A simple example of bathtub dynamics:
The flow of plastic bags into landfills is dramatically down from the 2005 rate. But the accumulation is up. This should be no surprise, because the structure of this system is:
The accumulation of bags in the landfill can only go up, because it has no outflow (though in reality there’s presumably some very slow rate of degradation). The integration in the stock renders intuitive pattern matching (flow down->stock down) incorrect.
Placing the flow and the stock on the same vertical scale, is also a bit misleading, because they’re apples and oranges – the flow of disposal has units of tons/year, while the accumulation has units of tons.
Also, initializing the stock to its 2005 value is a bit weird. If you integrate the disposal flow from 1980 (interpolating as needed), the accumulation is much more dramatic: about 36 million tons, by my eyeball.
Need to time model runs? One way to do it is with Vensim’s log commands, in a cmd script or Venapp:
LOG>MESSAGE|timing.txt|"About to run."
These commands were designed for logging user interaction, so they don’t offer millisecond resolution needed for small models. For that, another option is to use the .dll.
Generally, model execution time is close to proportional with equation count x time step count, with exceptions for iterative functions (FIND ZERO) and RK auto integration. You can use the .dll’s vensim_get_varattrib to count equations (expanding subscripts) if it’s helpful for planning to maximize simulation speed.
The NYT has an interesting article on the decline of the High Plains aquifer, which includes the famous Ogallala aquifer. Water tables are dramatically down (red) in many areas, making irrigation impractical.
Vast stretches of Texas farmland lying over the aquifer no longer support irrigation. In west-central Kansas, up to a fifth of the irrigated farmland along a 100-mile swath of the aquifer has already gone dry. In many other places, there no longer is enough water to supply farmers’ peak needs during Kansas’ scorching summers.
And when the groundwater runs out, it is gone for good. Refilling the aquifer would require hundreds, if not thousands, of years of rains.
This is a widespread, generic problem, and instance of the tragedy of the commons archetype:
Alternately, as an economist might put it, depletion of groundwater is typically an externality, with zero rent paid from users to owners (us).
There are three facets to management of the problem: the commons problem, detail complexity from the complex geology of aquifers, and dynamic complexity. Allocation of property rights solves the commons problem, but not the others (see Erling Moxnes’ interesting work on this).
Sniffing around for material for this post, I found it easy to get lots of complicated information about aquifers, but hard to find any simple stock-flow pictures that revealed their state or dynamics, like this:
This suggests that there’s some low-hanging fruit to be harvested through provision of simple feedback, as in the Climate Scoreboard.
The Tech Review Arxiv blog has a neat summary of new research on high blood pressure. It turns out that the culprit may be a feedback mechanism that can’t adequately respond to stiffening of the arteries with age:
The human body has a well understood mechanism for monitoring blood pressure changes, consisting of sensors embedded in the major arterial walls that monitor changes in pressure and then trigger other changes in the body to increase or reduce the pressure as necessary, such as the regulation of the volume of fluid in the blood vessels. This is known as the baroreceptor reflex.
So an interesting question is why this system does not respond appropriately as the body ages. Why, for example, does this system not reduce the volume of fluid in the blood to decrease the pressure when it senses a high systolic pressure in an elderly person?
The theory that Pettersen and co have tested is that the sensors in the arterial walls do not directly measure pressure but instead measure strain, that is the deformation of the arterial walls.
As these walls stiffen due to the natural ageing process, the sensors become less able to monitors changes in pressure and therefore less able to compensate.
More than 40 years after Schelling’s classic analysis, segregation appears to be alive and well:
As Schelling showed, it doesn’t take draconian measures for this behavior to emerge. It’s a robust (but suboptimal) outcome of weak coupling by positive feedback.