ptha based on psha – methodology and applicationsthis presentation focused on the suitability of...

PTHA Based on PSHA – Methodology and Applications

Frank I. González University of Washington, Dept. Earth and Space Sciences

This presentation focused on the suitability of the current version of Probabilistic Tsunami Hazard Analysis (Geist and Parsons, 2005; González, et al., 2009), which is based on Probabilistic Seismic Hazard Analysis (Cornell, 1968; SSHAC, 1997), for estimates of exceedance probabilities associated with tsunamigenic landslides. Early in the presentation, fundamental questions and a discussion by workshop participants focused on a basic assumption of PTHA – i.e., that probabilities of exceedance can be modeled as a Poisson distribution; although appropriate for earthquakes, a Poissonian probability distribution might not properly represent the underlying physics of tsunamigenic landslides. With resolution of this issue flagged as critical, the remaining components of the existing methodology were reviewed, and two applications of PTHA were presented and discussed -- the results of a previous study of Seaside, OR, and plans for a PTHA study of Crescent City, CA.

References

Cornell, C. A. (1968), Engineering seismic risk analysis, Bull. Seismol. Soc. Am., 58, 1583-1606.

Senior Seismic Hazard Analysis Committee (SSHAC) (1997), Recommendations for Probabilistic Seismic Hazard Analysis: Guidance on Uncertainty and Use of Experts, Main Report Rep. NUREG/CR-6372 UCRL-ID-122160 Vol. 1, 256 pp, U.S. Nuclear Regulatory Commission.

Geist, E. L., and T. Parsons (2005): Probabilistic Analysis of Tsunami Hazards, Nat. Hazards, 37 (3), 277-314.

González, F.I., E.L. Geist, B. Jaffe, U. Kânoğlu, H. Mofjeld, C.E. Synolakis, V.V. Titov, D. Arcas, D. Bellomo, D. Carlton, T. Horning, J. Johnson, J. Newman, T. Parsons, R. Peters, C. Peterson, G. Priest, A. Venturato, J. Weber, F. Wong, and A. Yalciner (2009): Probabilistic tsunami hazard assessment at Seaside, Oregon for near- and far-field sources. J. Geophys. Res., 114, C11023

F. I. González, UW/ESS

PTHA Based on PSHA: Methodology & Applications !

!!

Frank González!U. Washington -- Earth & Space Sciences!

!!!

NRC/USGS Workshop on Landslide Tsunami Probability !!

August 18-19, 2011!Woods Hole, Massachusetts"

Conclusions


◊ In principle, the formal PTHA mathematics doesn’t care about the nature of the sources – i.e., sources could be landslides

• Poisson assumption still appropriate • Uncertainty issues are similar

- Mean inter-event period - Source details (for stochastic approach) Seismic: magnitude, slip distribution, Landslide: volume, speed, etc, … - Tidal Stage

◊ Formal Risk Analysis: • PTHA extension to output forces on structures and/or other impact

indices, e.g., momentum flux = ( ζ + d )V2 • “failure PDFs”

PTHA derived from PSHA"


Cornell, C. A. (1968), Engineering seismic risk analysis, Bull. Seismol. Soc. Am., 58, 1583-1606.

Senior Seismic Hazard Analysis Committee (SSHAC) (1997), Recommendations for Probabilistic Seismic Hazard Analysis: Guidance on Uncertainty and Use of Experts, Main Report Rep. NUREG/CR-6372 UCRL-ID-122160 Vol. 1, 256 pp, U.S. Nuclear Regulatory Commission.

Geist, E. L., and T. Parsons (2005): Probabilistic Analysis of Tsunami Hazards, Nat. Hazards, 37 (3), 277-314.

Geist, E. L., T. Parsons, U. S. ten Brink, and H. J. Lee (2009), Tsunami Probability, in The Sea, v. 15, edited by E. N. Bernard and A. R. Robinson, pp. 93-135, Harvard University Press, Cambridge, Massachusetts.

González, F.I., E.L. Geist, B. Jaffe, U. Kânoğlu, H. Mofjeld, C.E. Synolakis, V.V. Titov, D. Arcas, D. Bellomo, D. Carlton, T. Horning, J. Johnson, J. Newman, T. Parsons, R. Peters, C. Peterson, G. Priest, A. Venturato, J. Weber, F. Wong, and A. Yalciner (2009): Probabilistic tsunami hazard assessment at Seaside, Oregon for near- and far-field sources. J. Geophys. Res., 114, C11023.

Context of PTHA applications at Seaside OR and Crescent City, CA


• Time Scales of Interest: 100 - 500 years -  FEMA Federal Insurance Rate maps -  Guidance for State Emergency Management Program

• Seismic sources only • Gradual Evolution in Inundation Mapping

-  Worst Case Scenario(s) -  Response Analyses -  PTHA

Scientifically defensible scenario(s)!Walsh, et al., 2003."


Credible Worst Case(s)

Seattle Fault: M=7.3 ~ AD 900-930

Tsunami Inundation Depth

Sensitivity Analysis"


Site-specific response to many scenarios

Tang, et al., 2006.

Probabilistic Tsunami Hazard Assessment (PTHA)

100-yr Tsunami"500-yr Tsunami"

Probability that wave height will exceed a given level within a certain period of time. Geist and Parsons (2005), González et al. (2009)


• Poissonian Probability

• Main Uncertainties

- Mean Inter-event Period of Earthquakes - Seismic Slip Distribution - Tidal Stage

• Spatial Distribution of Hazard Curves in Inundation Zone

Primary PTHA features"

PTHA Methodology"


• Assume Poissonian probability that wave height ζ will exceed level ζi in time T for source with recurrence rate µj (Tetra Tech Inc. ,1981; Ward, 1994)

Convention: i subscript for (specified) wave height level that

is exceeded j subscript for jth earthquake source

T = 1 year for Annual Probability µj = 1/TMj = inverse of mean interevent time for

the jth earthquake source

Models the probability of relatively rare events occurring in a fixed time if events occur with known average rate, independently of time since last event.

• Combined probability for multiple (independent) sources that level ζi will be exceeded

Schematic"


ζ50 , ζ100 , ζ500 … etc.!at every point (x,y):!

Sources: • Physical Parameters • Probability of

Occurrence Computational Grids: • Bathymetry • Topography

• Generation • Propagation • Inundation

• η(x,y) • u(x,y) • v(x,y)

Model Input"Model

Computations"Model"Output"

Exceedance Value Computations"Equations (1)-(6) in González, et al. (2009).


Must Update this Table for CC PTHA Study"


Near-Field detail (1 of 12)"

Model 14Mw 9.2

Model 9-13Mw 8.5-8.8

Model 1-8Mw 8.2-9.2

Local Cascadiasources - 12

All Sources: Far- & Near-field"

(TM is mean interevent time)

Construct a Gaussian approximation to PDF of (Tsunami + Tide) time series"


where for tides ξ , the series mean ζ0 and standard deviation σ ,

with ζ0 and σ approximated by a function of η and standard tidal parameters: ̂ tude A, the widths of the !m " A PDFs spread and theircenters decrease in height from MHHW toward MSL(datums for Seaside were computed from harmonicconstants by the method of Mofjeld et al. 2004b). Thedecrease in the maximum values occurs as the PDFsbroaden because the height integral of each PDF needsto be unity. As expected, the PDFs converge to that ofthe predicted tide as A becomes large compared withthe tidal range.

Figure 4 gives an example of how a Gaussian PDFoften closely resembles the shape of the empiricalPDFs, where the mean height !o and the standard de-viation # are computed from the latter

P$y% & B exp'"$y " !o%2"2#2(, B"1 & )2$#,

$1%

where B is chosen so that the height integral of P isunity. This leads to a compact characterization (Fig. 5)of the PDFs in terms of !o and # as functions of theinitial tsunami amplitude A for each coastal location.Note that !o is the most probable height for the com-bined tsunami and tide, while *1.96# gives the 95%confidence limits for Gaussian distributions. The inte-gral of (1) from a height y to + is the cumulative densityfunction that provides the probability that the maxi-mum tsunami height of an event will exceed the valueof y.

Figure 5 shows curves of !o and # for Seaside, Ko-

diak, Crescent City, and Hilo. The latter three stationshave a long history of damaging tsunamis, and numeri-cal tsunami models are often tested and calibrated us-ing these sites. Their tides are typical of the coastal tidesin the northern Gulf of Alaska, northern California,and Hawaii, respectively. While !o and # at Seaside,Kodiak, and Crescent City vary throughout the rangeA % 10 m (Fig. 5), these parameters reach their asymp-totic values much more quickly at Hilo because thetidal range is relatively small in Hawaii as comparedwith those in the other North Pacific regions.

4. Formulas for !o and "

It is possible to compute the mean height !o andstandard deviation # for each tsunami amplitude A andlocation of interest. However, this becomes very com-putationally intensive in numerical tsunami modelingwhen tsunami heights are estimated at high resolutionalong a section of coastline. It is therefore useful to lookfor empirical formulas for !o and # as functions of A,which can be put into the Gaussian PDF (1) when thisapproximation is acceptably close to the PDF for agiven purpose.

FIG. 4. PDFs computed from the time series of maximum tsu-nami wave heights and a Gaussian PDF with the same meanheight !o and standard deviation #.

FIG. 5. Analytic fits to (a) the mean height !o and (b) standarddeviation # as functions of tsunami amplitude A.

120 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24

Tidal Stage uncertainty"

Mofjeld, et al., (2007): Effects of tides on maximum tsunami wave heights: Probability distributions, J. Atmos. Ocean. Technol., 24 (1), 117-123.

Construct Gaussian approximation to PDF of (Tsunami + Tide)"


lar to the method used by Houston and Garcia (1978) intheir statistical study of tsunamis along the U.S. WestCoast.

Of particular interest in the present study are wherethe maximum wave heights tend to cluster in elevationabove MLLW and how the spread in elevation of thePDFs depend on the initial tsunami amplitude relativeto the tidal range. It is found that a simple Gaussianform fits the PDFs reasonably well. Furthermore, modi-fied exponential laws are found to closely approximatethe dependences of the PDF mean heights and standarddeviations on the initial tsunami amplitude; these twoparameters are sufficient to quantitatively determinethe Gaussian PDF. The coefficients in the exponentiallaws provide a concise characterization of the tidal ef-fects on the maximum tsunami heights for a given lo-cation.

In the next section, theoretical tsunamis are super-imposed on predicted tides on the open coast at Sea-side, Oregon. These mixed semidiurnal tides are typicalof those along the U.S. West Coast. This serves to il-lustrate the influence of the tides on the maximum ofthe total wave height (tsunami wave plus tide) for wavetrains of various initial amplitudes. This height is la-beled by the arrival time of the first tsunami wave peakso that time series (loci) of maximum wave heights canbe plotted as functions of the arrival time. In section 3,it is convenient to use the differences between theseheights and the initial tsunami amplitude in order tocompare PDFs when the initial amplitude is varied.Subsequent sections justify the modified exponentiallaws for the coefficients in the Gaussian approximationto the tsunami PDFs and present values of these coef-ficients for 29 U.S. Pacific tide stations plus the Seasidelocation. The discussion addresses the influence of the18.6-yr nodal cycle of the tides, the insensitivity to usingobserved or predicted tides for fitting the coefficients,and limiting the application of the theory to situationswhere nonlinear interactions between tsunamis and thetides can be neglected.

2. Tsunami time seriesFigure 1 shows a typical tsunami time series used in

this study. The wave period of 20 min is withinthe middle range (10–40 min) of major transpacifictsunamis striking the U.S. West Coast. The theoreticaltsunami arrives at Seaside, Oregon (46!00.1°N,123!55.7°W), at 0000 UTC 2 January 2004. The tides atSeaside are typical of those along the northwestern sec-tion of the West Coast; this is also the site for a proba-bilistic tsunami pilot study recently carried out by theFederal Emergency Management Agency (FEMA), theNational Oceanic and Atmospheric Administration

(NOAA), and the U.S. Geological Survey (USGS). De-caying exponentially in amplitude, the maximum tsu-nami height (4.91 m above MLLW) for this event thenoccurs at 1604 UTC, the next higher high water. Theuse of an exponentially decaying envelope to charac-terize the maximum wave heights along sections of tsu-nami time series is justified by the case studies andstochastic modeling of Mofjeld et al. (1997, 2000). InFig. 1 as well as elsewhere in the study, the decay co-efficient (" # 2.0 days) is set by observations of Pacific-wide tsunamis (e.g., Mofjeld et al. 2000). The predictedtides are based on 37 harmonic constants, where thosefor O1, K1, N2, M2, and S2 are from the Eastern NorthPacific 2003 (ENPAC 2003) tide model (for details, seeSpargo 2003; Mofjeld et al. 2004a); the others are in-ferred from observed relationships at South Beach, Or-egon (44°37.5$N, 124°02.6$W).

Moving the tsunami arrival time to progressivelylater times then generates time series for the maximumwave height as functions of tsunami amplitude and ar-rival time. Figure 2 shows the maximum wave height forsuccessive time series when arrival time is moved for-ward every 15 min over 1-min sampled predicted tidesand the tsunamis have initial amplitudes ranging from0.5 to 9.0 m. The result is a set of serrated patterns thatgrow in amplitude as the tsunami amplitude increases.For small amplitude tsunamis, the maximum heights

FIG. 1. Example of a water level time series consisting of atheoretical tsunami adding to predicted tides at Seaside, OR. Thetsunami arrives at 0000 UTC 2 Jan 2004 and then decays expo-nentially in time after the first wave. At the time resolutionshown, the rapidly oscillating (20-min period) time series appearsas a solid distribution between decaying envelopes.


(Fig. 2) are determined by the next higher high water orpossibly even later ones. At the larger amplitudes, themaximum heights are determined by the first few wavesin the tsunamis and the tidal stage during which theyoccur. As a result, the maximum heights of small tsu-namis tend to occur near mean higher high water(MHHW) plus the tsunami amplitude, with little varia-tion in height as a function of arrival time. In contrast,the maximum heights of large tsunamis form a distri-bution centered more closely to mean sea level (MSL)plus the tsunami amplitude, with a spread in heightsapproaching the diurnal tidal range.

3. Probability density functions

To get a quantitative description of the height distri-butions of maximum tsunami heights, we adopt a modi-fied version of the procedure used by Houston andGarcia (1978) in their study of expected 100-yr and500-yr tsunami heights along the U.S. West Coast. Timeseries like those in Fig. 2 are computed for a full yearthat corresponds to a time in the 18.6-yr lunar nodalcycle in which the nodal factors are near their averagevalues. In our case, 1992 is chosen since it is in themiddle of the present National Tidal Datum Epoch

1983–2001. Whereas Houston and Garcia (1978) as-sumed that the later waves in a tsunami had constantamplitude (set to 40% of the first wave amplitudes fromtheir numerical tsunami model) for 24 h after which theamplitude was zero, we use time series that decay ex-ponentially over five days, based on the observed be-havior of Pacific-wide tsunamis (e.g., Mofjeld et al.2000). We also use single period (20.0 min) tsunamis,which, as they are moved along the tidal time series,provide equivalent statistical results to an ensemble oftsunamis with randomly distributed periods (seeMofjeld et al. 2000, for a statistical discussion of tsu-nami time series).

Histograms of heights, binned every 0.1 m, are com-puted from each series that are then normalized (sumover the bins equal to unity) and interpolated with acubic spline to form continuous PDFs. The harmonicconstants for Seaside are from the tidal model ofSpargo (2003) and Spargo et al. (2004). All others areofficial NOAA harmonic constants posted on theNOAA/National Ocean Service (NOS)/Center forOperational Oceanographic Products and Services(CO-OPS) Web site (see online at http://tidesandcurrents.noaa.gov).

When the initial tsunami amplitude A is subtractedfrom the PDF heights, the distributions (Fig. 3) all havean upper limit in height corresponding to the maximumpredicted tide for 1992. With increasing tsunami ampli-

FIG. 2. Locus of the maximum tsunami wave heights (tsunamiplus tide) as a function of the arrival time of the first wave peakin each tsunami wave train. For each initial amplitude A (height ofthe first wave peak relative to the background water level), thetime series are generated by moving the arrival time sequentiallyin time. In this example, exponentially tsunami wave trains aresuperimposed linearly on predicted tides on the open coast atSeaside, OR.

FIG. 3. Probability distribution functions (PDFs) of the maxi-mum tsunami wave heights at Seaside, OR, based on exponen-tially decaying tsunamis with the indicated amplitudes. The tsu-nami amplitudes have been subtracted from the heights of thecorresponding PDF. Also shown is the PDF for the predictedtides.

JANUARY 2007 M O F J E L D E T A L . 119

tude A, the widths of the !m " A PDFs spread and theircenters decrease in height from MHHW toward MSL(datums for Seaside were computed from harmonicconstants by the method of Mofjeld et al. 2004b). Thedecrease in the maximum values occurs as the PDFsbroaden because the height integral of each PDF needsto be unity. As expected, the PDFs converge to that ofthe predicted tide as A becomes large compared withthe tidal range.

Figure 4 gives an example of how a Gaussian PDFoften closely resembles the shape of the empiricalPDFs, where the mean height !o and the standard de-viation # are computed from the latter

P$y% & B exp'"$y " !o%2"2#2(, B"1 & )2$#,

$1%

where B is chosen so that the height integral of P isunity. This leads to a compact characterization (Fig. 5)of the PDFs in terms of !o and # as functions of theinitial tsunami amplitude A for each coastal location.Note that !o is the most probable height for the com-bined tsunami and tide, while *1.96# gives the 95%confidence limits for Gaussian distributions. The inte-gral of (1) from a height y to + is the cumulative densityfunction that provides the probability that the maxi-mum tsunami height of an event will exceed the valueof y.

Figure 5 shows curves of !o and # for Seaside, Ko-

diak, Crescent City, and Hilo. The latter three stationshave a long history of damaging tsunamis, and numeri-cal tsunami models are often tested and calibrated us-ing these sites. Their tides are typical of the coastal tidesin the northern Gulf of Alaska, northern California,and Hawaii, respectively. While !o and # at Seaside,Kodiak, and Crescent City vary throughout the rangeA % 10 m (Fig. 5), these parameters reach their asymp-totic values much more quickly at Hilo because thetidal range is relatively small in Hawaii as comparedwith those in the other North Pacific regions.

4. Formulas for !o and "

It is possible to compute the mean height !o andstandard deviation # for each tsunami amplitude A andlocation of interest. However, this becomes very com-putationally intensive in numerical tsunami modelingwhen tsunami heights are estimated at high resolutionalong a section of coastline. It is therefore useful to lookfor empirical formulas for !o and # as functions of A,which can be put into the Gaussian PDF (1) when thisapproximation is acceptably close to the PDF for agiven purpose.

FIG. 4. PDFs computed from the time series of maximum tsu-nami wave heights and a Gaussian PDF with the same meanheight !o and standard deviation #.

FIG. 5. Analytic fits to (a) the mean height !o and (b) standarddeviation # as functions of tsunami amplitude A.


(Fig. 2) are determined by the next higher high water orpossibly even later ones. At the larger amplitudes, themaximum heights are determined by the first few wavesin the tsunamis and the tidal stage during which theyoccur. As a result, the maximum heights of small tsu-namis tend to occur near mean higher high water(MHHW) plus the tsunami amplitude, with little varia-tion in height as a function of arrival time. In contrast,the maximum heights of large tsunamis form a distri-bution centered more closely to mean sea level (MSL)plus the tsunami amplitude, with a spread in heightsapproaching the diurnal tidal range.

3. Probability density functions

To get a quantitative description of the height distri-butions of maximum tsunami heights, we adopt a modi-fied version of the procedure used by Houston andGarcia (1978) in their study of expected 100-yr and500-yr tsunami heights along the U.S. West Coast. Timeseries like those in Fig. 2 are computed for a full yearthat corresponds to a time in the 18.6-yr lunar nodalcycle in which the nodal factors are near their averagevalues. In our case, 1992 is chosen since it is in themiddle of the present National Tidal Datum Epoch

1983–2001. Whereas Houston and Garcia (1978) as-sumed that the later waves in a tsunami had constantamplitude (set to 40% of the first wave amplitudes fromtheir numerical tsunami model) for 24 h after which theamplitude was zero, we use time series that decay ex-ponentially over five days, based on the observed be-havior of Pacific-wide tsunamis (e.g., Mofjeld et al.2000). We also use single period (20.0 min) tsunamis,which, as they are moved along the tidal time series,provide equivalent statistical results to an ensemble oftsunamis with randomly distributed periods (seeMofjeld et al. 2000, for a statistical discussion of tsu-nami time series).

Histograms of heights, binned every 0.1 m, are com-puted from each series that are then normalized (sumover the bins equal to unity) and interpolated with acubic spline to form continuous PDFs. The harmonicconstants for Seaside are from the tidal model ofSpargo (2003) and Spargo et al. (2004). All others areofficial NOAA harmonic constants posted on theNOAA/National Ocean Service (NOS)/Center forOperational Oceanographic Products and Services(CO-OPS) Web site (see online at http://tidesandcurrents.noaa.gov).

When the initial tsunami amplitude A is subtractedfrom the PDF heights, the distributions (Fig. 3) all havean upper limit in height corresponding to the maximumpredicted tide for 1992. With increasing tsunami ampli-

FIG. 2. Locus of the maximum tsunami wave heights (tsunamiplus tide) as a function of the arrival time of the first wave peakin each tsunami wave train. For each initial amplitude A (height ofthe first wave peak relative to the background water level), thetime series are generated by moving the arrival time sequentiallyin time. In this example, exponentially tsunami wave trains aresuperimposed linearly on predicted tides on the open coast atSeaside, OR.

FIG. 3. Probability distribution functions (PDFs) of the maxi-mum tsunami wave heights at Seaside, OR, based on exponen-tially decaying tsunamis with the indicated amplitudes. The tsu-nami amplitudes have been subtracted from the heights of thecorresponding PDF. Also shown is the PDF for the predictedtides.

JANUARY 2007 M O F J E L D E T A L . 119

1. Time series = (predicted tides + synthetic tsunami). Tsunami = 20-min T, with exponential decay time of 2.0 days (Van Dorn, 1984). For 1-year record, vary tsunami arrival time and initial amplitude.

2. Locus of (tsunami+tide) as arrival time and initial amplitude are varied.

3. Computed PDFs of maximum tsunami wave height for a set of initial tsunami amplitudes

4. Example of Gaussian fit to computed PDF for 3 m amplitude tsunami.

Slip Uncertainty: Far-field Sources"


• Far-field Sources: Negligible … far-field earthquakes look more like point sources, and the detailed structure of the slip does not effect local wave heights.

To get the cumulative rate for the combined probability that the jth earthquake and (tsunami + tide) flood level ζi will both occur, multiply this by the mean earthquake recurrence rate νj = 1/TMj

The combined probability that flood level ζi will be exceeded by the sum of a tsunami η and the local tides ξ is the integral of the combined (tsunami + tide) pdf

νj = 1/TMj ̂

Recall … i => ith tsunami exceedance level, ζi , (specified) j => jth earthquake source (and associated max tsunami, ηj ) ̂

Slip Uncertainty: Near-field Sources"


• Near-field sources: Important … detailed structure of the slip has first order effect on local wave heights.

Therefore, use a stochastic approach … develop multiple near-field sources - randomly variable width and slip … but - constrain with constant moment magnitude of the earthquake - 12 found adequate to capture variability of the near-shore tsunami amplitude

(4c) is the combined probability for all near-field sources that (tsunami + tide) height will exceed level ζi (compare with previous expression (3a) for single, far-field earthquake).

and … (4d) is the cumulative rate for all 12 near-field sources, with

νj = 1/TMj

i => ith exceedance level ζi j => jth earthquake source and ηj

^

Hazard Curve"


and if we now specify a discreet set of exceedance levels ζi … say

• Finally … the cumulative rate for all sources, near- and far-field is

then, for all sources, the combined (Poissonian) probability that level ζi will be exceeded is

Schematic"


ζ50 , ζ100 , ζ500 … etc.!at every point (x,y):!

Sources: • Physical Parameters • Probability of

Occurrence Computational Grids: • Bathymetry • Topography

• Generation • Propagation • Inundation

• η(x,y) • u(x,y) • v(x,y)

Model Input"Model

Computations"Model"Output"

Exceedance Value Computations"Equations (1)-(6) in González, et al. (2009).


Next Application of PTHA: Crescent City, CA


• Context

Part of FEMA’s Risk Mapping, Assessment, and Planning (Risk MAP) Program and the BakerAECOM coastal engineering effort for the FEMA California Coastal Analysis and Mapping Project (CCAMP).

• Time Scales of Interest

-  FEMA Federal Insurance Rate maps -  100 years (500 years ?)

• Model Inputs Required

- Bathy/Topo Computational Grids: Adequate grids currently available

- Updated Sources: Location, Magnitude, Length, Width, Slip, Mean Recurrence Interval (TM)

Bathy/Topo Computational Grids

F. I. González, UW/ESS 234 236

40

41

42

43

44

45

46

47

48

49

50Crescent City Grids and Source csz01

Longitude

Latitude

A grid = 36 s ~ 785 m at 45 deg Latitude

B grid = 6 s ~ 130m

C grid = 1 s ~ 22 m 1/3 s ~ 7 m

NOAA > NESDIS > NGDC > MGGD > Bathymetry & Relief > Tsunami Inundation Gridding Project privacy policy

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Crescent City, CA 1/3 arc-second MHW Tsunami Inundation DEM

click on image above to view a larger version

DEM not to be used for navigation.

Download DEM Development Report (.PDF)

Download 1/3 arc-second DEM, Metadata File,Projection File, & Readme File (.zip 505MB)

View Metadata Record

Date Completed: Jul 14, 2010

Format: ESRI Arc ASCII

Horizontal Datum: WGS 84

Vertical Datum: MHW

Vertical Units: meters

Coverage: Bathy-topo

Registration: Grid-node

Source: NOAA/NGDC/MGG

Project URL:http://www.ngdc.noaa.gov/mgg/inundation/tsunami/

Contact: Barry W. Eakins, [email protected],303-497-6505

click here to view larger image of Crescent City 1/3 arc-second DEM

The Crescent City MHW DEM covers the coastal area surroundingCrescent City, California and includes southern Oregon. Thecoordinate boundaries are 123.88° to 125.25°W and 41.42°N to42.53°N.

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Is the planned coverage adequate ?�� Are there priority areas not covered ?

Must Update this Table for CC PTHA Study"


Near-Field detail (1 of 12)"

Model 14Mw 9.2

Model 9-13Mw 8.5-8.8

Model 1-8Mw 8.2-9.2

Local Cascadiasources - 12

All Sources: Far- & Near-field"

(TM is mean interevent time)

Need Update to CSZ Source Specification"


M ~ 9.1 M ~ 9.1

M ~ 8 – 8.5

New Research

Broader Conceptual Context for PTHA -- Risk Analysis"


• What is Risk Analysis ? A commonly accepted definition of Risk is: “Probability of a loss, dependent on three elements – hazard, vulnerability, and exposure – that

increases or decreases as any element increases or decreases.” [Crichton, 1999; WMO, 2008] A generalized equation is frequently used [WMO, 2008]:

Risk = function (Hazard x Vulnerability x Exposure) or, even more generally,

Risk = function (Hazard, Vulnerability, Exposure) where at least one of the three factors is probabilistic

• Hazard … vulnerability … exposure ? Many definitions exist. For example [Thywissen, 2006]:

Hazard: The physical aspects of the phenomena and the ability of the phenomena to inflict harm.

Vulnerability: Condition or process resulting from physical, social, economic and environmental factors which determine the likelihood and scale of damage from the impact of a given hazard [UNDP, 2004]

Exposure: Inventory of people or artifacts at risk by exposure to a hazard [UNDP, 2004]

• So … PTHA provides a probabilistic Hazard Factor for Risk Analysis

Conclusions


◊ In principle, the formal PTHA mathematics doesn’t care about the nature of the sources – i.e., sources could be landslides

• Poisson assumption still appropriate • Uncertainty issues are similar

- Mean inter-event period - Source details (for stochastic approach) Seismic: magnitude, slip distribution, Landslide: volume, speed, etc, … - Tidal Stage

◊ Formal Risk Analysis requires • PTHA extension to output forces on structures and other indices,

e.g., momentum flux = ( ζ + d )V2 , • “failure PDFs”

References


Crichton, D. (1999), The risk triangle, in Natural Disaster Management, edited by J. Ingleton, pp. 102 – 103, Tudor Rose, London, U. K.

Geist, E. L., and T. Parsons (2005), Probabilistic analysis of tsunami hazards, Nat. Hazards, 37(3), 277 – 314.

González, F.I., E.L. Geist, B. Jaffe, U. Kânoğlu, H. Mofjeld, C.E. Synolakis, V.V. Titov, D. Arcas, D. Bellomo, D. Carlton, T. Horning, J. Johnson, J. Newman, T. Parsons, R. Peters, C. Peterson, G. Priest, A. Venturato, J. Weber, F. Wong, and A. Yalciner (2009): : Probabilistic tsunami hazard assessment at Seaside, Oregon for near- and far-field sources. J. Geophys. Res., 114, C11023.

Mofjeld, H. O., F. I. González, V. V. Titov, A. J. Venturato, and J. C. Newman (2007), Effects of tides on maximum tsunami wave heights: Probability distributions, J. Atmos. Ocean. Technol., 24(1), 117 – 123.

Tang, L., C. Chamberlin, E. Tolkova, M. Spillane, V.V. Titov, E.N. Bernard, and H.O. Mofjeld (2006): Assessment of potential tsunami impact for Pearl Harbor, Hawaii, NOAA Tech. Memo. OAR PMEL-131, NTIS: PB2007-100617, 36 pp.

Tetra Tech Inc. (1981), Coastal Flooding Storm Surge Model, Federal Emergency Management Agency: Part 1. Methodology, Federal Emergency Management Agency, Washington, D. C.

Walsh, T.J., V.V. Titov, A.J. Venturato, H.O. Mofjeld, and F.I. González (2003): Tsunami hazard map of the Elliot Bay area, Seattle, Washington -- Modeled tsunami inundation from a Seattle fault earthquake, Washington State Department of Natural Resources Open File Report 2003-14, 1 plate, scale 1:50,000.

Ward, S. N. (1994), A multidisciplinary approach to seismic hazard in southern California, Bull. Seismol. Soc. Am., 84, 1293 – 1309.

World Meteorological Organization (WMO) (2008), Urban Flood Risk Management—A Tool for Integrated Flood Management, Associated Programme on Flood Management Document 11, in Flood Management Tools Series, 38 pp. (Available at http://www.apfm.info/ifm_tools.htm)

Submarine Landslide Workshop, Woods Hole, August 18-19, 2011

Probabilistic Tsunami Hazard Analysis

Hong Kie Thio URS Corporation, Los Angeles


Public reports on tsunami hazard

  http://www.gsi.gov.il/Eng/_Uploads/264Israel-Tsunami-Hazard.pdf

  http://peer.berkeley.edu/publications/peer_reports/reports_2010/web_PEER2010_108_THIOetal.pdf


Tsunami hazard - probabilistic   Integration over a broad range of seismic sources

with varying sizes and recurrence rates   Formal inclusion of uncertainties through logic trees

and distribution functions  Straightforward for offshore waveheights because of

linear approximation (analogous to stiff site condition)

 How do we extend probabilistic offshore waveheights to inundation (i.e. site behaviour)?


Probabilistic Seismic Hazard Analysis (PSHA)

  Basic Concept

Compute probability that magnitude Mi generates Acceleration, a > A (specified value).


PSHA – all sources &

Total Rate (a > A) º R = S S vij pij j i

Average Return Period of (a > A) º T = I/R


Hazard Curve


What is the final product?  Waveheight   Inundation   Flow depth - D   Flow velocity - V  Momentum - VxD  Drawdown, duration  Vorticity   ?


Magnitude/frequency of tsunami sources

Size of Tsunami (m)

Rec

urre

nce

Rat

e (1

/yr)

(a

nnua

l pro

babi

lity

of e

xcee

denc

e)-1

1

.1

.01

.001

.0001

1

10 100 1000

Distant Earthquakes

Local Earthquakes

Landslides Volcanoes

Asteroid Impact

Power et al., 2005


Uncertainties  Aleatory: Expresses the inherent uncertainty of the

physical process –  Source dimensions –  Location –  Included using distribution functions

 Epistemic: expresses uncertainty due to our lack of understanding of the physical process –  Recurrence times, block vs. flow model, bathymetry,

algorithms –  Included using logic trees

ptha based on psha – methodology and applicationsthis presentation focused on the suitability of...

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