Undertanding stocks and flows: The bathtub metaphor

I’m currently studying for a master’s degree in Business Strategy and the Environment at Birkbeck College in London University, and have been very struck by how basic concepts of environmental science are relatively poorly understood – even by our lecturers. A good example is the question of ‘stocks and flows’, which is fundamental to understanding carbon emissions. Nigel Lawson also illustrated his ignorance of this relationship in his recent sceptical tract, so here is a useful metaphor. I did not invent it (in fact it’s a basic model for all sorts of ‘stock and flow’ processes), but here goes.

Imagine that you are lying in the bath. You are up to your nose in water and more is still pouring in through the taps. But don’t worry – your nose is level with the overflow pipe, and as much water is flowing out again as the taps are letting in. But only just – the overflow can handle what is coming in right now but no more. So you are, for the moment, perfectly safe.

But what if the taps are opened just a little more? Leaving aside the very little room for manoeuvre further ‘adaptation’ of your bathtub ‘environment’ allows you, the fact is, an increase in inflow will not be met by an increase in outflow. No matter how small the increase is, you are now in great danger, to the point where you must eventually drown.

Notice that this result does not depend on how much extra water flows in – even the smallest increment will get you in the end. It does not matter how much water was in the bath already or how large or small the maximum inflow and outflow are. As soon as the former starts to exceed the latter, by no matter how little, you will drown.

Likewise for humanity’s collective carbon emissions. Regardless of how much more carbon is emitted from other sources, if the environment is adapted to reabsorb only pre-industrial levels of emissions, then adding more will quickly (in nature’s geological timescale) start to swamp the system. The sizes of both nature’s emissions and our own are irrelevant: even if the rest of nature emitted a hundred times as much carbon as humanity as a whole, the natural environment would still be drowning in carbon as soon as we started to increase the flow beyond what nature’s carbon ‘overflow pipe’ is able to remove again.

The same would happen with increased natural eruptions of carbon from natural sources, of course, and we would still have to deal with the consequences. In fact there is good evidence that massive natural changes in carbon levels have profoundly affected the survival of many species. But most such natural intrusions into the natural carbon cycle are erratic and average out over time to quite small net changes.

Industry in by no means such a slight or incidental factor. Indeed, everything we know about our actions to date point to industry being the single most important factor in the emergence of quality complete new era – what Paul Crutzen has called the Anthropocene.

This era will certainly prove to be the most fatal in a quarter of a billion years for most species on this planet. And right at the centre of its effects will be the ‘bathtub’ effect of stocks and flows.

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