Emergy & Complex Systems Day 1, Lecture 1…. Energy Systems Diagramming Energy Systems Diagramming A Systems language...symbols, conventions and simulation…

Emergy & Complex Systems

Day 1, Lecture 1….

Energy SystemsDiagramming

Energy SystemsDiagramming

A Systems language...symbols, conventions and simulation…



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?



To convert non-quantitative verbal models to… more quantitative, more accurate, more predictive, more consistent, and less confusing network diagrams

Why a systems language?



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…



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…



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

ENERGY SYSTEMS SYMBOLS

Systems Language…



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



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

.




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.




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



Language Conventions….

sources arrangedaccording totheir quality

Components arranged withinboundary according to theirquality

Used Energy



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.



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.




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




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)




Production & Consumption…a simple ecosystem.

Producer ConsumerEnergySource

Feedback

Diagramming Conventions….



.

Bio-mass

Plants

Bio-mass

Wildlife

Nutrients Nutrient Recycle

Used Energy

Forest Ecosystem

Sunlight

.

Bio-mass

Plants

Bio-mass

Wildlife


Used Energy

Forest Ecosystem

Sunlight

A more complex diagram of a forest...A more complex diagram of a forest...




. .

Bio-mass

Plants

Bio-mass

Wildlife


Used Energy

Forest Ecosystem

Sunlight

Goods &Services

Markets

Sales

Cutting

X


Adding more complexity...Adding more complexity...



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...




Renewable Sources

NaturalEcosystems

AgricultureGreenSpace

Commerce& Industry

Infra-Structure

PeopleGov't

$

Waste

Fuel Goods Services

People

Support Region

City

.

Bio-mass

Plants

Bio-mass

Wildlife


.

Bio-mass

Plants

Bio-mass

Wildlife



A city & support region...A city & support region...



$$

$

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




.

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




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



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




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...




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




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




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

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




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…




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.




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



Validation - Compare what is known about the real systems performance

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




Steps in Developing and simulating a model.

The usual approach…



Steps in Developing and simulating a model

Energy Systems approach



Ground water level

Direct rainfall

Runin

EvaporationTranspiration

Surface Outflow

Ground water recharge

Wetland hydrologyWetland hydrology

Modeling….



.

Wind

Rain Run- in

BiomassSoil

WaterSoilOrganicMatter

SurfaceWater

Surface Runoff

InfiltrationSun

Animals

Animals

Vegetation

ET

System Diagram of Wetland HydrologySystem Diagram of Wetland Hydrology

Modeling….



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


SurfaceWater

Surface Runoff

InfiltrationSun

Animals

Animals

Vegetation

ET

.

Wind

Rain Run- in

BiomassSoil


SurfaceWater

Surface Runoff

InfiltrationSun

Animals

Animals

Vegetation

ET

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Emergy & Complex Systems Day 1, Lecture 1…. Energy Systems Diagramming Energy Systems Diagramming A Systems language...symbols, conventions and simulation…