Introduction
model. As Albert Einstein is purported to have said: "Everythmg should
be made as simple as possible, but not simpler."
The relation between the spatial scale of some desired prediction or
understanding and the scale of heterogeneity inherent in the system is
essential to the process of simplification. Materials in nature tend to be
heterogeneous, not pure. One of the distinguishing features of human
activity is the tendency to categorize nature into its elements, purify the
naturally occurring mixtures, and reassemble the pure elements into new
arrangements. In nature, homogeneous materials, which are materials
with uniform properties throughout their volumes, tend to be rare. Obviously, if we go to fine enough scale, nothing is homogeneous; therefore
homogeneity depends on spatial scale. In environmental biophysics we
consider natural materials such as soil, rock layers, vegetation mixtures,
and animal coats. The principles that are commonly used in environmental biophysics are most easily understood and used with pure materials.
Therefore a key aspect of environmental biophysics is knowing when
assumptions of homogeneity are adequate, and when a meaningful solution to a problem requires some level of treatment of heterogeneity. Most
often we treat natural media as homogeneous but assign properties that
preserve the major influence of known heterogeneity.
Consider a soil, which consists of a mineral matrix made up ofparticles
of various sizes and characteristics, with organic matter at various stages
of decomposition, air, water, plant roots, worms, insects, fungi, bacteria,
etc. Soil certainly is a heterogeneous medium. However, we can simulate
heat transport on the scale of meters quite well by assuming soil to be
homogeneous with a thermal conductivity that depends on water content,
particle type and size distribution, and density. In the case of soil, the
heterogeneity usually is small (millimeters) compared to the scale on
which we desire to predict heat flow (meters). However, if we wish to
predict the temperature and moisture environments beneath individual
rocks on the surface of the soil because that is where some organism
lives, then we have to deal with the apparent heterogeneity by using
more complex descriptions. In the case of this heterogeneous material
called "soil," various bulk properties are defined such as bulk density,
heat capacity, air permeability, capillary conductivity, etc.
A second heterogeneous natural system of interest to us is a plant
canopy, which consists of leaves, branches, stems, h i t s , and flowers all
displayed with elegance throughout some volume and able to move in response to wind, heliotropism, growth, or water stress. Simple equations
have beenused quite successfully to describe light penetration and canopy
photosynthesis by assuming the canopy to behave like a homogeneous
green slime. In spite of the seeming inappropriateness of describing photosynthesis of a 50 m tall forest canopy by radiation penetration through
a green slime, a convincing intuitive argument can be forged using geometry and statistics of random distributions that is supported by direct field
measurements. In fact, statistics is one of the means used to appropri-
model. As Albert Einstein is purported to have said: "Everythmg should
be made as simple as possible, but not simpler."
The relation between the spatial scale of some desired prediction or
understanding and the scale of heterogeneity inherent in the system is
essential to the process of simplification. Materials in nature tend to be
heterogeneous, not pure. One of the distinguishing features of human
activity is the tendency to categorize nature into its elements, purify the
naturally occurring mixtures, and reassemble the pure elements into new
arrangements. In nature, homogeneous materials, which are materials
with uniform properties throughout their volumes, tend to be rare. Obviously, if we go to fine enough scale, nothing is homogeneous; therefore
homogeneity depends on spatial scale. In environmental biophysics we
consider natural materials such as soil, rock layers, vegetation mixtures,
and animal coats. The principles that are commonly used in environmental biophysics are most easily understood and used with pure materials.
Therefore a key aspect of environmental biophysics is knowing when
assumptions of homogeneity are adequate, and when a meaningful solution to a problem requires some level of treatment of heterogeneity. Most
often we treat natural media as homogeneous but assign properties that
preserve the major influence of known heterogeneity.
Consider a soil, which consists of a mineral matrix made up ofparticles
of various sizes and characteristics, with organic matter at various stages
of decomposition, air, water, plant roots, worms, insects, fungi, bacteria,
etc. Soil certainly is a heterogeneous medium. However, we can simulate
heat transport on the scale of meters quite well by assuming soil to be
homogeneous with a thermal conductivity that depends on water content,
particle type and size distribution, and density. In the case of soil, the
heterogeneity usually is small (millimeters) compared to the scale on
which we desire to predict heat flow (meters). However, if we wish to
predict the temperature and moisture environments beneath individual
rocks on the surface of the soil because that is where some organism
lives, then we have to deal with the apparent heterogeneity by using
more complex descriptions. In the case of this heterogeneous material
called "soil," various bulk properties are defined such as bulk density,
heat capacity, air permeability, capillary conductivity, etc.
A second heterogeneous natural system of interest to us is a plant
canopy, which consists of leaves, branches, stems, h i t s , and flowers all
displayed with elegance throughout some volume and able to move in response to wind, heliotropism, growth, or water stress. Simple equations
have beenused quite successfully to describe light penetration and canopy
photosynthesis by assuming the canopy to behave like a homogeneous
green slime. In spite of the seeming inappropriateness of describing photosynthesis of a 50 m tall forest canopy by radiation penetration through
a green slime, a convincing intuitive argument can be forged using geometry and statistics of random distributions that is supported by direct field
measurements. In fact, statistics is one of the means used to appropri-