What to do given that earthquake hazard maps often fail Seth Stein, Northwestern University Robert Geller, University of Tokyo Mian Liu, University of Missouri  NY Times CNN Tohoku, Japan March 11, 2011 M 9.1

NY Times 3/31/2011

Japan spent lots of effort on national hazard map, but 2011 M 9.1 Tohoku, 1995 Kobe M 7.3 & others in areas mapped as low hazard In contrast: map assumed high hazard in Tokai “gap” Geller 2011

Hazard map crucial for mitigation strategy Optimal level of mitigation minimizes total cost = sum of mitigation cost + expected loss Expected loss = ∑ (loss in ith expected event x assumed probability of that event) Less mitigation decreases construction costs but increases expected loss and thus total cost More mitigation gives less expected loss but higher total cost Because assumed probability taken from hazard map, inaccurate map biases mitigation - too low or too high Stein & Stein, 2012

Including risk aversion & uncertainty Consider marginal costs C’(n) & benefits Q’(n) (derivatives) More mitigation costs more But reduces loss Optimum is where marginal curves are equal, n* Benefit (loss reduction) cost Uncertainty in hazard model causes uncertainty in expected loss. We are risk averse, so add risk term R(n) proportional to uncertainty in loss, yielding higher mitigation level n** Crucial to understand hazard model uncertainty Stein & Stein, 2012

Too expensive to rebuild for 2011 sized tsunami Choosing policy involves politics, economics, geoscience “In 30 years there might be nothing left there but fancy breakwaters and empty houses.” NY Times 11/2/2011

Hazard maps fail because of - bad physics (incorrect description of earthquake processes) bad assumptions (mapmakers’ choice of poorly known parameters) bad data (lacking, incomplete, or underappreciated) bad luck (low probability events) and combinations of these (Tohoku!)

Detailed model of segments with 30 year probabilities Off Sanriku-oki North ~M8 0.2 to 10% Off Sanriku-oki Central ~M7.7 80 to 90% Assumption: No M > 8.2 Off Miyagi ~M7.5 > 90% Off Fukushima ~M7.4 7% Off Ibaraki ~M6.7 – M7.2 90% Sanriku to Boso M8.2 (plate boundary) 20% Sanriku to Boso M8.2 (Intraplate) 4-7% Expected Earthquake Sources 50 to 150 km segments M7.5 to 8.2 (Headquarters for Earthquake Research Promotion) J. Mori 8

Giant earthquake broke five segments 2011 Tohoku Earthquake 450 km long fault, M 9.1 Expected Earthquake Sources 50 to 150 km segments M7.5 to 8.2 (Headquarters for Earthquake Research Promotion) (Aftershock map from USGS) J. Mori

Planning assumed maximum magnitude 8 Seawalls 5-10 m high Stein & Okal, 2011 NYT Tsunami runup approximately twice fault slip (Plafker, Okal & Synolakis 2004) M9 generates much larger tsunami CNN

Didn’t consider historical record of large tsunamis NYT 4/20/11

Lack of M9s in record seemed consistent with model that M9s only occur where lithosphere younger than 80 Myr subducts faster than 50 mm/yr (Ruff and Kanamori, 1980) Disproved by Sumatra 2004 M9.3 and dataset reanalysis (Stein & Okal, 2007) Short record at most SZs didn’t include rarer, larger multisegment ruptures Stein & Okal, 2011

NY Times 3/21/11 Why?

Hazard maps are hard to get right: success depends on accuracy of four assumptions over 500-2500 years Where will large earthquakes occur? When will they occur? How large will they be? How strong will their shaking be? Uncertainty & map failure often result because these are often hard to assess

2010 M7 earthquake shaking much greater than maximum predicted for next 500 years 2001 hazard map http://www.oas.org/cdmp/document/seismap/haiti_dr.htm

2008 Wenchuan earthquake (Mw 7 2008 Wenchuan earthquake (Mw 7.9) was not expected: map showed low hazard based on lack of recent earthquakes Didn’t use GPS data showing 1-2 mm/yr (~ Wasatch) Earthquakes prior to the 2008 Wenchuan event Aftershocks of the Wenchuan event delineating the rupture zone

Maps are like ‘Whack-a-mole’ - you wait for the mole to come up where it went down, but it’s likely to pop up somewhere else.

What to do Continue research on fundamental scientific questions (geoscience community’s job!) Realistically assess map uncertainties and present them to help users decide how much credence to place in maps Develop methods to objectively test hazard maps - which hasn’t been done despite their wide use - and thus guide future improvements

Comparing map predictions shows the large uncertainties (~3X) resulting from different assumptions Stein et al, 2012 Newman et al, 2001

Testing analogy: evidence-based medicine objectively evaluates widely used treatments, often with embarrassing results Although more than 650,000 arthroscopic knee surgeries at a cost of roughly $5,000 each were being performed each year, a controlled experiment showed that "the outcomes were no better than a placebo procedure."

Test maps by comparison to what happened after they were published. Bad luck or bad map? Compare maximum acceleration observed to that predicted by both map and null hypotheses. A simple null hypothesis is regionally uniformly distributed hazard. Japanese map seems to be doing worse than this null hypothesis. Geller 2011

Avoid biases from new maps made after a large earthquake that earlier maps missed. Before 2010 Haiti M7 After 2010 Haiti M7 4X Frankel et al, 2010

A posteriori changes to a model are "Texas sharpshooting:” shoot at the barn and then draw circles around the bullet holes.

Challenge: Users want predictions even if they’re poor Future Nobel Prize winner Kenneth Arrow served as a military weather forecaster. As he described, “my colleagues had the responsibility of preparing long-range weather forecasts, i.e., for the following month. The statisticians among us subjected these forecasts to verification and found they differed in no way from chance. The forecasters themselves were convinced and requested that the forecasts be discontinued. The reply read approximately: "The commanding general is well aware that the forecasts are no good. However, he needs them for planning purposes." Gardner, D., Future Babble: Why Expert Predictions Fail - and Why We Believe Them Anyway, 2010