bice by xiaoyounan

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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)
•Experimentation — Question Asking
•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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