Understanding GHG emissions: Stock vs. Flows

by |July 18, 2011

In discussing climate change and greenhouse gas (GHG) emissions, a key distinction must be made between the stock of GHGs in the atmosphere, and the flow of GHGs, primarily emissions. Understanding this difference is crucial for designing and implementing policies to effectively address the problem. Because a bathtub is something that most of us are familiar with, we will use it to illustrate the difference between stocks and flows.

Imagine our atmosphere is a giant bathtub, but instead of being filled with water, it is filled with a viscous fluid, something like maple syrup or ketchup. In this analogy, the fluid can be thought of as CO2 in our atmosphere, with the total volume of the fluid representing the total amount, or “stock,” of CO2 in the atmosphere at any given point in time (currently, CO2 is at 390 parts per million). Like most bathtubs, this one has a faucet that can pump more fluid into the tub and a drain that can remove fluid. The fluid coming out of the faucet represents the “flow” of GHG into the atmosphere, and the drain represents sinks (e.g. oceans, forests) that naturally remove CO2 from the atmosphere.

In order to better understand how stocks and flows of greenhouse gases affect the stability of our climate, we will add some nuances to our bathtub. Unlike conventional bathtubs, this one is equipped with a special feature: a floater sits on top of the bathtub fluid and is connected to a heating device that delivers heat into the tub as a function of the height of the fluid. As the level of the fluid and the floater rise, more heat is delivered to the tub. Furthermore, the viscous fluid in our tub has a unique property: as it heats up, its viscosity increases, and it flows more and more slowly out of the tub.

Although this scenario is simplified, this increase in the fluid’s viscosity as a function of temperature (making the sink less efficient) exists in our real-life bathtub: the ocean is the world’s largest sink of CO2, and although it currently absorbs roughly 22-35% of man made CO2 emissions, its ability to absorb CO2 decreases as it warms. Furthermore, because the solubility of CO2 decreases with increasing temperature, as the top layer of the ocean warms it could lead to degassing of dissolved CO2, which would lead to further decreasing the net oceanic sink.

Until the industrial revolution, our bathtub was in a state of equilibrium, where the rate at which the liquid entered the tub (the flow) and exited through the drain (the sinks) was such that the total volume of the liquid in the tub (the stock), and therefore its height and temperature, was kept nearly constant. After the Industrial Revolution, industrialized societies began burning fossil fuels, emitting large amounts of CO2 into the atmosphere.

This is analogous to increasing the amount and rate of delivery of viscous fluid into the bathtub. The level and viscosity of the fluid in our bathtub have been increasing, even though some of it is still going down the drain. The amount of liquid entering the tub is now greater than the amount draining out of it, so the tub is no longer in equilibrium.

Now, remember that this bathtub is equipped with a special heater that delivers heat as a function of the fluid’s height. It is widely accepted that the current level of CO2 in the atmosphere exceeds by far the natural range over the last 650,000 years. That is, the level of “fluid” is steadily climbing. As a consequence, the floater rises, forcing the heater to deliver more and more heat to the tub; the liquid in the tub is therefore warming at an increasing rate.

Imagine that nations of the world magically stop emitting CO2 (turning off the faucet). Because the tub is draining so slowly, and because the heating of the fluid depends on the total stock in the tub and not the flow, the temperature of the bath will continue to rise  (above the temperature that was experienced when the tub was in equilibrium) until the level of the fluid falls back to its previous equilibrium level. This is what is meant by a “commitment to warming:” we have already added so much liquid to our tub that if we turn off the faucet, temperatures  will  continue to increase  for a very long time. This is the guiding principle behind the goal to keep the concentration of CO2 in the atmosphere at or below 450 ppm: paleoclimate data and models simulating the response of the climate to CO2 indicate that increasing the stock of CO2 beyond this point is likely to lead to dangerous and irreversible anthropogenic warming.

What insight does our bathtub analogy hold for the real climate crisis we face? First, it helps illustrate the important difference between emissions of greenhouse gases and their amount in the atmosphere. Furthermore, it shows that no matter what we do going forward, we are already committed to further warming. This simple analogy also helps us visualize why delaying action will make it harder to solve the problem: as we increase the height of the fluid in the bathtub and as its temperature increases, it becomes more difficult to return it to a safe level.

With respect to policy decisions, our analogy illustrates a critical aspect of policies that cut emissions: the aggregate reduction of all policies needs to be on a scale large enough to keep the final concentration of CO2 within the accepted ranges.  Policies that aim to curb the rate of emissions (the flow) need to be formulated with the overall concentration targets (the stock) in mind so that we end up with an amount that is within the “safe-zone” (around 450ppm). Multiple studies, including work published by Deutsche Bank with research from the Columbia Climate Center, highlight the fact that there is a significant “gap” between the overall impact of policies and the 450 ppm target.

Similar to our bathtub analogy, where draining the tub becomes harder as the stock builds up and the fluid warms, closing the “gap” between the impact of emission policies and overall concentration targets grows increasingly difficult the longer we wait. Although it is certainly feasible to achieve the goal through aggressive policies, the cumulative nature of GHGs in the atmosphere coupled with their long residence times means that we are running against the clock. Enough political will, at both domestic and international levels, must be mustered to construct policies that reduce flows consistent with the desired overall stock. To the misfortune of everyone on this planet, this is one particular case in which time is not on our side.

6 thoughts on “Understanding GHG emissions: Stock vs. Flows

  1. Juan Padilla says:

    Diego, great article
    Can you explain me better, why an how oceans capture the largest portion of CO2 over plantations?

  2. Diego Villarreal says:

    Hi Juan. CO2 is a gas that is soluble in water. When CO2 interacts with the surface of the ocean, some of it dissolves and reacts with water to form a range of neutral and negatively charged species (carbonic acid, bicarbonate, carbonate, etc). The actual mechanism of how carbon enters the ocean is somewhat complex, and you can read a general description here. But the very broad and general idea is that CO2 is “soaked up” by the ocean because a fraction of it dissolves in water.

    On the other hand, CO2 is taken by up by land plants and ocean algae via photosynthesis, where the carbon is converted into sugars using sunlight as the energy source, releasing oxygen in the process. So you can think about the carbon in CO2 getting “sequestered” into the carbohydrates that the plant synthesizes via photosynthesis.

    Interestingly, because trees outside of the tropics grow during the spring and shed during autumn, and because the bulk of land mass is in the northern hemisphere, the concentration of CO2 in the air varies depending on the time of the year. This cycle can be seen in the Keeling curve, and the Northern Hemisphere spring dominates the signal.

    For a more detailed discussion of the trends in land and ocean carbon uptake, you can look here.

  3. Benito says:


    How and what can a single individual do to partake in the reduction GHG other dran driving less?

    I am not sure that my single contribution will resolve the problem but would like to be part of a concerted effort.

  4. James Newberry says:

    Some questions:

    Isn’t the relevant planetary response of radiative forcing that due to total CO2 ppm,equivalent, not carbonic gas alone? Is this not already at a level something like 100 ppm less than a doubling from pre-fossil combustion (say 450 ppme), that is if the relatively temporary affect of today’s sulfates emissions are removed?

    Does this not seem to indicate the bath is beginning it’s overflow as we have this discussion about turning off the tap?

    Perhaps petroleum (etc.) is not a resource of energy after all, but a state of matter.

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