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```									STELLA Modeling as a Tool for
Understanding the Dynamics of
Earth Systems

Dave Bice
Dept. of Geology
Carleton College
Northfield, MN
Dbice@carleton.edu
Outline
•   Overview of the Modeling Process
•   Simplicity vs. Complexity in Model Design
•   Getting Acquainted with System Behaviors
•   Example of the Global Carbon Cycle
•   Educational Benefits of Modeling
The Modeling Process
•Develop Conceptual Model — Reservoirs, Processes, Relationships
•Simplify
•Find Data for Reservoir Initial Values, Fluxes
•Convert Conceptual Model to STELLA Diagram
•Mathematical Representation (Parameterization) of Processes
•Initial Testing of Model — Establishment of Steady State or Alternative
Control
•Test Model Against Observational Data (when possible)
•Interpretation of Results, Generation of More Questions, Further Experiments
From conceptual model to STELLA model
Simplicity vs. Complexity

Conceptual model for #3
Increasing simplicity
Comparison of Thre e Bathtub M ode ls
20.00

Simplest Model
Liters of Water

12.50
Most Realistic
Model
Intermediate
Model

5.00
0.00             7.50           15.00      22.50   30.00
Seconds
Increasing connections and complexity
A Syste m of Conne cte d Re se rv oirs Has a Shorte r Re sponse Time

Conne cte d Syste m of Re se rvoirs

1:   175.00
2:   200.00                                                                            f12
3:    10.00
4:                  1: W1 Connected
200.00                                                 W1    10        0.1 k12                200 W2
k21
0.5

1:    92.50
2:   117.50
3:     5.24                                           = 1/(k12+k21) = 1.67     f21
4:   100.00
3: W1 Isolated          All Flows are defined as the product of the two
components connected to the flows — i.e., k * W.

4: W2 Isolated                                   Isolate d Re serv oirs

1:    10.00              2: W2 Connected
2:    35.00                                                            W1                     W2
3:     0.48
4: 2.20e-05                                                            10                    200
k1                       k2
0.00             7.50                     15.00                    22.50                      30.00
0.1
0.5
Time
f1                     f2

W1 = 1/k1 = 10           W2 = 1/k2 = 2
Common System Behaviors I
Common System Behaviors II
Common System Behaviors III
Common System Behaviors IV
Common System Behaviors V
The Global Carbon Cycle
STELLA Diagram of Global C Cycle
Parameterization of Soil Respiration

 49.4 
Fsr  Soil                Tsenssr T 
1
INIT(Soil) 
Tsenssr  0.10
T  Tt  Tinit — in our model Tinit  0C
,
Parameterization of
Photosynthetic Uptake of Carbon
Pm ax pCO2eff 
Fp                  1  TsenspT 
Khs  pCO2 eff 
                                            
Pm ax   
K  pCO2
hs                           atm,init        pCO2 atm, m in  F p,init          
pCO2               atm, init      pCO2atm, m in 
Fp is the global rate of photosynthetic uptake of CO2 in GtC/yr.
Pmax is a parameter with units of GtC/yr that is used to force the equation for Fp to give the proper value
corresponding to the starting conditions of the model.
Khs = 62.5 ppm — the half-saturation value — the atmospheric CO2 concentration at which the rate of
photosynthesis, Fp, is half of the ultimate saturation value, given that particular temperature
pCO2atm,init = 280 ppm — the pre-industrial atmospheric CO2 concentration
pCO2atm,min = 30 ppm — value below which no photosynthesis can occur
pCO2eff = pCO2atm - pCO2atm,min— the effective atmospheric CO2 concentration
Fp,init = 100 GtC/yr — the initial value for global photosynthesis
Tsensp = 0.04 — establishes the increase of Fp per degree of warming
T = T - Tinit — temp. difference relative to initial temp., Tinit is set to 0
.

Rate of Global Photosynthetic Uptake of Carbon
122
Fp (Gt C/yr)

present-day conditions

61           half-saturation

(Atm varies;Temp held constant)

0
0 92.5                        1000.00               2000.00
pCO2min = 30 ppm             Atmospheric CO 2 (ppm)
Khs = 62.5 ppm
Ocean Carbonate Chemistry Scheme

Fatm oc  k oa  pCO 2 atm  pCO 2oc Aoc
Year        Fossil Fuel     Land-Use

0
Gt C/yr
0.350
GtC/yr
0.6                 Observed Increase in Atmos. CO2
10           0.525           0.6                                             360

Testing the
20           0.805           0.65
30           0.959           0.65
40           1.078           0.7                                             340
50           1.300           0.7

Model
60           1.638           0.8                                                     data from IPCC, 1995
320
70           2.586           1.1
80           4.084           1.3
90           5.292           1.25                                            300
100          6.098            1.5

Model Results                                             1850             1900            1950             2000

1: Soil                           2: Land Biota               3: pCO2 atm
1: 1585.00
2:
3:
645.00
370.00
Units are Gt C for Soil and Land Biota; ppm for CO2
The model results
closely match the
observed record for the
same time period. This
means that the carbon
1: 1560.00
2:  625.00                                                                                             cycle model generates
3:  325.00
meaningful results so
long as there is not
some kind of non-linear
mode switch that
becomes important in
1: 1535.00                                                                                             the future.
2:  605.00
3:  280.00
0.00              25.00             50.00               75.00            100.00

Years
Experiment: Looking into the Future
In these experiments, we start off with the emissions history of the last 100 years and then
project different emissions scenarios into the next 100 years.
a) Business-as-Usual — Projecting the curve of fossil fuel emissions using the most
recent slope
b) Stabilization — Emissions steady at current flux for the next 100 years
c) Reduction — Emissions drop to zero next year (dream on!)

650
Atmos CO2

450

Reduction
250
0.00      50.00              100.00            150.00          200.00

Years
Where did all the carbon go?

Stabilization scenario

Land Biota

Surface Ocean

Soil
Looking Farther into the Future

Stabilization scenario
Benefits of Modeling with STELLA
•Simple Graphical Interface, No Programming Skills Needed (can be used at
an introductory level)
•Model Construction Motivates Learning About Relevant
Processes
•Adds a Quantitative Dimension to the Learning Process
•Allows for Experiential Learning
•Watching the Dynamics Unfold Develops an Understanding of
Dynamics
•Leads to Development of Systems Thinking

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