Emergy & Complex Systems
Day 1, Lecture 1….
Energy Systems
Diagramming
A Systems language...symbols,
conventions and simulation…
Emergy & Complex Systems
Day 1, Lecture 1….
What is a system?
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)
Emergy & Complex Systems
Day 1, Lecture 1….
Why a systems language?
To convert non-quantitative verbal models
to… more quantitative, more accurate, more
predictive, more consistent, and less
confusing network diagrams
Emergy & Complex Systems
Day 1, Lecture 1….
Understanding systems…
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.
Emergy & Complex Systems
Day 1, Lecture 1….
Visualizing systems…
§  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.
Emergy & Complex Systems
Day 1, Lecture 1….
Systems Language…
ENERGY SYSTEMS SYMBOLS
System Frame: A rectangular box drawn to represent
the boundaries of the system selected.
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….
Symbols
continued...
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
Emergy & Complex Systems
Day 1, Lecture 1….
Symbols
continued...
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.
Emergy & Complex Systems
Day 1, Lecture 1….
Systems are organized hierarchically
H i er a r c h i c a l
L ev el s
I
I I
E
L
D
Energy
Source
C
S
J
P a r a l l el
IV
T
K
B
A
III
P r o c es s es
Z
Emergy & Complex Systems
Day 1, Lecture 1….
Language Conventions….
sources arranged
according to
their quality
Components arran ged within
boundary according to their
quality
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….
Procedures for Drawing a Systems Model
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.
Emergy & Complex Systems
Day 1, Lecture 1….
Procedures for Drawing a Systems Model
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, mining
Green – environmental areas, producers, production
Red – consumers (animal and economic), population,
industry, cities
Purple - money
Emergy & Complex Systems
Day 1, Lecture 1….
Procedures for Drawing a Systems Model
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)
Emergy & Complex Systems
Day 1, Lecture 1….
Diagramming Conventions….
Production & Consumption…a simple ecosystem.
Feedback
Energy
Source
Producer
Consumer
Emergy & Complex Systems
Day 1, Lecture 1….
Diagramming Conventions….
A more complex diagram of a forest...
.
Nutrients
Po si tive
Biomass
Sunlight
Fe edb ac
k
Biomass
Wildlife
Plants
Forest
Nutrient Recycle
Ecosystem
Used Energy
Emergy & Complex Systems
Day 1, Lecture 1….
Diagramming Conventions….
Adding more complexity...
..
P
Nutrients
Biomass
Sunlight
Plants
s
se
Goods &
Services
Cutting
Nutrient Recycle
Posi ti ve
ha
urc
Markets
Fe edback
X
Sales
Biomass
Wildlife
Forest
Used Energy
Ecosystem
Emergy & Complex Systems
Day 1, Lecture 1….
Diagramming Conventions….
A generic ecosystem...
H2O
Species
N
H2O
Biodiversity
Nutrients
B
Biomass
Sunlight
Consumers
Plants
O.M.
Ecosystem
Used Energy
Emergy & Complex Systems
Day 1, Lecture 1….
Diagramming Conventions….
.
Nutrients
Positive
Biomass
Plants
Nutrient Recycle
A city & support region...
Feedback
Biomass
Wildlife
Fuel
Services
Goods
People
Natural
Ecosystems
Renewable
Sources
Commerce
& Industry
Gov't
People
$
Agriculture
Green
Space
City
Support Region
InfraStructure
Waste
Emergy & Complex Systems
Day 1, Lecture 1….
Diagramming Conventions….
Ecological Engineering
Prices
Environmental
Recycle
Purchased
Inputs
Service to
Nature
Environ.
Sources
Reserves
Self designed
Environmental
Production
Stress
Economic
$
Uses &
ValuesAdded,
Human Design
Prices
Markets
$
Consumers
Impacts
Wastes
Ecological
Engineering Interface
$
Goods
Services
Fuels
Emergy & Complex Systems
Day 1, Lecture 1….
Diagramming Conventions….
Coupling humanity and environment
.
Tidal
Energy
Geologic
Processes
3.
1.
2.
Soils,
Wood
Sunlight
Fuels,
Materials
Recy
cle
Stock
Pile
Assets
Environmental
Systems
Economic
Systems
Wastes
Emergy & Complex Systems
Day 1, Lecture 1….
Picture Mathematics….
Drawing systems
diagrams
explicitly writes
mathematical
equations
expressing
relationships
between flows
and storages
Rain
Ra
W
Water
k9
Sun
Jo
k2
A
k3
J
k0
k1
B
k7
k4
Producers
k5
R
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
k8
k6
Consumers
Emergy & Complex Systems
Day 1, Lecture 1….
Picture Mathematics….
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
J1
J1 = k1*E
Emergy & Complex Systems
Day 1, Lecture 1….
Picture Mathematics….
Rate of Change Equation
Rate of change of
the storage “Q” is
equal to the
inflows minus the
outflows...
Q
E
J1
J3
J2
dQ/dt = J1 - J2 - J3
J1 = k1*E
J2 = k2*Q
J3 = k3*Q
dQ/dt = k1*E - k2*Q - k3*Q
Emergy & Complex Systems
Day 1, Lecture 1….
Picture Mathematics….
Simulation of TANK model
mjc - 10/99
Difference Equations
dQ/dt = J - K1*Q
J
J
Q
Initial Stores and Calibrated
Calibration
Coeffs.Stores and Flows
J=
4
J
4.00
Q=
0
Q
80.00
K1 = J1/Q
0.05
J1
4.00
J1
TANK
Sources
J
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Storages
Q
0.00
4.00
7.80
11.41
14.84
18.10
21.19
24.13
26.93
29.58
32.10
34.50
36.77
38.93
40.99
42.94
Flows
J1 = K1*Q
0.00
0.20
0.39
0.57
0.74
0.90
1.06
1.21
1.35
1.48
1.61
1.72
1.84
1.95
2.05
2.15
Increment
dQ/dt
4.00
3.80
3.61
3.43
3.26
3.10
2.94
2.79
2.65
2.52
2.39
2.28
2.16
2.05
1.95
1.85
J = Source
Q = Storage Quantity
Storages Q
90.00
80.00
70.00
Stored Quantity
Time
Days
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
60.00
50.00
40.00
30.00
20.00
10.00
0.00
0
50
100
150
200
Time, Days
250
300
350
Emergy & Complex Systems
Day 1, Lecture 1….
Picture Mathematics….
Equational structure…consumer
J2
E
Q
100
J4
J1
G
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
Emergy & Complex Systems
Day 1, Lecture 1….
Picture Mathematics….
Simulation model EXPO
mtb -9/99
J2
dq/dt= k1*E*Q-k2*E*Q-k3*Q
k1=
0.1
E=
k2=
0.03
Q=
k3=
0.05
Q
4
4
4.08
4.162
4.245
4.33
4.416
4.505
4.595
4.687
4.78
4.876
4.973
5.073
5.174
5.278
k1*E*Q
k2*E*Q
J3
J1
G
1
4
H
dQ/dt = J1 - J2 - J3
J1 = k1*E*Q
J2 = - k2*E*Q
J3 = - k3*Q
k3*Q
dQ/dt = k1*S*Q - k2*S*Q - k3*Q
0.4
0.408
0.4162
0.4245
0.433
0.4416
0.4505
0.4595
0.4687
0.478
0.4876
0.4973
0.5073
0.5174
0.5278
0.12
0.1224
0.1248
0.1273
0.1299
0.1325
0.1351
0.1378
0.1406
0.1434
0.1463
0.1492
0.1522
0.1552
0.1583
0.2
0.204
0.2081
0.2122
0.2165
0.2208
0.2252
0.2297
0.2343
0.239
0.2438
0.2487
0.2536
0.2587
0.2639
150
140
130
120
110
100
90
Q
Time
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
E
Q
100
80
70
60
50
40
30
20
10
0
1
18
35
52
69
86 103 120 137 154 171 188 205 222 239 256 273 290 307 324 341 358
TIME
Emergy & Complex Systems
Day 1, Lecture 1….
Modeling Definitions…
§  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)
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….
Modeling Definitions…
§  Validation - Compare what is known about the
real systems performance
§  Sensitivity - Analysis of how sensitive
outcomes are to changes in the assumptions.
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….
Modeling….
Wetland hydrology
Direct
rainfall
Evaporation
Runin
Transpiration
Surface
Ground water recharge
Outflow
Ground water level
Emergy & Complex Systems
Day 1, Lecture 1….
Modeling….
System Diagram of Wetland Hydrology
.
Rain
Animals
Run-in
M
Wind
or
Evap
an
sp
ira
tio
n
Vegetation
Surface Runoff
Surface
Water
Animals
Biomass
Sun
n
tio
ation
Tr
ET
ra
ig
Soil
Organic
Matter
Soil
Water
Infiltration
Emergy & Complex Systems
Day 1, Lecture 1….
Modeling….
.
Rain
Animals
Run-in
M
Wind
or
Evap
ation
Tr
ET
an
sp
ira
tio
n
Animals
Soil
Organic
Matter
Vegetation
Rain
0.102
0.101
0.098
0.095
0.109
0.106
0.103
0.109
0.106
0.103
0.100
0.097
0.094
0.002
0.000
0.000
0.014
0.000
0.000
0.007
0.000
0.000
0.000
0.000
0.000
0.000
Runin
0.000
0.000
0.000
0.003
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
Recharge
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
ET
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
Outflow
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Height(m)
0.102
0.101
0.098
0.095
0.109
0.106
0.103
0.109
0.106
0.103
0.100
0.097
0.094
Soil
Water
Infiltration
WETLAND WATER
LEVEL
WATER DEPTH (meters)
Q
Surface Runoff
Surface
Water
Biomass
Sun
Sun
1.000
1.000
1.000
1.000
1.000
1.001
1.002
1.002
1.003
1.004
1.005
1.007
1.008
ra
ig
n
tio
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
-0.1000
1
33
65
97 129 161 193 225 257 289 321 353
DAY