Disaster estimations - Part 1b/3 Understanding the probability of disaster

Part 1 of my post on modeling catastrophic risk covered measuring the probability that a risk even can occur. This probability can derived based on empirical evidence as well as from other computer models that underlie destructive forces of nature. A good example of a paper that talks about how such a model is built and used is outlined in this paper by Karen Clark, a renowned catastrophic risk modeler and insurer. The paper was a seminal one when it came out as it outlined a scientific method by which such risks could be estimated. The paper is titled "A formal approach to catastrophe risk assessment and management" and the link is here.

The paper outlines an approach to estimate losses from hurricanes impacting the US Gulf coast and the East Coast. The model has a probability assessment for hurricanes making landfall, developed using historical information (going back to about 1910) from the US Weather Service. While this is a great starting point and helps us get to a good estimate of at least a range of losses one can expect and therefore the insurance premiums one should expect to sell, there are important places where the model can be improved. One example is the cyclical nature of hurricane intensity over the last 100 years. Between 1950 and 1994, the Atlantic hurricanes have run through a benign cycle. Hurricane activity and intensity (as measured by the number of named storms and the number of major hurricanes, respectively) have shown an increase since 1994, though. So a model relying on activity from the 1950-1994 period is likely to be off in its loss estimates by more than 20%. See the table for what I am talking about.

How can a modeler correct for such errors in estimates? One way to correct for these estimates is to use the latest in scientific technology and modeling in estimating the probabilities. Developments in scientific understanding of phenomena such as hurricanes means that it is now possible to build computer models that replicate the physics behind the hurricanes. The dynamic physical models incorporate some of the more recent understanding of world climatology, such as the link between Sea Surface Temperatures or SSTs and hurricane intensity. Using some of these models, researchers have been able to replicate the increase in hurricane intensity seen in the last fifteen years in a way that the empirical models built prior to this period have not been able to. The popular science book about global warming called Storm World by Chris Mooney spells out these two different approaches to hurricane intensity estimation, and the conflicts between the chief protagonists of each of these approaches. Based on the recent evidence at least, the more physics based approach certainly appears to be tracking closer to the rapid changes to hurricane intensity. William Gray of Colorado State University, whose annual hurricane forecast has been lucky for many years has been forced to re-fit his empirical model for the rapid increase in hurricane intensity post-1995.

Finally, I leave you with another note about how some of the dynamic physical models work. This is from one of my favourite blogs which is Jeff Masters' tropical weather blog. The latest entry talks precisely about such a dynamic physical model built by the UK Met Office. And I quote:

it is based on a promising new method--running a dynamical computer model of the global atmosphere-ocean system. The CSU forecast from Phil Klotzbach is based on statistical patterns of hurricane activity observed from past years. These statistical techniques do not work very well when the atmosphere behaves in ways it has not behaved in the past. The UK Met Office forecast avoids this problem by using a global computer forecast model--the GloSea model (short for GLObal SEAsonal model). GloSea is based on the HadGEM3 model--one of the leading climate models used to formulate the influential UN Intergovernmental Panel on Climate Change (IPCC) report. GloSea subdivides the atmosphere into a 3-dimensional grid 0.86° in longitude, 0.56° in latitude (about 62 km), and up to 85 levels in the vertical. This atmospheric model is coupled to an ocean model of even higher resolution. The initial state of the atmosphere and ocean as of June 1, 2010 were fed into the model, and the mathematical equations governing the motions of the atmosphere and ocean were solved at each grid point every few minutes, progressing out in time until the end of November (yes, this takes a colossal amount of computer power!) It's well-known that slight errors in specifying the initial state of the atmosphere can cause large errors in the forecast. This "sensitivity to initial conditions" is taken into account by making many model runs, each with a slight variation in the starting conditions which reflect the uncertainty in the initial state. This generates an "ensemble" of forecasts and the final forecast is created by analyzing all the member forecasts of this ensemble. Forty-two ensemble members were generated for this year's UK Met Office forecast. The researchers counted how many tropical storms formed during the six months the model ran to arrive at their forecast of twenty named storms for the remainder of this hurricane season. Of course, the exact timing and location of these twenty storms are bound to differ from what the model predicts, since one cannot make accurate forecasts of this nature so far in advance.

The grid used by GloSea is fine enough to see hurricanes form, but is too coarse to properly handle important features of these storms. This lack of resolution results in the model not generating the right number of storms. This discrepancy is corrected by looking back at time for the years 1989-2002, and coming up with correction factors (i.e., "fudge" factors) that give a reasonable forecast.

If you go to the web-page of the UK Met Office hurricane forecast, you can find a link of interest Reinsurance companies. This link is to buy the hurricane forecast which the UK Met Office has obviously gone to great pains to develop. Their brochure on how the insurance industry could benefit from this research makes for very interesting reading as well.

The BP oil spill and the disaster estimations - Part 1/3

The BP oil spill is already the biggest oil spill in the US and is on its way to becoming an unprecedented industrial disaster, given the environmental impact of millions of barrels of oil gushing into the Gulf of Mexico. Even the most hardened of carbon lovers cannot but be moved at the sight of the fragile wildlife in the Gulf literally soaking in the oil. The ecosystem of the Gulf states which were already ravaged by unrestrained development and the odd super-cyclone is now being struck a death blow by the spewing gusher.

Could the specific chain of events leading up to this spill have been predicted? The answer is no. But that doesn't mean that the outcome could not have been anticipated. Given the technological complexity that some of the deep-sea oil drilling operations typically involve, there was always a measurable probability that one of the intermeshing systems and processes would give way and result in an oil-well that was out of control. As Donald Rumsfeld, Secretary of Defense in the Bush II administration put it, stuff happens. But where there has been an abject failure of human science and industrial technology has been in underestimating the impact of this kind of an event on a habitat and overestimating the power of technology to fix these kinds of problems.

Fundamentally, the science of estimating the impact of disasters can be broken down into three estimations:
one, an estimation that failure occurs
second, the damage expected as a result of the failure
the third, (which is probably a function of the second) are our capabilities in fixing the failure or mitigating the impact of the failure.

In this post, I will discuss the first part of the problem - estimating the probability of failures occurring.

There is a thriving industry and a branch of mathematics that works on the estimation of these extremely low probability events known as Disaster Science. The techniques that the disaster scientists or statisticians use are based on the understanding of the specific industry (nuclear reactors, oil drilling, aerospace, rocket launches, etc.) and is constantly refreshed with the our increasing understanding of the physics or science in general underlying some of these endeavours. The nuclear-power industry's approach analyzes the engineering of the plant and tabulates every possible series of unfortunate events that could lead to the release of dangerous radioactive material, including equipment failure, operator error and extreme weather. Statisticians tabulate the probability of each disastrous scenario and add them together. Other industries, such as aviation, use more probability based models given the hundreds of thousands of data points available on a weekly basis. Then there are more probabilistic approaches such as tail probability estimation or extreme event estimation which uses math involving heavy-tailed distributions for the probability estimation of such events occurring. Michael Lewis in his inimitable style talked about this in an old New York Times article called In Nature's Casino.

One variable that is a factor and often the contributing factor in many such disasters is human error. Human error is extraordinarily difficult to model, just based on past behaviour because there are a number of factors that could just confound such a read. For instance, as humans encounter fewer failures, our nature is to become less vigilant and therefore at greater risk of failing. Both lack of experience and too much experience (especially without having encountered failures) are risky. The quality of the human agent is another variable that has wide variability. At one time, NASA had the brightest engineers and scientists from our best universities join. Now, the brightest and the best go to Wall Street or other private firms and it is often the rejects or the products of second-rung universities that make it to NASA. This variable of human quality is difficult to quantify or sometimes difficult to measure in a way that does not offend people on grounds like race, national origin, age and gender. Let us suppose that the brightest and the best joining NASA previously came from colleges or universities where admission standards required higher scores on standardized tests. Now we know that standardized test scores are correlated with the socio-economic levels of the test takers and hence to variables such as income, race, etc. So now if NASA goes to lower rung colleges, does it mean that it was being more exclusive and discriminatory before (by taking in people with average higher scores) and is now more inclusive now? And can we conclude that the drop in quality now is a direct function of becoming more inclusive on the admission criteria front? It is never easy to answer these questions or even tackle the question without feeling queasy about what one is likely to find while answering the question.

Another variable, again related to the human factor is the way we interact with technology. Is the human agent at ease with the technology confronting him or does he feel pressured and unsure from a decision making standpoint? I have driven stick-shift cars before and I have been more comfortable and at ease with the decision making around gear changes when the car-human interface was relatively simpler and spartan. In my most recent car, as I interact with multiple technology features such as the nav system, the bluetooth enabled radio, the steering wheel, the paddle shifter, the engine revs indicator, I find my attention diluted and I have seen that the decision making around gear changes is not as precise as it used to be.