AMER. ZOOL., 32:217-224 (1992)
Quantifying Radiative Heat Gain in Animals'
GLENN E. WALSBERG
Department of Zoology, Arizona State University, Tempe, Arizona 85287-1501
SYNOPSIS. This paper summarizes some general approaches to quantifying radiative environments and estimating radiative heat loads on animals. Because natural radiation environments can be very complex, practical limits to their evaluation are most likely to arise
from difficulties in analyzing their patchy nature. Accurately estimating radiative heat loads
accrued by animals is particularly likely to be limited under practical conditions by difficulties
in determining effective animal surface area and quantifying effects of radiation penetrating
into fur or feather coats.
INTRODUCTION
Radiation is a potentially overwhelming
source of heat to animals. Short-wave (solar)
radiation under clear skies often exceeds
1,000 W m~2; long-wave radiation emitted
by terrestrial environments commonly
amounts to 200-400 W m~2. The irradiance
on an animal's surface can therefore be 1020 times the area-specific basal metabolic
heat production of typical endotherms.
Quantification of an animal's radiative heat
gain thus assumes major importance for
analyses of energy balance under natural
conditions. Selection of approaches used for
such analyses is necessarily dictated by the
type of organism studied and the questions
addressed. An important dichotomy is
between quantifying the radiative environment independent of animal properties or
quantifying the actual heat load acquired by
the animal. In the latter case, choice of
approach must reflect taxonomic concerns
and the time span appropriate for integration of data. Taxonomic concerns, for
example, include recognition that the fibrous
insulation of birds, mammals, and some
insects considerably complicates determination of heat transfer (Kovarik, 1964; Cena
andMonteith, 1975; Walsberg etai, 1978).
Appropriate time scales for data integration
also vary considerably. If the primary focus
of research is quantification of short-term
responses to thermal stress experienced by
the animal {e.g., Salzman, 1982; Bakken,
1989) then the small body size and consequent low thermal inertia of most animals
dictates a short time scale on the order of
minutes. In contrast, the energy budget of
most animals probably is balanced over
periods of at least a day because foraging
typically occurs in 24 hr cycles and because
even small endotherms usually can store
energy sufficient for a few days. Therefore,
research focussed on the thermostatic component of an animal's total daily energy
expenditure may allow much longer time
scales on the order of hours (e.g., Buttemer
et al, 1986; Weathers and Sullivan, 1989).
Complicating these concerns are routine (but
important) decisions balancing accuracy of
analysis against ease of data collection, and
fine analytical resolution against lumping of
data that may yield insights otherwise
obscured by a numerical haze.
QUANTIFICATION OF THE RADIATIVE
ENVIRONMENT
Natural radiative environments can be
excruciatingly complex. Organisms receive
long-wave radiation emitted from the atmosphere, the substrate, and other surroundings such as vegetation. Short-wave radiation is received from the direct solar beam
and scattered from the environment. Finally,
this spectral and spatial diversity is complicated by temporal changes. Coping with
such complexity is facilitated by segregating
radiation into major components. A natural
and useful division is between solar radiation and that emitted by terrestrial sources.
Thermally significant radiation is emitted
by the apparent "surface" of the sun, which
approximates a 6,000°K blackbody source
and
therefore is dominated by short-wave
1
From the Workshop on Biophysical Ecology: Meth- radiation. At sea level, the peak intensity of
ods, Microclimates, and Models presented at the Annual
Meeting of the American Society of Zoologists, 27-30 solar radiation occurs at about 520 nm. In
contrast, terrestrial sources are much cooler
December 1989, at Boston, Massachusetts.
217
218
GLENN E. WALSBERG
and dominated by long-wave radiation (e.g.,
peak emission at 20°C = 9,900 nm).
Although the solar spectrum extends into
that of terrestrial emission, this overlap can
be ignored for most practical purposes. This
is important not only for problems of measurement, but also because animal surfaces
typically are affected differently by terrestrial and solar radiation. Animal surfaces
usually absorb more than 95% of long-wave
radiation. However, solar radiation is used
for vision and consequently there have
evolved widely divergent patterns of shortwave reflectivity.
Quantification of solar radiation
Sensors used to quantify solar irradiance
can be classified as either blackbody sensors
or spectrally selective devices such as photovoltaic cells. While typically more expensive, the former are preferable because of
their spectral neutrality (Simidchiev, 1986).
Segregating direct and diffuse (scattered)
solar radiation usually is desirable (see
below). Although specialized instruments
(pyrheliometers) are available that measure
only direct solar radiation, economical
alternatives commonly are used that entail
using either a small disk or a shadow band
to shade a pyranometer from the solar beam
(Simidchiev, 1986). This allows measurement of diffuse solar irradiance and simultaneous measurement with an unshaded
sensor allows calculation of direct solar irradiance. Radiometers typically are placed
with the sensor surface horizontal, although
computation of heat gain to an animal usually requires knowledge of direct irradiance
normal to the solar beam. This can be calculated from the intensity on a horizontal
surface using Lambert's cosine relation
(Monteith, 1973). However, sensor surfaces
are not perfectly diffuse and their reflectivity
typically increases at low angles of incidence. The resulting underestimate of solar
input during such periods can be overcome
using a sensor oriented perpendicular to the
solar beam with the aid of a shadow rod.
Quantification of long-wave radiation
Although sensors responding only to longwave radiation are available (pyrgeome-
ters), most workers determine this component by measuring total radiation collected
by an all-wave radiometer (pyrradiometer)
and subtracting the short-wave component
that is measured independently using a
pyranometer. All-wave sensors typically differ from pyranometers in that the dome
shielding the sensor is composed of polyethylene film rather than glass. Unless oxidized or dirty, such films exhibit high transmissivity with little spectral dependance
within the appropriate wavebands (Funk,
1959). Several methods have been described
for construction of all-wave radiometers by
modifying commercially available devices
(e.g., Idso, 1971; Campbell et al, 1978).
Alternatively, long-wave irradiance can
be estimated by the Stefan-Boltzmann
equation (Monteith, 1973) and knowledge
of environmental temperature and thermal
emissivity (e). For most natural surfaces, e
equals 0.95-0.99. Assumptions regarding
this value are therefore unlikely to produce
an important error. A notable exception is
the atmosphere, the emissivity of which
varies substantially with humidity. Examples of formulae used to account for humidity effects are those of Brutsaert (1975) and
Idso and Jackson (1969).
Finally, one seemingly attractive technique for estimating atmospheric emission
should be avoided; this is the use of infrared thermometers. These devices are inappropriate for use in measuring radiative air
or "sky" temperatures because their wavelength response often is narrow and atmospheric emission is concentrated into discrete bands (Gates, 1962).
Coping with environmental complexity
Estimating the irradiance from a particular source is less likely to produce limiting
errors for the thermal ecologist than is the
task of estimating the relative contributions to an animal of sources in patchy natural environments. For example, the
hemisphere over an animal commonly contributes both long-wave and scattered shortwave radiation from a mosaic of sky, vegetation, and topographic features. The solar
beam may only reach a site between shading
objects for portions of a day that will sea-
RADIATIVE HEAT GAIN
sonally change. Analyses vary greatly in the
degree to which such environments are dissected. Perhaps the simplest method that
yields useful insights is merely dividing an
animal's radiant environment into upper
and lower hemispheres (e.g., Campbell,
1977). For more detailed analyses, a powerful technique is hemispherical or "fisheye" photography. Most commonly, hemispherical photography is used to quantify
the complex upper hemisphere over an animal (Walsberg and King, 1978a; Walsberg,
1981). Photographs are taken with the camera axis directed vertically and at dusk or
under cloudy skies when adequate light is
available but the sun is not visible. The photograph records the mosaic of sky, vegetation, and other features composing an overhead radiation environment (Fig. 1). A
marker placed in the field of view allows
later orientation of the photograph and plotting of solar paths. Data often extracted from
hemispherical photographs include estimates of long-wave irradiance and periods
of exposure to the solar beam.
Long-wave input to a site is estimated by
multiplying irradiance from different sources
(e.g., sky and vegetation) by the fractions of
the hemisphere that these sources occupy.
A simple analysis of long-wave radiative
input entails calculating irradiance from the
atmosphere (the unoccluded sky) and from
a canopy of vegetation. Unfortunately, fractional cover cannot be determined by simply measuring the total area of the photograph composed of canopy because area
relationships are distorted when a hemisphere is projected onto a plane. Rather, an
overlay grid is used to estimate fractional
cover in bands of elevation angles (Fig. 1)
and average values for each angular interval
are then mathematically projected onto a
horizontal plane to yield a grand average
value for the entire hemisphere (Fuchs et
al, 1976).
Quantifying the time at which a site is
exposed to the solar beam requires plotting
the sun's apparent overhead path onto the
photographs (Fig. 1). The sun's position at
a particular time can be described by its
angular altitude above the horizon (0°-90°)
and its azimuth (angular position relative
219
FIG. 1. Hemispherical photograph of the vegetative
canopy over the nest of a phainopepla (Phainopepla
nitens) and a grid used to analyze such photographs.
A sample solar path with hourly intervals marked is
also shown on the grid.
to north/south coordinates). Solar elevation
(#) can be calculated as (List, 1971):
<t> = sin~'[sin r sin 5
+ cos 5 cosT cos (15[t - tN])] (1)
Here, r = latitude, 8 = solar declination
angle, t = current time, and tN = time of
local solar noon. Solar declination angles
are tabulated in List (1971) or can be estimated using equations such as the following.
220
GLENN E. WALSBERG
5 = -23.45 cos(0.986D + 8.87)
(2)
Here, D is the day of the year (Jan 1 = day
1) and angles are in degrees. This equation
estimates 8 with an average absolute error
of 0.4° (range = 0-0.9°). The time of local
solar noon is calculated as
APPROACHES TO QUANTIFYING RADIATIVE
HEAT LOADS ON ANIMALS
The radiative heat load with which an
animal must cope physiologically equals, in
general, that acting on the surface of the
animal's metabolically active tissue (e.g., the
skin). Within a particular microenviron(3) ment, the radiative load acquired by an anit N = 12 + (LL - Lc)/15 + C
mal is sequentially affected by three classes
where L^ is the local longitude. L c is the of factors. First, animal size, shape, and oricentral meridian of the local time zone, equal entation determine the amount of radiation
to the nearest even multiple of 15°. C is a intercepted. Second, the fractional absorpcorrection required because of variation in tivity of the animal surface determines the
the angular velocity of the Earth's rotation proportion of intercepted radiation that
during the annual cycle. Values are tabu- generates heat. Third, the presence of an
lated in List (19 71) or can be estimated using insulating coat may importantly alter the
the following equation.
heat load transferred to the skin. The effect
of a heat load on the skin can, of course, be
= (-0.12sin[0.986D])
importantly altered by physiological pro- (0.16 sin[ 1.973 D])
cesses (e.g., sweating) or environmental
- (0.05 cos[ 1.973 D])
(4)
properties such as wind; such effects are
This formula estimates C (in hours) with an beyond the scope of the current analysis.
average absolute error of 0.007 hr (range:
Even a rudimentary model illustrates the
0-0.02 hr). Solar azimuth angle is deter- need for knowledge of a series of animal
mined from
properties that can be difficult to estimate:
cos a = (sin 8 ± sin <j> sin T)/cos <j> cos r
Q = («S)(A D I R )(Q S , D I R)
(5)
+ («S)(A D I F )(Q S ,DIF)
where a is the azimuth measured from due
(6)
+ («L)(ADIF)(QL)
south. Negative and positive values of sin
<j> are used, respectively, for morning and Here, Q is the heat load on the skin, as is
fractional absorptivity to solar radiation, aL
afternoon hours (List, 1971).
is
fractional absorptivity to long-wave radiHemispherical photography thus allows
ation,
AD1R is the animal surface area interdetermination of periods of exposure to
cepting
direct solar radiation, AD1F is the
direct sunlight as well as the fraction of the
animal
surface area intercepting diffuse
hemisphere composed of components with
radiation,
QL is long-wave irradiance, QS,DIF
contrasting long-wave emittances. Such data
is
short-wave
diffuse irradiance, and QS,DIR
can be combined with the measured intenis
direct
short-wave
irradiance. Note that
sity of these sources to estimate radiative
this
highly
simplified
model is appropriate
input to a site. A simplifying assumption is
only
for
naked
animals.
that both long-wave and diffuse short-wave
radiation are uniform in their intensity
across the hemisphere. Although violated Surface area
The surface area intercepting radiation
in nature to varying degrees, field experience indicates that resulting errors are varies not only between individuals but also
unlikely to limit the accuracy of a heat bud- for a particular individual depending upon
get for an animal living in a complex natural posture, orientation and radiation type.
habitat. Major advantages of this technique Elaborate optical techniques are available
are allowing use of data from a single set of to measure exposed surface areas (Halliday
radiometers to describe conditions occur- and Hugo, 1963; Veghte, 1975) as well as
ring simultaneously in many sites and facil- simpler methods that rely on estimating
itating analyses of the bases of variation in surface area by analogy to geometric shapes
(e.g., Mugaas and King, 1981; Scott et ah,
radiative environments.
RADIATIVE HEAT GAIN
1982) or estimating surface area from body
mass (Meeh, 1879; Walsberg and King,
1978a). A significant difficulty is that skin
surface area probably overestimates the
actual area intercepting radiation. In man,
for example, postural changes can reduce
the area exposed to diffuse radiation to
approximately 50% of skin area (Halliday
and Hugo, 1963). In the geometrically simpler case of perching birds, skin area averages 23% greater than the exterior surface
area intercepting diffuse radiation (Walsberg and King, 19786). Such difficulties are
exacerbated by the necessary dissection of
surface area into fractions exposed to differing components of the radiative environment (i.e., long-wave vs. short-wave radiation, direct vs. diffuse radiation). Workers
commonly assume that one-half of the animal's surface area receives downward diffuse radiation and that the other one-half
receives upward diffuse radiation. For direct
solar radiation, however, the appropriate
surface area equals that of the animal's
shadow on a plane perpendicular to the solar
beam. This area varies greatly with animal
shape and orientation and the importance
of such variation is, of course, illustrated by
many species' reliance upon it as a means
of behavioral thermoregulation. Because of
the complex shape of animals and the temporal variability of projected surface area,
its determination can be challenging. In
addition to measurements on live animals
and taxidermic mounts, estimating equations are available that rely upon an organism's similarity to a variety of geometric
shapes (e.g., Campbell, 1977). Unfortunately, the accuracy of such models has
rarely been evaluated (e.g., Clapperton et
al., 1965).
The importance of difficulties in estimating surface areas should not be discounted.
For example, a 10% error in the estimate of
exposed surface area is not unlikely but
would produce the same error in the calculation of long-wave radiation intercepted
under typical conditions (i.e., infrared environmental temperature = -20°-50°C) as
would be generated by a 6-8°C error in environmental temperature measurement. Even
larger errors are possible when evaluating
direct solar input, as surface area projected
221
on a plane perpendicular to the solar beam
can vary at least three-fold as an animal
changes orientation (Campbell, 1977).
Absorptivity
Estimating fractional absorptivity to
either long-wave or short-wave radiation
typically is less challenging than is measurement of surface area. Long-wave
absorptivity usually is approximated as
0.95-0.99. These values are typical of animal surfaces and resulting errors are unlikely
to be more than a few percent. Short-wave
absorptivity varies considerably, however,
and must be measured with devices such as
a reflecting spectrophotometer (e.g., Porter
and Gates, 1969) or a solar reflectometer
(e.g., Dunkle et al., 1960). The former yields
more information by describing variation
with wavelength, but requires integration
with data describing the spectral dependence of solar irradiance. Solar reflectometers yield only a single value for total
absorptivity to solar radiation; this can vary
somewhat with the changing spectral qualities of sunlight.
Radiation penetration into coats
Major difficulties in constructing radiative heat budgets occur when the animal
possesses an insulating coat of hair or feathers. In this case, the thermal load on the
skin depends upon the amount of the coat's
insulation through which radiation penetrates prior to absorption. If such absorption occurs largely near the outer coat surface, then a major fraction of the resultant
heat is lost to the environment and does not
act on the skin (Kovarik, 1964; Walsberg et
al., 1978). In contrast, if radiation penetrates deeply into a coat before being
absorbed, coat insulation importantly
retards heat loss to the environment and
increases the thermal load on the skin (Fig.
2).
Radiation penetration is affected by coat
structure and optical properties of hairs or
feathers. Plumage or pelage structure determines the distance that a photon travels
through a coat before being intercepted by
a coat element. Relevant structural properties include the diameter and density of
hairs or feathers and their angle to the pen-
222
GLENN E. WALSBERG
(Spermophilus lateralis and Spermophilus
saturatus) that differ in coloration (Walsberg, 1990). S. lateralis in Arizona possesses
much paler fur (solar reflectivity = 0.29)
Reflected
than does S. saturatus in Washington (solar
radiation
reflectivity = 0.19). Despite this major difHeat loss to
ference in reflectivity, solar heat gain to the
environment
skin is essentially identical in the two species. Important factors reducing heat gain
in the darker species are increased depth of
the middle fur layer and increased hair density in the outer fur layer that tends to reduce
radiation penetration. The net effect of such
differences is that the thermal consequences
of differing coat colors are balanced by alterations in the relative depth of light penetration (Walsberg, 1990).
Heat load
on skin
In a contrasting case, solar heat gain in
Sonoran Desert populations of the rock
FIG. 2. Fate of solar energy impinging on an animal
squirrel (Spermophilus variegatus) is subwith a coat of fibrous insulation. A fraction of sunlight
striking the coat is reflected away. Nonreflected radistantially altered between winter and sumation penetrates to varying degrees into the coat, where
mer without change in the animal's colorit is eventually absorbed. A portion of the heat resulting
ation
(Walsberg, 19886; Walsberg and
from radiation absorption flows outward and is lost to
Schmidt, 1989). With constant irradiance,
the environment. The remaining portion flows inward
and acts as a heat load on the skin. The relative frac- heat gain at low wind speeds is about 20%
tions of the total heat generated that flows out to the
lower in summer coats than in winter coats.
environment or acts as a heat load on the skin depends
Important factors producing this adaptive
upon environmental factors and the fraction of the coat
insulation through which sunlight penetrates. This pen- decrease in heat gain during the extremely
etration, in turn, depends importantly upon coat struc- hot summer months are changes in the therture and hair optical properties.
mal resistance of the inner fur layer and
changes in the optical properties of individual hairs.
Even though few species have been adeetrating radiation. Once intercepted, a photon's fate is affected by the optical properties quately studied, these examples do demof individual hairs or feathers (i.e., their onstrate that at least some animals have
fractional absorptivity, backwards scatter- modifications of coat structure and hair
ing, and forwards scattering). Both sets of optics that allow adjustment of heat gain
factors can vary spatially across the animal independently of surface appearance. This
and with angle of incidence. The roles of importantly allows thermal balance to be
these factors determining solar heat gain are uncoupled from the selection pressures
subsumed in models such as those of Wals- affecting the visual communication funcberg et al. (1978), Gebremedhin et al. (1983), tions of the coat.
and Walsberg (19886).
Thermal effects of radiation penetration Determining radiative heat gain using
can be large. Such penetration is estimated taxidermic mounts
to increase the radiative heat load on the
Although mathematical models are availskin up to 300% in cattle (Hutchinson and able that cope with the complexity of radiBrown, 1969) and up to 600% in pigeons ative heat transfer through coats, the diffi(Walsberg, 1983). In some species, such culty of quantifying requisite variables (e.g.,
processes reverse the effects of large differ- optical properties of individual hairs) and
ences in coat color (0ritsland, 1970; Wals- distributing the model across an animal's
berg et al., 1978) and are of adaptive impor- geometry probably are sufficient to daunt
tance, An example is two otherwise similar most workers. Empirical data indicate that
species of golden-mantled ground squirrels retreat to simpler models that ignore effects
Solar
radiation
RADIATIVE HEAT GAIN
223
of radiation penetration into coats may pro- atmosphere or terrestrial objects. Under
duce large errors (Walsberg et al, 1978; clear skies at low altitudes, for example, skyWalsberg, 1988a). This argues for use of light commonly equals 10-20% of total solar
alternative techniques to determine solar irradiance. Elaborate shielding to reduced
heat gain, such as measurement of operative such scattered light could significantly alter
temperature (Tg) using taxidermic mounts. both the long-wave and convective enviTE represents the sum of air temperature ronments. Another approach is to simply
and a temperature increment or decrement measure the elevation of TE over air temthat subsumes radiative and convective fac- perature. This difference reflects the sumtors (Bakken and Gates, 1975;Bakken, 1976; mary effect of all variances in the radiative
Robinson et al, 1976; Campbell, 1977). The environment from one in which radiation
difference between TE and body tempera- is received only from surroundings at air
ture (TB) equals the net thermal gradient temperature with e = 1 (a "blackbody envibetween an animal and its environment. Net ronment"). This subsumes effects of all
heat flow is proportional to this gradient short- and long-wave radiation; most ecodivided by the total thermal resistance of logically useful analyses would require subthe animal/environment system. In a poi- sequent dissection of these components.
kilotherm, TE equals the equilibrium body
CONCLUDING COMMENTS
temperature achieved by the animal in a
particular microclimate. In homeotherms,
Estimating an animal's radiative heat load
the net effect of the animal's heat produc- requires data describing irradiance, absorption and evaporative water loss is to main- tivity, surface area, and effects of radiation
tain TB different from TE. If a homeotherm penetrating into an insulating coat that may
maintained its normal heat transfer prop- be present. Efficiency of effort dictates that
erties at its interface with the environment methodological refinements be focussed on
yet had thermally insignificant rates of difficulties that act as the primary limit to
internal heat production and evaporative the accuracy of an analysis. Although quanwater loss, then the body would thermally tification of absorptivity and irradiance can
equilibrate with the environment and TB be complicated, such measurements are less
would equal TE. This is a theoretical basis likely to be the source of limiting errors than
for measurement of TE using a hollow metal is estimating surface area or radiation pencast of the animal's body covered by the etration into coats. Faulty estimates of suranimal's integument (Bakken and Gates, face area can readily produce overwhelming
1975). Such a mount can have essentially errors and effects of radiation penetration
the same heat transfer properties as a live can be large and of adaptive importance.
animal (e.g., size, shape, coat properties), Thus, practical limits to the accuracy of
yet is thermally passive. Either TE is mea- radiative heat budgets for animals are parsured using thermocouples implanted in the ticularly likely to result from either the
hollow metal cast or a heating wire is seemingly mundane task of estimating surimplanted in the artificial body and the face area or the challenging problem of anapower input required to maintain normal lyzing light scattering and heat flow through
skin temperature is measured (Bakken and layers of fibrous insulation.
Gates, 1975; Bakken et al, 1981).
Estimating radiative heat loads using taxACKNOWLEDGMENTS
idermic mounts essentially requires comThis paper is a by-product of research
parative measurements in the presence and supported by National Science Foundation
absence of radiation while keeping other grants BSR 80-04266 and BSR 85-21501.
factors constant. Such experiments can be
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