By: Dr. Chih-Hsiang Ho
University of Nevada, Las Vegas
December, 1996

    Reader's Note:   Dr. Chih-Hsiang Ho is a statistics professor in the Department of Mathematical Sciences at the University of Nevada, Las Vegas. He is internationally recognized for his work in the use of statistical models to assess the risk of future volcanic eruptions. He utilized that expertise to conduct a series of probabilistic volcanic risk assessments of Yucca Mountain sponsored by the Nevada Agency for Nuclear Projects. The following discussion summarizes those risk assessment studies.

Multiple-expert hazard/risk assessments have considerable precedent, particularly in Yucca Mountain site characterization studies. A certain amount of expert knowledge is needed to interpret the geological data used in a probabilistic data analysis. As is often the case in science, experts disagree on crucial points. Consequently, a lack of consensus in some studies is a sure outcome. In a paper by Ho and Smith (1996), they present a Bayesian approach to statistical modeling for volcanic hazard assessment for the Yucca Mountain site. Specifically, they show that the expert opinion on the site disruption parameter, p, is incorporated into the prior distribution, (p), based on the geological information that is available. Moreover, (p) can combine all available geological information motivated by conflicting but realistic arguments (e.g., simulation, cluster analysis, structural control, etc.). The incorporated uncertainties about the probability of repository disruption, p, will eventually be averaged out by taking the expectation over (p). They use the following priors in the analysis: (1) priors chosen for mathematical convenience: Beta (r,s) for (r,s)=(2,2),(3,3),(5,5),(2,1),(2,8),(8,2), and (1,1); and (2) three priors motivated by expert knowledge. Sensitivity analysis is performed for each prior distribution. The study concludes that estimated values of hazard based on the priors chosen for mathematical simplicity are uniformly higher than those based on the priors motivated by expert knowledge. And, the model using the prior, Beta (8,2), yields the highest hazard (=2.97x10-2). The minimum hazard is produced by the "three-expert prior" (i.e., values of p are equally likely for = 10-3, 10-2, 10-1). The estimate of the hazard is 1.39x10-3, which is only about one order of magnitude smaller than the maximum value. The term, "hazard," is defined as the probability of at least one disruption of a repository at the Yucca Mountain site by basaltic volcanism over the next 10,000 years.

Smith and Ho (unpublished manuscript, 1996) also evaluate the hazard based on three models: (1) a 3-D homogeneous Poisson process (HPP); (2) a 3-D nonhomogeneous Poisson process (NHPP); and (3) a Bayesian model (Ho, 1992, 1995) using U(0,8/75) as the prior for the repository disruption parameter (readers are referred to the articles of Ho (1992, 1995) for details). A 3-D Poisson model permits identification and quantification of volcanic phenomena distributed through space and evolving in time (i.e., spatiotemporal data). Specifically, they have addressed the following noteworthy features of the model: (1) the model is vulcanologically informative in solving problems of volcanic risk/hazard that depend on the location and time of future events; (2) the computation algorithms of the model fitting procedures are efficient; (3) the model is flexible enough to handle a large class of volcanic risk/hazard studies; and (4) the sensitivity of those statistical models, developed by the experts who have addressed the Yucca Mountain volcanic hazard/risk assessment problem, can be (objectively) evaluated.

The instantaneous temporal recurrence rate (at present time) estimated from a power-law process is about 5.90x10-6/year. The combined temporal-spatial recurrence rate calculated for the 3-D NHPP is between 1.36x10-9 and 3.54x10-9 /year x km2. The recurrence rate obtained based on a 3-D HPP (=1.88x10-9) is in this interval. For this study, the estimated overall probability of at least one disruption of a repository at the Yucca Mountain site by basaltic volcanism for the next 10,000 years (i.e., hazard) is: 1.50x10-4 for a 3-D HPP; 1.09x10-4 to 2.83x10-4 for a 3-D NHPP if is estimated as 2.3x10-4 to 6.0x10-4; and 3.14x10-3 for a Bayesian approach. They also note that the hazard based on an HPP and an NHPP are very comparable as long as the area of the sample region A (estimated as 1,953 km2 for the 3-D HPP) is bounded between 1,035 km2 and 2,701 km2.

Articles in scientific journals authored by C-H Ho.

1. Ho, C.-H and Smith, E.I. 1996. Volcanic Hazard Assessment Incorporating Expert Knowledge: Application to the Yucca Mountain Region, Nevada, U.S.A., Mathematical Geology (accepted).

2. Ho, C-H. 1996. Volcanic Time Trend Analysis, Journal of Volcanology and Geothermal Research (to appear).

3. Ho, C.-H. 1995. Sensitivity in Volcanic Hazard Assessment for the Yucca Mountain High-Level Nuclear Waste Repository Site: The Model and the Data, Mathematical Geology, 27: 239-258.

4. Ho, C.-H. 1992. Statistical Control Chart for Regime Identification in Volcanic Time Series, Mathematical Geology, 24: 775-787.

5. Ho, C.-H. 1992. Risk Assessment for the Yucca Mountain High-Level Nuclear Waste Repository Site: Estimation of Volcanic Disruption, Mathematical Geology, 24: 347-364.

6. Ho, C.-H. 1992. Predictions of Volcanic Eruptions at Mt. Vesuvius, Italy, Journal of Geodynamics, 15: 13-18.

7. Ho, C.-H. 1991. Time Trend Analysis of Basaltic Volcanism near the Yucca Mountain Site, Journal of Volcanology and Geothermal Research, 46: 61-72.

8. Ho, C.-H., Smith, E.I., Feuerbach, D.L., and Naumann, T.R. 1991. Eruptive Probability Calculations for the Yucca Mountain Site, U.S.A.: Statistical Estimation of Recurrence Rates, Bulletin of Volcanology, 54: 50-56.

9. Ho, C.-H. 1991. Nonhomogeneous Poisson Model for Volcanic Eruptions, Mathematical Geology, 23: 167-173.

10. Ho, C.-H. 1990. Bayesian Analysis of Volcanic Eruptions, Journal of Volcanology and Geothermal Research, 43: 91-98.

Unpublished manuscripts in preparation for submittal to scientific journals.

1. Ho, C.-H. and Smith 1996. A Spatial-Temporal/ 3-D Model for Volcanic Hazard Assessment: Application to the Yucca Mountain Region, Nevada.

2. Ho, C-H. 1996. Mount Vesuvius: Time Regimes in 1631-1944.