Emergy & Complex Systems
Day 1, Lecture 1….
Energy SystemsDiagramming
Energy SystemsDiagramming
A Systems language...symbols, conventions and simulation…
Emergy & Complex Systems
Day 1, Lecture 1….
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?
Emergy & Complex Systems
Day 1, Lecture 1….
To convert non-quantitative verbal models to… more quantitative, more accurate, more predictive, more consistent, and less confusing network diagrams
Why a systems language?
Emergy & Complex Systems
Day 1, Lecture 1….
Understanding environment and society as a system means thinking about parts, processes, and connections.
To help understand systems, it is helpful to draw pictures of networks that show components and relationships.
Understanding systems…
Emergy & Complex Systems
Day 1, Lecture 1….
With a system diagram, we can carry these system images in the mind. And learn the way energy, materials, and information interact.
By adding numerical values for flows and storages, the systems diagrams become quantitative and can be simulated with computers.
Visualizing systems…
Emergy & Complex Systems
Day 1, Lecture 1….
System Frame: A rectangular box drawn to represent the boundaries of the system selected.
ENERGY SYSTEMS SYMBOLS
Systems Language…
Emergy & Complex Systems
Day 1, Lecture 1….
Symbols continued...
Pathway Line: a flow of energy, often with a flow of materials.
SOURCE: outside source of energy; a forcing function..
STORAGE: a compartment of energy storage within the system storing quantity as the balance of inflows and outflows
Emergy & Complex Systems
Day 1, Lecture 1….
INTERACTION: process which combines different types of energy flows or material flows to produce an outflow in proportion to a function of the inflows.
PRODUCER: unit that collects and trnasforms low-quality energy 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...
Emergy & Complex Systems
Day 1, Lecture 1….
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 more switching functions where flows are interrupted or initiated.
BOX: miscellaneous symbol for whatever unit or function is labled.
Symbols continued...
Emergy & Complex Systems
Day 1, Lecture 1….
Systems are organized hierarchically
I I I I I I I V
A
B
C
D
E
J
K
L
S
T
Z
Hierarchical Levels
Parallel Processes
EnergySource
Emergy & Complex Systems
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Language Conventions….
sources arrangedaccording totheir quality
Components arranged withinboundary according to theirquality
Used Energy
Emergy & Complex Systems
Day 1, Lecture 1….
Procedures for Drawing a Systems Model
1. Draw the frame of attention that selects the boundary
2. Make a list of the important input pathways that cross the boundary
3. Make a list of the components believed to be important
4. Make a list of the processes believed to be important within the defined system.
Emergy & Complex Systems
Day 1, Lecture 1….
5. Remember that matter is conserved.
6. Check to see that money flows form a closed loop within the frame and that money inflows across the boundary lead to money outflows.
7. Check all pathways to see that energy flows are appropriate.
Procedures for Drawing a Systems Model
Emergy & Complex Systems
Day 1, Lecture 1….
8. If color is used, the following are suggested:
Yellow – sunlight, heat flows and used energy flows
Blue – circulating materials of the biosphere such as water, air, nutrients
Brown – geological components, fuels, miningGreen – environmental areas, producers,
productionRed – consumers (animal and economic),
population, industry, citiesPurple - money
Procedures for Drawing a Systems Model
Emergy & Complex Systems
Day 1, Lecture 1….
9. If a complex diagram has resulted (> 25 symbols), redraw it to make it neat and save it as a useful inventory and summary of the input knowledge. Redraw the diagram with the same boundary definition, aggregating symbols and flows to obtain a model of the desired complexity (perhaps 3-10 symbols).
(Odum and Odum, 1996)
Procedures for Drawing a Systems Model
Emergy & Complex Systems
Day 1, Lecture 1….
Production & Consumption…a simple ecosystem.
Producer ConsumerEnergySource
Feedback
Diagramming Conventions….
Emergy & Complex Systems
Day 1, Lecture 1….
.
Bio-mass
Plants
Bio-mass
Wildlife
Nutrients Nutrient Recycle
Used Energy
Forest Ecosystem
Sunlight
.
Bio-mass
Plants
Bio-mass
Wildlife
Nutrients Nutrient Recycle
Used Energy
Forest Ecosystem
Sunlight
A more complex diagram of a forest...A more complex diagram of a forest...
Diagramming Conventions….
Emergy & Complex Systems
Day 1, Lecture 1….
. .
Bio-mass
Plants
Bio-mass
Wildlife
Nutrients Nutrient Recycle
Used Energy
Forest Ecosystem
Sunlight
Goods &Services
Markets
Sales
Cutting
X
Diagramming Conventions….
Adding more complexity...Adding more complexity...
Emergy & Complex Systems
Day 1, Lecture 1….
Bio-mass
Plants
B
Nutrients
Used Energy
Ecosystem
Sunlight
H2O
H2ON
O.M.
Consumers
Bio-diversity
Species
Bio-mass
Plants
B
Nutrients
Used Energy
Ecosystem
Sunlight
H2O
H2ON
O.M.
Consumers
Bio-diversity
Species
A generic ecosystem...
Diagramming Conventions….
Emergy & Complex Systems
Day 1, Lecture 1….
Renewable Sources
NaturalEcosystems
AgricultureGreenSpace
Commerce& Industry
Infra-Structure
PeopleGov't
$
Waste
Fuel Goods Services
People
Support Region
City
.
Bio-mass
Plants
Bio-mass
Wildlife
Nutrients Nutrient Recycle
.
Bio-mass
Plants
Bio-mass
Wildlife
Nutrients Nutrient Recycle
Diagramming Conventions….
A city & support region...A city & support region...
Emergy & Complex Systems
Day 1, Lecture 1….
$$
$
Environmental Production
Consumers
Wastes
EnvironmentalRecycle
Reserves
Stress
Markets
GoodsServices Fuels
PurchasedInputs
Prices
Prices
Service to Nature
Impacts
Environ.Sources
EcologicalEngineering Interface
Self designed
Economic Uses &Values Added,Human Design
$$
$
Environmental Production
Consumers
Wastes
EnvironmentalRecycle
Reserves
Stress
Markets
GoodsServices Fuels
PurchasedInputs
Prices
Prices
Service to Nature
Impacts
Environ.Sources
EcologicalEngineering Interface
Self designed
Economic Uses &Values Added,Human Design
Ecological EngineeringEcological Engineering
Diagramming Conventions….
Emergy & Complex Systems
Day 1, Lecture 1….
.
So ils ,
Wood
TidalEnergy
Sunlight
Geologic
Processes
Environmental
Systems
Fuels,Materials
Stock Pile
Assets
WastesEconomicSystems
1.
2.
3.
.
So ils ,
Wood
TidalEnergy
Sunlight
Geologic
Processes
Environmental
Systems
Fuels,Materials
Stock Pile
Assets
WastesEconomicSystems
1.
2.
3.
Coupling humanity and environmentCoupling humanity and environment
Diagramming Conventions….
Emergy & Complex Systems
Day 1, Lecture 1….
Picture Mathematics….
W
B
A
J o J
R
k1
k2
k3 k4
k5
k6
k7k8
k0
k9
Ra
dW/dt = Ra - K2*R*W - K1*WdB/dt = k3*R*W - k4*B*A - k5*BdA/dt = k6*A*B - k7*A*B - k8*a
Sun
Rain
Water
ProducersConsumers
W
B
A
J o J
R
k1
k2
k3 k4
k5
k6
k7k8
k0
k9
Ra
dW/dt = Ra - K2*R*W - K1*WdB/dt = k3*R*W - k4*B*A - k5*BdA/dt = k6*A*B - k7*A*B - k8*a
Sun
Rain
Water
ProducersConsumers
Drawing systems diagrams explicitly writes mathematical equations expressing relationships between flows and storages
Emergy & Complex Systems
Day 1, Lecture 1….
J1
J1 = k1*E
Flows…are the result of FORCES
The units of energy flows are “power”…Joules/time
The units of material flows are “rates” …kg/time
E
Picture Mathematics….
Emergy & Complex Systems
Day 1, Lecture 1….
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
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 EquationRate of Change Equation
Rate of change of the storage “Q” is equal to the inflows minus the outflows...
Picture Mathematics….
Emergy & Complex Systems
Day 1, Lecture 1….
J Q
J1
TANK
J = SourceQ = Storage Quantity
JJ Q
J1
TANK
J = SourceQ = Storage Quantity
J
Simulation of TANK modelmjc - 10/99
Difference EquationsdQ/dt = J - K1*Q
Initial Stores and Calibrated Coeffs.Calibration Stores and FlowsJ = 4 J 4.00Q = 0 Q 80.00
K1 = J1/Q 0.05 J1 4.00
Time Sources Storages Flows IncrementDays J Q J1 = K1*Q dQ/dt
0 4 0.00 0.00 4.001 4 4.00 0.20 3.802 4 7.80 0.39 3.613 4 11.41 0.57 3.434 4 14.84 0.74 3.265 4 18.10 0.90 3.106 4 21.19 1.06 2.947 4 24.13 1.21 2.798 4 26.93 1.35 2.659 4 29.58 1.48 2.52
10 4 32.10 1.61 2.3911 4 34.50 1.72 2.2812 4 36.77 1.84 2.1613 4 38.93 1.95 2.0514 4 40.99 2.05 1.9515 4 42.94 2.15 1.85
Simulation of TANK modelmjc - 10/99
Difference EquationsdQ/dt = J - K1*Q
Initial Stores and Calibrated Coeffs.Calibration Stores and FlowsJ = 4 J 4.00Q = 0 Q 80.00
K1 = J1/Q 0.05 J1 4.00
Time Sources Storages Flows IncrementDays J Q J1 = K1*Q dQ/dt
0 4 0.00 0.00 4.001 4 4.00 0.20 3.802 4 7.80 0.39 3.613 4 11.41 0.57 3.434 4 14.84 0.74 3.265 4 18.10 0.90 3.106 4 21.19 1.06 2.947 4 24.13 1.21 2.798 4 26.93 1.35 2.659 4 29.58 1.48 2.52
10 4 32.10 1.61 2.3911 4 34.50 1.72 2.2812 4 36.77 1.84 2.1613 4 38.93 1.95 2.0514 4 40.99 2.05 1.9515 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
Stored Quantity
Storages Q
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
Stored Quantity
Storages Q
Picture Mathematics….
Emergy & Complex Systems
Day 1, Lecture 1….
J2
G
Q
100
J1
J4
J3
H
dQ/dt = J1 - J2 - J3 - J4 J1 = 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
J2
G
Q
100
J1
J4
J3
H
dQ/dt = J1 - J2 - J3 - J4 J1 = 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 structure…consumer
Equational structure…consumer
Picture Mathematics….
Emergy & Complex Systems
Day 1, Lecture 1….
J2
G
Q
100
J1J3
H
dQ/ dt = J 1 - J 2 - J 3 J 1 = k1*E*Q J 2 = - k2*E*Q J 3 = - k3*Q
dQ/ dt = k1*S*Q - k2*S*Q - k3*Q
E
J2
G
Q
100
J1J3
H
dQ/ dt = J 1 - J 2 - J 3 J 1 = k1*E*Q J 2 = - k2*E*Q J 3 = - k3*Q
dQ/ dt = k1*S*Q - k2*S*Q - k3*Q
E
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
1 18 35 52 69 86 103 120 137 154 171 188 205 222 239 256 273 290 307 324 341 358
TIME
Q
0
10
20
30
40
50
60
70
80
90
100
110
120
130
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150
1 18 35 52 69 86 103 120 137 154 171 188 205 222 239 256 273 290 307 324 341 358
TIME
Q
Picture Mathematics….
Emergy & Complex Systems
Day 1, Lecture 1….
Model – a simplified concept within the human mind by which it visualizes reality.
System – can be defined as a set of parts and their connected relationships.
(Odum and Odum, 1996)
Modeling Definitions…
Emergy & Complex Systems
Day 1, Lecture 1….
Modeling Definitions…
Steady State – when the storages and patterns in an open system become constant with a balance of inflows and outflows.
Equilibrium – refers to any constant state, but generally refers to a closed system when the storages become constant.
Emergy & Complex Systems
Day 1, Lecture 1….
Modeling Definitions…
Aggregation – simplifying a system, not fragmentation
• 5 to 20 units• Include energy and material budgets• Representation of levels of energy hierarchy• Include feedback pathways
Calibration – giving a model numerical values
Emergy & Complex Systems
Day 1, Lecture 1….
Validation - Compare what is known about the real systems performance
Sensitivity - Analysis of how sensitive outcomes are to changes in the assumptions.
Modeling Definitions…
Emergy & Complex Systems
Day 1, Lecture 1….
Steps in Developing and simulating a model.
The usual approach…
Emergy & Complex Systems
Day 1, Lecture 1….
Steps in Developing and simulating a model
Energy Systems approach
Emergy & Complex Systems
Day 1, Lecture 1….
Ground water level
Direct rainfall
Runin
EvaporationTranspiration
Surface Outflow
Ground water recharge
Wetland hydrologyWetland hydrology
Modeling….
Emergy & Complex Systems
Day 1, Lecture 1….
.
Wind
Rain Run- in
BiomassSoil
WaterSoilOrganicMatter
SurfaceWater
Surface Runoff
InfiltrationSun
Animals
Animals
Vegetation
ET
System Diagram of Wetland HydrologySystem Diagram of Wetland Hydrology
Modeling….
Emergy & Complex Systems
Day 1, Lecture 1….
Modeling….
Sun Q Rain Runin Recharge ET Outflow Height(m)1.000 0.102 0.002 0.000 0.001 0.002 0.000 0.1021.000 0.101 0.000 0.000 0.001 0.002 0.000 0.1011.000 0.098 0.000 0.000 0.001 0.002 0.000 0.0981.000 0.095 0.014 0.003 0.001 0.002 0.000 0.0951.000 0.109 0.000 0.000 0.001 0.002 0.000 0.1091.001 0.106 0.000 0.000 0.001 0.002 0.000 0.1061.002 0.103 0.007 0.001 0.001 0.002 0.000 0.1031.002 0.109 0.000 0.000 0.001 0.002 0.000 0.1091.003 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 0.1031.005 0.100 0.000 0.000 0.001 0.002 0.000 0.1001.007 0.097 0.000 0.000 0.001 0.002 0.000 0.0971.008 0.094 0.000 0.000 0.001 0.002 0.000 0.094
Sun Q Rain Runin Recharge ET Outflow Height(m)1.000 0.102 0.002 0.000 0.001 0.002 0.000 0.1021.000 0.101 0.000 0.000 0.001 0.002 0.000 0.1011.000 0.098 0.000 0.000 0.001 0.002 0.000 0.0981.000 0.095 0.014 0.003 0.001 0.002 0.000 0.0951.000 0.109 0.000 0.000 0.001 0.002 0.000 0.1091.001 0.106 0.000 0.000 0.001 0.002 0.000 0.1061.002 0.103 0.007 0.001 0.001 0.002 0.000 0.1031.002 0.109 0.000 0.000 0.001 0.002 0.000 0.1091.003 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 0.1031.005 0.100 0.000 0.000 0.001 0.002 0.000 0.1001.007 0.097 0.000 0.000 0.001 0.002 0.000 0.0971.008 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
WATER DEPTH (meters)
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
WATER DEPTH (meters)
.
Wind
Rain Run- in
BiomassSoil
WaterSoilOrganicMatter
SurfaceWater
Surface Runoff
InfiltrationSun
Animals
Animals
Vegetation
ET
.
Wind
Rain Run- in
BiomassSoil
WaterSoilOrganicMatter
SurfaceWater
Surface Runoff
InfiltrationSun
Animals
Animals
Vegetation
ET