Fishwick P.A. (editor) Handbook of Dynamic System Modeling

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28-22 Handbook of Dynamic System Modeling

constants, especially those with complex units, are not easily measured. By comparison, measurements

of the needed rates of production, metabolism, resource use and regeneration, and measurements of

the standing stock and energy content of biomass are commonly made in ecological studies. Even so, a

sufﬁciently complete set of measurements about the same system is very rare. A broad range of experience

and literature must be explored to come up with a set of preliminary numbers that can be used for model

calibration.

Moreover, the estimates must apply to the same time period. To correctly compute a constant, the

corresponding rates and storages must be in proper proportion. Average values for the rates and storages

are usually used because they integrate long time periods, so are thought to be in correct proportions.

A snapshot of synoptic measurements would provide a more precise set of estimates, but a specially

coordinated ﬁeld study would be required. Such a study would be very involved for a snapshot of the 80

or so variables involved in the marsh model given in Table 28.1.

Table 28.2 provides the list of nominal steady-state values for each storage and rate that were used in

calibrating the constants for the model in Table 28.1. The nominal values were estimated from many kinds

of information. The basis for each estimate is provided and any formula involved is also given in the

Table 28.2. The nominal values so provided are for illustrative purposes only. They are plausible, based

on general literature and experience of the author, but they may not apply adequately to a given marsh.

Nevertheless, an analysis of model output sensitivity to changes in constants can be done to help identify

the estimates that have the most signiﬁcant inﬂuence on the dynamics produced by the model.

28.5 Preparation for Simulation

Once in equation form with all constants speciﬁed, the process of simulation is no different from that

commonly used for nonlinear causal models in a wide variety of engineering and science ﬁelds. The same

issues of initial value selection, choice of integration procedure, speciﬁcation of simulation step size (time

interval), and evaluation of roundoff error must be addressed. The same heuristic analytical procedures

can be used, and the same limitations and pitfalls are present.

Because the resulting differential equations are seldom solvable analytically with calculus, Energy

Systems Language models are represented and solved numerically on a computer by whatever means

available. Historically, this effort began with analog computers, the use of which is now all but forgotten

by Energy Systems Language practitioners. Today, Energy Systems Language models are often represented

in programming languages for scientists and engineers such as FORTRAN, BASIC, PASCAL, and C.

28.5.1 Simulation Software and Energy Systems Language

Simulation software, such as Vensim

, STELLA

, and EXTEND

are valuable tools for conceptualizing

the system, documenting ﬂow equations, writing and integrating storage equations, and plotting output.

Both Vensim and STELLA were developed speciﬁcally for the systems dynamics approach begun by Jay

Forrester (1961, 1968), but these programs work equally well for many other approaches to dynamic

simulation modeling, including Energy Systems Language models. Vensim Personal Learning Edition was

used for the model given in Table 28.1. To date, this version is free for educational use and comes with

well-written and informative documentation.

When writing simulation models in a programming language such as BASIC, the order of equations

is very important. Constants and initial values must be given before the iterative loop that represents the

passage of time. Within the loop, ﬂow rates must be calculated before time is advanced, and storages

must be calculated immediately afterwards. Simulation languages free the modeler from the necessity to

properly sequence model equations, to program an integration procedure, and to plot output data.

Vensim is a registered trademark of Ventana Systems Inc., Harvard, MA; STELLA is a registered trademark of Isee

Systems Inc., Lebanon, NH; and EXTEND is a registered trademark of Imagine That Inc., San Jose, CA.

Dynamic Simulation with Energy Systems Language 28-23

TABLE 28.2

Assumptions and Formulas Employed to Set the Nominal St

eady-State Values of Storages, Flows, and Auxiliaries so that Model C

onstants could be Calibr

ated by

Back-Calculation with the Model Simulation Equations. Var

iables in Table are given in Alphabetical Order. Refer to the List of Mo

del Equations for th

e Meaning of each Variable

Variable and formula for nominal

Nominal Units

Basis for value used

steady-state value

value

J0FCS

=(0.6

∗

46.0e+3)

∗

1.05e+8

2.89800e+12 J/y

0.6 g-C/m

/y production, in 10,000 ha estuary

+500 ha of tidal creeks, 46 kJ/g-C

J0LM

=(150

∗

3.15576e+7)

∗

3.0e+7

1.42009e+17 J/y

Sunlight (150 W/m

) ×low marsh area (3000 ha)

JFCS0

=(J0FCS+MJbFCS+MJcFCS−JYield) 1.85351e

+13 J/y

All food assimilated by ﬁshes, crabs, and shrimps (but

not caught) is used in their own metabolism

JW2M2

=−0.4

∗

Rain

−1.80000e+10 kg-H

O/y Net export equal to 40% of rainfall

JW3M3

0.00000e+0 kg-salt/y Salt is at equilibrium,

so net exchange

JW4M4

=(MJ47+MJ49)−(MJa4+MJb4+MJc4) 2.68822e+5

kg-N/y Net nitrogen import from estuary equals uptak

e in marsh less regeneration in marsh

JW5M1

=MJ15+(MJ1a+MJ1b+MJ1c)−MJ71 0.00000e+0

J/y

Net detritus exchange with estuary is detritus buried plus that

assimilated minus that

produced in the marsh

JW6M5

=−MJ15D

−1.11644 e+6 kg-sediment/y Net sediment export

equals the detrital burial rate in marsh

Jyield =

0.00000e+0 J/y

No ﬁshes, crabs, or shrimps are caught in ﬁrst model run

MA07a

=J0LM

∗

(0.12/(1−0.02)

1.73889e+16 J/y

Light input

×portion (P) of light available for low marsh plants (albedo

12%)

adjusted for fraction assimilated by benthic microalgae (2%).

MA07b

=(MQ2

∗

MQ4

∗

MQ6/MQ3)

7.86156e+16 Complex Multiple of all production

effects indicated for low marsh plants except light and

standing stock.

MA09a

=0.12

∗

J0LM

1.70411e+16 J/y

Light input

×marsh total albedo (12%)

MA09b

=(MQ2

∗

MQ4

∗

MQ6/MQ3)

7.86156e+16 Complex Multiple of all production

effects indicated for benthic microalgae except light and

standing stock

MA20 =

MA07a

1.73889e+16 J/y

Same as light available for low marsh plants (

=MA07a)

MJ06 =

Tide

1.03752e

+14 J/y

Circulation energy equals the tidal energy inﬂux

MJ07 =0.01

∗

J0LM

1.42009e+15 J/y

Light input

×fraction assimilated by plants (1%)

MJ09 =0.02

∗

MA07a

3.47778e+14 J/y

2% of light assimilated by benthic microalgae after interception

by water and plants

MJ15 =0.03

∗

MJ71

1.89795e+13 J/y

3% of detritus input is buried in sediments

MJ15D =MJ15/17e+6

1.11644e+6 kg-sediment/y Energy content of amount

buried divided by 17 kJ/g

MJ1a =0.87

∗

MJ71

5.50406e+14 J/y

87% of detritus input is consumed by microbes

MJ1b =0.08

∗

MJ71

5.06121e+13 J/y

8% of detritus input is consumed by meiofauna

MJ1c =0.02

∗

MJ71

1.26530e+13 J/y

2% of detritus input is consumed by macrofauna

MJ20 =0.2

∗

Rain

9.00000e+9 kg-H

O/y Evaporation equivalent to 20% of rainfall (30 cm/y)

MJ207 =

0.4

∗

Rain

1.80000e+10 kg-H

O/y Transpiration equivalent to 40% of rainfall (60

cm/y)

MJ20E =

J0LM

∗

(1−0.01−(0.12/(1−0.02))) 1.23200e+17

J/y

Light for water evaporation is the portion neither assimilated

by low marsh plants

(1%), by benthic microalgae (2% after plant assimilation), nor

reﬂected (12%)

MJ47 =

(MJ07−MJ70)

∗

4.5e−08

3.19521e+7 kg-N/y 0.045 g-N is assimilat

ed by low marsh plants for every kJ of gross production

MJ49 =

(MJ09−MJ90)

∗

5.0e−8

8.69444e+6 kg-N/y 0.05 g-N is assimilat

ed by benthic microalgae for every kJ of gross production

(Continued)

28-24 Handbook of Dynamic System Modeling

TABLE 28.2

Continued

Variable and formula for nominal

Nominal

Units

Basis for value used

steady-state value

value

MJ60 =

0.9

∗

MJ06

9.33770e+13 J/y

90% of circulation energy inﬂux does not affect low marsh

plants

MJ607

=0.1

∗

MJ06

1.03752e+13 J/y

10% of circulation energy inﬂux is intercepted by plants

MJ70 =

0.5

∗

MJ07

7.10046e+14 J/y

50% of low marsh plant gross production is used in the plant

’s own metabolism

MJ706

=0.01

∗

(MJ07−MJ70)

7.10046e+12 J/y

1% of the net primary production of low marsh plants (befor

e transpiration) is used

in transpiration

MJ71 =

0.9

∗

(MJ07−MJ70−MJ706)

6.32651e+14 J/y

90% of the net primary production of low marsh plants bec

omes detritus

MJ7e =

0.1

∗

(MJ07−MJ70−MJ706)

7.02946e+13 J/y

10% of the net primary production of low marsh plants is

assimilated by insects

MJ90 =

0.5

∗

MJ09

1.73889e+14 J/y

50% of benthic microalgal gross produc

tion is used in the plant’s own metabolism

MJ9b =

0.5

∗

(MJ09−MJ90)

8.69444e+13 J/y

50% of benthic microalgal net production assimilated by

meiofauna

MJ9c =

0.4

∗

(MJ09−MJ90)

6.95555e+13 J/y

40% of benthic microalgal net production assimilated by

macrofauna

MJ9e =

0.1

∗

(MJ09−MJ90)

1.73889e+13 J/y

10% of benthic microalgal net production assimilated by

insects

MJa0 =

0.8

∗

MJ1a

4.40325e+14 J/y

80% of the detritus assimilated by microbes is used in micr

obial metabolism

MJa4 =

5.0e−8

∗

MJa0

2.20163e+7 kg-N/y

0.05 g-N is regenerated for every kJ of energy metabolized by micr

obes

MJab =0.6

∗

(MJ1a−MJa0)

6.60488e+13 J/y

60% of the net production of microbes is assimilated by meiofauna

MJac =0.4

∗

(MJ1a−MJa0)

4.40325e+13 J/y

40% of the net production of microbes is assimilated by macrofauna

MJb0 =0.9

∗

(MJ1b+MJ9b+MJab)

1.83245e+14 J/y

90% of the food assimilated by meiofauna is used in meiofaunal

metabolism

MJb4 =6.0e−8

∗

MJb0

1.09947e+7 kg-N/y

0.06 g-N is regenerated for every kJ of energy metabolized by meiofauna

MJbc =0.5

∗

(MJ1b+MJ9b+MJab−MJb0)

1.01803e+13 J/y

50% of the net production of meiofauna is assimilated by macrofauna

MJbFCS =0.5

∗

(MJ1b+MJ9b+MJab−MJb0)

1.01803e+13 J/y

50% of the net production of meiofauna is assimilated by ﬁshes,

crabs, and shrimps

in the estuary and tidal creeks

MJc0 =0.9

∗

(MJ1c+MJ9c+MJac

+MJbc)

1.22779e

+14 J/y

90% of the food assimilated by macrofauna is used in macrofaunal

metabolism

MJc4 =6.0e−8

∗

MJc0

7.36675e+6 kg-N/y

0.06 g-N is regenerated for every kJ of energy metabolized by macr

ofauna

MJcd =0.4

∗

(MJ1c+MJ9c+MJac

+MJbc

−MJc0) 5.45685e+12 J/y

40% of the net production of macrofauna is assimilated by rats and

raccoons

MJcFCS

=0.4

∗

(MJ1c+MJ9c+MJac

+MJbc

−MJc0) 5.45685e+12 J/y

40% of the net production of macrofauna is assimilated by ﬁshes,

crabs, and shrimps

in the estuary and tidal creeks

MJcg

=0.2

∗

(MJ1c+MJ9c+MJac

+MJbc

−MJc0) 2.72843e+12 J/y

20% of the net production of macrofauna is assimilated by birds

MJd0

=MJcd+MJgd

6.21195e+12 J/y

All food assimilated by rats and raccoons is metabolized (they are

top carnivores)

MJe0

=0.9

∗

(MJ7e+MJ9e)

7.89151e+13 J/y

90% of the food assimilated by insects is used in insect metabolism

MJef

=0.5

∗

(MJ7e+MJ9e−MJe0)

4.38417e+12 J/y

50% of the net production of insects is assimilated by spiders

Mjeg

=0.5

∗

(MJ7e+MJ9e−MJe0)

4.38417e+12 J/y

50% of the net production of insects is assimilated by birds

MJf0

=0.9

∗

MJef

3.94575e

+12 J/y

90% of the food assimilated by spiders is used in spider metabolism

MJfg

=MJef−MJf0

4.38417e+11 J/y

All of the net production of spiders is assimilated by birds

MJg0

=0.9

∗

(MJcg+Mjeg

+MJfg)

6.79591e+12 J/y

90% of the food assimilated by birds is used in bird metabolism

MJgd

=MJcg

+Mjeg

+MJfg−MJg0

7.55102e+11 J/y

All of the net production of birds is consumed (as eggs)

by rats and raccoons

Dynamic Simulation with Energy Systems Language 28-25

MQ1 =

MQ7

9.18000e+14 J

Organic detritus similar in quantity to live plant biomass

MQ2 =

(0.25

∗

0.125

+0.30

∗

0.50)

∗

3.0e+7

5.43750e+6 kg-H

Average water over marsh (inundated 25% of the time, 12.5

cm deep) plus water in

root zone (30 cm deep, 50% water content)

MQ3

=45

∗

MQ2/(1000−45)

2.56217e+5 kg-salt

Average marsh salinity of 45 g/kg-seawater

MQ4

=(200.0e−6

∗

14)

∗

(0.3

∗

3.0e+7)

2.52000e+4 kg-N

200 micromoles per liter of wet sediment in root zone

MQ5

=1767

∗

(0.3

∗

3.0e+7)

1.59030e+10 kg-sediment Sediment bulk densit

y of 1767 kg/m

in root zone)

MQ6 =

((WQ2

∗

9.8)

∗

0.5)

∗

0.3

1.47000e+11 J

Estuarine water force against gravity

×tidal amplitude (0.5 m) prorated for low

marsh (30% of total marsh area)

MQ7 =

(1.8e+3

∗

17.0e+3)

∗

3.0e+7

9.18000e+14 J

1.8 kg/m

at 17 kJ/g

×marsh area

MQ9

=(4.0

∗

21.0e+3)

∗

3.0e+7

2.52000e+12 J

4 g/m

at 21 kJ/g

×marsh area

MQa

=0.10

∗

MQ9

2.52000e+11 J

Microbial standing stock

∼10% that of benthic microalgae

MQb

=MQ9

2.52000e+12 J

Meiofauna standing stock similar to that of benthic micr

oalgae

MQc

=MQb

2.52000e+12 J

Macrofauna standing stock similar to that of meiofauna

MQd

=MQg/2

1.26000e+12 J

Raccoons and rats standing stock half that of birds

MQe

=Mqc

2.52000e+12 J

Insect standing stock similar to that of macrofauna

MQf

=0.10

∗

MQe

2.52000e+11 J

Spider standing stock

∼10% that of insects

MQg

=Mqc

2.52000e+12 J

Bird standing stock similar to that of macrofauna

QFCS

=(20

∗

23.0e+3)

∗

1.05e+8

4.83000e+13 J

20 g/m

at 23 kJ/g in 10,000 ha of coastal water and 500 ha of tidal cr

eeks

Rain

=(1.50

∗

3.0e+7)

∗

1000

4.50000e+10 kg-H

O /y Rainfall (150 cm/y)

×water density (1000 kg/m

) ×marsh area (3.0e

+7m

)

Tide

=0.5

∗

(1e+11

∗

9.8)

∗

705.797

1.03752e+14 J/y

Tidal amplitude (0.5 m)

×water force against gravity (9.8e

+11 N) ×

tidal

cycles/y (705.797)

WQ2

=(1.0

∗

1e+8)

∗

1000

1.00000e+11 kg-H

Water volume (depth of 1 m, area of 10,000 ha)

×density

WQ3 =

∗

WQ2/(1000−25)

2.56410e+9 kg-salt

Average salinity of 25 g salt per kg seawater

WQ4 =

(4e−6

∗

14)

∗

(1e+8)

5.60000e+3 kg-N

Inorganic nitrogen of 4

µmN×

water volume (1e+8m

)

WQ5 =(30

∗

17e+3)

∗

1.0e+8

5.10000e+13 J

30 g/m

suspended organic matter at 17 kJ/g

×water volume

WQ6

=70e−3

∗

1.0e+8

7.00000e+6 kg-sediment 70 g/m

suspended inorganic matter

×water volume

28-26 Handbook of Dynamic System Modeling

Some features offered in simulation software may not be appropriate for Energy Systems Language

simulation. In particular, storages should always be free to exceed physically impossible limits of the real

world should the model produce such behavior in a given simulation. Artiﬁcially preventing a storage

from going negative or from creating overﬂow errors will mask serious errors in the ﬂow equations, and it

can mask the use of an incorrect integration procedure.

The storage equations themselves must not be manipulated. They are derived from a mathematical

integration process. Manipulating the storage in ways other than through changes in ﬂow rates alters the

integration procedure, not the hypothesis. The greatest power of Energy Systems Language modeling is in

its ability to reject an erroneous hypothesis. Preserving this power must be done if the output is to be used

to evaluate the plausibility of the hypothesis.

The intensive focus on special diagramming symbols, layout, and equation-writing rules, and the neces-

sity for numerical integration procedures, when combined with the idea that ecologists and environmental

scientists should be the best ecological modelers, creates a compelling incentive for developing a simulation

language speciﬁcally to represent HT Odum’s Energy Systems Language. As noted by those who developed

DYNAMO, STELLA, and Vensim for easing simulation with Forrester’s Systems Dynamics approach, a

special simulation language can eliminate programming effort and numerical integration mistakes so that

those most knowledgeable about ecological systems need not also become experts in computer simulation

technique to test complex ideas. To date, however, no special simulation language has been forthcoming

for Odum’s Energy Systems Language.

28.5.2 Timescales and Numerical Integration

Energy Systems Language diagramming of complex systems may produce models with components that

operate over many timescales. This can lead to practical difﬁculties of numerical integration on a digital

computer, such as a tradeoff between roundoff error and truncation error, and misleading parasitic solu-

tions. Long central processing times are required for the computer, and output sampling is necessary if

available computer storage media is insufﬁcient to hold all the data generated by the model.

The timescaleof a given storage component is represented by the order of magnitude of its turnover time,

which is the amount stored divided by the sum of theinﬂows to it or the outﬂows from it. Turnover time can

be determined for any instant or averaged over various time periods. The steady-state turnover times for

the various components of the example model are given in Table 28.3. They span eightorders of magnitude.

TABLE 28.3 Turnover Times at Steady State (in Years and Days) for the 16 Storages Included in the Low Marsh

Subsector Model. Turnover Times Span Eight Orders of Magnitude

Storage Model Symbol Steady-State Value Units Years Days

Water in marsh MQ2 5.44 E6 kg-H

O 2.01E−4 0.074

Detrivorus microbes MQa 2.52 E11 J 4.58E−4 0.17

Nutrients in marsh MQ4 2.52 E4 kg-N 5.88E−4 0.22

Water circulation energy MQ6 1.47 E11 J 1.42E−3 0.52

Benthic microalgae MQ9 2.52 E12 J 5.79E−3 2.1

Marsh meiofauna MQb 2.52 E12 J 1.12E−2 4.1

Marsh macrofauna MQc 2.52 E12 J 1.63E−2 5.9

Marsh insects MQe 2.52 E12 J 2.74E−210

Marsh spiders MQf 2.52 E11 J 5.48E−220

Raccoons and rats MQd 1.26 E12 J 1.80E−166

Marsh birds MQg 2.52 E12 J 3.09E−1 110

Low marsh plants MQ7 9.18 E14 J 6.46E−1 240

Detritus in marsh MQ1 9.18 E14 J 1.45E0 530

Fishes, crabs, and shrimp QFCS 4.83 E13 J 2.37E0 866

Salt in marsh MQ3 2.56 E5 kg-salt 3.04E0 1100

Sediment and peat in marsh MQ5 1.59 E10 kg-sediment 1.42E4 5,200,000

Dynamic Simulation with Energy Systems Language 28-27

The model was successfully simulated using the Vensim Personal Learning Edition simulation language

with the fourth-order Runge–Kutta integration procedure selected and a tiny time step of 2.0e−7 y. Owing

to insufﬁcient computer storage media, output from every model variable was sampled every 0.001 y and

stored. Many trials of time steps were required before a satisfactory one was achieved. Solutions converged

below 5e−7 y and above 5e−8 y. Presumably, divergence with shorter time steps was caused by roundoff

error, and with larger time steps by truncation error.

At the chosen time step, a 12 y continuous run was not possible (the CPU kept running, but the

data recording to screen and disk stopped and the Vensim program became unresponsive and had to be

rebooted). To achieve a 12-y simulation, the model was run for 4 y and the ending values for storages were

set as the initial values for another 4-y run. This was repeated a second time to achieve 12 y of data.

28.6 Dynamic Output of the Marsh Sector Model

When all constants and initial conditions are set to six signiﬁcant digits, the model produces a ﬂat line

steady-state response in all model variables. This steady-state check helps to verify that the equations

are operating as intended. However, if any one of the initial conditions is set slightly off of the steady

state, oscillations begin within a simulated year or two. Larger changes in any initial condition cause the

oscillations to begin sooner, but the patterns that eventually result are similar in frequency, amplitude,

and irregular appearance. The oscillations occur because of the feedback structure of the model. All the

environmental conditions are constant.

Figure 28.6 provides an example set of patterns for 14 of the 16 storages when the model is simulated

for 12 y. These dynamics result when the initial value for the storage of raccoons and rats is halved from its

steady-state value, while the other initial values remain calibrated for steady state. The dynamic patterns of

the 16 storages differ widely. Salt and sediment, the two storages with the highest turnover times, did not

change at all during the 12-y simulation, so they are not plotted in Figure 28.6. The others oscillate over a

wide range of frequencies and amplitudes. Most of the patterns include some amplitude modulation. The

storages with higher frequency oscillations show frequency modulation.

Many of the storages cycle several times per year; the larger animals of the marsh cycle more slowly.

Rats and raccoons are at the top of the marsh food Web. Their quantities are generally low for 3 y and then

spike every fourth year or so. Birds exhibit a complex set of cycles. A twice a year cycle seems superimposed

on a 5-y cycle. The mean and amplitude of the higher frequency cycles build for about 3 y and then birds

suddenly decline and remain low for a couple of years.

Between years 8 and 10, several interesting differences in the output occur: not only do high densities of

raccoons, rats, and birds occur, but also the oscillations of the high-frequency variables cycle even faster,

benthic microalgae all but disappear, the oscillating spider density seems to skip a peak and then produces

the highest peak of the entire 12 y run, and ﬁnally, the highest peak level of insects occurs. A longer

simulation is needed to determine whether such behavior recurs periodically.

The interesting mix of patterns is typical of complex models developed with Energy Systems Language.

Suchpatterns could in fact exist in nature and go undetected. Ecological ﬁeld measurements are notoriously

variable, but are usually made too infrequently to capture the details of patterns such as those generated

by the model. Instead, the variation among repeated ﬁeld measurements is most often used to describe

a statistical variance around a sample mean. Yet average values resulting from ﬁeld data in this manner

become the data to which the model is calibrated in the ﬁrst place. The model output shows that signiﬁcant

nonrandom variation can result from deterministic processes like those represented in the marsh model.

The output from this preliminary model, however, is unlikely to be valid in any more than a general

sense. Some of the output is highly suspicious. Marsh macrofauna, for example, precipitously decline to

near zero after the ﬁrst ﬁve simulated years and remain in unrealistically low quantities for the remainder

of the 12-y simulation. Marsh macrofauna include ﬁddler crabs and marsh snails that are easily noticed

by anyone visiting a salt marsh in the southeastern United States. If the macrofauna of tidal marshes

28-28 Handbook of Dynamic System Modeling

1.5E15

0.0E00

6.E06

0.E00

0.0E00

1.5E07

1.1E11

1.6E11

0.E00

3.E15

0.E00

6.E13

0.E00

0246

Time (y)

81012

0246

Time (y)

81012

8.E13

Detritus (J)

MQ1

Water (kg)

MQ2

Nutrients (kg-N)

MQ4

Circulation (J)

MQ6

Marsh plants (J)

MQ7

Benthic

microalgae (J)

MQ9

Decomp.

microbes (J)

MQa

2.E14

0.E00

1.E28

1.E36

0.E00

8.E13

0.E00

8.E13

0.E00

6.E13

0.E00

1.E14

0.0E00

1.5E14

Melofauna (J)

MQb

Macrofauna

(log J)

MQc

Racoons and rats (J)

MQd

Insects (J)

MQe

Spiders (J)

MQf

Birds (J)

MQg

Fishes, crabs, and

shrimps (J)

QFCS

FIGURE 28.6 Dynamic output over 12 simulated years for 14 of the 16 storages represented in the marsh sector

model. The run resulted from a single deviation from steady-state conditions caused by halving the initial number of

raccoons and rats. The set of outputs includes a rich array of frequencies, amplitudes, and modulations.

periodically disappeared for years at a time, the loss would be noticed and widely reported, but no such

reports are on record.

28.6.1 Model Output Analysis

Additional work with the model may be justiﬁed whether or not the output from the model is plausible.

A thorough analysis will reveal the reasons for the model’s behavior, whether it is plausible or not. Model

output analysis involves systematic experimentation with altered initial conditions, test inputs, and model

constants, and sometimes with alternate equations or even alternate system identiﬁcations.

A sensitivity analysis of a model consists of running the model repeatedly, each time with a standardized

adjustment to a different model constant. Halving and doubling is a common adjustment. Normally, only

one constant is changed on each such rerun. The constant is reset to its original nominal value before the

next one is halved and doubled. In this way, a standardized test is made in which all changes are based

on an arbitrary but identical type of change, and all tests are independent of one another. The concern is

Dynamic Simulation with Energy Systems Language 28-29

not the realism of the adjustment, just that it is standardized so that relative inﬂuence of each coefﬁcient

on speciﬁc features of the model output can be identiﬁed and ranked. Further measurement of the real

system can be directed toward obtaining better understanding of the most inﬂuential parameters ﬁrst.

The ranking of constants by their relative inﬂuence on model output can be usefully compared to

a ranking based on the conﬁdence the modeler has in the nominal value used for the constant. Better

estimates would be sought ﬁrst for those constants with the highest combination of effectiveness in

creating change in the model output and uncertainty in the original estimate.

28.6.2 Model Validation

A model is an abstraction of the cause-and-effect mechanisms believed to operate in the system under

study. A complex simulation model must be treated as a scientiﬁc hypothesis about cause and effect that

is too complex to be evaluated wholly in the mind. Computer representation allows the consequences of

an imagined system to be revealed and evaluated against what is known to be true about the system under

study. The adequacy of the abstraction must be defended in all of its aspects, including its level of detail,

the validity of each mathematical representation, and the interpretation of output.

Conﬁdence is gained as the model passes repeated attempts to falsify it—a process called validation. If

the model produces plausible output on the computer, further examination is warranted using an interplay

between models, ﬁeld observations, and experimentation with the real system. This process of validation

will either cause the hypothesis to eventually be rejected, or will bolster conﬁdence in it. Model results

often lead to testable ideas that are explored experimentally or by careful observation of nature. Most

published simulation models in ecology await this process.

The utility often derives from model failure in spite of state-of-the-art thinking represented in it.

Hypothesis rejection is a powerful tool that deﬁnes the scientiﬁc method. Computer simulation of complex

hypotheses is a natural extension of the scientiﬁc method in the age of computers. Taken in conjunction

with observation and experimentation, computer simulation allows complex ideas to be tested.

With continued recycling between the marsh model, its output, and measurements from nature, the

knowledge and predictability of the marsh ecosystem will improve. The intriguing output and the obvious

failures stimulate thinking, identify key variables, and guide the planning of additional ﬁeld measurements

and experimentation. It is through the interaction of these facets that the understanding arises.

28.7 A Brief Comparison with Forrester’s Systems

Dynamics Approach

The many components and connections within Energy Systems Language models continually respond to

one another in a complex system of feedback loops. The loops account for the dynamic behavior of a

naturally self-organized system. Control and alteration of the self-organization process is often desired to

direct more of the energy into the human sector, or sometimes to restore the direction of self-organization

back to an earlier state, and to do so without unintended consequences.

The above description of the nature of the systems studied with Energy Systems Language would seem

to provide an ideal setting for the Systems Dynamics approach of Jay Forrester (1961, 1968). In Forrester’s

approach, a speciﬁc cause of a dynamic pattern is sought. Odum’s approach takes the opposite approach:

Energy System Language is used to propose a system structure and discover the dynamics that would result

if a system was organized as described. The two are reverse processes of one another.

The method of systems identiﬁcation involved in Energy Systems Language, while it can lead to a

simulation model ﬁlled with feedback processes, does not focus on feedback structure. In fact, the focus

is somewhat reversed from Forrester’s approach. Where the Systems Dynamics approach seeks loops to

account for existing dynamic patterns, simulation with Energy Systems Language links all essential energy

transformation and control processes thought to be present and identiﬁes the resulting dynamics that

could be produced.

28-30 Handbook of Dynamic System Modeling

The two methods can complement one another. They do not replace one another, nor are they at

philosophical odds. The two are simply focused differently. The founding difference of Odum’s approach

is the primary focus on energy ﬂow rather than on identifying feedback loops that account for observed

dynamics. Energy tracing, rather than an analysis of dynamics, identiﬁes the basic ﬂow and control

system. Instead of using feedback theory to provide the evidence for controls on ﬂows, generalizations

about the responses of organisms to the environment and to other organisms determine the rates of ﬂows

in ecosystem models.

When dealing with environmental systems, the two approaches can be used together to considerable

advantage, but few analysts are adequately trained in the practical aspects of both methods. A reason

for this separation may relate to the different contexts within which the methods developed—System

Dynamics from the perspective of industrial management, and Energy Systems Language from the theory

of ecosystem recognition and ecosystem development.

By examining industrial systems with wild inventory ﬂuctuations that could not be controlled through

traditional methods of industrial management, Forrester recognized that an unidentiﬁed system for oper-

ating the industrial plant had arisen on its own. It had self-organized, and no longer operated as designed.

Identifying this system within the conﬁnes of the industry included looking at how orders were received,

ﬁlled, and delivered, given the decisions made by various managers and other employees involved. For-

rester’s concept, originally called Industrial Dynamics, was to use features of the patterns of ﬂuctuation,

such as frequency, amplitude, and damping rates, as clues that would help uncover the self-organized

feedback loops that were operating. Once this was done, the system could be modeled on a computer, and

the likely causes of the problem demonstrated. Furthermore, the effects of different decisions could be

explored in the model, discussed among the managers, and eventually tried in the real system.

To bring this approach into the hands of industrial managers, Forrester encouraged the development

of special computer software that would be easier for the industrial manager to use than a higher level

programming language such as FORTRAN. In response, Alexander Pugh created the simulation language

DYNAMO. The award-winning success of this approach in industry caused it to be generalized to many

other types of self-organized systems. Forrester then changed the name of this approach from Industrial

Dynamics to Systems Dynamics and began a philosophy of general principles of system self-organization

in society and nature.

At the same time and completely separately, H.T. Odum, an ecologist who had studied global strontium

cycling, was writing about general principles of self-organization from an ecosystem perspective. His

observations of ecosystems were not so much based on noticing curious dynamic patterns, but instead

on the more basic work of identifying the details of a self-organized system by tracing energy ﬂows from

sunlight through plants, then animals, and ultimately the decomposers that consumed the remaining

energy in dead matter and recycled its component elements.

Like Forrester’s interest in easing the process of modeling for industrial managers, Odum wanted a

better way for ecologists to relate to the mathematical relationships that could be developed to represent

energy ﬂows through ecosystems and how they might be controlled by amounts of various living and

nonliving components, and the genetically programmed responses of organisms. Out of this effort came

a diagrammatic language, originally called Energy Circuit Language, and now called Energy Systems

Language by most of its main practitioners.

In its overall goal, Odum’s approach is similar to Forrester’s for its attempt to identify and formally

represent the dynamic behavior of self-organized systems of humanity and nature so that the consequences

of change can be better assessed. Odum began with an interest in ecosystems and, like Forrester, soon

generalized his theory to all open energy systems, including the systems of humanity and nature that have

led to many of the environmental concerns of today. Through Energy Systems Language as tool to express

a theory and philosophy of natural system organization and behavior, he established considerable evidence

for a strong relationship between the natural environment and the economy (Odum and Odum, 2001).

Aside from the wide difference in focus between their ﬁelds of study, an important difference between

Odum’s and Forrester’s approaches can perhaps be traced to the nature of data available for observ-

ing industrial inventory problems versus that for ecosystems. First, owing to the difﬁculties of ﬁeld

Dynamic Simulation with Energy Systems Language 28-31

measurement, ecosystem data are rarely obtained at a frequency that can distinguish temporal patterns

caused by feedback processes from random variation. Second, even when sufﬁciently frequent data are

collected, it is often impossible to separate the pattern generated by feedback processes within the ecosys-

tem itself from patterns generated by responses to regular changes in environmental factors. In general,

the most obvious dynamic patterns in ecological data are dominated by daily and seasonal changes in

light, temperature, rainfall, and other exogenous variables (forcing or driving variables). Unlike an out-

of-control industrial inventory, ecosystem data do not inspire particular curiosity about the feedback

processes involved. Most of the obvious dynamics are caused by feedback within a larger astronomical

system that is not the focus of ecological research.

Deviations from perfect tracking of exogenous variables might be found in the dynamics of key variables

of a system that could provide clues to feedback structure. This possibility, however, seems less likely to

occur to someone who examines the relatively uninspiring, exogenously driven, incompletely recorded

temporal variation found in most ecosystem data records. Such a notion is rather more likely to occur

to someone exposed both to systems ecology and to feedback analysis. With that combination comes the

imperative to monitor ecosystems frequently enough to recognize interesting patterns like those suggested

by the marsh model developed in this chapter.

28.8 Conclusions

The interesting dynamics produced by the marsh model could stimulate a closer look at the ﬂuctuations of

animal and plant biomass in ﬁeld or experimental settings. Conversely, a close look at actual dynamics from

the real system may force a completely new idea about system organization. In these alternate outcomes

lies the true value of modeling in environmental management. Models do not replace the need for real

system measurement and understanding. Instead they demand it and direct it.

Dynamic phenomena are the patterns of change we think happen through time. They are signals from

self-organized systems that we can analyze and attempt to explain. In contrast, a simulation model of a

self-organized system is a detailed hypothesis of how and why we think a given dynamic phenomenon

happens, and why certain changes may occur in response to new conditions. A computer provides a

mechanism for tracking complex networks of inﬂuences thought to be involved in causing change. The

output dynamics allow visualization of the dynamic consequences of thinking that way.

Energy Systems Language guides the imagination toward plausible constructs that follow reasonable

principles of self-organization. It also simpliﬁes equation speciﬁcation and provides a way to use scarce

information to estimate rate constants. The Energy Systems Language procedure does not replace the

judgment and real system understanding required to identify the system and evaluate the adequacy of a

given model.

Increased familiarity with the diagramming rules eases the process of representing an environmental

system with Energy Systems Language. Nevertheless, even among those most familiar with the theoretical

basis and instructions, to settle issues of how to diagram a process often requires intense thought and

discussion with others familiar with the process. Although equations can be developed from the diagram,

the complex reasoning for drawing it in a particular way can rarely be appreciated by those who were

not involved in its production. A lot of detail is represented in Energy Systems Language diagrams. The

diagram must be accompanied by considerable explanation even when presented to the most accomplished

users of this approach. Complete justiﬁcation of the logic behind each line of Figure 28.1, however, is

beyond the scope here. For greater insight into the derivation of the diagram in Figure 28.1, the interested

reader may refer to the source publication and the other contributions to the book edited by Coultas and

Hsieh (1997).

A simulation model of a self-organized system built with Energy Systems Language is a rigorous state-

ment of a complex hypothesis composed of many relational and quantitative estimates. It is unlikely

to be completely correct, but when used in conjunction with real system measurements, it forms a

basis for tracking, testing, and improving understanding of the environmental system that the model