A new argument against cooling by convective air eddies formed above sunlit zebra stripes

Test surfaces

We used smooth and hairy, homogeneous and striped (with different widths of black and white stripes) test surfaces. In order to mimic the curved zebra back, all test surfaces had a convex cylindrical shape (length: 15 cm, radius: 7 cm). In the schlieren measurements (see subsection “Schlieren imaging”), the cylinder’s horizontal long axis was perpendicular (Supplementary Fig. S1A,B) or parallel (Supplementary Fig. S1C) to the collimated horizontal light beam illuminating the target area, while the stripes were perpendicular (Supplementary Fig. S1A) or parallel (Supplementary Fig. S1B) to the cylinder’s long axis. Supplementary Tables S1 and S2 list the patterns, colours and names of the 8 smooth and 10 hairy test surfaces. The smooth surfaces were composed of cardboard squares (15 cm × 15 cm) (Supplementary Fig. S2). The hairy surfaces were composed of cattle, horse and zebra hides glued by dextrin to a cylindrical (length: 15 cm, radius: 7 cm) gypsum base (Supplementary Fig. S3). Surfaces hsc1(7b7w)perp, hsc1(8b7w)par, hsc3(3b2w)perp and hsgc3(3s2L)perp were used to model that the black stripes of zebras could be separately erected, while the white remained flat⁷. No animals were killed, the horse and cattle hides were provided by Hungarian horse and cattle keepers, while the zebra hide was obtained from a Hungarian zoological garden.

Thermography of lamplit test surfaces

Using a thermocamera (VarioCAM, Jenoptik Laser Optik Systeme GmbH, Jena, Germany, nominal precision of ± 1.5 K, with relative pixel-to-pixel precision < 30 mK) we measured the temperature distribution of all test surfaces under the same circumstances as occurred during the schlieren measurements. The validation and calibration of our thermocamera with a contact thermometer (GAO Digital Multitester EM392B 06554H, EverFlourish Europe GmbH, Friedrichsthal, Germany, nominal precision of ± 1˚C) were described in the Electronic Supporting Material of Horváth et al.¹³.

Along a horizontal straight line we calculated the followings: average T_ave ± standard deviation σ_T of the surface temperature T, minimum T_min and maximum T_max of T, average ΔT ± standard deviation σ_ΔT of the temperature difference between the adjacent local minima and maxima of T.

Schlieren imaging

We used schlieren imaging to study the airflow above lamplit test surfaces. The experimental setup of our schlieren device is schematically shown in Fig. 2. With this optical technique the spatiotemporal change of the temperature-dependent refractive index of air can be visualized¹⁴. In the schlieren images, we looked for nearly vertical dark-bright stripe pairs above the lamplit test surfaces, because these stripes visualize the air streams that could be the assumed convective eddies above sunlit zebra stripes possessing a cooling effect. Our schlieren setup was composed of two parabolic mirrors (Edmund Optics, Barrington, NJ, USA), both with a diameter of 15.2 cm and focal length of 152 cm (Fig. 2 and see also Supplementary Figs. S4 of Horváth et al.¹³). The lamplit test surfaces were placed into the horizontal collimated light beam of the schlieren equipment, the light source of which was composed of a white LED light (3 Watt, 4000 K). We recorded the schlieren images/videos with a Nikon D5600 DSLR camera used within 120 mm focal length in Full HD resolution (1920 × 1080 pixels). The blade in front of the lens was vertical, thus the horizontal component of the refraction became visible. To model the heating of the test surfaces by sunlight, we used a 400 W, 3500 K halogen lamp producing intense white light corresponding to sunlight (Everflourish Hungary Ltd., Budapest, Hungary) placed vertically above the target at a height of 60 cm. Below the lamp there was a vertical tube (length: 43 cm) with a square cross-section (19 cm × 14.5 cm), the inner walls of which were covered with aluminum foil to reflect the lamplight. The bottom of this tube was 17 cm above the target (test surface). Under the target area there was a horizontal plane mirror (100 cm × 70 cm) and a T-shaped stand covered with aluminum foil which held the test surface at the appropriate height. The function of the plane mirror and the aluminum covering of the stand was to minimize the warming up of the surrounding area.

After placing the test surface onto the T-holder in the target area, we waited 5 min to heat up the test surface by lamplight to a constant temperature. 5 min proved to be enough for the stabilization of the target’s temperature. Schlieren sequences were recorded when (i) the long axis of the cylindrical test surface was perpendicular to the camera’s optical axis (3 min, Supplementary Fig. S1A, B), (ii) the long axis was parallel to the optical axis (3 min, Supplementary Fig. S1C), and (iii) the test surface was removed from the T-holder in order to record the background (1 min).

Evaluation of schlieren images and video sequences

As a result of schlieren imaging, we got a video sequence of the air layer above a given lamplit test surface placed on the T-holder. We converted this video sequence to single png images cropped to 908 × 908 pixels (Supplementary Fig. S4A) and made them grey-scaled. Averaging the intensity value—ranging from 0 (black) to 255 (white)—of every pixel of the images of the 1-min-long sequence taken above the same lamplit air layer when the test surface was removed from the T-holder, we got the averaged schlieren image of the background (Supplementary Fig. S4B). Then, we composed the difference of the background image and the original image resulting in a filtered schlieren image (Supplementary Fig. S4C), the pixel intensity of which was calculated from the formula I_filtered = 125—(I_background—I_original), where I_background is the pixel intensity of the averaged background image (without the test surface) and I_original is the pixel intensity of the grey-scaled image with the test surface. This filtering was necessary to ensure a homogeneous middle grey (with a constant pixel intensity I_grey = 125) shade of the background. Note that if I_background = I_original, then I_filtered = 125.

To characterize the spatiotemporal change of pixel intensity induced by different air streams above a given lamplit test surface, we selected an upper (7 cm above the surface) and a lower (0.5 cm above the surface) horizontally elongated rectangular window (smooth surfaces: width of upper and lower windows was 612 pixels = 10.5 cm, hairy surfaces: width of upper and lower windows was 612 pixels and 698 pixels = 12 cm, respectively, height of both windows was 40 pixels = 0.7 cm above both surface types) in the filtered image (Supplementary Fig. S4D). Within both rectangles, we averaged the pixel intensity I for the vertical pixel column (40 pixels) along the horizontal axis x. The resulting I(x) curve was smoothed by a Gaussian filter with standard deviation of σ = 5. Then, we found the local minima of the Gaussian-smoothed curve I(x), which are shown by vertical lines in the top and bottom of the plots. The sites of these local minima of I(x) coincide with those of the bright-light stripe pairs of the filtered schlieren image visualizing air streams with gradient indices of refraction induced by local temperature gradients.

To characterize an I(x) curve, we counted the number N_min of local minima of I(x), the difference ΔI = I_max—I_min along this curve, and the average displacement d_ave of each local minimum. d_ave was calculated as follows: for the i-th local minimum, we found the closest local minimum in the frame recoded 1 s later, calculated the displacement d_i between these minima and averaged them as ({d_{{{text{ave}}}} = sum {d_{i} } /N_{{{text{min}}}} }). If there was no or only one local minimum, then d_ave = 612 (= pixel width of the selected window).

To analyze the behaviour of air streams above the lamplit test surfaces, we identified each local minimum of I(x) and characterized its movement with its lifespan t (from appearance to disappearance, e.g. t = 3 × 33 ms corresponds to 3 frames), covered distance d_covered (e.g. if the movement was 5 pixels to left between the 1st and 2nd frames, and the movement was 10 pixels to right between the 2nd and 3rd frames, then d_covered = 5 + 10 = 15 pixels), mean speed v_mean = d_covered/t, maximum distance d_max = x_max—x_min, and start–end distance d_se =|x_start—x_end| between its start (x_start) and end (x_end) points. For statistical analyses, we used only local minima with lifespan t > 1 s. Since in the upper rectangular window of the filtered schlieren images the lifespan t of local minima of I(x) was very short, we performed statistics only for the lower rectangular window.

For the statistical analysis of the characteristics of I(x) (N_min, ΔI, d_ave) and air stream behaviour (t, d_covered, v, d_max, d_se), we applied Principal Component Analysis (PCA) and fitted ellipses to component scores with 95% confidence interval. We applied Wilcoxon rank sum test with Bonferroni correction for the datasets. Because of the large sample size of the dataset N_min, ΔI, d_ave—for smooth test surfaces 4475 observations per surface and for hairy test surfaces 5369 observations per surface—, the Wilcoxon rank sum test would result in highly significant differences for almost all comparisons¹⁵. Therefore, we used a Monte Carlo approach, where we randomly selected 250 (≈ 5% of the full dataset) samples, ran the Wilcoxon rank sum test with Bonferroni correction, recorded the results, repeated this 499 times (to have 500 runs) and finally the average of the results of the 500 runs was calculated. The data evaluation was made by our custom-written scripts in Python programming language. For statistical analyses we used the R statistical package 3.6.3¹⁶.

Disturbance caused by an artificial wind and a butterfly

To demonstrate the influence of very weak winds on the air streams above lamplit test surfaces, we blew air by a compressor with a press of 1.6 bar from 1.5 m above the following test surfaces: ss1(8b7w), hsz(8b7w)perp, hsh1(8b8w)perp and hhbc. The compressor tube ended in an air-blow gun. Before the measurements, the air pressure was 4 bar in the 3-litre compressor tank, and the regulator was set to 1.6 bar. The compressor was turned off prior to recording a given sequence and during the measurement the air-blow gun was used to generate horizontal “wind” until the pressure decreased to 1 bar (atmospheric pressure). The artificial wind speed created by the compressor was measured (with accuracy < 0.1 km/h) with the same meteorological station (Conrad Electronic, equipment no: 672861) which was used in the field experiments of Horváth et al.⁵.

To demonstrate the instability of vertical air streams above the test surfaces, we recorded the trail/trace of a butterfly model in schlieren images above the following test surfaces: ss1(8b7w), hsz(8b7w)perp, hsh1(8b8w)perp and hhbc. The artificial cardboard butterfly (wingspan: 4.5 cm) hung from a thread (50 cm) weighted with an M6 size brass nut. This butterfly model was moved by the thread (swung left to right or shake up and down) above the illuminated surfaces and airflow patterns were recorded. The aim of this was to demonstrate that the tiny air disturbances caused by a butterfly can disrupt the upwelling air streams above sunlit zebra stripes.

Typical wind speed in the field

To demonstrate the typical range of wind speed in the open air in the summer months, we used the wind speeds recorded during the field experiments of Horváth et al.⁵ with an automatic meteorological station (Conrad Electronic, equipment no: 672861). This station was installed from 10 June to 19 September 2017 in a horse farm in Göd (47°43′N, 19°09′E, northern Hungary), where it measured the air temperature T_air and wind speed w continuously at a height of 1 m above the ground. Further details about the setup of this station can be read elsewhere⁵. We used Spearman rho test to find correlation between the measured wind speeds and air temperatures.

Ethical approval and informed consent

For our studies no permission, licence or approval was necessary. We confirm that no animals were killed specifically for the purpose of this study.

Source: Ecology - nature.com