ELECTRONIC SUPPORZTING MATERIAL
Migration by soaring or flapping: numerical atmospheric simulations
reveal that turbulence kinetic energy dictates bee-eater flight mode
Nir Sapir, Nir Horvitz, Martin Wikelski, Roni Avissar, Yitzhak Mahrer, and Ran
Nathan
RAMS VALIDATION
RAMS simulation output has been tested against measured data in different
parts of the world, at different biomes and at various temporal and spatial scales [S1–
S4]. Here, we tested the match between RAMS-simulated data and ground
measurements from seven meteorological stations of the Israeli Meteorological
Service (IMS) distributed throughout southern Israel, in relation to temperature, wind
velocity and wind direction. We examined the relationships between the 10 min
temperature and wind velocity data registered by the IMS and RAMS output using
linear regressions after the data has been tested and found to be normally distributed.
These analyses were made using SPSS 15.0 [S5]. We used the Mardia-WatsonWheeler test to examine if wind direction measured by IMS and simulated by RAMS
differed from each other. We also used the V-test to examine if the average mean
angle of the difference between the datasets is different than 0° [S6]. Oriana 2.02e
was used for circular statistical analyses [S7].
We illustrate in supporting figure 1 data from Hatzeva station collected during
eight consecutive days in May 2005. RAMS-simulated temperature fitted the
observational data exceptionally well (figure 1a; simulated temperature = 0.88 ×
measured temperature + 3.9, R2 = 0.83, p < 0.001). RAMS-simulated data
overestimated temperatures below 32.5 °C, and underestimated temperatures above
this value, yet the absolute difference between simulated and measured data in the
range of temperatures measured during the study period was smaller than 2.2 °C.
Wind velocity showed a higher degree of deviation from observed data (supporting
figure 1b; measured wind velocity = 0.58 × observed wind velocity + 0.96, R2 = 0.52,
p < 0.001). RAMS-simulated data overestimated wind velocity below 2.3 m s-1, and
underestimated wind velocity above this value so that under extremely strong wind
conditions of 10 m s-1, RAMS-simulated data were substantially lower (6.8 m s-1) than
measured data. Measured and RAMS-simulated wind direction (Supporting figure 1c)
had a nearly identical mean direction (288° and 290° for measured and RAMSsimulated data, respectively). Yet, these data differed statistically when the data were
paired in time (Mardia-Watson-Wheeler test, n = 1102, W = 136.2, p < 0.001). The
average difference between measured and RAMS-simulated data was 335°; hence
RAMS simulated wind direction with an average of 25° counter clockwise deviation.
We found that the average angle of the difference in wind direction was statistically
different from 0° (V-test, V = 0.45, u = 21.0, p < 0.001). No TKE field measurements
were available to validate RAMS-simulated TKE, yet RAMS has been shown to
predict TKE very well in other studies (e.g., Chan [S8]).
SUPPORTING REFERENCES
1. Avissar, R., Eloranta, E. W., Gurer, K. & Tripoli, G. J. 1998 An evaluation of the
large-eddy simulation option of the regional atmospheric modeling system in
simulating a convective boundary layer: A FIFE case study. J. Atmos. Sci. 55,
1109-1130.
2. Avissar, R. & Pan, H. 2000 Simulations of the summer hydrometeorological
processes of Lake Kinneret. J. Hydrometeorol. 1, 95-109.
3. Ter Maat, H. W., Hutjes, R. W. A., Ohba, R., Ueda, H., Bisselink, B. & Bauer, T.
2006 Meteorological impact assessment of possible large scale irrigation in
Southwest Saudi Arabia. Glob. Planet. Change 54, 183-201.
4. Zhong, S. Y. & Whiteman, C. D. 2008 Downslope flows on a low-angle slope and
their interactions with valley inversions. Part II: Numerical modeling. J. App.
Meteorol. Climatol. 47, 2039-2057.
5. SPSS Inc. 2006 SPSS for Windows, release 15.0.1. Chicago: SPSS Inc.
6. Batschelet E. 1981 Circular statistics in biology. London: Academic Press.
7. Kovach Computing Services. 2007 Oriana, version 2.02e. Wales: Kovach
Computing Services.
8. Chan, P. W. 2009 Atmospheric turbulence in complex terrain: verifying numerical
model results with observations by remote-sensing instruments. Meteorol. Atmos.
Physics 103, 145-157.
Supporting Table 1. Pearson correlation coefficients1 between TKE, temperature and
tailwind speed at 100 and 500 m altitude, and at variable altitude matching bird
altitude
Variable pair / Altitude
100 m
TKE – temperature
0.67*** 0.62***
0.64***
TKE – tailwind
0.07NS
0.24***
0.47**
Temperature – tailwind
0.30*** 0.34***
0.27NS
1
500 m
Exact (variable)
NS = not significance (p > 0.05), * = 0.05 > p > 0.01, ** = 0.01 > p > 0.001, *** = p
< 0.001
Supporting Table 2. Results of multinominal logistic regressions at 500 m altitude with comparisons between flight modes for each
variable1,2, after weighting the data negatively proportional to the sample size of each bird in the dataset
Factor
AIC
AIC Nagelkerke p F-M
p F-S p M-S p F-M
pseudo-R2
TKE
TKE
p F-S
p M-S
p F-M
p F-S
p M-S
p overall
TKE Temp. Temp. Temp.
TWS
TWS
TWS
model
TKE
447.7
0.0
0.521
***
***
NS
-
-
-
-
-
-
***
TKE, Temp., TWS
464.8
17.1
0.585
***
***
NS
***
NS
**
**
***
NS
***
TKE, Temp.
475.1
27.4
0.560
***
***
NS
***
NS
**
-
-
-
***
TKE, TWS
480.7
33.0
0.549
***
***
NS
-
-
-
NS
**
**
***
Temp., TWS
615.6 167.9
0.242
-
-
-
***
***
**
NS
**
NS
***
Temp.
621.1 173.4
0.215
-
-
-
***
***
***
-
-
-
***
TWS
653.4 205.7
0.117
-
-
-
-
-
-
**
***
**
***
1
TKE = Turbulence kinetic energy, Temp. = Temperature, TWS = Tailwind speed, F = Flapping, M = Mixed flight, S = Soaring-
gliding
2
NS = not significance (p > 0.05), * = 0.05 > p > 0.01, ** = 0.01 > p > 0.001, *** = p < 0.001
Supporting Table 3. Results of multinominal logistic regressions at 100 m altitude with comparisons between flight modes for each
variable1,2
Factor
AIC
AIC Nagelkerke p F-M
p F-S p M-S p F-M
pseudo-R2
TKE
TKE
p F-S
p M-S
p F-M
p F-S
p M-S
p overall
TKE Temp. Temp. Temp.
TWS
TWS
TWS
model
TKE, Temp., TWS
519.5
0.0
0.517
***
***
NS
NS
NS
**
*
**
NS
***
TKE, Temp.
523.5
4.0
0.501
***
***
NS
NS
*
***
-
-
-
***
TKE, TWS
524.7
5.2
0.499
***
***
***
-
-
-
*
**
*
***
TKE
534.1
14.6
0.472
***
***
***
-
-
-
-
-
-
***
Temp.
602.7
83.2
0.318
-
-
-
***
***
***
-
-
-
***
Temp., TWS
606.4
86.9
0.319
-
-
-
***
***
***
NS
NS
NS
***
TWS
646.3 126.6
0.046
-
-
-
-
-
-
NS
***
*
**
1
TKE = Turbulence kinetic energy, Temp. = Temperature, TWS = Tailwind speed, F = Flapping, M = Mixed flight, S = Soaring-
gliding
2
NS = not significance (p > 0.05), * = 0.05 > p > 0.01, ** = 0.01 > p > 0.001, *** = p < 0.001
Supporting Table 4. Results of multinominal logistic regressions of data with altitudinal information with comparisons between flight
modes for each variable1,2
Factor
AIC
AIC Nagelkerke p F-M
p F-S p M-S p F-M
pseudo-R2
TKE
TKE
p F-S
p M-S
p F-M
p F-S
p M-S
p overall
TKE Temp. Temp. Temp.
TWS
TWS
TWS
model
TKE, TWS
54.3
0.0
0.590
NS
*
*
-
-
-
**
NS
NS
***
TKE, Temp., TWS
57.3
3.0
0.607
NS
NS
*
NS
NS
NS
**
NS
NS
**
Temp., TWS
59.9
5.6
0.481
-
-
-
NS
NS
NS
*
NS
NS
**
TWS
60.3
6.0
0.38
-
-
-
-
-
-
**
*
NS
**
TKE
62.1
7.8
0.336
NS
**
*
-
-
-
-
-
-
**
TKE, Temp.
66.0
11.7
0.336
NS
*
NS
NS
NS
NS
-
-
-
*
Temp.
68.7
14.4
0.143
-
-
-
NS
NS
NS
-
-
-
NS
1
TKE = Turbulence kinetic energy, Temp. = Temperature, TWS = Tailwind speed, F = Flapping, M = Mixed flight, S = Soaring-
gliding
2
NS = not significance (p > 0.05), * = 0.05 > p > 0.01, ** = 0.01 > p > 0.001, *** = p < 0.001
Supporting Figure 1. An example of RAMS-generated data (filled circles) in relation to meteorological measurements (line) in the Arava Valley
(Hatzeva station 30°47'N 35°15'E) during eight days in spring 2005, including (a) temperature, (b) wind velocity and (c) wind direction data (left
panels). For temperature and wind velocity, measured and RAMS-simulated data are presented with a linear fit (mid panels), and for all three
variables a histogram of absolute deviations between measured and RAMS-simulated data is presented (right panels)
Supporting Figure 2. The relationships between meteorological variables simulated at
100 m above ground and bird flight mode. (a) TKE, (b) Temperature, (c) Tailwind.
For statistical details see Supporting Table 3.
a
Soaring-gliding flight
Mixed flight
Flapping flight
0.0
0.4
0.8
1.2
1.6
2.0
30
33
TKE (m2 s-2 )
b
Soaring-gliding flight
Mixed flight
Flapping flight
0
18
21
24
27
Temperature (°C)
c
Soaring-gliding flight
Mixed flight
Flapping flight
-4
-2
0
Tailwind speed (m s-1 )
2
4
Supporting Figure 3. The relationships between meteorological variables bird flight
mode with matching bird and atmospheric altitudinal data. (a) TKE, (b) Temperature,
(c) Tailwind. For statistical details see Supporting Table 4.
a
Soaring-gliding flight
Mixed flight
Flapping flight
0.0
0.4
0.8
1.2
1.6
2.0
2.4
TKE (m2 s-2 )
b
Soaring-gliding flight
Mixed flight
Flapping flight
0
18
21
24
27
30
33
Temperature (°C)
c
Soaring-gliding flight
Mixed flight
Flapping flight
-8
-6
-4
-2
0
Tailwind speed (m s-1 )
2