Risk, prediction and costs

Lecture outline:

**Risk what is it?****Prediction in environmental geology.****Chaos**.**What is a fractal**?**The significance of outlier events.**

Risk - what is it?

You need to get from here to there, and the two choices are by car or plane. Which is riskier and why? The light has just turned from green to orange, and given your speed and distance from the intersection do you step on the gas or the brake? Life is full of constant risk assessment, a lot of it "seat of the pants" and some of it informed and calculated. Can you guess what industry succeeds or fails on the basis of risk assessment (clue - they have a significant presence in Omaha)?

Which is riskier, building on a flood plain, or building on an adjacent mountain slope? How do you even answer such a question?

Considering the previous discussion, what are the components or risk?

risk exposure = probability of event occurring * the total loss or cost if the event occurs

Risk can be and at least partially quantified, and you may familiar with the fact that insurance companies routinely conduct such analysis. You may be less familiar with the fact that the number one pay out claim wise for insurance companies is natural disasters, and so they have looked at associated risk assessment in some detail. The probability of an event happening is often foremost in people's mind when they think of risk. The cost factor is less so.

The following numbers are fictional, but not totally unreasonable, and are used to illustrate a point.

- Probability of 7 RM earthquake in Omaha area = .1% in a year.
- Cost of 7 RM earthquake = $1,000,000,000
- Risk from the earthquake = .001 * $1,000,000,000 = $1,000,000 per year
- Probability of large tornado in same area = 10% in a year.
- Cost of large tornado = $10,000,000
- Risk = .1 * $10,000,000 = $1,000,000 per year
- Which do you worry about more?

This is one perspective that can be useful. At the end of lecture we will consider the significance of outlier events, which tend to be unusually low frequency but high cost events.

**What are units of risk?**

- deaths per million people per unit time
- cost in dollars per unit time
- how much is a life worth?

**Phenomena that produce societal risk that we will discuss in this course?**

- earthquakes, volcanic eruptions, flooding, tsunamis, meteorite impacts, land slides.
- illness from groundwater and/or soil contamination (e.g. toxins).
- resource depletion, e.g. soil or water.

**Audiences for risk assessment reports (who might use them)?** You may calculate your own **individual risk**. Insurance companies calculate the risk for their customers **(group risk)**. An engineer involved in building a nuclear power plant may calculate the risk for the population of all people within a certain distance. The costs will be quite different for all three even for the same event, and so the resulting risk will be quite different. Who the risk is being calculated for (individual or group) is therefore crucial.

**How to approach the cost/consequences side of risk assessment?** There are various approaches. A simple approach is to extrapolate on the basis of past case histories. That can be quite unsatisfactory for many reasons, one of which is changing conditions (economic, political, natural). Another powerful approach is **scenario construction - thinking through what could happen**. Below is one conceptual framework for scenario building.

This is a map of one conceptual approach to risk assessment. A trigger event would be what ever produces the natural disaster, for example a hurricane. Very often these are complex events and there are multiple specific elements that could cause loss of life or property (termed the event risk elements here). Then there is the human infrastructure, captured here as built elements. There is a matrix of possibilities of how the event risk element could affect the built element and the people within. In theory one could work out the cost for each matrix element and add then all up. However, there can also be links between the various built elements (e.g. think of a dam giving way during a flood). In practice the focus would be on critical built elements, ones of greater significance, greater potential risk.

Note that there can be multiple risks associated with some action or event. Consider the multiple risks of gambling:

- chances you will lose your money.
- chances you have an addictive personality when it comes to gambling.
- risk/cost of lost opportunity, if had done something else.

What are typical critical facilities (ones posing much greater risk, and therefore focused on in during risk assessment) in a city or elsewhere?

Interesting site comparing risk of various activities.

EPA site on comparative risk assessment for water quality (some heavy duty stuff here).

Prediction in environmental geology

This speaks to that first very important component of risk assessment.

Systems characterized by more regular, highly predictable behavior:

- orbital dynamics, seasons, night and day, tides.
- plate motions.

Systems characterized by unpredictable (chaotic) or very complex behavior:

- weather and hence flooding, and other hydrologic related events (droughts - Drought Center at UNL, drought risk page, hurricanes).
- earthquakes
- volcanic eruptions(?)
- turbulence
- the same system can exhibit both predictable and very simple behavior and at other times and other conditions complex and chaotic behavior (as we saw with the Verhultz equation and population dynamics).

Terminology: predictions versus forecasts.

Basic methodology of making predictions -** the best predictor of future behavior is past behavior. **If there is a statistically defensible mathematical relationship between frequency of occurrence and size, then you can use one to predict the other.

**Example of the method for predicting floods (e.g. the 100 year flood):**

Methodology of estimation of flood recurrence intervals (can be easily done in Excel, or a variety of other spread sheets):

* Obtain historical discharge data - source (United States Geological Survey).

* Rank the discharges from 1 the maximum on down to n the minimum discharge per year.

* Calculate recurrence interval: RI = (n+1) / rank. This is nothing but asking how often did a discharge of this size or bigger occur in the historic time span.

* Plot the log of the RI versus the discharge. Usually a line will fit the data fairly well. Compute best fit mathematical relationship for the data.

* Extrapolate mathematically from this history to longer time period of interest - 100 year flood or 1000 year flood, or interpolate for shorter periods of interest.

* example for Elkhorn River near Omaha, from Geodata analysis course.

**What is the basic assumption behind this type of analysis?** Flood recurrence interval in practice is more sophisticated than shown here, but the fundamental methodology is the same.

One could use the laws of physics and chemistry ant the state (topography, T, humidity, i.e. all the variables in those laws) of an area as input, to try and compute what will happen. This can be called a "deterministic" model. These are used to some degree, but why might other approaches produce better results in some cases?

**What else might we want to predict in environmental geology in addition to floods?**

This is the briefest of introductions to the science and concepts related to chaos through a lens of earthquakes and earthquake prediction.

What type of behavior characterizes chaotic systems?

- initial conditions sensitivity (
**butterfly effect**we identified before). - feedback processes.
- a continuous range of event sizes,
**fractal distributions (log-log linear relationships between size and frequency)**and fractal geometries. - strange attractors: geometric patterns of behavior on plots of activity.

Earthquake prediction as an example. Slider block(s) model for earthquakes.

**India Ocean tsunami example**: On Dec. 29, 2004 a very large 9.0 earthquake struck in the Indian Ocean. The earthquake was produced by roughly 15 meters of slip along a 1200 km long by 100 km wide area along a plate boundary fault (source). Locally uplift of the sea floor was greater than 20 meters. The hypocenter, the point of rupture initiation, was shallow, only 16 km deep. The earthquake occurred on a subduction zone, a type of plate boundary known to generate large, often submarine earthquakes. It caused large destructive sea waves called tsunamis that hit coastlines throughout the area. The waves swept over entire small islands, and penetrated inland in low lying coastal areas as much as two miles. The estimate of fatalities from both the tsunami and earthquake is something greater than 200,000 - the exact number will never be known. How often might you expect such phenomena to occur?

Short documentary on this video.

*Satellite image of tsunami generated by the earthquake from USGS.*

*Earthquake frequency plot for area with a 1000 km radius centered on Java-Sumatra trench, with a record of more than 4000 earthquakes.*

*Note what is being plotted here. It is simply generated by the linear best-fit line produced above. If you only need a 7.5 RM size earthquake to potentially produce a dangerous tsunami, how often would you expect that to occur?* *Consider what else in addition to a large earthquake is needed to produce a tsunami (i.e. do all large earthquakes produce tsunamis). *

*What is the topographic profile length in the above image?*

**Fractals connected to chaos.** Same motif repeated at different scales, **scale invariant**, fractional dimension.

- Cubic fracture model.
- Fractal island model. How long is the length of a coastline?
- Link to a number of examples of fractal geometries.

- Link to Yale course on fractals in nature.

Chaotic systems can follow rules, produce patterns.

Other examples of chaotic systems?

*Example of a partial fractal pattern, a variation on what is known as Sierpenski's gasket. It is partial because it is impractical to draw the smaller and smaller triangles inside the already small triangles. Something like this could represent a spongy mineral growth, which because of this fractal character could have interesting and even useful physical properties.*

The significance of outlier events in risk assessment

What is the biggest hurricane that can happen, the biggest earthquake, the biggest volcanic eruption??? The larger the event, the less likely, but possibly the more costly.

YouTube videos of recent Japanese tsunami (cost of which is estimated at $309 billion, >20,000 people killed, and a tsunami warning system and protective walls were in place):

- http://www.redflagnews.com/headlines/shocking-new-japan-tsunami-video-found-released .
- http://www.youtube.com/watch?v=ceym2c18OQM .

Yellowstone is perhaps one of the best examples of an outlier event. Major eruptions from here only happen with a recurrence interval of 100,000s of years. However, the ash from the eruptions in the past covered the entire country.USGS web site that describes Yellowstone eruption possibilities.