continuous time

t

to the discrete day

d

of the closest night. A power

transformation

p

is applied on bird densities to transform the highly skewed marginal distribution

into a Gaussian distribution (Figure A2 in Appendix B). Figure 3illustrates the decomposition of

Equation (1) during three nights.

Sep 27, 00:00 Sep 27, 12:00 Sep 28, 00:00 Sep 28, 12:00 Sep 29, 00:00

2016

0

20

40

60

80

Bird densities [bird/km2]

Time

Figure 3.

Illustration of the proposed mathematical model decomposition of Equation (1) with the

exception that the power transformation was not applied. Note that the values of

M

,

ι

, and

I

can be

either positive or negative.

2.3.1. Multi-Night Scale

At the multi-night scale, we model bird densities averaged overnight as a space-time Gaussian

process with a spatial trend (also called mean function), due to the general increasing bird densities

southwards (Figure 2a). Because of the relatively short duration of the dataset, no temporal component

is added in the trend. The trend at the multi-night scale is therefore modeled as a planar function,

µ(s=[slat,slon]) =wlatslat +w0, (2)

Remote Sens. 2019,11, 2233 5 of 24

where

slat

and

slon

are the latitude and longitude of location

s

;

wlat

is the slope coefﬁcient in latitude;

and

w0

is the value of the trend at the origin. Because no longitudinal trend is observed in the

data (Figure 1a), only latitude is used to conﬁgure the planar function (see Figure A3 in Appendix B).

If longer periods are considered, Equation (2) can be replaced by a spatio-temporal polynomial function

in order to handle the emerging patterns of long-term nonstationarity.

With the spatial trend accounted for by

µ

,

M

can be modeled as a Gaussian random process with

zero-mean.

M

is assumed to be 2

nd

order stationary, so that its covariance function

CM

(also called

autocovariance or kernel function) depends only on ∆s,∆t,

CM(M(s,t),M(s+∆s,t+∆t))=CM(∆s,∆t). (3)

The covariance function CMis modeled with the Gneiting type function [26]

CM(∆s,∆t)=C0δ∆s+CG

(∆t/rt)2δ+1exp

−(k∆sk/rs)2γ

(∆t/rt)2α+1βγ

. (4)

In Equation (4), the scale parameters

rt

and

rs

(in space and time, respectively) control the

decorrelation distances and, thus, the average extent and duration of the space-time patterns of

M

.

The regularity parameters 0

<α

and

γ<

1 (in space and time, respectively) control the shape of

the covariance function close to the origin. Values of

α

and

γ

close to 0 lead to sharp variations at

short lags, whereas values close to 1 lead to smooth variations of

M

. The separability parameter

β

controls the space-time interactions. When

β=

0 the space-time interactions vanish and the covariance

function becomes space-time separable.

CG

controls the amplitude of the covariance function. Finally,

C0

is a nugget effect which accounts for the uncorrelated variability of

M

, and

δ

is the Kronecker

delta function

C0δ∆s=(C0if ∆s=0

0 otherwise . (5)

Note that in contrast to a usual nugget

C0δ∆s,δt

, here we use a nugget in the space dimension

only

δ∆s

. This nugget accounts for the uncorrelated variability of

M

over space which can be caused

by persistent local geographical features affecting bird migration (e.g., topography and water body)

or possible bias of radar observation (e.g., ground scattering). The total variance of

M

is deﬁned as

CM(0, 0) = C0+CG.

2.3.2. Intra-Night Scale

At the intra-night scale, the main trend visible in the dataset is a bell-shape curve pattern

(Figure 2e–g) that results from the onset and sharp increase of migration activity after sunset, and its

slow decrease towards sunrise [

27

]. This trend is modeled with a curve template

ι

for all nights and

locations, deﬁned by a polynomial of degree 8,

ι(s,t) =

i=8

∑

i=0

aiNNT(s,t)i, (6)

where

ai

are the coefﬁcients of the polynomial and

NNT

(Normalized Night Time) is a proxy of the

progression of night, deﬁned such that the local sunrise and sunset occur at

NNT =−

1 and

NNT =

1 ,

respectively.

˜

I(s,t) = I(s,t)

σI(s,t), (7)

Remote Sens. 2019,11, 2233 6 of 24

where σI(s,t)is a polynomial function with coefﬁcients bithat models the variation of the variance

σI(s,t) =

i=10

∑

i=0

biNNT(s,t)i. (8)

This normalization allows to use a stationary covariance function for ˜

I,

C˜

I(∆s,∆t)=C0δ∆s,∆t+CG

(∆t/rt)2α+1exp

−(k∆sk/rs)2γ

(∆t/rt)2α+1βγ

. (9)

Note that modeling

I

through the covariance function of its normalized variable

˜

I

is equivalent to

modeling Idirectly with a nonstationary covariance function, which includes σI(s,t).

2.4. Bird Migration Mapping

The geostatistical model presented in Section 2.3 is used to interpolate bird density observations

derived from weather radars, and produces high resolution maps of both estimation (with

corresponding uncertainty) and simulation (see Section 2.4.2). In the case study presented in this paper,

the interpolation map is calculated on a spatio-temporal grid with a resolution of 0.2

◦

in latitude (43

◦

to 68

◦

) and longitude (

−

5

◦

to 30

◦

) and 15 min in time, resulting in 127

×

176

×

2017 nodes. Over this

large data cube, the estimation and simulation are only computed at the nodes located (1) over land,

(2) within 200km of the nearest radar and (3) during night-time ( −1<NNT(t,s)<1).

2.4.1. Estimation

The estimation is performed by applying universal kriging at both the multi- and intra-night

scales. We employ a two-step approach of universal kriging where the trends

µ

and

ι

are ﬁrst estimated

by ordinary least squares (see Appendix B.2 and B.3), and then subtracted from the observations. The

resulting random effects

M

and

˜

I

are parameterized by ﬁtting their covariance function (deﬁned in

Equations (4) and (9)) to the empirical covariance computed based on the detrended observations (see

Appendix B.4). Finally,

M

and

˜

I

are interpolated at any space-time location of interest,

s0

,

t0

, by simple

kriging (see Appendix C), denoted as

M(s0

,

t0)∗

and

˜

I(s0

,

t0)∗

. The ﬁnal estimation of bird density

Bp(s0,t0)∗is reconstructed based on Equation (1) as,

Bp(s0,t0)∗=t(s0)+M(s0,t0)∗+ι(t0)+σI(s0,t0)˜

I(s0,t0)∗. (10)

An important advantage of using kriging is that it expresses the estimation as a Gaussian

distribution, thus providing not only the “most likely value” (i.e., mean or expected value), but also a

measure of uncertainty with the variance of estimation. As

M

and

˜

I

are constructed independently,

the variance of estimation of Bp(s0,t0)∗can be computed with

var Bp(s0,t0)∗=var M(s0,t0)∗+σI(s0,t0)2+var ˜

I(s0,t0)∗. (11)

In the Gaussian process framework,

Bp(s0,t0)∗

and

var Bp(s0,t0)∗

are referred to as the

posteriori mean and variance, respectively.

The conversion of the transformed variable

Bp

(i.e., the expected value Equation (10) and variance

of Equation (11)) into bird density

B

, is possible through the use of a quantile function,

QB(ρ;s0,t0)

,

which returns the bird density value bcorresponding to a given quantile ρ:

QB(ρ;s0,t0)=inf{b: Pr(B(s0,t0)<b)≥ρ}. (12)

Remote Sens. 2019,11, 2233 7 of 24

The quantile function allows to describe

B

because the quantile value

ρ

is preserved through a

power transform. Therefore, the quantile function of Bis computed with

QB(ρ;s0,t0)=QBp(ρ;s0,t0)1/p=F−1

Bp(ρ)1/p, (13)

where

FBp(Bp)

is the cumulative distribution function of the Gaussian variable

Bp(s0

,

t0)

characterized

by its mean (Equation (10)) and variance (Equation (11)).

Consequently, we choose to characterize the estimation of the bird density

B(s0

,

t0)

by its median

and its quantiles 10 and 90 (i.e., uncertainty range).

2.4.2. Simulation

The geostatistical simulation of the random variable

B

consists of randomly drawing a realization

B(`)

among the set of all possible outcomes deﬁned by the probability of

B

conditional to the radar

observations (see Equations (10) and (11)) e.g., [

23

]. This is identical to sampling the posterior

probability in the Gaussian process framework.

Although kriging estimation is known to produce accurate point estimates, it leads to excessively

smooth interpolation maps [

28

], and thus fails to reproduce the ﬁne-scale texture of the process at

hand. This causes problems for applications in which the space-time structure of the interpolation

map matters, such as when a nonlinear transformation is applied to the interpolated map. This is

the case in our model, as the back power transformation creates skewed distributions of bird density.

Computing the total number of birds migrating is a prime example of the necessity of simulation.

Indeed, integrating the bird density estimation map would greatly underestimates this number, because

of its inability to reproduce peaks of bird densities. Instead, integrating multiple realizations would

produce an accurate distribution of the total number of birds.

The simulation of both

M

and

˜

I

is performed using Sequential Gaussian Simulation [

29

,

30

].

The simulation results in multiple realizations denoted as

{M(`)}

and

{˜

I(`)

}. The ﬁnal realization of

B

is simply computed using,

B(`)(s0,t0)=t(s0)+M(`)(s0,t0)+ι(t0)+σI(s0,t0)˜

I(`)(s0,t0)1/p. (14)

2.5. Validation

2.5.1. Cross-Validation

We tested the internal consistency of the model by cross-validation. It consists of sequentially

omitting the data of a single radar, then estimating bird densities at this radar location with the

model, and, ﬁnally, comparing the model-estimated value

Bp(s

,

t)∗

to the observed data

Bp(s

,

t)

.

The model is assessed by its ability to provide both the smallest misﬁt errors, i.e.,

kBp(s,t)∗−Bp(s,t)k

,

and uncertainty ranges matching the magnitude of these errors. Because it is more convenient to

quantify these two aspects with a normal variable, we used the transformed variable

Bp

and quantiﬁed

the model performance with the normalized error of estimation, deﬁned as

Bp(s,t)∗−Bp(s,t)

pvar (Bp(s,t)∗), (15)

where

var (Bp(s,t)∗)

is the variance of the estimation as deﬁned in Equation (11), which quantiﬁes the

uncertainty of the estimation. The numerator of Equation (15) measures the misﬁt of the model

estimation, and the denominator normalizes this misﬁt according to the estimation uncertainty

provided by the model. For instance, a normalized error of 1 corresponds to the estimation value being

one estimated standard deviation above the measured value. Consequently, an ideal estimation should

produce normalized errors of estimation that follow a standard normal distribution, because (1) the

Remote Sens. 2019,11, 2233 8 of 24

estimation should be unbiased (mean of zero) and (2) the uncertainty provided by the model should

correspond to the observed error (variance of 1).

In addition, we performed the same cross-validation procedure using a nearest-neighbor

interpolation method instead, thus allowing to benchmark the proposed approach.

The root-mean-square error (RMSE) and coefﬁcient of determination R

2

are used to assess

the performance of both the proposed model and the nearest-neighbor interpolation.

2.5.2. Comparison with Dedicated Bird Radars

A second validation of our modeling framework (from data acquisition by weather radars to

geostatistical interpolation) requires comparing the model-predicted birdmigration intensities with the

measurements of two dedicated bird radars (Swiss BirdRadar Solution AG, https://swiss-birdradar.

comswiss-birdradar.com) located in Herzeele, France (50

◦

53

0

05.6

00

N 2

◦

32

0

40.9

00

E), and Sempach,

Switzerland (47

◦

07

0

41.0

00

N 8

◦

11

0

32.5

00

E) (see Figure 1). These radars are located 50 km and 84 km,

respectively, to the closest weather radar. By comparison, the distance of the grid nodes to their closest

weather radar is on average 92 km (10–90 quantiles: 35–166 km).

These bird radars continuously register echoes transiting through a conical shaped beam (17.5

◦

nominal beam angle). The diameter of the radar beam cross-section varies from 50 m at 50 m agl to

500 m at 1500 m agl [

31

]. The individual echoes are aggregated over an hour to produce migration

trafﬁc rates (MTR) (bird/km/h) and an average speed of birds aloft (km/h). The bird density measured

by the bird radar is computed by dividing the MTR by the mean speed [32].

Using the model presented, we estimate bird density at the exact locations of the bird radars.

In order to account for the difference of time resolution, the estimations are ﬁrst computed every

15 min and then averaged over one hour. We subsequently assess the quality of the estimation and

uncertainty provided by the model by computing the normalized errors of estimation (Equation (9)).

In addition, we also compare our approach with a simple nearest-neighbor interpolation using the

RMSE and R2.

3. Results

3.1. Validation

3.1.1. Cross-Validation

The normalized error of estimation over all radars has a near-Gaussian distribution with a mean

of 0.01 and a variance of 1.08 (Figure A7 in Appendix D). The near-zero mean of the error distribution

indicates that the model provides nonbiased estimations of bird densities, where the near-one standard

deviation demonstrates that the model provides appropriate uncertainty estimates. The performance of

the cross-validation shows radar-speciﬁc biases (i.e., constant under- or overpredictions; Figure A8 in

Appendix Dand time series of each radar in Supplementary Material S2). The biases do not show any

clear spatial pattern (Figure A8 in Appendix D), suggesting that these radar-speciﬁc biases probably

originate from measurement errors, such as birds nonaccounted for (e.g., ﬂying below the radar) or

errors in the cleaning procedure (e.g., ground scattering).

Compared to a nearest-neighbor interpolation, the model performs better in the cross-validation

with a RMSE of 17.67 bird/km

2

and R

2

of 0.59 against a RMSE of 23.17 bird/km

2

and R

2

of 0.29 for the

nearest neighbor.

Remote Sens. 2019,11, 2233 9 of 24

3.1.2. Comparison with Dedicated Bird Radars

The daily migration patterns estimated by the model generally coincide well with the observations

derived from dedicated bird radars (Figure 4). Over the whole validation period, the normalized

estimation error has a mean of 0.49 and a variance of 0.77 at Herzeele radar location, and a mean

of

−

0.68 and a variance of 1.45 at Sempach radar location. These normalized estimation errors

indicate a tendency of the model to slightly overestimate bird densities in Herzeele (i.e., mean above 1)

and to underestimate them in Sempach, while providing overconﬁdent uncertainty in Herzeele and

underconﬁdent at Sempach.

These errors translate into a RMSE of 9.2 and 19.7 bird/km

2

and R

2

of 0.87 and 0.73 for the radar

in Herzeele and Sempach, respectively. Reference [

32

] reported relatively similar values of R

2

when

comparing the MTR of close-by weather radar and bird radar. By comparison, the nearest-neighbor

approach yields a RMSE of 9.7 and 31.7 bird/km2, and a R2of 0.85 and 0.59, respectively.

Bird densities [bird/km2]

0

50

100

150

Uncertainty range

Estimate

Closest radar

Bird radar

Sep 19 Sep 22 Sep 25 Sep 28 Oct 01 Oct 04 Oct 07 Oct 10

Date 2016

0

50

100

150

(a)

(b)

Figure 4.

Comparison of the estimated bird densities (black line) and their uncertainty range

(10–90 quantiles in gray) with the bird densities (red dots) observed using dedicated bird radars

at two locations in (

a

) Herzeele, France (50

◦

53

0

05.6

00

N 2

◦

32

0

40.9

00

E), and (

b

) Sempach, Switzerland

(47

◦

07

0

41.0

00

N 8

◦

11

0

32.5

00

E). Note that, because of the power transformation, model uncertainties are

larger when the migration intensity is high. It is therefore critical to account for the uncertainty ranges

(light gray) when comparing the interpolation results with the bird radars observations (red dots).

3.2. Application to Bird Migration Mapping

The main outcome of our model is to estimate bird densities at any time and location within the

domain of interest. This is illustrated by the estimation of bird density time series at speciﬁc locations

(e.g., Figure 4) and by the generation of bird density maps at different time steps (Figure 5).

Remote Sens. 2019,11, 2233 10 of 24

Although the estimation represents the most likely value of bird density (i.e., mean of estimation)

at each node of the grid (e.g., Figure 5), the simulation provides multiple values of bird density

according to their conditional distribution and reproduces more accurately the ﬁne-scale patterns

of migration (e.g., Figure 6). As explained in Section 2.4.2, the amplitude of peak migration is more

adequately illustrated in the realizations (Figure 6), compared to the smooth estimation map (Figure 5).

For each of the 100 realizations, we computed the total number of birds ﬂying over the whole

domain for each time step (Figure 7b). Within the time periods considered in this study, the peak

migration occurred in the night of 4–5 October with up to 121 million (10–90 quantiles: 118–124) birds

ﬂying simultaneously. Computing this on subdomains, such as countries, highlights geographical

differences in migration intensity. For instance, during the same night, France had 37 (35–39) million

birds aloft (89 bird/km

2

), Poland had 14 (13–15) million (65 bird/km

2

), and Finland only 2 (1.9–2.2)

million (30 bird/km2) (Figure 7c).

1 10 100 250

Daily average bird density [bird/km2]

18:00 19:00 20:00 21:00 22:00 23:00

00:00 01:00 02:00 03:00 04:00 05:00

Rain

Figure 5.

Maps of bird density estimation every hour of a single night (3–4 October). The sunrise and

sunset fronts are visible at 18:00 and 05:00 with lower densities close to the fronts and no value after the

front. The resemblance from hour-to-hour illustrates the high temporal continuity of the model. A rain

cell above Poland blocked migration on the eastern part of the domain. In contrast, a clear pathway is

visible from Northern Germany to Southwestern France.

1

10

100

250

Bird densities [bird/km2]

Rain

Realization 1 Realization 2 Realization 3

Figure 6.

Snapshot of three different realizations showing peak migration (4 October 2016 21:00 UTC).

The total number of birds in the air for these realizations was 125, 126, and 122 million, respectively.

Comparing the similarities and differences of bird density patterns among the realizations illustrates

the variability allowed by the stochastic model. The texture of these realizations is more coherent with

the observations than the smooth estimation map in Figure 5.

The spatio-temporal dynamics of bird migration can be visualized with an animated and

interactive map (available online at https://birdmigrationmap.vogelwarte.ch with a user manual

Remote Sens. 2019,11, 2233 11 of 24

provided in Appendix E), produced with an open source script (https://github.com/Rafnuss-PostDoc/

BMM-web). In the web app, users can visualize the estimation maps or a single simulation map

animated in time, as well as time series of bird densities of any location on the map. In addition, it is

also possible to compute the number of birds over a custom area and to download all data through a

dedicated API.

0

50

100

Sep 19 Sep 25 Oct 01 Oct 07

Date 2016

0

10

20

30

40

Total number of bird aloft [millions]

Full domain France Poland Finland Uncertainty range

(a) (b)

(c)

Figure 7.

Averaged time series of birds in migration and their associated uncertainty ranges (10–90

quantiles) over (b) the whole domain, and (c) France, Poland and Finland. (a) illustrates the location

and size of the three countries.

4. Discussion

The model developed here can estimate bird migration intensity and its uncertainty range on

a high-resolution space-time grid (0.2

◦

lat. lon. and 15 min.). The highest total number of birds

ﬂying simultaneously over the study area is estimated at 121 million, corresponding to an average

density of 52 bird/km

2

. This number illustrates the impressive magnitude of nocturnal bird migration,

and resembles the values of peak migration estimated over the USA with 500 million birds and a

similar average density of 51 bird/km

2

[

19

]. For more local results, interactive maps of the resulting

bird density are available on a website with a dedicated interface that facilitates the visualization and

export of the estimated bird densities with their associated uncertainty (https://birdmigrationmap.

vogelwarte.ch, see Appendix Efor a user manual).

4.1. Advantages and Limitations

This paper presents the ﬁrst spatio-temporal interpolation of nocturnal bird densities at the

continental scale that accounts for sub-daily ﬂuctuations and provides uncertainty ranges. In contrast

to the methods based on covariates, deemed more reliable for extrapolation in the future [

19

,

33

,

34

],

our interpolation approach relies solely on the strong space-time correlation of bird migration and

consequently does not require any external covariate per se (e.g., temperature, rain, or wind). Similarly,

local features such as the proximity to the ocean or the presence of mountains were not explicitly

accounted for in the model. Yet, the inﬂuence of these meteorological and geographical features on bird

migration is largely captured by the measurements of weather radars, so that, in turn, the interpolation

implicitly accounts for them. However, to take full advantage of these covariates, often available at

extensive scale, the model could be adapted to consider linear relationships with covariates, using the

standard frameworks of regression kriging, or possibly full co-kriging [23].

Remote Sens. 2019,11, 2233 12 of 24

The ﬁtted parameters of the model provide information on the broad scale bird migration (see

Appendix B). In particular, the covariance function of the model describes the general spatio-temporal

scale at which migration is happening (Figure A5 in Appendix B). For instance, even with the spatial

trend removed, the multi-night scale of bird migration (

M

) correlates at 50% at a distance of 300 km

(25%–500 km) and at 60% for one day to the next (25% at 3 days). These ranges qualitatively describe

the spatio-temporal extent of broad-front migration in the midst of the autumn migration season,

and highlight the importance of international cooperation for data acquisition and for the spread of

warning systems during peak migration events.

As a proof-of-concept, we used three weeks of bird density data available on the ENRAM data

repository (see Data Accessibility). As more data from weather radars become available, our analyses

can be extended to year-round estimations of migration intensity at the continental scale where weather

radar data are available with a good coverage, as is the case in Europe and North America. We also

signiﬁcantly preprocessed the bird density data, i.e., restricted our model to nocturnal movements,

and applied a strict manual data cleaning. This is because the bird density data presently made

available can be strongly contaminated with the presence of insects during the day, and birds ﬂying at

low altitude are not reliably recorded by radars because of ground clutter and the radar position in

relation to its surrounding topography. Once the quality of the bird density data has improved [

35

],

our model can be implemented in near-real-time and provide continuous information to stakeholders

and the public and private sectors.

Although the model introduced here is already a valuable tool for bird migration mapping, we see

several avenues for further development. For instance, in applications where the distribution of

bird density over altitudes is crucial, the model can be extended to explicitly incorporate the vertical

dimension. Furthermore, if ﬂuxes of birds, i.e., migration trafﬁc rates, are sought after, a similar

geostatistical approach can be used to interpolate the ﬂight speeds and directions that are also derived

from weather radar data. If one has access to the raw radial velocity, the method developed by [

36

]

would produce more accurate results.

4.2. Applications

Many applied problems rely on high-resolution estimates of bird densities and migration

intensities, and the model developed here lays the groundwork for addressing these challenges.

For instance, such migration maps can help identify migration hotspots, i.e., areas through which many

aerial migrants move, and thus, assist in prioritizing conservation efforts. Furthermore, mitigating

collision risks of birds by turning off artiﬁcial lights on tall buildings or shutting down wind energy

installations requires information on when and where migration intensity peaks. The probability

distribution function of our model can provide such information as it estimates when and where

migration intensity exceeds a given threshold. Such information can be used in shut-down on demand

protocols for wind turbine operators or trigger alarms to infrastructure managers.

Supplementary Materials:

The illustrations of the cleaned vertical-integrated time series of nocturnal bird

densities for all radars are available in supplementary materials http://www.mdpi.com/2072-4292/11/19/

2233/s1. The illustrations of the cross-validation of all radars are available in supplementary materials http:

//www.mdpi.com/2072-4292/11/19/2233/s2. The MATLAB livescripts of this article are available at https:

//rafnuss-postdoc.github.io/BMM. The cleaned vertical time series proﬁle are available at doi: https://doi.

org/10.5281/zenodo.3243397 [

37

]. and the ﬁnal interpolated maps are available at doi: https://doi.org/10.5281/

zenodo.3243466 [

38

]. The codes of the website (HTML, Js, NodeJs, Css) are available at https://github.com/

rafnuss-postdoc/BMM-web.

Author Contributions:

R.N., L.B., F.L., and B.S. conceived the study; R.N., L.B., and G.M. designed the

geostatistical model; R.N. developed and implemented the computational framework; and R.N., L.B., and B.S.

performed the analyses and wrote a ﬁrst draft of the manuscript; G.M., F.L. and S.B. contributed substantially to

the manuscript.

Remote Sens. 2019,11, 2233 13 of 24

Funding:

We acknowledge the ﬁnancial support from the Globam project, funded by BioDIVERSA, including the

Swiss National Science Foundation (31BD20_184120), Netherlands Organisation for Scientiﬁc Research (NWO

E10008), and Academy of Finland (aka 326315), BelSPO BR/185/A1/GloBAM-BE.

Acknowledgments:

This study contains modiﬁed Copernicus Climate Change Service Information 2019. Neither

the European Commission nor ECMWF is responsible for any use that may be made of the Copernicus

Information or Data it contains. We acknowledge the European Operational Program for Exchange of Weather

Radar Information (EUMETNET/OPERA) for providing access to European radar data, facilitated through a

research-only license agreement between EUMETNET/OPERA members and ENRAM (European Network for

Radar surveillance of Animal Movements). Mathieu Boos (Research Agency in Applied Ecology, Naturaconsta,

Wilshausen, France) kindly provided the BirdScan data for Herzeele in France.

Conﬂicts of Interest: The authors declare no conﬂicts of interest.

Appendix A. Data Preprocessing

Appendix Adescribes the full procedure applied to manually clean the time series of bird

densities. The raw dataset of bird density downloaded from the ENRAM data repository (https:

//github.com/enram/data-repository) has been previously published in [

21

]. The steps detailed

below are illustrated in Figure A1 for the radar located in Zaventem, Belgium (50

◦

54

0

19

00

N, 4

◦

27

0

28

00

E).

1.

Of the 84 radars contributing data during the study period, 11 radars are discarded because of

their poor quality due to S-band radar type, poor processing, or large gaps (temporal or altitude

cut). The same radars were removed in [

21

]. In addition, the four radars from Bulgaria and

Portugal were excluded because of their geographic isolation.

2.

The full vertical proﬁle was discarded when rain was present at any altitude bin (purple rectangle

in Figure A1). A dedicated MATLAB GUI was used to visualize the data and manually set bird

densities to “not-a-number” in such cases.

3.

Zones of high bird densities can sometimes be incorrectly eliminated in the raw data (red rectangle

in Figure A1). To address this, reference [

21

] excluded problematic time or height ranges from

the data. Here, in order to keep as much data as possible, the data was manually edited to

replace erroneous data either with “not-a-number”, or by cubic interpolation using the dedicated

MATLAB GUI.

4.

Due to ground scattering (brown rectangle in Figure A1), the lower altitude layers are sometimes

contaminated by errors or excluded in the raw data. We vertically interpolated bird density by

copying the ﬁrst layer without error into to the lower ones. This approach is relatively conservative

as bird migration intensity usually decreases with height in the absence of obstacles, and more so

in autumn [39].

5.

The vertical proﬁles were vertically integrated from the radar ground level (black line in

Figure A1c) and up to 5000 m asl.

6.

The data recorded during daytime are excluded. Daytime is deﬁned for each radar by the civil

dawn and dusk (sun 6◦below horizon).

7.

Finally, the data of 10 radars with high temporal resolution (5–10 min) was downsampled to

15 min to preserve a balanced representation of each radar.

The resulting cleaned time series of nocturnal bird densities are displayed in Figure A1d.

We provide the same ﬁgure than Figure A1 for all radar data in Supplementary Materials http:

//www.mdpi.com/2072-4292/11/19/2233/s1.

Remote Sens. 2019,11, 2233 14 of 24

09/20 09/22 09/24 09/26 09/28 09/30 10/02 10/04 10/06 10/08

Date

0

1

2

3

4

5

-5

0

5

Altitude [km]

-60

-40

-20

0

20

Reﬂectivity

0

1

2

3

4

5

Bird densities [bird/km2]

Bird densities [bird/km3]

0

20

40

60

0

1

2

3

4

5

(a)

(b)

(c)

(d)

Rain Ground Scattering

Ground

Gap

Figure A1.

Illustration of the cleaning procedure for the data of the Zaventem radar in Belgium

(50

◦

54

0

19

00

N, 4

◦

27

0

28

00

E). (

a

) Raw reﬂectivity. (

b

) Raw data of vertical bird density proﬁles. (

c

) Manually

cleaned vertical bird proﬁles. (d) Final bird densities (integrated over all altitudes).

Appendix B. Model Parametrisation

Appendix Bpresents the method of model parametrisation and discusses the meaning of model

parameters in terms of bird migration. Table A1 summarizes the calibrated parameters.

Table A1. Calibrated parameters.

Power transformation p=0.133

Spatial trend w0=2.566 , wlat =−0.024

Covariance of M C0=0.006, Cg=0.032, rt=1.24, rs=500, α=0.98, γ=0.71, β=0.95

Curve a=[0.04, −0.10, 0.07, 0.27, −1.29, −0.59, 2.86, 0.44, −1.92]

Curve variance b=[0.00, 0.00, 0.02, 0.04, −0.17, −0.17, 0.62, 0.26, −0.93, −0.12, 0.49]

Covariance of I C0=0.009, Cg=0.91, rt=0.07, rs=190, α=1, γ=0.4, β=1

Appendix B.1. Power Transform p

The value of power transformation

p

is inferred by minimizing the Kolmogorov–Smirnov criterion

of the p-transformed observations

B(s,t)p

. The Kolmogorov–Smirnov test (Massey, 1951) assesses the

hypothesis that the observations

B(s,t)p

are normally distributed. The optimal power transformation

parameter was found for

p=

1

/

7.5 and the resulting

Bp

histogram is displayed in Figure A2 together

with the initial data B.

Remote Sens. 2019,11, 2233 15 of 24

100 200 300 400

Histogram of bird densities [bird/km2]

0

5000

10000

0.4 0.8 1.2 1.6 22.4

Histogram of transformed bird densities

0

0.5

1

1.5

0

Figure A2.

Histogram of the raw bird densities data

B

(

top

) and the power transformed bird densities

Bpfor the calibrated parameter p=1/7.5 (bottom).

The ﬁtted distribution shows that the distribution of bird densities is highly skewed: the lowest

10% are below 1 bird/km

2

, the upper 10% are above 50 bird/km

2

, and the maximum density reaches

500 bird/km

2

. Consequently, the central value (mean of 19 bird/km

2

or median of 8 bird/km

2

) and

variance (753 bird

2

/km

4

) do not adequately characterize the distribution. A power transformation on

such skewed data creates signiﬁcant nonlinear effects in the back-transformation. For instance, the

symmetric uncertainty of an estimated value in the transformed space (quantiﬁed by the variance of

estimation) will become highly skewed in the original space. Consequently, the uncertainty of the

estimation of bird densities is highly dependent on the value of the power transform: low densities

estimations have a smaller uncertainty than high densities.

Such effects also have consequences from an ecological and conservation point of view. Indeed,

efﬁcient protection of birds along the migration route (from artiﬁcial light or wind turbines) requires

particular attention to the peak densities, during which the majority of birds are moving in a few nights.

These peaks can only be accurately reproduced by accounting for the high tail of the distribution.

This is done here by using a full distribution to quantify the uncertainty of the estimation.

Appendix B.2. Spatial Trend µ

The parameters of the spatial trend (

wlat

and

w0

) are calibrated on the nightly average of each

radar with an ordinary least square method. The resulting planar trend is shown in Figure A3a

together with the average transformed bird densities of each radar. The trend displays a strong

north–south gradient, which can be explained by the higher migration activity in southern Europe

during the study period. A 2-dimensional planar trend was initially tested in order to accommodate

the northeast–southwest ﬂyway. However, this more complex model did not signiﬁcantly improve

the ﬁt with data, and was therefore discarded. The detrended values illustrated in Figure A3b are

more stationary, with the exception of Finland and Sweden. Reference [

21

] also noted this difference

between these countries, but excluded the fact that this difference is due to errors in the data since

the southern Swedish radar shows consistent amounts of migratory movements with a neighboring

German site. Figure A3b highlights the central European continental ﬂyway as illustrated by the arrow.

Remote Sens. 2019,11, 2233 16 of 24

Transformed bird densities

-0.3

-0.2

-0.1

0

0.1

0.2

1

1.2

1.4

1.6

Transformed bird densities

Figure A3.

Fitted trend with averaged observations at radar location (

left

) and detrended data (

right

).

Appendix B.3. Curve Trend ιand Variance σI

Figure A4 displays the intra-night scale component

Bp−µ−M

of the weather radar data

together with the ﬁtted polynomial curve trend

ι

(Equation (6)) and polynomial variance function

σI

(Equation (8)). The curve reveals that migration is mainly concentrated between 10% and 90% of the

night-time with slightly larger densities of birds in the ﬁrst half of the night. The larger variance at the

beginning and end of the night is partly due to the power-transformation of the raw data.

-1 -0.5 0

Normalized Night Time (NNT)

-1

-0.5

0

0.5

Transformed bird densities

-0.5 1

Figure A4.

Intra-night scale component of the weather radar data (black dots) and ﬁtted curve trend

(black line). The shaded gray areas each denote 1-, 2-, and 3-σIﬁtted.

Appendix B.4. Covariance Functions of M and I

The parameters of the space-time covariance functions (

C0

,

CG

,

rt

,

rs

,

α

,

γ

, and

β

) of

M

(Equation (4)) and

I

(Equation (9)) are inferred by minimizing the misﬁt between the covariance

function and the empirical covariances of the weather radar data. The empirical covariances are

derived for several lag-distances and lag-times on an irregular grid.

The calibrated covariance functions provide some information about the degree of spatial and

temporal correlation of the bird migration process. Indeed, the absolute value of bird density covariance

should also include the effect of trend and power transformation. The ﬁtted spatial covariance at the

multi-night scale

M

(Figure A5a) is ﬁtted with a large spatial nugget (16%), suggesting a signiﬁcant

variability of bird density uncorrelated in space. This can be explained by either local features of the

migration process or radar measurement errors. It is important to recall that since the weather radars

are relatively well-spread (Figure 1b), the spatial covariance of both

M

and

I

is poorly constrained for

small lag-distances (approximately less than 100 km), and consequently the uncertainty of the nugget

value is large. The temporal covariance of

M

has an asymptotic behavior with 20% covariance after

Remote Sens. 2019,11, 2233 17 of 24

6 days (Figure A5b) because no temporal trend was used. Note that as the covariance of

M

is evaluated

only on a discrete 1-day lag-time, the shape of the covariance between 0 and 1 is artiﬁcially created to

ﬁt the Gneiting function.

M

and

µ

account for most of the spatial covariance of bird density, but some

spatial correlation is still present at the intra-night scale as suggested by Figure 1c. The temporal

correlation of

˜

I

is high for short lags (67% at 0.04 days, or 1 hr), indicating consistent measurements

from each weather radar.

Distance [km] Time [day]

200 400 600 8000

0

0.01

0.02

0.03

200 400 600 8000

0

0.2

0.4

0.6

0.8

1

0 0.04 0.08 0.12 0.16 0.2

0 2 4 6

1 3 5

Covariance

(b)(a)

(c) (d)

~

Figure A5.

Illustration of the calibrated covariance function of the multi-night scale

M

(

a

,

b

) and the

intra-night scale ˜

I(c,d).

Appendix C. Kriging

Appendix Cprovides detailed explanations for the kriging estimation. Note that this procedure

is identical to Gaussian regression in the ﬁeld of machine learning, where the kriging estimation is

equivalent to the mean of the posterior distribution (i.e., conditional to the known location).

Kriging provides an estimated value of a random variable

X

(either

M

or

I

) at the target point

(s0,t0)based on a linear combination of known data points {X(sα,tα)}α=1,...,n0with

X(s0,t0)∗=

α=n0

∑

α=1

λαX(sα,tα). (A1)

The kriging weights

Λ=[λ1,· · · ,λn0]T

are determined by minimizing the variance of the

estimation under unbiased conditions which leads to the following linear system, commonly referred

to as the kriging system,

Cα,αΛ=Cα,0, (A2)

where

Cα,α

is the cross-covariance matrix of the observations and

Cα,0

is the covariance matrix between

the observations and the target point. These covariances are computed using the ﬁtted covariance

function of Equation (4) or Equation (9). The kriging weights can be solved using

Λ=C−1

α,αCα,0

,

and are subsequently used in Equation (A1) to compute the kriging estimate. Figure A6 illustrates the

value of the kriging weights for the kriging estimation of the multi-night scale at an unknown location

(red dot).

Remote Sens. 2019,11, 2233 18 of 24

28-Sep

29-Sep

55

Time

30-Sep

20

50

Latitude 15

Longitude

10

45 5

0

-14

-10

-6

-2

Kriging Weight Value (log-scale)

Figure A6.

Illustration of the kriging weight values computed for the kriging estimation of

M

at an

unknown location (red dot). Here we illustrate only the neighbors within +/

−

1 day and a spatial

extent of 600 km.

In addition to the estimated value

X(s0,t0)∗

, kriging also provides a measure of uncertainty with

the variance of estimation,

var X(s0,t0)∗=CX(0, 0)−Λ>Cα,0 (A3)

Appendix D. Cross-Validation

Appendix Dprovides additional details on the cross-validation described in Section 2.5.1.

Figure A7 displays the histogram of the normalized error of estimation (Equation (15)) when all

data across all radars are considered. The mean of the distribution is close to zero which indicates that

the estimation is unbiased (i.e., on average, the estimation neither underestimates (mean below 1) nor

overestimates (mean above 1) bird density). Its variance is slightly above 1, which indicates a small

tendency to underestimate the uncertainty range (i.e., on average, the kriging variance is too small).

Overall, the cross-validation indicates a good performance of the model.

In order to test radar-speciﬁc performance, the normalized error of estimation is computed for

each radar. As displayed in Figure A8, their respective mean and variance do not reveal any clear

spatial pattern, thus suggesting no spatial biases in the estimation. However, the large absolute value of

the mean of the normalized error of estimation (color scale) indicates a strong variability in the model

performance for each radar. The model underestimates or overestimates bird density at some radar

locations with a mean of 1.5 times the variance of estimation. The time series comparing estimations of

the cross-validation with the observed data for each radar are provided in Supplementary Material

http://www.mdpi.com/2072-4292/11/19/2233/s2.

Remote Sens. 2019,11, 2233 19 of 24

-4 -2

0

0.1

0.2

0.3

0.4

Normalized error of estimation with mean: 0.01 and variance: 1.08

2 40

Figure A7.

Histogram of the normalized error of estimation (Equation (15)) over all radars. The red

curve is the standard normal distribution which should be matched by the histogram in case of ideal

estimation.

0.5

-1

-1.5

0.5

0

1

1.5

1

1.5

0.5

Mean

Variance

Figure A8.

Illustration of the performance of the cross-validation with the mean and variance of the

normalized error of estimation (Equation (15)) at each radar location. Negative or positive mean values

respectively indicate an under- or overestimation of the model estimation. The reproduction of the

variance is illustrated by a black circle: a perfect variance would match the color circle while a smaller

circle indicates an underconﬁdence (uncertainty range too large).

Appendix E. Manual for Website Interface

Appendix Edescribes the web interface developed for the visualization and querying of the

interpolated data. The website is available on https://birdmigrationmap.vogelwarte.ch and the code

on https://github.com/Rafnuss-PostDoc/BMM-web. The web interface is displayed in Figure A9

with annotations and further details below.

Remote Sens. 2019,11, 2233 20 of 24

Figure A9. Illustration of the website interface with annotations for each interactive component.

Appendix E.1. Block 1: Interactive Map

The main block of the website is a map with interactive visualization tools (e.g., zoom and pan).

On top of this map, three layers can be displayed:

•

The ﬁrst layer illustrates bird densities in a log-color scale. This layer can display either the

estimation map or a single simulation map. Users can choose using the drop-down menu (1a).

•

The second layer displays the rain in light-blue. The layer can be hidden/displayed using the

checkbox (1b).

•

The third layer corresponds to bird ﬂight speed and direction, visualized by black arrows.

The checkbox (1c) allows users to display/hide this layer. Finally, the menu (1d) provides a

link to (1) documentation, (2) model description, (3) Github repository, (4) MATLAB livescript,

and (5) Researchgate page.

Appendix E.2. Block 2: Time Series

The second block (hidden by default on the website) shows three time series, each in a different tab (2a):

•Densities proﬁle shows the bird densities [bird/km2] at a speciﬁc location.

•Sum proﬁle shows the total number of birds [bird] over an area.

•MTR proﬁle shows the mean trafﬁc rate (MTR) [bird/km/h] perpendicular to a transect.

A dotted vertical line (2d) appears on each time series to show the current time frame displayed

on the map (Block 1). Basic interactive tools for the visualization of the time series include zooming

on a speciﬁc time period (day, week or all periods) (2b) and general zoom and auto-scale functions

(2e). Each time serie can be displayed or hidden by clicking on its legend (2c). The main feature of

this block is the ability to visualize bird densities at any location chosen on the map. For the densities

proﬁle tab, the button with a marker icon (2f) allows users to plot a marker on the map, and displays

the bird densities proﬁle with uncertainty (quantile 10 and 90) on the time series corresponding to this

Remote Sens. 2019,11, 2233 21 of 24

location. Users can plot several markers to compare the different locations (Figure A10). Similarly, for

the sum proﬁle, the button with a polygon icon (2f) allows users to draw a polygon and returns the

time series of the total number of birds ﬂying over this area (Figure A11). For the MTR tab, the ﬂux of

birds is computed on a segment (line of two points) by multiplying the bird densities with the local

ﬂight speed perpendicular to that segment.

Appendix E.3. Block 3: Time Control

The third block shows the time progression of the animated map with a draggable slider (3d).

Users can control the time with the buttons play/pause (3b), previous (3a) and next frame (3c).

The speed of animation can be changed with a slider (3e).

Appendix E.4. API

An API based on mangodb and NodeJS allows users to download any time serie described in

Block 2. Instructions can be found on https://github.com/Rafnuss-PostDoc/BMM-web

Appendix E.5. Examples

Figure A10.

A print-screen of the web interface developed to visualize the dataset. The map shows the

estimated bird densities for the 23 September 2016 at 21:30 with the rain mask appearing in light blue

on top. The domain extent is illustrated by a black box. The time series in the bottom show the bird

densities with quantile 10 and 90 at the two locations symbolized by the markers with corresponding

color on the map. The button with a marker symbol on the right side of the time series allows users to

query any location on the map and to display the corresponding time series.

Remote Sens. 2019,11, 2233 22 of 24

Figure A11.

Print-screen of the web interface with the simulation map for the 3 October 2016 at 23:00.

The bottom pane shows the time series of the total number of birds within the color-coded polygon

drawn on the map. The button with the polygon symbol on the right side of the time series allows to

query the total number of birds ﬂying within any polygon drawn on the map.

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