SCEC Award Number 14070 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Trimming of the UCERF 3 Logic Tree with Portfolio Loss Exceedance Curves
Investigator(s)
Name Organization
Keith Porter SPA Risk LLC
Other Participants Kevin Milner, Ned Field
SCEC Priorities 5c SCEC Groups EEII, WGCEP
Report Due Date 03/15/2015 Date Report Submitted 11/14/2016
Project Abstract
 The size of the logic tree within the Uniform California Earthquake Rupture Forecast Version 3, Time-Dependent (UCERF3-TD) model poses a challenge to risk analyses of large portfolios. An insurer or catastrophe risk modeler concerned with losses to a portfolio of California assets might have to evaluate a portfolio 57,600 times to estimate risk in light of the entire possibility space of hazard. Which branches of the UCERF3-TD logic tree matter most, and which can be ignored? We employed two model-order-reduction techniques to find a subset of UCERF3-TD parameters that must vary and fixed baseline values for the remainder such that the reduced-order model produces approximately the same distribution of loss that the original model does. The two techniques are (1) a tornado-diagram approach we employed previously for UCERF2, and (2) an apparently novel probabilistic sensitivity approach that appears better suited to functions of nominal random variables. The new approach produces a smaller reduced-order model with only 60 leaves. Results can be used to reduce computational effort in loss analyses by several orders of magnitude.
Intellectual Merit We address the question, how strongly do earthquake rupture forecast uncertainties--including many of SCEC's basic questions of earthquake science--influence societal risk? In answering that question, we encounter another much broader one: how to systematically reduce a mathematical model that involves many uncertain nominal numbers. By "nominal numbers" we mean numbers that don't indicate either magnitude or order, like football jersey numbers. In the present case the nominal numbers are indices to competing models of maximum magnitude off faults, recurrence probability models, etc. In previous work, we trimmed UCERF2 with a model-order-reduction (MOR) technique adapted from decision analysis called tornado diagram analysis. Here, we develop and exercise a new probabilistic MOR search algorithm better tailored for models with uncertain nominal numbers. The new algorithm proves far superior to tornado diagram analysis for UCERF3-TD in that it found a much smaller reduced-order-model that still reasonably approximates UCERF3-TD. The new technique found a satisfactory ROM model with only 60 leaves of the original 57,600 on the UCERF3 logic tree. (These include UCERF3's 5,760 earthquake-rupture-forecast leaves, 5 possible GMPEs, and 2 possible models of Vs30.) The smallest satisfactory ROM we found with a tornado diagram has 1,200 leaves; small but not as small as the new method produced. SCEC can target the remaining leaves--spatial PDF, Vs30, scaling relationship, and total M ≥ 5.0 rate--for special study to reduce their uncertainty.
Broader Impacts The new probabilistic model order reduction technique addresses a general mathematical problem that others seem not to have dealt with yet: how to reduce a large mathematical model that contains many nominal random variables. Such problems ought to be numerous. There must be other disciplines where one must select among two or more competing models of quantities where not all the models share the same mathematical form, i.e., where they differ in more than just the particular values of their coefficients.
Exemplary Figure Figure 5. Cumulative distribution function of the original model (black) and reduced-order models (red) by incremental probabilistic model-reduction search: (a) solution 1, and (b) slightly superior solution 2