Global Climate Change and Energy
Stock and Flow
In this simulation, we see what happens when you change how fast water flows into a bathtub. When the water flows into the tub at a greater rate than it is flowing out, what happens?
Click on the image for an animation in which you can control the flow of water into the bathtub.
The level of the water in the tub rises, until the tub eventually overflows. What happens when the water flows out faster than it flows in? The level of the water begins to go down. Finally, we see that if we keep the water flowing in at the same rate it is flowing out, the water level stays steady.
This bathtub simulation shows a “stock and flow” structure that can be found in physical and social systems all around us. A stock is an accumulation. The water in the bathtub is the stock. Look around and you’ll see stocks everywhere. The amount of something (e.g., the number of trees in a forest or how many people are in a sports stadium) is called a "stock." Stocks are changed by inflows and outflows. A flow is the rate at which anything—whether it be water, money, or even rumors—flows into and out of the stock. In our bathtub simulation, the faucet controls the flow into the stock; the drain at the bottom of the tub allows water to flow out.
Stocks and flows play a key role in generating some of the most perplexing dynamics we encounter. For example, stocks accumulate past events. Studies of the pesticide DDT have shown that even though DDT use was reduced from its 1971 levels to zero by the year 2000, DDT levels in fish remained above 1971 levels beyond the year 1995. DDT takes up to 6 months to evaporate from the surfaces of plants and buildings. But it remains in the tissue of fish for up to 50 years. The amount of DDT in fish tissue is a stock. Let’s look at a few more everyday stock-and-flow structures and see how they work.
In a small fir-tree forest we can think of the number of trees as the stock. In a lumber business the trees are cut down at a fixed rate. This removal is a flow out of the stock. A fixed number of trees are planted every year to replenish the forest, and there is an average amount of time for trees to reach maturity. In this scenario, the forest system is in balance; the inflow of trees is equal to the outflow represented by logging.
Click on the image for a simulation of logging and planting in a fir forest.
Now let’s consider a different scenario: the demand for logs goes up so the harvesting of trees increases to a somewhat higher fixed rate. The planting of trees is increased to compensate. Common sense says that the forest will remain the same size, but this will not happen. Why? The number of trees in the forest is a stock. The rates at which fir trees are planted is the flow into the stock. The flow out is the rate at which trees are cut down. As we saw in the bathtub example, stocks decrease if the rate of flow into the stock is less than the rate of flow out of the stock. If the fir trees are cut down at a faster rate than new trees are planted and allowed to mature, the stock of fir trees will go down.
You can imagine your bank account as a kind of bathtub—the amount of money in it just keeps getting greater and greater as long as you keep making deposits and accrue interest. The balance in your bank account is a stock; it accumulates over time. Making withdrawals is like a drain. If withdrawals—the flow out of the bank account—are greater than the flows in through deposits and interest, what happens to your “stock” of money? The stock, your balance, of money goes down.
We can use stock-and-flow thinking to consider a country’s national debt as well. The national debt is the amount of money that a government owes to lenders. For example, when you buy a government bond, you are lending money to the government. The amount owed to you and other lenders is the national debt.
Click on the image for an animation in which you can see how the stock and flow of a country's national debt is like the flow of water in and out of a bathtub.
One might think that a country will reduce its national debt if it reduces its budget deficit, right? The budget deficit is the difference between the government’s income, mostly from taxes, and its expenditures. This is usually figured for a year at a time. If expenditures are greater than income, there is a deficit. The government must borrow money to make up the difference. This increases the national debt.
Let’s think about this question using the bathtub as a metaphor. A country’s national deficit is similar to the flow of water into a bathtub; the deficit is the rate at which the country borrows money. The country’s national debt is like the water in the bathtub. It is the stock of accumulated debt. By turning the faucet down and reducing the deficit, the rate at which the debt accumulates will slow down, but the debt itself will still keep accumulating. To reduce the stock of debt would require that the flows out of the stock be greater than the flows in. This would require paying off the debt at a higher rate than money is borrowed.
If we think of a stock as a "nation's wealth," the focus might be on turning up the faucet, by spurring economic growth. This would increase the inflow into the stock. Another way to increase a stock is to reduce the outflow. An example of reducing outflow to increase a nation’s wealth would be repairing and maintaining old equipment and investing in new equipment.
Click on the image for an animation in which you can see how the stock and flow of greenhouse gases is like the flow of water in and out of a bathtub.
How is our bathtub related to climate change?
Let’s envision the Earth as a tremendous bathtub. Imagine the concentration of greenhouse gases (GHG) as the water in the bathtub—the stock. Flowing from the faucet into the stock of greenhouse gases are GHG emissions. The drain or flow out of the bathtub represents the rate at which carbon dioxide (CO2) and other greenhouse gases are removed from the atmosphere by the oceans, biomass, and other sinks.
Most climatologists agree that due to deforestation and saturation of other carbon sinks, human GHG emissions are almost twice the rate of removal. The bathtub is filling twice as fast as it is draining. Even if policies to mitigate climate change caused GHG emissions to fall, atmospheric GHG concentrations would continue to rise unless emissions fell to the removal rate. For the stock of greenhouse gases in the atmosphere to actually go down, the outflow—the removal rate—would have to be greater than the inflow—GHG emissions.