2.2 Categorías y Dimensiones
2.2.2 La Enseñanza-Aprendizaje del Habla Inglesa
The following items are areas in which additional research could improve the proposed risk- based evacuation/sheltering decision support tool:
o The methodology presented here is customized for the Northern Gulf of Mexico Coast. Future research could also apply the methodology to other areas
o To utilize the methodology in other areas landfall error would need to be recalculated to account for the different ways in which hurricanes approach different coastlines. On the Eastern US coast, hurricanes which may typically approach on parallel tracks have different landfall errors.
o Terrain differences not present on the Northern Gulf Coast may need to be accounted for when considering flood hazard
o High winds
o Tornado risk should be better quantified
o Risk to inhabitants of a structure should be better correlated with structural damage states
o Storm surge flooding
o Better values for inland flooding should be obtained o More refined scale should be used for flood depths
o Probabilistic surge models based on historic forecast error should be performed at longer forecast periods
o Better quantify structural damage from storm surge o Rainfall Flooding
o Determine probabilistic rainfall using historic track error o Better flood prediction model
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Detailed hydraulic survey should be performed in study area
Studies correlating rainfall return periods (input) with flood severity should be performed
o Additional population vulnerabilities
o Elderly/vulnerable portions of the population should be better accounted for o Individuals without transportation should be considered
o Account for the likelihood of ignoring evacuation order o Decision processes
o Expand decision process to consider possibility and impact of infrastructure damage
o Better quantification of evacuation risk
o Determine acceptable risk and fatalities in evacuation and sheltering by conducting a detailed survey of emergency management personnel
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APPENDIX A. CALCULATION OF WIND RISK
The wind risk calculation for Franklin from Section 4.4.1 for the 96 hour forecast period will be presented. The landfall error functions are given in Section 3.1.3.1 and are as follows:
458 . 10 84 . 13 x (A1) 961 . 15 364 . 10 x (A2)
x is the distance from landfall in hundreds of miles. For the 96 hour forecast period, Gustav was 1105 miles from landfall (x=11.05). The error analysis from Equations A1 and A2 yields a mean standard landfall error of 163.4 miles and a standard deviation of 130.5 miles. Using this landfall error, Gustav‟s landfall position is simulated N times and each individual simulation is correlated to the forecast wind field. The forecast wind field used in the analysis (from HAZUS) appears in Figure A.1.
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The wind field in Figure A.1 was divided into a grid with 5 mile by 5 mile squares. The coverage of the grid included the entire forecast wind field. Areas forecast as having less than 50 mph winds were decreases away from the hurricane track at a rate of 1 mph per grid. This grid was then moved randomly, with the grid location for Franklin being the constant. For each simulation, the wind speed in the Franklin grid was recorded. It should be noted that wind speed cannot be less than zero.
Microsoft Excel was used for this simulation, and the expression
NORMINV(RAND(),µ,σ) was used to randomly sample the landfall error distribution. Mathematically, this is expressed as follows:
x i x
i u
x 1( ) (A3)
where 1(ui)is the inverse of the standard normal distribution and is given as: ) 1 2 ( 2 ) ( 1 1 i i erf u u (A4)
where ui is a probability and here is taken as a randomly generated number between 0 and 1.
The error function is defined as:
x t dt e erf 0 2 2 (A5)
For analysis purposes, a simulation was used in which 5,000 runs were performed. This simulation appears in histogram form in Figure A.2. This number was based on an adequate number of simulations being performed to obtain reasonable data without running excessive and time-consuming simulations. Simulations were performed with increasing numbers of runs within the simulation until a point (5000 runs) was reached in which the number of runs did not significantly affect the results of the simulation. For this forecast period, a 10,000 run simulation was also performed for comparison purposes. This simulation appears in histogram form in
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Figure A.3. This simulation was performed to compare the results with the previous simulation and to determine the adequateness of the 5,000 run simulation. As can be seen in Table A.1, the results of the two simulations are very similar.
Figure A.2 Simulation Used in Analysis (N=5000)
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Table A.1 Comparison of Simulations 5000 10000
Mean 52.84 52.33
Standard Deviation 34.97 34.75
Once the mean and standard distribution of the wind speeds correlating to landfall error are found, they are combined with historic intensity error for the 96 hour forecast period (µ=- 5.28, σ=26.88) as described in Section 3.1.4.1 and the overall mean and standard deviation for the wind speed probabilities are obtained.
The overall wind speed mean and standard deviation were determined as follows: 56 . 47 ) 28 . 5 ( 84 . 52 ) ( ) (L V I V V 11 . 44 88 . 26 97 . 34 2 2 2 ) ( 2 ) (L V I V V
The mean and standard deviation found are then used to create a distribution of the wind speed probabilities for Franklin by plotting a distribution using the normal distribution function (Equation A6). x is taken from as the lower and upper limits of the histogram. If the upper limit of the histogram is less than 200, the upper limit is taken as 200. This allows for the distribution to tail off and also allows for the capsulation of higher wind speed probabilities if needed.
2 2 2 ) ( 2 1 ) ( x e x f (A6)
These probabilities appear in Figure A.4.
Once the distribution above is obtained, it can be combined with the damage functions to obtain the risk to structural damage from the approaching storm. The damage functions for the sample structure appear in Figure A.5.
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Figure A.4 Wind Speed Probability Distribution at 96 Hour Forecast
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Once the wind speed probability distribution and the damage functions are obtained, the structural risk can be determined. The expression for the expected level of damage is determined from the following expression which is presented in Section 3.4.1:
i i i f h dh h D D E[ ] ( ) ( ) (A7)
This expression can be approximated as:
n i i ip h D D E 1 ) ( ] [ (A8)
This calculation is performed using the wind speed probabilities from Figure A4 and the Damage Curves from Figure A.5. Di correspond to the Damage Curves p(h)i correspond to the wind speed
probability distribution. The expression is summed over the series i =1,2…200, where i is in miles per hour (3 second gust). Table A.2 shows the risks to structural damage from each HAZUS damage state. These probabilities are the probability of experiencing at least each Damage State.
Table A.2 Risks from High Winds Damage State P (%) 1 - Minor Damage 16.9 2 - Moderate Damage 6.7
3 - Severe Damage 2.1 4 - Destruction 0.8
The same damage curve functions were used for each forecast period, and the only difference in each forecast period was the forecast wind field, which produced a new wind speed probability distribution and subsequently the probability of the structure experience the different damage states.
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APPENDIX B. TESTS FOR NORMALITY
The landfall errors determined in Section 3.1.3.1 were tested for normality using the Shapiro-Wilk test. This test is valid for small to medium sample sizes up to n≈3000. The Shapiro-Wilk statistic, W, is a ratio of the best estimate of variance to the sum of squares estimate of variance. It is given as:
n i i n i i x wx W 1 2 1 2 ) ( ) (
Where xi is a data point, µ is the sample mean, and w is an estimate function of the sample means
and variances. Table B.1 presents the results of the test for each distance bin. N is the number of