• TABLE OF CONTENTS
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 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix I: Tables of data for...
 Appendix II: Notes to tables 6,...
 Appendix III: Scaled equations...
 References
 Biographical sketch






Title: Energy basis for Miami, Florida, and other urban systems
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Permanent Link: http://ufdc.ufl.edu/UF00098167/00001
 Material Information
Title: Energy basis for Miami, Florida, and other urban systems
Physical Description: xiii, 248 leaves. : diagrs., map ; 28 cm.
Language: English
Creator: Zucchetto, James John, 1946-
Publication Date: 1975
Copyright Date: 1975
 Subjects
Subject: Energy consumption -- Florida -- Miami   ( lcsh )
Energy policy -- Mathematical models   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 241-247.
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: James John Zucchetto.
 Record Information
Bibliographic ID: UF00098167
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000585025
oclc - 14174116
notis - ADB3657

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Table of Contents
    Title Page
        Page i
        Page i-a
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    List of Tables
        Page v
        Page vi
    List of Figures
        Page vii
        Page viii
        Page ix
    Abstract
        Page x
        Page xi
        Page xii
        Page xiii
    Introduction
        Page 1
        Page 2
        Page 3
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        Page 21
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        Page 23
        Page 24
    Methods
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
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        Page 32
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    Results
        Page 40
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    Discussion
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    Appendix I: Tables of data for Florida and Dade County
        Page 198
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    Appendix II: Notes to tables 6, 7, 8, 11, 13, 14, 18, 19, 20, 21, and 22
        Page 209
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    Appendix III: Scaled equations for models simulated
        Page 237
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    References
        Page 241
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    Biographical sketch
        Page 248
        Page 249
        Page 250
Full Text















ENERGY BASIS FOR MIAMI, FLORIDA,
AND OTHER URBAN SYSTEMS






By



JAMES JOHN ZUCCHETTO


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


1975













ACKNOWLEDGMENTS


A great deal of.appreciation is expressed to Dr. H. T.

Odum, my committee chairman, for his knowledge, inspiration,

and great insight. I am especially grateful for having

studied in his systems ecology program which has given me

so many new ideas and insights into the nature of the physi-

cal world.

Many special contributions were made by other members of

my committee: Drs. S. E. Bayley, W. C. Huber, C. D. Kylstra,

and B. E. Swanson.

Special thanks to Michael Kemp for checking my calcula-

tions, Sandra Brown for exceptional help with my solar energy

calculations, and my fellow graduate students in the systems

ecology program.

Many thanks to Barry Peterson of the South Florida

Regional Planning Council for directing me to sources of data

and information.

The work was sponsored by a United States Environmental

Protection Agency Traineeship and by the United States Atomic

Energy Commission (Contract At-(40-10-4398)) project entitled

"Simulation and Evaluation of Macroenergetic Models of Envir-

onment, Power, and Society," H. T. Odum, principal investi-

gator.


94













TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS . . . . ... . . .... .. ii

LIST OF TABLES . . .... .. . . . v

LIST OF FIGURES . . . . . .. . .... .vii

ABSTRACT . .. . . . ... ..... . . x

SINTRODUCTION . ... . . . .. . . 1

Dissertation Research Outline . .. . . 7
Description of the Study Area .. . ..... 9
Review of'Previous Miami Studies . . . ... 15
Summary of Urban Modeling Approaches . . . 17

METHODS . .. .. ... . . ..... .. . 25

Description of Modeling Language . . . . 25
Model Development ..... ...... . 25
Data Assembly and Evaluation . . . .. 28
Simulation Procedure .. ... . .. ... 31
Energy-Economic Budget Calculations ...... 33

RESULTS . . . .... . . . . . . 40

Data on Miami-Dade County . . . .. .... 40
Urban Indicators . . . .. . . .... 59
General Overall Model of Miami-Dade County .. . 77
Urban Mini-Model Driven by External
Storage of Fossil Fuels and Linear
Price Functions ; . . .. . ..... . 86
Urban Mini-Model Driven by External
Linear Functions for Energy and Price . ... .98
Tourist Mini-Model for Miami-Dade County .... .106
Energy-Economic Calculations . . . . .. 119
The Role of Solar Energy Technology
in the Miami-Dade Urban System . . . . 142








TABLE OF CONTENTS Continued


Page

DISCUSSION . . . . . . . . ... . .160


SComparison Between Urban and Natural Systems
SEffects of Available Fossil Fuel Energy .
-Effects of External Price .........
Competitiveness of Miami-Dade County . .
Future Outlook and Recommendations for
Miami-Dade County . . . . . .
Other Urban Patterns . . . . . .
Summary . . . . . . . . .

APPENDIX

I TABLES OF DATA FOR FLORIDA AND DADE COUNTY


. . 160
. . 163
S. 167
. . 171

. . 174
. . 183
. . 195


. 198


II NOTES TO TABLES 6, 7, 8, 11, 13, 14, 18,
19, 20, 21 AND 22 . . . . . . ... .209

III SCALED EQUATIONS FOR MODELS SIMULATED . . .. .237

LIST OF REFERENCES . . . . . . . ... .241

BIOGRAPHICAL SKETCH . . . . . . . ... .248













LIST OF TABLES


Table Page

1 Energy Quality Factors Relating Different
Work Processe's .. . . .. .. 38

2 Cross-Correlation Coefficients Between the
First Differences for Selected Urban
Indicators ... . . . . . . . . 57

3 Percentage Difference Between 1963 and 1971
Values for Several Urban Parameters . . .. 58

4 Urban Indicators . . . . . . . .. 61

5 Long-Range Urban Indicators . .. . . . 64

6 Storages and Flows for Model in Figure 19. 80

7 Flows and Storages for Model in Figure 20 . 91

8 Storages and Flows for Tourist Model in
Figure 27 . . . . . .. . . 111

9 Major Money Flows in the Miami-Dade Urban
System for 1972 . . .. . . . . 123

10 Land Areas Within Dade County in Units of
Square Kilometers . . . ..... . 125

11 Major Energy Flows in Dade County for 1972 . 131

12 Fossil Fuel Energy, Total Natural Energy
and Their Ratio from 1950 to 1972 . . . 137

13 Flows and Storages for Solar Water Heater
for a Family of Four in Dade County . . .. 146
0
14 Flows and Storages for Electric and Gas
Water Heaters for a Family of Four . . . 149

15 Difference in Per Capita Fossil Fuel and
Capital Expenditures Between Solar Water
Heaters and Electrical or Gas Water
Heaters for Dade County . . . . .... 150








LIST OF TABLES Continued


Table Page

16 Fossil Fuel Savings and Capital Expendi-
tures for the Replacement of Electric
Water Heaters by Solar.Water Heaters Over
a Ten-Year Period in Dade County .. . . 152

17 Similarities Between Natural Ecosystems
and Urban Systems . . . . . .... 162

18- Storages and Flows for South Vietnam Model . 187

19 Energy Data for Florida Not Including
Electrical Utilities . . . . . . . 199

20 Dade County Data for Selected Urban
Indicators . . . . . . . .. . 200

21 Dade County Per Capita Data for Selected
Urban Variables . .. .. . . . .. 204

22A Rate of Change per Year for Selected Urban
Variables in Dade County ........ .. .207

22B Rate of Change or First Differences for
Selected Urban Variables. . . . . . 208













LIST OF FIGURES


Figure Page

1 Simplified model of an urban system showing
flows of money, natural energies, and
fossil fuel resources into the system .. . 5

2 Map of Florida showing the location of the
urban region of Dade County ... ... ... . 11

3 The symbols of the energy circuit language
used in this dissertation . . . . . 27

4 Examples illustrating the concept of
energy quality. . . ... .. ....... .36

5 Fossil fuel energy consumption for Dade
County .. . . . . . . . . . 44

6 Population statistics for Dade County . .. .46

7 Total and per capital water consumption for
Dade County from 1950-72 . . . . .... 48

8 Total and per capital budget for Dade
County from 1950-72 . . . .... ... . 48

9 Economic measures for Dade County ...... 50

10 Measures of structure for Dade County . .. .52

11 Measures of structure for Dade County . .. .54

12 Total population and developed land for
Dade County from 1920-72 . ..... . . .. 66

13 Several parameters in Dade County as a
function of total fossil fuel energy ... . .68

14 Building structure and economic flows as
functions of fossil fuel energies . . ... 70

15 Effective buying income, sales tax
collections, and total budget as func-
tions of electrical plus gasoline energy
supporting the system of Dade County . .. 72








LIST OF FIGURES Continued


Figure Page

16 Rate of change per year for total energy,
electrical energy, and gasoline energy
for yearly intervals from 1950-51 to
1971-72 . . . . . . . .... . 72

17 Rates of change for economic flows and
water consumption in Dade County . . . .. 74

18 Rates of change for labor force, population
and number of telephones in Dade County . 76

.19 Overall detailed model of the Miami-Dade
urban system showing values for flows
and storage . . . . . . . ... 79

20 Simplified urban model of Miami-Dade County
driven by outside storage of fossil fuels,
external income, and linear price functions . 90

21 Simulation results for model in Fig. 20 . . 93

22 Simulation results for model in Fig. 20 . .. 95

23 Simulation results for the model in Fig. 20 97

24 Simplified urban model of Miami-Dade County
with inflows of fossil fuel energy and
external income with linear external price
function . . . . . . . . . . 101

25 Simulation results for model in Fig. 24 . .. 103

26 Simulation results for model in Fig. 24 . .. 105

27 Tourist model for Miami-Dade County with
major money flows . . . . . . .. 110

28 Simulation results for tourist model in
Fig. 27 . . . . . .. . . . . 114

29 Simulation results for tourist model in
Fig. 27 ... . . . . . . . ... 116

30 Simulation results for tourist model in
Fig. 27 with fossil fuel storage double
that used for simulation results shown
in Figs. 28 and 29 . . ........ .118


viii








LIST OF FIGURES Continued


Figure Page

31 Pie diagrams illustrating the distribution
of fossil fuels for 1950, 1960, and 1972 . . 122

32a Aerial map of Miami-Dade County . . . .127

32b Land use map of the Miami-Dade urban region
derived from aerial photograph . . . .. 129

33 Diagram showing major energy and economic
flows for Dade County . . . . . . 135

34 Major energy and money flows for a solar
water heater . . . . . . . . 145

35 Major energy and money flows for an elec-
trical and natural gas water heater . . . 148

36 Diagram summarizing energy flows for four
different types of water heaters . . . . 158

37 Diagram showing relationships of energy
flows to prices . . . . . . . . 173

38 Urbanization model for South Vietnam . . .. 186

39 Simulation results for South Vietnam model . .191

40 Simulation results for South Vietnam model
showing urban sector as a function of
U.S. aid . . . . . . . . . . 193








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 MIAMI, FLORIDA,
AND OTHER URBAN SYSTEMS


by

James John Zucchetto

March, 1975

Chairman: Howard T. Odum
Major Department: Environmental Engineering Sciences

This dissertation presents a systems study of Miami,

Florida, with data collected for the years 1950-72, cross-

correlation analysis of the data, calculation of urban in-

dices, computer simulation of mathematical models, construc-

tion of a land use map, calculation of major economic, fossil

fuel and natural energy flows, estimations of energy avail-

able from solar energy technology, and a theory relating eco-

nomic competitiveness to the ratio of natural to fossil fuel

energies. The urban system of Miami and Dade County, Florida,

was used as a study area but the theory and approach could be

used for any urban system.

An overall detailed model of the urban region of Miami,

Florida, was created showing major flows and storage in the

system and time series data were collected for 1950-72.

Cross-correlation analysis showed significant levels of cor-

relation between the rate of change of fossil fuel use and

the rates of change of population, budget, sales tax, income,








building structure, and number of telephones. Calculation

of several urban indicators for 1972 showed a fossil fuel

energy density of 300 Kcal/m /day in the urbanized area, a

per capital energy consumption of 53.8 x 106 Kcal/capita/yr,

a ratio of natural to fossil fuel energies of 0.25, a devel-

oped area of 260 square miles, a building growth of 150

million square feet, and a rate of development of 6.5 square

miles per year. Tables and graphs of these and other vari-

ables are presented from 1950 to 1972 to identify trends.

Based on the overall model of Miami, several mathemati-

cal models for the Miami-Dade region were simulated using

analog computers. These models consisted of systems of first

order in time, non-linear differential equations which in-

cluded fossil fuel energy flows, main economic flows, exter-

nal price functions, building structure, naturalenergies, and

population. .These equations were derived from a general

theory ofhuman systems based on energetic and ecological

principles. These models were simulated for several linearly

increasing functions for price and several sets of available

energy functions. Based on existing available energy trends

and the rate of increase of price, the urban .region of Miami

and Dade County should reach a maximum point of growth around

1976. If additional net energy above past levels can be

supplied in the future, then growth may continue until 1985

with the population leveling at about 1.6 million. 'Increas-

ing prices for fuels cause structure to peak earlier and

sooner while diminishing the use of fossil fuels.








Tables of economic and energy flows were constructed

through calculation or estimation. To calculate the, energies

associated with the natural systems in the county a land use

map was drawn and subsystem areas determined. Estimating the

productivities of these systems on a per area basis then

allowed calculation of total energy flows. The energies

associated with winds, tides, waves, and fresh/salt water

concentration gradient were also calculated. These energies

were compared to fossil fuel energies by using the concept of

energy quality and it was found that the ratio of natural to

fossil fuel energies changed from 0.77 in 1950 to 0.25 in

1972. It was hypothesized that regions with higher natural

to fossil fuel energy ratios can compete more effectively

since they have greater natural energy subsidies.

It was calculated that recycling of garbage could pro-

duce, at most, 2.7% of the fossil fuel energy consumption

while solar energy technology used for hot water heating

could save, at most, 3.5% of the total fossil fuel energy

used in 1972. The energy flows associated with primitive,

electrical, natural, gas, and solar water heaters are pre-

sented. The relationship of prices, money, and energy flows

are discussed for urban regions in general and related to the

future of Dade County in particular.

As a final point of interest, an order-disorder formula-

tion of the urbanization of South Vietnam was constructed

which included main flows of money, growth of natural and

urban systems, and destruction due to herbicides and general

xii








warfare. Results are presented for an herbicidal pulse last-

ing five years and different levels of U.S. aid.


xiii












INTRODUCTION


Perhaps the most complex and least understood systems

of man are cities and urban regions which seem necessary for

exchanges of energy, information, money, and goods between

men and institutions. Understanding of urban systems is des-

perately needed for coping with the last thirty years of the

twentieth century because of the intense and rapid changes

occurring. The United Nations estimated that the urban popu-

lations of the underdeveloped countries will quadruple by the

year 2000 and that those of the developed nations will double.

Will this trend continue or will it change as a function of

available world supplies of energy? Can energy predictions

be used to implement accurate and adequate planning for the

basic needs of these urban populations? Can-economic forces

driving migrations be ultimately reduced to energetic consid-

erations and these be used to predict migrations, availability

of jobs in cities, and mechanization of agriculture on the

farms?

The energy crisis of 1973 dramatically outlined the
dependence of the American economy and its subsystems on

fossil fuel energies. In order to relate the structure and

functions of cities and their supporting regions to energy,

models and calculations were made to show main principles for








urban growth and change considered in overview. In this

study a general energy basis. for cities is presented.

Detailed applications, evaluations, and simulations were

applied to Miami-Dade County, Florida and other cities.

The contributions of natural system energies -are impor-

tant in Dade County because of their multiplier effects on

tourist flow and the general life support of the basic func-

tions of maintaining air and water quality. Is there a

limit to fossil fuel development in relation to natural ener-

gies above which the system loses tourist or economic viabil-

ity? What is the value of these energies to a future steady-

state urban system for possible energy futures? The future

will be characterized either by a low level of fossil fuel

availability and no net nuclear energy source or further

growth based on new energy sources. By taking a macro-scale

approach to the urban system this dissertation presents a

theoretical framework for understanding cities.

Urban growth in the United States has accelerated in

recent decades. This has facilitated competition with the

rest of the world by maximizing growth rates and the utili-

zation of unused energy reserves. Urbanization has followed

the maximum power principle which says that those systems

survive and compete best which maximize their power flow

(Lotka, 1922). High energy components.of cities have emerged

and have required enormous resources for support so that the

city system can continue to function. Is this trend shift-

ing? Since there is little experience with a steady-state








economy, serious study and thought are needed to determine the

characteristics and behavior of a steady-state city. There.

is a plethora of studies on individual projects and aspects

of cities, including population, transportation, economics,

racial distributions, housing, water supply, etc., but very

few studies for an urban region as a whole with consideration

of some basic parameters and with energy as a common denomi-

nator for appraisal, of the basic outside forcing functions.

Many have felt that a model of an entire urban region is too

complicated, with thousands of parts recognized when one

examines a city in micro-scale. However, if a complex system

is considered at a macro-scale level by lumping components, a

manageable model can be constructed to show gross effects

which eventually are propagated down to the micro-scale level

(Odum and Peterson, 1972).

A very simple model showing some of the basic inflows to

a city along with some of the principal storage within the

system is diagramed in Fig. 1 (for an explanation of the

symbols, see Fig. 3 in the Methods section). The source

labeled income represents the flow of money entering the

system and is shown to be pumped by natural energies. This

represents, for example, tourism. The source labeled re-

sources includes all the purchased energy and materials neces-

sary such as fossil fuels, food, water, goods and people and

the source labeled free natural energies represents the work

services of the natural system in support of man. The inter-

nal storage consist of structure, money available to spend,














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and number of people. The structure, population and money

storage of the system act in multiplicative action to add

new structure and population to the system. Money flow from

outside can come from many sources. The heat sink drains

from storage represent depreciation while those at the mul-

tiplier symbols represent heat losses due to energy conver-

sions. Can a model as simple as this with its aggregation

show, through simulation, the change in the growth of struc-

ture as a function of changes in the supply of money and

resources along with changes in prices occurring in the larger

economy encompassing the city? Simulation results of models

similar to this are presented. Theoretical studies are in-

cluded to suggest a class of overview mini-models which can

be generally substituted for detailed city models with simi-

lar results.

American urban systems have been characterized by rapid,

successional type growth without much recycle. The model in

Fig. 1 does not show any explicit recycle pathways but if

this were a steady-state or declining city recycle pathways

would be included. In natural ecosystems there is a cycle

of growth and decay in which the dead parts are reorganized

into living structure through an interaction with an outside

energy source, usually sunlight. This can be thought of as

a general order-disorder cycle which is representative of

all processes in nature. This principle is applied later

in this dissertation to the urbanization of an entire country,

namely, South Vietnam.








Dissertation Research Outline


The purpose qf this dissertation is the study of the

energy-economic basis for urban systems with specific refer-

ence to the region of Miami-Dade County, Florida. To this

end models were developed which indicated the response of

the urban system to available energy and outside price func-

tions over time. Time-series data were collected for the

urban system of Miami-Dade County for as many of the gross

parameters of the urban system as it was possible to collect

data for. These parameters included energy consumption,

building structure, population, money flows, land development,

water consumption, tourist flows, transportation structure

(vehicles), waste generation, etc.

The creation of conceptual and mathematical models were

accomplished using the energese symbols (H. T. Odum, 1971) for

detailing the overall system functions and interactions.

These models are usually too complicated for simulation but

indicate major pathways, interactions and, along with descrip-

tive tables indicating numerical values, allow comparisons

between the magnitudes of different pathways. Starting with

the overall complex model of the urban system, several simpli-

fied models were derived and simulated in order to determine

the response over time to different energy functions, price

functions and money income. Although the exact numerical

value of certain parameters is uncertain, e.g., available

energy, simulations are conducted for parameter variation so


1







that families of curves are generated. This at least gives

an estimate of a predicted value range for variables of

interest within the system. All of these models involve the

solution of systems of first order, non-linear equations,

which means they contain first derivatives with respect to

time and products of two or more state variables, equations

of the form

BQi P
t iK + fi(Q'l ..QN IN lIj.
K=j
i = 1,2, ..., N
.where Ij and IiK are some general forcing functions, Qi are

the state variables, fi is a non-linear function, and N is

the number of equations. The combined system of equations

represents a system of Nt order. Thus, the simulations con-

tained herein investigate the behavior of non-linear system

theory applied to urban systems along with the applicability,

sensitivity and validity of such formulations. This is of

importance because of the overwhelming use of linear, economic

models. Aside from simulation results correlation analysis

was conducted and interpretation of the time-series data was

attempted. The accumulation of the data for the Miami region

is important in itself for:they can serve as a reference for

other studies.

Land areas of subsystems contained within Dade County

were calculated from land-use maps derived from aerial photo-

graphs. These subsystems included urban and natural systems

such as residential and commercial areas, swamps, hardwood








hammocks, and mangrove swamps. Estimates were made of the

productivity of each of these systems and an energy system

spectrum was calculated. The general theory of urban systems

is discussed and calculations of basic energy indicators were

made for the Miami-Dade system which can serve as yardsticks

for comparisons with other urban systems. Energy budget cal-

culations were also made to estimate the energetic value of

money flows in the system and contributions from solar energy

technology were estimated.


Description of the Study Area


Located in the southern portion of the state of Florida,

latitude 25047' North and longitude 80* West, the Miami-Dade

County region is an area of approximately 2,000 square miles

(see Fig. 2). Originally covered by vegetation of the type

found in the Everglades National Park, it has rapidly been

transformed since extensive drainage, dredge and fill opera-

tions, and agricultural and urban development began in the

early 1900's. Most of the urban development has occurred

along an above-sea level strip of land paralleling the east

coast known as the coastal ridge. In the process of growth,

many species of plants and animals have been destroyed and

as much as 90% of the wildlife of the Everglades has dis-

appeared. However, the magic of the name Miami as a subtrop-

ical paradise was maintained for a long time and tourists

were attracted by the sunny beaches, mild weather, natural




























Fig. 2. Map of Florida showing the location of the
urban region of Dade County.




























GULF OF
MEXICO


STUDY AREA,
DADE COUNTY


ATLANTIC
OCEAN


FLORIDA








subtropical ecosystems, sea breezes and moderate temperatures

maintained by the offshore Gulf Stream. Summer temperatures

average 81F, winter temperatures 61F, relative humidity is

usually between 50 and 85, and 60 inches of rain fall per year.

The .additional diversity of luxury hotels coupled with the

natural systems acted as a magnet for tourism and money in-

come. Up until recently tourism was the main source of in-

come with some 10 million tourists visiting the county in

1973. In recent years the economy diversified with light

industry and aircraft related businesses, and Miami has become

a major embarkation point to Latin America and Europe. Manu-

facturing plant employment increased from 29,000 in 1954 to

77,000 in 1970.

The northern portion of the county is heavily urbanized

(>10 persons per acre) with this urbanization continuing

northward into Broward and Palm Beach Counties; this developed

coastal strip is known as the Gold Coast. Miami Beach is an

island off the east coast, world famous, and intensely devel-

oped with large, high-rise hotels and apartments. The major

means of transportation is the automobile with the Palmetto

expressway, 1-95, U.S. 1, and Old Cutler Road acting as main

arteries through the region. As in most other large American

cities there are concentrations of poor people in and around

the downtown area with high crime rates, low income, and sub-

standard housing. The average income level is higher in the

southwest and southern portions of the developed area and is

characterized by modern, single family residences. Urban


r








development has proceeded southward, influenced directly by

southbound U.S. 1.- Growth is also taking place about. Home-

stead and these two urbanized areas are creeping toward each

other along the U.S. 1 route. The western and southern por-

tions of the county are covered by extensive areas of marsh

grasses with intermittent hardwood hammocks and cypress domes.

The county is also covered by 238 x 106 sq. meters (59,000

acres) of agricultural land, tomatoes being a principal crop.

Along the southern 'and eastern coasts are systems of mangrove

trees. The major power station is located at Turkey Point.

The southern portion of Florida has long had plentiful

quantities of water during the rainy season with large sheet

flows occurring from areas north of the county near Lake

Okeechobee to the southwestern and southern shores of Dade

County. These large flows of water occur mainly along the

Shark river slough. The county is also underlain by an

extensive, shallow fresh water aquifer known as the Biscayne

aquifer, 1,500 square miles of which lie within Dade County.

Approximately 38 inches of rainfall passes through the Dade

County portion of the aquifer, which is approximately 2.72 x

10 gallons per day. This aquifer is the result of extensive

formations of permeable limestone rock; this rock is the only

mineral resource in the county. The county is also underlain

by a deep aquifer (approximately 800 feet deep) of brackish

and salt water known as the Floridian aquifer, which is

separated from the Biscayne aquifer by a layer of impermeable

rock. In an attempt to control floods, manage water supplies,








and develop agriculture and urban areas the Federal govern-

ment has created an extensive system of canals, levees, dams

and pumps to regulate water flow.. The canals prevent flood-

ing by passing water quickly to the sea, but this lowers the

water table, increasing the chances for salt-water intrusion.

Local pumping near the coastline has also increased salt-

water intrusion. The majority of water that used.to flow to

the Everglades has been diverted, a major reason for the

extensive decline in that ecosystem. This system of man-made

water control structures has radically changed the makeup of

the county. Biscayne Bay borders the county on the east and

pulse discharges of water from the canals stress this aquatic

habitat.

The population of Dade County in 1973 was approximately

1.3 million, starting from a mere seventeen hundred people in

1900 and net in-migration was approximately 40,000 people per

year. There were large migrations of Cubans in the late

1950's and early 1960's because of the Cuban revolution.

They migrated into the downtown area and the approximately

300,000 Spanish-speaking residents of the county, 200,000 of

whom are Cuban, give it a distinctly Spanish flavor.' Migra-

tions of blacks from the rural areas have resulted in 189,000

blacks living mainly in the downtown areas. Politically, the

county consists of 27 municipalities which were incorporated

in 1957 under the Metropolitan Dade County Government, while

40% of the population still lives in unincorporated areas of

the county.








Review of Previous Miami Studies


There have been many reports compiled dealing with the

economic, historical, physical, and social aspects of the

Miami-Dade region. The following paragraphs summarize many

of the reports which have been published dealing mainly with

the economic and physical aspects.

The Metropolitan Dade County Economic Survey (November,

1970) gives a brief review of the economic and social state of

Dade County including statistics on business, climate, health,

education, economic indicators, transportation, .utilities,

population and services. It focuses on the attractive aspects

in order to encourage business and people to migrate into the

county. The report, "Profile of Metropolitan Dade County:

Conditions and Needs" (Goode, 1972), is a compilation of spa-

tial and temporal data for population, environment, economy,

housing, health, education, leisure time, public safety,

transportation and social services. The report contains well-

illustrated maps depicting such things as racial distributions,

transportation systems, incidence of disease, parks, incidence

of crime, environmental quality index, and other parameters.

The report, "Facts and Figures Show How DADE DOES IT RIGHT"

(1972), put out by the Miami-Metro Department of Publicity

and Tourism is a compilation of information showing employ-

ment, income, indebtedness, budgets and several indicators

of growth which are supposed to indicate the viability,

attractiveness and growth potential of the region. Greeley








and Hansen (1972) evaluated fifteen wastewater disposal plans

and recommended construction plans for wastewater treatment

facilities based on projected population growth. Hartwell

et al. (1973) summarized the limits of water availability to

Dade County and attempted to show in a general way the stress

of increasing population on the water supply and other parts

of the system. Studies by Klein (1957,1965,1971), Kohout and

Klein (1967), Meyer and Hull (1967), Hull and Galliher (1970),

Galliher and Hull (1969), Parker et al. (1944) and Leach and

Grantham (1966) deal with hydrological conditions and the

effects of water discharge and pumping on various areas of the

county. Salt water intrusion is mapped as is fresh water head.

Road and expressway development plans for midtown Miami based

on anticipated growth are contained in "Multiple Use Opportun-

ities for Midtown Miami" (1971). Several ecological studies

of specific systems within Dade County have been completed by

Bader and Roessler (1972), Wilson (1973), and McCoy (1973).

These studies dealt with Biscayne Bay, soil arthropods, and

algal mats. The Dade County Economic Base Study (1960) ana-

lyzes Dade County's personal income position. For a develop-

ment just north of Dade County, Veri (1972) tried to assess

the impact of the development on the surrounding area, a small-

scale systems approach. It was concluded that the impact on

the existing neighborhood would be undesirable and that popu-

lation increases in the region should be greatly curtailed.

Several investigators have attempted to look at the

problems of South Florida and Dade County in a holistic or








interdisciplinary fashion. Marshall (1972) discusses the

carrying capacity of South Florida and the interaction and

interdependence between the Everglades and the Gold Coast.

The implication is that the South Florida system is already

overtaxed and as the Everglades goes, so goes South Florida.

Buchanan (1973) in the RALI report has provided a sampling of

information for 1,800 square miles in the southern part of

Dade County which should help in creating solutions for repre-

sentative problems in the county. This report seems to focus

on the technological alternatives which are necessary to pro-

vide the services needed for an expanding population. First

Research Corporation (1973) conducted economic studies for

the state of Florida by dividing the state into five market

areas. One of these areas included Dade and Broward Counties,

containing the area known as the Gold Coast, a strip running

along the coast. This study attempted to predict future mar-

ket demand by projecting past population and economic growth

into the future and thus predicting demand. No effect of out-

side energy and inflationary pressures was included in this

analysis.


Summary of Urban Modeling Approaches


While this dissertation emphasizes an energetic-ecological

approach to urban systems there are other modeling approaches

which have been applied. The following paragraphs briefly

describe some approaches used by other investigators.


L








Economic-Demographic Models

Economic based models. The external sector is the

exclusive generator of growth with an assumed linear rela-

tionship between the level of external activity and that of

local activity. Growth depends on external demand and supply

factors are disregarded. No consideration is given to avail-

able energy (Yujnovsky, 1972).

Income expenditure models. Aggregates of components in

the economy are defined based on sources of regional income

and product. This goes a step beyond the previous model in

that local demand is considered. There are extensive data

requirements and field research necessary. For example,

V+ M= C + I + G + X


where V = regional product,

M = imports,

C = regional consumption,

I = regional investment,

G = regional government expenditures, and

X = regional exports.

The method still lacks supply or available energy consider-

ations (Yujnovsky, 1972).

Input-output analysis. Disaggregates the economy into

n sectors so that production of one sector can be expressed

by means of


n
X. = E X.. + Yi
j=1


(i = 1,2, ...n)







where Xi = total production of sector i,

X.. = production of sector i to be used as input
J3 to sector j, and

Y. = final demand.

Now, X.. = A..X

where Aij is the input-output coefficient as the minimal

input required to produce a unit of a particular output.

Substituting

x = Ax + y (matrix)

x = (I-A)'1 y
which is a set of linear, simultaneous equations. Basically,

it is an accounting scheme to keep track of the interdepen-

dence of different sectors of the economy and is applicable

for a system in equilibrium or for small changes about the

reference or nominal systems.

Programming models. These consist of linear equations

for which some objective function is met such as maximizing

net income or minimizing the total cost of the use of resources.

The market is defined in advance as a set of fixed prices for

all consumption goods (Yujnovsky, 1972).

Simulation. Attempts to take into account the complex

interdependence, feedbacks and non-linearity of social sys-

tems. It is assumed that the levels and rates of change of

a set of components describe the state and changes of the

system (Forrester, 1971). These models are usually not spa-

tial in character although they could be used as such.








Demographic models. Population prediction models which

have socio-economic variables as important parameters. The

phenomenonof migration is poorly understood and usually jobs

are used as a main attraction. Gravity, diffusion and proba-

bility models have been used to describe migration (Yujnovsky,

1972). This is probably where energy available .to urban and

agricultural regions should be considered.

Spatial Distribution. Models

Location theory. Revolves about the theory that the

location of a city will coincide with the least transport

cost location with respect to the source and market of raw

materials.

Central place theory. Central place refers to the loca-

tion of a city as an area performing retail and service func-

tions for surrounding areas. The two results of this theory

are that the area served increases exponentially with the

population size of the center and that the total number of

establishments varies exponentially with both population size

of center and total population densities (Berry, 1964).

Rent theory. Each activity in the urban area minimizes

the sum of rent and transportation costs. Various schemes

are developed for trade-offs between these costs and expres-

sions are assumed for these costs as functions of distance

(Yujnovsky, 1972).

Gravity models. Distributes residential population by

relating places of residence to places of employment and








allocates service activity by relating its employment to the
spatial distribution of population. The number of trips

between two areas i and j is given by

-b
V. = Vi2 -
S k Akdik

where Vi = total number of trips generated at i,

dik = measure of distance between. zones i and k, and
A = = a-const'ant.

Transportation and trip generation models. These models

are concerned with trip generation as a function of socio-
economic variables, trip distribution, choices among differ-

ent modes of transportation, estimates of travel demand and
predictions of traffic volume at both micro-macro and inter-

intra urban levels (Yujnovsky, 1972).
Ekistics. The term ekistics has been used extensively

by Doxiadis (1963) and means the study of human settlements.
Doxiadis, an architect, has chosen to look at the general

spatial patterns of cities from an historical, cultural and

functional point of view. Unlike most of the previous

approaches mentioned above, Doxiadis chooses to rely more on

intuitive judgment when trying to design a functional pattern
to meet human needs. In particular, his consulting firm has
proposed a transportation network and master plan for down-
town Miami which relies heavily on the automobile although it
has provision for the implementation of a mass transit scheme








(Doxiadis Associates, Inc., 1967). Ekistics could also be

considered a holistic approach to city spatial planning.

System or Holistic Urban Models

Although the models described above have been viewed as

presenting explanations of various aspects of urban systems,

they all are restricted to limited parts of the city, e.g.,

transportation. They also suffer from an economic viewpoint

of the world without consideration of some of the basic

biologic-energetic laws which drive and limit natural systems

and which, theoretically, are an integral part of urban sys-

tems. For the most part, use is made of linear equations for

description since the techniques for the solution of linear

equations are well established. The following paragraphs

describe models or views of the world from a macro-system

point of view in an attempt to pick out the important vari-

ables of the city, connect them into a system, and pick out

some important principles which can be used to make judgments

about city properties and behavior.

General system theory. It has been recognized that

cities or urban areas define operating systems with inter-

locking parts which exhibit certain properties and perhaps

obey several general laws of system behavior. Built into

these system approaches may be economic, social, ecological,

etc., biases. One of the distinct advantages of a general

system approach is that it is not restricted to a particular

field of study.or a linear description of the system.








Energetic-ecological approach. Several investigators

have attempted to look at several aspects of urban and human

systems in terms of biological, energetic and ecological

points of view deriving from the vast knowledge that has been

compiled on the workings of natural systems in order to under-

stand man and his systems, even. though they are influenced in

as yet unexplained cultural ways. H. T. Odum (1971) applies

energy concepts and systems thinking to the systems of man and

much of this approach is incorporated in this dissertation.

Holling (1969) outlines the similarities between ecosystems

and social systems with special reference to ecological sta-

bility. A predator-prey model is used to model land develop-

ment where land acquisition is analogous to predation.

In Ian McHarg's book Design with Nature an approach is

presented which attempts to combine the various properties of

an area, e.g., physiography, geology, hydrology, plant associ-

ations, historical value, etc., in a systematic way in order

to develop in optimum locations. Maps are created of each

property indicating its value (based on a scale of 1 to 10,

for example) by means of shading from black to clear. All of

the maps are then overlaid and the areas which come out the

darkest Cor lightest, depending on the reference) are con-

sidered most suitable for development. The technique suffers

from the fact that each property is assumed to be independent

and if any weighting factor is used it is up to the investi-

gator to make value judgments among the different properties.

This approach is an admirable technique for.trying to bring








together and unite the systems of man and nature in a spatial

way--no calculations are made of energetic value. Essentially,

it is an architect's ecologically oriented attempt at planning

which needs to have a quantitative theory wedded to it.













METHODS


Description of Modeling Language


All symbols used in the model diagrams have been estab-

lished by H. T. Odum in the development of his energy lan-

guage. A description, explanation and mathematical descrip-

tion of these symbols can be found in Odum (1971,1972). The

symbols used in this.thesis are summarized in Fig. 3.


Model Development


Based on previous modeling experience, urban studies,

ecological principles, energetic concepts, and discussions

with various people, preliminary models are constructed with

the aid of the symbols described in Fig. 3. A pictured repre-

sentation has advantages over mathematical equations in that

it allows one to identify interactions more easily. A list

of the major outside forcing functions is compiled along with

the major storage (state variables) within the system. The

topological structure of the model is then created by making

assumptions about the interactions between the outside sources

and the internal storage. This determines the pathways

entering, leaving and internal to the system. The conceptual-

ization of the model also aided in the data gathering process


___














Fig. 3. The symbols of the energy circuit language used
in this dissertation (Odum, 1971,1972).

a. Outside source of energy supply to the system
controlled from outside; a forcing function
(E).
b. Constant flow source from outside;
J2 = k2JoX/(kr+k1X), Jr = krJ0' J1 = k1XJ0.

c. A pathway whose flow is proportional to the
quantity in the storage or source upstream
(J = klE). The heat sink represents the
energy losses associated with friction and
backforces along pathways of energy flow.

d. Storage of some quantity in the system.
The rate of change equals inflows minus
outflows (Q = J-kQ).

e. Interaction of two flows to produce an out-
flow which is some function of these flows;
usually a multiplicative output, i.e.,
f(X,Y) = kXY.

f. Transactor symbol for which money flows in
one direction and energy or matter in the
other direction with price (P) adjusting
one flow (JI) in proportion to the other,
J2Jl = PJ2
g. A combination of "active storage" and a
"multiplier" by which potential energy
stored in one or more sites in a subsystem
is fed back to do work on the successful
processing and work of that unit; auto-
catalytic.

h. Production and regeneration module (P-R)
formed by combining a cycling receptor
module, a self-maintaining module which it
feeds, and a feedback loop which controls
the inflow process by multiplicative and
limiting actions, e.g., the green plant.

i. Sensor of the magnitude of flow, J.











by helping to identify important pathways. Numerical data

were then compiled from the literature for the various stor-

ages, pathways and outside sources. Some of' the data were

approximated by using state or national average per capital

data.


Data Assembly and Evaluation

Collection and Organization

By going to city agencies in Miami, state agencies in

Tallahassee., and searching library reports and documents, a

library of reports was gathered containing information on the

urban system of Miami-Dade County. Data on such things as

total energy consumption, total budget, effective buying in-

come, population, number of telephones, building structure,

retail sales, taxes, water consumption and land development

were collected, graphed and tabulated by year from 1950 to

1972. Data for all years were not always available so that

the most recent values found were used in the models and cal-

culations. The consumption of fossil fuels such as natural

gas and liquid fuels was estimated based on values for the

state (Minerals Yearbook, Mineral Industrial Surveys). A

table of fossil fuel consumption for Florida from 1950-72 is

contained in Appendix I. Total; per capital, and rates of

change for the variables mentioned above are also contained

in Appendix I. Graphs of the data plotted as a function of

time and energy are contained in the Results section. Land








areas for urban and natural areas were obtained by planimet-

ering maps (see Table 10) and aerial photographs (January,

1973).

Cross-Correlation Analysis

For two functions X and Y which are changing with time,

it is sometimes desirable to know how.well correlated in time

these functions are. Correlation in this sense means how

well two signals track each other in time. For example, if

the two signals are ramps of equal slope they would be said

to be well correlated; likewise, ramps of equal slope but of

opposite sign would be negatively correlated. The cross-

correlation function (see Lee, 1960) between two continuous

signals, X and Y, is defined by

T
Xy(T) = lim If X(t)Y(t+r)dt
T+co -T

where the signals are considered over the interval (-T,+T).

The parameter T is the shift in time between the two signals

for which the cross-correlation function is calculated. Two

sinusoidal functions of equal frequency and in phase would be

strongly correlated. As these two signals were shifted in

time they would become less correlated until they were com-

pletely out of phase. They would then be strongly negatively

correlated. The correlation function can be normalized to

obtain a correlation coefficient defined by

rxy() = XY( T) a- a _.;








where aX= /iFx7T

GY = YY W.

If the two functions X and Y.are not continuous but discrete

values of the functions are known then the correlation func-

tion is defined by

K
XY( = 1 I X iYi
i=l

where r is the shift in time between the two functions X and

Y and K is the number of data points. The correlation coeffi-

cient is defined as above.

If the two functions are both non-stationary (containing

a trend) then one may not necessarily "cause" the other. For

example, the increasing population of New York could be corre-

lated to the increasing price of tea in China, even though

they have no relationship to each other. For Miami-Dade

County all variables have been increasing up until 1972. To

avoid the non-stationary nature of the functions a cross-

correlation analysis was done for the first differences (rate

of change) of the various parameters to see if these corre-

lated. .This cross-correlation function is given by


_Ay(T) E I K Ax) fAYl
i=l i+T

and this equation was used to construct Table 2. AX/At and

AY/At represent the rates of change of X and Y. Again the

correlation coefficient is defined as


i








r m ^AX-AY(
AX-AY 7 aa

where tX = -/AXAx(O)


The program used to calculate the cross-correlation

function is called CORR and is contained in the Nuclear Engi-

neering Sciences computer center, University of Florida.


Simulation Procedure


Simulation Model

Although a very complex model containing many storage

and pathways can ultimately be simulated on a digital com-

puter, important results can be obtained by other methods.

Simplifying complex models by lumping storage and eliminat-

ing small flows but maintaining the essence of the model

allows analog simulation, reduces chances of error, and pre-

vents the model from overwhelming the researcher with too

much detail. After a suitable model.is decided upon, the

equations representing it are solved on an analog computer

and output curves generated.

Writing, Scaling and Programming of Equations

Associated with each model diagram is a set of first

order differential equations (Nth order system) which describe

the rate of change of the state variables. The equations are

obtained by setting the rate of change with time of a state

variable equal to the inputs minus the outputs to that storage.








These pathway flows will be equal to some constant, K, times

a product of state variables and sources. This coefficient

can be calculated knowing the value of the flow and the state

variables and sources. In order for the equations to be

solved on the analog computer they must be scaled, i.e., the

maximum value that a state variable will achieve should

correspond to the maximum voltage output of the computer.

For an example of scaled equations see the details of simula-

tions in the appendices. An analog diagram is then drawn to

represent the equations with each storage corresponding to an

analog integrator. This diagram is then programmed on the

computer for solution. The numerical coefficients in the

differential equations are transformed into potentiometer

settings on the analog computer.. For example, given the

equation


Q1 = .0Q1Q2 .3Q1

where Qlmax = 10 and Q2max = 10. Then


1 = .05(10)(10) ax .3(10) Qa
[Imax} ['2max 'Imax

where the ratios in brackets are now the scaled computer

values and cannot exceed the maximum voltage of the computer
since Qmax corresponds to the maximum voltage. The entire

equation is then divided by QIMax in order to scale Q1 the

Same as Q1. This means that one second of computer time will

correspond to the unit of time which the real-world problem








is expressed in. If flows are expressed as per year then
one second of computer time will represent one year. The
equation resulting by dividing by QlMax = 10 is

S 1 1 1 ff2 1Q
= 05(10) lx L- .3q---
1Max 1Max 2Max LMax

The coefficient of the product [Q1][Q2] is equal to .5 and

is the value that a potentiometer will be set at. Likewise,
the potentiometer setting for the last term is .3.


Energy-Economic Budget Calculations

Since there are no money flows in nature a method by

which natural and man-made systems can be compared is to use
energy flow as a measure of useful work. The gross produc-
tion of natural vegetation can be estimated and used as a
measure of the useful work necessary to maintain a given eco-
system. The work performed by the natural energies of wind,
waves, and tides can also be calculated. Work processes in
man-made systems can be measured by fossil fuel and money

flows. In order to compare the energy flows associated with
natural and man-made systems, a common unit of energy is
necessary which measures equal ability to do useful work.
For example, how much work can 1 Kcal of sunlight do compared
to 1 Kcal of coal.








Energy Concentration Factor and
Energy Value of Money

Consider Fig. 4a, which is a simplified diagram of the

process of converting coal into electricity (Lem, 1973). The

box represents a power plant which is driven by inputs of

coal and purchased goods and services. The dollar value of

goods and services has been converted to Fossil Fuel Work

Equivalents by using the conversion factor of 25,000 Kcal/

dollar (Odum, 1974a). This ratio has been obtained by taking

the ratio of total sunlight falling on the United States per

year (in Fossil Fuel Work Equivalents, FFWE) plus the fossil

fuel used per year and dividing by the Gross National Product

of the U.S. This ratio is a measure of the fossil fuel work

that one dollar can generate in the economy. There is some

-disagreement as to the magnitude of the dollar to kilocalorie

ratio. Kylstra (1974) has calculated the ratio from 1947 to

1972 with the ratio in 1972 about 22,000 Kcal/dollar. The

natural energies included in this calculation did not include

the offshore marine productivities so that the ratio may be

somewhat higher. The natural energies were calculated by

taking the solar energy falling on the United States and con-

verting to FFWE's by dividing by 2,000. The actual value is

probably somewhere between 22,000 and 25,000 Kcal/dollar for

1972. This energy to dollar ratio has been steadily decreas-

ing since 1947 so that the approximate figure of 25,000 Kcal/

1A Fossil Fuel Work Equivalent (FFWE) is the amount of
useful work that 1 Kcal of fossil fuel is capable of doing.


__ _
























Fig. 4. Examples illustrating the concept of energy
quality. (From H. T. Odum, unpublished papers.)

a. Diagram showing major inputs necessary
to generate electricity and upgrade energy
concentration (quality). It is seen that
1 Kcal of electricity is generated from
approximately 4 Kcal of fossil fuel inputs.

b. Energy chain showing the upgrading of
energy from dilute solar energy to con-
centrated electrical energy. Boxes
represent energy conversion processes.
Numbers in parentheses are energy concen-
tration factors showing the number of
Kcal of energy needed to generate 1 Kcal
of electricity.










Purchased Goods
and Services


5.65 x 1012 kcal
Electricity


14.9 + 5.9 .
5.65 3


Organic
Matter


I








dollar will introduce some error into several calculations.

Since the conversion of natural energies to FFWE is also

approximate, the value of 25,00.0 Kcal/dollar should suffice

as a reasonable approximation. This number is an average

value -for dollar flows of goods and services which have been

affected by many sectors of the economy. It can be seen from

Fig. 4 that the ratio of the Kcal value of fossil fuel inputs

to the Kcal value of the electrical output is 4. In the

process coal has been upgraded to a higher quality and more

versatile form form of energy, namely, electricity. Four

Kcal units of coal are necessary to produce one Kcal of elec-

tricity. It is said that the fossil fuel work equivalent of

electricity is four, or that the energy concentration factor

of electricity relative to coal is four.

This same concept can be applied to other forms of

energy such as sunlight and organic matter by consideration

of the chain of energy processes necessary to go from sun-

light to electricity. Figure 4b diagrams in simple form the

energy conversions between sunlight and electricity. Tenta-

tive energy concentration factors for several types of energy

are listed in Table 1. Dividing a given type of energy flow

by this factor will give the energy available in Fossil Fuel

Work Equivalents. This concept of energy concentration

(quality) is in a theoretical phase following from the idea

that energy storage must be of an upgraded higher quality.

Lotka's principle also requires that energy must be upgraded

and stored to accelerate inflow and effective use. The








Table 1

Energy Quality (Concentration) Factors
Relating Different Work Processes


Energy Quality
Energy Conversion Process (Concentration) Factora

Sunlight to Gross Production 100

Gross Production to Wood 10

Wood to Fossil Fuel 2

Wood to Electricity 8

Gross Production to Fossil Fuel 20

Sunlight to Fossil Fuel 2000

Tidal Energy to Fossil Fuel 0.3

Hydrostatic Head to Fossil Fuel 0.3

Fresh/Salt Water Concentration
Gradient to Fossil Fuel I0(?)

Total Work Done in U.S. per Dollar 25000 Kcal/Dollar

aThe Energy Quality Factor is a ratio of total energy
inputs (including all subsidies) to energy output from the
conversion process. By using appropriate sets of ratios,
different forms of work can be converted to the same
equivalent type and then compared or summed. Energy Quality
Factors are preliminary and subject to readjustments. See
Odum (1974a), Kemp (1974), Young et al. (1974), and Costanza
(1975).





39


numbers in Table 1 should be considered approximate and pre-

liminary.

Theoretically, then, all energy flows of man and nature

can be compared by reducing them to the same common denomi-

nator of FFWE's. Likewise, the money flows of human systems

can be interpreted as the work they require in the economy

by the conversion factor of 25,000 Kcal/dollar (Kcal of

fossil fuel work). Thus, all the work contributions of man

and nature can be compared on an equal basis (see Table 11).












RESULTS


Data on Miami-Dade County


In this section data are assembled from many sources

for combination in energy models toward understanding the

urban system. One of the most difficult aspects of under-

standing cities in terms of an energy framework is getting

data in energy units. In human systems the standard unit of

measure is money and most data are in dollars. However, for

every dollar flow in the economy there is an exchange of goods

and services. These goods and services were the net result

of the accumulation of processes in the economy which were

dependent on energy support. In effect, a dollar can buy a

number of kilocalories of useful.work which was done in the

general economy (see Methods; Odum, 1971). Dollar statistics

give some indication of the energy intensity of the systems

which they characterize. For example, the budget of a city

is representative of the energy going into maintenance of

those parts of the city considered public domain. Data were

compiled by referring to many of the publications listed in

the references (Dade County Economic Base Study, 1960; Dade

County Budget; Existing Land Use Study, 1961; Economic Survey

of Dade County, 1970; Dade Does It Right, 1972; see Table 6)

and constructing the graphs over time given in Figs. 5-11.








The numerical data for each year used to construct these

graphs are presented in Tables 20 to 21 in Appendix I with

notes explaining the numbers. The graphs were constructed by

connecting successive data points with straight lines. There

was one data point for each year. Data points are not shown

on.the graphs for purposes of simplification.

Energy data for gasoline- and electrical consumption were

obtained from publications of the Department of Transportation

and Metropolitan Dade County agencies. Numbers for natural

gas, residual and distillate fuel, kerosene and liquid petro-

leum were based on Florida consumption of these fuels as

listed in the Minerals Yearbook and Mineral Industrial Surveys.

Figure 5 presents gasoline consumption and total energy con-

sumption where total energy is the sum of gasoline, natural

gas, distillate and residual fuel, kerosene, liquid petroleum

and four times the electrical energy as explained in the notes

to Tables 19 and 20. This energy is expressed in Kcal of

fossil fuel. Population figures are shown in Fig. 6, water

consumption in Fig. 7, total budget in Fig. 8, dollar flows

in Fig. 9, number of telephones in Fig. 10, number of vehicles

.in Fig. 11, and building structure in Figs. 10 and 11. One

of the most difficult parameters to find information for is

physical growth of a city, either in terms of square feet or

mass. Figure llb was. constructed by using the financial data

available for new construction each year and dividing by the

average cost per square foot ($8.50/ft2).


I _








Trends and Peculiarities

Looking at the data plotted in Figs. 5-11 it is seen

that the trends are similar to those experienced in the rest

of the country during a time of expanding energy, i.e., con-

tinual growth from 1950-72, except for a period during the

late fifties and early sixties. If the rates of change for

these parameters are looked at in Figs. 16-18 it is seen that

the rates of change for total energy, effective buying income,

sales tax, budget, and number of telephones have been increas-

ing, indicating a power function for the growth of these

parameters. The rates of change for water consumption, labor

force, and population seem to have oscillated. Perhaps this

is because these variables are subject to the random influence

of weather and migrations.

There seems to have been fairly gradual growth from 1950

to about 1967 with the latter part of the sixties and early

seventies characterized by rapid and accelerated growth.

The birth rate (Fig. 6a) has been steadily declining since

reaching a high in 1958 and the total increase in population

seems to be following an oscillating curve due to migrations

(Fig. 6b). It is interesting that several of the curves

leveled for several years from the late fifties to the early

sixties. During this period of time there were two large

migrations of Cubans and the Miami Metropolitan government

was created. The influx of Cubans brought in capital and

created a larger tax base which may explain why the budget

and sales tax leveled. There may have also been greater




























Fig. 5. Fossil fuel energy consumption for Dade County.

a. Graph of total and per capital gasoline
sales in Dade County from 1950-72.

b. Total and per cavita fossil fuel con-
sumption including natural gas, liquid
fuels, and electrical energy from
1950-72.
























0
2





0
0
m


w-


bi

2


02





















cY
-1 J









I-
pF
a.




























Fig. 6. Population statistics for Dade County.

a. Total population and births (natural
increase) per year for Dade County
from 1950-72.

b. Net migration and total increase in
population for Dade County from
1950-72.






46










1.5- -15 ,


a

O
10



NATURAL INCREASE

S0.5- -5 -
S-
SI-

D-!

0

1951 1960 1970

(0)


ii



zhi

2 w
kw






TOTAL INCREASE
a.
.0



(b)
I .




I..- / \ I\TOTAL INCREASE A '






S20- \\ /__. NET POPULATION -20 2
I- I \V" MIGRATION _.

a.-

1951 1960 1970


(b)
























Fig. 7. Total and per capital water consumption for
Dade County from 1950-72.



















Fig. 8. Total and per capital budget for Dade County
from 1950-72.













40
z
09
z-
04j







40-
C0
0-


















-40
ZL. 60




















go
100
0
-u
** **%

00.


WZ
4 20-









0,
4
-J




-J
a:

S
0

S200-1




0

1001


5-


II 1960 1970

Fig. 8


Fig.7


-a
a.

0
o
-200




o

I-
-100 m


TOTAL


CAPITAL


--




























Fig. 9. Economic measures for Dade County.

a. Total and per capital retail sales and
sales tax collections for Dade County
from 1950-72.

b. Total and per capital effective buying
income for Dade County from 1950-72.
















































































I I
1960 1970

(b)


-J
0
I0




u


















U.
lI"



cW











a,
-I
-I



o,





0


0
2


m


i-




u


4-



3-



2-



I-




1950


a,

-s
-j
0
a





SIf
2
4





a-
4
0r
U


EFFECTIVE


EFFECTIVE BUYING

INCOME PER CAPITAL




























Fig. 10. Measures of structure for Dade County.

a. Total and per capital value of building
permits for Dade County from 1950-72.

b. Total and per capital number of tele-
phones for Dade County from 1950-72.















0






04
aO








Z
0 h





m





0
o




























SOC
oi
z








0











5a
o."



















Us
01
0
2
I-
2












m

2


1950 1960 1970






























Fig. 11. Measures of structure for Dade County.

a. Number of vehicles (autos, buses, and
trucks) for Dade County from 1950-72
in millions.

b. Approximate total building structure
for Dade County from 1950-72 in millions
of square feet.


I






























1960


1970


NUMBER OF VEHIICLLESS








efficiency introduced due to the consolidation of the many

separate municipalities.


Cross-Correlation Analysis

Cross-correlation analysis was performed for the time

series data presented in the previous section. This type of

analysis gives a measure of how well two functions track each

other in time. It is usually important to determine the

causal variable which the other variables in a system follow.

For a city or any complex system it is sometimes difficult to

determine which is the cause and what are the effects. Based

onthermodynamic considerations energy seems to be a necessary

and primal variable for urban systems. However, once a city

system is established, changes in the population or money

supply could also be construed as causal actions, at least

over a short period of time. Eventually, energy and resources

would become the primal cause. This section attempts to give

some measure to the relationship of energy and population to

several urban indicators.

Since most of the data have increasing trends (non-

stationary) the first differences (yearly changes) were cross-

correlated (see Methods). First differences of the variables

are presented in Figs. 16 to 18. The cross-correlation func-

tion used can be found in the Methods section on page 30.

Table 2 presents.calculated values of the cross-correlation

coefficient between first differences. First differences for

population and total energy were cross-correlated with the








first differences of other urban variables. The greater the

correlation between variables the closer the correlation

coefficient is to one.. Figures 16 to 18 show how many data

points were .used for each of the correlations since one data

point was associated with each year. As can be seen from

Table 2, total energy and population rates of change corre-

late quite well with changes in other variables except for

water consumption and retail sales. The reason for the

retail sales negative correlation is unknown while that of

water consumption may be related to random effects of weather.

To put in perspective the change in energy consumption

compared to that of other parameters, Table 3 was constructed

to compare the percentage difference between 1962 and 1972

values for the number of telephones, retail sales, effective

buying income, sales tax, total budget, population, building

structure, number of tourists and total energy. It can be

seen that a 77% increase in total fossil fuel energy has. been

accompanied by a 107% increase in effective buying income, a

250% increase in sales tax, a 130% increase in the budget,

and a 100% increase in the number of tourists. The number of

telephones, retail sales, and building structure changes have

been about the same percentagewise .as the change in energy

consumption. Total population increased by 23.5%.








Table 2

Cross-Correlation Coefficients Between
the First Differences for Selected Urban Indicators


First Differences Correlateda


Cross-Correlat on
Coefficient"


Population

Population

Population

Population

Population

Population

Population

Population

Population


Total

Total

Total

Total

Total

Total

Total

Total


Energy

Energy

Energy

Energy

Energy

Energy

Energy

Energy


Total Energy

Water Consumption

Total Budget

Sales Tax

Gasoline Consumption

Effective Buying Income

Retail Sales

Value of Building Permits

Number of Telephones

.o Population

o Water Consumption

,o Total Budget

o Sales Tax

.o Effective Buying Income

o Retail Sales

o Value of Building Permits

o Number of Telephones


aFirst differences of the variables shown in this column
were correlated (see page 30 in Methods).
Cross-correlation coefficient given by equations on page
of Methods section. This coefficient is a measure of how
well two functions track each other in time. The maximum
value of the coefficient is one and indicates high correla-
tion. The time shift, T, between the two functions was equal
to zero for the coefficients calculated for this table (see
page 29 in Methods section).


0.93

-0.0062

0.92

0.56

0.901

0.69

-0.5

0.9

0.92

0.93

-0.17

0.83

0.65

0.716

-0.65

0.79

0.85








Table 3

Percentage Difference Between 1963 and 1971
Values for Several Urban Parameters


Item

Total Energy

Number of Telephones

Retail Sales

Effective Buying Income

Sales Tax

Budget

Population

Building Structure

Number of Tourists


Percent
Difference

77.0

67.1

78.5

107.0

250.0

130.0

23.5

76.0

100.0


percent difference was calculated by
subtracting the value in 1963 from the
value in 1971 and dividing by the value
in 1963. This was multiplied by 100 to
convert to percent.








Urban Indicators


The description of an urban system requires numerical

information for parameters which indicate the state of the

system. Traditionally, such things as population, area,

population density, labor force, number of jobs and economic

information have been tabulated. Recently, since the increase

in environmental awareness, measures of environmental health

and pollution have been introduced. Such things as number of

comfort days and rainfall indexes are used to indicate weather

conditions. These measures are used to compare different

urban systems and build models.

Several other measures are needed and may possibly re-

place some of the above-mentioned ones for some purposes.

For example, energy density (total energy consumed/unit area)

may give a more realistic picture of the intensity of urbani-

zation than population density. As can be seen from Table 4

the energy density of the Miami-Dade urban area is 300

Kcal/m2/day compared to a New York City value of 4,000

Kcal/m2/day (Odum and Peterson, 1972). Anyone who has visited

these two areas can perceive the difference in intensity of

these cities. Energy density could also be used to classify

different types of subsystems within the city (Wetterqvist

et al.; Brown, 1973). Total energy use per capital is a

succinct measure of the activity in the city; this parameter

can reflect the economic vitality of a population in a city.








Although most cities don't contain many large natural

ecosystems, they do contain parks, open spaces, and trees.

The ratio of the gross photosynthesis of this vegetation to

the total energy consumption is an indication of the level of

development of the city and the support from free natural

work. The productive energies of vegetation, the natural

energies of winds, water, waves, and sun provide free work

services in a region. The ratio of all natural energies

(vegetation and physical) to total energy (fossil fuel) use

is important and may be a measure of tourist competitiveness

with other competing urban regions.

Other indicators of urban areas include number of tele-

phones (a measure of the communication web), retail sales,

effective buying income (income left after taxes), sales tax

collections, water consumption, budget, number of vehicles,

net migration, square feet of buildings built (measure of

structure), total energy consumed, and money incomes and

expenditures. Another interesting measure is the ratio of

floor space area built to that of the urbanized area, i.e.,

the ratio of growth in the vertical direction to that in the

horizontal direction. In Table 4 it is referred to as the

vertical/horizontal growth ratio. This ratio is an indica-

tion of three-dimensional growth. Table 4 is a list of the

main urban indicators used for Miami-Dade County with their

numerical values. for 1971 or 1972 (see Tables 20 and 21 in

Appendix I and Table 11 for more complete information on

these parameters).








Table 4

Urban Indicators


Total for Per Capita for
Item 1972 1972


Budget
Developed Area
Economic Subsidiesc
Effective Buying Incomea
Energy Density in
Developed Aread
Expenditures
Fossil Fuel Consumptiona
Labor Forcea
Net Migrationa
Number of Telephonesa
Number of Vehiclesa
Populationa
Population Density in
Developed Areaf
Retail Salesa
Ratio of Total Natural
Energies to Fossil Fuel
Consumption
Sales Tax Collectionsa
Structure Built in a Year
Structure Existing
Total Natural Energies3
Vertical/Horizontal
Growth Ratio^
Water Consumption


$173xl06
260 mile2
$1.48x109
$5x109
300 Kcal/m2/day

$6.8x109
74x1012 Kcal.
643x103
47x103
1.093x106
880x103
1.37x106
5.27x103/mile2

$2.82x109
0.25


$179x106
150x106 ft2
1100x106 ft2
18.9xl012 FFWE
0.365

60x109 gal


$126
.00019 mile2
$1080
$3722


$4964
53.8x106 Kcal
.47
.034
.814
.64




$2183


$133
110 ft2
800 ft2




44.4x103 gal


aThese items can be found in the Data section by looking
at the graphs of these variables. Values can also be found
in Tables 20 and 21 in the Appendix.

bplanimetered from aerial photographs (see Table 10).








Footnotes to Table 4 continued

Consists of transfer payments plus federal subsidies to
agencies. See notes 6 and 7 to Table 6.
Calculated by taking total fossil fuel use and dividing
by the developed area:

73.63x1012 Kcal/yr 1 mile2
Energy density =2 6
260 mile 2.59x106 m
1 year
x 365 days

Energy density = 300 Kcal/meter2/day

eSee Table 9.

Calculated by taking total population and dividing by
developed area:

Population density = 37x06 people 5.27x10/mile2
260 mile

gSee Table 11 for a list of productivities for the natu-
ral and developed areas. The total energy of the natural
systems is 18.9x1012 FFWE. In units of chemical energy this
would be 20 times as great or 275x1012 Kcal. The ratio of
natural energies in FFWE to total fossil fuel consumption is
18.9/73.63 = .25.
hSee note 22 to Table 6.

iSee note 23 to Table 6.

JSee Table 11. An FFWE is equivalent to 1 Kcal of fossil
fuel.
kThis was calculated by taking the approximate growth in
square feet of structure and dividing it by the increase in
developed land area from 1960 to 1972. This is a measure of
vertical vs. horizontal growth. Thus, the ratio from 1960
to 1972 was

Vertical/horizontal growth ratio =
1110x106 ft2-520x106 ft2
(260-202) mile

590x106 ft2
2 mile 27 88x106 ft2
58 mile x( mile2 Z
Smile
Vertical/horizontal growth ratio = .365








Many of the above-mentioned indicators are only parts

of the overall Miami-Dade County system. Indicators of long-

range growth for the system are those which reflect the growth

of the system as a whole. Two of these parameters are devel-

oped land and population, both of which are plotted in Fig.

12 from approximately 1900 to 1972. The graph of developed

land was constructed by planimetering maps from the Dade

County Planning Department, Research Division, 1973. The

shape of the curve is suggestive of logistic growth. The

data which were used to construct these curves are presented

in Table 5, which also includes the rate (velocity) of devel-

opment computed by taking the total development over ten-year

increments and dividing by ten to get an average yearly rate

of development. Another indicator of long-range growth is

total fossil fuel energy consumed, a plot of which is pre-

sented in Fig. 5b from 1950-72. It should be possible to

determine various storage and flows in the system if the

total energy needed to support a given level of structure is

known. Figures 13 to 15 show effective buying income, retail

sales, total budget, number of telephones, number of tourists,

sales tax, and building structure as a function of the total

fossil fuel energy supporting the system and as a function

of the sum of electrical and gasoline energy consumption.

Several of these curves are almost straight-line growth

curves while others are close to piecewise linear; the slope

of the curve for sales tax in Fig. 15 seems to be increasing,











-4-4





S400
w 4




4 0



M 4)
0 h-1










44






0$..
-1 0










+3 0
0a4














o4 c
be














































c4)
m -H
Q 2

id
C 3





a4o







o 3
'0 (3


*H W
40






Pc.


o C o 0 0 ('
M') n o t- '
0) l) 0m m a 0)
r4 r1 -1 -4 r- -4


0
4)

U
*H



n


C

E- a4






0O


o r- o o
















C) 4') n bt) Ln '

N M a- Ol u3 a

















S 0) -- n n \0
0oo 0 (' Ln 0 (












Ln 1n Ln



o 0 0 0 0 l












-l C4) '0 0 0 L- '0
C- (4 (C4 ('


c4)
40
P4-









ed
tn





0
g
1-










0*
a
&

0 *-
%%j
CI.1
0
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.--I
M














)rl
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4-1 c









c 0
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c o




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^g























R,


00
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Cd




90
o
qi4












0


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kC1







P. tn
.0










04)0
(-4- -4



4-)
0
Cdc













0
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Cd
















04)

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4-)
0 4)
-4






-4












oldood jo -ON 'UO!lDlfdod
o 0
3 0 x
0 to


0 0
0 0
ciJ
solINA eajonbS 'puo-1 padolOAOeQ



























Fig. 13. Several parameters in Dade County as a func-
tion of total fossil fuel energy.

a. Total budget, retail sales, and effective
buying income as a function of total
fossil fuel energy supporting the system
of Dade County.

b. Number of tourists, number of telephones,
and sales tax collections as a function
of total fossil fuel energy supporting
the system of Dade County.





















Effective
Buying Inco


Retail


.0
.o


2200-
- -



0
-o



4-


20 40 60
Total Energy, 1012 kcal

(a)


I I I
20 40 60 8
Total Energy, 1012 kcal


')

O




Eo0
0






-4 0
3



-2 vO
0.

S.-
-3 .|



Y I


SII


80
80


-4)

-1000r

-800 C0
|o
-600 |.-_


-400
oo

-200 z

0


I I I


0

S200-
CD
'O

0


V)



0


I


























Fig. 14. Building structure and economic flows as func-
tions of fossil fuel energies.

a. Building structure as a function of total
fossil fuel energy supporting the system
of Dade County for two different rates of
depreciation.

b. Effective buying income, number of tourists,
number of telephones, and retail sales as
functions of electrical plus gasoline energy
supporting the system of Dade County.














150
Co



:100


CO

50-



0

0



_o
Co
o
" 15-




a a10-
0 10

a=
0
I...
5,- 3

o00 5-
z Uz

0
0
C


Building Structure


(a.)







Retail Sales



No. f No. of
No. of X Tourists
Telephones /


v'Effective Buyin


Income


g


Co
Ob

0-
-3 -
0




-0



0


I I I
) 10 20 30
Electrical & Gasoline Energy, 1012kcal
(b.)


I I I I
20 40 60 8
Total Energy, 10 kcal






















Fig. 15. Effective buying income, sales tax collec-
tions, and total budget as functions of
electrical plus gasoline energy supporting
the system of Dade County.
















Fig. 16. Rate of change per year for total energy,
electrical energy, and gasoline energy for
yearly intervals from 1950-51 to 1971-72.
All units in 1012 Kcal (FFWE).

















4



0

0
-a

0

z
0

a













z
0
0
2
0
2

a















w

v
0

















1. -
hi





hI







2

-Jo




0

w w


-4 F

04 V)

-00
ILLC

01-
4W
0:


Fig. 15


YEARLY INCREMENTS

Fig. 16


0,
0:
4
120.






40
.o
1-

hi'






'40 ,1

4




























Fig. 17. Rates of change for economic flows and water
consumption in Dade County.

a. Rate of change per year for effective
buying income, retail sales and sales
tax for yearly intervals from 1950-51
to 1971-72.

b. Rate of change per year for total budget
and water consumption for yearly inter-
vals from 1950-51 to 1971-72.











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Fig. 18. Rates of change for labor force, population
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a. Rate of change per year for labor force
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b. Rate of change per year for number of
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76








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77 \


indicating a power function relation to the sum of electri-

cal and gasoline energies in the system.

If the city indicators discussed above are plotted on

a graph as a function of time (Figs. 5 to 11), then trends

(rates of change) can be identified. 'This is further needed

information when comparing different urban systems in addi-

tion to Table 4 of city indicators. The rate of change

(velocity) of flows and storage in the system can be derived

from the graphs over time. The rates of change of all the

urban parameters are graphed'in Figs. 16 to 18 from 1950-72.

These graphs are further discussed and analyzed in the Data

section.


General Overall Model of Miami-Dade County


This section presents an overall macro-model of the

Miami-Dade system for purposes of describing system components,

interactions, and numerical values of flows and storage.

Figure 19 is the diagrammatic representation of the system

with accompanying Table 6, which.delineates numerical values

and associated calculations and assumptions. The circled

numbers of Fig. 19 refer to pathway numbers in Table 6. The

outside forcing functions have been grouped into three main

categories, namely., fossil-fuel energy and goods, natural

energies, and money inputs. This grouping was chosen so that

Fig. 19 represents a general urban model since all urban

regions depend on these outside forcing functions to greater



















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or lesser degree. For example, for an industrial city an

industry storage and outflow of industrial goods in exchange

for money would be substituted for tourism. As can be seen

from the diagram, the major forcing functions for the Miami-

Dade region include fossil fuel and food energies, tourist

dollar flow, federal economic subsidies, sales of goods,

population migration, natural energies, and external land

available for development. The flow of tourists in and out

of the region has been represented by the tourist money coming

into the system which is inversely proportional to the price

of goods and services in the external (U.S.) economy. In

fact, all prices have been assumed to be determined by the

economy of the United States as. a whole, which reflects world-

wide fuel availability and inflation.

The main storage which have been chosen to represent

the system are private structure, roads and vehicles, popu-

lation, government structure, water supply, developed land,

wastes, and money. It can be seen that the production of

structure and people is dependent on an interaction of all

segments of the system, i.e., complex systems are highly

integrated. This interaction depends on the natural energies

of the system which are necessary for survival and provide

work services for man. The wind energies of the system are

especially important in maintaining the air quality of the

system which serves-as an.attraction for people and tourists.

Depreciation on all structures has been included to represent

decay and is assumed to be 5%/year for a mean building life








of 20 years.. The entire system is enclosed in the hexagonal

symbol representing an autocatalytic system.

Another main aspect of the model are the pathways of

money flows. These include the external sources and sinks

of money along with the internal cycles of wages and sales

which account for distribution within the system. It is seen

that developed land is generated by available monies within

the system for purchase of external, land. In a sense the

model is the superimposition of two models, one depicting

the flow of energy, people and goods through the system while

the other describes the money flows. These two systems are

connected.through price interaction equations (see Fig. 3 and

later simulated models).


Urban Mini-Model Driven by External Storage
of Fossil Fuels and Linear. Price Functions


In Fig. 20 is a simple model.which aggregates the struc-

ture of the city (meaning square feet of buildings) into one

storage and the money available for spending into another

storage. It is assumed that the growth of structure, repre-

sented by J2, is a product function of the structure Q1, the

money storage, M, and the fossil fuel, F, which means that all

three variables are necessary for growth to occur. If, for

example, money flows out of the system M will decrease with

a resulting decrease in the rate of growth, a consequence of

limited capital. Compensating for the growth of structure is

an assumed depreciation rate of 5% per year, represented by a




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