Extra Supplementary Material
Heat transfer model of emperor penguin
Surface area and characteristic dimensions
A simple geometric model of an emperor penguin Aptenodytesforsteri was represented by main body (prolate spheroid), head (sphere), beak (cone), flippers and feet (flat plates) (Fig. 1). A specimen (Hunterian Museum, Catalogue: Z1125) mounted in a realistic upright stance was used to provide representative body dimensions and body surface areas for heat transfer calculations.
The surface area of the main body trunk (m2)was determined by:
where and a and b are the semi-major and minor axes lengths, respectively [1]. a was taken to be half the body length from the black neck collar to the base of abdominal feathers (0.34 m), b was half the maximum diameter of the body trunk (0.16 m) determined from a measurement of girth taken under the flippers. The beak area was a cone where the radius r was half the maximum width at the base of the beak (0.01 m) and hypotenuse s was approximated by beak length (0.11m). The area of the head was approximated by a sphere minus the base of a cone (beak): where the diameter d was taken to be the mean (± standard error) of head height and width (0.11±0.004 m) measured from the bottom of black head plumage and r as above. Flippers were approximated as flat rectangles of length l and width w, and were determined by tracing outlines onto 1mm squared graph paper. The flipper length was the maximum diagonal length from top to bottom of flipper (0.28±0.011 m) and mean flipper width (0.065±0.0002 m).
The surface area of each foot was obtained by tracing its outline onto 1 mm2 graph paper. The mean surface area of a single foot in contact with the ground was 0.0036±0.0004m2. The total surface area of a foot was therefore approximated as twice the measured area. As emperor penguins often rest on theirtarsometatarsus joint, this area was also traced from the museum specimen and averaged 0.0006±0.00008 m2 or 17% of the lower surface area of the foot. For radiation and convective calculations the characteristic dimension of the foot was taken to be maximum foot width, f (0.056±0.0025 m). The thickness of the foot, t was determined from the mean thickness of metatarsi (mean = 0.014 m SE = 0.001). The total surface area of an average emperor penguin was calculated to be 0.56 m2 which was within previously measured values [1, 2].
Surface Area (m2) / % Total surface area / d (m) / Nusselt RelationshipTrunk (excluding flippers) / 0.471 / 83.8 / 0.32 / Prolate Nu =0.24Re0.6
Head and beak / 0.040 / 7.2 / 0.11 / Sphere Nu =0.34Re0.6
Flippers (outside surface only) / 0.036 / 6.5 / 0.065 / Flat plate Nu =0.032Re0.8
Feet / 0.014 / 2.5 / 0.056 / Flat plate Nu = 0.032Re0.8
Total / 0.562
Table 1.Calculated surface area, percentage of total surface area, characteristic dimensions for heat transfer calculations of emperor penguin and relationship between Nusselt and Reynolds numbers [7].
Heat transfer
A distributed parameter heat transfer model was used to estimate total heat exchange, (W) for an emperor penguin by summing heat transfer from each body region (head, trunk, flippers and feet) assuming that the penguin was in thermal equilibrium with its surroundings [3]:
(1)
Radiation
As measurements were undertaken during mid-winter (1h50-2h50 light/24h) solar heat gain was assumed to make a trivial contribution to heat transfer. Radiative heat loss was determined by solving the radiation balance at the surface. Heat loss by radiation was the difference between radiation emitted from the penguin’s surface, and radiation gained from the environment, such that:
(2)
Radiation emitted from each body part of surface area, A with surface temperature Ts (K) was determined according to:
(3)
Where is emissivity of bird plumage (=0.98,[4]) andis the Stefan-Boltzmann constant (5.67 x10-8 Wm-2K-1). We assumed that each part of the body exchanged radiation equally with sky and surroundings such that amount of radiation absorbed was equal to the mean flux from sky and ground surface:
(4)
where A (m²) is the radiative area and, al is the long wave absorptivity (=emissivity)of the penguin.Ld(Wm-2) and Lu(Wm-2) are the downward and upward radiative heat fluxes from sky and snow surface, respectively.The downward radiative flux was estimated using the empirical relationship measured in Antarctica [5]:
(5)
whereTa is air temperature (K),h the specific humidity (gkg-1) and c the cloud cover (oktas).
The upward radiative flux was determined by:
(6)
whereis the emissivity of ground surface (snow = 0.97, [6]) and Tg (K) the ground ice temperature.
Convection
Heat transfer by convection, from each region of the body was calculated by:
(7)
Forced convection is the dominant mode of heat transfer in wind (≥ 0.5 ms-1 in this study) such that the heat transfer coefficient was determined by:
(8)
where k is the thermal conductivity of air (0.0225 Wm-1oC-1 at -20oC), d (m) is the characteristic dimension of each body part in the direction of air flow and Nu is the dimensionless Nusselt number. The Nusselt number is a measure of the ratio of buoyant to viscous forces. It depends on shape and can be related to the dimensionless Reynolds number, from , where u is the wind speed (ms-1), d the characteristic dimension (m) and the kinematic viscosity of air (11.6 x 10-6 m2s-1 at -20oC). The relationship between Nu and Re has been determined empirically for a range of geometric shapes and flow regimes (Table 1).
Conduction
Emperor penguins commonly cover the upper surface of their feet by abdominal feathers and therefore a bird will lose heat by conduction, qconfrom the lower surface of its feet to the snow surface such that:
(9)
wherek is the thermal conductivity of the foot tissue (Wm-1oC-1) of thickness x (m). The thermal conductivity of foot tissue was taken to equal skin conductivity (0.502 Wm-1oC-1)[8]. Emperor penguin feet remain above freezing and the minimum heat loss by conduction was estimated from minimum foot temperature of 3.3°C [9]. The temperature of ground surface underlying the foot was assumed to equal the surface temperature of surrounding snow surface. If feet were not visible it was assumed birds were resting on their tarsometatarsus where area in contact with ground was 17% of foot area. When standing or walking, the foot will also lose heat by radiation and convection from the upper surface (as above).
Latent heat loss
Latent heat loss for emperor penguins was estimated from previous measurements of the evaporative water loss that remained constant between -47 and 20 oC and averaged 5.85 g h-1[1]. The vaporisation of 1g water requires 2.43 kJ, therefore latent heat loss for an emperor penguin is equivalent to 4.0 W.
Data
Input data for the model was taken from surface temperature measurements of emperor penguins and meteorological data recorded at the breeding colony of Pointe Géologie in Terre Adélie (66o40’S 140o 01’E), Antarctica in June 2008 (ESM2). Where surface temperature data weremissing for a particular body part for an individual, the missing value was computed using regression with air temperature from GLM models (see paper).
References
1.Pinshow, B., Fedak, M.A., Battles, D.R., Schmidt Nielsen, K. 1976 Energy-expenditure for thermoregulation and locomotion in emperor penguins. Am. J. Physiol.231,903-12.
2.Le Maho, Y., Delclitte, P., Chatonnet, J. 1976. Thermoregulation in fasting emperor penguins. Am. J. Physiol.231,913-22.
3.McCafferty, DJ, Gilbert, C, Paterson, W, Pomeroy, PP, Thompson, D, Currie, J, Ancel, A. 2011 Estimating metabolic heat loss in birds and mammals by combining infrared thermography with biophysical modelling. Comp. Biochem. Physiol.A-Molec. Integ. Physiol. 158, 337-345.
4.Hammel, H.T. 1956 Infrared emissivities of some arctic fauna. J. Mammal.37, 375-8.
5.Cho, H.K., Kim, J., Jung, Y., Lee, Y.G., Lee, B.Y. 2008 Recent changes in downward longwave radiation at King Sejong Station, Antarctica. J. Climate.21, 5764-76.
6.Kondo, J., Yamazawa, H. 1986. Measurement of snow surface emissivity. Boundary-Layer Met.34,415-6.
7.Monteith, J.L., Unsworth, M.H. 1990 Principles of environmental physics. London: Edward Arnold.
8.Gates, D.M. 1980 Biophysical Ecology. Berlin: Springer – Verlag.
9.Prévost, J, Sapin-Jaloustre, J. 1964 A propos des premieres mesures de topographie thermique chez les Spheniscides de la Terre Adelie. Oiseau.34, 52-90.
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Extra Supplementary Material
Fig.1. Geometric model of emperor penguin. Definition of terms given in text.
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