44.380 Introduction to Critical Infrastructure Protection Spring 2016

Chapter 3 – Theories of Catastrophe

Self-Organization Criticality

School of Criminology and Justice Studies University of Massachusetts Lowell

What is the nature of major catastrophes? Power laws and exceedance probability Per Bak Sandpiles Food network extinctions Self-Organized Criticality (SOC) Relationship to infrastructures Policy implications?

Disasters appear to be random: Tipping Point - Little things magnify into big things Unexpected Timing - Unpredicted earthquake Unexpected Magnitude - Hurricane damage Similar across all sectors:

• Stock market tipping points • Surprise terrorist attacks • Airplane, automobile, train accidents “just happen” • Epidemics break out for no apparent reason • World powers rise and fall

The complex adaptive system explanation: Catastrophes are a result of emergence Nonlinear reactions to small perturbations Self-organized criticality (SOC):

• Slow build-up of instability • Near inflection or tipping point • Random perturbation has big effect • Avalanche occurs unexpectedly

Major claims: Natural disasters obey a fractal power law regardless of

type of disaster. Fractals (power laws) are produced by randomness. Not necessary to identify “cause-and-effect” when

randomness is the underlying property of a system. Disaster strikes where the underlying system has reached a

state of self-organized criticality (SOC).

• A power law expresses a functional relationship between two variables, where

one varies as a power of another. • Fractal (dimension) of PML risk: q > 1 system is resilient; q < 1 system is fragile • SOC stems from increasing efficiency and optimizing system performance, which

eliminates redundancy and surge capacity. Self–organized (CIKR) systems are not usually redundant, non-surge single point of failure systems with bottlenecks, overly concentrated assets and inadequate backup capacity.

Power Law is of the form: F(x) = ax-q

Frequency vs Consequence: Probability that an incident will occur with consequence, x

Exceedence: Cumulative probability of frequency data

Of

Exceedence describes the percentage of time an event or occurrence, stream-flow in this example, is greater than or equal to the defined event or occurrence (stream-flow).

Source: Analysis associated with Nez Perce settlement of water rights claims in the Snake River Basin, Idaho Water Resource Board, 2004.

Qavg = 45 CFS Qmedian = 38 CFS = 50% exceedance flow Q80% = 25 CFS = low flow 80% exceedance flow Q10% = 75 CFS = 10% exceedance flow

BTW Sand Pile Experiment: Drop sand particles one at a time. Conical-shaped forms At some point, slides occur of differing sizes. Slide timing is unpredictable. Distribution of avalanche size forms a fractal pattern.

Bak, Chao Tang, Kurt Weisenfeld (BTW), “Self-Organized Criticality: An Explanation of 1/f Noise”, Physical Review Letters, 1987)

Critical Point = Tipping Point: Metastable systems “teeter on the verge” of

instability. Meta-stability means it could be either “smooth

sailing” or failure. Small fluctuations can lead to large change; self-

organization.

SOC equates with fragility or lack of resiliency and is the main source of fragility.

Per BTW, SOC is defined as: A property of a system that operates near its critical point,

i.e. near an attractor (. …build-up approaches its tipping point…. …reaches an instability or non-equilibrium point

Bak, “How Nature Works: “The Science of Self-Organized Criticality”, 1996; Turcotte, Smalley, Solla, Nature, 1985; Katz, Nature, 1986 and Bak, Tang, Wiesenfeld, Physical Review Letters, 1987.

Cumulative Likelihood (EP) Prob(Consequence > x). EP of avalanches obeys a power law: large

“avalanches” are rare, small are more common. Fractal = self-similar = scale-free Self-organized criticality = instability is formed by

itself In simple terms, the higher the probability of occurrence of an event the lesser the consequence ; and the lower the probability of occurrence, the greater the consequence .

What is “Scale Free”? Same shape, no matter the scale Scaling by factor of 2 yields same shape Fractal-like: magnifying a portion of the function yields the function

Long (or fat) Tail More representative than a linear or exponential relationship Linear relationship steadily declines to zero; not a reality Exponential declines slower, but eventually declines further Power law declines rapidly; tapers off;

takes longer to reach lower probability.

Well-known 80-20% Rule 80% of the cumulative probability occurs in first 20% of cases. Applying concept to disasters means that 20% of the occurrences

results in 80% of the damage.

Risk vs. Consequence

High-Risk: Exceedance Probability (EP) declines slowly Low-Risk: EP declines rapidly

Let’s look at past extinctions: 99% of all species are now extinct – earth’s about 4.5 billion years;

species survive between 0.5 and 5 million years, conceivable that 99% of species that ever lived are no longer with us

65 milliion years ago: KT (Cretaceous-Tertiary Mass Extinction) event wiped out 70% of life, including the dinosaurs

250 M years ago: Permian–Triassic extinction - earth's most severe known event; 95% of marine species; 70% of terrestrial vertebrates ; only known mass extinction of insects

Are extinctions predictable? What is the cause-effect link? What today could cause extinction?

Terrorist Attacks and Natural Disasters occur randomly They are unpredictable Randomness ->Self-Organization Criticality (SOC) -> Collapse Risk decreases as consequence increases The link between risk and consequence is not linear (80-20 rule).

Policy: Back away from SOC Sub-optimal operation (lower efficiency) Addition of “surge capacity” (higher cost) Decrease “connectivity” (regulatory)

Prevention v. Response High Risk => Prevention Low Risk” => Response

44.380 Introduction to Critical Infrastructure Protection Spring 2015

Chapter 3 – Theories of Catastrophe

Theories of Collapse

School of Criminology and Justice Studies University of Massachusetts Lowell

Normal Accident: Tightly coupled systems are prone to collapse, even though the initial fault is minor or “normal”.

Punctuated Equilibrium: Self-organized systems collapse and then restructure after a period of adaptation; and repeat the process of self-organization, collapse and adaptation.

Tragedy of the Commons (TOC): Unsustainable systems eventually collapse when they exceed their carrying capacity Typically due to individuals acting in their own self-interest.

Paradox of Enrichment: Too much “enrichment” may lead to collapse, if a system’s carrying capacity is exceeded.

Competitive Exclusion Principle (CEP): Competitive systems tend to eliminate all but one competitor, because sooner or later, one competitor gains a small advantage over all others, and grows faster and becomes fitter than all others. Leads to a monopoly, in general, which reduces redundancy and

diversity, and may lead to collapse.

Paradox of Redundancy (POR): Redundancy may actually lower resiliency in some systems because redundancy increases the number of components that may fail. It is a paradox because redundancy is often sited as a method of

increasing resilience, although it may not.

NAT is distinguished by three key components: Sometimes, two or more failures come together in an unexpected way

Failures cascade faster if the system is tightly coupled When there is catastrophic potential, consequences are catastrophic.

NAT and Nuclear Power Perrow studied Three-Mile Island and Bhopal India Chemical Disasters.

• Chain reactions start small and grow in magnitude as they spread • Catastrophic potential increases consequences

Figure 3.1 in Text

Perrow, Charles, “Normal Accident Theory”, Princeton University Press (1999)

The sliding block model of earthquakes provides another illustration of NAT. Tightly coupled systems are more likely to cascade Cascades obey long-tailed power laws

Sliding block simulation of earthquakes explains why the Gutenberg-Richter scale obeys a power law.

Figure 3.1 in Text

Bak’s Sand Pile. Grains of sand accumulate until landslides occur Size and time of landslides are long-tailed

Bak’s Theory of Self-organized Criticality Complex systems self-organize; transition from randomness to

structure Self-organization increases until reaching SOC SOC reduces resilience and increases fragility Faults are magnified by SOC leading to complete collapse Collapse is followed by chaotic adaptation and recovery The cycle repeats itself

Sand pile collapses obey a long-tailed power law exceedence probability in size and elapsed time between landslides. • Bak, P., Tang, C. & Weisenfeld, K. (1987). Self-organized

criticality: An explanation of 1/f Noise, Physical Review Letters • Lewis, Ted G., Bak’s Sand Pile, Agile Press, 2011

Figure 3.1 in Text

Tragedy of the Commons is a parable describing why some systems are unsustainable while others are sustainable Ranchers share a pasture, called the commons – grass is a prey. Each individual rancher decides how many cows to put out to pasture –

cows are predators Each rancher benefits from the sale of his or her herd of cows. Predator-prey system is viable when cows and grass are in balance.

Can you give an example of this principle in today’s world?

How do we know if a system is sustainable? State space diagram plots the state of a system at time “t” in terms of a

predator and prey. Systems can be:

• Stable • Oscillating or meta-stable • Unstable

State Space in general Single point – no change. Smooth line in one direction - stable change. Ellipse - oscillating meta-stability. Spiral - trending toward a point (blowing up) or collapse (when it

reaches zero)

Figure 3.5 in Text

Table 3.6 b

Table 3.6 a – From 1960-1980 construction was stable, but from 1980-2010, construction began to decline towards the zero; the power grid became unstable from 1980 to 2010 and was trending towards collapse.

Table 3.6 b - Investment has not kept pace with growth in the economy

Table 3.6 a

Michael Rosenzweig observed: “… If the food supply of a prey such as a rabbit is overabundant,

its population will grow unbounded and cause the predator population (such as a lynx) to grow unsustainably large. This may result in a crash in the population of the predators and possibly lead to local eradication or even species extinction.”

When enrichment exceeds a carrying capacity, a stable system becomes unstable.

Enrichment of either predator or prey can destroy the commons.

Predator and prey synergistically establish a limit called the carrying capacity (CC). CC is the maximum population of a given species that a

given environment can sustain

CC is the maximum possible utilization of a finite resource

CC is the tipping point of a complex system that transitions it from growth to decline

CC is the maximum excess utilization of an infinite resource.

Minsky Moment Occurs when the financial carrying capacity of a certain sector of

the economy is reached.

The 2008 Meltdown $6 trillion loss in housing sector

Home ownership increased from 45% prior to the depression to 60%-65% in 1980s/1990s and peaked near 70% before collapse

Ownership greater than 65% oscillated falling to less than 65%.

This suggests that 65% is the approximate economic carrying capacity for this sector.

Georgii Frantsevich Gause discovered the competitive exclusion principle in 1932.

Over time, no two species within an ecological niche can coexist forever.

When two species compete, one will be slightly more efficient than the other and will reproduce at a higher rate as a result.

The more capable species crowd out the weaker species. The less efficient and weaker species either go extinct or

are marginalized

The internet monoculture is the result of CEP. Can you give an example?

TCP/IP and other Internet protocols have eliminated redundancy, resiliency and immunity to viruses Can you cite a recent example of this?

The number of major ISPs is diminishing. Bandwidth ownership is narrowing Anti-Net neutrality is a form of monopoly Alterative “species” are non-existent or extinct.

Why could this be a problem for protecting CI?

POR: Redundancy may reduce resiliency in complex systems. As redundancy increases via adding more components to a

system, the number of connections among redundant parts also increases.

As the number of connections increase, the opportunity for greater spreading of cascading failures also increases.

SOC increases with density of connections, hence, a redundant system becomes less resilient.

More connections means more spreading, which leads to a lower fractal dimension; this equates with lower resilience.

For which CI is redundancy important? Why? For which CI is resilience important? Why?

Figure 3-10 in Text

Each theory tries to explain risk. All theories define risk factors affecting expected loss.

Exceedence distributions capture risk factors in the form of a risk profile

Risk profiles can be changed into probability estimates of future events

PML Risk profiles can be converted into projections of future disasters, attacks, collapses, and accidents.

Every theory can produce an estimate based on Exceedence Probability.

Figure 3-9 a. & b. in Text