Archive for the 'Sustainability' Category

Early warnings of catastrophe

There are warning signs when the active structure of a system is changing. But a new paper shows that they may not always be helpful for averting surprise catastrophes.

Catastrophic and sudden collapses of ecosystems are sometimes preceded by early warning signals that potentially could be used to predict and prevent a forthcoming catastrophe. Universality of these early warning signals has been proposed, but no formal proof has been provided. Here, we show that in relatively simple ecological models the most commonly used early warning signals for a catastrophic collapse can be silent. We underpin the mathematical reason for this phenomenon, which involves the direction of the eigenvectors of the system. Our results demonstrate that claims on the universality of early warning signals are not correct, and that catastrophic collapses can occur without prior warning. In order to correctly predict a collapse and determine whether early warning signals precede the collapse, detailed knowledge of the mathematical structure of the approaching bifurcation is necessary. Unfortunately, such knowledge is often only obtained after the collapse has already occurred.

To get the insight, it helps to back up a bit. (If you haven’t read my posts on bifurcations and 1D vector fields, they’re good background for this.)

Consider a first order system, with a flow that is a sinusoid, plus noise:

`Flow=a*SIN(Stock*2*pi) + disturbance`

For different values of a, and disturbance = 0, this looks like:

For a = 1, the system has a stable point at stock=0.5. The gain of the negative feedback that maintains the stable point at 0.5, given by the slope of the stock-flow phase plot, is strong, so the stock will quickly return to 0.5 if disturbed.

For a = -1, the system is unstable at 0.5, which has become a tipping point. It’s stable at the extremes where the stock is 0 or 1. If the stock starts at 0.5, the slightest disturbance triggers feedback to carry it to 0 or 1.

For a = 0.04, the system is approaching the transition (i.e. bifurcation) between stable and unstable behavior around 0.5. The gain of the negative feedback that maintains the stable point at 0.5, given by the slope of the stock-flow phase plot, is weak. If something disturbs the system away from 0.5, it will be slow to recover. The effective time constant of the system around 0.5, which is inversely proportional to a, becomes long for small a. This is termed critical slowing down.

For a=0 exactly, not shown, there is no feedback and the system is a pure random walk that integrates the disturbance.

The neat thing about critical slowing down, or more generally the approach of a bifurcation, is that it leaves fingerprints. Here’s a run of the system above, with a=1 (stable) initially, and ramping to a=-.33 (tipping) finally. It crosses a=0 (the bifurcation) at T=75. The disturbance is mild pink noise.

Notice that, as a approaches zero, particularly between T=50 and T=75, the variance of the stock increases considerably.

This means that you can potentially detect approaching bifurcations in time series without modeling the detailed interactions in the system, by observing the variance or similar, better other signs. Such analyses indicate that there has been a qualitative change in Arctic sea ice behavior, for example.

Now, back to the original paper.

It turns out that there’s a catch. Not all systems are neatly one dimensional (though they operate on low-dimensional manifolds surprisingly often).

In a multidimensional phase space, the symptoms of critical slowing down don’t necessarily reveal themselves in all variables. They have a preferred orientation in the phase space, associated with the eigenvectors of the eigenvalue that’s changing at the bifurcation.

The authors explore a third-order ecological model with juvenile and adult prey and a predator:

Predators undergo a collapse when their mortality rate exceeds a critical value (.553). Here, I vary the mortality rate gradually from .55 to .56, with the collapse occurring around time 450:

Note that the critical value of the mortality rate is actually passed around time 300, so it takes a while for the transient collapse to occur. Also notice that the variance of the adult population changes a lot post-collapse. This is another symptom of qualitative change in the dynamics.

The authors show that, in this system, approaching criticality of the predator mortality rate only reveals itself in increased variance or autocorrelation if noise impacts the juvenile population, and even then you have to be able to see the juvenile population.

We have shown three examples where catastrophic collapse can occur without prior early warning signals in autocorrelation or variance. Although critical slowing down is a universal property of fold bifurcations, this does not mean that the increased sensitivity will necessarily manifest itself in the system variables. Instead, whether the population numbers will display early warning will depend on the direction of the dominant eigenvector of the system, that is, the direction in which the system is destabilizing. This theoretical point also applies to other proposed early warning signals, such as skewness [18], spatial correlation [19], and conditional heteroscedasticity [20]. In our main example, early warning signal only occurs in the juvenile population, which in fact could easily be overlooked in ecological systems (e.g. exploited, marine fish stocks), as often only densities of older, more mature individuals are monitored. Furthermore, the early warning signals can in some cases be completely absent, depending on the direction of the perturbations to the system.

They then detail some additional reasons for lack of warning in similar systems.

In conclusion, we propose to reject the currently popular hypothesis that catastrophic shifts are preceded by universal early warning signals. We have provided counterexamples of silent catastrophes, and we have pointed out the underlying mathematical reason for the absence of early warning signals. In order to assess whether specific early warning signals will occur in a particular system, detailed knowledge of the underlying mathematical structure is necessary.

In other words, critical slowing down is a convenient, generic sign of impending change in a time series, but its absence is not a reliable indicator that all is well. Without some knowledge of the system in question, surprise can easily occur.

I think one could further strengthen the argument against early warning by looking at transients. In my simulation above, I’d argue that it takes at least 100 time units to detect a change in the variance of the juvenile population with any confidence, after it passes the critical point around T=300 (longer, if someone’s job depends on not seeing the change). The period of oscillations of the adult population in response to a disturbance is about 20 time units. So it seems likely that early warning, even where it exists, can only be established on time scales that are long with respect to the natural time scale of the system and environmental changes that affect it. Therefore, while signs of critical slowing down might exist in principle, they’re not particularly useful in this setting.

The models are in my library.

Catastrophic Collapse Can Occur without Early Warning: Examples of Silent Catastrophes in Structured Ecological Models

Fight or flight in resource modeling

A nice reflection on modeling in emotionally charged situations, from Drew Jones, Don Seville & Donella Meadows, Resource Sustainability in Commodity Systems: The Sawmill Industry in the Northern Forest:

Through the workshops and discussions about the forest economy, we also learned that even raising questions of growth and limits can trigger strong defensive routines …, both at the individual level and the organizational level, that make it difficult even to remain engaged in thinking about ecological limits and, therefore, taking any action. Managing these complex process challenges effectively was essential to using systems modeling to help people move towards well-reasoned action or inaction.

… We were presenting our base run to a group of mill executives and landowners from five different companies. During the walk-through of the base-run behavior of mill capacity (which begins to contract severely several decades in the future) we found that a few participants quickly dismissed that possibility, saying, ‘‘Sawmill capacity in this region will never shrink like that,’’ and aggressively pressing us on what factors we had included so that (we presume) they could uncover something missing or incorrect and dismiss the findings. Their body language and tone of voice led us to believe the participants were angry and emotionally charged.

… we came to identify a recurring set of defensive routines, that is, both emotionally laden reflexive responses to seeing the graphs of overshoot in which participants did not connect their critique to an underlying structural theory, or simply disengaged from thinking about the questions at hand. … When we encountered these reactions, we found ourselves torn between avoiding the conflict (the ‘‘flight’’ reaction; modifying our story to fit within their pre-existing assumptions, de-emphasizing the behavior of the model and switching to interview mode, talking about the systems methodology rather than implications of this particular model) or by pushing harder on our own viewpoint (the ‘‘fight’’ reaction; explaining why our assumptions are right, defending the logic behind our model). Neither of these responses was effective.

Back to the presentation to the industry group. During a break, after we had just survived the morning’s tensions and had struggled to avoid ‘‘fight or flight,’’ Dana [Meadows] walked up to us, smiling, and said, ‘‘Isn’t this going great?’’ ‘‘What?!?,’’ we thought.

‘‘The main purpose of our modeling,’’ she said ‘‘is to bring people to this moment—the moment of discomfort, of cognitive dissonance, where they can begin to see how current ways of thinking and their deeply held beliefs are not working anymore, how they are creating a future that they don’t want. The key as a modeler who triggers denial or apathy is to bring the group to this moment, and then just breathe. Hold us there for as long as possible. Don’t fight back. Don’t qualify your conclusions about what structures create what behaviors. State them clearly, and then just hold on.’’

Sharing Systems

I’m at the 30th Balaton Group meeting this week. A group of us just put our heads together to think about online approaches to teaching and sharing systems thinking and systems modeling. The basic question was, if you needed thousands of systems thinkers in a hurry, how could you scale up systems education quickly?

My list of interesting things people might want to do online:

• Model building
• Group model building (in the spirit of SUNY Albany work)
• Collaborative modeling (e.g., a distributed team working on federated modules of a model, but not necessarily involving the client and group conceptualization processes)
• Collaborative causal loop diagramming
• Model code sharing and reuse
• Model consumption
• Online games (playing through a simulation in real time) – possibly multiplayer
• Online simulations (interactive experimentation with a model) – possibly with a social aspect as at Climate Colab

Much can already be done through online model services like Forio and other means. However, I think there’s a lot more to be done. In particular, we’re weak on providing shared model transparency and quality control for any but the simplest models.

Some interesting systems & sustainability online learning links that came up in the conversation:

http://www.unep.org/ieacp/iea/

http://ecotippingpoints.org/

http://www.cotelco.net/

http://www.bfi.org/

http://www.seedsystems.net/

http://www.clexchange.org/

http://www.watersfoundation.org/

http://climateinteractive.org

http://www.systemswiki.org/index.php?title=Main_Page

http://insightmaker.com/

http://forio.com/

http://dt.asu.edu/

Is London a big whale?

Why do cities survive atom bombs, while companies routinely go belly up?

Geoffrey West on The Surprising Math of Cities and Corporations:

There’s another interesting video with West in the conversations at Edge.

West looks at the metabolism of cities, and observes scale-free behavior of good stuff (income, innovation, input efficiency) as well as bad stuff (crime, disease – products of entropy). The destiny of cities, like companies, is collapse, except to the extent that they can innovate at an accelerating rate. Better hope the Singularity is on schedule.

Thanks to whoever it was at the SD conference who pointed this out!

Why is the arctic brown?

I’m blogging from a 757, somewhere over the North pole, returning from a sustainability meeting in Iceland. The world below is a wilderness of sea ice and clouds. I’d expect brilliant white, but there’s actually a brown haze over the landscape. It’s stratified, much like the odd sight of half-white, half-brown clouds one occasionally sees when flying into a polluted city. Where does it come from? Chinese coal fumes? Russian fires? American SUV tailpipes? Icelandic airplane exhaust?

You are what you eat

I’m on my way home from the 29th meeting of the Balaton Group, held in Iceland. Iceland seems to be rising gracefully from it’s financial crisis, with introspection into the values that led to it and a renewed interest in sustainability. Author Andri Magnason visited us at dinner, and talked a bit about Iceland and his wonderful book, Dreamland – A Self-help Manual for a Frightened Nation. I picked up a copy in the airport (can’t get it at amazon yet) and got halfway through on the plane – I highly recommend it.

Another Magnason project is a book of Bonus Poetry, named for and spoofing the Icelandic Walmart.

You are what you eat
My grandfather was 70% water
He was 70% the stream
that trickled past his farm
he was the 30%
the sheep that grazed on his mountain
he was the fish swimming in his lake
he was the cow eating
in his field
he was the stream, he was the grass,
the mountain and the lake
I am not 70% water
perhaps 15% mineral water
the rest is beer and coca cola
I am italian pasta, swiss cheese
danish pork and chinese rice
american ketchup
runs through my veins
you are what you eat
I am a miniature of the world
no
I am a miniature of Bonus

Waiting for a miracle at Lake Mead

Lake Mead has dropped another ten feet since I wrote about its open-loop management,

My hypothesis is that the de facto policy for managing water levels is to wait for good years to restore the excess withdrawals of bad years, and that demand management measures in the interim are toothless. That worked back when river flows were not fully subscribed. The trouble is, supply isn’t stationary, and there’s no reason to assume that it will return to levels that prevailed in the early years of river compacts. At the same time, demand isn’t stationary either, as population growth in the west drives it up. To avoid Lake Mead drying up, the system is going to have to get a spine, i.e. there’s going to have to be some feedback between water availability and demand.

An article in the Arizona Republic confirms my thinking,

To slow the lake’s years-long decline, river users have built a reservoir west of Yuma to catch unused runoff, paid farmers to leave fields unplanted and are negotiating with Mexico to leave some of its allocation in Lake Mead while its farmers recover from an earthquake.

None of the steps will yield significant amounts of water, but together, they could keep Lake Mead from sinking below the drought triggers, buying time until a wet winter can replenish some of the water lost to drought.

“It’s time that we need,” said David Modeer, general manager of the Central Arizona Project, which moves water from the Colorado River to Phoenix and Tucson. “The reservoirs have shown they’re resilient. After a 12-year drought, they’re still half-full. What we do now will be worth it to stay out of a shortage.”

Managers are assuming that a return to historic rainfall patterns will save their bacon. But if climate models are right, and the Southwest will be on the losing end of trends in precipitation, that won’t happen. Even if they’re wrong, increasing demand can easily overwhelm restored rainfall. At some point, the loop will have to close – the question is how. Will property rights get reallocated and price signals aligned so that people live within the limits of supply? Or will the lake wind up permanently depleted? There are some signs of improved cooperation among states, but Nevada appears to be betting on failure:

if the reservoir fell below elevation 1,050 feet, one of the tunnels Nevada uses to draw water from the lake would sit above the waterline and would be useless. Nevada is working on a new, deeper tunnel

Green labeling is just a waypoint

Alan Atkisson wonders, Can a Glass of Orange Juice in Sweden be “Climate Smart”? He concludes, Maybe consumer items like this could be labeled, “Relatively less climate-stupid.” I agree.

For green labeling to actually work, there must be a “green information” system parallel to the money economy, and people must pay attention to it. That’s a booming business right now.

Optimistically assuming that all end users have the insight and altruism needed to make the correct environment/money tradeoff, that creates tremendous evolutionary pressure on the production system to evade the intent of the labeling by using cheaper not-so-green alternatives in hidden upstream locations. To paraphrase Groucho, greenness is the key to business success – if you can fake it, you’ve got it made. The evasion need not be so cynical; it simply requires incomplete information, for example sourcing products from places where measurement systems are incomplete. I really rather doubt that we’ll ever have life cycle analysis for every product performed with the same stringency now enforced by money auditing systems.

The optimistic assumptions above are probably misplaced. Altruism is great, but I hate to rely on it, as it’s not clear to me that it’s an ESS. But insight is probably the real constraint. Life cycle analysis is good stuff, but even if it were practical to pass many attributes through the supply chain, with firm-level attribution, the result is complex information about tradeoffs that’s better suited for engineers than for consumers. Add to that the challenges people already face, like making good decisions about saving for retirement and educating children, and I think it’s hard to do much more than muddle minds.

Just as marketers associate cars with love, green labels foster the paradoxical conclusion that some consumption benefits the environment. That may be true for a few goods, but for the most part, it’s not. We should be using green information to examine our broad patterns of consumption, more than to choose what to put in the shopping cart. That might mean non-consumptive tradeoffs, like having more leisure time and less stuff.

Green labeling is great in many cases today, where prices and other incentives are blatantly misaligned with public goods, but ultimately fixing the incentives will get us a lot farther than labeling. That means pricing resources we value upstream, so that value percolates through supply chains as a price signal. In my ideal world, the price tag itself would be a green label.

For green labeling to actually work, there must be a “green information” system parallel to the money economy, and people must pay attention to it. Optimistically assuming that all end users have the insight and altruism needed to make the correct green-money tradeoff, that creates tremendous evolutionary pressure on the production system to evade the intent of the labeling by using cheaper not-so-green alternatives in hidden upstream locations. The evasive response need not be cynical, it simply requires incomplete information, i.e. sourcing products where measurement systems are incomplete. I really rather doubt that we’ll ever have life cycle analysis for every product performed with the same stringency now enforced by money auditing systems. Green labeling is great in many cases today, where prices and other incentives are blatantly misaligned with social goals, but ultimately fixing the incentives will get us a lot farther than labeling.

The model that ate Europe

arXiv covers modeling on an epic scale in Europe’s Plan to Simulate the Entire Earth: a billion dollar plan to build a huge infrastructure for global multiagent models. The core is a massive exaflop “Living Earth Simulator” – essentially the socioeconomic version of the Earth Simulator.

I admire the audacity of this proposal, and there are many good ideas captured in one place:

• The goal is to take on emergent phenomena like financial crises (getting away from the paradigm of incremental optimization of stable systems).
• It embraces uncertainty and robustness through scenario analysis and Monte Carlo simulation.
• It mixes modeling with data mining and visualization.
• The general emphasis is on networks and multiagent simulations.

I have no doubt that there might be many interesting spinoffs from such a project. However, I suspect that the core goal of creating a realistic global model will be an epic failure, for three reasons. Continue reading ‘The model that ate Europe’

John Sterman on solving our biggest problems

The key message is that climate, health, and other big messy problems don’t have purely technical fixes. Therefore Manhattan Project approaches to solving them won’t work. Creating and deploying solutions to these problems requires public involvement and widespread change with distributed leadership. The challenge is to get public understanding of climate to carry the same sense of urgency that drove the civil rights movement. From a series at the IBM Almaden Institute conference.