On High-Probability, High-Consequence Events

My friends in the nuclear weapons community have, over the years, helped me understand the tools for thinking about low-probability, high-consequence events, like a warhead accidentally going off. You really don’t want that to happen, so even though averaged across all possible futures the average badness might be relatively low, it’s worth spending some time and energy thinking through ways of reducing the probability of the high-consequence event.

But if the chance of the truly horrific event is somewhere betwen 57 and 95 percent over the next four decades? Holy crap. If you’ve seen that coming and haven’t already started doing an awful lot to try to drive that number down, your system for solving societal problems is seriously fucked up.

57 to 95 percent is the estimated probability of the levees in California’s San Joaquin-Sacramento Delta failing between now and 2050, according to a new report that Rober Service talks about in yesterday’s Science magazine (subscription). Put another way, there’s at least a 57 percent chance that the system that delivers water to half of all Californians will stop delivering water to half of all Californians:

By 2050, the chance of widespread levee failures is as high as 95%, due to runoff from the northern Sierras, which is predicted to be more concentrated in the late winter and early spring, and the increasing risk of earthquake, according to a report last summer by the Public Policy Institute of California (PPIC). If that occurs, salt water from the San Francisco Bay would rush in to fill the voids, dramatically increasing the salinity of water in the delta, possibly making it undrinkable. Adding sea-level rise to the equation–as climate models predict–brings the date of levee failures closer. “It will happen,” says Ellen Hanek, a PPIC economist in San Francisco.

update: Of possible interest to those who follow discussions of journalism and science, when I first wrote this post, I took Service’s word for the 95 percent figure he used in his article without taking careful note of the “as high as” qualifier he used. When I reread the post and noticed the qualifier, I went and found the original PPIC report and found that they actually say this:

[T]he best possible failure probability under rapid rates of sea level rise, high seismic risk and increasing inflows is approximated by the island with least current combined risk of failure from flooding and earthquakes at 2 percent per year, for a cumulative probability of failure of 57 percent by 2050. For the high end of risk, we used the current estimated combined flood and earthquake annual failure probability of the western Delta islands of approximately 7 percent per year, or a cumulative probability of failure of 95 percent by 2050.

So 57 and 95 percent reasonably bracket the risk as estimated by PPIC, and don’t materially change the “holy crap” tone of my reaction. (And I haven’t read the whole report, just found the section that explained their risk numbers in brief.)


  1. I will blog on this (thanks for reminding me), but I will note right now that failure of the levees (really dikes, since the “islands” are really polders, i.e., below sealevel…) would mean little to the ecosystem, a LOT to the people with land underwater and MUCH MORE to the delta water exporters…

    That’s their excuse for a peripheral canal, but it’s my excuse to see that SoCal lives off “its” water. I am NOT saying this as a NorCal partisan, but as someone tired of the bad economics/ecology of moving water all over the place.

  2. The report basically recommends accepting that most of the islands will have to be abandoned (flooded) and that a PC is the only practical option for maintaining exports in the face of this change. That degree of realism is a step forward, but the problem is that unlike the present water transfer arrangement a PC will make possible the near-complete destruction of the Delta ecosystem. I’m not sure it’s going to be possible to pass any sort of PC proposal without requiring massive changes in Central Valley and SoCal water use, but I’m pretty sure they’ll try to pass a window-dressing-only version before considering any such thing. Note that the principal funder of the study was Stevie Bechtel, it being a small world after all.

    I’ll look forward to your post, David.

  3. It appears that the calculated probability of failure in the PPIC report (which I have not read in its entirety yet) is (1 – probability of not failing) and the probability of not failing is viewed as a constant for every year from now until 2050.

    If the yearly probability of failing is 7% then the yearly probability of not failing, for this example, would be 93%.
    Does anyone know whether this constant yearly probability of failing is a reasonable assumption for the Sacramento delta?

    I would think that the probability of failing each year is not a constant but depends on what happened last year. For instance, if there was a small earthquake one year, one that would not generate a real failure, then the levees would be strengthened and the probability of failure in the following year and for subsequent years would drop dramatically.

    In statistical terms, such a process is not modeled by a constant probability of failure but is often modeled by a Monte Carlo version of a Markov process. In such a modeling, small partial failures are included and modify subsequent yearly predictions. The Monte Carlo approach comes in because it is not known in what year the small failure would occur so averaging over each possible occurrence is important.

    Could someone tell me where the failure estimate in this report came from and whether the assumptions about failure are generic or are matched to real world events, such as partial failures, changing technology, or changing political climate?


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