Proceedings of a Workshop on Statistics on Networks (CD-ROM) (2007) / Chapter Skim
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Robustness and Fragility--Jean M. Carlson, University of California at Santa Barbara
Robustness and Fragility--Jean M. Carlson, University of California at Santa Barbara
Pages 317-342
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From page 317... ...
Robustness and Fragility 317
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From page 318... ...
This is also an invitation and a question for all the people who work on problems in sociology, what can we do from the point of view of passing information from the scale of the modeling and the geophysical phenomena up to where it has a real impact, which is on sociological issues such as response as well as policy and planning and so on. I think we've got to do that better.
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From page 319... ...
Even correcting for inflation, you see that there is an overall increase in terms of global economic losses associated with natural disasters. This goes hand-in-hand with increased population in the world, and a lot of the population increase is associated with less developed countries.
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Figure 4 drives this home. Each set of bars represents a different large city's expected population growth over coming decades.
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You can see that Tokyo is considered to be at high risk because of all of the geophysical kinds of phenomenon such as tsunamis, and so are the coastal cities in the United States. This is a natural hazard risk index.
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From page 323... ...
The poorest nations dominate in terms of deaths from natural disasters, but industrialized nations dominate the economic costs. What are you trying to protect, how is a natural disaster measured if you try to think about where you are going to put your resources?
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From page 324... ...
Each dot represents one increase in the cumulative number, so does the largest event, second largest event and so on. FIGURE 8 This is a power law distribution, and what that means in that the worst event, the events that dominate the losses, are much worse, orders of magnitude worse than a typical event.
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We have used some of the simple kinds of models that arise in physics in order to try to show how robustness issues change these models, and robustness trade-offs lead to new fragilities and sensitivities. One hallmark of this is these kinds of power laws.
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From page 326... ...
It doesn't mean they are the same, but it does mean that we are sharing tools. More and more we need to share those tools and we also need to be able to talk to each other, because our cascading failures pass from natural disasters into social systems and our network communication systems as well.
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From page 327... ...
We then based it on data compression, so it has to fit there. FIGURE 11 In this graph, "rank" is just frequency of possibility as a function of size, measured obviously differently in these two different cases, but the straight-line parts of the slope are really signatures of the power laws.
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From page 328... ...
I went with John and some colleagues of mine in the geography department at the University of California, Santa Barbara, and looked at issues associated with real forest fires. We had this nice statistical fit -- how does that compare to real fires?
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From page 329... ...
FIGURE 13 The statistics also provide an excellent statistical agreement between this very simplified HOT model and about the best data set that exists for fires, as shown in Figure 14. This is a starting point for lots of other things that you could do to think about more realistic fire models.
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From page 330... ...
Another important point is that regular burn cycles for forests are an intrinsic part of the ecosystem dynamics. If you don't have regular burn cycles, when you do burn, biodiversity increases in the recovery period.
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In dollars, geophysical phenomena are large, but when it comes to the number of people affected, these are fairly well localized in regions like California in the United States, and in terms of number killed. Over the period 1970-2000, there was an increase an increase in the number of natural disasters recorded worldwide, with the increase in damage going up in a very steady way over that period.
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From page 332... ...
There are weak interfaces in between tectonic plates where stresses accumulate that create a slipping event when the material along the interface fails, and that sets off waves that radiate through the ground. Figure 16 shows a lateral fault, which is like the San Andreas Fault, but there are different kinds of faults.
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A simple answer is 200 million years of continental drift, as the Indian plate slides under the Asian plate. Figure 18 shows that collision, with the red area being the portion that slid and caused the Sumatran earthquake.
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This just shows how significant the Sumatran quake was. FIGURE 19 This particular earthquake is not the lateral kind, the kind of earthquake that makes tsunamis happen at subduction zones.
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in Figure 20, and when it goes down something goes up. This happens underwater, so you have this water that doesn't want to sit like this and it has to cope with that.
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FIGURE 22 There are all kinds of simulations of the Sumatran tsunami. We have a simulation of the disturbance traveling across the ocean in these simulations, and you can estimate how long it will be until it hits various coastal places.
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Along the Pacific Coast in the United States we are always at risk for tsunamis. The biggest chance for tsunamis is most likely up in Alaska and in the Chile fault.
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There is also a lot of effort going on to predict what's vulnerable by modeling so there's a lot of interesting work in progress going on out there with the urban area topography. The thing that you can do here regarding something like earthquakes is couple with field research; go out and measure the hot spots in the ocean, and you can tell what is going to spin up the tsunami rate.
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From page 339... ...
It comes all the way up to global economic issues, politics and natural resources on large scales. I think the thing that is so striking is how a shock, like a hurricane, to a about robust-yet-fragile system can lead to cascading failures all the way up the chain.
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From page 340... ...
So, dealing with uncertainty in seismic hazard analysis requires addressing the horizontal challenges -- identifying the range of physical behaviors that are plausible -- and also addressing the vertical challenges, such as uncertainty management and how to pass information between scales in a useful way. You might think of seismic hazard analysis as being represented by the elements in Figure 27, and to some extent they are there in the background.
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From page 341... ...
FIGURE 27 There needs to be more rigorous statistical methodology for combining data in these uncertain worlds, and also to incorporate physical constraints that come from modeling and simulation and ground motion estimates and so on. In this issue of dealing with uncertainty, vertical challenges really dominate our ability to estimate things like losses and risk to human life.
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From page 342... ...
When you have a country like the United States, which basically is self-insuring against natural disasters, one can usually look at the historical record, and one of your early slides did that, to sort of give you a forecast of what the total costs are going to be in any given year. That sets the level at which money must be collected in order to maintain a balance on that.
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