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First published online December 14, 2006
Journal of Experimental Biology 210, 82-90 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02612
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Analyzing the effect of wind on flight: pitfalls and solutions

Judy Shamoun-Baranes1,*, Emiel van Loon1, Felix Liechti2 and Willem Bouten1

1 Computational Biogeography and Physical Geography, Institute of Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands
2 Swiss Ornithological Institute, 6204 Sempach, Switzerland


Figure 1
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  		Fig. 1. A graphic representation of the relationship between a, g and w, the orthogonal components xa, ya, xg, yg, xw, yw, {alpha} (heading), {gamma} (track or ground direction), {omega} (wind direction).

 

Figure 2
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  		Fig. 2. The relation between Va and Vg-Va for different combinations of Vw and {omega}-{gamma} (A, {omega}-{gamma}=0°; B, {omega}-{gamma}=45°; C, {omega}-{gamma}=90°; D, {omega}-{gamma}=135°). In each subplot Vg varies from 1-15 m s-1, and the isoclines represent constant Vw (2, 4, 6, 8 m s-1). Note that A represents pure tailwind conditions and C represents pure side winds in relation to the ground vector. To ensure a biologically realistic representation, A is constrained as follows: Vg>Va and Vg>Vw. In B, circles represent constant Vg (15 m s-1) and a varying Vw (2,4,6 and 8 m s-1), + symbols represent constant Vw (6 m s-1) and varying Vg (2, 5, 8 and 11 m s-1), see Fig. 3 for the individual vectors. See Fig. S1 (supplementary material: online appendix) for animated 3-D visualizations of these figures.

 

Figure 3
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  		Fig. 3. The relation between Va and Vg-Va where {omega}-{gamma}=45° expressed in vectors. Circles represent constant Vg (15 m s-1) and a varying Vw (2,4,6 and 8 m s-1), + symbols represent constant Vw (6 m s-1) and varying Vg (2, 5, 8 and 11 m s-1). All the points shown here are subsets of those in Fig. 2B.

 

Figure 4
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  		Fig. 4. An illustration of the correlations that arise in random Vg and Vw data as a function of variance Vg/variance Vw and {omega}-{gamma}. (A) {omega}-{gamma}=45°, (B) {omega}-{gamma}=135°. In all cases, the variance of Vw =4 m2 s-2. In the top row, Vg does not vary. In the second row, variance of Vg =1 m2 s-2 and in the bottom row, variance of Vg =4 m2 s-2. Va is calculated on the basis of Vg, {gamma}, Vw and {omega}.

 

Figure 5
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  		Fig. 5. Rose plot histogram of flight heading (left) and track direction (right) for each data set as follows (A) SRD (simulated random data), (B) SWI (simulated wind influence), (C) APM (autumn passerine migration). Note that 0° direction depicts north in our analysis (y>0) and 90° depicts east (x>0).

 

Figure 6
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  		Fig. 6. Graphical representation of traditional test of the influence of wind on air speed (Va in relation to Vg-Va). Three data sets were used (A) SRD (simulated random data; no relation between wind and flight) (B) SWI (simulated wind influence) (C) APM (measured autumn passerine migration dataset). In each dataset N=880.

 

Figure 7
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  		Fig. 7. The predicted relative influence of the wind components (xw and yw, left and center respectively) on air speed (Va) for each dataset (A) SRD (simulated random data; no relation between wind and flight) (B) SWI (simulated wind influence) (C) APM (autumn passerine migration). The form of each GAM is Va~lo(xw, 0.8, 2)+lo(yw, 0.8, 2). The y-axis represents the contribution of xw and yw on Va. The solid line is the fitted functional response and the broken lines represent the 2x standard error curves, the circles represent the partial deviance for each observation point. The local minima in Fig. 7B correspond with xg (6 m s-1) and yg (3 m s-1) in the SWI dataset. Figures on the far right represent the observed (y-axis) vs fitted Va (m s-1) (x-axis); note that the x and y axis are not always equally scaled.

 

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© The Company of Biologists Ltd 2007