6th System Dynamics Summer School, July 2019 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!) 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

Historical Elevations of Mono Lake Mono Lake: Ideal for Birds Closer Look at the Eared Grebes So Much Information on Mono Lake!

And everything is interconnected!! 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) How do we put everything into the model? And how do we keep track of all the interconnections? We dont 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 The Reference Mode (target pattern) with Business as Usual The Expected Pattern

if exports are reduced half way through the simulation First Model: Oops! the stock of Water in Lake falls below zero! 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. 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. Equilibrium Diagram KAF = thousand acre feet,

KAF/yr = thousand acre feet per year Lets 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 Surface Area is a Nonlinear function of volume of water in the lake ~ means nonlinear lookup in Stella

The nonlinear lookup in Vensim Lookup for area Water in Lake A bathemetric survey provided good data for the

nonlinear relationship. This was Stellas Graphical Input Device for the Interface layer, where we can see movement along the graph during the

simulation For example, if volume is just over 1,000 KAF, the surface area is around 25 Kacres, as shown on the Equilibrium Diagram. surface area

evaporation 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. 20.00 15.00 10.00 5.00

0.00 0 5,000 10,000 15,000

20,000 Value curve showing the $/MWh value of providing wind integration services as a function of installed wind capacity (in MW) in Ontario, Canada. Time for in-class Exercises Equilibrium Diagram: Global Hydrologic Cycle

Stocks are in cubic kilometers of water, Flows are in cubic kilometers of water/year Equilibrium Diagram: Global Rock Cycle Stocks are measured in Pg, short for Petagrams; Flows are in Petagrams per hundred million years Equilibrium

Diagram: Carbon Stored in a Tropical Forest Stocks are measured in GT, short for Gigatons;

Flows are in GT/year 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.