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ENERGY BASIS FOR HIERARCHIES IN URBAN
AND REGIONAL LANDSCAPES
By
MARK T. BROWN
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1980
ACKNOWLEDGMENTS
The author was fortunate in having Dr. H. T. Odum as major
professor. His special way of perceiving life was an inspiration and
lent insight into understanding the complexities of many new areas of
study.
My supervisory committee included J. F. Alexander, J. P. Heaney,
E. E. Pyatt and E. M. Starnes who contributed to this dissertation
through their time and energy in reviewing drafts and in discussions
of theoretical concepts. Much help was received from C. D. Kylstra
and I. Winarsky, who were of invaluable assistance through their
personal and intellectual support.
Special thanks are due to the graduate students of Systems
Ecology for sharing many new insights and concepts.
Initial drafts of this dissertation were typed by J. Breeze,
proofing and final typing by J. Cox, and drafting by C. Alfonso . .
all of whom labored long and hard to bring the manuscript to
fruition.
Mapping of the South Florida Region and Lee County was supported
under joint contract to the Division of State Planning, Department of
Administration, State of Florida, and the National Park Service, U.S.
Department of the Interior, H. T. Odum principal investigator.
Mapping of the St. Johns region was supported under joint contract to
the Jacksonville Area Planning Board and the St. Johns River Water
Management District, H. T. Odum principal investigator. Initial
studies of the Ft. Myers urban area were funded by Lee County Board of
County Commissioners, the author, and G. V. Genova principal investi-
gators. Preliminary studies of the Gainesville urban area were funded
by the Division of State Planning, Department of Administration, State
of Florida, J. F. Alexander principal investigator.
Support was also received from the Department of Energy on
contract EY-76-5-05-4398 entitled "Energy Models of the United States"
with the Department of Environmental Sciences, H. T. Odum principal
investigator.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ............................................................ ii
ABSTRACT .................................................................viii
CHAPTER 1 INTRODUCTION.............................. ..................... 1
Theoretical Concepts ................................................ 6
An Energy Basis for Hierarchies.................................. .6
Energy Constraints.............................................. 7
Energy Quality and Embodied Energy............................... 9
Energy Quality and Transport Costs...............................10
Energy Quality and Frequency of Energy Sources...................11
Energy Quality and Power Density.................................12
Energy Spectral Distributions of Hierarchies.....................14
Previous Studies of Hierarchy.........................................15
Hierarchy as Concept............................................. 18
Hierarchical Construction and Rate of Evolution..................22
Hierarchical Systems and Connectivity............................23
Hierarchically Organized Systems and Stability...................24
Central Place Theory .............................................25
Settlement Location............................................ 29
Rank Size and Primacy of Cities..................................30
Landscape Evolution............................................ ..32
Social Process Model of Urban Growth.............................33
Hierarchical Distribution of Components in Systems...............35
Hierarchy in Social Systems.......................................37
Computer Simulations of Hierarchically Organized Systems.........42
Description of the Study Area........................................43
South Florida Study Area........................................ 43
St. Johns Study Area............................................ 46
Lee County Study Area...................... .......................47
Ft. Myers Urban Study Area...................................... 47
Gainesville Urban Study Area.....................................48
Plan of Study ......................................................... 48
CHAPTER 2 METHODS........................................................50
General Methods and Definitions.......................................50
Evaluation of Observed Hierarchies....................................55
Regional Analysis .................................................. 55
Land Use Maps ....................................................55
Gross Productivity of Land Uses..................................56
Classification of Cities by Average Power Density................65
Energy Budgets of Regions........................................65
Power Base for Cities............................................67
Investment Ratios....................................... .......68
Analysis of Energy Flow and Structure of Urban Systems ................68
Land Use Maps................................................. 69
Urban Land Use Power Densities...................................69
Average Urban Power Densities....................................75
Structure of Urban Land Uses.....................................75
Development Density and Imports/Exports...............................76
Analysis of Counties within Florida..............................76
Analysis of States within the United States......................77
Analysis of Countries............... .............................78
Embodied Energy Transformation Ratios (Quality Factors),
and the Range of Goods ............................................ 78
Embodied Energy .................................................. 79
Transformation Ratios (Quality Factors)..........................80
Calculation of Transformation Ratios.............................80
The Range of Goods............................................... 83
Simulation Models of Hierarchical Organization and
Energy Spectra.................................................. 83
CHAPTER 3 RESULTS....................................................... 89
Similarities of Differing Systems and Scales..........................89
Regional Hierarchies and Energy Spectra...............................99
Regional Land Use.............................................. 99
Energy Flow and Structure in Regional Systems...................114
The Landscape of Cities within Regions..........................120
The Flows of Energy in a Regional Hierarchy: Lee County........145
Development Density and Import/Exports...............................166
Development Density and Exports of Counties in Florida..........166
Development Density and Exports of States within
the United States.......................................... 187
Development Density and Exports of Countries....................187
Energy Flow and Structure in Urban Systems...........................192
Power Density and Volume of Structure...........................192
Chemical Potential Energy of Urban Land Uses....................198
Transformation Ratio (Quality Factor) of Urban Structure........203
Embodied Energy, Transformation Ratios (Quality Factors),
and the Range of Goods.......................... ..................208
Embodied Energy and Transformation Ratios .......................208
The Range of Transport of Goods.................................211
Simulation of Models of Hierarchical Organization and
Energy Spectra.................................................. 211
Theoretical Models.............................................. 213
Aquatic Food Chain............................................ 239
CHAPTER 4 DISCUSSION ................................................... 275
Rank Size Distribution of Components of Hierarchies..................276
Distribution of Increasing Quality Value in Hierarchies..............276
Evaluation of Embodied Energy and Transformation Ratios in
Hierarchically Organized Systems..................................277
Energy Quality in an Ecosystem Hierarchy.............................277
Energy Quality and Spatial Effect....................................283
Energy Convergence in Landscape Hierarchies..........................284
Energy Divergence (Dispersion) in Landscape Hierarchies..............284
Control Actions of High Quality Components...........................285
The Range of Transport of Goods as a Function of Quality.............286
Primary and Secondary Energy Sources and Their Effect on Hierarchies.287
Frequency of Energy Sources and Time Constants of Components.........288
Stability Through the "Filtering" Actions of Hierarchies.............291
High Quality Stress and Stability....................................293
A Theory of Regional Boundaries Derived from Place in the
Landscape Hierarchy...............................................293
Land Use Planning and Carrying Capacity..............................295
Parting Thoughts and Suggestions for Future Research.................299
APPENDIX 1-DESCRIPTION OF THE ENERGY LANGUAGE.............................301
APPENDIX 2-DESCRIPTION OF LAND USE CLASSIFICATION FOR REGIONAL
LAND USE MAPS........................................................ 303
APPENDIX 3-CHEMICAL POTENTIAL ENERGIES OF REPRESENTATIVE COMMODITIES......313
APPENDIX 4-TOTAL AREA, EMBODIED ENERGY, AND CHEMICAL POTENTIAL
ENERGY OF URBAN LAND USES IN THE UNITED STATES.........................315
APPENDIX 5-DYNAMO PROGRAMS FOR MODELS AND SIMULATION RESULTS
PRESENTED IN FIGURES 3.26 THROUGH 3.53.................................318
REFERENCES ................................................................347
BIOGRAPHICAL SKETCH ................................................ ...... 358
Abstract of Dissertation Presented to the Graduate Council of
the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ENERGY BASIS FOR HIERARCHIES IN
URBAN AND REGIONAL LANDSCAPES
by
Mark T. Brown
August 1980
Chairman: Howard T. Odum
Major Department: Environmental Engineering Sciences
Flows of energy were related to the hierarchical organization
of urban and regional systems to test theories of energy control of
landscapes. Energy models and spectral graphs were used to represent
landscape systems as hierarchical organizations and show common
patterns. Data were assembled from landscapes of Florida and other
systems of the nation.
Regional networks of cities, land use, urban structure, energy
sources, and quality of goods were related to hierarchical
organization. The hypothesis of selection for maximum power was used
to explain the relevance of hierarchical organization of systems,
where spatial extent of components and frequency of energy sources
were related to energy quality and convergence of energy.
The embodied energy inflowing to cities was used as a means of
classifying hierarchical role of cities, and range of region as well
as area of region were calculated. The five classes of cities that
resulted had total embodied energy flow per year in Calories of coal
equivalents (CE) as follows: 182.4 x 1012 Cal CE/yr, 89.0 x 1012
Cal CE/yr, 16.7 x 1012 Cal CE/yr, 4.9 x 1012 Cal CE/yr, and 0.6
viii
x 1012 Cal CE/yr. Range of region was derived by dividing
embodied energy flow of each city by the average embodied energy flow
for the region in which it was embedded, and varied from a high value
of 50.0 miles for the largest city to 2.9 miles for the smallest.
The propensity to import and export was related to the
development density of regions and then position in hierarchy. A
series of nomographs were drawn where exports increased in an apparent
linear relationship with development density. In general, the
nomograph derived suggested the following relationship between exports
and development density:
Exports/sq mi = C x Development Density (expressed as dollars of
Gross Domestic Product [GDP]/sq mi), where C varied from 0.13 to 0.285
depending on the size of region.
The power density and volume of structure associated with 11
different urban land uses were calculated using data from Ft. Myers
and Gainesville, Florida. Volume of structure and power density were
strongly related as both increased simultaneously with increasing
complexity of land uses.
Energy transformation ratios (quality factors) were calculated
for a number of goods and energies from dollar costs per pound and
were used to estimate the range of goods. Quality factors for goods
ranged from 1.3 Cal CE/Cal for finished wood to 2230 Cal CE/Cal for
computers. Ranges (or the distance traveled to obtain a good),
expressed in the number of miles traveled to obtain a pound of good
varied from 0.5 miles/lb for finished wood to 381 miles/lb for
computers. The energy quality of urban structure collectively was in
the range of 20 Cal CE/Cal.
The dynamic properties of 7 configurations of hierarchically
organized models were analyzed through computer simulation. The
models were organized in a five-compartment chain of autocatalytic
consumers with outside driving energy sources. The most stable form
had multiplicative feedback interaction from higher order components
to lower order components, and second order drain on each component.
Other configurations showed marked instability and oscillation when
perturbed away from the steady state solution.
A simulation of hierarchical organization was done using a model
of Lake Conway ecosystem previously evaluated. Simulations tested
were: stocking, harvesting, and pulsing energy source. The simulation
of perturbation responses suggested that stability is enhanced by
hierarchic organization.
The theory of energy control of hierarchically organized systems
provided suggestions for determining carrying capacity of human
activity in regions, and possible effects on the organization of the
landscape with decreasing availability of fossil fuels.
It is suggested that regional landscapes of man and nature form a
hierarchy with qualities measurable from their embodied energy, and
that spatial distribution of quality, value, and human activity may be
predicted from energy distributions.
CHAPTER 1
INTRODUCTION
Complex systems such as ecosystems, industrial processes, and
networks of cities in the landscape appear to be organized in webs of
energy flow with multiple levels of components (Fig. 1.la). These may
be visualized in simplified form with diagrams as in Fig. 1.1b. The
patterns have spatial manifestations, with many small units converging
energy to a few larger ones (see Fig. 1.la). Understanding these
hierarchical patterns is a major objective in the sciences of
environmental and human settlement. This dissertation is an
investigation of the relation of energy flows to hierarchies of the
regional and urban landscape.
Energy storage and flows throughout the landscape accompany
spatial hierarchies, as in Fig. 1.2a, and can be represented as
spectra, as in Fig. 1.2b. Theories developed to account for these
hierarchical patterns may be based, in part, on the theory that
systems compete for power, and survive by developing a structure of
energy flows that maximizes useful power. The maximum power principle
was enuciated by Lotka (1922) and additional corollaries were proposed
by Odum (1967, 1971, 1975, and Odum and Odum 1976). The type and form
of web adapting to different combinations of energy from the
environment produces different spectral distributions and spatial
patterns, which may be predicted from simple models.
Figure 1.1 The web of energy flow and components of complex systems.
(a) Showing many small components converging energy to a few large
ones; and
(b) a simplified diagram where like components are grouped, and
hypothetical flows of energy between components are indicated.
INCREASING SIZE OF COMPONENTS
DECREASING NUMBER OF COMPONENTS
Control Action Feedback
INCREASING QUALITY OF ENERGY
DECREASING QUANTITY OF ENERGY
Figure 1.2. Hierarchies that develop in a hypothetical landscape as a result of
energy storage and flows.
(a) Spatial hierarchy of hexagonal land areas, where smaller areas
converge energies to larger areas, and larger areas in turn
feed back energies to the smaller ones.
(b) Simplified energy circuit model organized as a chain of
autocatalytic units. Each unit represents all the land area at
each level of the landscape hierarchy.
(c) Hypothetical energy spectral distribution resulting from theory
of successive energy transformations. The general trend is for
landscape hierarchies to be composed of many small components
and fewer and fewer larger components.
&
Energy analysis diagrams help to relate energy flow and kinetics
of system performance, since they are a way of writing differential
equations that are easy to relate to data on energy flow. The energy
diagrams also help to provide overviews of organizational relation-
ships, and may help to combine concepts of economics, geography, and
ecology.
In this dissertation data on regional and national patterns of
landscape organization are used to test theories of energy flow con-
trol of hierarchy. Simulation models are developed to quantitatively
relate ideas of mechanism and energetic to web structure, spatial
pattern, and spectral distributions observed in the hierarchies of
humanity and nature. Systems studied were two urban areas in Florida
(Ft. Myers and Gainesville), two large watersheds of Florida (the St.
Johns River Basin, and the Kissimmee Okeechobee Basin), a county in
southwest Florida (Lee County), the national patterns of energy flow,
and for comparison, various other types of hierarchies.
Theoretical Concepts
An Energy Basis for Hierarchies
Given in Figs. 1.1 and 1.2 are simplified energy circuit models
(Odum 1971) that depict energy flow and storage in hierarchically
organized systems. These diagrams show energy flow and control action
feedbacks in five compartment (level) hierarchies, and are the basic
configuration for the organization of data in this investigation of an
energy theory of hierarchically organized systems.
The following concepts and theories about the relationship of
energy, its spatial distribution and resulting hierarchies, are
postulates and are the basis for examining data on systems of Florida
and the nation.
Energy Constraints
Systems operate under the constraints of the First and Second
Laws of Thermodynamics, and Lotka's Maximum Power Principle (Lotka
1922) and corollaries as proposed by Odum (1975) and Odum and Odum
(1976) and are organized in a manner to remain competitive and stable
and increase inflowing energy when excess energy is available.
The organization of complex systems in a hierarchy of energy flow
and control action feedbacks may be a fundamental principle of all
systems of man and nature. As systems concentrate energy and build
storage, gradients of potential energy are created at each level of
concentration; but at the same time, much energy is degraded at each
level as a necessary by-product of production. Thus less and less
potential energy is available at each level to support successive
levels; and a hierarchy may emerge as a consequence of the "Law of
Degradation of Energy."
A basic question that is analyzed in this dissertation that
follows from the law of degradation of energy is "what relationship,
if any, exists between the total energy inflowing to a system and the
distribution of that energy amongst the levels within the system?" To
address this question, regional landscapes, urban landscapes, and a
natural ecosystem are organized as hierarchies and their energy
budgets and the distribution of energy within them are analyzed.
Complex systems not only concentrate energy in landscape
hierarchies, but disperse energy as well through divergence of
feedbacks and control actions. Inflowing energy is concentrated and
converged in successive levels of hierarchies as storage of high
quality energy, and is fed back in dispersing actions from higher
levels to lower ones. In general, as energies are stored and become
more concentrated through landscape convergence, they occupy less
area, but their spatial effect becomes greater. This spatial aspect
of hierarchically organized systems is addressed in this dissertation
by analyzing data from the regional landscapes of south Florida and
the St. Johns Rivers Basin, Lee County, Florida, and by analyzing the
quality and range of transport of various goods.
The principle of selection for maximum power suggests that those
systems that survive in competition with alternative choices are those
that develop the most power inflow and use it most effectively to meet
the needs of survival. Systems maintain competitive position, and
remain adapted and stable by building storage of high quality energy,
feeding back work and control actions from storage to increase
inflowing energy, generating diversity to increase energy inflowing
from other sources, and exporting energies to other systems to obtain
energies that are in short supply. Hierarchical organization of
systems may be a form of specialization that enables the development
of high quality storage that when fed back have higher amplifier
value than their cost. Thus hierarchical organization may enhance the
total systems ability to increase energy inflow, and remain adapted
and stable. The question of stability resulting from hierarchical
organization is addressed in this dissertation by simulating various
configurations of five level hierarchy models and simulating
perturbations of hierarchically organized systems to test recovery and
overall effect of stress.
Energy Quality and Embodied Energy
Odum (1976, 1977, 1978, 1978a) and Odum and Odum (1976) suggest
that there is a quality to energy which is a measure of its ability to
do work. Quality of energy is related to the degree to which it is
concentrated; with dilute energies like sunlight, winds, waves, and
other natural energies having lower quality than the more concentrated
energies of fossil fuels.
The quality of an energy is derived from the embodied energy of
flows and storage that are the result of the convergence property of
systems. Energy quality factors (transformation ratios) are defined
as the ratio of heat energy produced by a system to the total energy
utilized to power the system. As energies are converged in
hierarchies, less heat equivalent energy is produced in successive
levels as energy is dissipated at each level. The embodied energy at
each level is the total energy that powers the entire system; thus the
ratio of embodied energy to heat equivalent energy (quality factor)
increases with each successive level in the hierarchy.
Under the constraints of the Maximum Power Principle, a
theoretical relationship between the costs and the effect of an energy
is related to its quality. The Maximum Power Principle suggests that
systems that maximize their flows of energy survive in competition,
and that surviving systems are those that can generate inflows of
energy at least equal to the costs of doing so. Therefore, in the
long run, the costs of upgrading an energy must at least equal its
effect in causing to inflow more energy.
The quality of many energies and materials are calculated in this
dissertation from embodied energy. Energy quality is related to
position in a regional landscape system and in an aquatic ecosystem,
and is calculated from the total energy required to power each system
as suggested by Odum (1978).
Energy Quality and Transport Costs
In general, as the quality of energies increases, their
concentration increases as well. One theory held by Odum (see Odum et
al. 1976) suggests that transportation costs decrease with increasing
quality of energy as suggested by their increasing concentration.
Since the embodied energy in a good or energy is believed to be a
measure of the quality of that good or energy, it follows that as
embodied energy per unit of good or energy increases, the energy costs
of transportation per unit decreases. Theory suggests, then, that the
greater the embodied energy in a good or energy, the greater is the
range of the good or energy; where range is defined as the distance
over which the good or energy is transported to point of end-use.
Ranges of transport for many goods were related to the quality of
the goods, based on the theory of value of effect (utility) rather
than on a theory of minimizing costs. The embodied energy of goods is
strongly related to the concept of market area as enunciated by
Christaller (1966) for different order goods originating from
different order central places; is shown in this dissertation to be
related to spatial effect in graphs of the spatial distribution of
incoming energies and market areas of cities.
Energy Quality and Frequency of Energy Sources
Recently, Odum (1980) and Alexander (1978) in earlier studies of
the cycles of order and disorder, have suggested that the quality of
an energy is related to its frequency in the time domain. Others (see
Simons 1973) have suggested that frequency and place in hierarchy are
related to the extent that high frequency is associated with low place
in hierarchical order and low frequency with high hierarchical place.
Theory suggests that systems and components of systems may be
adapted to certain frequencies of energy inflow, and that the
magnitude and frequency of energies in the environment may be of
fundamental consequence in selecting which systems survive the test of
time. Examples of adaptation to differing frequencies are common.
Ecosystems and associated structure that live in areas of daily tidal
influence show many adaptations to the frequency of tidal exchange.
Seasonal frequencies in temperate climates control behavior of animal
population, select for certain plant species, and select against
others.
One mechanism for adaptation to certain frequencies of energy
inflow may be the relative time constant of systems. Systems and
components of systems with very short time constants, in general are
associated with high frequency energy inflows, while the reverse is
true for systems with long time constants. Components of systems at
different levels in hierarchies may be adapted to certain frequencies
of energy inflow as a consequence of their time constants. The
general trend is for time constants to increase with increasingly
higher order in the hierarchy.
Adaptation to high frequency may be easier than adaptation to low
frequency; for high frequency energies are believed to be low in
quality, and magnitudes of energies tend to be lower. Thus systems
with long time constants "perceive" high frequency as relatively
constant inflow, but very low frequency inflow may be perceived as
less predictable and "pulsing" in character. Alexander (1978) has
suggested that energies that are considered catastrophic are those
with very low frequency such as earthquakes, volcano eruptions,
floods, and hurricanes; and suggests that adaptation to less
predictable pulses such as these are less common than adaptation to
higher frequency energy inflows.
The relationship of frequency to energy quality and the time
constants of components of hierarchically organized systems is
analyzed in this dissertation using data from the regional landscapes
of south Florida and the St. Johns study areas. Simulations of
different configurations of hierarchically organized models where time
constants are varied and where frequency of inflowing energy sources
are varied are also analyzed to test the relationship of frequency to
time constant of components.
Energy Quality and Power Density
One measure of the intensity of energy utilization in the
landscape is power density (Odum, Brown, and Costanza 1976), or the
rate of energy flow per unit area (Cal/acre year). In this
manner, the energy intensity of one area can be compared on a relative
scale with others. In urban systems, power density is considered to
be the rate of embodied energy consumption per unit area, and in
natural ecological systems of the landscape, power density is the rate
at which energy is fixed, as measured by gross primary production.
While it may seem that two different measures of power are being
applied here, it must be remembered that it is embodied energy that is
being considered, and that there is no difference between production
and consumption. That is to say, if one expressed the output of any
process in equivalent energies of the input, then production is equal
to the embodiment of all input energies.
Urban land-use power densities are expressed as two different
types: electrical and other primary fuels power density, and embodied
energy of goods and services power density.
Total power density of urban land uses is the addition of two
types of energy inflows: that inflowing from electricity and other
primary fuels, and that embodied in goods and services.
High power densities are only possible where there are sufficient
high quality energies inflowing to sustain them. Thus, the degree of
complexity and amount of structure per unit area is in direct
proportion to the amount of high quality energy available. Due to the
convergence of energies in hierarchies, less and less total structure
is associated with higher levels, but the structure in each level is
of a higher quality.
Power densities of urban land uses in the Ft. Myers and the
Gainesville study areas are analyzed in this dissertation and compared
to structural properties as well as place in hierarchy, and a quality
factor (transformation ratio) is calculated for urban structure as a
whole. A classification scheme that is based on power density is
developed for cities and is related to market area (as proposed by
Christaller 1966) and support area.
Energy Spectral Distributions of Hierarchies
The complex systems of multiple levels of components appear to be
organized in webs of energy flow. However, when visualized as chains
of energy flow, as in Fig. 1.la, much of the complexity disappears and
a useful overview appears. Viewed, as in Fig. 1.1b, complex systems
may be simplified as energy chains where energy is transformed in
series. In each step some energy is used, some is dispersed, and some
energy is upgraded in quality and passed on to the next unit in the
chain.
In various recent publications, Odum (1977, 1979; and Odum and
Odum 1976) suggests that systems are organized in hierarchical fashion
to increase total power flow by cascading energy up the chain and
control actions back down. Low quality energies are concentrated,
increasing their quality, and passed on to the next step in the chain.
An energy spectrum results that has many downstream components and
fewer and fewer upstream components. When graphed, as in Fig. 1.2,
the organization exhibits a declining exponential function when energy
per unit is plotted against the number of units having that energy
intensity.
If additional higher quality energy sources are available in the
environment, then systems develop whose energy sources are a mixture
of high and low quality, and the spectral distribution may not show a
simple exponential decay. High quality sources are utilized in the
system where their quality nearly matches that of the energy intensity
of the units in the spectrum (Odum 1979). A spectrum results that has
a "hump" where the second higher quality source is introduced, as
shown in Fig. 1.3.
When regional landscapes are organized as a hierarchy of
components, higher quality energy sources such as fossil fuels and the
goods derived from them, are seen to inflow and interact at levels in
the hierarchy where their quality nearly matches the quality of the
components at that level. Models of regional landscapes developed in
this dissertation incorporate this feature, and theoretical models are
developed to test the theory that energy spectral distributions are
altered significantly when secondary, high quality energies are
introduced into hierarchical organizations.
Previous Studies of Hierarchy
Many theories for hierarchical organization, and the resulting
distributions of components, dating from antiquity, are presented in
the following section. In all, the theories, observations, and
explanations presented in this review comprise a general overview of
hierarchy theory, spatial distribution in hierarchies, regional
economic theory as it relates to hierarchy, hierarchy in social
organization, geographic models for hierarchically organized
landscapes, and various other aspects of hierarchically organized
systems. Few previous studies have dealt with the energy control of
landscape hierarchies, but may with the economic aspects and some with
the physical constraints of hierarchical organization.
Figure 1.3. Energy spectrum that results from the introduction of a second
energy source of higher quality. Theory suggests that the second
higher quality source is introduced where its quality nearly
matches that of the units in the chain.
N
Ns
N
N
S\ 04
1000 2000 3000
1000 2000 3000
ENERGY PER
INDIVIDUAL
(b)
-_j
z 10 -
LU
,-
w
103-
0
L-
0
Z i -
4000
5C00
18
Hierarchy as Concept
Hierarchy denotes a mode of thought that asserts order into a
conception of the universe in terms of precisely arranged levels of
organization. Usually the levels are vertical in dimension . from
small to large; many to few; simple to complex. Plato provided a
basis for hierarchic levels of existence in what has been termed "the
principle of plentitude," which is to say that the levels of existence
are interlocked so as to yield a full universe. This principle sets
the stage for an infinite universe (The Dialogs of Plato, translated
by B. Jowett).
Aristotle, on the other hand, conceived of a finite universe
where "nature proceeds little by little from things lifeless to animal
life in such a way that it is impossible to determine the exact line
of demarcation, nor on which side thereof an intermediate should lie"
(Historia Animalium, Book VIII, Chapter I, p. 558a, translated by D.
W. Thompson).
The conception of a hierarchically organized universe was made
explicit by numerous writers during the Renaissance, and given a new
descriptive phrase . the scale of nature" (Milton, Paradise
Lost, Book V, line 9, p. 113), yet still very much grounded in the
ideas of Plato and Aristotle.
During the Middle Ages hierarchy played an important role,
especially in the work of Saint Thomas Aquinas, where he suggests that
formal distinction always requires inequality. "Hence in natural
things, species seem to be arranged in degrees; as the mixed things
are more perfect than the elements, and plants more than minerals, and
animals than plants, and men than other animals; and in each of these
one species is more perfect than others (Summa Theologica, First
Part Question 47, Article 2, vol. 2, p. 260).
This concept of hierarchy entered the eighteenth century deprived
in most instances of its religious overtones, as Locke wrote of the
"Chain of Being" in An Essay Concerning Human Understanding (1690).
".. the species of creatures should also, by gentle degrees, ascend
upward from us . as we see they gradually descend from us
downwards" (Book III, Chapter VI, Article 12, vol. 2, p. 217).
Gradually the concept of hierarchy was extracted from its narrow
confines as an explanation of the "Creator's Order" and scientific
thought prevailed. With the publication of The Origin of Species in
1859, Darwin converted the traditional "Scale of Nature" into a
hierarchical system which for all intents and purposes was a system of
classification only, not a reflection of reality. In his summary to
Chapter 14 Darwin states . I have attempted to show that the
arrangement of all organic beings throughout all time in groups under
groups--that the nature of the relationships by which all living and
extinct organisms are united by complex, radiating, and circuitous
lines of affinities into a few grand classes, . all naturally
follow if we admit the common parentage of allied forms . ." (Darwin
1859, p. 456).
By the turn of the twentieth century the term hierarchy was in
frequent use; from taxonomy to models for a hierarchical universe. As
the amount of published scientific literature has grown exponentially
in the last 80 years so has the number of scientists using the term,
the idea, the concept, in the analysis of physical, biological and
social systems (Whyte 1969). Most notable in the latter years are:
Woodger, Whyte, Von Bertalanffy, Simon, Wilson, Weiss, and Laszlo.
Woodger (1937) defined the principles of hierarchical order using
mathematical logic, and previous to this (Woodger 1929) suggested an
"organismic theory" of biology where the organism is a hierarchical
system. Further, he says that ". . the organism is a hierarchical
system with an organization above the chemical level . that
requires investigation at all levels . ." (Woodger 1929, p. 14).
Whyte (1949) calls for a "unitary principle" of nature that could
account for the development of regular spatial forms. The principle
states that asymmetry decreases in isolable (capable of being
isolated) processes. Whyte treats nature as processes rather than as
objects or products and concludes that nature is a disturbed system of
systems, and there is never anywhere a final end to process. He sees
systems as being parts of other more extensive systems that develop
their own inner symmetry always in relation to their next larger
system, and so to conform to the general state of the universe.
The hierarchical mode of organization is suggested by Von
Bertalanffy (1932) as a fundamental principle of biological law, and
becomes a major principle of his General System Theory. In later work
Von Bertalanffy (1933) identified four types of hierarchical order:
division hierarchy, spatial hierarchy, genetic hierarchy, and
hierarchical segregation. Most recently he suggests two possible
divisions of hierarchy: structural and functional hierarchies, but
hints that "In the last resort, structure and function may be the very
same thing . ." (Von Bertalanffy 1968, p. 27).
Simon (1962) in his paper "The Architecture of Complexity"
suggests that complexity frequently takes the form of hierarchy, and
defines a hierarchical system as a system composed of interrelated
subsystems, each of the subsystems being in turn hierarchic in
structure until we reach some lowest level of elementary subsystem.
Laszlo (1972) suggests that all living things are phases in the
organization of the biosphere, and that they are wholes in one cut and
parts in another, and their own parts are systems on their own level,
and even their parts are that, until one scrapes the bottom of the
hierarchy with the atom and its elementary particles.
Whyte (1969) traces the idea of hierarchy from Plato's sequence
of higher and lower levels to the present, and suggests that the time
has arrived for the gradual development of a comprehensive physical
theory of the structural hierarchies of nature. He goes on to suggest
that structural hierarchies are more easily understood in terms of
discrete particles, rather than by using a field or continuum
representation. Here Whyte is using particle as Bunge uses level.
Bunge (1960, 1969) addresses the subject of hierarchy by enumerating
the use of the term level. He identifies nine different meanings for
the notion of level, but considers an appropriate definition of level
to be grades of being ordered, not in arbitrary ways, but in one or
more evolutionary series. He limits the use of the notion of level to
include both the idea of emergence in time without restricting the
direction, and the fact that level structure need not be restricted to
linear gradation . but can be parallel or branched.
Mesarovic and Macko (1969) generate a mathematical theory of
coordination within hierarchical systems based on linear programming
models of minimizing overall costs by deriving values for local
control and input (at sublevels). They contend that the explanation
of the functioning of a hierarchical system should not be attempted in
terms of the overall goal, but rather in terms of the specific goals
valid for each particular level. Further, they suggest that a
frequently made mistake is to assume the highest level unit is in
charge of the overall goal. It has its own goal . that of
coordination . and the overall goal is achieved only by the
combined action of all units.
Hierarchical Construction and Rate of Evolution
Simon (1962, 1973) argues that the advantage of modularization as
outlined in the image of two watchmakers, one who makes watches in
modules, the other assembling watches element by element, suggests
that complex systems evolve far more quickly when hierarchically
organized. Simon (1973) states:
Specifically, on the simplest assumptions, the mathematical
model shows that if a system of K elementary components is
built up in a many-level hierarchy, and S components, on the
average, combine at any level into a component at the next
higher level, then the expected time of evolution for the
whole system will be proportional to the logarithm to base S
of K. In such a hierarchy, the time required for systems
containing, say, 1025 atoms to evolve from systems
containing 1023 atoms would be the same as the time
required for systems containing 103 atoms to evolve from
systems containing 10 atoms.
Another property of hierarchical systems is that they are nearly
decomposable. Decomposable systems (as outlined by Simon 1962, 1973)
are systems that can be broken up (in thought or analysis) into
subsystems such that the interactions within the subsystem are
relatively strong and numerous. Wilson (1969) calls the boundaries
along which systems can be decomposed natural interfaces, and suggests
that these interfaces can also be identified through the existence of
some form of closure. There are two forms of closure: tropological
closure . the encompassing by closed surfaces of a spatial
neighborhood that coincides with or bounds the extension of a physical
object, and temporal closure . a type of closure associated with
a neighborhood in time that coincides with or bounds the donation of
an entity. He suggests that a group may be defined not only by
interactions, but by operations and defines these as cyclical closure.
Levels may also be distinguished by a characteristic time or
frequency, which is to say that each level is temporally closed; thus
space and time are forms of closure.
Hierarchical Systems and Connectivity
A fundamental property of systems is their connectivity, or the
number of subsystems and the strength of their interaction. Levins
(1973) argues that any collection of interacting subsystems will
naturally evolve away from a homogeneous (uniform) totally connected
network (considered to be maximum complexity) to simple, persistent
relations, that are hierarchical in nature. These hierarchical
relations within a single network will overlap with like relations in
other networks causing dynamics that again will be too complex, and
which in turn will evolve into new hierarchical simplifications. This
complexity of connectivity is self-limiting, such that any small scale
connections that do not become hierarchically organized lose
significance.
Platt (1969) gives theorems of boundary conditions effecting
connectivity, and the relationship of boundary conditions to internal
structure of subsystems within networks. He suggests that when
comparing systems of different sizes (complexities) that connections
with the environment that are carried on over the whole boundary
surface at one level of sizes are carried on through specialized gates
at higher level sizes, and that the number of connections of any
system (subsystem) in general has a lower dimensionality than the
number of nodes within the subsystem itself.
Hierarchically Organized Systems and Stability
Levins (1973) suggests that low connectivity (and thus a high
degree of hierarchical organization) gives high repeatability,
allowing such systems to be selected. Thus, natural selection results
in a hierarchical structuring of clusters of components. At any level
components within the same cluster interact strongly, but different
clusters interact only loosely.
Weiss (1971), using variance to describe stability, suggests that
the total variance of a whole system is infinitely less than the sum
of the variances of its aggregate/components. The total system
preserves a high degree of invariability. He suggests that stability
results from hierarchically derived coordinating interactions, for
with incessant erratic fluctuations of components' local environments
total harmonious performance is impossible.
In general, overall increases in the level of organization tend
to increase cybernetic stability of systems and the diversification of
their properties, and structural instability and decreasing numbers
(Laszlo 1972). Thus, structural stability is proportional to
primativeness in level of organization, whereas cybernetic stability,
manifested as an increasing variety of self-stabilizing functions and
properties, is proportional to complexity. Laszlo (1973) gives the
example of complex organisms, such as mammals, as being more
vulnerable than protozoa, but are able to cope with environmental
changes that could be lethal to the latter.
Central Place Theory
Walter Christaller in 1933 (1966), suggested a basic theory to
answer the questions: Why do urban hierarchies exist, and what
determines the size and spacing of cities and the configuration of
their market areas in such hierarchies? To control extraneous
variables in answering these questions, Christaller made some
simplifying assumptions: First, he assumed identical consumers
distributed uniformly over an unbounded plane, and second, access
between all points of the plane was equally easy in any direction.
Therein lies much of the criticism of central place theory.
Christaller's conceptual framework may be summarized in six
points:
1. The market town's main function is to provide goods and services
for the surrounding market area, and those market towns are
located centrally within their market areas.
2. The more goods and services provided, the higher is the order of
the central place.
3. Low order goods (convenience goods) that are purchased frequently
are provided by low-order places because the maximum distance
consumers will travel (range) is small.
4. Higher-order places are fewer in number and are more widely spaced
than lower-order places providing goods with greater ranges.
5. Consumers have a basic desire to travel as little as possible to
obtain the goods and services they need, and producers must have a
minimum sales level (depending on the range of the good) to make a
profit. Thus, a hierarchy of central places exists to facilitate
both consumer and producer.
6. Hierarchies have three spatial forms, organized according to:
1. A marketing principle
2. A transportation principle
3. An administrative principle
The marketing principle assumes that the location of a central
place of any order is at the midpoint of each set of three neighboring
places of the next higher order. Thus, a hexagonal market area was
derived where the corners of the hexagon are occupied by centers whose
order is one less than the order of the center at the centroid of the
hexagon. This first principle generated a rule of 3, or each center
of a higher order is surrounded by the equivalent of 3 market areas of
the next lower order.
A satisfactory transportation system is difficult to establish
under such a spatial organization. To accommodate transportation
networks, Christaller adjusts his original thesis somewhat so that the
distribution of central places is most favorable when as many
important places as possible lie on one traffic route between two
important towns. By shifting centers from the apex of the hexagon to
the midpoints of the sides of the hexagon, a nesting of hexagons
inside one another according to a rule of 4 is achieved (for every
center of a given order there will be 4 market areas of the next lower
order, and 3 places of the next lower order). But another problem
arose: the overlapping of smaller regions across the boundaries of
higher-order complementary regions is inconsistent with administrative
organization. To solve this dilemma, the central place of
higher-order administers to the total area of the six surrounding
low-order market areas, thus following a rule of sevens.
August Losch (1954) took Christaller's model one step further;
still assuming, however, a wide homogeneous plane containing only
self-sufficient farms that are regularly distributed in a hexagonal
pattern. He then showed how an economic landscape could be built from
the lowest order centers upwards.
Losch thought it desirable because of the complexities of the
real world, to devise a compound hierarchy incorporating all the
possible arrangements of hexagons. An economic landscape around a
single metropolitan center resulted. The landscape was divided into
six city-poor and six city-rich sectors surrounding each metropolitan
center.
Both Christaller and Losch agree that the triangular/hexagonal
arrangement of production, or consumption sites represented the
optimal spatial organization for a single good. Their fundamental
difference is in the way spatial patterns of centers and market areas
are built. Their theories of spatial patterns among cities are based
on three concepts: range, threshold, and hierarchy.
These theories do not help to understand the interrelationships
between the size and spatial structure of the regional urban hierarchy
and regional growth. Richardson (1973) states that this difficulty
arises from the fact that there are no satisfactory theories for
explaining how hierarchies evolve, for Christaller's central place
theory, and Losch's market areas have no serious dynamic content and
thus have little value for exploring the regional growth process.
The critics of central place theory have identified at least four
specific weaknesses (see Beckmann 1955; Van Boventer 1969; Henderson
1972; and Timbergen 1968). First, central place theory assumes a
homogeneous plane. Second, it assumes a uniform geographical
population distribution, with no adjustment made for uneven population
distribution and greater local demand of large urban areas. Third,
interurban trade is unidirectional, i.e., large urban areas export to
smaller areas, but smaller areas do not export to larger ones. And
fourth, the rigid spacing is inconsistent with this uneven demand
generated by different sized urban areas.
Henderson (1972) developed a linear programming model which
eliminates uniform population distribution, and allows two-way trade.
Dokmeci (1973) presents a linear programming model that allows two-way
trade, and transport costs are minimized subject to cost constraints.
Purver (1975) developed a mixed integer linear programming model which
determines the optimal spatial allocation of productive and
residential activities in a central place framework. The model allows
two-way trade and eliminates uniform population densities.
While central place theory does not address adequately the
question of how hierarchies evolve, it does address why they evolve.
The cornerstone of central place theory is economies of scale; which
provide the only incentive for urban areas to arise in the central
place model.
Theorists have used gravity models and equations of diffusion for
allocating regional influence of centers and calculating the spread of
innovation from center to center; and more recently the use of
information theory to suggest the probability of spatial diffusion
(see Mansfield 1963; Beckmann 1970; Berry 1972; Hagerstrand 1966;
Isard and Peck 1954; and Beckmann 1956). However, while these models
do address the question of gradients, and flows of information from
center to center, there still remains the question of how hierarchies
evolve.
Settlement Location
Since the first explicit statement of a regional urban hierarchy
by Christaller (1966) in 1933, much empirical evidence has been
gathered and analyzed to support the concept of a hierarchically
organized landscape of urban centers. Early models of spatial
interaction like those of Reilly (1929) and Tuominen (1949),
suggesting that the pull exerted by a place varies directly with its
size and decreases outwards with distance, were the beginning of
settlement location theory. Known as regular cluster models, they
suggest that smaller places are not likely to develop as close to
large places as they are to one another. Empirical evidence of
clustering is not conclusive; however Brush (1953) and later Dacey
(1962) analyzing hamlets in Wisconsin, found that clustering of
hamlets was apparent in areas furthest from larger towns.
Spacing of settlements is shown to be linked to the size of
settlement by Brush and Bracey (1955) in studies of settlement
patterns in Wisconsin and southern England. Later studies by Olsson
and Persson (1964) and Thomas (1961), using regression analysis, show
strong correlations between size of city and spacing for regions in
Sweden and Iowa.
The tendency of the landscape to have hierarchy is widely
observed. It is a common observation that there are very many small
cities and fewer larger cities in regions, and that the larger cities
provide a greater variety of goods and services than do smaller
cities. This is the fundamental organization principle of the central
place models of Christaller (1966) and Losch (1954). Using the notion
of threshold of a good, Berry and Garrison (1958a) have shown how
hierarchies arise in the landscape, and given satisfactory explanation
of a hierarchy of shopping centers within urban areas.
Rank Size and Primacy of Cities
Zipf (1941) and Stewart (1947) have suggested that there is a
mathematical relationship between rank of cities and population size.
Zipf's relationship takes the form of
PI
Pr =
r9
That is, the population of the rth ranking city, Pr, equals the
population of the largest city, P1, divided by rank r raised to an
exponent which generally has a value very close to unity. This
relationship was derived empirically, but Zipf argued that when it
held for an entire country, it indicated that national unity is
maintained through an integrated urban system.
At approximately the same time, Jefferson (1939) suggested the
concept of the primate city or where the largest city is several times
greater in population than the second ranked city. Other authors have
applied the term to whole distributions of cities (see Redfield and
Singer 1954).
MacArthur (1957) suggested an approach to the study of the
structure of animal communities by rank-abundance curves, by plotting
rank (commonest to rarest) on the abscissa and abundance on the
ordinate. A semi-log graph was used that resulted in straight line
graphs much like those observed by Zipf for cities. In later work by
Hutchinson and MacArthur (1959) a mathematical model was constructed
in which the properties of the niche of different species are defined
by numbers of kinds of different environmental elements. The model
implied few very small species with a rapid increase in number of
species up to a modal size and a slow decline in number to unity as
the size increased. When data for mammal fauna were graphed, a
relatively good fit with the model was approached, but many later
papers found poor fits.
Rank size irregularities have been associated with the existence
of integrated systems of cities in advanced countries by Berry and
Garrison (1958) and Beckmann (1958). Others have suggested that
primacy be associated with over urbanization, colonial economies, and
subsistence and peasant economies. In all, the regularities suggest
relationships between urban centers, and differences in regularity are
noticed with different economic and cultural structures, but the rank
size, and primacy relationships are not theoretical models and little
theoretical evidence is given as to why, or how these relationships
exist, except to suggest that there is a close correlation with rank
size regularities and the hierarchical landscape postulated by
Christaller.
Landscape Evolution
Leopold and Langbein (1962) suggested a theory of landscape
evolution based on entropy expressed in terms of probability of
various states. Essentially they introduce the concept that the
distribution of energy in river profiles tends toward the most
probable and that such profiles approach the condition in which the
downstream rate of production of entropy per unit mass is constant.
Drawing from the theory of Prigogine (1955), they introduce the
principle that stable stream systems must correspond to the stationary
state of any open system where the rate of production of entropy per
unit volume corresponds to a minimum compatible with the conditions
imposed on the system. Hence, a stable river system corresponds to
the principle of least work. They suggest the river channel has the
possibility of internal adjustment among hydraulic variables to meet
the requirement for maximum probability, and those adjustments tend
also to achieve minimization of work. While they were dealing
primarily with river profiles and the hydrologic character of
landscapes later theorists have suggested that the same concepts apply
to the landscapes of cities (see Woldenburg 1968, 1969, 1970;
Woldenberg and Berry 1967; Curry 1967; Semple and Golledge 1970;). In
general, current urban geographic theory suggests that urban systems
minimize entropy production by the "least work principle" (or least
effort as theorized by Zipf, 1949), and that spatial hierarchical
order is a function of the probability of all possible states.
Inherent in their theory is the assumption that urban system compo-
nents operate under constraints of competition, and that considerable
competitive advantage is gained with entropy minimization.
Berry (1972) suggests that central-place phenomena maintain
open-system equilibria as a result of allometric growth, and this
property is the result of continued energy inflows. Curry (1967)
suggests that frequency analysis and diffusion characteristics of
particles in space have relevance in understanding central place
phenomena, and processes of urban growth.
Social Process Model of Urban Growth
Park, Burgess, and McKenzie (1925) defined the processes of urban
growth (and in a general sense the evolution of landscape hierarchies)
as: concentration, centralization, segregation, invasion, and
succession, operating at all levels of aggregation. Their hypothesis
was that competition and the reciprocal benefits resulting from
exchange of goods and services are the basis for community.
A brief discussion of each of the five processes summarized from
McKenzie (1925), follows. Concentration: McKenzie (1925) defined
concentration as the tendency of an increasing number of persons to
settle in a given area or region to facilitate the most efficient
spatial distribution for the utilization of natural resources. Size
and stability are functions of food supply and role in the wider
environment through production and distribution of commodities, which
both are determined by the community's competitive status.
Centralization: centralization is described as a temporary form of
concentration, implying a congregation of people in a locality for a
definite purpose. It is the process of community formation. Thus,
civilization is a product of centralization. McKenzie (1925) states
that local points of centralization are in competition with other
points for the attention and patronage of the inhabitants of the
surrounding area and are in a temporary stage of unstable equilibrium
with other competing centers. The degree of centralization, then, is
a measure of its competitive status under prevailing cultural and
economic conditions. Segregation: Economic factors are the basic
attribute for selection and thus segregation of activities,
populations, and structure. Under competition, differentiation and
segregation result as a sorting and selecting process for the most
advantageous location and status. Invasion: Invasion is applied to
all factors-populations, structure, communities, or utilities; it is
the process of group displacment. It may involve population
displacement, or the encroachment of one area of segregation upon
another. Again, its main driving force is competitive status of
groups in relation to other groups of like kind. Succession:
Succession results from invasion. However, not all invasion results
in succession. There are generally considered to be four stages to
succession. The first is invasion, followed by reaction or
resistance. The third stage is the influx of the new group, and
fourth, climax or the achievement of a new equilibrium. In general,
invasion and the resulting successional stages can be brought about
with almost any type of change in the physical, economic, and to a
lesser extent, social factors. These changes result in competitive
advantage of one group over the existing group.
These theories generated the concentric-zone hypothesis of urban
form as outlined by Burgess (1930). It proposed that a city can be
divided into a series of five concentric circles. 1. central business
district; 2. zone of transition; 3. zone of workingmen's homes; 4.
middle class zone and 5. the commuters' zone.
Hierarchical Distributions of Components in Systems
In 1927, Pareto (1971) defined human society as a hierarchical
collectivity, and postulated what was termed Pareto's Law on the
distribution of income. Using the number of individuals receiving
incomes at or above a certain amount plotted against the amounts of
these incomes (in other words, a cumulative distribution), he derived
the following relationship:
N A
Xa
or,
log N = log A a log X
where N represents all the number of individuals at or above a
certain income limit, X, and A and a are constants. When log N was
plotted against log X, a straight line was obtained with slope (a)
equal to approximately -0.2.
Pareto asserted that the law was true for all countries and for
all times and deduced from it that, owing to the rigidity of the
distribution, there was only one way to increase economic welfare
(i.e., the share of the poorer classes in the national income), and
that was to increase total production of the economy.
Zipf (1965) in later work based on his original rank size
distribution of cities (Zipf 1941), found much the same relationship
as Pareto when he graphed empirical data of such things as: number of
businesses versus number of businesses of like kind, number of
employees versus number of specific occupations, and as mentioned
earlier, size of cities versus their rank. Zipf's number-frequency
relationships have the same form as do those of Pareto, and are
expressed by the equation:
log Y = C a log X
where Y is the number of individuals in any class X, and C and a are
constants.
Both Pareto and Zipf suggest that these relationships indicate a
measure of organization and that departures from straight line slopes
indicate disunity (Zipf 1941) or inequality (Pareto 1971).
Odum, Cantlon, and Kornicker (1960) postulated a hierarchical
organization of ecological communities using a cumulated logarithmic
species-diversity index, where the number of occupational niches are
related on a per capital support basis. They suggest that the
hierarchy postulate explains why the species-diversity index is a
measure of organization at the macroscopic level, since the equations
for each are similar.
Hierarchy in Social Systems
A classical theory of social organization is outlined by Weber
(1946, 1947) for formally organized causal systems such as
bureaucracies. Weber theorized that the size of administrative
structure is a direct function of increasing size of organization, and
that there is a very strong relationship between the size of an
organization and the division of labor; the larger organization, the
more subdivided are the responsibilities.
Later empirical studies by Blau and Schoenher (1971) and Blau,
Heydebrand, and Stauffer (1966) suggest two generalizations that
confirm Weber's theories on the organization of social systems: first,
that increasing size generates structural differentiation in
organizations along various dimensions at decelerating rates; and
second, that structural differentiation in organizations enlarges the
administrative component.
Weber's chief concern was of the administration of nation-states
and other large scale undertakings, such as armies and political
parties. A question that was at the center of his work was how to
design an efficient organizational structure for such large scale
systems. And, thus, the Bureaucratic Model evolved which he described
as a technically superior instrument for accomplishing complex tasks
(Weber 1947). Inherent in the model was the concept of hierarchy; in
that, a highly bureaucratic organization must have a firmly ordered
hierarchy of both structure and channels through which decisions and
information flow from lower to higher levels.
Weber's Bureaucratical model dominated social organization theory
until the open system (or natural system) model of organizations
suggested by Thompson (1967). His model does not take the environment
as a given, but assumes that an organization's environment is a major
force that shapes its goals, structure, and survival. Thompson's book
(1967) was a turning point in social organization theory with the
incorporation of such environmental concepts as natural selection,
resource utilization and scarcity, and efficiency; and treats the
various characteristics of organizational structure (hierarchy,
specialization, and so forth) as both internally generated, and as a
response to organizations' adaptations to their environments.
Monane (1967), in his book A Sociology of Human Systems, defines
social systems as open systems whose internal structure of components
are organized in a hierarchical fashion, where power increases and
number of individuals decreases as one moves up the social hierarchy.
In his model of social action Monane (1967) outlines the effects of
increasing populations. Social interaction increases at a much faster
rate, the number of parts and degree of specialization increases,
rules become more formalized, variation in norms increases, deviate
behavior increases, the ratio of formal norms to informal norms
increases, the number of levels in the influence and authority
hierarchies increase, the number of authority rank systems increase,
the problems of interactions vertically in the same hierarchy or
between hierarchies increases, the potential for conflict and friction
among the parts increases, the number of coordinative problems and the
need for coordination increases, and decentralization of authority
increases, but at the same time the most influential parts may
maintain or increase their influence.
The previous study offers little to further understanding of how
and why hierarchies exist, although Monane suggests that a significant
feature of component action is the tendency to cluster in particular
areas of a social system rather than to be evenly distributed
throughout. He suggests that clustering heightens action; and an
amplification spiral will emerge as components who want a great deal
of contact move closer to one another.
Aldrich (1979) proposes the following definition for social
organizations: goal directed, boundary-maintaining, activity systems,
and suggests what he terms a Population Ecology Model for
organizational development. Borrowing heavily from ecological theory,
the model represents an attempt to explain the process underlying
change. Aldrich refers to his model as a natural selection model, and
emphasizes that the primary objective of all organizations is to work
toward a better fit with their environment, by manipulating the nature
and distribution of environmental resources. Using the concepts of
Emery and Trist (1973) in categorizing environments, Aldrich presents
two types of environments and two types of resource distributions that
have direct effects on the complexity and survival of organizations.
Environments are either stable or unstable, and resources are
distributed either in a concentrated or dispersed manner. Thus, there
are four types of environment/resource patterns: stable environments
with concentrated resources, unstable environments with concentrated
resources, stable environments with dispersed resources, or unstable
environments with dispersed resources.
Recent theorists (see Aldrich 1979; Weick 1976; Glassman 1973;
Landau 1969; and Buckley 1967) portray organizations as
loosely coupled, hierarchic systems. Loose coupling is a central
characteristic of social organizations and such systems exhibit
relative independence of momentary environmental change (Glassman
1973). Due to hierarchic organization and weak connections between
some system components, loose coupling and hierarchic structure are
important system properties of social organizational structure because
they help us to understand the emergence and persistence of complex
forms and strategic adaptations made by individual organizations
(Aldrich 1979).
Weick (1976) listed seven advantages of loose coupling for
organizations:
1. Loose coupling allows portions of the organization to persist
and evolve independently of other parts.
2. Loose coupling provides an organization with a selective
sensing mechanism.
3. Loose coupling is an excellent system for allowing local
adaptations of organizational subunits.
4. Loosely coupled systems permit the retention of a greater
number of mutations and novel solutions than do tightly
coupled systems.
5. Loose coupling permits the confinement of a breakdown in one
part so that it doesn't affect the rest of the organization.
6. Loose coupling may permit greater self-determination by
persons in organizational subunits.
7. A loosely coupled organization could be relatively
inexpensive to operate.
Blau (1972) showed that hierarchic structure of organizations
increased with increases in size and complexity, based on his analysis
of five types of work organizations: government employment security
offices, government finance offices, department stores, universities
and colleges, and hospitals. But Glassman (1973) suggests that
hierarchy is often a consequence of constraints imposed by
governments. Under these circumstances, hierarchy is not a result of
organizational adaptation to local environments, but rather a
consequence of constraint from above. Glassman states this is
particularly true of the social services sector, and gives as an
example the specification of the Comprehensive Employment and Training
Act of 1973, that federal, state, and local components were to be
arranged in a hierarchy of authority.
In all, the Population Ecology Model of Aldrich (1979) leads to
the expectation of finding highly similar forms of organizations in
similar environments. Similar social structural conditions, resource
distributions, and environmental exigencies should lead to convergence
of highly adaptive forms (Aldrich 1979), and that two central
characteristics of complex social organizations are hiererchic
ordering of subunits and loose coupling of components.
42
Computer Simulations of Hierarchically Organized Systems
Smith (1970) simulated models of three and four trophic levels
connected in series with and without internal recycling, to show the
effects of enrichment in mathematical models of aquatic systems.
Using digital simulation, he found, in general, that enrichment had
decreasing effect on trophic levels from plants to predators.
Comparison between the three trophic level model and that of the four
levels showed that the above trends were somewhat reversed in the four
trophic level model.
Overton (1975, 1977) has applied a hierarchical structure to
modeling of the Coniferous Biome. Ecosystems are decomposed into
sub-units in a hierarchical manner, and mathematical models are built
of the sub-units finally connected back again to achieve a whole
system model.
Using a digital simulation technique, Costanza (1979) modeled the
spatial growth of land use in south Florida, which resulted in
computer-generated maps of embodied energy intensity. The resulting
maps of land use embodied energy intensity had relatively good fit
with historical growth trends, and generated a spatial hierarchy of
land use.
In an earlier study, Costanza (1975) mapped incoming energies of
both natural and fossil fuel origin and overlayed these with land use
to show the distribution of land use within landscapes that results
from the spatial character of incoming energies.
Description of the Study Areas
Shown in Fig. 1.4 are the three regional areas of Florida and
two urban areas that were investigated in this dissertation. The
boundaries of the St. Johns study area correspond to the district
boundaries of the St. Johns River Water Management District, and those
of the south Florida study area correspond to the district boundaries
of the Central and South Florida Flood Control District as they were
in 1973. The boundaries of Lee County are the political boundaries,
and the study area limits for each of the urban areas of Ft. Myers and
Gainesville were drawn where the concentrations of urban land use
diminished into the natural landscape that surrounds (see methods
section for details of boundary conditions for urban study
areas).
South Florida Study Area
South Florida is an area of intense urban development along both
coasts with an extensive wetland system of marshes and swamps in
between. Its coastal areas are the basis for attracting seasonal
influxes of tourists that support a large segment of the economy.
Previous studies (Odum and Brown 1976) indicate that the economy of
south Florida is largely a tourist economy with nearly 33% of the
total income coming from these sources. Agricultural sales amount to
6.2% of the income, and industrial sales 21.9%. The study area
encompasses approximately 16,670 square miles.
In the last 20 years south Florida has experienced very rapid
growth, with current populations estimated to be approximately 3.6
million people. Because of the attractiveness of coastal locations
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and the extensive areas of marsh and swamps in the center, urban
development has been confined to a narrow strip along the east coast
stretching from the Palm Beaches to Miami, where population density
averages 4500 people per square mile, and to the southwest coastal
areas of Naples and Ft. Myers (population density 1340 people/sq mi).
The central area of the Kissimmee River Basin is mostly agricultural
lands, with improved pasture the predominant use. South of Lake
Okeechobee and immediately adjacent to it are extensive areas of muck
agriculture where sugar cane is the main crop.
The ports of Miami and Port Everglades in Ft. Lauderdale are
international shipping ports. Miami receives and ships chiefly trade
goods many of which originated and are destined to South America,
while Port Everglades is the main port of entry in south Florida for
refined oil.
St. Johns Study Area
The St. Johns study area is an area of moderate urban development
with agriculture and forestry inland, and drained by one major river.
Jacksonville on the northeastern coast is the major city and has port
facilities for international trade. The coast has areas of intense
development around Jacksonville, Daytona, and Titusville where tourism
is a major industry. Inland, the landscape is a diverse mosaic of
agriculture, forestry, urban development, and natural lands.
The study area encompasses approximately 11,930 square miles and
has a population estimated at 2.7 million people, giving a gross
population density of 230 people per square mile. The largest
population densities are around Jacksonville (4280 people/sq mi),
Daytona (1950 people/sq mi), Gainesville (2950 people/sq mi), and
Orlando (1200 people/sq mi).
Lee County Study Area
Lee County is located on the southwest Florida Gulf Coast. The
Caloosahatchee River flowing from Lake Okeechobee to the Gulf bisects
the county and empties into and supports with contributions of
nutrient rich waters a very productive estuary. The coast is lined
with numerous islands all surrounded with mangrove and some high
energy beaches on the extreme Gulf side.
The county has two predominant locations of population density,
the city of Ft. Myers on the Caloosahatchee River and Ft. Myers Beach
on an island in the Gulf. The area is retirement oriented with
numerous developments throughout the county that attract retired
workers from the north.
The economy is predominantly a tourist economy, with large
contributions from transfer payments, and some agriculture sales.
Experiencing recent very rapid growth, the county population is now
approximately 215,000 people with a population density of 280 people
per square mile.
Ft. Myers Urban Study Area
Ft. Myers is located in Lee County, Florida, on the banks of the
Caloosahatchee River in southwest Florida. The county seat of
government, Ft. Myers, is also the major commercial center for the
surrounding counties of Hendry, Charlotte, and north Collier, as well
as a center of higher education, having southwest Florida's only
community college.
The city has a major regional airport and is serviced by rail
transport and planned interstate highway. With such transportation
links the city is the major center of tourist influx and agricultural
exports for southwest Florida.
Gainesville Urban Study Area
Gainesville is located in Alachua County in central Florida. The
county is an agricultural county with Gainesville the only major
metropolitan concentration of population. Gainesville is also a
county seat of government, and a center of higher education, having
the University of Florida.
The city is the major commercial center for surrounding counties
of Levy, Gilchrist, Marion, Putnam, Clay, Bradford, and Union.
Located adjacent to the city is a major regional airport and
interstate highway, affording easy transportation links to other
metropolitan areas to the north and south.
Plan of Study
In this study the hierarchical organization of the landscape
and resulting energy spectrum of energy storage and flow were
investigated at three levels: the regional level of ecosystems and
urban land uses, the organization of cities in the landscape, and the
organization of land uses within cities. In addition, the relation-
ship of intensity of development to the spatial area of influence was
investigated at different levels of organization in the nation, the
state, and within districts of the state. The specific plan for the
analysis of regions, districts and subdistricts is as follows.
First, maps were made of ecosystems and land uses at two levels
of study; the regions of Florida and cities within these regions;
Spectra of energy storage and energy flow were calculated from power
density data and land-use information.
Second, energy spectra for many different types and sizes of
systems were constructed to understand general trends of energy flow
and storage.
Third, generalized models of each urban land-use type were
evaluated, and a generalized hierarchical model of urban land uses was
drawn and energy flows between levels or sectors of the urban system
were evaluated.
Fourth, specific analysis of the external energy requirements of
areas of different sizes, and an energetic evaluation of the range of
goods and services (or threshold of goods and services) was
conducted.
Fifth, a series of theoretical models of hierarchical
organization were simulated on analog and digital computers to explore
different energy flow and storage characteristics under different
organizations and pathway configurations. Then data from an aquatic
ecosystem of Florida were used to test theories of hierarchical
distribution and resulting energy spectra.
CHAPTER 2
METHODS
General Methods and Definitions
A graphic language is used throughout this dissertation to
describe energy flow and interaction in complex systems. The language
is a graphic means of depicting systems as Nth order differential
equations, since each symbol represents a mathematical relationship of
either energy flow, interaction, or storage relative to time. Given
in the appendix is a description of the language and accompanying
mathematical equations. For a complete description of the language
and its development see Odum (1960, 1967, 1971, 1973, and 1976).
Simple diagrams are drawn of many systems to help organize thinking
and show what energy flows and interactions are of most importance,
while in the section on simulation of theoretical models of
hierarchically organized systems, the diagrams are used as a means of
writing differential equations to be programmed on the computer.
The flows of energy through the landscape are measured in heat
Calories. However, Odum (1976, 1977, 1978) suggests that energy has a
quality associated with the degree to which it is concentrated. High
quality energies are those that are more concentrated and thus can do
more work per unit of heat energy, while low quality energies are more
dispersed and can do less work per unit of contained heat energy. In
this dissertation, energies are presented in both their heat
equivalents and in terms of their quality by expressing them in
Calories of Coal Equivalents (Cal CE). By converting energies to coal
equivalent Calories, all energies are expressed in the same form whose
ability to do work is familiar. Given in Table 2.1 are the energies
used in this study, and their equivalence factors, as well as their
quality expressed in Calories of coal equivalents.
The energy embodied in goods and services is one measure of their
quality, and is found by summing up all the energies that are used in
making a good or service. In most instances, because of the
complexities involved in tracing back through the production process,
it is not possible to directly account for all the energy that is
embodied in a good or service. Thus, Odum (1976) suggests that when a
purchase of goods and services represents a purchase of an average mix
of the goods and services in the national economy, a conversion factor
from dollars to energy may be used. The conversion factor is
calculated using equation (2.1).
Xt
7t= Zt (2.1)
where X = Total energy use in the U.S. including embodied energy of
the environment in Cal CE, Y = U.S. Gross National Product, and Zt =
Cal CE/$ in year t.
Since energy use and GNP are changing, and since inflation
affects the relationship between energy and money, a conversion factor
is needed for every year. Given in Table 2.2 are conversion factors
of representative years for converting the dollar costs of goods and
services to Calories of embodied energy.
Table 2.1. Energy transformation ratios (quality factors) used in this study.
Transformation ratio
Energy type Footnote Cal CE/Cal
Sunlight a 1/2000
Sugar of gross production
still distributed over
the landscape a 1/200
Wind a 1/27
Wood still distributed
over the landscape b 1/2.2
Coal a 1/1
Finished wood b 1.3
Ocean waves reaching shore a 1.35
Gasoline b 1.4
Elevated water a 1.5
Tide a 1.6
Water purity a 1.8
Natural gas b 2.0
Electricity a 4.0
Food (except meat) b 4.4
Steel b 4.4
Meat b 15.0
Misc. goods b 75.0
Phosphate a 293
aFrom Odum 1980.
bCalculated as part of this study. See Table 3.31.
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Evaluation of Observed Hierarchies
The trends of hierarchical organization and energy spectra were
graphed semi-logarithmically for systems of differing scales and
complexity. Data were gathered from various sources in the literature
and from various local, state, and federal agencies in published
reports and in some cases unpublished data.
Regional Analysis
Three regional areas of differing character and size were
analyzed for total energy budgets, land use, and resulting
hierarchical organization: the Kissimmee Everglades Basin in south
Florida, a subtropical region of relatively intense urban development;
the St. Johns River Basin, a region on the coast of central Florida
dominated by a major river, and agricultural lands with moderate urban
development; and Lee County, Florida, an area in southwest Florida
that is a coastal county with extensive tourism and an agricultural
base inland. This county has experienced recent, very rapid urban
growth.
Land Use Maps
Land use maps for the St. Johns Basin and Lee County were con-
structed from aerial photographs at a scale of 1:77, 117 or approxi-
mately 1 inch equals 1 mile. Photographs used were false color infra-
red and black and white infrared photographs taken in 1973. The land
use map for the south Florida region was prepared during previous
studies (Odum and Brown 1976). Land use categories for each of the
56
regional areas are given in Table 2.3 and descriptions are given in
Appendix 2. Land use areas were delineated directly from photo
graphs and transferred to controlled base maps, and then reduced to a
scale of 1:250,000 (for south Florida and the St. Johns basins) and
enlarged to a scale of 1:80,000 (Lee County, Florida). Presented in
Figs. 2.1, 2.2, and 2.3 are examples of specific areas of each map at
their original scales since the format of the original maps precludes
their inclusion, and reductions are so small as to make worthless any
information they contain. The regional map of south Florida, and the
Lee County map are published elsewhere (see Odum and Brown 1976) and
the regional map of the St. Johns study area may be obtained from
either the St. Johns River Water Management District office in
Palatka, Florida, or the Center for Wetlands at the University of
Florida, Gainesville.
Land use areas were measured in the following manner: south
Florida maps were cut up and weighed on analytical balance, where a
conversion factor of grams/acre was used to convert from weight to
area; St. Johns River Basin Maps were cut up and a leaf area index
machine that measures area using light sensitive photocells was used
to measure area directly. A conversion from square centimeters to
acres was necessary to convert machine measured area to acres of
land use. Lee County areas were cut up and measured in the same
manner as those for the south Florida study area.
Gross Productivity of Land Uses
Published estimates (see Odum and Brown 1976) of gross primary
production for natural ecosystems were used for natural and
Table 2.3. Land use classification system used in mapping regional areas.
South Lee
System St. Johns Florida County
Urban Open land x x x
Recreation x x x
Residential (low density) x x x
Residential (medium density) x x x
Residential (high density) x x
Industrial x x x
Mining x
Commercial and services x x x
Institutional x
Transportation x x x
Utility and communicative x x
Agricultural Improved pasture x x x
Cropland x x x
Citrus groves x x x
Nursery and speciality crop x
Confined feeding operation x
Planted pine x
Clear-cut areas x
Sugar cane x x
Natural Grassy scrub x x x
Sand pine scrub x x
Sandhill community x
Pine flatwood x x x
Xeric hammock x
Mesic hammock x x x
Swamp hammock x
Hardwood swamp riverinee) x
Riverine cypress x
Cypress dome x x x
Bayheads and bogs x x x
Wet prairie x x x
Freshwater marsh x x x
Rivers and streams x x x
Lakes and ponds x x x
Reservoir x x x
Borrow pit x
Tidal flat x x x
Beach and dune x x x
Coastal hammock x
Salt marsh x x x
Mangroves x x x
Spoil bank x
Table 2.3. (continued)
South Lee
System St. Johns Florida County
Medium-salinity plankton estuary x x x
Oligohaline system x x x
Neutral embayment x x x
Marine meadow x x x
Coastal plankton x x x
High velocity channel x x x
Oyster reefs x x
Coral reefs x x
Emerging new systems associated
man x x
Figure 2.1. Detail of land use map of the south Florida study area, showing the
land uses of the coastal region around the Palm Beach area.
Numbered land use classification systems and descriptions of land
use categories are given in Appendix 2. Approximate scale: 1 inch
equals 4 miles.
"C o20 to a
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Figure 2.2. Detail of land use map of the St. Johns study area, showing the
land uses of the coastal region around Daytona and New Smyrna Beach
and inland. Numbered land use classification systems and
descriptions of land use categories are given in Appendix 2.
Approximate scale: 1 inch equals 4 miles.
DAYTONA
BEACH
NORTH
04O I 2 3 MILES
4APPROX. SCALE
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ilri
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zi
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Figure 2.3. Detail of land use map of Lee County, Florida, showing the land
uses in the vicinity of Ft. Myers and the Caloosahatchee River.
Numbered land use classification systems and descriptions of land
use categories are given in Appendix 2. Approximate scale: 1 inch
equals 1 mile.
agricultural land uses (see Table 2.4). Urban land use power
densities were calculated from studies in Ft. Myers and Gainesville,
Florida (see Analysis of Energy Flow and Structure of Urban
Systems).
Classification of Cities by Average Power Density
An average city power density was determined for all cities
within each region by using averages derived in detailed studies of
the two urban areas, Gainesville and Ft. Myers, Florida (see overall
power density of urban study areas). The area of each city is not
necessarily the actual area within legal city limits, rather it is the
area that when viewed from aerial photographs that is contiguous with
all urban land uses. In some cases this area may be smaller than
actual city limits, and in other cases where suburban sprawl is
evident, the area may be considerably larger.
Energy Budgets for Regions
The energy budget of a region is made up of renewable energies of
sunlight, winds, tides, waves, and rain; and nonrenewable sources of
fuels, goods, and services. Renewable energies are calculated using
methods developed in previous studies of regions (see Odum and Brown
1976) and the calculations are given as notes to tables. Nonrenewable
energies are calculated from land use power densities and fuel
consumption data for each region.
Energy flow and the energy in structure may be expressed in two
ways. First, it may be in actual heat Calories that are associated
with the flow or storage. And the second is to express the flow or
storage in embodied energy (sometimes referred to as sequestered
Table 2.4. Estimates of gross primary production (GPP) and total structure
associated with ecosystems of south Florida landscape (from Odum and
Brown 1976).
Subsystem Subsystem
gross productivity structure
Subsystem x 106 CE/acre yr x 106 CE/acre
Improved pasture 5.1 24.7
Vegetable crops 21.3 294.8
Tree crops 9.6 74.9
Sugar cane 22.2 313.1
Grassy scrub systems 4.0 16.5
Pineland systems 6.4 80.1
Hardwood systems 7.7 235.9
Lakes and ponds 1.4 7.4
Cypress domes and
strands 7.3 214.5
Wet prairie 5.4 51.6
Scrub cypress 5.8 61.3
Freshwater marsh 7.4 228.7
Sawgrass marsh 8.1 273.7
Beach and dune
systems 0.3 4.0
Salt flats 0.3 4.0
Scrub mangroves 1.0 7.2
Saltwater marsh 5.0 29.5
Mangroves 7.3 218.4
energy) and reduce the energies to equivalents of one type such as
coal equivalents. Energy transformation ratios (quality factors)
given in Table 2.1 are multiplied by the heat Calories of the
particular flow or storage, thus converting heat Calories to coal
equivalent Calories (CE Cal). Energy transformation ratios are
expressed as Cal CE/Cal heat for the particular energy or
material.
Power Base for Cities
The land area surrounding a city that is necessary to average the
power density of the particular city to that of the region is
considered to be the range of the city and is the area that is
required as a power base for the processing and upgrading of dilute
natural energies. Once the average power density of the overall
region is known, city ranges or their power base areas were determined
by dividing total inflowing embodied energy for each type of city by
the regional average power density as follows:
Rt = (2.2)
where E = Total inflowing embodied energy (Cal CE/yr), P = regional
average power density (Cal CE/acre yr), and Rt = area of range
of city in year t.
Spatially, the areas are mapped using circles of the proper
dimension to encircle each city by calculating diameter from area of
range. The resulting map of each of the regions graphically describes
the interaction of high quality fossil fuels and natural resident
energies, or the concept of investment ratio.
Investment Ratios
The investment ratio is a measure of the matching of high quality
energies with lower quality resident energies, under the theory that
when ratios are high, high quality energy is being used in excess, and
may be doing lower quality tasks where lower quality energy may be
better utilized. The ratio is expressed as Calories of high quality
energy per Calorie of low quality energy; both expressed in embodied
energy of one type.
It = -E (2.3)
where E = calories of high quality energy, S = calories of sunlight
energy, and It = Investment ratio in year t.
A regional energy budget expressed in this manner becomes a
measure of the fossil fuel based energy intensiveness of the region.
Investment ratios for regions were calculated using equation (2.3)
above.
Analysis of Energy Flow and Structure of Urban Systems
Two urban areas were analyzed in detail for total energy
budgets and power densities, energy budgets and power densities of
land uses within the urban areas, and resulting hierarchic
organization of the urban landscape: Ft. Myers, Florida, an urban
area on the southwest coast of Florida whose main economic inputs are
from tourism, and is a government center and Gainesville, Florida, an
urban area in central Florida that is a governmental center, and
center of university education.
Land Use Maps
Land use maps were drawn from aerial photographs at a scale of 1"
= 2000'. Table 2.5 lists the land use classification used.
Photographs used were black and white infrared aerial photographs
taken in the following years: 1973 for the Ft. Myers urban area, and
1974 for the Gainesville urban area. The study areas were delineated
from the photographs where contiguous areas of development were
considered to be part of the urban areas whether or not they fell
inside of city limits. All area measurements were based on this area
rather than on published data of the area within official city limits.
Ground truthing of land use maps was done by windshield survey.
Measurements of areas from land use maps was done by cutting the
individual land uses from the map and weighing on an analytical
balance. A conversion factor was used to derive area in acres from
weight of paper.
Urban Land Use Power Densities
Power density is a measure of energy flow per unit of time per
unit of area. In this study power density is expressed in units of
Cals CE/acre year. Power density is expressed as the addition of
energy consumption of fuels and electricity per unit area (referred to
as direct power density), and consumption of the energy embodied in
goods and services per unit area (referred to as indirect power
density). Total power density results from the addition of both of
these types of input energies. The generalized land use model in Fig.
2.4 was used to evaluate energy consumption by land use.
Table 2.5. Land use classification system used in mapping the urban study areas
of Gainesville and Ft. Myers, Florida.
Map code System name
1 Cleared land
2 Recreation and open space
3 Low density single-family residential
4 Medium density single-family residential
5 High density single-family residential
6 Low density mobile home
7 Medium density mobile home
8 High density mobile home
9 Low density multiple-family residential
10 Medium density multiple-family residential
11 Commercial strip
12 Commercial mall/shopping center
13 Central business district (CBD)
14 Industrial
15 Transportation terminals
16 Power plants and utility
17 Schools
18 Universities and community colleges
Agricultural
19 Improved pasture
20 Cropland
21 Citrus groves
22 Planted pine
Natural
23 Grassy scrub
24 Melaleuca
25 Sand pine scrub
26 Sandhill community
27 Pine flatwood
28 Xeric hammock
29 Mesic hammock
30 Swamp hammock
31 Hardwood swamp riverinee)
32 Riverine cypress
33 Cypress dome
34 Wet prairie
35 Freshwater marsh
36 Rivers and streams
37 Lakes and ponds
38 Reservoir and borrow pits
Figure 2.4.
Generalized land use diagram used to evaluate power densities of
urban land uses. Flows A through G are expressed in embodied
energy of the same type (Cal CE).
Direct power density = D + E
Indirect power density = F
Total high quality power density = D + E + F
Total heat calories used = H
D + E + F
Investment ratio = A
Ratio of high quality to low quality energy = A + B + C
Total embodied energy of product = G
UNUSED POTENTIAL ENERGY
The average direct power density for each of the land use
classifications were calculated by first selecting a representative
sample of structures in each of the land use types, and then obtaining
yearly energy consumption data from local utility records for each of
the selected structures. A mean yearly energy consumption for typical
structures in each of the land uses was calculated, and when
multiplied by the number of structures in a land use area gave the
total direct energy consumption of that land use. The total direct
energy consumption of a land use was then divided by the area (in
acres) of the land use area to obtain the direct power density.
Energy consumption data were taken from Regional Utility Board of
Gainesville-Alachua County and Gainesville Gas Corporation billing
records in the Gainesville, Florida, study area. Billing records of
Florida Power and Light Corporation were used for the Ft. Myers,
Florida, study area. There were no central natural gas distribution
companies in the Ft. Myers area, and very little gas is consumed in
southern Florida (Division of State Planning 1976). Thus, natural gas
consumption was not considered to make up a large portion of the total
energy consumption of the land uses in the Ft. Myers study area.
The consumption of gasoline by vehicular traffic within each land
use was not used to calculate power densities of land uses, but was
used to calculate overall power densities of urban areas (see average
urban power density).
In general, the sample size of structures within each of the land
use categories was ten percent (10%). However, the large number of
residential consumers necessitated a different sampling technique.
Ten examples of each residential land use type were selected and ten
(10) structures within each of these types were used to calculate
average consumption of direct energy. A 10% sample size of commercial
structures in the commercial strip category was used to calculate
average direct energy consumption. Commercial malls and shopping
centers were considered separate land uses from that of the commercial
strip, and since there were only three such land uses in each of the
study areas, a 100% sample size was used. A 10% sample size was used
for the central business district (CBD) and that of industrial land
uses, of each of the study areas. A 10% sample size of schools was
used, but since there was only one university in each study area (they
were considered to have different functions and thus power densities
than that calculated for the land use category of schools) and energy
consumption data for each was readily available, power density was
calculated directly.
Indirect power density was calculated for the land use categories
in the Ft. Myers study area only. A detailed model of energy flow
between the main sectors of the local economy for the year 1973 was
evaluated to obtain the energy embodied in goods and services that
were consumed in the residential, commercial, industrial, and
construction sectors of the economy. Evaluation of the flows of
dollars between sectors of the economy were used and converted to
embodied energies using a conversion factor of 21,000 Cal CE/$.
Embodied energy in goods and services that were consumed in each
of the subcategories of residential and commercial land uses were
derived by assuming that goods and services consumed were proportional
to that portion of the total direct energy that was consumed by each
subland use category.
Average Urban Power Densities
The overall power density of each of the study areas was obtained
by adding transportation energy consumption to direct energy
consumption and embodied energy of goods and services consumed by land
uses. The total area of each land use was multiplied by its
appropriate power density, thus giving the energy consumption by land
uses within the urban area. The energy consumed in transportation was
added to this figure to obtain total energy consumption, and divided
by the area within the study area to obtain average urban power
density.
A ratio of land use energy consumption to energy consumed in
transportation was derived to facilitate the calculation of power
densities of all urban areas in each of the regions in the regional
analysis section.
Structure of Urban Land Uses
The structure associated with each land use was calculated for
the Gainesville urban study area in the following manner. Property
tax records of the City of Gainesville were used to evaluate the
assessed value and total square feet of structure for different land
uses. The same structures for each land use type that were used in
the calculation of power densities were used to evaluate the average
structure (expressed in both cu ft and in Cal CE per acre of different
land uses). The energy embodied in structure was calculated by
multiplying the assessed value (assessment is 100% in the City of
Gainesville) by a conversion factor of 20,000 Cal CE/$ for 1973. The
conversion factor is an estimate of the total energy in the U.S.
economy divided by the U.S. Gross National Product for 1973. The
actual conversion factor is 19,600 Cal CE/$ (see Table 2.2), but
rounded to 20,000 Cal CE/$ for this study.
The volume of structure associated with each of the land use
categories in the Ft. Myers study area was derived by measuring the
square feet of structure from aerial photographs at a scale of 1" =
2000' for approximately a 10% sample of all structures in all land use
categories. Using heights of structure that were derived from
windshield survey, volume of structure was calculated by multiplying
area of structure by average height.
Development Density and Imports/Exports
One measure of production and consumption in regional systems
is gross domestic product (GDP) as determined from the total flow of
dollars within a regional economy. While domestic product is not
always available for regions, it may be determined from employment
data and averages for productivity per employee in each economic
sector.
Analysis of Counties within Florida
Gross domestic products for 15 counties in Florida were
determined from employment data, and "development density" was
calculated by dividing GDP by land area of each county.
Location quotients (or what might be called export multipliers)
for each county were determined in the following manner: employment
data for eight broad economic sectors (agriculture, manufacturing,
wholesale and retail trade, government, services, transportation and
public utilities, banking and finance, and construction) were obtained
from Bureau of Economics and Business Research (1978) for each county.
Percent employment by economic sector was determined and compared to
the same data for the U.S. economy. Departures from the U.S. percent
employment were considered to indicate that portion of each economic
sector that was export employment (for a detailed discussion of
location quotients and methods, see Heilbrun 1974).
Exports were determined by multiplying number of export employees
in each economic sector by the productivity per employee for that
sector. Productivity per employee was determined from Florida State
data obtained from the Bureau of Economics and Business Research
(1978) by dividing domestic product in each economic sector by the
number of employees in that sector. It was assumed that local
differences in employee productivity were negligible.
Analysis of States within the United States
Gross domestic product was determined as in the county analysis
except that U.S. data were used for employee productivity.
Development density was determined by dividing GDP by the area of each
of the selected states. Export multipliers, and total exports were
determined using state employment data obtained from the U.S. Dept. of
Commerce, Bureau of Census (1977) and using the method outlined for
the above counties.
Analysis of Countries
Gross domestic product and exports were obtained from United
Nations (1977) for 21 selected countries. No calculations are
necessary since published data are available directly.
Embodied Energy, Transformation Ratios (Quality
Factors), and the Range of Goods
One basic principle of central place theory that explains how
the locational patterns of cities lead to the broad dispersion of
market towns or central places of differing sizes throughout the
landscape in hierarchies is the principle of interdependence of
urbanization and trade. It is believed that cities are the
instruments by which the specialized regions of a national economy are
tied together, and that the main function of cities is to provide
goods and services for surrounding market areas.
Other essential features of central place theory concern the
range and thresholds of goods and services provided by market places.
The range of a good is the distance a consumer is willing to travel to
obtain the good, and therefore, they can be thought of as having some
inherent "quality" or ordering. Convenience goods and other goods
that are purchased frequently are considered to be low-order goods,
while goods purchased less often, or goods of a specialized nature are
considered higher-order goods.
The threshold of a good or service is the minimum sales level
necessary for the seller to make a profit. Generally, the greater
range of a good, the greater is the threshold.
Another way of ordering goods is to order according to the energy
that is embodied in the good. As mentioned earlier, the maximum power
principle as enuciated by Lotka (1922) and amplified by Odum (1967,
1971, 1975) and Odum and Odum (1976) suggests that energy is utilized
in the functions and productive processes of systems only if outputs
from these processes, when fed back, cause to inflow to the system at
least as much energy as their cost. This suggests then, that the
energy that is embodied in goods and services is, in some manner,
proportional to the energy realized when the good or service is fed
back in the economy.
Embodied Energy
Previous work by Odum and others (see Odum 1980, and Odum and
Brown 1976) has developed the embodied energy in energy sources and
some goods that appear in Table 2.1. Where embodied energies for
goods and energies did not exist, they were calculated from the dollar
costs using the appropriate conversion factor from Table 2.2. Current
retail dollar costs per pound of material were obtained from various
sources under the assumption that retail costs reflect all energies
that are embodied in a good, including those of human labor, up to the
point of final demand. When dollar costs per pound are multiplied by
the dollar to energy conversion factor listed in Table 2.2, the result
is energy in Calories CE per pound of material.
Tranformation Ratios (Quality Factors)
The transformation ratio has the dimensions of Cal CE/Cal heat
and is one measure of the quality of a good or energy. Transformation
ratios were calculated for a number of goods and energy by first
calculating embodied energies, second evaluating actual energies (or
heat energy), and third dividing embodied energies by actual energies.
The resulting ratio has the dimensions of Calories of embodied energy
per Calorie of heat energy as in equation 2.4 below:
T = (2.4)
where EE = Calories of embodied energy in coal equivalents, EH =
Calories of heat (as measured by free energy), and T = transformation
ratio in Cal CE/Cal.
Calculation of Transformation Ratios
Transformation ratios were calculated as shown in Fig. 2.5, using
the general equation above 2.4. When the ratios are determined for
large aggregates of systems, slight variation in the general method
described above is necessary to avoid double counting. In Fig. 2.5
the feedback (B) is partially fossil fuel energy, and partially
environmental energies that are upgraded through environmental
systems. To avoid double counting, the environmental energies are
subtracted from the total feedback energy, if they are significant.
In Fig. 2.5, that portion of the feedback energy (Af) that is
the result of the upgrading of the lower quality energy from the left
(A) is subtracted from the feedback pathway (B).
Figure 2.5.
Diagram showing the general method for calculating transformation
ratios. The portion of the feedback energy (Af) that is directly
from the low quality energy inflow at the left (A) is subtracted
from the feedback pathway (B).
TRANSFORMATION
PROCESS
TRANSFORMATION RATIO =
FOR ENERGY SOURCE
TRANSFORMATION RATIO =
FOR STORAGE
A+(B-Af)
A
A +(B-Af)
C
1Af
I
/
/ MAIN
SYSTEM
The Range of Goods
The range of selected goods was calculated from embodied energy
per pound and the energy costs per pound to ship by most common
carrier from retail distribution point to end use point. Most
consumer goods were assumed to be transported by private automobile,
and most building products, industrial tools, and electronic equipment
by truck. Odum (1976), using the data of Hurst, estimated that the
average energy costs per mile for private automobile, including the
high energy value of the driver to be 5.4 x 103 Cal CE/mile. A
similar value for truck transport was used. By dividing embodied
energy/lb by energy cost/lb mile, range is determined.
Simulation Models of Hierarchical Organization and Energy Spectra
A series of theoretical models were simulated on both digital
and analog computers to test hypotheses and evaluate structure and
characteristic properties of systems organized in hierarchical
fashion. As the models grew in complexity and insight was gained, a
final model that was a synthesis of previous models was simulated
using data from the literature for an aquatic ecosystem.
Models were drawn using the energy circuit language and computer
programs were written directly from the graphic model. The facilities
of the Northeast Regional Data Center on the campus of the University
of Florida were used for digital computer simulation, and Dynamo
Simulation language (Pugh 1970) was used. Some models were simulated
on an EAI Miniac analog computer. Digital programs for each model are
given in Appendix 5.
Since the energy circuit language is a way of writing
differential equations in graphic form, the differential equations for
each model may be taken directly from each diagram. They are written
separately for convenience as well. The simulation models had one
thing common to all. Each is a chain of five (5) autocatalytic
components, connected in series. Differences in the successive models
are in the kinetics of the connections between components; with the
first models having simple linear flows between components, and later
models being more complex.
Figures 2.6 and 2.7 show autocatalytic components that have
constant flow energy sources as examples of computer programming. In
Fig. 2.6 the differential equation, Forrester Diagram (Forrester
1963), and Dynamo equations are given for the energy diagram. In Fig.
2.7 the differential equation and analog diagram are given.
Figure 2.6.
Example of Forrester diagram (Forrester 1963) and Dynamo equations
for digital simulation of a simple autocatalytic module, expressed
first as an energy language diagram.
ENERGY CIRCUIT MODEL
EQUATIONS:
JR -= Jo
I + (CQ)
Q = k|JRQ k2JRQ k3Q -k4Q
FORRESTER DIAGRAM
DYNAMO EQUATIONS
L Q.k = Q.J + DT(J,.Jk J2.Jk J3.Jk J4.Jk)
R Ji.kL = k *JR.k *Q.k
R J2.kL = k2*JR.k*Q.k C k = Coef
R J3.kL = k3*Q.k C k2 = Coe
R J4.kL = k4*Q.k C k3 = Coe
Jo
A JR I= +(Co0Q.k)
N Q = Initial Condition
ficient
efficient
efficient'
C k4 = Coefficient
C Co = Coefficient
Figure 2.7. Example of differential equation and analog diagram for analog
simulation of simple autocatalytic module.
ENERGY CIRCUIT MODEL
EQUATIONS
JR Jo
I + (CoQ)
Q = kIJRQ k2JRQ k3Q k4Q
ANALOG DIAGRAM
CHAPTER 3
RESULTS
Similarities of Differing Systems and Scales
Empirical evidence of hierarchical trends in large scale,
complex systems of the landscape are presented as energy spectra in
graphical form, where the number of units in each level of the
hierarchy are graphed on the vertical axis, and the power per unit (or
power density per unit) is graphed on the horizontal axis. The
systems depicted are complete networks of components, where it is
clear that there is some directional flow of energy that is
concentrated from dilute sources to more concentrated uses at
differing scales of the landscape.
Figure 3.1 is an energy spectrum of cities in Florida. Zipf
(1941), using population and rank of cities, described a frequency
distribuiton that existed for cities in the United States and other
countries. He empirically reasoned that all countries that exhibited
internal unity would have a distribution with slope -1; and that
departures from this standard slope suggested disunity. Wherever
there were departures from the standard slope, i.e., where the slope
was not smooth, but tended to vary either positively or negatively
from the ideal, he suggested that forces were in operation that would
Figure 3.1.(a) Energy spectrum of cities in Florida graphed semi-logarith-
mically, showing the trend of frequent occurrence of low power
cities and less frequent occurrence of the very high power
cities in the landscape.
(b) Log-log plot of the energy spectrum of cities in Florida, after
Zipf (1941), showing a negative slope of approximately 1.
Notes to Fig. 3.1.
Data on population of incorporated cities of the State of Florida are from
the Bureau of Economic and Business Research, University of Florida (1977).
Power density is calculated from population data by multiplying city population
by 2.5 x 105 Cal CE per capital per year, which is the average energy
consumption per capital in the U.S. in 1973.
The distribution of city power density was done graphically, where cities
with similar power densities were grouped together and assigned a weighted
average power density.
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