Complexities of Animal Energetics
203
are many cases, however, where our simplifying assumptions are too restrictive, and can lead to incorrect conclusions. The limitations we have
imposed on latent heat loss exclude any analysis of sweating. A more
complete analysis, however, will be given in Ch. 13. We also failed to
consider heat loss by conduction to the ground or other substrate (even
though the equations for that are given in Ch. 8). Perhaps the most serious
omissions are a failure to consider the possibility that radiation can penetrate the animal coat, and the failure to consider the three-dimensional
nature of the animal. To add these complexities goes beyond the objectives of this book, but excellent work has been done in both areas, and we
briefly refer to the results of that work.
Our energy balance equations are essentially for a one-dimensional animal. We assume that the heat is well enough mixed internally to maintain
an essentially constant internal temperature. We also chose a single characteristic dimension and a single Rabs value for the animal in spite of the
fact that we know both of these values vary widely over the surface of the
animal. Coat conductance also varies substantially fromplace to place depending on the thickness of the coat and exposure to wind. Bakken (198 1)
addressed these issues with what he calls a two-dimensional operative
temperature model. This new model just divides the animal up into many
zones (head, legs, body in sun, body in shade, etc.), each of which can be
adequately analyzed by an equation similar to Eq. (12.11). An operative
temperature for each zone is also computed. The overall energy budget is
thenjust the area-weighted average of all zones. From this kind of analysis
he concludes that in strong wind or sun the one-dimensional model can
give substantially different results than the two-dimensional model. In
one example, the operative temperature from the two-dimensional model
was 6°C lower than for the one-dimensional model.
If radiation penetrates the coat of an animal, the location of energy
absorption ceases to be the outer boundary of the coat. Dissipation of
heat, however, still occurs at the outer boundary, so the effective radiation
heat load on the animal is higher. This is a kind of miniature greenhouse
effect. Walsberg et al. (1978) determined that, for small animals with
high boundary layer conductances, radiation penetration is important in
determining the optimum coat color for animals in desert environments.
Solar radiation penetrates to deeper depths in white coats than black.
Even though the total energy absorbed by a black coat is much greater
than that absorbed by a white one, the additional heat load from radiation
penetration of the white makes the black coat more suitable for desert
environments. Observations of coat color in desert dwelling animals seem
to confirm this result.
In sparse animal coats, both long and shortwave radiation penetrate the
coat, and it becomes impossible to treat the animal-environment interface
as a definite boundary as we have in this chapter. To deal with it properly
as a continuum, computer models must be used. Porter et al. (1994) have
developed such models and have shown them to work well in ecological
applications. The model has the advantage that it properly treats all of the
203
are many cases, however, where our simplifying assumptions are too restrictive, and can lead to incorrect conclusions. The limitations we have
imposed on latent heat loss exclude any analysis of sweating. A more
complete analysis, however, will be given in Ch. 13. We also failed to
consider heat loss by conduction to the ground or other substrate (even
though the equations for that are given in Ch. 8). Perhaps the most serious
omissions are a failure to consider the possibility that radiation can penetrate the animal coat, and the failure to consider the three-dimensional
nature of the animal. To add these complexities goes beyond the objectives of this book, but excellent work has been done in both areas, and we
briefly refer to the results of that work.
Our energy balance equations are essentially for a one-dimensional animal. We assume that the heat is well enough mixed internally to maintain
an essentially constant internal temperature. We also chose a single characteristic dimension and a single Rabs value for the animal in spite of the
fact that we know both of these values vary widely over the surface of the
animal. Coat conductance also varies substantially fromplace to place depending on the thickness of the coat and exposure to wind. Bakken (198 1)
addressed these issues with what he calls a two-dimensional operative
temperature model. This new model just divides the animal up into many
zones (head, legs, body in sun, body in shade, etc.), each of which can be
adequately analyzed by an equation similar to Eq. (12.11). An operative
temperature for each zone is also computed. The overall energy budget is
thenjust the area-weighted average of all zones. From this kind of analysis
he concludes that in strong wind or sun the one-dimensional model can
give substantially different results than the two-dimensional model. In
one example, the operative temperature from the two-dimensional model
was 6°C lower than for the one-dimensional model.
If radiation penetrates the coat of an animal, the location of energy
absorption ceases to be the outer boundary of the coat. Dissipation of
heat, however, still occurs at the outer boundary, so the effective radiation
heat load on the animal is higher. This is a kind of miniature greenhouse
effect. Walsberg et al. (1978) determined that, for small animals with
high boundary layer conductances, radiation penetration is important in
determining the optimum coat color for animals in desert environments.
Solar radiation penetrates to deeper depths in white coats than black.
Even though the total energy absorbed by a black coat is much greater
than that absorbed by a white one, the additional heat load from radiation
penetration of the white makes the black coat more suitable for desert
environments. Observations of coat color in desert dwelling animals seem
to confirm this result.
In sparse animal coats, both long and shortwave radiation penetrate the
coat, and it becomes impossible to treat the animal-environment interface
as a definite boundary as we have in this chapter. To deal with it properly
as a continuum, computer models must be used. Porter et al. (1994) have
developed such models and have shown them to work well in ecological
applications. The model has the advantage that it properly treats all of the