Lecture1 Diagramming

8/3/2019 Lecture1 Diagramming

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Emergy & Complex Systems

Day 1, Lecture 1.

Energy SystemsDiagramming

A Systems language...symbols,conventions and simulation


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A system is a group of parts which are

connected and work together. Systems with

living and nonliving parts are called

ecosystems (which is short for ecological

systems).(Odum, Odum, and Brown, 1997)

What is a system?


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To convert non-quantitative verbal modelsto more quantitative, more accurate, more

predictive, more consistent, and lessconfusing network diagrams

Why a systems language?


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Understanding environment and society as a systemmeans thinking about parts, processes, andconnections.

To help understand systems, it is helpful to drawpictures of networks that show components andrelationships.

Understanding systems


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With a system diagram, we can carry thesesystem images in the mind. And learn the wayenergy, materials, and information interact.

By adding numerical values for flows andstorages, the systems diagrams become

quantitative and can be simulated with computers.

Visualizing systems


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System Frame: A rectangular box drawn to represethe boundaries of the system selected.

ENERGY SYSTEMS SYMBOLS

Systems Language

E & C l S


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Symbols continued...

Pathway Line: a flow of energy, often with a flowof materials.

SOURCE: outside source of energy; a forcing function..

STORAGE: a compartment of energy storage within the systemstoring quantity as the balance of inflows and outflows

E & C l S t


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INTERACTION: process which combines different types

of energy flows or material flows to produce anoutflow in proportion to a function of the inflows.

PRODUCER: unit that collects and trnasforms low-qualityenergy under control interactions of higher quality flows.

CONSUMER: unit that transforms energy quality, stores it,and feeds it back autocatalytically to improve inflow

.


E & C l S t


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TRANSACTION: a unit that indicates the sale of goods or

services (solid line) in exchange for payment of money(dashed line).

SWITCHING ACTION: symbol that indicates one or moreswitching functions where flows are interrupted orinitiated.

BOX: miscellaneous symbol for whatever unit or function islabled.




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Systems are organized hierarchically



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Language Conventions.

sources arranged

according to

t heir quality

Components arranged within

boundary according to their

q u a l it y

Used Energy



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Procedures for Drawing a Systems Model

1. Draw the frame of attention that selectsthe boundary

2. Make a list of the important input pathways

that cross the boundary

3. Make a list of the components believed to beimportant

4. Make a list of the processes believed to beimportant within the defined system.



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5. Remember that matter is conserved.

6. Check to see that money flows form a

closed loop within the frame and thatmoney inflows across the boundary lead tomoney outflows.

7. Check all pathways to see that energy

flows are appropriate.




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8. If color is used, the following are suggested:

Yellow sunlight, heat flows and used energy flowsBlue circulating materials of the biosphere such

as water, air, nutrientsBrown geological components, fuels, miningGreen environmental areas, producers, productionRed consumers (animal and economic), population,

industry, citiesPurple - money




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9. If a complex diagram has resulted (> 25symbols), redraw it to make it neat and saveit as a useful inventory and summary of the

input knowledge. Redraw the diagram withthe same boundary definition, aggregatingsymbols and flows to obtain a model of thedesired complexity (perhaps 3-10 symbols).

(Odum and Odum, 1996)




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Production & Consumptiona simple ecosystem.

Producer ConsumerEnergy

Source

Feedback

Diagramming Conventions.



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Emergy & omplex Systems

Day 1, Lecture 1.

.

B i o -

mass

Plants

B i o -

mass

Wildl i fe

Nutrients

Positive Feedback

Nutrient Recycle

Used Energ y

Forest Ecosystem

Sunlight

A more complex diagram of a forest...




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gy p y

Day 1, Lecture 1.

. .

Bio -

mass

Plant s

B io -

mass

Wildl i fe

Nutrients

Posit iv e Feedback

Nutrient Recycle

Used Energy

Forest Ecosystem

Sunlight

Goods &

Services

Markets

Sales

Pur cha se s

Cutting

X


Adding more complexity...



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gy p y

Day 1, Lecture 1.

Bio -

mass

Plant s

B

Nutrients

Used Energy

Ecosystem

Sunlight

H2O

H2O N

O.M.

Consumers

Bio-

diversity

Species

A generic ecosystem...




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gy p y

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Renewable

Sources

Natural

Ecosyst ems

Agric ult ure

GreenSpace

Commerce

& Industry

Infra-

Structure

PeopleGov't

$

Waste

Fuel Goods Services

People

Support Region

Cit y

.

Bio -

mass

Plants

Bio -

mass

Wildlife

Nutrients

Positive Feedback

Nutrient Recycle


A city & support region...



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gy p yDay 1, Lecture 1.

$$

$

Environment al

Production

Consumers

Wastes

Environmental

Recycle

Reserves

Stress

Markets

Goods

Services

FuelsPurchased

Inputs

Prices

Prices

Service to

Nature

Impacts

Environ.

Sources

Ecological

Engineering Interface

Self designed

Economic

Uses &

ValuesAdded,

Human Design

Ecological Engineering




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.

Soils,

Wood

Tidal

Energy

Sunlight

Geologic

Processes

Environment al

Systems

Fuels,

Materials

Stock

Pile

Assets

Wastes

Recycle

Economic

Syst ems

1 .

2 .

3 .

Coupling humanity and environment




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Picture Mathematics.

W

B

A

Jo J

R

k1

k2

k3 k4

k5

k6

k7

k8

k0

k9

Ra

dW/dt = Ra - K2*R*W - K1*W

dB/dt = k3*R*W - k4*B*A - k5*B

dA/dt = k6*A*B - k7*A*B - k8*a

Sun

Rain

Water

ProducersConsumers

Drawing systemsdiagramsexplicitly writes

mathematicalequationsexpressingrelationshipsbetween flowsand storages



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J1

J1 = k1*E

Flowsare the result of FORCES

The units of energy flowsare powerJoules/time

The units of materialflows are rateskg/time

E




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J1J3

J2

E

Q

dQ/dt = J1 - J2 - J3

J1 = k1*E

J2 = k2*Q

J3 = k3*Q

dQ/dt = k1*E - k2*Q - k3*Q

Rate of Change Equation

Rate of change ofthe storage Q isequal to theinflows minus theoutflows...


Emergy & Complex SystemsD 1 L 1


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J Q

J1

TANK

J = Source

Q = Storage Quantity

J

Simulation of TANK modelmjc - 10/99

Difference Equations

dQ/dt = J - K1*Q

Initial Stores and Calibrated CoCalibration Stores and Flows

J = 4 J 4.00

Q = 0 Q 80.00K1 = J1/Q 0.05 J1 4.00

Time Sources Storages Flows Increment

Days J Q J1 = K1*Q dQ/dt

0 4 0.00 0.00 4.00

1 4 4.00 0.20 3.80

2 4 7.80 0.39 3.61

3 4 11.41 0.57 3.43

4 4 14.84 0.74 3.26

5 4 18.10 0.90 3.10

6 4 21.19 1.06 2.94

7 4 24.13 1.21 2.79

8 4 26.93 1.35 2.65

9 4 29.58 1.48 2.52

10 4 32.10 1.61 2.39

11 4 34.50 1.72 2.28

12 4 36.77 1.84 2.16

13 4 38.93 1.95 2.05

14 4 40.99 2.05 1.95

15 4 42.94 2.15 1.85

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

0 50 100 150 200 250 300 350

Time, Days

Storages Q


Emergy & Complex SystemsD 1 L t 1


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J2

G

Q

10 0

J1

J4

J3

H

dQ/dt = J1 - J2 - J3 - J4J1 = k1*E*Q

J2 = - k2*E*Q

J3 = - k3*Q

J4 = - k4*Q

dQ/dt = k1*S*Q - k2*S*Q - k3*Q - k4*Q

E

Equational structureconsumer


Emergy & Complex SystemsD 1 L t 1


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Day 1, Lecture 1.

J2

G

Q

100

J1J3

H

dQ/dt = J1 - J2 - J3

J1 = k1*E*Q

J2 = - k2*E*Q

J3 = - k3*Q

dQ/dt = k1* S*Q - k2*S*Q - k3*Q

E

Simulation model EXPO

mtb -9/99

dq/dt= k1*E*Q-k2*E*Q-k3*Q

k1= 0.1 E= 1

k2= 0.03 Q= 4

k3= 0.05

Time Q k1*E*Q k2*E*Q k3*Q0 4

1 4 0.4 0.12 0.2

2 4.08 0.408 0.1224 0.204

3 4.162 0.4162 0.1248 0.2081

4 4.245 0.4245 0.1273 0.2122

5 4.33 0.433 0.1299 0.2165

6 4.416 0.4416 0.1325 0.2208

7 4.505 0.4505 0.1351 0.2252

8 4.595 0.4595 0.1378 0.22979 4.687 0.4687 0.1406 0.2343

10 4.78 0.478 0.1434 0.239

11 4.876 0.4876 0.1463 0.2438

12 4.973 0.4973 0.1492 0.2487

13 5.073 0.5073 0.1522 0.2536

14 5.174 0.5174 0.1552 0.2587

15 5.278 0.5278 0.1583 0.2639


Emergy & Complex SystemsDay 1 Lecture 1


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Model a simplified concept within the humanmind by which it visualizes reality.

System can be defined as a set of parts andtheir connected relationships.

(Odum and Odum, 1996)

Modeling Definitions



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Steady State when the storages andpatterns in an open system become constantwith a balance of inflows and outflows.

Equilibrium refers to any constant state, butgenerally refers to a closed system when thestorages become constant.



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Aggregation simplifying a system, notfragmentation

5 to 20 units

Include energy and material budgets Representation of levels of energy hierarchy Include feedback pathways

Calibration giving a model numerical values



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Validation - Compare what is known about thereal systems performance

Sensitivity - Analysis of how sensitiveoutcomes are to changes in the assumptions.




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Steps in Developing and

simulating a model.

The usual approach



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Steps in Developing and

simulating a model

Energy Systems approach

Emergy & Complex SystemsDay 1, Lecture 1.


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Wetland hydrology

Modeling.



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D y , L .

System Diagram of Wetland Hydrology

Modeling.



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y ,

Modeling.

Sun Q Rain Runin Recharge ET Outflow Height(m)

1.000 0.102 0.002 0.000 0.001 0.002 0.000 0.102

1.000 0.101 0.000 0.000 0.001 0.002 0.000 0.101

1.000 0.098 0.000 0.000 0.001 0.002 0.000 0.098

1.000 0.095 0.014 0.003 0.001 0.002 0.000 0.095

1.000 0.109 0.000 0.000 0.001 0.002 0.000 0.109

1.001 0.106 0.000 0.000 0.001 0.002 0.000 0.106

1.002 0.103 0.007 0.001 0.001 0.002 0.000 0.103

1.002 0.109 0.000 0.000 0.001 0.002 0.000 0.109

1.003 0.106 0.000 0.000 0.001 0.002 0.000 0.1061.004 0.103 0.000 0.000 0.001 0.002 0.000 0.103

1.005 0.100 0.000 0.000 0.001 0.002 0.000 0.100

1.007 0.097 0.000 0.000 0.001 0.002 0.000 0.097

1.008 0.094 0.000 0.000 0.001 0.002 0.000 0.094

WETLAND WATER

LEVEL

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

1 33 65 97 129 161 193 225 257 289 321 353

DAY

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Lecture1 Diagramming