Title: Energy basis of disasters and the cycles of order and disorder
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00097464/00001
 Material Information
Title: Energy basis of disasters and the cycles of order and disorder
Physical Description: xiii, 232 leaves : ill. ; 28 cm.
Language: English
Creator: Alexander, John Franklin, 1943-
Copyright Date: 1978
Subject: Natural disasters -- Mathematical models   ( lcsh )
Disasters -- Mathematical models   ( lcsh )
Order (Philosophy)   ( lcsh )
Cycles   ( lcsh )
Force and energy   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 221-231
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by John Franklin Alexander, Jr.
 Record Information
Bibliographic ID: UF00097464
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 - 000074574
oclc - 04695311
notis - AAH9848


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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.


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,


Table P.Eg.


IN FIG'uPE 19. . . . . ... . .... .. 6.

INJ FIGURE 21 . . . . . . . . . . .95




DISASTERS . . . . . . . . . . . 1: 0

DISASTERS . . . . . . . . .. . . 123




QUAKE OF FEBRUARY 4, 1976 . . . . . . . 153

IN /ARIOUS CITIES ill GUATE'lALA. .. . . . . . 162



Figure Page

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 . . . . . . . . .


Firqre Page

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

1 *.

Figure Page

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



John Franklin Alexander, Jr.

August 1976

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

con'vergernce ,ct'vorl:.

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

observed results.

<1 1

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.


| PF.CUCLJ ,. /

\' I,'
"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.

Global Model

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-

ating body.

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.

P- 1
[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

the sea.

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
verde experiment.
(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


,,M ,tk Jie

18 CCI


ri PrI

. 6 ".' . ,j

NUC.. C.E'..' .

PT T7,<: IN


K(LM- T En

.i CUT C'EN-E 5 : C ,m

SC;P AC, .' 'ERN

e .

.L E, 4 ":" .3 ,"n lLy '.


-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 ."..'

C '

.; .c..n


F '



-- --

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^ \

- C- -An 1

2r 3

f '

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

circuit language.

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
rlotagua Fault.
(a) Map of Guatemala showing the location of the
department of El Progreso (Alerander ard
Sipe, 19771.
(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
) .- HOtjDUR.S
/ ...... .- ..- 'I ELP.FOGRESO



/ MORAa; *N g ;RiJT.5&
/ ...CflSAGUAS iaff j i.
/ ^. .--, ,...-*.- ,.
-. EL JIC^aR.

1L A PA 2.

( b)


25 20 15 10 5 0
k Iometer

90o. 8. 70. -.-
N RI H I '91 I P

I? 0 I I~:


I I N. zc T;PL F' ,-I }'--


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^ .
T, J

Ea 22

0 E_ Erhquaxe Carrcge




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-
ical symbols.
(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.







C-ONTqr OL IN,:l: rS


._1 -



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
the system.
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.

Figure II.




x f f ( '.,Y)


i "

G -











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:

Q:. (9)

Substituting equation 9 into equation 3 and solving for Jr yields equa-

tion 1C:


QJ +
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

0 C-K,


Substituting equation 10 into equation 1 yields the desired results in

equation 11:
'., 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-

tion 15:

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.

Simulation Procedures

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

electromagnetic radiation.

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
disaster-amplifier ratio.
Order-disorder ratio
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

Figure 13.


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

Richter, 1969).

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
I i


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

equivalent energy.

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

Appendix II.

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
source E.
(;) Order-disorder model and simulation results
with an ordering energy source Ei and a
disordering energy source E-.



02= I-0, TIME

b 1.

0) 1 1

a, K= rcEQ Z0,Q 0 4 8
02- 1- TIME


0 0
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



, I


(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.

Figure 14.

O, = KI,EG,Q- K,ES0,i
0, = Q,-0,


K- J.0, Q-
I. I'_ K201Q
Q,= QT-b,


Model iNo. Steady-state Solution Steady-cstae Value

k I E Or
Iss k1E + k-

kI E iT K.
k0 -or

Iss l 1 k, E-

Ki E T k- E or 0
Ol.s klE-

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
E :.E


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

Figure 15.

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
02 07-C
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

stored fuel.

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-

tion 30.

Figure 17. Simulation of the periodic buildup and pulse genera-
tion property of the exponential surge model in
Figure 16t..


o 05
-' ,1 ,

i I i

4i ,

x 0 5-
I r I /

y \y r \\ ,

o 5 12 15 240 5 30

,\ Q



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

and 33.

: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

disorder state.

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 --

- .1

Ii- a
*lo .6- -- A

0 c 0 *-
S0 -= R -=
3 Ca
3 U, I- =

*= aO M

-- a
-- 0 Q .

1 U. ci 2

-J O

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

Lj^ nr.
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.

h. w
r1 1+ Q 1 K

- .30103 K,0, KsQ

0: CI K.:-1 Qb

Q. K3O1Q2 KQ- K'-Q ':-_Qi

Figure 19.


\ j C'.CULATL, CN L l -,U
v l 4,600 l, 4,0


E// '" JTcE) I

5\ 7
,, / f y I

"' R .
1^4^ /M7^

[ ___

S ?j. l V ."I r0 7 0

c-I .-- -0 3.-

-4 -,O CV C
+ '-. e- *l- V

o e1 i 0 >o o C
ct 0 0"
: > -. *- = = 3 )

-. .) *- .. .- .j U x
aa E

- 2 2i - W CU 3) -
. a 4 TO L
.1 .4 -.l V *0- : 4
_l ) <- Z3 '4- V
S - in 3

: > V CI 3 =x
a *.- .4 r3 4.! 3) 4-4
L4_ -I .- *o u o '0 -''

C. 4 1) C GJ *3 C -
4r *-. - -_ -4 C 0

. *i 0 'J L. -+ V 20 -
C: 2.- 'I '. '0 '0 V. .3 3 i'-C .
C - -- 1 *-'' *' J 00

- 3 .1- = < .. I < u .l 1] <
' 'V 0 i i i C uV cA i i. =

O a ,-' a 3- -- o
2 La 'V 'V 0. 1 Li '

3- S

u u u u u
00 e 0 -o a

L. T- C TI TO -

- ,--
* --C 'V V C

U. 3) V 'V C L -- 13_
U 4- V 3 4 4C '
- a I- -- '_ a- c3

L,- -: r o a o n -o "o *

O I- I- I .-_ I

-. CC - -- -1


o- a - C
C* I C - -i
4-c - I -

cc a:

- i_) I TO


o.. *-,,

S .t u -. '
> o

- --
0. 4 = 5

Sr i 0 -
rl), C ',- .- -

a I. a C "
1=. .- .01

S= C 0-

0 S

i &M *i l ci
'_ 'I u_ '_ 'J '- '-

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