Tag: bathtub dynamics

The Acid Bathtub

I noticed a few news items on the SO2 allowance market today, following up on the latest auction. Here’s the auction history:

SO2 allowance auction prices

The spot permit price has collapsed, from a high of $860/ton in the 2006 compliance stampede, to $62. That’s not surprising, given the economic situation. What is a little surprising is that the forward price (allowances for use starting in seven years) fell to $6.63 – a tenth of the previous low, spot or forward. What’s going on there? Do plants expect a seven-year recession? Are utilities hoarding cash? Do they expect the whole market to unravel, or to become irrelevant as climate policy imposes a more tightly-binding constraint?

Continue reading “The Acid Bathtub”

Bathtub Still Filling, Despite Slower Inflow

Found this bit, under the headline Carbon Dioxide Levels Rising Despite Economic Downturn:

A leading scientist said on Thursday that atmospheric levels of carbon dioxide are hitting new highs, providing no indication that the world economic downturn is curbing industrial emissions, Reuters reported.

Joe Romm does a good job explaining why conflating emissions with concentrations is a mistake. I’ll just add the visual:

CO2 stock flow structure

And the data to go with it:

CO2 data

It would indeed take quite a downturn to bring the blue (emissions) below the red (uptake), which is what would have to happen to see a dip in the CO2 atmospheric content (green). In fact, the problem is tougher than it looks, because a fall in emissions would be accompanied by a fall in net uptake, due to the behavior of short-term sinks. Notice that atmospheric CO2 kept going up after the 1929 crash. (Interestingly, it levels off from about 1940-1945, but it’s hard to attribute that because it appears to be within natural variability).

At the moment, it’s kind of odd to look for the downturn in the atmosphere when you can observe fossil fuel consumption directly. The official stats do involve some lag, but less than waiting for natural variability to shake out of sparse atmospheric measurements. Things might change soon, though, with the advent of satellite measurements.

My Bathtub is Nonlinear

I’m working on raising my kids as systems thinkers. I’ve been meaning to share some of our adventures here for some time, so here’s a first installment, from quite a while back.

I decided to ignore the great online resources for system dynamics education and reinvent the wheel. But where to start? I wanted an exercise that included stocks and flows, accumulation, graph reading, estimation, and data collection, with as much excitement as could be had indoors. (It was 20 below outside, so fire and explosions weren’t an option).

We grabbed a sheet of graph paper, fat pens, a yardstick, and a stopwatch and headed for the bathtub. Step 1 (to sustain interest) was turn on the tap to fill the tub. While it filled, I drew time and depth axes on the graph paper and explained what we were trying to do. That involved explaining what a graph was for, and what locations on the axes meant (they were perhaps 5 and 6 and probably hadn’t seen a graph of behavior over time before).

When the tub was full, we made a few guesses about how long it might take to empty, then started the clock and opened the drain. Every ten or twenty seconds, we’d stop the timer, take a depth reading, and plot the result on our graph. After a few tries, the kids could place the points. About half way, we took a longer pause to discuss the trajectory so far. I proposed a few forecasts of how the second half of the tub might drain – slowing, speeding up, etc. Each of us took a guess about time-to-empty. Naturally my own guess was roughly consistent with exponential decay. Then we reopened the drain and collected data until the tub was dry.

To my astonishment, the resulting plot showed a perfectly linear decline in water depth, all the way to zero (as best we could measure). In hindsight, it’s not all that strange, because the tub tapers at the bottom, so that a constant linear decline in the outflow rate corresponds with the declining volumetric flow rate you’d expect (from decreasing pressure at the outlet as the water gets shallower). Still, I find it rather amazing that the shape of the tub (and perhaps nonlinearity in the drain’s behavior) results in such a perfectly linear trajectory.

We spent a fair amount of time further exploring bathtub dynamics, with much filling and emptying. When the quantity of water on the floor got too alarming, we moved to the sink to explore equilibrium by trying to balance the tap inflow and drain outflow, which is surprisingly difficult.

We lost track of our original results, so we recently repeated the experiment. This time, we measured the filling as well as the draining, shown below on the same axes. The dotted lines are our data; others are our prior guesses. Again, there’s no sign of exponential draining – it’s a linear rush to the finish line. Filling – which you’d expect to be a perfect ramp if the tub had constant volume per depth – is initially fast, then slows slightly as the tapered bottom area is full. However, that effect doesn’t seem to be big enough to explain the outflow behavior.

Bathtub data

I’ve just realized that I have a straight-sided horse trough lying about, so I think we may need to head outside for another test …

Update: the follow-on to this is rather important.

Risk Communication on Climate

John Sterman’s new Policy Forum in Science should be required reading. An excerpt:

The strong scientific consensus on the causes and risks of climate change stands in stark contrast to widespread confusion and complacency among the public. Why does this gulf exist, and why does it matter? Policies to manage complex natural and technical systems should be based on the best available scientific knowledge, and the Intergovernmental Panel on Climate Change (IPCC) provides rigorously vetted information to policy-makers. In democracies, however, the beliefs of the public, not only those of experts, affect government policy.

Effective risk communication is grounded in deep understanding of the mental models of policy-makers and citizens. What, then, are the principal mental models shaping people’s beliefs about climate change? Studies show an apparent contradiction: Majorities in the United States and other nations have heard of climate change and say they support action to address it, yet climate change ranks far behind the economy, war, and terrorism among people’s greatest concerns, and large majorities oppose policies that would cut greenhouse gas (GHG) emissions by raising fossil fuel prices.

More telling, a 2007 survey found a majority of U.S. respondents (54%) advocated a “wait-and-see” or “go slow” approach to emissions reductions. Larger majorities favored wait-and-see or go slow in Russia, China, and India. For most people, uncertainty about the risks of climate change means costly actions to reduce emissions should be deferred; if climate change begins to harm the economy, mitigation policies can then be implemented. However, long delays in the climate’s response to anthropogenic forcing mean such reasoning is erroneous.

Wait-and-see works well in simple systems with short lags. We can wait until the teakettle whistles before removing it from the flame because there is little lag between the boil, the whistle, and our response. Similarly, wait-and-see would be a prudent response to climate change if there were short delays in the response of the climate system to intervention. However, there are substantial delays in every link of a long causal chain stretching from the implementation of emissions abatement policies to emissions reductions to changes in atmospheric GHG concentrations to surface warming to changes in ice sheets, sea level, agricultural productivity, extinction rates, and other impacts. Mitigating the risks therefore requires emissions reductions long before additional harm is evident. Wait-and-see policies implicitly presume the climate is roughly a first-order linear system with a short time constant, rather than a complex dynamical system with long delays, multiple positive feedbacks, and nonlinearities that may cause abrupt, costly, and irreversible regime changes.

Continue reading “Risk Communication on Climate”

The Deal We Ain't Got

Today, Drew Jones and I presented a simple model as part of the Tällberg Forum’s Washington Conversation, ‘The climate deal we need.’ Our goal was to build from some simple points about the bathtub dynamics of the carbon cycle and climate to yield some insights about what’s needed. Our aspirational list of insights to get across included,

  • stabilizing emissions near current levels fails to stabilize atmospheric concentrations any time soon (because emissions now exceed uptake of carbon; stabilization continues that condition, and the residual accumulates in the atmosphere)
  • achieving stabilization of atmospheric CO2 at low levels (Hansen et al.’s 350 ppm) requires very aggressive cuts (for the same reason; if carbon cycle feedbacks from temperature kick in, negative emissions could be needed)
  • current policies are not on track to meaningful reductions (duh)
  • nevertheless, there is a path (Hansen et al.’s “where should humanity aim” paper lays out one option, and there are others)
  • starting soon is essential (the bathtub continues to fill while we delay – a costly gamble)
  • international negotiation dynamics are tricky due to diversity of interests, coupled problem spaces, and difficulty of transfers (simulations shadow this)
  • but everyone has to be on board or little happens (any one major region or sector, uncontrolled, can blow the deal by emitting above natural uptake)

A good moment came when someone asked, “Why should we care about staying below some temperature threshold?” (I think a scenario with about 3.5C was on the screen at the time). Jim Hansen answered, “because that would be a different planet.”

The conversation didn’t lead to specification of “the deal we need” but it explored a number of interesting facets, which I’ll relate in a few follow-on posts.

Three climate negotiators walk into a bar …

Analogies can be dangerous when you don’t know their limitations, but they can be a good way of distilling a lot of technical details into a central point. A flurry of emails last week resulted in this story at Climate Interactive, about some inebriated decision makers who can’t predict the consequences of their actions. It reminds me of another favorite, cited in Cloudy Skies:

The article gives a fascinating insight into the way international politics struggles with complex technical issues. I was inspired to set up an experiment to test some of the ideas, and hit upon the analogy of using my bath instead of the Earth and taking the water as carbon dioxide. I jammed the plug firmly, and turned one tap to full. I observed that the bath was filling with water. I turned the flow down to 80% – a massive 20% reduction – only to discover that it was still filling but slightly more slowly. At this point I was joined by my neighbour, an American. He pointed out that reducing the flow by 20% was out of the question; we haggled for a bit before agreeing on a reduction to 94.8%. We thought the 5.2% reduction had a nice ring to it. Oddly, the bath was still filling up with water at almost the same rate that it had been initially. My friend then gave me a five pound note to turn the tap down by another 20%. I did so. He then turned on the other tap to exactly counter the 20% saving. I complained, only to be told that he had bought my credits, whatever that means. He then rushed out, returning with a bucket which he put under the second tap. I was so impressed that I did not notice for a moment that the bath was still filling up and that the bucket would soon overflow. We decided we had experimented enough for one day and went off to the pub. We were on our third pint when we remembered that the experiment was still running.

Letter to The Chemical Engineer from A. Lodge (1999)

Unfortunately, even in simple systems, intuition often deserts us. The fact that mental models fail to capture the essence of climate dynamics is but one symptom of this. This Thursday, Drew Jones and I will present a simple model designed to close the gap at the Tällberg Forum’s Washington Conversation, “the climate deal we need.”