1. 3rd Meeting The Mono Lake Case & the Value of
6th System Dynamics Summer School, July Andrew Ford, Instructor, Intermediate Track
3rd Meeting The Mono Lake Case & the Value of
Equilibrium Diagrams
An Equilibrium Diagram is a model diagram with numbers and units written in place so we can check that the flows are in balance.
The diagrams help us become more familiar with the numbers. They also help us become more familiar with the units and check the units “in our head.” (my view: Units checking is very important, too important to be left to the software!)

2. Outline first half of the Meeting
A is for get Acquainted with the Mono Lake problem Modeling strategy & Reference Mode 1st, 2nd and 3rd Model of Mono Lake
An EQUILIBRIUM DIAGRAM for the 3rd Model

4. Historical Elevations of Mono Lake

5. Mono Lake: Ideal for Birds

6. Closer Look at the Eared Grebes

7. So Much Information on Mono Lake!
And everything is interconnected!!

8. Yes, everything is interconnected
When we try to pick out anything by itself,
we find it hitched to everything else in the Universe
John Muir My First Summer in the Sierra
(Boston: Houghton Mifflin, 1911, page 110 of the Sierra Club Books 1988 edition)

9. We don’t try. Our job is to simplify.
How do we put everything into the model? And how do we keep track of all the interconnections?
We don’t try. Our job is to simplify.
This model will focus on the hydrology system. The goal is to simulate the decline and the possible recovery of the lake if exports can be reduced

10. The Reference Mode (target pattern) with “Business as Usual”
The Expected Pattern if exports are reduced half way through the simulation

11. First Model: Oops! the stock of “Water in Lake” falls below zero!

12. The second model is better because the surface area changes with the volume of water in the lake. As the lake shrinks, the evaporation declines, and the lake will reach a new equilibrium.

13. This is the final model in Chapter 5
This is the final model in Chapter 5. It includes changes in the evaporation rate due to changes in the specific gravity (i.e., the salinity) of the water.

14. Equilibrium Diagram
KAF = thousand acre feet, KAF/yr = thousand acre feet per year

15. Let’s guess the 4 equations with “Friendly Algebra”?
The 5th equation (specific gravity) does not use “Friendly Algebra.”
The remaining 3 variables use an x-y graph for the Nonlinear Relationship

16. Surface Area is a Nonlinear function of volume of water in the lake
The nonlinear lookup in Vensim
~ means nonlinear lookup in Stella
A bathemetric survey provided good data for the nonlinear relationship.
For example, if volume is just over 1,000 KAF, the surface area is around 25 Kacres, as shown on the
Equilibrium Diagram.
This was Stella’s Graphical Input Device for the Interface layer, where we can see movement along the graph during the simulation

17. But if “Good Data” on the nonlinear relationship is not available, remember to rely on all sources of information.
Sometimes we can specify two or three points with confidence and then draw a reasonable curve through the points, as illustrated below.
With uncertainty about the curve, we can create low, medium and high versions. Then we use sensitivity testing to see if the shape of the curve has an important impact on the model results.
Value curve showing the $/MWh value of providing wind integration services as a function of installed wind capacity (in MW) in Ontario, Canada.

18. Time for in-class Exercises

19. Equilibrium Diagram: Global Hydrologic Cycle
Stocks are in cubic kilometers of water, Flows are in cubic kilometers of water/year

20. Equilibrium Diagram: Global Rock Cycle
Stocks are measured in Pg, short for Petagrams; Flows are in Petagrams per hundred million years

21. Equilibrium Diagram: Carbon Stored in a Tropical Forest
Stocks are measured in GT, short for Gigatons; Flows are in GT/year

22. Blood Storage in the Human Circulatory System Final Exercise: Bring your answer after the afternoon break
Total storage is 4,800 ml, just under the 5 liters of blood in the average person. Each flow is the size of the stock divided by an average time for that stock. For example, the left heart time is 2.1 seconds, and the outflow from the left heart is 168 ml divided by 2.1 seconds. This gives 80 ml/sec for the cardiac output flow. What are the values of the other five flows if the system is in equilibrium? What are the time intervals for the other five stocks? Hint, to check your results. If you add the six time intervals, it should take 60 seconds to complete the cycle.