1. Systems Thinking – Modeling a System

2. A simple example of a dynamic system – a bathtub
The balance between the inflow through the faucet and the outflow through the drain determines how much water accumulates in the tub.
Instructor – notes for emphasis
This is an open system - we are not keeping track of where the water is coming from [source] and going to [sink]
The faucet and drain can be adjusted to any flow rate [or flux] we want
Even if level of water in the bathtub remains constant, individual water molecules are still moving through the system.
This bathtub is a dynamic system because material is flowing through the system and the rates of flow and the amount of water in the tub may change over time
Although this is a simple example, there are analogies all around us in the Earth System and society
Image created by K. Kreutz
Is this system open or closed?

3. Examples in the Earth System
Inflow (runoff, precipitation)
Outflow
(stream outlet)
Creative Commons
Reservoir (pond)

4. Examples in the Earth System
Inflow (snowfall)
Creative commons
Outflow (melting, icebergs)
Reservoir (glacier)

5. Examples in the Earth System
Respiration and
Decomposition
Photosynthesis
Atmospheric CO2
760 Gton(C)
Image by K. Kreutz
Data from Kump et al., The Earth System, 2010, Chapter 8
60 Gton(C)/year
60 Gton(C)/year
Outflow
Reservoir (atmosphere)
Outflow

6. Examples in society Inflow (entrance) Outflow (exit) Reservoir
Creative commons
Reservoir
(parking lot)

7. https://openclipart.org/detail/231056/bank
Examples in society $ $ $
Outflow (spending)
Creative Commons
Inflow (income)
Reservoir
(Bank account)

8. Why use a systems model? Bathtub
Systems diagrams are useful for showing relationships in a system:
Systems models are useful for quantifying relationships in a system, and allowing system behavior to be explored experimentally:
Bathtub
10 liters
1 liter/minute
1 liter/minute

9. Systems model of the bathtub
STELLA is a software package that allows the user to build icon-based dynamical systems models
The goal is to take the systems diagram of a bathtub and simulate in a STELLA model
A STELLA model of the bathtub system includes a reservoir for the bathtub, and two flows that represent the faucet and drain
Inflow
Reservoir
Outflow

10. Model: icon-based representation of the system
Unit 3 Bathtub Model
Model: icon-based representation of the system
Instructors – notes for emphasis
Why do this at all? While generic, the bathtub model can be used to simulate behavior that is applicable to any system in Earth Science or society.
Equation: mathematical representation of the system - STELLA does the calculations for us
Output: graph of the system model output as it runs - in this case, the change in the water in bathtub with time

11. Systems modeling Inflow Reservoir Outflow
The bathtub model is simple enough that we could just do the calculation of flows and reservoir size with each time step by hand
BUT, when a system is more complicated, a systems model becomes necessary to keep track of everything
For example, below is a systems model for the Earth’s energy balance (i.e., inflow of energy from the Sun, the Earth reservoir of energy, and outflow of energy back to space)
Inflow
Reservoir
Outflow