Volcanoes produce large amounts of ash that

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1 GIS-Based Indices for Comparing Airline Flight-Path Vulnerability to Volcanoes Jeffrey A. VanLooy and Thomas J. Cova Center for Natural & Technological Hazards, University of Utah Volcanic ash can cause physical damage to an aircraft to the point of mechanical and electrical malfunction. In the event of an ash plume, aircraft would likely be diverted or grounded, leading to economic losses. This article presents two indices to compare the economic vulnerability of flight paths to volcanic ash plumes. The first index includes three factors for a flight path: wind direction, distance to the volcano, and flight-path attributes (i.e., number of flights per day, number of potential passengers, and average ticket cost). The second index compares the threat posed by different volcanoes to an airline flight-path network. A case study is presented for two airlines in the northwest United States to a Mt. Adams eruption. The results show that although the first airline has more flight paths in the region, the second airline is slightly more vulnerable due to the spatial relationships of its flight paths to the volcano and their attributes. Key Words: aircraft, index, volcano, vulnerability. Volcanoes produce large amounts of ash that pose a hazard for aircraft. Ash plumes can travel thousands of kilometers from the immediate area of a volcano and may precipitate engine failure (Heffter, Stunder, and Rolph 1990). This has occurred many times throughout the world over the past twenty-five years, with some of the most serious cases in Alaska (Kienle et al. 1986; Swanson and Kienle 1988; Casadevall 1994). During the eruption of the Redoubt Volcano, located approximately 120 km southwest of Anchorage, Alaska, several aircraft came in contact with the ash plume while en route to Anchorage. One aircraft traveling from Amsterdam had all four engines fail while approaching the airport (Brantley 1990). Although the engines eventually restarted as the aircraft descended below the plume, the event could have been a disaster. Overall, the Redoubt eruption damaged several aircraft, caused numerous cancellations, and led to more than $2 million in lost revenue at Anchorage International Airport (Casadevall 1994). The hazard that volcanic ash poses to aircraft has led to mitigation efforts that include warning systems and predictive models to assist aircraft in plume avoidance. Some of these warning systems help pilots avoid the dangers of a volcanic ash plume in real time (Evans 1994; Foreman 1994). Others use models of past volcanic events to determine potential ash plume areas that should be avoided by pilots (Sullivan and Ellis 1994; Versteegen et al. 1994). Due to the serious hazard volcanic ash presents to aircraft, airlines may be concerned about the potential for flight-path disruption that could result in an economic cost due to the rerouting or grounding of aircraft. A recent example in the United States occurred when Mount St. Helens in Washington State released a plume in the fall of 2004, and another example occurred in Alaska during the winter of 2006 with the eruption of the St. Augustine Volcano. Existing warning systems and predictive models are very useful in aiding aircraft in dynamically avoiding ash plumes, but they were not designed to aid in determining the economic vulnerability of flight paths to a potential volcanic disruption. The objective of this article is to present GISbased indices to compare the relative vulnerability of flight paths to potential ash plumes from active volcanoes. The indices include factors associated with the percentage of annual winds (PAW) from a given direction around the volcano, the closest distance of the flight path to A prior version of this article received first place in the student paper competition at the 2004 Great Plains/Rocky Mountain AAG meeting, for which the lead author is especially grateful. We also thank two anonymous reviewers for their constructive comments that greatly improved this article, as well as Scott Bridwell and Adam Sobek of the University of Utah, Department of Geography, for their knowledgeable assistance with GIS. The Professional Geographer, 59(1) 2007, pages r Copyright 2007 by Association of American Geographers. Initial submission, February 2004; revised submissions, November 2005 and March 2006; final acceptance, May Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, and 9600 Garsington Road, Oxford OX4 2DQ, U.K.

2 GIS-Based Indices for Comparing Airline Flight-Path Vulnerability to Volcanoes 75 the volcano, and flight-path attributes (e.g., number of flights per day). They can be used to determine the relative vulnerability of flight paths or to determine the threat presented by a volcano (or volcanoes) to an airline s entire flight-path network. The flight-path vulnerability index (FVI) and the average flight-path vulnerability index (AFVI) can then be used to compare the potential for revenue loss due to the rerouting and grounding of flights if a particular volcano releases a plume. This article begins with background on the dangers of volcanic ash plumes to aircraft. The next section describes the FVI and its three components, as well as the AFVI. A case-study is presented for the Pacific Northwest of the United States that compares the flight-path vulnerability of two airlines to a volcano in the region. The article concludes with a discussion of the results and directions for future research. Background Volcanic ash poses a hazard to aircraft due to its adverse effects on visibility as well as the detrimental effects it might have on an engine. Ash can cause abrasion on mechanical parts and windshields and it can clog fuel lines and other essential passageways (Foreman 1994). Furthermore, the electrical charge within the ash can cause arcing and the subsequent malfunction of electrical components (Labadie 1994). These adverse effects of volcanic ash have caused many aircraft over the past twenty-five years to experience problems similar to those encountered by aircraft flying into Anchorage during the Redoubt Volcano eruption. In the Northern Australia Indonesia region during the 1980s, at least six aircraft encountered in-flight problems due to volcanic ash ( Johnson and Casadevall 1994). During the eruption of Galunggung Volcano in Indonesia in the summer of 1982, two aircraft experienced failure of all four engines of the 747s while flying through the plume (Smith 1983; Tootell 1985). The engines were restarted after the planes glided down to lower elevations outside of the plume, but this would not have been possible if the fuel nozzles had been clogged (Brantley 1990). Given that aircraft have encountered ash plumes in Southeast Asia, Australia, Alaska, the northwest United States, and Japan, it is important to understand the geography of flight paths and their potential interaction with volcanic ash plumes. Most ash-plume warning systems send real-time data to air-traffic controllers and pilots using seismic ground observations, eye witnesses, and unmanned airborne vehicles (Evans 1994). Ash-plume hazard models use geographic information systems (GIS) data layers to help determine the path of an ash plume. These layers include topography, meteorological data such as wind direction, and other types of volcanic data including past eruptions (Sullivan and Ellis 1994). These models aid in real-time decision making to avoid ash plumes during a release, but they do not allow an analyst to compare the economic vulnerability of flight paths to a potential ash plume. A few studies have been conducted following volcanic eruption to determine the gross loss of revenue to airlines. For example the Redoubt Volcano eruption in Alaska caused a significant reduction in passengers, and thus a loss of revenue, through Anchorage (Miller 1993; Tuck and Huskey 1994). The objective of this article is to provide a more systematic methodology for examining flightpath vulnerability in advance of any volcanic disruption. Vulnerability modeling with GIS has gained favor in recent years for hazards in general (Cutter, Mitchell, and Scott 2000; Rashed and Weeks 2003) and transportation hazards in particular (Cova and Conger 2004). GIS has also been applied to create models to assist in relief and reconstruction efforts following a natural disaster (Chang 2003). Although remote sensing has been used to observe volcanic activity to assist in hazard mitigation in the event of an eruption (Oppenheimer 1997), no models have been developed to reveal the relative economic vulnerability of flight paths or the hazard that a volcano presents to an airline network. Methods The indices presented in this article incorporate three variables for each flight path: wind direction, distance to the volcano, and flight-path attributes. Each variable is entered into a component equation that determines the relative vulnerability of that variable for a particular flight path. The values returned for each component range between 0 (the least vulnerable path) and 1 (the most vulnerable path). The

3 76 Volume 59, Number 1, February 2007 three values returned are multiplied by weights between 0 and 1 that sum to 1. Finally, the sum of the three values multiplied by their respective weights returns the vulnerability index for a particular flight-path. This section defines the components and the construction of the index in greater detail. The first variable involves determining the distance each flight path travels through the PAW in each direction around the volcano. The region around each volcano is divided into quadrants (North, South, East, and West) where each quadrant is assigned to a value between 0 and 1 representing the percentage of annual winds around the volcano. The values of the quadrants sum to 1 or 100 percent of the winds around the volcano (including the percentage of calm winds if necessary). The second step in composing the index is to determine the closest distance between the flight path and the volcano. The closer the path is to the volcano the greater the likelihood that it will be affected by an ash plume. However, a flight path that is closer to the volcano and traveling through a quadrant with a relatively high PAW will likely be more vulnerable it will more likely experience ash than will a flight path that is equally close to the volcano but is traveling through a quadrant with a low PAW. Therefore, the closest distance of each flight path to the volcano in each PAW quadrant is determined. The first two variables are concerned with the physical relationship between a flight path and a volcano, but the third component is comprised of flight-path attributes including the number of daily flights that occur along a flight path, the number of potential passengers traveling along that path, and the average ticket cost for flights along the path. The focus of this variable is the economic value of a flight path; clearly, more flights, passengers, and higher ticket costs result in greater loss should a volcano disrupt the path with an ash plume. In short, the greater the economic value of a flight-path, the more vulnerable an airline is to revenue loss either in terms of rerouting aircraft around the ash plume or the grounding of flights. Flight-Path Vulnerability Formulation The focus of the first component is wind direction. As a flight path connects an origin to a destination, it may pass through several winddirection quadrants relative to a volcano. This means that the flight path will likely consist of different segments of varying potential for vulnerability depending on the wind direction (Figure 1). To account for this variability, the length of a flight-path segment in each of the quadrants (as shown on flight-path 2 in Figure 1) is measured and normalized to the longest and shortest distances of all segments across the quadrants. This number is then multiplied by the percentage of annual winds within the particular quadrant, which allows the sum of the values to be distributed from 0 to 1. This is expressed in the following equation: W i ¼ X4 j¼1 S ij S sa q j ; S la S sa ð1þ where S ij is the distance of segment S through quadrant j for flight-path i, S sa is the shortest distance of all flight-path segments out of all quadrants a, S la is the longest distance of all flight-path segments out of all quadrants a, and q j is the percentage of annual winds in quadrant j. The value W i returned from Equation (1) is the vulnerability score concerning wind direction for flight-path i. The closest distances along the flight path in each of the PAW quadrants to the volcano is determined by measuring the closest distance of the flight-path segments to the volcano, as is depicted on flight-path 2 in Figure 1. Much like the wind direction component, the closest distance component is also normalized to the shortest and longest distances of all segments across the quadrants. Once the distances are determined, the values are entered into the equation D i ¼ X4 j¼1 1 d ijd sa q j ; d la d sa ð2þ where d ij is the closest distance from the volcano to the individual segment of flight-path i in wind quadrant j, d sa is the shortest distance of all individual flight-path segments to the volcano out of all wind quadrants a, d la is the longest distance of all individual flight-path segments to the volcano out of all wind quadrants a, and q j is the percentage of annual winds in quadrant j. The value D i returned by Equation (2) is the vulnerability score concerning distance to the

4 GIS-Based Indices for Comparing Airline Flight-Path Vulnerability to Volcanoes 77 Figure 1 Determining the closest distance from flight-path segments to a volcano in addition to the distances the flight-path segments travel through the percentage of annual wind ( PAW) direction quadrants radiating from a volcano. The PAW percentages in this figure were determined from data from Station #24243 Yakima/Air Terminal, WA (Office of the Washington State Climatologist 2005). volcano for flight-path i, which also ranges in value from 0 to 1. The third component equation is a simple measure comparing the number of flights per day, the number of potential passengers, and the average ticket cost for a flight path. This equation divides the number of each of the three components for a flight path by the highest number of each component across all flight paths: P i ¼ 1 f i þ p i þ c i ; ð3þ 3 f h p h c h where f i is the number of flights for flight-path i, f n is the flight-path with the highest number of flights, p i is the number of potential passengers for flight-path i, p h is the flight path with the highest number of potential passengers, c i is the average ticket cost for flight-path i, and c h is the flight path with the highest average ticket cost. The values of the three components are then summed and multiplied by one-third. The value P i returned by Equation (3) is the vulnerability score concerning attributes for flight-path i. The scores returned from Equations (1) (3) are then weighted to represent the importance of the individual variables. Finally, the three weighted variables are summed to return a value describing the vulnerability of an individual flight-path. This composite value represents the potential vulnerability of the flight path to an ash plume. The equation for the FVI value V i appears below, where w1, w2, and w3 are the weights for the separate variables that sum to 1: V i ¼ w1wi þ w2di þ w3pi: ð4þ The final FVI value V i for each path will also range between 0 and 1. For example, a flightpath with a FVI value of 1 would indicate that each of the three components is the most vulnerable relative to the other observed flight paths, where a flight path with an FVI of 0 indicates that each of the three components is the least vulnerable of all the observed flight paths. However, it is likely that no flight path will contain all of the most or least vulnerable components and therefore a typical analysis would

5 78 Volume 59, Number 1, February 2007 show that all of the flight paths observed result in FVI values between 0 and 1. The value V i returned by Equation (4) for each individual flight-path can be aggregated into a larger index for an entire flight-path network. This second index, the AFVI, is determined by summing the individual flight-path vulnerability scores and dividing by the number of flight paths. This returns a value between 0 and 1, and when compared with other AFVI scores for the same flight paths it determines which volcano in the region poses the greatest threat to a flight-path network (a higher value implies greater threat). This is expressed as H k v ¼ P nk i¼1 V k i n k ; ð5þ where Hv k is the AFVI presented by volcano v to airline k, Vi k is the FVI for path i, and n k is the number of flight paths for airline k. When comparing two or more airlines it is important to note that the maximum value for each of the variables is across all airlines, as the result of each equation is normalized to a particular set of flight paths. Therefore, this vulnerability index only calculates the potential economic vulnerability of a flight path to a volcanic ash release relative to other flight paths. The purpose of the index is not to quantify the absolute vulnerability of a flight path to a volcano. Instead, it provides an analyst with indices of vulnerability for each of a set of flight paths; these indices can then be utilized in preparing contingency plans such as alternative flight paths and rerouting, should a volcano release an ash plume and disrupt flight paths. Utilizing GIS to Calculate the Vulnerability Indices The time-consuming process of computing these indices can be made easier through the use of GIS. The concepts and tools used in GIS are simple and take a minimal amount of time once the data are entered into the system. First, it is important to note the characteristics of the map projection used in conjunction with the flight paths and PAW quadrants. When placed directly over the volcano of study, the Gnomonic Polar projection is ideal for these indices. This particular projection preserves direction from the center point as well as great circle lines, which is what most flight paths will follow. There may be deviations along a flight path, but a particular airline may take note of this and correct for the directional differences when entering the data. Preserving wind direction from the volcano is crucial to the indices as it is important to know where all flight paths enter and exit each quadrant. One shortfall in using this projection is that distance is distorted with increasing distance from the center point. This distortion is 1 3 percent at about 151 (approximately 1,600 km) from the center point and does not make a significant difference in the results as compared to results calculated using a great circle distance calculator. However, this particular characteristic of the projection helps in determining the study area for the indices. Even though volcanic ash can travel distances greater than 1,600 km, a limit to the study area is needed to calculate the distances a flight path travels through each PAW quadrant. A 1,600-km radius study area covers a large area that is most likely be affected by a significant eruption, such as the 1980 Mt. St. Helens eruption. This event distributed trace amounts of ash as far away as the Great Plains, approximately 1,600 km away. Once the study area boundary is calculated, the four PAW quadrants need to be determined, with each quadrant covering one of the four cardinal directions from the volcano. This means creating four quadrants with the north quadrant covering from northwest to northeast, the east quadrant covering from northeast to southeast, the south quadrant covering from southeast to southwest, and the west quadrant covering from southwest to northwest (Figure 1). The next step in the GIS process is to add the flight paths and clip them from the study area and PAW quadrants so that each flight path has a set of path segments in each PAW that it travels through as well as a full flight path that travels through the study area. Once this is done, the length of each segment can be calculated with the length script found in the Environmental Systems Research Institute s (ESRI) ArcGIS tm. The distance of each segment from the volcano is determined by using the join tool for the individual flight-path PAW segments. Using this tool, the flight paths are joined with the

6 GIS-Based Indices for Comparing Airline Flight-Path Vulnerability to Volcanoes 79 volcano by activating the variable that calculates the closest distance from a point to the layer being joined (in this case the flight paths). The only attributes that need to be imported are the flight-path attributes (i.e., number of flights per day, number of potential passengers, and average ticket cost). With all of the flight-path attributes, flight-path segment lengths, and distances from the volcano entered, the GIS field calculator can then be used to determine the vulnerability indices. Case Study for the Pacific Northwest of the United States The Pacific Northwest of the United States is an active tectonic region with many volcanoes in the Cascade Range including Mt. Baker, Glacier Peak, Mt. Rainier, Mt. St. Helens, Mt. Adams, Mt. Hood, and Mt. Jefferson. These volcanoes are classified as stratovolcanoes with geologically (and historically) recent activity (Gardner et al. 1995; Scott et al. 1995; Waitt, Mastin, and Beget 1995; Wolfe and Pierson 1995; Scott et al. 1997; Hoblitt et al. 1998; Walder et al. 1999). Some of the volcanoes, such as Mt. Adams (Scott et al. 1995), have not had significant activity over the past 10,000 years; others, such as Mt. St. Helens and Glacier Peak, erupt more frequently (Wolfe and Pierson 1995; Waitt, Mastin, and Beget 1995). Nevertheless, this does not mean that Mt. Adams is not a risk to the surrounding area (Scott et al. 1995). Because of the potential vulnerability of a flight path to a volcanic eruption, the index presented in this article was not designed to take into account the probability of an eruption, but rather the vulnerability of a certain flight path (as compared to other flight paths) if a volcano releases ash. Two airlines were compared in regard to their flight paths in the northwest United States using equally weighted factors in the vulnerability index (i.e., 0.33). Due to the lack of data regarding actual flight-path information because of concerns such as security, interpolated flightpaths were analyzed using Euclidian distances between the observed cities. Data concerning ticket costs, number of flights per day, and number of potential passengers were restricted to information found on Internet web sites (Alaska Airlines 2005; Southwest Airlines 2005). The PAW information was obtained from a web site of annual winds at Yakima, Washington, which was the closest station found to Mt. Adams (Office of the Washington State Climatologist 2005). Therefore, the results of this case study are only an example of how the index works using the best data available. Access to more accurate data would improve the results. The first set of results was calculated for Alaska Airline s flight paths and their interaction with a possible Mt. Adams eruption. The second set of results was calculated for Southwest Airlines flight paths and their interaction also with a possible Mt. Adams eruption. For both airlines flight paths, only domestic flights arriving in or departing from the northwest States of Washington, Oregon, and Idaho were included. Due to this restriction, only the cities of Seattle, Portland, Spokane, and Boise had flights into this region for either airline, but both airlines fly to all four cities (Figure 2). Vulnerability for Interpolated Flight Paths Between Alaska Airlines Cities Alaska Airlines has many flights originating from the four observed cities in the northwest United States, with most of the connecting cities located in California and Alaska (Figure 3A). A few connecting cities are located across the country as far away as the East Coast. The results calculated for Alaska Airlines flight-path vulnerability to Mt. Adams volcanic activity show that of the thirty-five flights traveling to the northwest United States, the paths with the highest vulnerability are just east of Mt. Adams from Seattle to cities east of the Rocky Mountains, including Washington, Denver, New York, and Boston (Figure 3B). Many of the flights in the midlevel range connect Seattle with cities to the south in California, most using flight paths just west of Mt. Adams. The flight paths leading from Portland are in the low-level range of vulnerability and typically travel southsoutheast of the volcano. The flight path with the lowest vulnerability for Alaska Airlines is from Portland to Sacramento (Table 1). In regard to the PAW quadrants, flight-paths from Portland to connecting cities in California pass through lower PAW quadrants and also have lower vulnerability scores (Figure 3B). In contrast, flights from Seattle to Southern California pass close to the west side of Mt. Adams but also through higher PAW quadrants and thus have higher relative vulnerability scores.

7 80 Volume 59, Number 1, February 2007 Figure 2 The study area in the northwest United States. PAW ¼ percentage of annual winds. Overall, for Alaska Airlines the majority of the most vulnerable flight paths are from Seattle eastward, with a great distance of the path traveling in the PAW quadrant that has the highest percentage of annual winds. Furthermore, many of the flight paths travel relatively close to the volcano. However, one particular flightpath, which has a moderate vulnerability index relative to the other flight paths, travels from Seattle to Anchorage (V i ¼ 0.39) but does not travel as close to the volcano as other paths nor does it travel in a PAW quadrant with high annual winds. After conducting a sensitivity analysis of this flight path it appears that the vulnerability index is elevated due to the relatively large number of flights per day (32) and the associated high number of passengers (4,516). After adjusting these numbers to represent a lower number of flights per day (2) and fewer potential passengers (284), the vulnerability index drops significantly (V i ¼ 0.18). Depending on the size of a Mt. Adams eruption, volcanic ash might or might not disperse over the Seattle area, but the potential would be moderately vulnerable for disruption of the high-traffic Seattle-to-Anchorage flights. Vulnerability for Interpolated Flight Paths Between Southwest Airlines Cities Southwest Airlines has slightly fewer flight paths originating in the northwest United States than does Alaska Airlines. However, the majority of its destination cities on flight paths originating from the northwest are located in western states, similar to those of Alaska Airlines (Figure 4A). For Southwest Airlines, a total of thirty-three flight paths were found. Note that despite the lower number of flight paths compared with Alaska Airlines, Southwest Airlines flight paths throughout the northwest are more dispersed.

8 GIS-Based Indices for Comparing Airline Flight-Path Vulnerability to Volcanoes 81 A Figure 3 (A) Interpolated flight paths for Alaska Airlines connecting to cities in the northwest United States, and (B) flight-path vulnerability for Alaska Airlines interpolated flight paths. PAW ¼ percentage of annual winds Kilometers 1,600 B Seattle to Anchorage Mt. Adams Alaska Airlines Cities Flight-path Vulnerability Index PAW Quadrants (Percent) Kilometers 54 Calm Winds: 5% The results of the FVI for Southwest s paths are similar to Alaska Airlines flight paths, with most of the highly vulnerable paths passing close to Mt. Adams (Figure 4B). The most vulnerable flights paths connect Seattle to cities east of Mt. Adams, outside of the study area; the least vulnerable paths connect Portland to cities in California and Nevada, which are significantly south of Mt. Adams. However, some of the less vulnerable paths pass closer to Mt. Adams than some of the highly vulnerable paths. Two flight paths with similar overall distances within the study area were compared: Seattle to Chicago and Portland to Phoenix. The path from Seattle to Chicago has a higher vulnerability index (0.48) when compared with the path from Portland to Phoenix (0.26), which passes closer to the volcano but also travels through a lower PAW quadrant (Table 2). The flight-path attributes between the two paths are

9 82 Volume 59, Number 1, February 2007 Table 1 Interpolated Alaska Airlines flight-path vulnerability scores in comparison with interpolated Southwest Airlines flight-path vulnerability scores to a Mt. Adams eruption (35 paths) Flight path Index Flight path Index Seattle to Washington 0.49 Seattle to Burbank 0.30 Seattle to Orlando 0.48 Seattle to Sacramento 0.29 Seattle to Denver 0.48 Portland to Orange County 0.29 Seattle to Phoenix 0.48 Seattle to Spokane 0.28 Portland to Denver 0.47 Seattle to Palm Springs 0.27 Seattle to New York 0.44 Portland to Los Angeles 0.25 Seattle to Boston 0.42 Portland to San Diego 0.25 Seattle to Tucson 0.42 Portland to Phoenix 0.24 Seattle to Los Angeles 0.41 Seattle to Juneau 0.24 Seattle to Anchorage 0.39 Seattle to Reno 0.23 Seattle to Orange County 0.36 Seattle to Fairbanks 0.20 Seattle to San Diego 0.36 Portland to Anchorage 0.20 Seattle to Boise 0.33 Portland to San Jose 0.20 Spokane to Los Angeles 0.31 Portland to Oakland 0.20 Seattle to San Fransisco 0.31 Seattle to Ketchikan 0.18 Seattle to Ontario 0.30 Seattle to Sitka 0.17 Seattle to San Jose 0.30 Portland to Sacramento 0.15 Seattle to Oakland 0.30 Mt. Adams AFVI 0.30 Notes: All values were rounded to the nearest hundredth. AFVI ¼ average flight-path vulnerability index. nearly identical with the exception that the path from Seattle to Chicago has an average ticket cost of $478 and the Portland to Phoenix path has an average cost of $440. A sensitivity analysis for the Portland to Phoenix flight path was conducted whereby the average ticket cost was increased to $478, the same cost as the Seattle to Chicago path. This resulted in an increase in the vulnerability index for the Portland to Phoenix path by 0.01, which indicates that the flightpath attributes between these two flight paths do not differ significantly. Instead, it appears that the difference between these two flight paths is due to the Seattle to Chicago path traveling its greatest distance through the higher PAW quadrant. Overall, Southwest Airlines has a significant number of flight paths traveling to the east of Mt. Adams. In general, this appears to cause the vulnerability scores to be higher due to the distances traveled through the high PAW quadrant. Unlike Alaska Airlines, Southwest Airlines does not have any flight paths northwest of Seattle, which appears to be the direction least likely to be vulnerable to a Mt. Adams eruption. Discussion For the two airlines in this case study, the flight paths with the highest vulnerability scores travel through the higher PAW quadrants, pass close to the volcano, and contain a relatively high number of flights per day, number of potential passengers, and average ticket cost. However, some of the flight paths that are relatively far from the volcano and travel through low PAW quadrants have high vulnerability scores because of their relatively high economic value due to the high flight-path attribute scores. Grounding these flights would have a greater economic impact on the airline. Another aspect of this research is the average flight-path vulnerability index. The AFVI value (0 to 1) scores the threat of a volcano to the entire airline in that region. When the AFVI is calculated for other volcanoes, the values can be compared to determine which volcano presents the greatest threat to an airline. The AFVI for Mt. Adams for the Alaska Airlines flight paths is 0.30 (Table 1), and for Southwest Airlines it is 0.32 (Table 2). This implies that if an eruption were to occur from Mt. Adams, Southwest Airlines would potentially be slightly more economically vulnerable than Alaska Airlines. This difference could actually be considered statistically insignificant, but it is an interesting difference as Alaska Airlines has more flight paths in the northwest United States than does Southwest Airlines. This demonstrates that the FVI and the AFVI reveal subtle elements of vulnerability that would not be apparent in a study that relied solely on the number of flight paths to determine the potential

10 GIS-Based Indices for Comparing Airline Flight-Path Vulnerability to Volcanoes 83 A Figure 4 (A) Interpolated flightpaths for Southwest Airlines connecting to cities in the northwest United States, and (B) flight-path vulnerability for Southwest Airlines interpolated flight paths. PAW ¼ percentage of annual winds Kilometers B 900 Seattle to Chicago Portland to Phoenix Mt. Adams Southwest Airlines Cities Flight-path Vulnerability Index PAW Quadrants (Percent) Kilometers Calm Winds: 5% economic vulnerability of an airline to a volcanic eruption. This case study compared two airlines flightpaths potential economic vulnerability to the eruption of only one volcano. An airline may wish to compare the potential vulnerability of its flight paths for many different volcanoes in a region to determine which volcano would most likely affect the revenue of the airline if an eruption were to occur. If an analyst were to use the vulnerability index discussed in this article, more accurate information could improve the analysis. This case study provides one example of how the index works, and the best available data were used. As noted, the flight-path attributes data were obtained from web sites provided by the airlines, and the data for the percentage of annual wind directions were obtained from a weather station in Yakima, Washington. An airline would be able to provide more accurate

11 84 Volume 59, Number 1, February 2007 Table 2 Interpolated Southwest Airlines flight-path vulnerability scores in comparison with interpolated Alaska Airlines flight-path vulnerability scores for a Mt. Adams eruption (33 paths) Flight path Index Flight path Index Portland to Chicago 0.55 Seattle to Spokane 0.28 Portland to Kansas City 0.53 Seattle to Sacramento 0.27 Seattle to Albuquerque 0.52 Portland to Phoenix 0.26 Seattle to Kansas City 0.49 Spokane to Salt Lake City 0.26 Seattle to Nashville 0.48 Seattle to San Jose 0.26 Seattle to Chicago 0.48 Seattle to Reno 0.25 Seattle to Phoenix 0.46 Portland to Oakland 0.24 Seattle to Salt Lake City 0.42 Portland to Sacramento 0.24 Seattle to Las Vegas 0.42 Portland to Las Vegas 0.23 Portland to Spokane 0.39 Boise to Spokane 0.23 Boise to Seattle 0.34 Portland to San Jose 0.22 Portland to Salt Lake City 0.34 Portland to Reno 0.20 Portland to Albuquerque 0.33 Boise to Las Vegas 0.20 Boise to Portland 0.32 Boise to Salt Lake City 0.19 Seattle to Oakland 0.31 Boise to Oakland 0.19 Spokane to Oakland 0.30 Boise to Reno 0.18 Spokane to Las Vegas 0.30 Mt. Adams AFVI 0.32 Notes: All values were rounded to the nearest hundredth. AFVI ¼ average flight-path vulnerability index. information for its own purposes. Finally, if an analyst were to use these indices to determine the potential loss of revenue, the resulting scores could be translated into potential loss of revenue in dollars. Conclusion The vulnerability index described in this study combines three variables to determine a vulnerability score for flight paths traveling in a volcanically active region. An aggregate volcanic hazard index can also be calculated to understand the hazard that a particular volcano presents to a given airline. This index does not incorporate the likelihood of any one flight being adversely affected by an eruption and therefore is not a risk index for a potential volcanic eruption (Cova and Conger 2004). Instead, the index determines the relative vulnerability of a particular flight path if a volcano in the region should erupt. Furthermore, vulnerability is not expressed in terms of potential physical damage to an aircraft, but rather in the form of a unitless surrogate for revenue loss by an airline. The case study in this article presents the vulnerability scores of two airlines for one volcano in a region with many potential volcanic hazards. More research could be conducted in the northwest United States as well as in other volcanically active regions of the world (e.g., Indonesia) to understand the potential vulnerability of flight paths to volcanic eruptions. Such studies could include determining the vulnerability of an airline to all volcanoes in a region, thereby allowing for a composite vulnerability index for an airline to all volcanoes an index that could be compared with composite vulnerability indices for other airlines. Results could be improved with more accurate and detailed information, which might include (i) an alternative path that would be used in the event of an eruption; (ii) the altitude of the flight through a wind quadrant, which would involve expanding the index to a three-dimensional model; and (iii) the possibility of ash plumes changing size over the eruption time, which would add a fourthdimension to the index. Finally, entering the exact geography of the flight path (or the mean approximation of a flight path, as not every flight follows the same path), including turns, to refine the measure of distance through a PAW quadrant, as well as adjusting the number of PAW sections for sensitivity analysis, should be considered in improving the results. Understanding the vulnerability of any particular flight path to a volcanic eruption is important in understanding the potential economic impacts due to the rerouting or grounding of flights (Vowles 2006). In addition, by understanding the relative vulnerability of a set of flight paths, it is possible to determine the volcano that would most impact a network.

12 GIS-Based Indices for Comparing Airline Flight-Path Vulnerability to Volcanoes 85 Finally, understanding which volcanoes are most hazardous may aid in understanding how an eruption would affect airline revenue. Literature Cited Alaska Airlines New flight reservations, aspx (last accessed 23 May 2006). Brantley, S. R The eruption of Redoubt Volcano, Alaska, December 14, 1989 August 31, U.S. Geological Survey Circular Casadevall, T. J The eruption of Redoubt Volcano, Alaska: Impacts on aircraft operations. Journal of Volcanology and Geothermal Research 62: Chang, S. E Transportation planning for disasters: An accessibility approach. Environment and Planning A 35: Cova, T. J., and S. Conger Transportation hazards. In Handbook of transportation engineering, ed. M. Kutz, New York: McGraw Hill. Cutter, S. L., J. T. Mitchell, and M. S. Scott Revealing the vulnerability of people and places: a case study of Georgetown County, South Carolina. Annals of the Association of American Geographers 90: Evans, J. E Development of a real-time ATC volcanic ash advisory system based on the future aviation weather system. In Volcanic ash and aviation safety: Proceedings of the First International Symposium on Volcanic Ash and Aviation Safety, ed. T. J. Casadevall, U.S. Geological Survey Bulletin Foreman, P. M Warning systems and pilot actions. In Volcanic ash and aviation safety: Proceedings of the First International Symposium on Volcanic Ash and Aviation Safety, ed. T. J. Casadevall, U.S. Geological Survey Bulletin Gardner, C. A., K. M. Scott, C. D. Miller, B. Myers, W. Hildreth, and P. T. Pringle Potential volcanic hazards from future activity of Mount Baker, Washington. U.S. Geological Survey Open-File Report Heffter, J. L., B. J. B. Stunder, and G. D. Rolph Long-range forecast trajectories of volcanic ash from Redoubt Volcano eruptions. Bulletin of the American Meteorological Society 71: Hoblitt, R. P., J. S. Walder, C. L. Driedger, K. M. Scott, P. T. Pringle, and J. W. Vallance Volcano hazards from Mount Rainier, Washington. U.S. Geological Survey Open-File Report Johnson, R. W., and T. J. Casadevall Aviation safety and volcanic ash clouds in the Indonesia- Australia region. In Volcanic ash and aviation safety: Proceedings of the First International Symposium on Volcanic Ash and Aviation Safety, ed. T. J. Casadevall, U.S. Geological Survey Bulletin Kienle, J., J. N. Davies, T. P. Miller, and M. E. Yount eruption of Augustine Volcano: Public safety response by Alaskan volcanologists. EOS 67: Labadie, J. R Mitigation of volcanic ash effects on aircraft operating and support systems. In Volcanic ash and aviation safety: Proceedings of the First International Symposium on Volcanic Ash and Aviation Safety, ed. T. J. Casadevall, U.S. Geological Survey Bulletin Miller, T. P Volcanic ash and aircraft. In United States Geological Survey yearbook, fiscal year 1992, U.S. Geological Survey. Office of the Washington State Climatologist Wind Rose Plot: Station #24243 Yakima/Air Terminal, WA, climate.html#clim (last accessed 23 May 2006). Oppenheimer, C Surveillance and mapping of volcanoes and their emissions by satellite remote sensing. Geography 82: Rashed, T., and J. Weeks Assessing social vulnerability to earthquake hazards through spatial multicriteria analysis of urban areas. International Journal of Geographic Information Science 17: Scott, W. E., R. M. Iverson, J. W. Vallance, and W. Hildreth Volcano hazards in the Mount Adams region, Washington. U.S. Geological Survey Open-File Report Scott, W. E., T. C. Pierson, S. P. Schilling, J. E. Costa, C. A. Gardner, J. W. Vallance, and J. J. Major Volcano hazards in the Mount Hood region, Oregon. U.S. Geological Survey Open-File Report Smith, W. S High-altitude conk out. Natural History 92: Southwest Airlines Standard reservations. (last accessed 23 May 2006). Sullivan, T. J., and J. S. Ellis Ash cloud aviation advisories. In Volcanic ash and aviation safety: Proceedings of the First International Symposium on Volcanic Ash and Aviation Safety, ed. T. J. Casadevall, U.S. Geological Survey Bulletin Swanson, S. E., and J. Kienle The 1986 eruption of Mount St. Augustine: Field test of a hazard evaluation. Journal of Geophysical Research 93: Tootell, B All 4 engines have failed: The true and triumphant story of flight BA-009 and the Jakarta Incident. Auckland: Hutchinson Group. Tuck, B. H., and L. Huskey Economic disruptions by Redoubt Volcano: Assessment methodology and anecdotal empirical evidence. In Volcanic ash and aviation safety: Proceedings of the First International Symposium on Volcanic Ash and Aviation

13 86 Volume 59, Number 1, February 2007 Safety, ed. T. J. Casadevall, U.S. Geological Survey Bulletin Versteegen, P. L., D. D. D Autrechy, M. C. Monteith, and C. R. Gallaway Defining a keep-out region for aircraft after a volcanic eruption. In Volcanic ash and aviation safety: Proceedings of the First International Symposium on Volcanic Ash and Aviation Safety, ed. T. J. Casadevall, U.S. Geological Survey Bulletin Vowles, T. M Geographic perspectives of air transportation. The Professional Geographer 58: Waitt, R. B., L. G. Mastin, and J. E. Beget Volcanic-hazard zonation for Glacier Peak volcano, Washington. U.S. Geological Survey Open-File Report Walder, J. S., C. A. Gardner, R. M. Conrey, B. J. Fisher, and S. P. Schilling Volcano hazards in the Mount Jefferson region, Oregon. U.S. Geological Survey Open-File Report. Wolfe, E. W., and T. C. Pierson Volcanic-hazard zonation for Mount St. Helens, Washington, U.S. Geological Survey Open-File Report JEFFREY A. VANLOOY is a Ph.D. candidate in the Center for Natural & Technological Hazards, Department of Geography, University of Utah, Salt Lake City, UT jeffrey.vanlooy@geog.utah.edu (corresponding author). His research interests include remote sensing, geomorphology, and climate change. THOMAS J. COVA is Associate Professor of Geography and Director of the Center for Natural & Technological Hazards, Department of Geography, University of Utah, Salt Lake City, UT, cova@geog.utah.edu. His research interests are hazards, transportation, and GIS.