The issue can be posed in terms of finding a level of hazard mitigation that minimizes total cost to society. That cost is the sum of mitigation costs, such as earthquake resistant construction or tsunami defences, plus the expected loss for future earthquakes assuming a given level of mitigation. The expected loss is the sum of losses in various expected events times the assumed probability of each event. As shown, the optimal level of mitigation is the minimum of the cost curve. Less mitigation decreases construction costs but increases the expected loss and thus total cost. More mitigation gives less expected loss but higher total cost.
Similar situations arise for other natural hazards including river flooding and hurricanes,
and in dealing with the effects of global warming. The optimal level of mitigation minimizes the
total of losses and mitigation costs, and depends on the assumed hazard model.
Our ability to find this optimal level of mitigation that balances resources
used for hazard mitigation with other societal needs (schools, hospitals, etc.),
thus depends on our ability to
estimate the probabilities of future events and their effects, and
the uncertainties in these estimates. One of our key lines of research, discussed in the short video below, is
exploring how to make policy given these uncertainties.
For an overview of the work with Jerome Stein, click here for an article excerpted from the Brown Daily Herald, or here. This work is also the subject of a new textbook "Playing Against Nature" (Wiley-Blackwell).
About the book and ordering information
EOS article about a course based on the book
The uncertainties in estimating hazards are illustrated by the fact that it is becoming increasing clear that standard earthquake hazard mapping methods often fail to predict what happens in large destructive earthquakes. We are exploring why this is the case. In general, the problem is that large earthquakes are much more variable in space, time, and magnitude than we often infer from the limited historical record.
A striking example is the March 2011 M 9.1 earthquake off Tohoku, Japan, which
occurred in an area shown by the Japanese national earthquake hazard map to
have relatively low hazard. The short video below explains what went wrong and why.
The figure shown, from Geller ("Shake-up time for Japanese seismology": Nature, 472, 407-409, 28 April 2011) (download pdf of article here) illustrates his point that
"The regions assessed as most dangerous are the zones of three hypothetical 'scenario earthquakes' (Tokai, Tonankai and Nankai; see map). However, since 1979, earthquakes that caused 10 or more fatalities in Japan actually occurred in places assigned a relatively low probability. This discrepancy -- the latest in a string of negative results for the characteristic earthquake model and its cousin, the seismic-gap model -- strongly suggests that the hazard map and the methods used to produce it are flawed and should be discarded."
The hazard map reflected the assumption that magnitude 9 earthquakes would not occur off the Tohoku coast, which led to tsunami defences being built only for a much smaller earthquake than actually occurred, as described by the New York Times (download pdf of article here).
A M9 earthquake involves more slip on a larger fault area, resulting in a larger tsunami because the maximum tsunami run-up height is typically about twice the fault slip (Okal and Synolakis, 2004). Thus the March earthquake generated a huge tsunami that overtopped even 10-meter sea walls, causing enormous damage including crippling nuclear power plants. (For a copy of a video showing the tsunami overtopping the seawall, click here.)
For our paper (Stein and Okal, 2011) about why the hazard mapping failed to expect a magnitude 9 earthquake, click here. Among the problems was the perception that such large earthquakes would not occur subduction zones like this, where the subducting plate is geologically old, as discussed here.
Such problems occur around the world in different tectonic environments, as recently summarized by R. Kerr (Seismic crystal ball proving mostly cloudy around the world, Science, 332, 912-913, 2011.)A striking example, noted by Mian Liu (University of Missouri), is that the 2008 Wenchuan (Sichuan province) M 7.9 earthquake occurred on a fault predicted by the hazard map to have low seismic hazard. Another example is the convergent boundary between Africa and Eurasia in North Africa (Swafford and Stein, 2007). The 1999 Global Seismic Hazard Map showing peak ground acceleration expected at 10% probability in 50 years predicts a prominent hazard "bull-eye" at site of the 1980 M 7.3 El Asnam earthquake. The largest subsequent earthquakes to date, the May 2003 M 6.8 Algeria and February 2004 M 6.4 Morocco events (stars) did not occur in the predicted high hazard regions. The 2010 M 7.1 Haiti earthquake similarly occurred on a fault mapped in 2001 as having low hazard, producing ground motion far greater than the map predicted would occur in 500 years.
As a result, new hazard maps are sometimes made after a big earthquake that the earlier maps missed. The question is whether and how much better the new map predicts than the older one, which may take a while - sometimes hundreds of years - to assess.
A major problem is that although such hazard maps are widely used in many countries, their results have never been objectively tested. Such testing would show how well the maps worked, give a much better assessment of their true uncertainties, and indicate whether or not changes in the methodology over time resulted in improved performance. Most fields of science have had the embarrassment of learning way from objective testing that some commonly used methods don't actually work. For example, a study in 2002 found that although more than 650,000 arthroscopic knee surgeries at a unit cost of roughly $5,000 were being performed each year, a controlled experiment showed that "the outcomes were no better than a placebo procedure" (download pdf of article here).
The failures illustrate that hazard maps often have very large uncertainties, due to our limited knowledge and limited data available, which are often not recognized by their users. Hence we are exploring two related questions discussed in subsequent pages:
How can these uncertainties be assessed and communicated?
What causes these uncertainties?
For overviews of this work to date, see
2014 overview "How much hazard mitigation is enough?" Click here
Short 2014 overview video "Recognizing and acknowledging uncertainty in natural hazard assessment" Click here
2014 overview lecture "Why earthquake hazard maps often fail and what to do about it." Click here for powerpoint
5-minute video summary presented at the 2012 UNAVCO science workshop "Bad assumptions or bad luck: Tohoku's embarrassing lessons for earthquake hazard mapping". Click here to watch
Keynote lecture from the 2011 ESF conference on Extreme Geohazards: "Why natural hazard maps (forecasts, warnings, etc) often fail and what to do about it." (Stein, S., R. Geller, and M. Liu). Click here to watch lecture or click here for powerpoint
Lecture from the 2012 conference on mathematics in the geosciences: "Playing against nature: formulating cost-effective natural hazard policy given uncertainty" (Stein, S. and J. Stein). Click here for powerpoint
Listen to Voice of America radio story here or read the story here
Listen to BBC radio story here or (mp3) here
AGU Blogosphere story "Simple Math Gives Readers X-Ray Vision"
Innovation Blog story "Deep Uncertainty"
Recent publications for this project:
Brooks, E., S. Stein, and B. Spencer, Investigating the effects of smoothing on the performance of earthquake hazard maps, Seism. Res. Lett., submitted, 2015. Click here for pdf
Stein, S., Assessing and mitigating natural hazards in a very uncertain world, in Routledge Handbook of Risk Studies, A. Burgess, A. Alemanno and J. Zinn (eds), in press, 2015. For pdf click here
Stein, S., M. Liu, T. Camelbeeck, M. Merino, A. Landgraph, E. Hintersberger and S. Kubler, Challenges in assessing seismic hazard in intraplate Europe, in Seismicity, Fault Rupture and Earthquake Hazards in Slowly Deforming Regions, A. Landgraph, S. Kubler, E. Hintersberger and S. Stein (eds), Geological Society of London, Special Publications series, volume 432, 2015. For pdf click here
Stein, S., M. Liu, B. Spencer, and E. Brooks, Promise and paradox: why improved knowledge of plate tectonics hasn't yielded correspondingly better earthquake hazard maps, in Plate Boundaries and Natural Hazards, Amer. Geophys. Un. monograph in press, 2015. Click here for pdf
Brooks, E., M. Diggory, E. Gomez, A. Salaree, M. Schmid, N. Saloor, and S. Stein, Should Fermi have secured his water heater?, Seism. Res. Lett., in press, 2015. Click here for pdf
Brooks, E., S. Stein, and B. Spencer, Comparing the performance of Japanese earthquake hazard maps to uniform and randomized maps, Seismological Research Letters, 87, 1, 2016. Click here for pdf
Stein, S., B. Spencer, and E. Brooks, Bayes and BOGSAT: issues in when and how to revise earthquake hazard maps, Seism. Res. Lett., 86, 6-10, 2015. Click here for pdf
Stein, S., B. Spencer, and E. Brooks, Metrics for assessing earthquake hazard map performance, Bull. Seismol. Soc. America, 105, 2015. Click here for pdf
Stein, S., J. Kley, D. Hindle, and A. Friedrich, Exploring natural hazard policies with bike helmets and bus fares, EOS, 96, doi:10.1029/2015EO027187, 31 March 2015. Click here for pdf
Stein, S. and A. Friedrich, How much can we clear the crystal ball?, Astronomy and Geophysics, 55, 2.11-2.17, 2014. Click here for pdf
Stein, J.L. and S. Stein, Formulating natural hazard policies under uncertainty SIAM/ASA J. on Uncertainty Quantification, 1, 42-56, 2013. Click here for pdf.
Stein, S. and J.L. Stein, How good do natural hazard assessments need to be?, GSA Today, 23, no. 4/5, doi: 10.1130/GSATG167GW.1 (April/May), 2013. Click here for pdf
Stein, S. and J.L. Stein, Shallow versus deep uncertainties in natural hazard assessments, EOS, 94, 14, 133-140 (2 April), 2013. Click here for pdf
Stein, S., R. Geller, and M. Liu, Why earthquake hazard maps often fail and what to do about it, Tectonophysics, 562-563, 1-25, 2012. Click here for pdf
Stein, S. and R.J. Geller, Communicating uncertainties in natural hazard forecasts, EOS, 93(38), 361-362, 2012. Click here for pdf
Stein, J.L. and S. Stein, Rebuilding Tohoku: a joint geophysical and economic framework for hazard mitigation, GSA Today, 22(9), 42-44, October 2012. Click here for pdf
Stein, J.L. and S. Stein, Gray Swans: comparison of natural and financial hazard assessment and mitigation, Natural Hazards, DOI 10.1007/s11069-012-0388-x, 2012. Click here for pdf. This analysis comparing weaknesses in hazard assessment and mitigation policies shown by the Tohoku earthquake and 2008 U.S. financial disaster draws on concepts from the book Stochastic Optimal Control and the U.S. Financial Debt Crisis by J. L. Stein (Springer, 2012)
Stein, J.L. and S. Stein, Formulating natural hazard policies under uncertainty, SIAM News, 45/10, 6-7, 2012. Click here for pdf.
Stein, S., R. Geller, and M. Liu, Bad assumptions or bad luck: why earthquake hazard maps need objective testing, Seis. Res. Lett., 82, 623-626, 2011. Click here for pdf
Other sources for this project:
For a general discussion about understanding earthquake hazard maps from Earth Magazine in 2009 click here
For papers illustrating the uncertainties in hazard maps (pdf) click here and here
For a paper discussing biases that can cause future earthquake sizes to be misestimated (pdf) click here
For a discussion about the effects of the spatial sampling window (pdf) click here
Stein, S. and E. Okal, The size of the 2011 Tohoku earthquake needn't have been a surprise, EOS, 92, 227-228, 2011. For pdf click here
Liu, M., S. Stein, and H. Wang, 2000 years of migrating earthquakes in North China: How earthquakes in mid-continents differ from those at plate boundaries, Lithosphere, 3, doi: 10.1130/L129, 2011. For pdf click here
Stein, S., Why seismologists can't predict earthquakes, 2010 Academy of Europe Lecture. For pdf click here
Stein, S. and J. Hebden, Time-dependent seismic hazard maps for the New Madrid seismic zone and Charleston, South Carolina areas, Seis. Res. Lett., 80, 12-20, 2009. For pdf click here
Swafford, L. and S. Stein, Limitations of the short earthquake record for seismicity and seismic hazard studies, in Continental Intraplate Earthquakes, Special Paper 425, 49-58, S. Stein and S. Mazzotti, eds., GSA, Boulder, CO, 2007. For pdf click here
Stein, S., A. Friedrich, and A. Newman, Dependence of possible characteristic earthquakes on spatial sampling: illustration for the Wasatch seismic zone, Utah, Seis. Res. Lett., 76, 432-436, 2005. For pdf click here
Stein, S. and A. Newman, Characteristic and uncharacteristic earthquakes as possible artifacts: applications to the New Madrid and Wabash seismic zones, Seis. Res. Lett., 75, 173-187, 2004. For pdf click here
A. Newman, J. Schneider, S. Stein, and A. Mendez, Uncertainties in seismic hazard maps for the New Madrid Seismic Zone, Seis. Res. Lett., 72, 653-667, 2001. For pdf click here