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Examples of Manuscript Components and Description of Electronic SCEC 2013-2014 Annual Report: Trimming the UCERF3 Hazard Logic Tree Prepared for Southern California Earthquake Center Zumberge Hall of Science 169 University of Southern California 3651 Trousdale Parkway Los Angeles, CA 90089-0742 By Keith Porter and Charles Scawthorn SPA Risk LLC Denver CO, USA 19 February 2015 Trimming the UCERF 3.3 logic tree, 2013-2014 annual report 19 Feb 2015 Abstract. This report summarizes an effort to quantify the sensitivity of societal risk to branches in the logic tree of the Uniform California Earthquake Rupture Forecast version 3 (UCERF3, Field et al. 2014). It uses a deterministic sensitivity study sometimes called a tornado-diagram analysis to identify logic-tree branches that matter most to the probability distribution of expected annualized loss (EAL) to California woodframe single-family dwellings. The value of EAL varies between branches of UCERF3. Each branch of the logic tree has an associated marginal probability (in the Bayesian sense) or weight (in the language of frequentists), so EAL has a probability distribution. We identified the branches that matter most to that distribution: probability model, ground motion prediction equation (not an element of UCERF3, but important to EAL), total magnitude-5 rate, and choice of off-fault spatial seismicity probability density function. One can fix the other 5 parameters at arbitrary baseline values without a large bias in CDF of EAL. Varying only these 4 rather than 9 parameters, one can reduce by 99.6% the computational effort required to calculate the distribution of EAL without a substantial difference in the results. www.sparisk.com ii Trimming the UCERF 3.3 logic tree, 2013-2014 annual report 19 Feb 2015 Table of Contents 1 INTRODUCTION AND OBJECTIVES .............................................................................................. 6 2 PROGRESS OF THE WORK .............................................................................................................. 9 2.1 COMPLETED WORK .......................................................................................................................... 9 2.2 LIMITATIONS ................................................................................................................................. 14 3 CONCLUSIONS .................................................................................................................................. 15 4 REFERENCES CITED ....................................................................................................................... 16 www.sparisk.com iii Trimming the UCERF 3.3 logic tree, 2013-2014 annual report 19 Feb 2015 Index of Figures Figure 1. Sensitivity of California statewide expected annualized loss to UCERF2 uncertainties (Porter et al. 2012) ............................................................................................... 7 Figure 2. Portfolio of woodframe single family dwellings ..................................................... 10 Figure 3. Vulnerability functions for woodframe single-family dwellings ............................ 10 Figure 4. Cumulative distribution function of EAL from California woodframe single-family dwellings ................................................................................................................................. 11 Figure 5. Tornado diagram of EAL for California woodframe dwellings .............................. 13 Figure 6. EAL for California woodframe single-family dwellings using the trimmed UCERF3.3 logic tree (red line) versus the full tree (black line) ............................................. 14 www.sparisk.com iv Trimming the UCERF 3.3 logic tree, 2013-2014 annual report 19 Feb 2015 Index of Tables Table 1. UCERF3.3 branches (along with branches for the ground motion prediction equation).................................................................................................................................... 8 Table 2. Sample of California portfolio .................................................................................... 9 Table 3. Layout of inventory table ............................................................................................ 9 Table 4. Tornado diagram results for EAL in California woodframe dwellings .................... 12 Table 5. Tree-trimming of UCERF3.3 considering EAL in California woodframe dwellings ................................................................................................................................................. 13 www.sparisk.com v Trimming the UCERF 3.3 logic tree, 2013-2014 annual report 19 Feb 2015 1 INTRODUCTION AND OBJECTIVES This report summarizes a study funded by the Southern California Earthquake Center. The goal of this project is to assess the sensitivity of selected measures of societal risk to selected branches in the hazard model, in particular to the branches of the Uniform California Earthquake Rupture Forecast version 3 (UCERF3, Field et al. 2014). This report was delayed to accommodate peer review of that publication. By “measures of societal risk” is meant expected annualized loss—either economic or human deaths and injuries—or aspects of the loss-exceedance curve for the same measures. A loss- exceedance curve here means a relationship between loss and mean exceedance frequency. If one can identify a subset of branches that dominate uncertainty in risk, a future risk calculation can focus solely on those branches. The analyst can take the other branches at arbitrary, deterministic values, and thus reduce the computational effort of calculating risk. If the uncertainties that matter can be reduced by further scientific inquiry, one can prioritize future research. We found in prior research (Porter et al. 2012) that the three uncertainties that matter most to UCERF2 were the choice of probability model, ground motion prediction equation (not an element of UCERF2, but an important element of risk), and the magnitude-area relationship. We used a deterministic sensitivity sometimes called a tornado-diagram analysis to produce that knowledge (Howard 1988). The tornado diagram depicts which of two or more uncertain input parameters matter most to a quantity of interest. Let us denote the quantity of interest by y, the input uncertainties as x1, x2, etc., and the functional relationship between them as y f x12, x ,... xin ,... x (1) Each xi is expressed either with a cumulative distribution function or merely reasonable low, typical and high values. Let us denote low, typical, and high values of xi by xilow, xityp, and xihigh, respectively. One first calculates a baseline value of y: ybaseline = f(x1typ, x2typ, ... xityp, ... xntyp) (2) Next, one quantifies the sensitivity of y to variability in each xi using a measure called swing: yilow = f(x1typ, x2typ, ... xilow, ... xntyp) (3) yihigh = f(x1high, x2typ, ... xihigh, ... xntyp) (4) www.sparisk.com 6 Trimming the UCERF 3.3 logic tree, 2013-2014 annual report 19 Feb 2015 swingi = | yihjgh - yilow | (5) One then sorts the xi parameters in decreasing order of swing and plots the results in a horizontal bar chart. The horizontal axis measures y. The uppermost (top) horizontal bar in the chart measures yi with where i is the index for the input parameter with the largest swing. Its left end is the smaller of {yilow, yihigh}. Its right end is the larger of {yilow, yihigh}. The next horizontal bar measures yj where j is the index for the x-parameter with the 2nd-largest swing. Its left end is the smaller of {yjlow, yjhigh}. Its right end is the larger of {yjlow, yjhigh}. The result looks like a tornado in profile. A vertical line is drawn through ybaseline. The result can look like Figure 1, from our previous work on UCERF2. One can then model y as a function of the 2 or 3 or 4 x- parameters that matter most, fixing the rest to their baseline values. Probability model Empirical BPT, 0.3 GMPE CB2008 AS2008 Magnitude-area relationship Ellsworth Hanks & Bakun A-fault solution type Unsegmented Segmented Connect more B faults? True False Deformation model D2.6 D2.2 Fault-slip rates A priori Mo-rate bal Median and B-Faults b-value 0.0 0.8 weighted avg 0.5 1.0 1.5 2.0 Expected annualized loss, $ billion Figure 1. Sensitivity of California statewide expected annualized loss to UCERF2 uncertainties (Porter et al. 2012) The present research aims to perform a tornado-diagram analysis of UCERF3. The UCERF2 logic tree contained 480 logic tree branches. Adding 4 choices of ground motion prediction equation, the total number of branches was 1,920. UCERF3 contains 5,760 branches. With 5 choices of ground motion prediction equation, the total number of branches is 28,800. Despite the greater complexity of UCERF3, the concepts and procedures for trimming its logic tree are the same as in Porter et al. (2012). The uncertainties and their respective numbers of branches are shown in Table 1. www.sparisk.com 7 Trimming the UCERF 3.3 logic tree, 2013-2014 annual report 19 Feb 2015 Table 1. UCERF3 branches (along with branches for the ground motion prediction equation) Variable Branches Cumulative branches 1. ProbModel 4 4 2. GMPE 5 20 3. TotalMag5Rate 3 60 4. SpatialSeisPDF 2 120 5. DeformationModels 4 480 6. ScalingRelationships 5 2400 7. MaxMagOffFault 3 7200 8. SlipAlongRuptureModels 2 14400 9. FaultModels 2 28800 As with the tree trimming of UCERF2, the present analysis requires the following components. 1. An estimated portfolio of assets exposed to shaking—building occupants, building value, etc. The
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