what is the `reasonable worst case'?mar 08, 2020 · i the idea of areasonable worst case...
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![Page 1: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/1.jpg)
What is the ‘Reasonable Worst Case’?
Jonathan (Jonty) Rougier
Rougier Consulting Ltdwww.rougierconsulting.com
&School of Mathematics
University of Bristol
ADMLC meeting, March 2020
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Introduction
I With a hazard class, we find a wide range of events, varying inall sorts of ways that affect damage and harm.
I The idea of a Reasonable Worst Case (RWC) is to select anexamplar event for the hazard class, primarily to allow easiercomparison across hazard classes (although there are otherways to achieve this).
I One critical feature, which is applicable across all hazardclasses, is a notion of event size, although the precisedefinition often depends partly on what can be measured.
I Above a (usually low) threshold, frequency of hazard eventsdiminishes with size (thank goodness). A good starting-pointfor a RWC is the question – What size event?
![Page 3: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/3.jpg)
Introduction
I With a hazard class, we find a wide range of events, varying inall sorts of ways that affect damage and harm.
I The idea of a Reasonable Worst Case (RWC) is to select anexamplar event for the hazard class, primarily to allow easiercomparison across hazard classes (although there are otherways to achieve this).
I One critical feature, which is applicable across all hazardclasses, is a notion of event size, although the precisedefinition often depends partly on what can be measured.
I Above a (usually low) threshold, frequency of hazard eventsdiminishes with size (thank goodness). A good starting-pointfor a RWC is the question – What size event?
![Page 4: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/4.jpg)
Introduction
I With a hazard class, we find a wide range of events, varying inall sorts of ways that affect damage and harm.
I The idea of a Reasonable Worst Case (RWC) is to select anexamplar event for the hazard class, primarily to allow easiercomparison across hazard classes (although there are otherways to achieve this).
I One critical feature, which is applicable across all hazardclasses, is a notion of event size, although the precisedefinition often depends partly on what can be measured.
I Above a (usually low) threshold, frequency of hazard eventsdiminishes with size (thank goodness). A good starting-pointfor a RWC is the question – What size event?
![Page 5: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/5.jpg)
Introduction
I With a hazard class, we find a wide range of events, varying inall sorts of ways that affect damage and harm.
I The idea of a Reasonable Worst Case (RWC) is to select anexamplar event for the hazard class, primarily to allow easiercomparison across hazard classes (although there are otherways to achieve this).
I One critical feature, which is applicable across all hazardclasses, is a notion of event size, although the precisedefinition often depends partly on what can be measured.
I Above a (usually low) threshold, frequency of hazard eventsdiminishes with size (thank goodness). A good starting-pointfor a RWC is the question – What size event?
![Page 6: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/6.jpg)
Explosive eruptions in Iceland
Source: https://en.wikipedia.org/wiki/2011_eruption_of_Grimsvotn
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Explosive eruptions in IcelandLarge (at least 0.1 Gt) explosive eruptions in Iceland
Source: LaMEVE database, dated 07/06/2018. Eyjafjallajokull (2010)was 0.1 Gt; Grımsvotn (2011) was 0.25 Gt.
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Explosive eruptions in Iceland1-year Exceedance Probability curve
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Explosive eruptions in Iceland1-year Exceedance Probability curve
![Page 10: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/10.jpg)
Explosive eruptions in Iceland
1-year Exceedance Probability curve 1-year EP
The probability of atleast one eruption atleast as large asGrımsvotn (1783) in thenext year is about 0.009,or 1-in-111.
The ‘return period’ forsize s is reasonablydefined as 1 / the 1-yearEP for size s: ‘meanyears to wait until anevent of size at least s’.
EPs can be for anyduration; 100-year EPsare common forinfrastructure.
![Page 11: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/11.jpg)
Explosive eruptions in Iceland
1-year Exceedance Probability curve 1-year EP
The probability of atleast one eruption atleast as large asGrımsvotn (1783) in thenext year is about 0.009,or 1-in-111.
The ‘return period’ forsize s is reasonablydefined as 1 / the 1-yearEP for size s: ‘meanyears to wait until anevent of size at least s’.
EPs can be for anyduration; 100-year EPsare common forinfrastructure.
![Page 12: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/12.jpg)
Explosive eruptions in Iceland
1-year Exceedance Probability curve 1-year EP
The probability of atleast one eruption atleast as large asGrımsvotn (1783) in thenext year is about 0.009,or 1-in-111.
The ‘return period’ forsize s is reasonablydefined as 1 / the 1-yearEP for size s: ‘meanyears to wait until anevent of size at least s’.
EPs can be for anyduration; 100-year EPsare common forinfrastructure.
![Page 13: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/13.jpg)
‘Reasonable Worst Case’ scenario
Exemplar event that stands in for the whole EP curve
I My suggestion:1. Big enough to cause substantial harm (obvs)
2. Not so big as to have incalculable losses
3. An historical event can be very usefulI A convenient label (‘another Grımsvotn’)I Likelihood from the 1-year EP curve (see below)I Lots of incidental detail to help assess impact
I If your RWC is the largest event in the last h years, then, under amild stationarity condition, your 1-year EP is 1/(h + 1) ≈ 1/h.
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‘Reasonable Worst Case’ scenario
Exemplar event that stands in for the whole EP curve
I My suggestion:1. Big enough to cause substantial harm (obvs)
2. Not so big as to have incalculable losses
3. An historical event can be very usefulI A convenient label (‘another Grımsvotn’)I Likelihood from the 1-year EP curve (see below)I Lots of incidental detail to help assess impact
I If your RWC is the largest event in the last h years, then, under amild stationarity condition, your 1-year EP is 1/(h + 1) ≈ 1/h.
![Page 15: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/15.jpg)
‘Reasonable Worst Case’ scenario
Exemplar event that stands in for the whole EP curve
I My suggestion:1. Big enough to cause substantial harm (obvs)
2. Not so big as to have incalculable losses
3. An historical event can be very usefulI A convenient label (‘another Grımsvotn’)I Likelihood from the 1-year EP curve (see below)I Lots of incidental detail to help assess impact
I If your RWC is the largest event in the last h years, then, under amild stationarity condition, your 1-year EP is 1/(h + 1) ≈ 1/h.
![Page 16: What is the `Reasonable Worst Case'?Mar 08, 2020 · I The idea of aReasonable Worst Case (RWC)is to select an examplar event for the hazard class, primarily to allow easier comparison](https://reader033.vdocuments.site/reader033/viewer/2022051922/600f7fda5a51c148fd5b64a2/html5/thumbnails/16.jpg)
‘Reasonable Worst Case’ scenario
Exemplar event that stands in for the whole EP curve
I My suggestion:1. Big enough to cause substantial harm (obvs)
2. Not so big as to have incalculable losses
3. An historical event can be very usefulI A convenient label (‘another Grımsvotn’)I Likelihood from the 1-year EP curve (see below)I Lots of incidental detail to help assess impact
I If your RWC is the largest event in the last h years, then, under amild stationarity condition, your 1-year EP is 1/(h + 1) ≈ 1/h.