ENERGY BASIS OF CISaSTEPS ArlD THE
CYCLES 0: ORDER AND DISORDER
JOH:I FPPA.'KLIfI ALE
A DISSERTATION P"ESENTE: T(. T E Tlh- R.D:PTE CUNCl;!L OF
THE L'I!VF.R IT.' OF Fli, PIDA
I: PARTIAL FLUL.FILL'ilT OF THE FECOIPEi'~ENTS FO "-HE
DEGREE OF WO:CTOR OF Pii:LLCSC'FH
UNIVEPSIT" OF FLORIa,,
Appreciation is expressed to Dr. Howard T. Odum, my committee crair-
man, for hi; inspiration, knowledge, and deep insight into ecological
problems of man and nature. I am greatefui for haj ng qj-";td underDr ('Gaum orn
many exciting projects and stud.; in his systems ecology program ir the
Department of Environmental Engineering Sciences from which I ha ,e
developed a keen sense of appreciation for ecological and energy Fri.,-
ciples wnich organze the wrrlo.
Many contributions were made by members of my committee: Fr. Djjl
Doughty in the field after tne Guatemala earthquake; Dr. jim BurnI. *.itn
simulation; Dr. W.:yne Huber \jith local energies; Dr. Charles Roes-sler
with ion i:in.; radiation. Also, assistance was prc',ided by Or. Jeromar
il11 iman's 3,avi.:e on economic aspects of disasters. Professor Eyron
Spangler advised on the engineering aspects of disasters.
Investigation was carried out under the sponsorship; of the United
States Department of Energy (contract EY-76-S-05-41392 project entitled
"Energy Analysis and Models of the United States" and the United States
Nuc'.ar Regulator; C3;mmn sion ,(contract NPC-04-77-1231 project entitled
"The Ener.; Anl.,sis .of Envircnmental Vaiues." H. T. Odurr. principal
irnestigator. ',.'or in Guatemala was sponsored by the United 3'a.':
.Agency fcr nte.rnai'.onai Development (contract AID 520-2.62 project
enti led "A C:ncTieheonsi~l Plan for the Reconstruction of El Pr.c3rEo,
uuatemala." john F. Ale/arder, Jr., principal inve;t'gatcr.
Thanks are eAtended to Joan Ereese and Linda fate- for assisting
in typing drafts. David Jass for drafting of figures, Diar.e Goddard
for editing, and Rossina Fernandez for final typing the manuscript.
TABLE OF CONTENTS
ACYNOWLEDGEMENTS . . . . . . . . . .. . . i i
LIST OF TABLES . .. . . . . . . . . . v11
LIST OF FIGURES . . . .. . . . . . . .. .. vii
ABTPACT. . . . . . . . . . . . .... .
INr TPODUCT . . . . . . . . . . . . . 1
Theory of Order, Disorder, and flaterial Cycling .
Catastrophic Consumption and Pulsing. ..... .. -
Secordary Disorder and Caioading. . . . .....
Global Model . . . ...... . .... ... . .. ii
The Global Energy Web and Natural Disasters.. . . ..... .
Energy Ouality and Embodied Energy .. . ...... .
Energy Erbcdied in Rad'ation . . . ... . . 16
Pr'eious Work on the Theory of Order, Disorder, and ul:in3. 13
Previous Work on Natural Disasters . . . . . . 0
DE:criction of SnLdy S situations and Previorus Jor'l. ..... 24
Global Models of Ato;.3her :c, Oceanic, .:igi:cal,
Geological, and Urban 5,stems . . . . . .. .
The Tropica; Rain Forest at El Verde, Pua'-r Ric;
and the Effect r additionn . . . . . . . -
JoHrstown, Penisylvania, Ind t.e Failjars or th,. .cun
Dam . . . . . . . . . .
Guatemala and the Ertnouare of FeFruar-, 4, '97'. . ..
IETI-'ODS ..... ............... .......... -
Description of Modeling Language and Smbols .. ..... !
Development of Models. . . . . . . . . .. .
limiting Factors ar.nd Different
Data Assembiy and Evaluation of Models . . . . . .
Simulaticn Procedures .. . . . . . . .. . .
.lculation of Ratios. . . . .. .. . . . 54
Calculatior cf Spatial Distribution of Suisnic Enery.. . 55
Plan of Study. . . ....... .. .. . .. .
RESULTS . . . . . . . . . . . . . -
Simulation anoa analysis of Order-Cisorder Models .... . .
Si.it:i rg Pulse Models . . . . . . .
E..ponential Surge Model . . . . . . 71
Evaluation of Global Energy l eb and Disasters. . . . 7'
Atmospheric Circulation and Storms. . . . 33
Oceanic Circulation . . . . . . . . . '
Photosnthetic Production. Animals, and Fire . .. '9
Plate Tectonic;, Volcanoes, and Earthquales . . .. 105
Uroan Structure, Fire, Disasters, and War . . .. 113
The Glotal Energy 'leb and Energy Ouality of Disasters 121
Evaluation and Simulation of the Fadiation Stre:s on a Tro-
pical Pain Forest at El Verde, Puerto Rico . . . . 122
Evaluation of the Pain Forest Model . . . . . 12
Simulation of the Order-Disorder Process in the Pain
Forest Ecosystem. . . . ... ... . . . ..134
Calculation of Order-Disorder Energy Patios for the
Pain Forest . . ...... . . . . . 131
Evaluation and Simulation of the Jonnstown Flood of 1839 . 16
Ealuation of the tlodel ... . . . . . .. . 139
Simulation of the South Fork Dam Failure and the Des-
truction of Johnstown . .. . . . . . . 113
Disaster-Amplifier Patios for Johnstown and the Flood l16
EJaluation and Simulation of the Guactemala Earthquake of 19'5 146
Evaluation of the Model . . . . . . . . 14
Simulation of the Earthquake and Secondary Distribution 156
Calculation of Disaster-Amplifier Parics. . . .. 154
DISCUSSION . .. . . . . . . . . . . . . 164
The Dynamics of Pulsing Systems. . . . . . .. 16
The Cciing of Matter . . . ... ....... . 164
Energy Convergence and Storage. . . . ... . . 165
Exponential Surges and Energy Pulses. .. . . .. 1
System Control through Cascading. ........... 166
Dynamic Behavior of Energy Cycling :cdels .... . .166
Glcbal Energy N.eb ... ........ . . .... . 166
Energy Quality, A Universal Energy Conversion Facccr. 167
Embodied Solar Energy, A Universal Measure. . . .. 1. .
Disas-er-Amplifier Ratios, A Measure of Control . . 168
The Frequency of Pulsing and Contrnl. .. .. . 169
Control of Global Cycles by Solar Pulses. . . . 16)
Disasters . . . . . . .. . . . 170
The Energy Cost and Benefit of Disasters. . ... !70
The Distribution of Disaster Pulses as a Ccntrol Device 173
Common Aspects of Disaster and Disorder in Different
Systens ............. . ....... ..
Puls;ng and a. imum Power . . . . . . . .. 175
Disaster Plann:ng and Future Pesearch. .... ..... .. 176
APPENDIX 1 NOTES TO TABLES 2-7, 9, 1, AND 11. . . . . 1.-2
ADPErNDIY 11 DYNAO1 PPOGRAMS. ....... . . ...... . li
LIST OF PEFEREN!CES . . .. ... . . .21
BIOGjiRAPHICAL SKETCH ... .. . .. . .. .. ;l,
LIST OF TABLES
1 STEADf-STATE SOLUTIONS AND STEADY-STATE VALUES FOR
THE ORDER-DISORDEP MIrJIMOELS Inr FIGURE 14.. . . . 69
2 EVALUATION, NAME. AND DESCRIPTION OF ENEP'Y FLOWS
AND STORAGE FOR GLOBAL ATMOSPHERIC SECTOR rlODEL
IN FIG'uPE 19. . . . . ... . .... .. 6.
3 EVALUATION. NAME 41D DESCRIPTION OF ENERGY FLOWS
AND STORAGE FOR THE OCEANII SECTOR OF THE MODEL
INJ FIGURE 21 . . . . . . . . . . .95
4 EVALUATION, NAME. AND DESCRIPTION OF ENERGY FLOIS
AND STORAGE FOR BIOSPHERE 'OOEL Ir: FIGURE 22 .... 102
5 EVALUATION. rAME, ANr DESCRIPTION OF ENERGY FLOWS
III GEOLOGICAL SECTION OF GLOBAL MODEL III FIGURE 23. . 10
6 EVALUATIOr, NAME, AND DESCRIPTION OF ENERGY FLOWS
ArD STORAGE FOR FLOODS AND CITIES OF FIGURE 24 . .. 116
i GLOBAL DISASTER-AilPLIFIEF: RATIOS FGP CITIES ANjD NATURAL
DISASTERS . . . . . . . . . . . 1: 0
8 ENERGY QUALITY FACTORS FOP GLOBAL PROCESSES AND
DISASTERS . . . . . . . . .. . . 123
9 GAMMA RADIATION AND SOLAR RADIATION STORAGE AND
FLOWS FOR MODEL OF RAIN FOREST IN FIGURE 27 . .. 129
10 EVALUATION. NAME, AND DESCRIPTION OF ENERGY FLOWS
AND STORAGE FOR JOHNSTOWN FLOOD MODEL. . . . . 10
11 EVALUATION;. NAME, AND DESCRIPTION OF ENERGY FLOWS
AND STORAGE FOR EARTHQUAKE MODEL IN FIGURE 32 . . 1
1 ENERGY ABSOPBED PER SQUARE METER OF ADOBE HOUSE BY
ISOSEI'rAL INTENSITY :'CI.ES FOR GUATEMALA EARTH-
QUAKE OF FEBRUARY 4, 1976 . . . . . . . 153
1. DISASTER-AMPLIFIER FACTORS FOR SECONDARY DISASTERS
IN /ARIOUS CITIES ill GUATE'lALA. .. . . . . . 162
LIST OF FIGURES
1 Energy circuit models of order and disorder. ..... .
2 Energy circuit models of order-disorder cycle with
catastrophic energy pulsing in the disordering loop. .
3 Energy circuit model of concept of cascading of
energy pulses which may be regarded as disasters,
to smaller elements of the systems . . . .. 10
4 Model of the global crust composed of energy flous
of atmosphere, ocean, biological, geological, and
urban subsystems . . . . . . . . . 13
5 Energy circuit translation of economic model of risk .. 2
6 Location maps and diagram of Puerto Rico and El Verde
Esper Ent . . . . . . . . . . . 3!
7 Location map of Johnstown and the South Fork dam . . 3
S Location maps of Guatemala, El Progreso, and the Motagua
Fau lt . . . . . . . . . . . . 39
9 Maps of damage to adobe structures and earthquake
intensity in Guatemala . . . . . . . . 41
10 Energy circuit language group smb'ols. . . .. .
11 Energy circuit language mathematical s,mtols used to
construct modules in Figure 3. .... ....... .
12 Order-aisorder model in energy circuit language,
illustrating the incorporation of internal and
external limiting fac o s. . . . . . . .
13 Crder-disorder model illustrating energy flows used ;n
calculating the order-disorder ratio and the disaster-
amplifier rn tio . . . . . . . . . .
14 A comparison of several order-disorder models and their
simulation results . . . . . . . . .
15 Energy circuit disorder model of disaster typical of
previous fire and epidemic models of otner researchers. 73
16 Order-disorder energy circuit model with catastrophic
energy, pulse generated by consumer module. .. ... . 75
17 Pesult: of simuJlation of julse model in Figures 15 and
16. . . . . . . . . .. . 7 S
18 Web model of global energy. . . . .. . . 81
19 Energy circuit diagrams of atmospheric system . . 8 5
20 Global distribution of solar energy with latitude . 90
21 Energ; circuit models of the oceanic systems of the
eartn . . . . . . . . . . . . 94
22 Energy circuit models of biological energy concentration
process of the world. . . ... . . . . 101
13 Energy circuit model of earth's geological system . 107
:4 Urban order-disorder model with depreciation, fire, war,
and natural disasters in disorder process .. . . i
25 Global energy web model diagramed in energy circuit
Sanguag . . . . .. . . . . . . 119
26 Order-disorder model of gamma ray stress on tropical
rain forest at El Verde, Puerto Rico. . . . . 125
27 Evaluated order-disorder model of qamma ray radiation
stress on tropical rain forest in El Verde. Puerto
Rico . . . . . . . . . . . 128
28 Gamma radiation field and effects on tropical rain
forest at El Verde. . . . . . . . . 131
29 Pesul-s of simulation of order-disorder gamma ray model
in Figure i7 . . . . . . . . . . 133
30 Energy circuit nodEl of Johnstown, Pennsylvania, 1329,
and the disruptior generated by the catastrophic
failure of the Scutr Fork Dam . . . . . .. 133
31 Simulation results of failure of tne South Fork Dam
model in Figure 30. . . ... . . . . 145
32 Eartnquake order-disorder model for Guatemala eartn-
qua.e . .. . . . . . . . . . . . 143
33 Energy distribution in Guatemala from tne major event,
February) 4, 1976 earthquake. . . . . . . .156
34 Simulation results of earthquake model in Figure 32.. 15.
35 Structural damage of towns in Guatmjala a; i function
of earthquake energy dissipated by the adobe houses. 160
36 Conceptjal model illustrating possible mechanisms for
control of global energy cycles by Solar Pulsing 172
37 A test of the effect of pulsing on the principle of
maximum power . . . ... . . . . . .17j
Abstract of Dissertation Presented to tre Graduate Council
of the University of Florida in Partial Fulfillment of the
Pequirements for the Degree of Doctor of Philosophy
ENERGY BASIS OF DISASTERS AND THE
CYCLES OF OPDEP AND DISORDER
John Franklin Alexander, Jr.
Chairman: Howard T. Odum
Major Department: Environmental Engineering Science
A quantitative theory of cycles o-der and disorder was applied to
the earth and evaluated to form an energy Lasis for the global ccles,
surges, and disasters. Energy circuit language was used to diagram the
world system and show a common pattern in the order-disorder processes.
Storms, floods, forest fires, volcanic eruptions, earthquakes, ur-
ban fires, and *.jars were modeled as the catastropnic release of ener.t
previously converged ind stored. Released energy, disordered and re-
cycled material available to stimulate a new cycle of growitn. Cascadir.g
of catastrophic processes of disasters was modeled .ith a world '.wab.
The feedback in the global energy wecb wias provided by the control action
of disaster pulses. The global model .ias presented in ooth diagrammatric
and differential euation form with the er'ergy flo:.s and storages e/ai-
uar.ed. Order-disorder models of the atmospheric, oceanic, biological,
geologic3!, and urban systems of earth were connected to form an energy
The global energy model was used to calculate energy quality
factors (ratio of energy of one type gernrating energy of anocner type)
for the earth's, major energy transformations. The ratio of solar energy.
required to produce a catastrophic event to the energy released in the
event (Calories per Calorie) was found to be 1 < 10":1 for volcanoes.
5 < lO :1 for earthquakes, 1 A 105:1 for urban fires, floods, and wars.
2 x i0':1 for forest fires, and 2 w 10I:1 for storms. The energy; qual-
Ity factors of stored er.erg; were used to calculate emitsodied solar energy.
The hypothesis of selection for maximum power was used to e.plarin
the prevalence of systems that recycle structure b) the catastrophic
release of energy pulses generated in disasters. The solar energy em-
bodied in the disordered city structure was found to be 1.4. 1.3, and
1.7 times the solar energy embodied in storm. flood, and seismic pulses
of the global web.
The dynamic properties of several configurations of models of ere
cycles order-disorder were analyzed by solving the model in differential
equation form and through computer simulation. The most suitable model
has a production function supplying energy to a consumer that alternaial!
shifts from linear Flow to a surge of exponential growth causing an
Suitability of order-disorder models were further tested b, appli-
cation to three case studies: (a) effect of gamma radiation stress on
5 tropical rain forest in Puerto Rico; ,b) the disordering of Johrnitcn,
Pennsylvania, by the great flood of 1889; and (c) the destruction of El
Progreso, Guatemala. by the earthquake of 1976. The dynamic effects of
the flood on Jonnstown and the earthquake on El Progreso were Todeled
with tw.o order-disorder models in cascade ana simulated. The resulting
graphs of the destruction of the towns studied compared favorabtl with
The energy flous thac produced order in the radiation, flood, and
earthquake case were 13,000. 970. and 7,700 rimes the energy flows
required to generate disorder when measured in neat equivalent;. When
expressed in embodied solar equivalents, the ratio of ordering energy
to disordering energy was found to be 1:1 for radiation disordering
and from 25:1 to 25:1 for pulse disordering.
The theory provided suggestions for land-use policy. Energy ratios
that provide a quantitative basis for disaster planning can be developed
for a local environment of pulsing energy.
Possibilities were considered that cycles of order and disorder of
tne earth are synchronized by Cycles of sunspots. Energy quality and
pulse amplifier ratios of solar flares may be high enough to control
many global cycles.
A major problem in environmental science is the nature of c ,/cles
of order, disorder, and dilasters. How are the..e related tc. the solar
energies that drive most processes on earth? Ho'; do .he patterns of
the biosphere linit the roles of humanity and provide planning prin-
ciples? In this dissertation, energy analysEs, energy system's crn-
cepts, and simulation methods are used to test theories re'i;rg
order and disorder. Included are eailuations o; ear'.hquak.es. floo'.
ionizing radiation, solar fla-es, and the world ener; web'. -.pec'fir
case studies include the ga.mrra irradiar-on of a tropical rain forest.
the Johnstown flood of 18:39. and the i;uiatemral ert.hqu:.- of 197..
Tne ability to converge energy, in space and time : r.yctin
matter may be a fundamental principle cf all sys'teCs of man and na u':.
As systems build structure by concentration :f energy in 'he form of
ordered matter, potential energy gradients are creAeed. The storage
of energy that are formed become sources cf even steeper potent-';
gradients. Extensive competition exists for the use of concertratej
forms of energy. The principle of selection for ma.Jimum power sug-
gests that the "Sstem that can process storage .nost effect .'el.' ll
cut conpeie the ctnar systems When energy is processed at jery high
ratespulses are generated that are transmitted against. the cjncentr:a-
tion uradient performing a control on the surrounding creas irnd on the
energy convergence w.eb. These surges are oft'n regarded as disasters.
Theory of Order. Disorder, and Material Cycling
Figure la is the basic configuration of the order-disorder model
diagramed in energy circuit language (H. T. Odum, 1971) that was used
throughout this research (see Methods section). The system converges
energy to power the production of structure by transforming disordered
matter into ordered state (lower entrop}), however, the entropy of the
total process increases as much as the energy required to power the pro-
duction process is degraded as waste heat. The structure built up in
the production process continuously undergoes depreciation in such a
manner that the stored energy is dissipated as waste heat and the
material recycles to form disordered matter.
The energy circuit model in Figure lb is similar, ecepr. an external
energy source drives the consumption-recycle process. In this model the
rate cf material recycle is proportional to the magnitude of tne stress
energy source. In both of the models in Figure 1, the matter is cycled
as energy flow through the system. In one the energy driving recycle is
only from its own storage.
A basic question, analyzed in this dissertation and illustrated by
the order-disorder model in Figure 1, is "what relationship, if any, e.iszs
between the energy required to order a system versus th3t required to dis-
oroer it." In order to address this question, the model w-as evaluated
using data from several examples and simulated. E.'amples ircludec irradia-
tion of a tropical rain forest at El Verde, PuertoRico. and the catastrophic
Figure 1. Energy circuit models of order and disorder.
ai) Ener]y circuit of basic process of crder
and disorder believed to be characStristic
of all systems of man and nature; re:,cle
uses stored energy.
jb) Basic order-disordermodel with discroering
process driven by external energy source.
destruction of Johnstown, Pennsylvania, and El Progreso, Guatemala.
Catastrophic Consumption and Pulsing
As systems build up substantial storage of energy in the struc-
ture form of ordered matter, massive potential gradients are formed. As
the gradient becomes larger, the production of order by tie system often
exceeds the loss due to depreciation through linear processes such as
diffusion. This, therefore, increases the possibility and opportunity ,
for a consumer system to form that will further concentrate the stored
energy and release a pulse of energy in a control action. To e>plin
this concept, the order-disorder models in Figure 2, similar to the pre-
viously introduced model, were developed. An autocatalytic or self-
generating consumer system was added in the disordering energy flow
path to further concentrate stored energy. in the system diagramed in
Figure 2a, a trigger pulse, or seed, is required to start the consumer
system; however, once triggered the system will grow at an e.spoi',ential
rate until the energy storage in the form of order in the producer
system is consumed. This growth of the consumer system produces 3n
energy control pulse that is exponential at first and fades as t"e
storage are exhausted.
The model in Figure 2b is similar except the system is capable of
self-tr'ggering; that is, when the energy storage in the producer sys-
tem reaches threshold, the consumer system self-activates. Consumer
systems that can process large quantities of energy at hi;h rate; pro-
duce catastrophicpulses of energy when activated. The order-disorder
models in Figure 2 are suggested is a dynamic system that can simulate
the concentration, storage, and catastrophic release process found in
many systems of man and nature, of which natural disasters are a sKecUil
Figure 2. Energy circuit models of order-disorder c)cle with
catastrophic energy pulsing in the disordering
(a) E:.ternal; triggered disaster.
fD) Self-:tr.gered disaster.
OFrQEi JLL4. r. PULSE
ENERGY / /-
| PF.CUCLJ ,. /
"PF ---,_/ "_,_"
I "u .-- ,,\ ,/ ",,//
case. Data from the catastrophic collapse of 5 dam resulting fro.T the
e-:ponential growth of turbulence were used to evaluate the model. Sim-
ulations were performed and the results compared to field observation
for the Guatemala earthquake and the Johnstown flood.
Secondary Disorder and Cascading
Two order-disorder models with catastrophic consumer systems were
cascaded to extend the theory to explain and simulate the secondary,
disruptions created by a major disaster pulse such as an earthquake.
Once the surge of consumption starts it may generate waves of disor-
dering energy spreading into surrounding energy convergence systems.
Figure 3 is an energy circuit diagram of this concept. In the mcool,
the energy storage increases until the energy flow in the disoruered
loop is great enough to generate a dynamic structure, which feeds
back onme of the energy to pump more. This results in eponential
growth of the storage of Linetic energy until the potential energy is
effectively exhausted. lihen sufficient energy is coupled to the
structure of the impacted system, tne potential energy stored in the
impacted system is released causing a secondary disaster. Some notable
examples of secondary events triggered by earthquakes are glven by
Aye (1975): (1) failure of man-made structures such as buildinqs and
bridges; (2) avalanches, landslides, rockslides, and other natural dis-
ruptiors, (31 fire; (4) floods and flash floods from tidal ,av'es and
ruptured dams. and !5) volcanic eruption. Niot that each of the above
events involves the cascaded release of potential energy stored in the
structure of the secondary source. The cascading of disasters is
believed to be of considerable importance in understanding the dynamic
behavior of systems under the high stress of natural disaster pulses.
Figure 3. Energy circuit model of concept of cascading of
energy pulses which may be regarded as Jdisaster:.
to smaller elements of the systems.
The multiple hazard phenomena must be included in a disaster theory to
make it plausible for application to real world ca;es.
This theory was tested by evaluation of the model with data from
an earthquake and the secondary destruction of several towns. Sinul3-
tions were performed and compared to observed destruction.
The global model in Figure 4 connects energy concentration, stor-
age, and consumer subsystems into a web. This energy web provides a
framework that helps to explain the nature snd function of disasters
in a global context. The model also outlines a conceptual network for
evaluating the flows and storage of energy that power various global;
processes. The web is composed of self-regulating units that success-
fully converge energy of the sun. Each module produces order and
releases it with a pulsed consumption that forms a temporary high
energy system. To survive in competition this pulse of energy must
couple with or feed back to other systems. Pulsing the energy trat ;s
fed back in a control action produces an amplifier effect in disor-
dering and recycling other systems. Systems that survive are those
that become organized and adapted to operate in a regime o' pulses
and use these pulses to power recycling processes and other means to
achieve maximum power.
The Global Energy Web and Natural Disasters
Natural disasters have been a subject of oreat interest -o hu.Tan-
it, throughout recorded history. Earthquakes. volcanoes, flocon. st.:rnt,
fires, and epidemics take a great toll in life and property. Hazaras in
the United States cu-rantly generate an economic less in excess of one
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billion dollars per .ear, with all data indicating that this will become
an ever-growing problem (Uhite and Haas, 1975). Pulse disasters are a
major parr of all systems of nature with cata;troFhic energy. releases.
often with cascading effects, causing many smaller systems to be disor-
dered. Energy concepts of order and disorder provide a systematic means
of disaster analsis and help explain and generalize about natural di-
sasters. The theory, is that global processes concentrate, store, and
catastrophically release energy according to a common pattern,thus
creating natural disasters.
Enerqv Oualit, and Embodied Eneray
Energy ;ualit) theory) as deJeloped by H. T. Odum (1971) and re-
cently amplified (Odum, 1976j was built on the laws of energy. The law
of energy conservation provides the bssic underpinnings for all energy
circuit diagraTs. In a first law energy diagram, the average heat
equivalent stored or flowing per unit of time is used to evaluate t"ih
model. lihin evaluated in heat equivalents, all systems of man and
nature conserve energy, that is, the sum of all the flows into a s)s-
ten less the flows of energy out must equal the net changes in the
energy storage. The system models in this dissertation neet the first
law requirement. Unfortunately, heat equivalent measures provide no
information relating to the potential value of energy flow or storage
fcr performing work or controlling a system.
Working *ith the law of energy degradation provides insight into
assigning a value to a particular energy flow or storage. The law of
energy degrnationn states tha: in all useful processes some energy
Tmust be degraded, thus losing its ability to do work. The concept is
incorporated into energy circuit language bj requiring 'ioet sins or
energy degradation pathwa. s on all energy flows, processes, aid scor-
ages. The quantity of energy dissipated by each energy concentration
process is also evaluated in heat equivalents in energy circuit dia-
grams, even though these energy patnwas can do no useful worn on this
The concept of energy quality place; an embodied energy measuring
cost in energy units on the concentrated flows and storage wlhicn re
a resultant of the energy convergence property of system:. Energy
quality factors for systems are defined to be the ratio of tne heat
equivalent energy produced or upgraded by a system to the quantity of
energy required to power the system.
The maximum power principle makes it possible to relate %alue cal-
culated on a basis of energy used to value based on effect of energy
flow. The maximum power principle proposes that s ytem; that maxiimize
their flows of energy survive in competition (Lotka. 1922). The theo-
retical relationship between cost quality: and effect quality 1i grounded
in the idea that the surviving system nult effectively use its energy;
flows and storage to survive in competition. Hence, in the long run.
energy cost must equal energy effect.
Solar energy is used as the basis for all energy quality calcula-
tion; in tiis dissertation. EB constructing a global energy uet model.
which was evaluated in heat equivalent, the energy quality of the major
er.ergi convergence and control p-ocesses of the world were calcJlated
based on the quantity of solar energy required to power the syste.n as
suggested by OJum 1973).
Energy Embodied in Padiation
A method is proposed for calculating the energy embodied in electro-
magnetic radiation. For calculations in the biosphere web energy quail i5r
factors are calculated based on the quantity of energy required to pro-
duce a certain energy in open systems flow. Embodled energy is then cal-
culated by nrultilrying measured energy flows in heat calories b, the
energy quality factor (Odum, 1973).
In the proposed method for the energy embodied in electromagnetic
radiation, energy quality factors are based on the absolute temperature
of the radiation energy source. The concept is based on the fact that
more enerqj is required per degree Kelvin to raise the temperature of
the population of molecules. The mean energy of the photon emitted from
radiation peak of the energy source is proportional to the temperature
of the source. W en's displacement law states that the photon wave-
length maximum enission max i. related to absolute temperature of the
radiating body by
ma P (12 1)
where P : 2.89 < 10" m i; (Posenberg. 1974). Given the wavelength of
electromagnetic radiation, the energy per photon e may be calculated
from Planck's constant.
ema = h (2)
.:he-e Planck's constant h = 1.53 v. 10- Cdl sec and c is the velocity
of light (c = 3 A 10 M m sec 1).
Substituting equation 2 into equation 1 produces a direct rela-
tionship between the energy of the photons emitted from the peak of
the electromagnetic spectrum and the absolute temperature of the radi-
e ma, T ('') Cal ('a)
where k. = 1.6 < 10-' Cal 'K Thus the average energy of the photons
emitted from the peak of the radiation spectrum of a blackbtody is in
proportion to the temperature and the constant of proportlonalit1 IS
It is postulated that in order to build a system crat can Support
and sustain high temperature, some form of molecular en ergy convergence
chain must be formed. The total energy required to support -he s.-tem
increases in proportion to the temperature obtained.
Since the energy per photon is proportional to the temperature of
the source, it may be possible to relate the energy quality, of certain
energy photons to the energy in the population of molecules required
to produce the photons.
The blackbod temperature of the sun. 6,000', (9.8 x 10-1 Ca1
photons) formed a reference for energy quality calculations per phor:n.
For example the earth's mean surface temperature is about 30'; thus,
at its spectral peak it gives off 4.92 < 10- Cal photons, which have
an energy quality; factor 0.05. A 60,00. sunspot would emit photons
wi-h a relative energy quality factor o' 10.
Divergence of radiation is not directly addressed by the proposed
method of calculiating the embodied energy of radiation. The question
of the relationship between pioton flux aensity and the quantity of
energy, required :o or)duce th,? radiation is not answered.
Previous Work on the Theor: of Order. Di.order. and Pulsing
Previous study of order-disorder theory was developed with energy
circuit language, a systems diagram and a mathematical framework.
by H. T. Odum (1971). A general model of order and disorder was
recognized as Michaeiis-lnenton Kinetics. Odum and fellow researchers
have used energy circuit language to study and rodel specific catastro-
phic events previously. Jeff Richey (19`0) disordered microcosms; Odum
(1970c) measured order-disorder relations with the irradiation of a trop-
ical rain forest and considered order-disorder model of war and toe ef-
fects of herbicides in South Vietnam (1974). Energy. in food chains and
webs were found to maximize power for survival by conserving and storing
energy; in high quality consumers and releasing energy in pulses.
A massive report on the Pain Forest Pesearch Project was prepared
under H. T. Odum's direction by the multidisciplinary scientific field
team. Two parts of the report relate directly to the concept of order
and disorder as applied to a natural ecosystem. Dienes (1970) developed
a 'inetic model of the radiation response of the forest ecosystem to
field irradiation based on a chemical reaction t'pe system of equillb-
rium equations as in equation 3:
:,L <<3 (3)
where = normal state; (~ partially damaged state; X\ = lethal state;
I and ';; = rate constant corresponding to radiation induced chance; and
KI = radiation independent rate constant describing recovery of the sys-
tem. Dienes used the model to calculate survival ve-sus distance from
radiation source fcr various sets of hypothetical coefficients. In .. T.
Odum's (1970c) ecological analysis of the system at El Verde, the clas-
sic washout curve of the chenostat was used to explain the effect of
the radiation stress, yielding similar results to Dienes' model and the
observed effect on natural system. Probably more significantly, however,
from the standpoint of this research, the ratio of disordering energy P;
to potential energy flux for reordering the system was calculated by
Odum who found that in a zone where destructive action balanced repair
rates the gamma ray energy input was only about 1/10.000 of that due to
photosynthesis (Odum, 1970c).
A recent innovation in mathematics is ) catastrophe theory by Pene
Thom (1975). In Thom's theory, models for elementary catastrophes sre
constructed from higher order differential equations. Surfaces are
generated from all the points of the functions where the first deri'a-
tive is equal to zero. Thom produced fold, cusp, sallowtail, butter-
fly, hyperbolic, elliptic, and parabolic surfacesin this manner Pos-
sibly the interesting point of Thom's work is the use of higher order
terms in the differential equations describing the surface that are
similar to the result of interacting several energy flows in a web
A theory related to the theory of order and disorder developed here-
in is the theory of risk as it is used in economics. Hirshlerfer and
Shapiro (i970) analyzed the appropriate discount rate for capital invest-
ments. In tnis oaper risk of catastrophic loss is treated as a deprecia-
tion flour similar to technological obsolescence and physical depreciation.
Risk probabilities are based on historical or perceived probabilities of
disaster, such as depression, war, or drought. In mathematical forr
Hirshleifer ar.d Shapiro inciroorate risk into the standard calculation
of the present value of one dollar of future money, as given in equation
4, by increasing the standard discount rate by risk factor.
[1 i r+ (4)
Where 1 = rate of interest and r is the rate of risk.
Thurow and Taylor (1966) proposed a model for generation of the
capital stock K as given in equation 5:
K = I dK aK (5)
where I is investment. d is physical depreciation, and a is technologi-
cal obsolescence. Incorporating risk into Thurow and Taylor's model
yields equation 6:
K = I dK aK rK (6)
where r is the rate of risk.
Figure 5 is a translation of the Thurow and Taylcr model into
energy circuit language drawn in the format of an order-disorder model
of Figure 1. Note that depreciation and obsolescence are driven by
internally built accumulation of capital assets while risk is an ex-
ternally powered process.
Previous Work on Natural Disasters
Pelativel. few studies provide a basic theory of natural disasters.
Most research has dealt with descriptions and analyses of specific
events, such as reports on the Alaska earthquake and tsunami on Good
Friday, ;arch 27, 1964 (Rogers, 1970), Hurricane Agnes of June 1i72
(Nationai Advisory Committee on Oceans and Atmospheres, 72), and the
Lubbock, Te\as, storm of May 11, 1970 (Tlorrpson, 1970). Another common
Figure 5. Energr circuit translation of economic model of rii.
The diagram is based or Thurow and Taylor (1966r
capital stock generation model.
:* C ITA L :
.- I- (,J.i-'K -rK
disaster research procedure is to look at one component in several
types of disasters. Notable examples would be Dacy and funreather's
(1969) economic analysis of natural disaster economic d isruption and
Cochrane's (1975) analysis of the disrupting effect; of natural hazards.
Dacy and Kunreuther deieioped an economic framework for anal, ing the
economic problems resulting from disasters, analyzed short-tern recover.,
across several case catastrophes, looked at empirical evidence of long-
term disaster recovery, and tried to describe the report of federal
policy on disaster mitigation. Cochrane focused on what population;
were destroyed and how much of the burden of loss and recon:tru:tion rwa3
borne by whom.
Approaches that are not disaster theory per se do merit recognition
including Ericksen's (1975S scenario methodology for natural ha:arj re-
search and Friedman's (1975) computer simulation of natural hazard
assessments. Ericksen synthesizes observed results from cross-sectional
analysis of disasters at progressive longitudinal steps to qualitatiJel,
describe what might happen to specific communities in future disasters.
Ericksen's methodology was based on the work of Kahn and W'iener (1967).
Friedman (1975) had a similar but more quantitative approach in using
computer mapping to simulate the possible risk of destruction of future
earthquakes, Urricanes, and inland flooding fOr variouss geographic
areas of tne Lnited Stdtes. Friedman's interest was stimulated bi hi;
employmcnL by '.e Traveler's Insurance Compan) ard their concern ojer
the spatial distribution of loss of life and property in the future.
Description of Study Situations and Previous Uork
In this section previous work on energy cycles of the earth are
reviewed and relaZed to natural disasters. The sites and systems of
special study and the disordering events of interest are described
including the tropical rain forest at El Verde, Puerto Rico, and the
disordering effects of radiation; the setting for the City of Johnstown,
Pennsylvania, 1,.9, and the disastrous effects of the failure of the
South Fork Dam; and the town of El Progreso, Guatemala, and the catas-
trophic effect of the earthquake of February 4, 1976.
Global Models of Atmospheric, Oceanic, Biological, Geoloaical, and Urban
s t ems
General circulation model' of the atmosphere are normally developed
using a grid technique integrating the equations over large regions,
cften a hemisphere or the whole globe, using a finite differencing
scheme with as small as practical integration step. The grid might be
200 km square horizontally and divided into as many as 18 layers ierti-
cally. (Frisken. 1973). Significant examples of uses of this technique
are found in Smagorinsly (1969) and Oliaer et al., (1970:i). General cir-
culation model: attempt to simulate the daily dynamic process cf the
earth's atmosphere, while climatological models generally terd to con-
centrare more heavily on modeling annual means.
Houghton (1954) developed a schematic representation of the flows
of energy in the atmosphere. Houghton estimated that the transport of
energy toward the ooles ty the atmosphere and by the sea would reach a
maximum of 1 x 10'" Cal d-1 across the 40rll latitude circle. Budyto
(1969) and Sellers (1969) e'parded Houghton's schematic model to a math-
ematical mean annual zonally averaged energy balance model. The effect
of solar radiation on variations on the climate of the earth i; a
central feature of the model. Further development of the theory of
energy balance climate models b., lorth (1975) has shon that a -n- ll 1 aria-
tion of the solar mean can trigger an ice age in the nodiel. So~e what
parallel to the developments of llrimate model;. considerable attention
has been placed on the development of global biological pr.oductivity
Estimates of global production by Llebig (1E62),whichvere e
polated from a single cominunity, were refine- 1 D, Schroeder (1919) b:
distinguishing four land coninunity types. Helmut Lieth (1975) d-eeloped
a spatial model of the primary productivity of the biological system of
the earth-based .qorld climate data that included 20 vegetation tyrpei.
These were not dynamic; that is, there is no feedback from the vegetation
cover of the earth to the global climate. The patterns of vegetricn of
the earth that wre analyzed and tabulated by '.hittaker and Likens (1975)
provided a useful summary of the production and stoc-;, ir the 'l:obi
Another approach to global biological s.,stem modeling has teen in
the carbon balance of the world. Eolin (1970) diagramed a carbon a odel
of the biosphere, finding the vast majority of carbn trapped in sedi-
ments amounting to 39 metric tons per square meter of the earth's Sur-
face. However, onl'. a few tenths of a percent of the immense ma:. or
carbon is on cr rear the earth's surface. Bi estimating detritus t,
ecosystem t:,oe for te earth, Schlesinger (1977) found 2.S kg m of
carbon for the world's surface in detritus.
Mathematical models of the sea are usually, restricted to irdi.'idual
components of marine systems running on very larce data bases w'th
little effort toward deJeloprent of a comprehensive model (Walsh, 1972).
Ekman .'j1905) showed vind stress, acting at the sea's surface, put nomen-
tum into the ocean in a thin boundary layer. Elman's theory is normally
included in general circulation models of the sea (Holland, 19771.
Sverdrup (1947) developed a vorr.city balance theory to ihich Stommel
(1943) added bottom friction to e.-plain closed basis circulation. Holland
and Sierdrup's work was the taisi for general circulation models of the
sea. Models of the ocean's tide were based on the incorporation of
rNeUton's second law by Laplace in 1776 to e.
on the sea (Hendershott, 1377). Se:nonal models of the thermoclines
attempt to e.xplain the heat e.,change between the atmosphere and :ne
ocean that produces larje horizontal-scale changes at the temperature
structure in surface laers of the ocean (Niler. 1977). Charney (1955),
who developed a theory to explain geostrophic adjustment, used the
theory coastlines known as the coastal jets such as the Gulf Stream.
Modeling of the sea is often fragmented among circulation, waves,
nutrient, producti..it:y, ooplankton, and phytoplankton models as if
the', were independent processes. Odum (1975) considered ways of com-
bining physical, chemical, and biological units in a single model of
Sand transport on beaches and shoreline evolution geological sim-
ulation techniques have teen documented by Harbaugh and Bonnam-Carter
(190.). The -rocesses of erosion, transport. deposition, and consoli-
dation form the basis for models of marine sediment models.
Dynamic modeling c- the earth's crust. supported by the Vire-
Matthews Hypothesis, proposes that anomalies in the earth's magnetic
field are due to cycles in the earth's magnetic field. The cycles set
the magnetic properties of the basaltic rocks of the earth's ocean crust
as they formed on the ocean ridges. F'agnetic patterns in basaltic roc:ks
in the crust underlying the sea floor and the age of sediments on the
sea floor provide conclusive evidence of the sea floor's spreading from
the ocean ledges at appro:..inatelD. 2 cm yr-' (Clark, 1971). Hayakawa
(1976) included continental drift. midocean ridge. volcanoes, orogenesis,
and other geological phenomena in a pictoral energy balance model of the
earth's crust. Ha.akaua's model was evaluated by estimating energy flows
from geophysical data.
A dynamic global web iodei of human systems and resources was made
Sb J. Forrester (1970) with the support and encouragement of tne Club
of Pomne. Forrester's work witn world model inq was followed b,' an e..-
tensively documented work by Mleado \s et al. (1974). Eoth models were
diagramed in s:,stems dynamics language IForrester. 1i9701 and simulate
with DYrlIrO (Pugn, 1970).
Hubbert (1971) evaluated a schematic global energy web highlighting
flows in the atmospheric system with some attention to aggregate tioljg-
ical, geological, and oceanic enerc'g flows. In Hubbert s work, concern-
tration and storage of energy are central, especially, those in fotsil
fuels. However, the only catastrophic releases of energy considered are
geologic in nature. H. T. Odum has developed several global energy
models (udum. 197?; 1973). A global minimodel was developed, evaluated,
and simulated by Alexander et al. '"76) to es-ima-e long-term United
States fossil fuel availability. A recent energy wet model of the bio-
sphere (Odum. 1978) treats storms anj volcances as hign quality, control
mechanisms whicn consume ene-gy concentrated by the atmospheric and
continental sedimentary cycles, respectively.
Tre Tropical Pain Forest at El Verde, Puerto Rico and the Effect of
As part of a major postwar research effort by the United States to
quantify the effects of irradiation on the environment, a field e.peri-
ment was set up at El Verde, Puerto Pico, by the Atomic Energy Commis-
sion in 1963. A goal of the research wis to perform a detailed study
of the disordering effect of gamma radiation on a tropical rain forest
Radiation studies with similar design were done at Brookhaven
National Laboratory and at Rhinelander, Wisconsin. At ErooRhaven, the
chronic effectof irradiation on terrestrial ecosystems were studied
(Ioo:dwell, 1963). Woo:dwelI and Rebuck (1967) analyzed the effects of
chronic gamma irradiation on oak and pine forests. Canoy (1972).
writing a dissertation under the direction of H. T. Odum. r.ejsured the
deoxyriboncicleic acid (DrNA of radiated vegetation at Brookhaven and
at El Verde b5 relating molecular order and information to the pattern
of stress. Highest NIA levels were found at boundary where ordering
and disordering rates were similar.
The radiation source used in Puerto Rico under Dr. Odum's jirec-
cion was later moved to Enterprise Radiation Forest near Phirelander,
';i3consin, where a similar exDosure of a major northern forest type
aspen) was conducted (Rudolph, 1974; Zavitkovski, 1977). In the pre-
irradiation siJdy, detailed analyses of the ecological community--
including solar raditnion, lichens, flora, plant communities, temporal
and partial .-et:er.'s. leaf-litter production, and vertebrates and
small-mmmmal popultiocns--were performed. The effects of gamma irradia-
tion on northern forest communities was predicted by Zavitkovski et al.
(1974). in the recently completed radioecolo.lcal studies, e.,.tensive
investigations were made into the ecological effects or gamma radia-
tion. Of special interest to this research was the radiation effect
on biomass production of ground vegetation studied b. ZaitL'.ovsli and
Salmonson (1977: and the response of the forest ecotone to ionizing
radiation studied by Murphy et al. (1977). 4 result of their research,
which relates directly to the theory of order and disorder. ia- the
large increase in the number of seedlings they found in the irradia-
tion recycled area.
Puerto Rico is a Caribbean island located between 1:ri' and 19''"
latitude and 55'11 longitude. El Verde station was constructed in
the tropical rain forest region of the Luquillo Mountaine cf eastern
Puerto Pico (see Figure 6a). The steady flow of ,arim moist air from
the 1.2 m sec- prevailing easterly trade wind provides a uniformly
wet climate with a mean temperature of 22.6'C, a relative humidity of
91 percent, an absolute humidity of 13.7 g m- an insulation of 3.:?0
Cal m,' d-1. and an annual rainfall of 3,750 mm. Climate fluctuations
were found to be small, for e.,.ample temperature had only a 21 to 2"'C
diurnal range and a 2' seasonal mean fluctuation (Odum~ et al., 1970).
The vegetation of the area is the lush tropical forest traditionally
characteristic of rain forest, nith high diversity of plants ar.d insects,
outtress roots. road thin leaves, bromeliads, lianas, trunk bark heavy
with growth, and an open ground story in deep shade. The area is known
as the Tabanuco Forest after the principal tree, the tabanuco. With a
rainfall of greater than 102 rii every month, droughts were r.ct experienced
Figure 6. Location maps and diagram of Puerto Rico and El
(a) Iap of Puerto Rico showing east location of
El Verde (idu.m, 1970a).
Ib) 'ain base map for studies at the E! 'Uerde
site (Odum, 1970a,.
(c) El Verde station and vicinity showing some
principal locations of activity (Odum.
:, C, *
i ~ C' i
PiIC n NI
S LEPTO PRlO
.. ... NUCLEAR CENTE
,,M ,tk Jie
. 6 ".' . ,j
NUC.. C.E'..' .
PT T7,<: IN
EL. NQI E
K(LM- T En
.i CUT C'EN-E 5 : C ,m
SC;P AC, .' 'ERN
FIELC 3TATIO ,N 7-
.L E, 4 ":" .3 ,"n lLy '.
METRO TC ER
3 CrNTPCL CENTER _.
-LE: a 9 m .I 76m
-itrA T "YL s.-Z.E
DIlTCN C2NTE3 S..:rT:L.: E
.. mJ.^^ ,
".'. E;"T F)
J. :UT CE'TSQ.-- Tr.'iER
"---" o, .,*^ ^
S3'rD.iCRC 'ljE ."..'
r [ .
Dy tre forest ecosystems. For example, the tropical rain forest in the
El Verde study area had never experienced fire (Odum, 197Oa).
The rain forest project studio was concentrated around the radia-
tion source and two control locations. Figure 6b is a plan view of the
irradiation and the south control area while Figure 6c diagrams the
ecological and irradiation experiment. The irradiation was provided Dy
a 10,000 curie cesium source for 93 days in early 196E. Another 6 years
were required for analyzing the results of the irradiation stress on
the ecosystem. including comparison studies with two control sites.
The soutn control .ite was undisturbed while the north control was
denuded o' vegetation to resemble the irradiation site. Substantial
stress was imposed on tne ecosystem by the high field gamma radiation.
Johnsto.n, Penns,lvania, and the Failure of the South Ford [Dam
Johnstown, Pennsylvania, is a heavily industrialized city located
121 km east of Pittsburg, Pennsylvania. in a valley of the Allegheny
fountains (see Figure 7a). The town was founded at the confluence of
two medium-sized mountain strearrs,Stony Creek and the Little Conemajgh
Piver, which join at central Johnstown to become the Conemaugh River.
Above Johnstown, the two streams and their tributaries drain 6EO sz 0i
of valley and mountainside (Gilbert, 1977). The point of confluence
provided water transport and the level floodplain encouraged development.
These coupled with the area's rich coal deposits made Johnstown a natural
place for eighteenth-century European settlers to start a town (F:gure
Johnstown received national attention when on May 31, 13S9, 6 to 8
in of rain sent Stony Creek and the Little Conenaugh into the streets
of the town anz breached what was then the world's largest earthen dam,
Figure 7. Location map of Johnstown and the South Fork Dam.
(a)i ap of Pennsylvania showing location of
Johnstown in relationship to other major
Pennsylvania c cities.
(b) General map of the region of the Johnsto"n
disaster and the watersned of the South
Forks. This map is the first correct one
published, tne decided differences betNeen
it and those which have yet appeared else-
where being due to inaccuracies in the
latter. It reproduces by kindness of G.
W. Colton & Co. from an old and scarce
county map of 1867, on a scale of 1 1.4
in per mi. The topography on this Tap is
made accuratelJ to scale from sketches
made on the ground (Engineerina Neas, 18893).
Sl SOUjTH F i -K'
.- o ,,,. -,,-' ,_, L^ \
H FOAK CAM
*ScUTH FORK 'ESEfVOCIRR,40CcCas .
- C- -An 1
3CUNIDAR' CF CRAINAGE ARaEcA'
14 mi up the Little Conemaugh at South Fork, releasing a 420-acre lake.
which was 65 ft deep at places (Engineering Society of Western Pennsl-
,ania. 1839). The water in the lake overflowed the dam in a low spot
in the center and eroded the entire '00-ft-i:ng. 70-ft-high earthen
structure on the down river side. allowing the earthen wall to fail
under the extreme pressure, and sending a wave descending into Johnstown.
The entire 540 million cu ft of water was released behind a 40-ft wave
that took approximately one hour to reach Johnstown. Very large quan-
tities of energy were released as the wave roared down the ';ile.carr.ing
buildings, trees, houses, factories, and even locoTmoti'es. It hit rne
town with virtually no warning, scouring most of the town to bedrock.
drowning 2,200 people, and creating $17 million property damage. Figure
6b shows the path of the flooduawe.
Floods are nothing new for Penns>lvania, for of 2.300 comTiuniries
in the state, 2,4683 re located in proven flood zones (Gilbert, 1977).
However, Johnstownians. believing this to be a freak accident. rebuilt
on the same floodplain onl, to be hit by another torrential rainstcrn
on March 17, 1936. The amount of rain water was compounded b:, meeting
snow from the mountains. In the 1936 Flood no dams broke, but the
flocd crest took 25 lies and did 541 million in property damage to a
city which h had more than doubled in size. With two floods in 50 years
the U.S. Army Corps of Engineers spent $7 million on a flood control
project to make Johnstown the "flood free city" (Gilbert, 1977).
On July 19, 1977, Johnstown experienced a rainstorm which whas
expected to move away by midnight but stopped, releasing an incredible
11.87 in of water between July 19 at 9 pm and 4 am on July 20), creating
a severe flash flood and breaching five small earthen dams. The most
serious was the Laurel Run Dam. which was 42 ft high and impounded 22
acres, generating a 15-ft wave directly in-o to the Comenaugh Piver.
This third Johnztown flood took approximately 100 lives and was respon-
sible for 5350 million in property damage (Gilbert, 1977).
E.:cellent field documentation of the 1889 failure of the South
Fork Dam make the test of constructing and evaluating a dynamic model
for the event feasible. The Engineering Pecord (1891) and Engineering
News (l1359b) provided detailed engineering descriptions of the failure
of the South Fork Dam, the path of the flood wave. and the destruction
of Johnstown. In addition, several authoritative historical accounts
of the flood have been published. The most notable are a Ph.D. disser-
tation by Shappee (1940) and a book by McCullough (1963).
Peport. on the 1936 flood are much more sketchy even though
property damage as measured in dollars was greater. However, some
water flow data were compiled by the United States Geological Survey.
The 1977 flood has brought Johnstown new fame and several rathe- e-.en-
Aive scientific fact collections are now available from the National
Oceanic and Atmospheric Administration 11977) and United States Geologi-
cal Survey (Ambruster, 1978; Brua and Humrphries, 1973).
Gilliland (1975i modeled the failure of a slime pond dam and the
disordering effect of the phosphorus spill on the Peace River in energy
Guacemala and the Earthquake cf Februar/ 4, 1976
The Suitemral earthquake of February 4. 1976, and the catastrophic
destructO on of El Progreso was used as the field test of the theory of
energy concentri:ion, storage, and catastrophic release triggering sec-
ondary catastrophic events. F'uch of the supporting fieldwork in this
research was done in the Department of El Progreso with a land area of
19,922 km- which is mapped in Figures 6, 8, and 9. Detailed arnalis
was performed on the capital of the department, also named El Progreso,
which has a municipal land area of 2'0 km- and a central urban area of
approximately 1.5 km2.
The source of energy in the Guatemalan earthquake was tne cm per
year annual westerly motion of the North American Plate of the earth
crust with respect to the Caribbean Plate. The plate movement had
stored great quantities of potential energy in stress built up in the
lotagua Fault over the past two centuries. Figure Sc is a map of the
junction )f the North American Plate and Caribbean Plate of the tec-
tonic system of the earth (Tarr and Ling, 1376).
El Progreso experienced almost total destruction by the earthquake
of February 4, 1976, due to its relatively close proximity to the
Miotagua Fault rupture and earthquake epicenter and to trne softness of
the alluvial soil on which the ado.e structures of the tmun were
Previous research on the Guatemala earthquake has been priiaril.'i
concerned with scientific documentation of the geological characteris-
tics of the event, its size, magnitude, and the geographic distribution
of the destruction generated b, the earthquake. The most useful scien-
tific summary studies were carried out by the Comite de Emergencia,
Guatemala (1976) and the United States Geological Survey (Espinosa et
al., 1976). The mios in Figure 9 summarize the data on the damage to
adobe structure and the estimated earthquake intensity distribution in
Guatemala (Espinosa et al.,1976). In addition to development of a re-
construction plan for El Progreso (Alexander and Sipe, 1977), mar,# other
Figure 3. Location maps of Guatemala, El Progreso, and the
(a) Map of Guatemala showing the location of the
department of El Progreso (Alerander ard
(b) Map of the Department of El Progreso showing
the location of the municipality in relation
to the other seven municipalities (Aletander
and Sipe. 1977).
(c) Motagua fault zone junction of Caribbean and
north American Plate. Jordan (1975) modi-
fied ty Tarn and King I1976i.
/ -- -- -- HO.D'RAS
GUETAMALLA L F GR
) .- HOtjDUR.S
/ ...... .- ..- 'I ELP.FOGRESO
SAN .iAGUS71 SLN
/ MORAa; *N g ;RiJT.5&
/ ...CflSAGUAS iaff j i.
/ ^. .--, ,...-*.- ,.
-. EL JIC^aR.
EL PPOGREE .^\
SAN ANTUO 0
1L A PA 2.
25 20 15 10 5 0
90o. 8. 70. -.-
N RI H I '91 I P
I I 1 NORTH AMERICAN PLATE
I? 0 I I~:
COCOS PLATE AZ rL
I I N. zc T;PL F' ,-I }'--
OUTH AMEFIC N PLATE
ercaror rcIerr;pn 1
sc le ..0. 5- N
Figure 9. flaps of damage to adobe structures and earthquake
intensity. in Guatemala.
(a) Contour map showing damage to adobe-type struc-
tures caused by the February 4 earthquake
(Espinosa et al., 1976).
(b) Isoseismal map of intensity distribution from
spread of the main event. Intensity, is mea-
sured by the Modified riercialli Scale
(Espinosa et l1., 1976).
S T ^ c. ^. ,,^, / .L^ .
0 E_ Erhquaxe Carrcge
SEL ?: -PROGRE
N EL PROGRE:0
foreign governments are sponsoring reconstruction projects throughout
Guatemala. The only other formal study of the effect of the Guatemala
ewrthouake on Ei Progreso was a cadastre mapping project sponsored by
the Guatemalan National Geographic Institute (Giron, 1976). The des-
truction was so great that identification of landmarks to identify
property ownership was a substantial problem. El Progreso was studied
in detail by the author (Alexander and Sipe, 1977).
Description of Modeling Language ar. Symbols
The symbols used in the systems diagrams were established by Howuri
T. Odum (1971) and are part of the energy circuit language. The language
combines several powerful approaches which show energetic and provide
insight into the mathematical description of a sister, while also illus-
trating the process under study in a holistic manner Energy circuit
language contains a hierarchy of symbols, which allow the diagraming of
several levels of complexity in one model
Aggregate symbols are summarized in Figure 10. They consist of the
cycling receptor module, the self-maintaining module, the production
module, and the logic module. The modules are constructed by comtiiir'n
members of the set of mathematical symbols presented in Figure il.
Energy circuit models are normally constructed by arranging math-
ematical symbols within group symbols to show systems and to facilitate
comprehension of the concepts embedded in the model. Standard c.:onven-
tion also calls for arranging the model so that subsystems, which con-
centrate dilute energy, are at the l1ft while erergy flows increase ir
quality toward the right of the diagram. Heat sinks are always used
to show loss of degraded energy from the system. This creative use or
symbols and organization provides several levels of hierarchy. The
highest level is formed by arranging the diagram by energy concentra-
tion or quality, the intermediate Ly use )f group symbols, while the
Figure 10 Energy circuit language group symbols (H.T. Odun.1971j.
Each group symbol is made up of a set of mathemat-
(a) The cclinq receptor has the condition of con-
servation of matter that is ordered by input
energy flow and is degraded and recycled with
output of energy.
(b) The self-maintaining consumer module processes
energy and feeds back control to other parts
of the s:,stem.
'c) The production module fixes low cualit, energy ,
and the control of a consumer module.
(d) The logic module performs discrete operations
based on control inputs.
I UT MCDLLE OUTPUT
C-ONTqr OL IN,:l: rS
INPUT I M:CUL ",UTFUjT
Energy circuit language mathematical symbols used
to construct nodules in Figure 8 (H. T. Odun, 1971).
(a) Outside source of energy supply to the sys-
tem controlled by external system and not
affected by energy demand on the internal
system; a forcing function E.
(b) Constant flow source of energy from outside
tc) A pathway whose flow is proportional to the
quantity in the upstream storage; J = KIE.
(d) Storage of some quantity in the system. The
rate of change of the storage'Q with time
equals the inflows minus outflows; 0 = J KQ.
(e) Interaction of two flows to produce an output,
which is a function of the two flows or stor-
ages driving the flows. For multiplicative
interaction; f(.,Y) = KXY.
(f) Transactor symbol for which -one; flows in
one direction and energy flows in the other
with price (P) adjusting one flow Ji in pro-
portion to the other; JI = PH .
(g) Senscr of the magnitude of flow, J symbol
also used to sense storage ); J: = RJ .
(h) Constant gain amplifier multiplies the in-
flow JI by a constant A. Power is extracted
from energy source E; Jt = AN.
(j) Logic switch turns flcw on or off base on
logic such that the output equals the incut
when logic is one and zero when ';ogic is
off; on J- = JI, off J = n.
(k) Logic ccmparitor compares A with B to provide
a logic signal C; if A : B C = 1, if A c B
C = 0.
HEAT SINK (e)
x f f ( '.,Y)
(e) INTER ACTION
() SENSOR ;F PC'N J
LOGIC SWITCH 1I
CONSTANT FL-w SOUFCE (b)
J Q Q
C INSTANT G-IN AMPLE FIE R
LOGIC CCMPARATOR (I
the dynamic and kinetic detail is constructed with the mathematical
Development of Models
The models in this dissertation were developed in a sequential
order starting with the basic order-disorder model in Figure 1. A
family of this type of models was constructed and analyzed mathemat-
ically by setting up each model in differential equation form, setting
the rate of change equal to zero, and solving for the steady-state
solutions. Dynamic characte'isticc were next tested by simulating each
model in the family of order-disorder models as depicted by Figure 1.
A preferred order-disorder model was tested by modeling the previous
studies on the effect of gamma radiation stress of a tropical rain
forest at El Verde, Puerto Pico.
A catastrophic consumer pathway was added to the basic order-
disorder as shown in Figure 2. The family of similar models was ana-
lyzed and simulated to test the models' dynamic behavior. The model of
catastrophic energy release was tested by simulating the failure of the
South Fork Dam (which generated the Johnstown flood of 1889) and the
Guatemala earthquake of 1976.
NeKt, two order-disorder models were connected in cascade and
tested by simulation of the Guatemala earthquaKe and the secondary des-
truction of El Pronreso and the Johnstown flood and the secondary des-
truction of Johnstown. Figure 3 describes the basic configuration. Ey
connecting units in & web, a more general model was developed as a metn-
odological guide fcr calculation of a cower spectrum for global disasters
and for es:imation of qLantity of solar energy embodied in generic types
of natural hazards and their disruptive pulses of energy. The model
summarized in Figure 4 is a global energy budget model that relates
the atmospheric, oceanic, biological, geological, and urban processes
responsible for concentration and storage of solar energy to power
storms, floods, earthquakes, fires, and volcanoes.
Limiting Factors and Differential Equations
The energy circuit models developed in this research incorporate
internal and external limiting factors. Internal limits result from
the shortage of disordered matter in the cycling modules. External
limits are provided by energy flow sources such as solar radiation.
Both limits to growth are incorporated in diagrammatic and differential
equation form of the models. Figure 12 is a typical example, illus-
trating the use of internal and external limits to growth in the same
order-disorder model. The differential equation for the energy storage
term QI is given below:
Ol Jr 'i : K- Q(7)
The energy flow J is split between J, and Jr as in equation ?:
J J: + Jr. (3)
The energy consumption of the system is given by equation 9:
Substituting equation 9 into equation 3 and solving for Jr yields equa-
r Kn Q- + 1
Figure 12. Order-disorder model in energy circuit language,
illustrating the incorporation of internal and
external limiting factors. The internal limit
is provided by conser.'ation of matter in the
order-disorder loop. The external limits to
growth are a result of the use of a constant
flow energy) source.
K, J 0 -.
i. K 02
Substituting equation 10 into equation 1 yields the desired results in
'., J Q.
0 0= YK% (11)
Rearranging equation 9 defines Ko
K] J Q:' (12)
Requiring conservation of mass such that the total mass in the
storage Q0 and Q2 to constant C yield equation 13:
C = 3; 01 + 0:, (13)
where K is the mass per unit energy for tne system under study.
Sol.ing for Q yields equation 14:
02 = C K 01. (14)
Substituting equation 14 into equation 11 to remove Q, yields equa-
KIJC .KJKQ l
Ql 1 7 KC KKQl K,'0 (15)
Equation 15 is a differential equation describing the behavior of
the model in Figure 12 and incorporating the internal limit imposed by
conservation of matter and the external limit of a constant flow energy
rata Assembly and Evaluation of Models
The energy circuit models in Figures I to 4 were used as a guide
for collection and organization of data. Data were assembled from
literature for evaluation of global models. A table was constructed for
each energy flow and storage in the model. The table contains the energy
value of the flow, or storage with each calculation documented b, a note
in Appendix I. Each data source was referenced to the appropriate re-
search and, when possible, several measures or estimates were used for
each reference value.
A set of simultaneous nonlinear differential equations was developed
for each of the energy circuits models of the case study disasters. Ini-
tial conditions and coefficient: for each model were calculated from the
table of energy flows and storages that was constructed to document the
model. Mathematical solutions were used to develop the behavioral prop-
erties of the basic order-disorder model used as a basis for this re-
search. However, this was not feasible for more complex, models.
Numerical approximation techniques and solution by analogous system
were used to study and simulate the dynamic behavior of the disaster
models. Numerical approximation zas the most straightforward simulation
method. During early stages of model development, simulations were tested
on a Hewlett Packard 25 programmable calculator. However, more e\tonsive
computer runs were performed with the simulation language D'YAMO (Pugh,
1970). Working with DYNAMO offered the advantages of a large, dynamic
range of modern digital computers. Thus, the models could be simulated
without going thrcugn a scaling procedure necessary with aralog simula-
tion. DYNAIPO models i.ere developed directly from the energy circuit dia-
gram so that one level equation was written for each state variable
(storage tank). while one rate equation was written for each energy flow
pathway. Digital computer programs such as DYNAMO, simulate nonlinear
differential equation solutions by mathematical approximation. To insure
reasonable accuracy with Euler integration technique, a time step of 0.1
percent of the disaster duration was used as a ma.iimum. Thus, many com-
putations are required for one simulation run, rendering the digital
much slower than analog computer methods that continuously solve the set
of nonlinear equations. A TektroniA digital computer terminal and time-
sharing techniques were used to carry out model development and simula-
tion. Some of the models were scaled and wired on the analog computer
to provide hands-on immediate response. Analog simulation was used for
sensitivity analysis to study relative response of the system to each
parameter. information gained from analog simulation was used to plan
runs on the D'rlNA1 version of the model. The data for storage and
flows that were determined to be sensitive by analog or digital simula-
tion were reverified and checked for accuracy with a second or third
reference, and when possible by several independent techniques of cal-
culating the energy flows and storage used in evaluating the models.
Calculation of Ratios
In addition to evaluation and simulation, the energy circuit models
in this dissertation were used as systematic guides to energy analysis
of energy flows. Several types of ratios of energy flows were calcu-
lated to idd to the quantitative understanding of natural hazards and
their disruptive effects. As explained in this section, three important
ratios calculated are energy quality, embodied energy, order-disorder
ratios, and disaster amplifier ratios.
Energy quality factors were calculated from the evaluated biosphere
web as diagramed in Figure 4 LOdum, 1978). Under the web concept all of
the energy flows are interrelated in such a way that each is produced
as a by-product of all the others. Taking this point of *;iew, the
total incident solar energy to the world is required to produce all
energy flows and build all the structures. In the example of global
net primary production, rain, wind, dry air, and nutrients of the soil
are all known to be necessary energy flows as direct radiant solar
energy. Once the global energy web is evaluated, the energy flow in a
specific process is divided by the total solar energy necessary to
power the earth. For this research the mean solar incident radiation
was used as the basis for all energy quality calculation except for
Embodied energy factors were calculated by multiplying an energy
flow in a specific case by the global quality factor, which was devel-
oped from the energy web model in Figure 4.
The order-disorder model diagramed in Figure 13 illustrates the
energy) flows used in calculating the ratio of the energy required to
produce order to the energy reQuired to produce disorder in the system.
The ratio was calculated by dividing flow A by flow C in Figure 13.
When the ratio of the storage of order, which is recycled to disorder
(flow B). to the flow of energy required to pump the recycling process
is calculated, flow B is then divided by flow C. For purposes of
clarity, the first is referred to as the order-disorder ratio, whlle
the second 13 designated as the disaster-amplifier ratio.
Calculation of Spatial Distribution of Seismic Energy
A method is proposed for calculation of the spatial distribution
of seismic energy from observed field intensities measured on the
Order-disorder model illustrating energy flows used
in calculating the order-disorder ratio 3nd the
Energy required to produce order = A
Energy required to produce disorder C
Disaster amplifier ratio
Storaae of order disordered externally A
Energy required to produce disorder C
CRCER-CISCROER RATIC = -
CISASTE. -AMFLIFIER RATIO = --
Modified Mlercalli scale. Intensity is a subjective numerical inde< de-
scribing the effect of an earthquake on man, on structure, and on the
surface of the earth. The Modified Mercalli scale of 1931 has intensity
rankings from I to X[I (see legend on Figure 30b for definition of scale;
Espinosa et al., 1976; Richter, 1958). acceleration A was calculated
from the intensities discussed above using equation 16 (Gutenberg and
log a = 1/3 1/2 (I6)
If energy was distributed uniformly, one could find the dissipation
per unit of land area by dividing the total energy by the total land
area affected; however, this is not a realistic assumption. For the
calculations, it was assumed that energy was uniformly distributed in
each isoseismal zone. Equation 17 mathematically gives this relation-
ei = E si' Ai (17)
where ei is the energy dissipated per unit area of zone, i, Esi is the
total seismic energy dissipated in zone i, and A. is the land area of
zone i. Energy was related to acceleration by combining the following
two equations (Gutenberg and Richter, 1969):
E si= c t (A /T) (18)
where c is a zransmissicr constant, t is the duration of the wave group,
and T is the period of vibration, all of which were constant for the
case under study Ai is the amplitude of the ground motion for zone i.
Amplitude Ai was related to acceleration ai as shown in equation 19
(Gutenberg and Richcer, 1969):
ai (A /T) 0r2/T
and then substitute equation 19 into equation 1S. combining constant;
to form a new constant c, which yields equation 20.
ei = c a (201
The constant of proportionality c was then evaluated by substituting
equation 17 into equation 20 to get equation 21.
c = E ./( A.ai ) (21)
Substituting equation 16 into equation 21 and rearranging. yields the
desired relationship between energy distribution and earthquake
n 0.66 I-I
E, ( C A 1. (22)
Plan of Study
The theory of cycles of order and disorder was first developed by
analyzing several possible configurations of order-disorder models. The
analysis was carried out bt calculation of the steady-state solution to
the models in differential equation form. The dynamic properties of the
model ,ere tested using simulation techniques. As a refinement of the
order-discrder concept, a consumer nodule was added to the order-d'sorder
model. The catastrophic energy release properties of the model were ini-
tially analyzed for steaoa-sLate properties of the differential equation
form of the family of models. Dynamic characteristics were analyzed
using simulation techniques.
An energy basis for disasters was developed by connecting order-
disorder models to form a global energy, web model with pathways for
cascading of catastrophic release processes. The resulting model was
then used to evaluate the energy quality of natural disasters and to
illustrate the control action of their pulsing. The first section of
the results develops, evaluates, and documents this model by diagraming
the atmospheric, oceanic, biological. geological, and urban systems of
the world, their energy flows, and their interconnection. Then energy
ratios were calculated from energy flows in the evaluated models. Quan-
titative comparison of order-disorder ratios were made with all of the
energy) flows involved in a common unit of measure as calories of solar
To verify the theory of cycles of order and disorder, three disas-
ters were studied with models, energy evaluation, and simulation data
from an irradiation disordering experiment in a tropical rain forest
was used to evaluate a pulsing order-disorder system. The model was
simulated and compared to field observations. An order-disorder model
containing a catastrophic consumer module was evaluated for the failure
of the dam, which created the major disaster at Johnstown. Two models
were connected, so their effect could be cascaded and evaluated for a
major earthquake and the secondary disruption of several cities. The
flood and earthquake were simulated and the results were compared to
Cield observation. Finally ratio of ordering and disordering energies
".ere assembled to consider theories of energy flow in disasters.
Simulation and Analysis of Order-Disorder Models
Results of the study of several possible order-disorder models are
presented in this section, starting with a simple model and progressing
to more complex examples. Differential equations to describe the behav-
ior of each are also presented along with time simulations of each model.
All of these models have the connon characteristic of materials cycling
as a mechanism to capture, concentrate, and store energy and are mathe-
maticallk constrained to conserve matter. Figure 1,la is the basic
order-disorder model which was first applied in enzyme reactions
(Michael ius-renton, 1913). The behavior of the level of order 'ji is
described by differential equation 22.
01 = kEQ- k0 (22
Requiring conservation of matter yields equation 23.
0-. = 0T Qi (23)
Substituting equation 23 in equation 22 yields a single differential
equation which describes the model behavior of equation 24.
Qi = kiE(T Q ) r Qi (
To find the szeaa,-state solution. Qi was set equal to zero and
equation 2. 4 as soled for Qss yielding equation 25.
ss = ( k ) OT (25)
Assuming E constant and substituting kl for kiE in equation 25,
produces equation 26. Let C0 = 1, K, = 0.6, K = 0.2, and El = 1
0k = 0.6. = 0075. (26)
This form of the solution appears often in problems invol.'ing dis-
tribution of a resource between two states. Figure 14a also shows tne
result of a D'lAMAO (Pugh, 1970) simulation of this order-disorder model.
lote that the steady-state value determined both mathematically and by
simulation is the same.
Similar analysis and simulation were performed for each model in
Figures 1Jb through h. The analyses are summarized in Table 1, while
the simulation results of each model with the same pathway coefficients
and energy source values were shown parallel to the energy circuit model
diagr3m. The documentation of each simulation model is contained in
The series of models presented in this section all used only one
differential equation in the simulaticn model. The second equation
dropped out 'hen the constraint of holding total matter constant was
The jrcer-disorder model in Figure 14b incorporates the addition
of a feedback: of some of the order, Q, to pump more ener.g. The con-
servation of natter imposed gives this model logistic characteristics
as seen in the simulation results. This mcdel has two steady-state
solutions. Figure 14c incorporates an external energy source, E, to
pump the recycle process. The simulation results are the same as
Figure 11. A comparison of several order-disorder models and
their simulation results. In all simulation tre
following values were used:
Ei = I, E = I, i = 1. = .2
Also conser.at:on of matter nas imposed on each
(a) Simple order-disord.er model arnd sr.ulation
results with one energy source Ei.
(b) Order-disorder model and simulation result
with autocatalytic feedback and one energy
(;) Order-disorder model and simulation results
with an ordering energy source Ei and a
disordering energy source E-.
02= I-0, TIME
0) 1 1
a, K= rcEQ Z0,Q 0 4 8
02- 1- TIME
Q2 1 -1 71M F"
UZ*I-, / s \
0, l-, 04 8
Figure 14. Continued
(d) Autocatalytic crder-disorder model and simula-
tion results ordering energy source El and
disordering energy source E:.
(e) Autocatalytic order-disorder model and simula-
tion results with cooperation feedback in order
loop and cubic drain on disorder loop.
(f) Autocatalytic order-disorder model and simula-
tion results with square drain in disorder
loop and an disordering energy source.
K0 W E Qi 2- K E,2
Q, I -Q,
"K 'A K 2 E 3
", = KI,, l,- ," 2
.- : I 0, K
(g) Dual autocatalotic order-disorder model and
simulation results which behaves like a
(h) Autocatalytic order-disorder model and sim-
ulation results with constant flow energy
(i) Simple order-disorder model simulation re-
sults with tio differential equations.
O, = KI,EG,Q- K,ES0,i
0, = Q,-0,
K- J.0, Q-
I. I'_ K201Q
TABLE 1. STEADY-STATE SOLLiTIO'IS ArD STEAD(-STATE VALUES FOR THE ORDER-
DISORDEP. MINIMODELS IN FIGIPE 14.
Model iNo. Steady-state Solution Steady-cstae Value
k I E Or
Iss k1E + k-
kI E iT K.
Iss l 1 k, E-
Ki E T k- E or 0
1sQ = K E1 0TE-
iss I T- E or o
0 *i r T
iss E 1 + kE- 0
E k E.
Iss = o--- r
0.67 or 0
0.67 or 0
0 .75 or 0
0.75 or 0
1 to C
Figure 14a. thus this is another form of the Michaelius-Menton kinetics.
Figure 14d is the logistic model with the addition of an external energy
source to pump the recycle process. Figure 14e illustrates the effect
of using the square of the order 01 to pump order and disorder with two
external energy sources. Figure 14f is another configuration of the
order-disorder model which has logistic behavior and also uses dual
energy sources for order and disorder processes. Figure 14g is an un-
usual order-disorder model, which behaves as a flip-flop circuit. This
may be unrealistic for there is no depreciation on the storage except
through the dual production functions of order and disorder. Figure 14h
incorporates internal and external limits to form a logistic behavior.
The external limit is provided by a constant Flow energy source and the
internal limit provided by material cycling.
To determine that this mathematical manipulation would not affect
the simulation result, the model in Figure 14i was simulated. The
model diagramed in Figure 14i is the sane as Figure 14a. This simula-
tion was performed using differential equations 27 and 28.
Q = K IE10 K2Qi (27)
0: = KQ K3E1IQ (23)
To insure stability, in the model, (KI) was set equal to (K3) as in a
Lotka Loop. Figure 14i also shows the result of the simulation, and
it was 'dentical to the results obtained in Figure 14q. Thus identical
simulation results were obtained for the order-disorder models with two
differential equations in Figure 14i when the coefficients were balanced
as with one differential equation and the conservation of matter con-
straint in Figure 14q.
Switching Pulse Models
A previous energy circuit model used a threshold approach to modeling
disasters or disorder in processes, such as fire or epidemic. A switcri
controlled by a logic threshold was used to model the disruption process
(Odum, 19741. Two logic configurations of the model are given in Figure
15. The behavior of the model is simple and adequate for a first order
approximation to modeling catastrophic events. When the level in the
storage Qi exceeds a present threshold T, the disaster pathwa. K: is
logically switched on and remains conductive until the energy storage ),
is depleted below its self-extinguishing threshold, T2. Also, the model
may be triggered by applying a logic pulse at P. The limitations of this
model are apparent when the simulation is examined over the period of the
disaster. However, this model does not explain the dynamic behavior of
the disaster. It simply replicates observed result;' destruction.
Exponential Surge Ilodel
To facilitate the simulation of actual disaster processes sucn as
fire, earthquakes, and floods, a dynamic model was developed capable
of explaining energy concentration, storage, and catastrophic release
in the disaster process. As a minimum, the model needed the long-term
characters of the logically switched one in Figure 1E. Previous wo.r'
by other researchers with fire has shown the energy in the fira to
increase exponentially until the source of fuel is consumed by the fire
(Byram et al., 1966j. These previous findings suggested that an exponen-
tial growth model would be appropriate for modeling the fire. Figure 16o
is an energy circuit order-iisorder model with the logic oathuay replaced
by an autocatalytic consumer, fire. In this model, the fire was triggered
by an energy pulse applied to the fire energy storage 03. Once initiated,
Energy circuit disorder model of disaster typical of
previous fire and epidemic models of other re-
searchers. Disorder process is logically switched.
(al Model with external trigger required.
ib) lodel with internal threshold trigger
Q, =KE, 'J-K.S| KQ,I
Q =Q T-'.1
S = I if flip-ficl is seT
S =0 it flip- iop is reset
KI = QE ,- 1i 1 K
Figure 16. Order-disorder energy circuit model with catastrophic
energy, pulse generated by consumer module.
,a) Model with external control pulse required.
.b) Model with internal threshold for pulse
0 = K:, E Q:- KO Q03- 1.,Q .
Q =QT-'l .- E-
Q; =K50103- K',603. E- '0'
Q, = KIE C,- KQIQ 3- K3
Q3 =K.Q|,03-K5 3*K!3
the fire grew exponentially until the fuel source was consumed to the
point of self-extinction. However, this model could not self-start.
To incorporate the self-starting characteristic into the model,
the linear drain pathway, which represents depreciation, was fed into
the disaster energy storage Q,. As long as the drain or depreciation
of 03 is greater than the inflows, the model was stable, and the order
or potential energy in Q0 could be increased. However, if Q0 became
large enough so that the depreciation of Qi exceeded the losses from
Qi, the autocataljtic fire model reached a critical point where it
could self-start and grow until the energy source Q0 was consumed.
This model was also capable of periodic oscillation as shown in Figure
16. The storage of energy grows to a threshold and periodically/ dis-
This model has se'.eral advantages over the logic model in addition
to replication of uoper and lower thresholds. Because it actually
models the disaster, if preventive measures can be taken in time, the
disaster may be extinguished. For example, the fire may be controlled
or extinguished by cooling the disaster energy storage Q3 as 's done in
fire fighting with water. It is also possible to control the disaster
growth and extinguishing rate based on the characteristics of the
The order-disorder model in Figure 16b had good dynamic character-
istic for disaster model used in this research. The model conforms to
the convention of conservation of matter such that the sum of storage
are constant QT as in equation 29.
01 + 0Q *: T (29)
The level cf orde- or stress in the disaster 0i was described by equa-
Figure 17. Simulation of the periodic buildup and pulse genera-
tion property of the exponential surge model in
-' ,1 ,
i I i
x 0 5-
I r I /
y \y r \\ ,
o 5 12 15 240 5 30
I0 II 12 13 I1 15 ,.
i ~- lEO: k, (OQ i:'). ('0)
Catastrophic energy release uas controlled by the autocatalytic energy
release pathway l-(0O + QIQj). ',hen Qs is small, this term is dominated
by the linear depreciation kQi The value of energy storage in the
decay pathway Q3 is described tv equation 31.
Q5 = (k .3)Q1Qi ksQ3 + K.Q1 (-1)
Equations 30 and 31 may be used to :oive for steady-state jaluel of Qj
and 0, by setting the Q, and Q-, equal to zero. yielding equationns 32
:IE T (32)
kss E k, lI (ss)
C1 c k- (ss) 1 '1i(.-s)(
t Kl i.ss) (32)
iss- : K'.- j(r;s ) + kz k' jm'ss)
Also, threshold for catastrophic release is given by equation .':
=Q t =- k k. 'I, k (3J)
that is, if Qi, Q1t, the model will catastrophically switch to the
The decay path of the disaster is controlled by the value of k;,
which is the time constant of the catastrophic decay.
Evaluation of Global Enerar, Web and Disasters
Figure 13 is an energy circuit model th at tenpts to synthesize
concepts about the earth using concepts from geology. meteorology,
-I- I --
*lo .6- -- A
0 c 0 *-
S0 -= R -=
3 U, I- =
*= aO M
-- 0 Q .
1 U. ci 2
2 0 E 01 z *..
Ct. 0 I+ .L"
C" I z j >
.0 :- -- 1
S 0 < *
a *- u > C -
a- 3: n=3 F
a L. i -
'a E -r 1.3*-
OW l 4 3 3
S 0* C r :<
i-i- tJ 3 *
LL l i'11a -
SE. i/ '"r i
/ i / ",'D OE f-
/ >',l *, 4
J, 'E t I, -
[K i -
i b .= t I u
f 3 L;'
'A l ^ _______
oceanography, economics, and ecology. It shows the global structural
mechanisms that concentrate energy in space and time. store energy, and
eventually release the energy in catastrophic pulses that seem natural
disasters to people.
Studies of energy flow and concentration processes in the biosphere
are usually constrained by the boundaries of the discipline. Parts of
the global energy model deJeloped in this section have been studied by
meteorologists, oceanographers, ecologists, geologists. and economists,
with each group concentrating on Uinetics, energy flows, and catastrophic
phenomena in their respective fields. However, energy is known to flow
across the areas covered by disciplines in the real world. A catastrophic
event in one field often triggers secondary disruptions in many fields.
Modeling the concentration, storage, and catastrophic release
mechanism produced fundamental insight into the behavior of disasters.
Conceptually, each natural disaster occurrence is viewed as a disrup-
tion of a storage following a peak in the normal glotal energy cycle.
Earthquakes, volcanoes, tidal waves, rock slides, and other disruptive
geological hazards are viewed as momentary nonlinear pulses of energy
generated by bottlenecks, uhich produce a temporary concentration of
potential energy. Floods, lightning, hurricanes, and tornados result
from a rapid release of excess potential energy stored :n atmospheric
systems. Forest fire is the result of catastrophic release of chemical
potential energy stored by biological systems in organic matter. Urban
fire and war can be modeled as releases from storage of society, often
disordered oy earthquakes, floods, storms, tsunamies, and volcanoes.
The world model suggests interrelationships of natural disasters
and the energy trajectory required for them. It allows energy flows
from various energy sources to be compared.
National quantitative comparison of sectors, disaster phenomena.
and ratios of flow can be made if all of the energy flows involved are
put in a cormrion unit of measure such as heat equivalents. Calories of
embodied solar energy, and energy quality factors. These were evaluated
for the world model and are given by sector next.
Atmospheric Circulation and Storms
Figure 19 i; the atmospheric sector of the global natural hazard
model in Figure 18, which was the wet used for calculation of the solar
energy quality of rain, wind, and storms. To calculate the energy qual-
ity of storms, it was first necessary. to evaluate the model from the
available global energy data. Figure 19a presents the nodel in concep-
tual form, while 19b is in mathematical form with differential equations.
Table 2 documents the energy flow and storage evaluation of the world's
atmospheric system with detailed calculations provided in Appendix I.
Storms, such as cyclones, hurricanes, tornados, and thunderstorms,
are powered by warm moist air conducted toward polar latitudes of the
earth as excess heat from tropical latitudes. Storms are formed by the
atmospheric systems acting as a mechanism to release e
ties of potential energy tnat could not be released in a competitive way
by simple diffusion. The release of excess energy built up across fronts
produces turbulence. The wind pumps more energy through the atmospheric
system. The turtulence also provides a positive feedback tj the ocean
by producing waves which in turn supply more water vapor energy to power
the storm and to provide rain for the land systems of the earth.
The advent of the satellite .ade direct measurement of global para-
meters possible. Meas'remer.ts from space platforms essentially confirm
Energy circuit diagrams of atmospheric system.
(a) Conceptual drawing of energy circuit model
of atmosphere used to illustrate energy
quality calculation for weather and wind.
Energy flows are in Cal m-2d-' while stor-
ages are in Cal m-.
(b) Atmospheric sector of global energy web
model in Figure 13 with differential equa-
tions. This energy circuit cycling recep-
tor module was evaluated for the major
flows of energy in the atmosphere. Table
1 provides documentation for the model.
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