Lecture 4 - Earth system science and system models

Lecture outline: Introduction, system model components, how to assemble a system model, in class exercise.

Introduction

John Muir (1869) "When we try to pick out anything by itself, we find it hitched to everything else in the Universe."

Photo of John Muir in 1875. Obtained from: https://en.wikipedia.org/wiki/File:John_Muir_by_Carleton_Watkins,_c1875.jpg.

John Muir was a well known and very influential naturalist, who early on recognized the complexity of the world around us. Earth system science focuses on trying to understand that complexity - how life (the biosphere), water (the hydrosphere), the air (atmosphere), and the rocks and soil (the geosphere) are linked. With the advent of computers we now have a much greater ability to explore that complexity.

What are complex systems that we need to understand from an environmental geology perspective?

• plate tectonics, fault systems and earthquakes.
• the carbon cycle and related climate change.
• aquifer systems and water management.
• coastlines
• soils.
• plankton populations.

Why do we need system models?

• Nature and complexity of questions we are asking and problems facing us demand it, the primary example of which is climate change.
• The concept of emergent properties is crucial (for example, exponential behavior that results from linking two linear relationships). System models can identify emergent properties.
• System science and models are a natural next step after a reductionistic approach in  advancing science.
• When quantified and compared against history, these are can be tests of the conceptual model. Does it produce realistic results (or how realistic are the results, what percentage of the data or system behavior can the model explain or reproduce?).
• Working system model can produce useful predictions could not get otherwise. Global Circulation Models (GCMs) that we will discuss again more toward the end of the class are one example.

What are the four fundamental components of a system model (this is review and expansion of a topic from the first lecture)?

1. reservoirs: these are what your are interested in keeping track of. They can be the volume of water in a lake, or the amount of carbon dioxide in the atmosphere, or the amount of energy in a lava flow.
2. inputs and outputs (transfer processes): These can be divided into inflows, that increase the reservoir, or outflows that decrease the reservoir size. For water examples might be evaporation or seepage. For the energy of a lava flow an inflow might be sunlight, and an outflow might be radiation of heat out into space.
3. variables: these are factors that influence the rate of a transfer process, or influence another variable. As you might guess, one of the most critical variables in earth science is temperature. Humidity, acidity, pressure, population are also common examples of variables in system diagrams.
4. rules: these are what can turn the system diagram into a working model. Rules indicate how variables influence transfer processes. They often take the form of an equation, but can take other forms.
• If you were to actual have a running, working computer model another component of the model would be initial conditions - the values for reservoir amounts, and variables that you provide as initial input for the model.

How to assemble a system model? The first step is often an initial brainstorm to make three lists, one of all of the relevant reservoirs for the entity of interest (e.g. water), one of all the transfer processes, and the last list of the variables. You will likely add more as you assemble these basic components into a system model. The below describes some iconography and some basic rules and strategies of linking these components.

Consider a glacier system that you want to model to better understand why glaciers might advance or retreat. The image to the right provides an example, and is the Wellesley Glacier in Alaska (image from USGS site Introduction to Glaciers: https://www2.usgs.gov/climate_landuse/glaciers/intro_glaciers.asp). What are examples of each of the 4 system model components for a glacier? The image below provides an example of how to start for three of them. Note how a consistent symbology for the 3 different components (reservoirs, transfer processes and variables) is used. You can practice by thinking of other components that are involved in how glaciers behave.

How then to combine these into a system model. Some "rules" follow.

Two reservoirs are always connected by an intervening transfer process. There should be an arrow to indicate the direction of transfer. One transfer process should not be directly linked to another, there should always be an intervening reservoir. The image below is an example.

You can connect two different types of reservoirs through the variables that control them. You can not connect them directly as you can't have a reservoir of carbon feed into a reservoir of gold. However, the amount of carbon in the environment could be a variable that influences whether gold precipitates from hot circulating waters and so the system model for gold could be in this way linked to the system model for carbon. This, then, is an even more complicated system diagram where you are modeling two different types of quantities.

Variables only influence a transfer process and can not be linked to reservoirs. Variables should not be in a direct linking position between reservoirs. If the variable influences the rate of a transfer process then the arrow should point from the variable to the transfer process. The quantity in a reservoir can serve as a variable, either for a transfer process directly connected to that reservoir, or to another transfer process. You could show the nature of the influence with a plus or minus sign. A plus sign would be that as the variable increases the transfer process rate increases and a negative sign the opposite. Examples of possible connections are shown below, with one error on the example to the right.

This way of thinking is very useful for developing conceptual models. However, once we add rules and use computers we can use these models for prediction purposes. Stella software provides a good introduction into these possibilities.

Some examples of earth system models - Carlton examples.

In class exercise – modeling dam reservoir volume (circa 30 minutes).

The objective is provide a system model for the volume of a water reservoir, a body of water behind a dam. The environmental implications and significance should be clear. We will work in groups. At points the groups will report to the whole, so that the shared information can be used by the groups in the next step. The following are steps.

1. Groups will identify reservoirs, inflow and outflow processes, and variables for the water reservoir. (Note that we are using the term reservoir in two different ways. One it is a body of water we are modeling. The other is as an abstraction, a component in a system model where some quantity of interest can reside. In this case the water reservoir is just one reservoir in our model for the amount of water, and there are other reservoirs. Science and other disciplines often ‘hijack’ a common term and give it special meaning in a certain context.) The components you come up with should be part of the groups report. Make sure everyone in the group has there name on this report, as it will be handed in. (5 minutes)
2. Groups will report on the reservoir, transfer processes and variables that they have identified, which will be captured on the board. (5 minutes)
3. Groups will then assemble there own linkages between reservoirs with the intervening transfer processes using the suggested iconography. This should be part of the group’s report. (15 minutes)
4. Asking for contributions from each group, an initial class diagram will be developed on the board, with the instructor acting as facilitator. (7 minutes)
5. Each group will then have the opportunity to modify their diagram based on what they learned in the previous step. Getting it right is important. The group should discuss and identify any feedback loops inherent in their diagram? Describe the feedback loops you identify in your report. (5 minutes)
6. Please hand in your report, making sure everyone's name is on it.