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Keywords:

  • Hurricane Irene;
  • emergency planning;
  • ensemble forecasting;
  • exigent analysis;
  • wind damage

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[1] In late August 2011, Hurricane Irene damaged property along the U.S. East Coast, making landfalls in the Carolinas and in the New York metro area. At each initial forecast time, the ECMWF forecast ensemble provides a measure of the possible outcomes. For each ensemble member the maximum sustained wind predicted at each location is used to estimate the expected property damage due to wind. “Worst-case” or exigent scenarios are developed that are consistent with the range of forecasts in the ensemble. Exigent scenarios are potentially useful to emergency responders and planners and applicable to any area of geophysics for which spatial uncertainty is represented by an ensemble of realizations. For the case of Hurricane Irene, the exigent patterns of damage are centered on New York Harbor and the mouth of the Chesapeake Bay.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[2] Hurricane Irene raked the U.S. East Coast during the period 26–30 August 2011, making landfall at Cape Lookout, North Carolina at 1200 UTC 27 August 2011 as a hurricane and then, 24 hours later, making two additional official landfalls in New Jersey and New York as a tropical storm [Avila and Cangialosi, 2011]. Hurricane Irene did indeed cause substantial damage, but it could have been a lot worse. In preparing for an event like Irene, emergency planners must consider a range of “what-if” scenarios. Here we demonstrate a particular type of “worst-case” or exigent scenario that may be derived from the forecast ensembles created by operational centers like ECMWF and NCEP. For this demonstration we consider only wind damage.

[3] A simple approach to creating a worst-case wind scenario from a forecast ensemble is to take the overall maximum wind speed at each location for all forecast times for all ensemble members. This in fact may be a reasonable approach if one is interested in planning for a single locality, but not if one is interested in creating a worst-case scenario for an entire region, since the varying tracks of the different ensemble members will result in an unrealistically wide geographic area of strong winds in the overall maximum wind speed field. This naive univariate approach to constructing a worst-case scenario would have a damage swath that is inconsistent with the spatial covariance structure of the ensemble of wind fields. Another simple approach would choose that ensemble member with the greatest forecast damage. The forecast storm in the chosen ensemble member would be more intense and/or would track more closely to heavily populated areas than in other ensemble members.

[4] Using Hurricane Irene as an example, the goal of this paper is to estimate dynamically-consistent and state-dependent exigent scenarios from a forecast ensemble for planning purposes. For each ensemble forecast and at each location, a user-specified definition of damage relates the expected property damage to the maximum forecast sustained wind speed. We use an exceedingly naive estimate of damage due to wind (Section 2), but the exigent analysis method is amenable to using more sophisticated damage functions (Section 5). Beyond hurricanes, exigent analysis can be applied to many other situations. (Gombos and Hoffman, Ensemble-based exigent analysis. Part I: Estimating worst-case weather-related forecast damage scenarios,Weather and Forecasting, submitted manuscript, 2012) applied it to heating degree days and to freezing conditions for Florida citrus for a cold air outbreak of January 2010. We envision other planning applications including tornado potential, road conditions, and route planning. In addition, exigent analysis is applicable to any area of geophysics for which ensembles are produced and spatial uncertainty estimates are desired (Section 6).

[5] The precise definition of worst-case or exigent is the scenario that maximizes the estimated damage with respect to “reasonable” perturbations about the ensemble mean (Section 3). By reasonable, we mean within confidence bounds defined by a user-specified uncertainty level, say 90%, and by the covariance of the ensemble of damage forecasts. Mathematically, the exigent analysis damage perturbation, derived from the Lagrange multiplier method, maximizes the area-wide damage subject to the constraint of being on an equal probability ellipsoid in the phase space of the damage state vector (seeAppendix A). Section 4 describes the exigent damage maps for three different forecast initial times and compares these to damage maps based on ECMWF analyses and on the ensemble mean. Section 5 discusses possible future refinements and Section 6 includes a summary and describes potential extensions and applications of the exigent analysis method.

2. Wind Damage Parameterization

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[6] To estimate property damage due to winds at a particular location, we must specify the wind conditions, the relationship between wind and damage, and the property value. We will write the damage at a grid point i as wipi. Here pi = f(Vi) is the fractional damage at the grid point and is a function of the wind speed Vi at the grid point. The weight given to the grid point, wi, is the total property value at that grid point and is a known constant.

[7] The relevant wind at a grid point is taken to be the near surface maximum sustained wind speed forecast over the course of the event. Winds used here are 10 m winds from the THORPEX Interactive Grand Global Ensemble (TIGGE) database [Bougeault et al., 2010] for each of the 50 ECMWF ensemble members. The forecasts begin every 12 hours from 00 UTC 23 August through 12 UTC 26 August 2011. The surface wind fields are archived by TIGGE every 6 hours on a reduced Gaussian grid with 320 latitudes in each hemisphere. This grid has a resolution of approximately 0.281° in latitude and 30 km in the zonal direction. We interpolate 10-mu- andv-wind components to a 1/4 × 1/4° grid.

[8] Empirical evidence shows that damage begins at some threshold value of wind speed, increases with wind speed, and asymptotes to 100% damage for high enough wind speed [Unanwa et al., 2000]. We use the parameterization of Emanuel [2011], where damage increases with the cube of the excess of wind speed (V) over the threshold wind speed (Vt, t for “threshold”, taken here as 30 kt). The equation for fractional damage is f = α3/(1 + α3), where α = (VVt)/(VhVt) for V > Vt and zero otherwise. The parameter Vh (taken here as 110 kt) is the speed at which 50% of property is damaged (h for “half”).

[9] We use U.S. census data on occupied household values from the 2010 5-year American Community Survey [U.S. Census Bureau, 2011]. This implies we consider only residential, not commercial, property. This database gives the number of occupied homes in each of twenty classes in each census block group. (Each home is assigned to the class with the closest property value. The class property values, in thousands of dollars, are 5, 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 45, 55, 65, 75, 85, 95, 112.5, 137.5, 162.5, 187.5, 225, 275, 350, 450, 625.5, 875 and 1000.) From this we estimate the total residential value in each census block group, which we then aggregate to the value of wi at the nearest grid point of the 1/4 × 1/4° grid. There are over 200,000 census block groups nationwide, but geographic size and population counts vary widely. Since the maximum recorded value is $1,000,000, property values in some wealthy neighborhoods will be underestimated. Figure 1 displays the resulting grid of residential property value. The dominant feature in the figure is the Washington to Boston corridor. (Note that values in billions of dollars per grid point are displayed with a base 10 logarithmic scale.)

image

Figure 1. Occupied household values in the eastern U.S. Color scale is in terms of the base 10 logarithm of value per grid point in billions of dollars.

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3. Exigent Analysis

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[10] The damage functional, Jd = Σi wipi = wTp, is the area-wide total damage. Here, we collect thepi for all grid points into a fractional damage state vector p (damage state hereafter), thereby defining a phase space for the spatial distribution of the fractional damage. Similarly, we collect the wi into a weight vector w of property values. The ensemble of damage states is a cloud of points in this phase space. (Note that damage at a grid point increases only with wind speed above Vt, but the damage functional generally increases with both the intensity of the storm and the overlap of the storm wind swath with regions of high property values.) We define the exigent damage state(ExDS) as the linear combination of ensemble members that maximizes the damage functional, subject to the constraint that the ExDS must be within the confidence bounds defined by a user-specified uncertainty level and the damage ensemble covariance.

[11] For the purpose of quantifying the aforementioned confidence bounds we will assume that the damage states have a multi-Gaussian (mG) distribution and that the sample covariance matrix of the damage ensemble is an accurate estimate of the true damage covariance matrix. Then the confidence bounds are ellipsoidal surfaces in the damage state phase space (Appendix A), and the ExDS is the damage state that maximizes Jd among all the possible damage states that are on or within, for example, the 90th percentile confidence bound ellipsoid of the damage ensemble. Surfaces of constant Jd are parallel hyperplanes stacked from lowest to highest value of Jd in this phase space. Therefore the extreme values of Jd on or within the ellipsoid will be the values of Jd for the two hyperplanes tangent to the ellipsoid, and one point of tangency is the ExDS. Appendix A summarizes the mathematics and solves the optimization problem using the method of Lagrange multipliers.

[12] Note that our analysis is linear once we have calculated the damage at the grid points for each ensemble member. As a result, a change to the confidence level changes the size of ellipsoid, but otherwise the phase space geometry is unchanged—the ellipsoid's shape and orientation and therefore its relation to the parallel hyperplanes are unchanged. Therefore, only the magnitude, not the pattern of the ExDS perturbation (with respect to the ensemble mean), is changed if the confidence level is changed. (See equation (A4)).

4. Hurricane Irene Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[13] For each initial forecast time (00 UTC 23 August through 12 UTC 26 August), we calculate the damage state and damage functionals for the ensemble mean and from the exigent analysis. The value of the damage functional for various scenarios—the ECMWF analyses, the ECMWF ensemble mean, and the ExDS—are given in Table 1. For the ECMWF analyses, wind fields every 12 hours from 00 UTC 25 August to 12 UTC 31 August 2011 are used to calculate the maximum wind speed. (Each analysis wind field is a control forecast initial time wind field from the TIGGE database.) For each ensemble forecast, wind fields every 6 hours from the start of the forecast out to five days are used to calculate the maximum wind speed.

Table 1. Total Damage Values ($B)a
ScenarioMeanS.D.Exigent
  • a

    Each row except the last gives the ensemble mean damage functional, the ensemble standard deviation of the damage functional, and the damage functional of the exigent analysis for the forecast initial time indicated. The last row gives the damage functional estimated from the ECMWF analyses.

00 UTC 23 Aug0.080.120.51
12 UTC 23 Aug0.190.311.46
00 UTC 24 Aug0.470.612.91
12 UTC 24 Aug0.590.673.12
00 UTC 25 Aug0.520.412.00
12 UTC 25 Aug0.730.642.76
00 UTC 26 Aug0.750.482.23
12 UTC 26 Aug1.080.653.52
Analyses0.59

[14] In Table 1, we see a general increase of the ensemble mean damage functional as the forecast initial time advances. Beginning 00 UTC 24 August the ensemble mean damage functional is similar to or larger than the damage functional estimated from the ECMWF analyses. The ensemble standard deviation of damage functional (also given in Table 1) is larger than the ensemble mean damage functional for early forecasts and smaller for later forecasts. The exigent damage functional values are much larger, typically 3 or 4 standard deviations greater than the mean.

[15] Figure 2 shows the damage map from the ECMWF analyses. In this and subsequent figures of damage maps, we contour the values of wipi. The best track for Irene is shown as a plus sign within a circle, every 12 h, with the location at 12 UTC 27 August highlighted in magenta. Best track positions are from the B-deck of the Automated Tropical Cyclone Forecast (ATCF) system [Sampson and Schrader, 2000] for the period while Irene was a hurricane, and then starting 12 UTC 28 August from Table 1 of Avila and Cangialosi [2011]. This figure shows what “actually happened”—assuming the correctness of the ECMWF analyses, the parameterization of wind damage, and the census data property values. In the ECMWF analyses, damage is greatest around Albemarle Sound just north of Cape Hatteras, North Carolina, at the entrance to Chesapeake Bay in the Virginia Beach-Norfolk area, at Long Beach on southwestern Long Island, and surrounding the eastern reaches of Long Island sound, especially on the North Fork.

image

Figure 2. Damage map from analyses. Color scale is in terms of the base 10 logarithm of damage per grid point in millions of dollars. Green indicates no damage.

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[16] Figure 3shows the ECMWF ensemble mean and exigent analysis damage maps for the forecast initial time of 12 UTC 24 August, 72 h before the North Carolina landfall. The official forecast track from the A-deck of the ATCF for the ECMWF forecast for this initial time is shown every 12 h, with the forecast position at 12 UTC 27 August highlighted in magenta. The ensemble mean damage map (Figure 3a) agrees with the analyses damage map in many places, but adds areas of damage, notably along the New Jersey Atlantic coast, around New York Harbor centered on Jamaica Bay, around Narragansett Bay, and along Cape Cod and Massachusetts Bay. The exigent damage map (Figure 3b) is greater than the mean at all locations previously discussed and has much greater inland penetration of damage, especially in the DelMarVa peninsula, New Jersey, and eastern Massachusetts.

image

Figure 3. Damage maps from the forecast of 12 UTC 24 August 2011, for the (a) ensemble mean and (b) exigent analysis. As in Figure 2. Units as in Figure 2.

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[17] Figure 4 shows the exigent damage maps and forecast tracks for forecast initial times 24 and 48 hours later than Figure 3. The forecast of 12 UTC 25 August (Figure 4a) tracks Irene more to the west, with exigent damage concentrated in South Carolina, the mouth of the Chesapeake Bay, the New Jersey coast and both ends of Long Island. In this forecast, eastern Massachusetts, excluding Cape Cod, is spared. For the forecast initialized one day later at 12 UTC 26 August (Figure 4b), the forecast track and damage patterns are intermediate between those with initial times of 12 UTC 24 and 25 August, but the level of damage is greater at the mouth of the Chesapeake and around New York Harbor.

image

Figure 4. Exigent analysis damage maps from the forecasts of (a) 12 UTC 25 and (b) 26 August 2011. As in Figure 2. Units as in Figure 2.

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5. Some Current Limitations and Future Refinements

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[18] In reality, most damage ensembles are too small, biased, and/or uncalibrated to give a precise estimate of true forecast damage covariance. Therefore, an exigent analysis is dependent on the quality of the forecast ensemble, which is in turn dependent on the size of the ensemble and on the quality of the forecast model, data assimilation system, and method of generating ensemble members. Potential future refinements could help to address these limitations. Efforts to bias correct and calibrate forecast ensembles are generally useful, but grid point by grid point statistical post-processing will not correct the bias and/or calibration of feature attributes such as hurricane track and intensity. Instead it should be more beneficial to bias correct hurricane intensity and track as a function of forecast length, as done byWilliford et al. [2003]. A similar approach to calibrating the forecast dispersion might be developed and then the track and intensity corrections could be applied to the ensemble forecast wind fields.

[19] Exigent analysis requires mG statistics for the associated confidence quantile q to be more than just a label. Forecast errors for some meteorological variables, such as temperatures and wind components, are approximately mG. However, most damage functions are nonlinear with the result that most damage ensembles are not mG. This is the case in the examples presented here. Possible future refinements to exigent analysis are to apply Gaussian anamorphosis transformations to the damage ensemble or to formulate exigent analysis directly in terms of the mG meteorological variables. Both approaches lead to nonlinear constrained optimization problems that should be amenable to standard methods.

[20] The damage function used here (Section 2) is a highly simplified parameterization, but since we operate on the damage ensemble (Section 3), any method for calculating the damage at each grid point for each ensemble member could be used. For example, the HAZUS-MH hurricane wind model [Vickery et al., 2006a, 2006b] could be applied to the evolving wind fields forecast by each ECMWF ensemble member. Since the HAZUS results are losses for each census tract, these data could be accumulated at the nearest grid points, and since they are losses, not fractional damage, w = 1. Furthermore, comprehensive commercial catastrophe models (aka CAT models) that are used by insurers to quantify risk could be used to estimate losses for each ensemble forecast. For hurricanes, CAT models include damage due to wind, rain, surge, and inland flooding, and have property inventories with detailed building characteristics.

6. Concluding Remarks

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[21] In this paper, we described and demonstrated a method of exigent analysis to generate worst-case scenarios from ensemble forecasts of damage from Hurricane Irene (2011). The exigent analysis method finds a damage state (or equivalently, a damage map) that results in maximum event-wide damage and that is constrained to be statistically feasible with respect to the ensemble covariance. The exigent damage state (ExDS) provides a compact view of what might have happened—a multivariate uncertainty bound (i.e., worst-case scenario) that is consistent with the dynamics and statistics of the forecast ensemble. Luckily, in the case of Hurricane Irene, the worst case did not occur; exigent damage functional values were found to be as high as $3.52B at the 90th percentile confidence quantile as compared to $0.59B estimated from the analyses.

[22] Exigent analysis has direct applications to emergency situations affecting life and property. The exigent damage maps presented here could be used as extreme but definitely possible scenarios by emergency responders or others planning for a devastating hurricane striking the mid-Atlantic and New England regions. Exigent analysis of ensemble forecasts is very flexible and can be applied in many other situations. We can, for example, redefine the property value weights to be zero except in some region of interest to find the worst case for that region. In addition, exigent analysis can be combined with ensemble regression [e.g.,Gombos et al., 2012] to determine the antecedent conditions associated with the ExDS. These antecedent conditions might be used to understand the atmospheric dynamics that may lead to the exigent scenario [Gombos et al., 2012] or, when real-time observations align with the exigent antecedent conditions, to alert emergency responders before the next model run. Exigent analysis also has potential to guide weather modification experiments by estimating optimal timing and location of cloud seeding.

[23] Whenever spatial uncertainty is represented by an ensemble of realizations, exigent analysis can be used to provide worst-case scenarios. Potential applications range from emergency response and planning to the analysis of climate model outputs. For example, given an ensemble of climate model mean July 2100 surface temperatures, exigent analysis could determine worst-case scenarios either in terms of energy demand or in terms of heat-related emergency room visits or fatalities for some particular region or for the entire Northern Hemisphere.

Appendix A:: Method of Solution

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[24] The ExDS is the p that maximizes Jd = wTp, subject to the constraint of being within the confidence bounds at the specified uncertainty level q (Section 3). Equivalently, for the purpose of this development, since the contribution from the ensemble mean is fixed, we now define the exigent analysis as that damage perturbation (p′) that maximizes the perturbation damage functional

  • display math

The confidence bounding ellipsoid discussed in Section 3 is given by

  • display math

where S is the sample covariance matrix of the ensemble and Qp2 is the value of the inverse χ2 function of the confidence quantile q. Then, under the stated assumptions, the probability that the true damage perturbation is within the ellipsoid defined by equation (A2) is q. In the examples shown q = 0.9. Since the shape of the ellipsoid is defined by S, we say the perturbations on the ellipsoid are constrained by the forecast ensemble covariance. All points on the ellipsoid are at the qth uncertainty quantile and the exigent damage perturbation (ExDP) is that point on the ellipsoid that maximizes Jd. In other words, the ellipsoid defines a hyper-dimensional confidence interval and the ExDP gives the maximizing point on that confidence interval. (The ExDP is always on the ellipsoid, as explained inSection 3.) A more comprehensive discussion of exigent analysis is given by (Gombos and Hoffman, submitted manuscript, 2012).

[25] To find the constrained maximum we apply the method of Lagrange multipliers to maximize

  • display math

where λ is a Lagrange multiplier. (Gombos and Hoffman, submitted manuscript, 2012) show that the maximizing solution of equation (A3) is

  • display math

where Qw2 = wTSw. Once S is estimated, either from the ensemble or otherwise, the calculation is as follows: w and q are given, Qp2involves a look-up of the inverseχ2 function, z = Sw is a matrix times a vector, and then Qw2 is just the dot product wTz. For numerical stability and efficiency, the calculation is done in terms of the leading principal components (PCs) of the eigenvectors of S. (Problems would otherwise arise since the dimension of S is much greater than the size of the ensemble.) The number of PCs and the degrees of freedom for the inverse χ2 function are taken to be the same. Estimates of the number of PCs vary among the several techniques tried. We used the median of these estimates, which varied from 10 to 15 for different forecast initial times.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information

[26] The authors gratefully acknowledge funding provided by the National Science Foundation grant 0838196.

[27] The Editor thanks the two anonymous reviewers for assisting in the evaluation of this paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information
  • Avila, L. A., and J. Cangialosi (2011), Hurricane Irene, Trop. Cyclone Rep. AL092011, 45 pp., Natl. Hurricane Cent., Miami, Fla. [Available at http://www.nhc.noaa.gov/2011atlan.shtml.]
  • Bougeault, P., et al. (2010), The THORPEX interactive grand global ensemble, Bull. Am. Meteorol. Soc., 91, 10591072, doi:10.1175/2010BAMS2853.1.
  • Emanuel, K. (2011), Global warming effects on U.S. hurricane damage, Weather Clim. Soc., 3, 261268, doi:10.1175/WCAS-D-11-00007.1.
  • Gombos, D., R. N. Hoffman, and J. Hansen (2012), Ensemble statistics for diagnosing dynamics: Tropical cyclone track forecast sensitivity revealed by ensemble regression, Mon. Weather Rev., in press.
  • Sampson, C. R., and A. J. Schrader (2000), The automated tropical cyclone forecasting system (version 3.2), Bull. Am. Meteorol. Soc., 81, 12311240.
  • Unanwa, C. O., J. R. McDonald, K. C. Mehta, and D. A. Smith (2000), The development of wind damage bands for building, J. Wind Eng. Ind. Aerodyn., 84, 119149.
  • U.S. Census Bureau (2011), 2006–2010 American community survey (United States), report, Washington, D. C.
  • Vickery, P. J., J. Lin, P. F. Skerlj, L. A. Twisdale Jr., and K. Huang (2006a), HAZUS-MH hurricane model methodology. I: Hurricane hazard, terrain, and wind load modeling, Nat. Hazards Rev., 7, 8293, doi:10.1061/(ASCE)1527-6988(2006)7:2(82).
  • Vickery, P. J., P. F. Skerlj, J. Lin, L. A. Twisdale Jr., M. A. Young, and F. M. Lavelle (2006b), HAZUS-MH hurricane model methodology. II: Damage and loss estimation, Nat. Hazards Rev., 7, 94103, doi:10.1061/(ASCE)1527-6988(2006)7:2(94).
  • Williford, C. E., T. N. Krishnamurti, R. C. Torres, S. Cocke, Z. Christidis, and T. S. V. Kumar (2003), Real-time multimodel superensemble forecasts of Atlantic tropical systems of 1999, Mon. Weather Rev., 131, 18781894.

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Wind Damage Parameterization
  5. 3. Exigent Analysis
  6. 4. Hurricane Irene Results
  7. 5. Some Current Limitations and Future Refinements
  8. 6. Concluding Remarks
  9. Appendix A:: Method of Solution
  10. Acknowledgments
  11. References
  12. Supporting Information
FilenameFormatSizeDescription
grl29473-sup-0001-t01.txtplain text document1KTab-delimited Table 1.

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