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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
.
Symbols continued...
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.
Symbols continued...
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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.
Procedures for Drawing a Systems Model
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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
Procedures for Drawing a Systems Model
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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)
Procedures for Drawing a Systems Model
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Production & Consumptiona simple ecosystem.
Producer ConsumerEnergy
Source
Feedback
Diagramming Conventions.
Emergy & Complex Systems
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.
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...
Diagramming Conventions.
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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
Diagramming Conventions.
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...
Diagramming Conventions.
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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
Diagramming Conventions.
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
Diagramming Conventions.
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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
Diagramming Conventions.
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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
Picture Mathematics.
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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...
Picture Mathematics.
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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
Picture Mathematics.
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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
Picture Mathematics.
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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
Picture Mathematics.
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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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Modeling Definitions
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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Modeling Definitions
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.
Modeling Definitions
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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
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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