Visitor Use Computer Simulation Modeling to Address Transportation Planning and User Capacity Management in Yosemite Valley, Yosemite National Park

Visitor Use Computer Simulation Modeling to Address Transportation Planning and User Capacity Management in Yosemite Valley, Yosemite National Park Final Report Steve Lawson Brett Kiser Karen Hockett Nathan Reigner Virginia Polytechnic Institute and State University Robert Chamberlin Janet Choi Resource Systems Group, Inc. March, 2008

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TABLE OF CONTENTS Chapter 1 - Introduction... 1 Chapter 2 - Study Sites... 5 Chapter 3 - Data Collection... 13 Visitor Surveys... 13 Visitor Counts... 18 Chapter 4 - Data Analysis and Modeling... 29 Visitor Survey Data Analysis and Modeling... 29 Visitor Counts Data Analysis and Modeling... 43 Model Algorithm and Programming... 50 Chapter 5 - Simulation Analysis of Current Visitor Use and User Capacities... 57 Chapter 6 - Summary of Findings, Limitations, and Recommendations... 65 Summary of Study Results and Findings Visitor Surveys... 65 Bridalveil Fall Visitor Survey... 66 El Capitan Meadow Visitor Survey... 66 Mirror Lake Visitor Survey... 68 Vernal Fall Visitor Survey... 69 Yosemite Falls Visitor Survey... 70 Summary of Study Results and Findings Visitor Counts... 71 Summary of Study Results and Findings Visitor Use Simulations and User Capacity Estimates... 72 Study Limitations and Recommendations for Additional Research... 75 References... 82 Appendix A - Bridalveil Fall Visitor Survey Instrument... 83 Appendix B - El Capitan Meadow Visitor Survey Instrument... 85 Appendix C - Mirror Lake Visitor Survey Instruments... 87 Appendix D - Vernal Fall Visitor Survey Instruments... 91 Appendix E - Yosemite Falls Visitor Survey Instrument... 95 Appendix F - Yosemite Valley Visitor Use Modeling Visitor Survey Log... 97 Appendix G - Visitor Survey Data Outlier Analysis Results... 101 Appendix H - Histograms of Hiking Times on Trails and Lingering Times at Attractions... 105 Histograms of Hiking Times and Lingering Times Bridalveil Fall... 106 iii

Histograms of Lingering Times El Capitan Meadow... 112 Histograms of Hiking and Bicycling Times Trail to Mirror Lake... 115 Histograms of Hiking Times Trail to Vernal Fall... 121 Histograms of Hiking Times and Lingering Times Yosemite Falls... 125 Appendix I - Method of Independent Replications Analysis Results... 131 Appendix J - Bridalveil Fall Visitor Survey Data Codebook... 147 Appendix K - El Capitan Meadow Visitor Survey Data Codebook... 151 Appendix L - Mirror Lake Visitor Survey Data Codebooks... 155 Appendix M - Vernal Fall Visitor Survey Data Codebooks... 167 Appendix N - Yosemite Falls Visitor Survey Data Codebook... 179 Appendix O - Timestamp Data Event Codes... 183 iv

Chapter 1 Introduction The number of visitors to Yosemite National Park increased fourfold in the last four decades of the 20 th century to more than four million visitors per year; today the park accommodates over three million visits annually. The challenges associated with this intensive visitation to the park are exacerbated by the fact that much of the park s visitor use is concentrated in Yosemite Valley. The mile-wide, seven-mile long Yosemite Valley comprises merely four percent of the park s total area, but the valley and the roads within the valley accommodate 98 percent of all park visitation. Furthermore, visitor use peaks during the summer months, with 31 percent of all park visits occurring during July and August (National Park Service, 2007). The design and layout of roads, parking, and facilities within Yosemite Valley were never meant to accommodate the intensive amount of vehicle traffic they receive today. Consequently, traffic congestion in Yosemite Valley is common during periods of peak visitation. For example, afternoon traffic departing from Yosemite Valley can create up to a twomile gridlock, resulting in drivers spending nearly two hours traveling one mile to exit the valley. Furthermore, on a typical day from May to September, up to 1,900 day use vehicles at a time are in Yosemite Valley competing for approximately 1,200 designated day use parking spaces. During the summer, the main day use visitor parking area fills to capacity between 11:00 AM and 1:00 PM. Shuttle bus service is provided in Yosemite Valley, in part to help alleviate traffic congestion on park roads. However, on days with high visitation levels, shuttle buses operating on the valley system are often crowded to the point that no additional visitors can board (National Park Service, 2007). 1

The combination of traffic congestion on roads in Yosemite Valley, a shortage of parking spaces for day use visitors, and crowded shuttle buses during peak periods of visitation cause resource degradation and diminish the quality of visitors experiences. Thus, the National Park Service (NPS) is engaged in planning processes that will include decisions about how to manage vehicle traffic in Yosemite Valley and other parts of the park. Changes made to the transportation system within Yosemite Valley as a result of these planning efforts are likely to be important in reducing traffic-related issues along the park s transportation corridors, but may have unintended consequences on social and resource conditions at visitor attractions within the valley. For example, it is possible that changes to the frequency and/or routes of shuttle service in Yosemite Valley could increase crowding at popular attraction sites in the valley. Thus, transportation planning decisions in Yosemite Valley are inextricably linked to user capacity management. Over the last decade, the NPS has used research and planning to address user capacity in Yosemite Valley through the formulation of indicators and standards of quality (National Park Service, 1997). Indicators of quality are defined as measurable, manageable variables that reflect the essence or meaning of management objectives related to resource protection and the visitor experience. Standards of quality are defined as the minimum acceptable condition of indicator variables. Indicator variables are monitored over time, and management actions are applied as needed to ensure that standards of quality are maintained. Studies were conducted in 1998 and 1999 to assist the NPS in identifying crowding-related standards of quality for popular attraction sites within Yosemite Valley (Manning, 2007; Manning et al., 2003). Results of these studies suggest that the number of visitors on trails and at attraction sites (e.g., the base of Yosemite Falls) are important indicators of the quality of visitors experiences in Yosemite Valley. 2

Furthermore, the study results provided visitor-based standards for crowding-related indicators including: 1) the number of people at one time (PAOT) at the base of Bridalveil Fall and Yosemite Falls; and 2) the number of people per viewscape (PPV) on trails to Bridalveil Fall, Mirror Lake, Vernal Fall, and Yosemite Falls. The primary purposes of the study presented in this report are to: 1) model visitor use of five popular attraction sites in Yosemite Valley; 2) estimate user capacities at each of the five study sites; and 3) estimate day-use user capacities for Yosemite Valley. Computer simulation models of visitor use were developed for five study sites in Yosemite Valley. The models were designed to account for the modes of transportation visitors use to access the study sites and used to estimate the number of people that can be accommodated at each site without violating crowding-related standards of quality. The models were also used to estimate the maximum number of day use visitors that can be accommodated in Yosemite Valley per day without violating crowding-related standards of quality at the five study sites. The crowding-related standards used in this study were formulated based on results of the research conducted in Yosemite Valley during the summers of 1998 and 1999. Thus, the results of this study are intended to assist the NPS in managing vehicle traffic and shuttle service in Yosemite Valley in a manner that accounts for user capacities of key attraction sites within the valley. The research presented in this report includes three components. The first component of the study involved visitor surveys and visitor counts to collect information about visitor use and behavior at five study sites in Yosemite Valley. The second component of the study used discrete-event systems simulation software to develop models of visitor use and behavior based on data collected at each of the five study sites. The third component of the study involved simulation analyses with the study models to estimate user capacities for each of the five study 3

sites and Yosemite Valley. Within the third component of the study, visitor-based standards of quality derived from research conducted in Yosemite Valley during the summers of 1998 and 1999 were incorporated into the simulation analyses as a basis for user capacity estimates. The report is organized as follows: Chapter 2 describes the five sites in Yosemite Valley for which visitor use models were developed in this study; Chapter 3 describes the visitor survey and visitor counting methods used to collect information about visitor use and behavior at the five study sites; Chapter 4 describes the methods used to analyze and model the visitor use data collected at each of the five study sites; Chapter 5 reports the results of simulation analyses performed with the visitor use computer simulation models, including estimates of user capacities for each of the study sites and Yosemite Valley; and Chapter 6 provides a summary of study findings, limitations, and recommendations for additional research. Appendices in the report include copies of the visitor survey instruments used in the study, codebooks for the electronic data files compiled from the visitor surveys and visitor counts, and tabular results of statistical analyses performed within the modeling phase of the study. All electronic data and model files associated with this study are archived with Yosemite National Park, including visitor survey data files, visitor count data files, and visitor use model files. 4

Chapter 2 Study Sites As stated, the purpose of this study is to model visitor use and estimate user capacities at five popular attraction sites in Yosemite Valley and for Yosemite Valley. The five sites selected for the study include: 1) Bridalveil Fall; 2) El Capitan Meadow; 3) the trail to Mirror Lake; 4) the trail to Vernal Fall; and 5) Yosemite Falls. These five sites were selected for the study because they are among the most popular destinations within Yosemite Valley, are thought to be important to the quality of visitors experiences of the valley, receive intensive amounts of visitor use during the summer, and are accessed by multiple modes of transportation. A scoping trip to the park was conducted during April, 2007, during which time researchers from Virginia Tech consulted with the NPS to define the geographic boundaries of each study site for the purposes of data collection and modeling. Based on this scoping trip, schematic diagrams of each study site were developed and used to guide the selection of sampling locations. Within the study, there were two primary types of sampling locations where field staff were stationed to conduct visitor surveys and visitor counts access points and attraction site boundaries. Access points are places where visitors enter and exit the study sites (e.g., trailheads), while attraction site boundaries are places where visitors enter and exit specific attraction areas within the study sites (e.g., the viewing platform at the base of Bridalveil Fall). All sampling locations are marked on the schematic diagrams of the study sites with text boxes numbered X1-XN, where N is the total number of sampling locations within the study site. A site description and schematic diagram for each of the five study sites are included in the remainder of this chapter, while specific sampling procedures are described in the next chapter of this report. 5

The Bridalveil Fall study site includes two sampling locations, including one access point and one attraction site boundary (Figure 1). The single access point into the Bridalveil Fall study site (X1) is located on the trail to Bridalveil Fall, at the junction of spur trails to the Bridalveil Fall parking lot and roadside parking on Southside Drive. The attraction site boundary (X2) is located at the junction of the trail to Bridalveil Fall and the viewing platform at the base of the fall. The length of the trail to the base of Bridalveil Fall between sampling locations X1 and X2 is 119 meters. The primary modes of transportation used to access Bridalveil Fall during the summer months include: 1) private vehicles and tour buses parked in the Bridalveil Fall parking lot or on the roadside along Southside Drive; 2) bicycles from various points of origin in Yosemite Valley; and 3) pedestrian access via the Valley Loop Trail. The Bridalveil Fall Trail and the viewing platform at the base of the fall are pedestrian use only. Figure 1. Bridalveil Fall study site schematic diagram. 6

The El Capitan Meadow study site includes a total of four sampling locations, all of which are access points (Figure 2). The four access points into El Capitan Meadow are located on the northern edge of the meadow along Northside Drive (X1-X4). The distance from the eastern-most point of the X1 access point to the western-most point of the X4 access point is 773 meters. The primary modes of transportation used to access El Capitan Meadow during the summer months include: 1) the Yosemite Valley shuttle bus service, which drops visitors off at the El Capitan Bridge just east of El Capitan Meadow; 2) private vehicles and tour buses parked along the roadside of Northside Drive; 3) bicycles from various points of origin in Yosemite Valley; and 4) pedestrian access via the Valley Loop Trail. The meadow itself is pedestrian use only. Figure 2. El Capitan Meadow study site schematic diagram. 7

The Mirror Lake study site includes a total of two sampling locations, both of which are access points (Figure 3). Both access points into the Mirror Lake study site are located on the trail to Mirror Lake one at the junction with the paved bicycle path near the bathrooms (X1), and one near the bathrooms adjacent to Mirror Lake (X2). The length of the trail to Mirror Lake between sampling locations X1 and X2 is 655 meters. The primary modes of transportation used to access the trail to Mirror Lake during the summer months include: 1) the Yosemite Valley shuttle bus service, which drops visitors off at the Mirror Lake Junction shuttle bus stop; 3) bicycles from various points of origin in Yosemite Valley; and 4) pedestrian access from various overnight accommodations and day use parking areas in the valley. The trail to Mirror Lake is primarily pedestrian and bicycle use. However, persons with physical disabilities are allowed vehicle access to the trail to provide universal access to Mirror Lake. Vehicle use of the trail was not accounted for in this study because it constitutes a nominal amount of the overall use of the trail. 8

Figure 3. Mirror Lake study site schematic diagram. 9

The Vernal Fall study site includes a total of two sampling locations, both of which are access points (Figure 4). One access point into the Vernal Fall study site is located at the Happy Isles Trailhead (X1), while the other access point is located at the northwest end of the first bridge over the Merced River on the trail to Vernal Fall (X2). The length of the trail to Vernal Fall between sampling locations X1 and X2 is 1,156 meters. The primary modes of transportation used to access the trail to Vernal Fall during the summer months include: 1) the Yosemite Valley shuttle bus service, which drops visitors off at the Happy Isles shuttle bus stop; 2) private vehicles parked at the Trailhead Parking lot east of Curry Village; 3) pedestrian access from various overnight accommodations and day use parking areas in the valley; and 4) bicycles from various points of origin in Yosemite Valley. The trail to Vernal Fall is pedestrian use only. Figure 4. Vernal Fall study site schematic diagram. 10

The Yosemite Falls study site includes a total of five sampling locations, including three access points and two attraction site boundaries (Figure 5). One access point into the Yosemite Falls area (X1) is located on the trail to Yosemite Falls, just north of the bathrooms and the junction with the Valley Loop Trail where it enters from the west. A second access point (X5) is located on the trail to Yosemite Falls, northeast of the Lower Yosemite Fall shuttle bus stop. The third access point into the Yosemite Falls study site (X4) is located on the trail to Yosemite Falls, at the junction with the Valley Loop Trail where it enters from the east. The two attraction site boundaries (X2 and X3) are located at either end of the bridge across Yosemite Creek at the base of the falls. The length of the trail to Yosemite Falls between sampling locations X1 and X2 is 334 meters, while the length of trail between sampling locations X5 and X3 is 287 meters. The primary modes of transportation used to access Yosemite Falls during the summer months include: 1) the Yosemite Valley shuttle bus service, which drops visitors off at the Lower Yosemite Falls shuttle bus stop; 2) private vehicles parked at Camp 6 day use parking, Yosemite Village, Yosemite Lodge, and along the roadside on Northside Drive; 3) tour buses parked at Yosemite Lodge; 4) bicycles from various points of origin in Yosemite Valley via the multi-use path; and 5) pedestrian access from various points of origin in Yosemite Valley via the Valley Loop Trail and multi-use path. The trails within the Yosemite Falls study site, and the viewing platform at the base of the fall, are pedestrian use only 11

Figure 5. Yosemite Falls study site schematic diagram. 12

Chapter 3 Data Collection Visitor surveys and visitor counts were administered during the summer of 2007 at each of the five study sites in Yosemite Valley to collect information about visitor use and behavior needed to construct simulation models of visitor use at the study sites. This chapter of the report describes the visitor survey and visitor counting methods used in this study, beginning with the visitor survey methods. Visitor Surveys Visitor surveys were administered to random samples of visitors at each of the five study sites in Yosemite Valley during the summer of 2007. The purpose of the visitor surveys was to collect information needed to develop site-specific visitor use models, including: 1) visitors group sizes; 2) the modes of transportation visitors use to travel to the study sites; and 3) the length of time visitors spend hiking the trails and lingering at attractions within the study sites. Site-specific survey cards were designed by researchers at Virginia Tech, in consultation with Yosemite National Park, and were reviewed and approved by the Virginia Tech Internal Review Board and the Office of Management and Budget. Appendices A-E contain copies of the survey cards administered at each of the five study sites, and Appendix F contains a copy of the survey log used to record information about survey response rates. Site-specific visitor survey data files in Excel format have been archived with Yosemite National Park and codesheets corresponding to the data files are contained in Appendices J-N. The number of visitor survey sampling days conducted at each study site ranged from four days at Bridalveil Fall and Yosemite Falls to eight days at Mirror Lake, with sampling 13

occurring at only one study site on any single sampling day (Tables 1-5). On each visitor survey sampling day, a survey administrator was located at each sampling location (i.e., each access point and attraction site boundary) within the selected study site from 10:00 AM to 5:00 PM (refer to the previous chapter of the report, entitled Study Sites, for schematic diagrams and descriptions of specific sampling locations for each study site). Surveyors stationed at access points recruited groups arriving to the study site to participate in the visitor survey. Each time a surveyor at an access point recruited a visitor group for the survey, the surveyor asked the group what mode of transportation they used to travel to the study site and recorded this information on the survey card. The surveyor also recorded the size of the visitor group, the date, and the current time. The surveyor then handed the card to the visitor group and instructed them to carry the card during their visit to the study site and to hand the card to each survey administrator they passed during their visit. Surveyors stationed at access points also collected survey cards from participating groups as they exited the study site and recorded the current time. Surveyors stationed at attraction site boundaries collected visitor survey cards from study participants each time they passed their sampling locations and recorded the current time. Surveyors then returned the survey cards to participants, and instructed them to continue carrying the cards and to hand the cards to each surveyor they met during their visit. Surveyors at access points collected survey cards from exiting visitors, and at sites with shuttle service, asked participating groups if they intended to ride the shuttle bus. Thus, the visitor survey cards contained information about the amount of time visitor groups spent hiking on each section of trail and/or lingering at each attraction within the study sites, as well as information about the proportion of visitors intending to ride the shuttle bus at the end of their visit to the study site. 14

Table 1. Bridalveil Fall visitor survey card sampling effort. Date Day of Week Solicitations Accept Refuse Unusable a LB Refuse b 07.02.2007 Monday 123 103 20 16 5 07.03.2007 Tuesday 120 110 10 4 4 07.04.2007 Wednesday 119 97 22 3 7 08.23.2007 Thursday 93 85 8 2 5 Total 455 395 60 25 21 a Unusable includes cards that were not returned and those that contained no useable data. b LB Refuse were refusals due to a language barrier with the potential respondent. Table 2. El Capitan Meadow visitor survey card sampling effort. Date Day of Week Solicitations Accept Refuse Unusable a Observations b 07.24.2007 Tuesday 99 99 0 1 23 07.28.2007 Saturday - - - - 24 07.29.2007 Sunday 105 105 0 4 32 07.30.2007 Monday - - - - 52 07.31.2007 Tuesday - - - - 77 08.01.2007 Wednesday - - - - 39 08.03.2007 Friday - - - - 47 Total 204 204 0 5 294 a Unusable includes cards that were not returned and those that contained no useable data. b Lingering times in El Capitan Meadow recorded through direct observation rather than visitor surveys. Table 3. Mirror Lake visitor survey card sampling effort. Date Day of Week Solicitations Accept Refuse Unusable a LB Refuse b 06.25.2007 Monday 162 124 38 19 5 07.07.2007 Saturday 139 122 17 10 4 07.10.2007 Tuesday 95 87 8 3 0 07.11.2007 Wednesday 121 93 28 5 3 08.15.2007 Wednesday 175 162 13 12 1 08.28.2007 Tuesday 59 51 8 10 1 08.30.2007 Thursday 43 43 0 0 0 09.09.2007 Sunday 113 107 6 5 2 Total 907 789 118 64 16 a Unusable includes cards that were not returned and those that contained no useable data. b LB Refuse were refusals due to a language barrier with the potential respondent. 15

Table 4. Vernal Fall visitor survey card sampling effort. Date Day of Week Solicitations Accept Refuse Unusable a LB Refuse b 06.24.2007 Sunday 132 115 17 7 1 08.08.2007 Wednesday 213 203 10 24 0 08.24.2007 Friday 172 143 29 28 5 08.29.2007 Wednesday 128 125 3 8 1 08.31.2007 Friday 136 133 3 19 1 09.08.2007 Saturday 165 156 9 15 3 09.15.2007 Saturday 180 167 13 25 3 Total 1126 1042 84 126 14 a Unusable includes cards that were not returned and those that contained no useable data. b LB Refuse were refusals due to a language barrier with the potential respondent. Table 5. Yosemite Falls visitor survey card sampling effort. Date Day of Week Solicitations Accept Refuse Unusable a LB Refuse b 07.25.2007 Wednesday 260 217 43 24 16 07.26.2007 Thursday 239 204 35 19 10 07.27.2007 Friday 231 195 36 6 11 08.02.2007 Thursday 216 197 19 11 3 Total 946 813 133 60 40 a Unusable includes cards that were not returned and those that contained no useable data. b LB Refuse were refusals due to a language barrier with the potential respondent. To track visitor survey response rates, surveyors stationed at access points recorded a survey log entry for each visitor group asked to participate in the study (see Appendix F for a copy of the survey log used at all five study sites). Information recorded on the survey log for each contacted group included: 1) current time; 2) visitor group size; 3) whether the group accepted or refused to participate; 4) the visitor survey card ID number for those groups who participated; and 5) comments concerning the contact, as needed (e.g., if a group refused to participate due to a language barrier). Visitor groups who were unwilling or unable to participate in the study were thanked for their consideration. The survey log data were intended to be used to examine whether those who refused to participate were systematically different than those visitor groups who did participate in the study (i.e., whether the survey data may be subject to 16

non-response bias). However, response rates at all five study sites were relatively high, ranging from 79.6% at Yosemite Falls to 97.5% at El Capitan Meadow (Tables 6-10). Thus, there were too few refusals to conduct robust statistical tests for non-response bias at all of the study sites, except Yosemite Falls. Results of an independent samples t-test of means suggest that groups who participated in the survey at Yosemite Falls did not differ significantly from those that refused, with respect to group size (t = 1.546, p-value = 0.214). These results, coupled with the high response rates at all five study locations, suggest that the visitor survey data are not likely to be biased due to systematic differences between study participants and visitor groups who did not participate in the study. Table 6. Bridalveil Fall visitor survey response rate. Overall a Minus LB a, b Acceptance Rate 81.3% 85.3% Refusal Rate 18.7% 14.7% a Unusable surveys treated as refusals. b LB were refusals due to a language barrier with the potential respondent. Table 7. El Capitan Meadow visitor survey response rate. Overall a Acceptance Rate 97.5% Refusal Rate 2.5% a Unusable surveys treated as refusals. Table 8. Mirror Lake visitor survey card response rates. Overall a Minus LB a, b Acceptance Rate 79.9% 81.4% Refusal Rate 20.1% 18.6% a Unusable surveys treated as refusals. b LB were refusals due to a language barrier with the potential respondent. 17

Table 9. Vernal Fall visitor survey card response rates. Overall a Minus LB a, b Acceptance Rate 81.3% 82.4% Refusal Rate 18.7% 17.6% a Unusable surveys treated as refusals. b LB were refusals due to a language barrier with the potential respondent. Table 10. Yosemite Falls visitor survey card response rate. Overall a Minus LB a, b Acceptance Rate 79.6% 83.1% Refusal Rate 20.4% 16.9% a Unusable surveys treated as refusals. b LB were refusals due to a language barrier with the potential respondent. Visitor Counts Visitor counts were conducted at each of the five study sites in Yosemite Valley during the summer of 2007. The counts were conducted to document the number of visitors arriving to the study sites, by time of day and access point. The site-specific counting procedures used to collect information about visitor arrivals were designed by researchers at Virginia Tech, in consultation with Yosemite National Park. Data collection for the visitor counts was administered on handheld computers (PDA s) using a program scripted by Resource Systems Group, Inc. entitled Event Counter. Visitor counts were conducted on three weekdays and two weekend days at each study site, with sampling occurring at only one study site on any single sampling day. Due to staffing constraints, visitor counts and visitor survey sampling were conducted on different days. On each day visitor counts were conducted, a data collector was stationed with a PDA at each access point into the selected study site from 10:00 AM to 5:00 PM (refer to the chapter of the report entitled Study Sites for schematic diagrams and descriptions of access point locations for each 18

study site). The PDA s contained the Event Counter program designed for recording timestamps (current data and time, to the second) each time a visitor entered the study site. Figure 6 illustrates the graphical user interface for the Event Counter program used to record timestamps for visitor arrivals. The lettered buttons were used to differentiate arrivals by visitor characteristics, as needed. For example, for visitor counts conducted at Mirror Lake, the A button was used to record a timestamp for each pedestrian arrival, while the C button was used to record a timestamp for each arriving bicyclist. Similarly, at El Capitan Meadow, the lettered buttons were used to differentiate arrivals by mode of transportation used to travel to the meadow (i.e., private vehicle, tour bus, shuttle bus, etc.), and at Bridalveil Fall the lettered buttons were used to differentiate between arrivals from roadside parking and arrivals from the Bridalveil Fall parking lot. At Vernal Fall and Yosemite Falls it was not possible to observe visitors transportation modes of arrival from the counting locations. Thus, all arrivals at these two sites were recorded generically (i.e., not differentiated by mode of transportation or any other characteristic) using the A button. Each time a lettered button was tapped on the PDA screen, a timestamp and lettered code were written to an ASCII text file in the format illustrated in Figure 7. Site-specific timestamp data files in ASCII text format have been archived with Yosemite National Park and a codesheet of site-specific event codes is contained in Appendix O. 19

Event Counter 3:25 A B D C E F G H I J K L M N O P Total Events: 125 Figure 6. Display of Event Counter program interface. Device: VT_Dell Event: Begin Session 2007-07-30 10:04:57 Event: A 2007-07-30 10:47:19 Event: A 2007-07-30 10:47:19 Event: C 2007-07-30 10:50:28 Event: A 2007-07-30 10:50:29 Event: C 2007-07-30 10:53:00 Event: C 2007-07-30 10:53:00 Event: C 2007-07-30 10:53:38 Event: A 2007-07-30 10:53:38 Event: A 2007-07-30 10:57:12 Event: C 2007-07-30 11:13:16 Event: C 2007-07-30 11:13:16 Event: C 2007-07-30 11:13:16 Event: C 2007-07-30 11:13:17 Event: C 2007-07-30 11:13:37 Event: C 2007-07-30 11:13:37 Event: C 2007-07-30 11:13:37 Event: C 2007-07-30 11:13:38 Event: A 2007-07-30 11:14:52 Event: A 2007-07-30 11:22:42 Event: A 2007-07-30 11:30:45 Figure 7. Example of Event Counter data format. 20

The timestamp data were summarized to report the total number of visitor arrivals per day (10:00 AM to 5:00 PM) for each of the five study sites (Tables 11-15). Of the five study sites, Yosemite Falls received the highest level of visitor use during the sampling period, with an average of 3,274 visitors per day, while El Capitan Meadow had the lowest visitation, with an average of 385 visitors per day. The timestamp data suggest that visitor use of all of the study sites except Vernal Fall has decreased since the user capacity studies conducted in 1998 and 1999. Changes in average daily visitation to the study sites ranged from a 31% decrease in visitor use at Mirror Lake, to a 4% increase at Vernal Fall. However, it should be noted that while visitor counts conducted as part of the studies in the 1990 s and the current study occurred during the summer months, the exact dates differed. Therefore, some of the differences in visitation across the two studies may be due to the timing of visitor counts. Furthermore, visitor counts were conducted for only three days at each study site during the studies in 1998 and 1999, and only five days during 2007 sampling. Thus, the precision of average daily visitation estimates from the two studies is somewhat limited due to relatively low sample sizes. The confidence intervals in Tables 11-15 document the precision of the 2007 visitation estimates. In addition to using the timestamp data to generate summaries of total daily visitation, the timestamp data were used as a primary input into the computer simulation models of visitor use at each study site. The methods used to model these arrival data and the visitor survey data are described in the next chapter of the report. 21

Table 11. Bridalveil Fall visitor arrivals a, by sampling date 2007 (10 AM 5 PM) Parking Lot Arrivals Roadside Parking Arrivals Sampling Date Day of Week Number Percentage Number Percentage Total Arrivals b 06.23.2007 Saturday 2,349 78.4% 649 21.6% 2,998 06.26.2007 Tuesday 2,027 82.6% 427 17.4% 2,454 06.27.2007 Wednesday 1,838 84.0% 349 16.0% 2,187 06.29.2007 Friday 1,767 85.6% 297 14.4% 2,064 07.01.2007 Sunday 2,055 86.6% 318 13.4% 2,373 Mean 2,007 83.4% 408 16.6% 2,415 95% Confidence Interval +/- 198.8 +/- 3% +/- 125.8 +/- 3% +/- 315.5 a Based on visitor counts at X1 access point noted on the schematic diagram of Bridalveil Fall (P. 6). b Average total arrivals to Bridalveil Fall between 10 AM and 5 PM during summer 1999 data collection = 2,788. Thus, 2007 data suggest a 13% decrease in average total arrivals to Bridalveil Fall between the hours of 10 AM and 5 PM. 22

Table 12. El Capitan Meadow visitor arrivals, by sampling date 2007 (10 AM 5 PM) 23 Sampling Roadside Parking b Shuttle Arrivals c Other d Total Date Day of Week Access Point a Number Percentage Number Percentage Number Percentage Arrivals X1 74 47.1% 57 36.3% 26 16.6% 157 07.28.2007 Saturday 07.30.2007 Monday 07.31.2007 Tuesday X2 218 80.4% 1 0.4% 52 19.2% 271 X3 135 97.8% 3 2.2% 0 0.0% 138 X4 12 100.0% 0 0.0% 0 0.0% 12 Total 439 76.0% 61 10.6% 78 13.5% 578 X1 38 30.4% 79 63.2% 8 6.4% 125 X2 59 100.0% 0 0.0% 0 0.0% 59 X3 61 82.4% 0 0.0% 13 17.6% 74 X4 6 28.6% 0 0.0% 15 71.4% 21 Total 164 58.8% 79 28.3% 36 12.9% 279 X1 71 39.4% 100 55.6% 9 5.0% 180 X2 201 97.6% 1 0.5% 4 1.9% 206 X3 75 100.0% 0 0.0% 0 0.0% 75 X4 1 100.0% 0 0.0% 0 0.0% 1 Total 348 75.3% 101 21.9% 13 2.8% 462 a Refer to the schematic diagram of El Capitan Meadow (P. 7) for the locations of access points. b Arrivals from private vehicles and tour buses parked on roadside along El Capitan Meadow. c Arrivals on foot from the El Capitan Bridge shuttle bus stop. d Arrivals on foot or bicycle from any location other than the El Capitan Bridge shuttle bus stop or from roadside parking along El Capitan Meadow.

Table 12 (continued). El Capitan Meadow visitor arrivals, by sampling date 2007 (10 AM 5 PM) 24 Sampling Roadside Parking b Shuttle Arrivals c Other d Total Date Day of Week Access Point a Number Percentage Number Percentage Number Percentage Arrivals X1 50 66.7% 14 18.7% 11 14.7% 75 08.01.2007 Wednesday 08.03.2007 Friday X2 147 86.5% 0 0.0% 23 13.5% 170 X3 43 87.8% 0 0.0% 6 12.2% 49 X4 16 94.1% 0 0.0% 1 5.9% 17 Total 256 82.3% 14 4.5% 41 13.2% 311 X1 47 40.2% 62 53.0% 8 6.8% 117 X2 79 71.8% 0 0.0% 31 28.2% 110 X3 58 100.0% 0 0.0% 0 0.0% 58 X4 11 100.0% 0 0.0% 0 0.0% 11 Total 195 65.9% 62 20.9% 39 13.2% 296 Mean Overall 280.4 71.7% 63.4 17.2% 41.4 11.1% 385.2 95% Confidence Interval Overall +/- 99.1 +/- 8.1% +/- 28.1 +/- 8.4% +/- 20.5 +/- 4.1% +/- 114.1 a Refer to the schematic diagram of El Capitan Meadow (P. 7) for the locations of access points. b Arrivals from private vehicles and tour buses parked on roadside along El Capitan Meadow. c Arrivals on foot from the El Capitan Bridge shuttle bus stop. d Arrivals on foot or bicycle from any location other than the El Capitan Bridge shuttle bus stop or from roadside parking along El Capitan Meadow.

Table 13. Mirror Lake visitor arrivals a, by sampling date 2007 (10 AM 5 PM) Pedestrian Arrivals Bicycle Arrivals Sampling Date Day of Week Number Percentage Number Percentage Total Arrivals b 08.10.2007 Friday 507 62.5% 304 37.5% 811 08.13.2007 Monday 516 61.1% 328 38.9% 844 08.14.2007 Tuesday 558 65.0% 301 35.0% 859 08.18.2007 Saturday 619 69.8% 268 30.2% 887 08.19.2007 Sunday 492 69.1% 220 30.9% 712 25 Mean 538 65.5% 284 34.5% 823 95% Confidence Interval +/- 45.0 +/- 3% +/- 36.6 +/- 3% +/- 59.3 a Based on visitor counts at X1 access point noted on the schematic diagram of Mirror Lake (P. 9). b Average total arrivals to Mirror Lake between 10 AM and 5 PM during summer 1999 data collection = 1,189. Thus, 2007 data suggest a 31% decrease in average total arrivals to Mirror Lake between the hours of 10 AM and 5 PM.

26 Table 14. Vernal Fall visitor arrivals a, by sampling date 2007 (10 AM 5 PM) Sampling Date Day of Week Total Arrivals b 07.19.2007 Thursday 1,524 07.20.2007 Friday 1,614 07.21.2007 Saturday 2,454 07.22.2007 Sunday 1,749 07.23.2007 Monday 1,755 08.11.2007 Saturday 2,370 Mean 1,911 95% Confidence Interval +/- 318.9 a Based on visitor counts at X1 access point noted on the schematic diagram of Vernal Fall (P. 10). b Average total arrivals to Vernal Fall between 10 AM and 5 PM during summer 1998 data collection = 1,836. Thus, 2007 data suggest a 4% increase in average total arrivals to Vernal Fall between the hours of 10 AM and 5 PM.

Table 15. Yosemite Falls visitor arrivals, by sampling date 2007 (10 AM 5 PM) 27 X1 Access Point a X4 Access Point a X5 Access Point a Total Sampling Date Day of Week Number Percentage Number Percentage Number Percentage Arrivals b 07.12.2007 Thursday 2,023 64.0% 17 0.5% 1,120 35.4% 3,160 07.13.2007 Friday 1,943 65.6% 32 1.1% 986 33.3% 2,961 07.14.2007 Saturday 2,807 69.1% 42 1.0% 1,214 29.9% 4,063 07.15.2007 Sunday 2,201 67.0% 21 0.6% 1,064 32.4% 3,286 07.16.2007 Monday 1,971 68.0% 19 0.6% 909 31.4% 2,899 Mean 2,189 66.7% 26 0.8% 1,059 32.5% 3,274 95% Confidence Interval +/- 315.3 +/- 2% +/- 9.3 +/- 0% +/- 103.3 +/- 2% +/- 409.8 a Refer to the schematic diagram of Yosemite Falls (P. 12) for the locations of access points. b Average total arrivals to Yosemite Falls between 10 AM and 5 PM during summer 1998 data collection = 4,147. Thus, 2007 data suggest a 21% decrease in average total arrivals to Yosemite Falls between the hours of 10 AM and 5 PM.

28

Chapter 4 Data Analysis and Modeling Data from the visitor surveys and visitor counts described in the previous chapter of the report served as the primary inputs into the computer simulation models of visitor use at the five study sites developed in this study. However, a series of data formatting and data analysis steps were required prior to implementing the visitor survey and visitor counts data within the computer simulation models. This chapter of the report describes the analysis and modeling procedures used to construct the computer models of visitor use at the five study sites. The procedures described below were performed independently for each of the five study sites in order to construct site-specific models of visitor use. Visitor Survey Data Analysis and Modeling The visitor survey data served as the source for four primary types of inputs to the computer simulation models developed in this study: 1) frequency distributions of visitor group sizes; 2) frequency distributions of visitors modes of transportation used to visit the study sites; 3) hiking times on the trails in the study sites; and 4) lingering times at attractions within the study sites. The first step in the analysis of visitor survey data involved screening the data for outlier cases with respect to group size, hiking time on trails, and lingering time at attractions. The purpose of this was to remove cases with group sizes, hiking times, and/or lingering times that are numerically distant from the rest of the data and consequently exert inordinate influence on averages and standard deviations of these variables. The decision rule for classifying cases as outliers was based on the distance of variable values from the interquartile range, and was operationalized through the following equations: 29

Outlier, lower bound < Q1 3*IQR (1) Outlier, upper bound > Q3 + 3*IQR (2) where: Q1 = 1 st quartile Q3 = 3 rd quartile IQR = Q3 Q1 Cases with outlier values for group size, hiking time, and/or lingering time were excluded from the analysis and modeling described below. In situations where a case had outlier values for one or more, but not all three of the variables, the case was only excluded from analysis and modeling of the variable(s) for which outlier values were observed. For example, a case with an outlier group size value but non-outlier values for hiking time and lingering time would be excluded from analysis and modeling of visitor group sizes, but retained for analysis and modeling of hiking and lingering times. The results of outlier analyses for each of the five study sites are reported in Appendix G. The outlier analysis results reported in Appendix G include the threshold values for upper and lower bound outliers, the number of cases excluded as upper and lower bound outliers, and the resulting sample sizes after excluding outliers. After outlier cases were removed, a series of statistical tests was performed to compare hiking times and lingering times, by mode of transportation used to visit the study site. In cases where only two modes were compared, Independent Samples t-tests were performed to compare mean hiking and lingering times. For example, t-tests were used to test for differences between visitor groups who parked in the Bridalveil Fall parking lot and those who parked along the roadside on Southside Drive, with respect to mean hiking times on the trail to Bridalveil Fall and mean lingering times at the base of Bridalveil Fall. In cases where more than two modes were 30

compared, One-Way Analysis of Variance (ANOVA) with Tukey Post-Hoc Multiple Comparisons was used to compare mean hiking and lingering times. For example, ANOVA with Tukey Post-Hoc Multiple Comparisons were performed to compare shuttle bus riders, drivers of private vehicles who parked at the Trailhead Parking Lot, and pedestrians from overnight accommodations in Yosemite Valley, with respect to hiking times on the trail to Vernal Fall. Statistically different mode groups were treated as independent samples in the remaining analyses and the differences were accounted for within the computer simulation models. In cases where there were no statistical differences in hiking and/or lingering times, by mode of transportation, the data for statistically similar mode groups was aggregated and modeled as a single sample. The next step within the analysis was to test for differences in hiking times and lingering times at each study site, by visitor group size. To do this, the frequency distribution of group sizes was examined to select a cutoff point to categorize each visitor group within the visitor survey data as a large group or small group. Next, Independent Samples t-tests were performed to compare hiking times and lingering times, by group size category. The tests were performed by mode of transportation in cases where statistically significant differences by mode were detected in the previous analysis step described above. For example, tests were conducted to assess whether the amount of time visitors spend lingering at the base of Yosemite Falls differs significantly depending on the size of the group. These tests were performed separately for groups who arrived to Yosemite Falls by private vehicle, shuttle bus, tour bus, pedestrian, and bicycle. Statistically different groups based on these tests were treated as independent samples in the remaining analyses and the differences were accounted for within the computer simulation models. In cases where there were no statistical differences in hiking and/or lingering times, by 31

group size, the data for statistically similar groups was aggregated and modeled as a single sample. As a result of the two stages of analysis described above (i.e., tests of hiking and lingering times, by mode of transportation and group size), means and standard deviations of hiking and lingering times were computed for all independent samples of visitor groups (Tables 16-21). In addition, the distributions of hiking and lingering times for each independent sample of visitor groups were inspected to select distributions with which to fit the data within the computer simulation models (see Appendix H for histograms of hiking and lingering times used for the purposes of fitting distributions). These results were used to define and parameterize (i.e., specify means and standard deviations) distributions of hiking and lingering times within the computer simulation models, from which simulated visitor groups are assigned hiking and lingering times for their simulated visits to the study sites. 32

Table 16. Mean and standard deviation of hiking times on trail to Bridalveil Fall and lingering time at base of Bridalveil Fall. Standard Activity Group Type n Mean (mm:ss) Deviation (mm:ss) Hiking from trailhead a to the Small Group (1-4 People) 81 2:50 0:58 base of Bridalveil Fall Large Group (5-14 People) 252 3:08 0:56 Hiking from the base of Small Group (1-4 People) 81 2:50 1:08 Bridalveil Fall to trailhead a Large Group (5-14 People) 237 3:13 1:29 Lingering at the base of Small Group (1-4 People) 81 11:43 11:59 Bridalveil Fall Large Group (5-14 People) 246 16:53 14:14 a Refers to the X1 access point noted on the Bridalveil Fall schematic diagram (P. 6). Table 17. Mean and standard deviation of lingering time in El Capitan Meadow. Mode Access Point a Group Type n Mean (mm:ss) Standard Deviation (mm:ss) Private Vehicle X1 Shuttle Bus X1, X2, X3, X4 NA b 173 17:24 13:11 Private Vehicle X2, X3, X4 Small (1-3 People) 208 7:11 7:00 Large (4-10 People) 94 12:19 9:09 Other c X1, X2, X3, X4 NA 19 17:07 12:58 a Refer to El Capitan Meadow schematic diagram (P. 7) for locations of access points. b Difference in lingering times between small and large groups is not statistically significant. c Due to small number of observations, delays were entered into the model as an empirical distribution rather than as a theoretical distribution with parameters (i.e., mean and standard deviation) specified. 33

Table 18. Mean and standard deviation of hiking and biking times on trail to Mirror Lake. Mode of Travel Activity Group Type n Mean (mm:ss) Standard Deviation (mm:ss) Hiking from trailhead a Small Group (1-3 People) 54 7:09 3:01 Pedestrian to Mirror Lake Large Group (4-10 People) 39 8:21 3:28 Small Group (1-3 People) 37 4:06 2:03 Hiking from Mirror Lake to trailhead a Large Group (4-10 People) 30 4:27 3:08 Biking from trailhead a N/A b 94 7:39 3:14 to Mirror Lake Bicycle Biking from Mirror Lake to trailhead a N/A b 68 4:23 2:46 a Refers to X1 access point noted on the Mirror Lake schematic diagram (P. 9). b Difference in biking times between small and large groups is not significantly different. Table 19. Mean and standard deviation of hiking time on the trail to Vernal Fall. Travel Direction Group Type n Mean (mm:ss) Standard Deviation (mm:ss) Hiking from trailhead a to first Small Group (1-3 People) 275 24:46 7:26 bridge on Vernal Fall Trail Large Group (4-10 People) 202 28:37 7:59 Hiking from first bridge on Small Group (1-3 People) 257 20:36 5:29 Vernal Fall Trail to trailhead a Large Group (4-10 People) 175 22:13 5:60 a Refers to Happy Isles Trailhead, noted as X1 on the Vernal Fall schematic diagram (P. 10). 34

Table 20. Mean and standard deviation of hiking times on trails to Yosemite Falls. Mean Group Type (mm:ss) Trail Segment Hiking from west trailhead a to base of Yosemite Falls Standard Deviation (mm:ss) NA b 6:56 2:03 Hiking from east trailhead c to base of Yosemite Falls Hiking from the VLT d to base of Yosemite Falls Small group (1-4 people) 10:20 2:26 Large group (5-10 people) 11:27 2:30 Small group (1-4 people) 5:04 1:12 Large group (5-10 people) 5:36 1:14 Hiking from base of Yosemite Falls NA b 6:20 2:14 to west trailhead a Hiking from base of Yosemite Falls NA b 10:21 3:17 to east trailhead c Hiking from base of Yosemite Falls to VLT d NA b 5:04 1:36 a Refers to the X1 access point noted on the Yosemite Falls schematic diagram (P. 12). b Large group and small group hiking times did not differ significantly. c Refers to the X5 access point noted on the Yosemite Falls schematic diagram (P. 12). d Refers to the X4 access point noted on the Yosemite Falls schematic diagram (P. 12). 35

Table 21. Mean and standard deviation of lingering time at base of Yosemite Falls. Mode Group Type n Mean (mm:ss) Standard Deviation (mm:ss) Private Small group (1-4 people) 144 13:48 19:46 Vehicle Large group (5-10 people) 41 25:28 28:14 Shuttle Bus Tour Bus Small group (1-4 people) Large group (5-10 people) Small group (1-4 people) Large group (5-10 people) 157 25:09 28:35 30 11:11 11:28 Walk Bike Small group (1-4 people) 147 15:52 17:11 Large group (5-10 people) 35 29:37 27:13 Small group (1-4 people) 25 20:00 25:27 Large group (5-10 people) 11 40:05 30:15 The next step within the visitor survey data analysis was to conduct a series of Chi- Square tests to compare group size distributions, by mode of transportation. The results of these tests were used to generate frequency distributions of visitor group sizes, accounting for differences in group size by mode of transportation (Tables 22-26). In cases where no differences in visitor group size distributions by mode of transportation were detected, a single distribution of group sizes was used within the computer models. In cases where statistical differences in visitor group size distributions by mode of transportation were detected, mode-specific distributions of visitor group sizes were used within the computer models. The visitor group size distributions are used within the computer simulation models to assign group sizes to simulated visitor groups. 36

Table 22. Visitor group size distribution, by parking location Bridalveil Fall. Group Size Origin 1 2 3 4 5 6 7-9 10+ n Roadside Parking 0.0% 29.2% 16.9% 21.3% 10.1% 7.9% 9.0% 5.6% 89 Parking Lot 1.8% 37.2% 12.8% 24.4% 8.9% 5.3% 5.7% 3.9% 282 Chi-Square, χ 2 = 6.377, p = 0.497 Table 23. Visitor group size distribution, by mode of arrival and access point a El Capitan Meadow. Group Size Mode Access Point 1 2 3 4 5 6 7+ n Private X1, X2, and X3 21.1% 31.9% 16.9% 17.8% 5.1% 3.9% 3.3% 332 Vehicle X4 34.8% 17.4% 4.3% 13.0% 13.0% 0.0% 17.4% 23 Shuttle Bus X1, X2,X3, and X4 15.0% 36.7% 14.2% 10.0% 12.5% 5.0% 6.7% 120 Other b X1, X2,X3, and X4 20.0% 33.3% 0.0% 20.0% 6.7% 6.7% 13.3 15 Chi-Square, χ 2 = 31.039, p = 0.002 (test excludes Other due to low sample size) a Refer to the schematic diagram of El Capitan Meadow (P. 7) for locations of access points. b Includes tour bus, bicycle, pedestrian via the Valley Loop Trail, and unobserved modes. 37

Table 24. Visitor group size distribution, by mode of arrival and access point a Mirror Lake. X1 Access Point Group Size Mode 1 2 3 4 5 6+ n Shuttle 2.6% 34.7% 18.1% 21.3% 11.4% 11.9% 193 Walked From Overnight Accommodations 7.3% 43.9% 9.8% 14.6% 14.6% 9.8% 41 Private Vehicle and Other b 7.9% 44.7% 13.2% 21.0% 5.3% 7.9% 38 Bike 8.3% 34.0% 15.5% 23.7% 7.1% 11.4% 97 Chi-Square, χ 2 = 13.120, p = 0.593 X2 Access Point Group Size n Mode 1 2 3 4 5 6+ Pedestrian 3.5% 39.4% 14.6% 21.2% 7.7% 13.6% 287 Bicycle 10.5% 31.3% 13.4% 28.3% 6.0% 10.5% 67 Chi-Square, χ 2 = 8.302, p = 0.140 a Refer to the schematic diagram of Mirror Lake (P. 9) for locations of access points. b Includes visitors who parked private vehicles at day use parking locations and walked. Table 25. Visitor group size distribution, by mode of arrival and access point a Vernal Fall. X1 Access Point Group Size Mode 1 2 3 4 5 6 7+ n Shuttle 3.4% 43.9% 8.4% 21.0% 7.4% 5.4% 10.5% 296 Walked From Overnight Accommodations 8.3% 30.0% 11.7% 21.6% 6.7% 5.0% 16.7% 60 Trailhead Parking 4.6% 53.9% 13.8% 13.8% 7.7% 0.0% 6.2% 65 Other b 8.3% 36.7% 11.7% 26.7% 5.0% 3.3% 8.3% 60 Chi-Square, χ 2 = 21.595(a), p = 0.250 X2 Access Point Group Size Mode 1 2 3 4 5 6 7+ n Pedestrian 5.8% 40.4% 15.5% 20.6% 5.5% 5.3% 6.9% 432 a Refer to the schematic diagram of Vernal Fall (P. 10) for locations of access points. b Includes visitors who parked private vehicles at day use parking locations other than Trailhead Parking and walked; and visitors who rode a bicycle. 38

Table 26. Visitor group size distribution, by mode of arrival and access point a Yosemite Falls. X1 Access Point Group Size Mode 1 2 3 4 5 6 7+ n Private Vehicle b 2.3% 37.6% 12.0% 25.6% 13.5% 1.5% 7.5% 133 Shuttle Bus 0.0% 26.1% 15.3% 26.8% 10.8% 8.9% 12.1% 157 Tour Bus 16.7% 33.3% 6.7% 36.7% 0.0% 3.3% 3.3% 30 Walk c 5.7% 41.5% 11.3% 22.6% 11.3% 1.9% 5.7% 53 Bike 2.5% 40.0% 7.5% 25.0% 12.5% 0.0% 12.5% 28 Chi-Square d, χ 2 = 8.529, p = 0.074 X4 Access Point Group Size Mode 1 2 3 4 5 6 7+ n Private Vehicle b 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0 Shuttle Bus 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0 Tour Bus 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0 Walk c 25.0% 40.0% 10.0% 10.0% 0.0% 5.0% 10.0% 20 Bike 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0 All visitors entering at X4 access point were pedestrians from the Valley Loop Trail. X5 Access Point Group Size Mode 1 2 3 4 5 6 7+ n Private Vehicle b 2.2% 36.3% 23.1% 16.5% 9.9% 4.4% 7.6% 91 Shuttle Bus 4.3% 45.7% 13.0% 15.2% 8.7% 4.3% 8.8% 46 Tour Bus 0.0% 25.0% 75.0% 0.0% 0.0% 0.0% 0.0% 4 Walk c 3.9% 32.3% 15.5% 29.0% 12.3% 3.9% 3.1% 155 Bike 0.0% 25.0% 6.3% 31.3% 6.3% 18.8% 12.3% 16 Chi-Square d, χ 2 = 4.305, p = 0.401 a Refer to the schematic diagram of Yosemite Falls (P. 12) for locations of access points. b Includes visitors who parked a private vehicle at Yosemite Lodge or on roadside along Northside Drive c Includes visitors who parked a private vehicle at or rode a shuttle bus to Yosemite Village, including Camp 6 day use parking, and walked; and visitors who walked on the paved bike path or Valley Loop Trail. d Due to low counts in some cells, Chi-squares results are based on comparison of distributions of small (1-4 people) and large (5-13 people) groups. 39

Finally, the visitor survey data were used to generate frequency distributions of transportation modes used to travel to the study sites (Tables 27-31). For study sites with multiple access points, separate mode frequency distributions were generated for each access point. The mode of transportation distributions are used within the computer simulation models to assign transportation modes to simulated visitor groups. It should be noted that these transportation modes refer to the mode of transportation used to travel to the study site (e.g., shuttle bus, private vehicle, tour bus, etc.), not the mode of transportation used while visiting the study site. In fact, all study sites are pedestrian use only, except the trail to Mirror Lake, which is primarily intended for pedestrian and bicycle use. Further, the mode of arrival is of particular interest in this study, as the relative frequency with which visitors use various modes of transportation to visit the study sites is a potentially important policy lever available to the NPS to manage user capacity and transportation in Yosemite Valley. Incorporating arrival mode distributions into the design of the study models provides the capability to use the models to simulate the effects of mode share changes on crowding-related indicators of quality and related user capacity estimates for the study sites. Table 27. Parking location for visit to Bridalveil Fall. Roadside Parking on Southside Drive Bridalveil Fall Parking Lot Number Percentage Number Percentage 89 24.0% 282 76.0% 40

Table 28. Transportation mode of arrival, by access point a El Capitan Meadow. Private Vehicle b Shuttle Bus Other c Access Point Number Percentage Number Percentage Number Percentage X1 47 27.6% 117 68.8% 6 3.6% X2 227 94.5% 3 1.3% 10 4.2% X3 58 100.0% 0 0.0% 0 0.0% X4 23 88.5% 0 0% 3 11.5% Chi-Square, χ 2 = 288.858, p = <0.001 a Refer to the schematic diagram of El Capitan Meadow (P. 7) for locations of access points. b Private vehicles parked on roadside of Northside Drive. c Includes tour bus, bicycle, pedestrian via the Valley Loop Trail, and unobserved modes. Table 29. Transportation mode of arrival, by access point a Mirror Lake. Walked from Access Shuttle Bus Overnight Accommodations Bicycle Private Vehicle and Other b Point Number Percentage Number Percentage Number Percentage Number Percentage X1 197 52.7% 41 11.0% 98 26.2% 38 10.1% Access Point Pedestrian Bicycle X2 - - 288 80.9% 68 19.1% - - a Refer to the schematic diagram of Mirror Lake (P. 9) for locations of access points. b Includes visitors who parked private vehicles at day use parking locations and walked. Table 30. Transportation mode of arrival Vernal Fall Walked from Overnight Shuttle Bus Accommodations Trailhead Parking Other a Number Percentage Number Percentage Number Percentage Number Percentage 296 61.5% 60 12.5% 65 13.5% 60 12.5% a Includes visitors who parked private vehicles at day use parking locations other than Trailhead Parking and walked; and visitors who rode a bicycle. 41

Table 31. Transportation mode of arrival, by access point a Yosemite Falls. Access Private Vehicle b Shuttle Bus Tour Bus Walk c Bike Point Number Percentage Number Percentage Number Percentage Number Percentage Number Percentage X1 134 31.5% 161 37.8% 32 7.5% 55 12.9% 44 10.3% X4 0 0.0% 0 0.0% 0 0.0% 20 100.0% 0 0.0% X5 93 29.2% 48 15.1% 4 1.3% 155 48.7% 18 5.7% χ 2 = 179.93, p < 0.001 (includes all starting locations) χ 2 = 135.99, p < 0.001 (excludes starting location X4) a Refer to the schematic diagram of Yosemite Falls (P. 12) for locations of access points. b Includes visitors who parked a private vehicle at Yosemite Lodge or on roadside along Northside Drive c Includes visitors who parked a private vehicle at or rode a shuttle bus to Yosemite Village, including Camp 6 day use parking, and walked; and visitors who walked on the paved bike path or Valley Loop Trail. 42

Visitor Counts Data Analysis and Modeling The visitor count data were used to model the arrival of visitors to the study sites, by time of day. To do this, a series of computations was performed with the visitor count data to construct what are termed visitor group interarrival time distributions. The visitor count data were used to calculate mean arrivals, by 30 minute time interval, for each access point within each study site. In cases, where it was possible to observe mode of arrival from the access points where visitor counts were conducted, separate tables of arrivals, by 30 minute time interval, were generated by mode this includes: 1) arrivals, by mode at El Capitan Meadow; and 2) arrivals to Bridalveil Fall from the Bridalveil Fall parking lot versus roadside parking on Southside Drive. Tables 32-36 report the arrival data, by 30 minute intervals, derived from the 2007 visitor counts, as well as analogous data from the 1998 and 1999 user capacity studies conducted in Yosemite Valley. It should be noted that during the 2007 study, visitor counts were conducted from 10:00 AM to 5:00 PM, while visitor counts during the 1998 and 1999 studies generally occurred from 7:00 AM to 8:00 PM. The 1998 and 1999 visitor count data were used to estimate early morning and late afternoon/evening arrivals for 2007. In particular, the rates at which 1998 and 1999 arrivals increased from 7:00 AM to 10:00 AM and decreased from 5:00 PM to 8:00 PM were applied to the 2007 data to extrapolate to the time periods during which data were not collected. This approach was validated by comparing plots of the 1998 and 1999 data to plots of the 2007 data and finding that the data from the two studies exhibited similar morning and evening arrival trends. The 2007 estimated arrivals data for 7:00 AM to 10:00 AM and 5:00 PM to 8:00 PM were generated in order to design the 2007 visitor use models to simulate the same hours of the day simulated with visitor use models developed in the 1998 and 1999 studies. The 2007 estimated arrivals are noted in italics in Tables 32-36. It should be noted that El Capitan 43

Meadow was not included in the 1998 and 1999 user capacity studies. Therefore, it was not possible to estimate morning and evening arrivals to El Capitan Meadow, and the El Capitan Meadow model simulates visitor use only for the hours of 10:00 AM to 5:00 PM. Table 32. Mean visitor arrivals to Bridalveil Fall, by time of day 1999 and 2007. Time of Day Via Roadside Parking 2007 Via Parking Lot 2007 Total 2007 Total 1999 7:00 AM-7:30 AM 0 2 2 3 7:30 AM-8:00 AM 1 5 6 6 8:00 AM-8:30 AM 3 13 16 15 8:30 AM-9:00 AM 6 28 34 35 9:00 AM-9:30 AM 10 48 58 59 9:30 AM-10:00 AM 15 74 90 91 10:00 AM-10:30 AM 22 146 168 122 10:30 AM-11:00 AM 39 148 187 165 11:00 AM-11:30 AM 34 174 208 251 11:30 AM-12:00 PM 32 190 222 269 12:00 PM-12:30 PM 38 186 224 260 12:30 PM-1:00 PM 30 163 193 173 1:00 PM-1:30 PM 42 148 190 189 1:30 PM-2:00 PM 27 148 175 218 2:00 PM-2:30 PM 31 128 159 217 2:30 PM-3:00 PM 29 128 157 178 3:00 PM-3:30 PM 28 126 154 235 3:30 PM-4:00 PM 22 117 139 183 4:00 PM-4:30 PM 18 111 129 167 4:30 PM-5:00 PM 16 95 111 160 5:00 PM-5:30 PM 22 107 129 144 5:30 PM-6:00 PM 23 113 136 151 6:00 PM-6:30 PM 13 66 79 88 6:30 PM-7:00 PM 9 42 50 56 7:00 PM-7:30 PM 6 28 34 37 7:30 PM-8:00 PM 2 11 13 15 Total 518 2,545 3,063 3,487 Note: Numbers in italics denote estimated arrivals. 44

Table 33. Mean visitor arrivals to El Capitan Meadow, by time of day, mode of transportation, and access point a 2007. 45 All Modes Time of Day X1 X2 X3 X4 Total X1 X2 X3 X4 Total X1 X2 X3 X4 Total Private Vehicles Shuttle Bus Other b 10:00 AM-10:30 AM 3 5 4 0 12 5 0 0 0 5 0 0 1 0 1 18 10:30 AM-11:00 AM 9 15 4 2 30 6 0 0 0 6 0 0 0 0 0 36 11:00 AM-11:30 AM 3 17 7 1 28 3 0 0 0 3 1 0 0 0 1 32 11:30 AM-12:00 PM 1 18 6 0 25 5 0 0 0 5 1 0 0 0 1 31 12:00 PM-12:30 PM 7 3 5 1 16 7 0 1 0 8 1 0 0 0 1 25 12:30 PM-1:00 PM 11 3 5 0 19 2 0 0 0 2 1 0 0 0 1 22 1:00 PM-1:30 PM 1 7 7 3 18 4 0 0 0 4 1 0 0 0 1 23 1:30 PM-2:00 PM 1 7 3 0 11 4 0 0 0 4 1 0 0 0 1 16 2:00 PM-2:30 PM 4 1 9 0 14 6 0 0 0 6 1 0 0 0 1 21 2:30 PM-3:00 PM 2 10 5 0 17 7 0 0 0 7 0 0 0 0 0 24 3:00 PM-3:30 PM 2 15 5 0 22 5 0 0 0 5 2 10 2 0 14 41 3:30 PM-4:00 PM 4 14 3 0 21 4 0 0 0 4 1 2 0 0 3 28 4:00 PM-4:30 PM 6 14 7 0 27 3 0 0 0 3 1 0 0 3 4 34 4:30 PM-5:00 PM 3 12 5 2 22 1 0 0 0 1 1 10 0 0 11 34 5:00 PM-5:30 PM 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 Total 57 142 75 9 283 62 0 1 0 63 12 22 3 3 40 386 a Refer to the schematic diagram of El Capitan Meadow (P. 7) for the locations of access points. b Includes arrivals by tour bus, bicycle, pedestrian access via the Valley Loop Trail, and arrivals for which mode was not observed.

Table 34. Mean visitor arrivals to Mirror Lake, by time of day and access point a 1999 and 2007 Time of Day X1 2007 X2 2007 Total 2007 X1 1999 X2 1999 Total 1999 7:00 AM-7:30 AM 1 3 4 4 1 5 7:30 AM-8:00 AM 2 5 7 6 2 8 8:00 AM-8:30 AM 1 13 14 4 7 11 8:30 AM-9:00 AM 1 10 11 3 5 8 9:00 AM-9:30 AM 6 10 16 18 5 23 9:30 AM-10:00 AM 10 17 27 31 9 40 10:00 AM-10:30 AM 15 26 41 45 13 58 10:30 AM-11:00 AM 32 32 64 85 27 112 11:00 AM-11:30 AM 48 53 101 111 47 158 11:30 AM-12:00 PM 65 66 131 96 69 165 12:00 PM-12:30 PM 66 53 119 84 84 168 12:30 PM-1:00 PM 73 48 121 87 84 171 1:00 PM-1:30 PM 75 53 128 79 101 180 1:30 PM-2:00 PM 79 54 133 113 118 231 2:00 PM-2:30 PM 64 33 97 112 105 217 2:30 PM-3:00 PM 60 50 110 83 101 184 3:00 PM-3:30 PM 63 39 102 86 98 184 3:30 PM-4:00 PM 73 56 129 83 92 175 4:00 PM-4:30 PM 58 44 102 64 67 131 4:30 PM-5:00 PM 51 31 82 62 80 142 5:00 PM-5:30 PM 52 28 80 63 72 135 5:30 PM-6:00 PM 36 25 61 44 63 107 6:00 PM-6:30 PM 16 20 36 20 52 72 6:30 PM-7:00 PM 16 10 26 19 27 46 7:00 PM-7:30 PM 9 7 16 11 18 29 7:30 PM-8:00 PM 7 9 16 8 22 30 Total 979 795 1,774 1,421 1,369 2,790 Note: Numbers in italics denote estimated arrivals. a Refer to the schematic diagram of Mirror Lake (P. 9) for the locations of access points. 46

Table 35. Mean visitor arrivals to Vernal Fall, by time of day and access point a 1998 and 2007. Time of Day X1 2007 X2 2007 Total 2007 X1 1998 X2 1998 Total 1998 7:00 AM-8:00 AM 213 4 217 212 3 215 8:00 AM-8:30 AM 54 6 60 54 4 58 8:30 AM-9:00 AM 97 9 106 96 6 102 9:00 AM-9:30 AM 108 13 121 107 8 115 9:30 AM-10:00 AM 164 14 178 163 9 172 10:00 AM-10:30 AM 157 15 172 156 9 165 10:30 AM-11:00 AM 210 31 241 213 10 223 11:00 AM-11:30 AM 204 53 257 197 40 237 11:30 AM-12:00 PM 203 87 290 225 80 305 12:00 PM-12:30 PM 204 110 314 194 93 287 12:30 PM-1:00 PM 164 141 305 149 111 260 1:00 PM-1:30 PM 142 171 313 124 124 248 1:30 PM-2:00 PM 138 187 325 145 130 275 2:00 PM-2:30 PM 126 191 317 85 170 255 2:30 PM-3:00 PM 103 169 272 110 157 267 3:00 PM-3:30 PM 88 226 314 76 198 274 3:30 PM-4:00 PM 64 215 279 81 211 292 4:00 PM-4:30 PM 62 204 266 52 195 247 4:30 PM-5:00 PM 45 196 241 29 176 205 5:00 PM-5:30 PM 52 177 229 33 159 192 5:30 PM-6:00 PM 32 191 223 20 172 192 6:00 PM-6:30 PM 36 176 212 23 158 181 6:30 PM-7:00 PM 26 146 172 17 131 148 7:00 PM-7:30 PM 3 124 127 2 111 113 7:30 PM-8:00 PM 2 12 14 1 21 22 Total 2,697 2,868 5,565 2,564 2,486 5,050 Note: Numbers in italics denote estimated arrivals. a Refer to the schematic diagram of Vernal Fall (P. 10) for the locations of access points. 47

Table 36. Mean visitor arrivals to Yosemite Falls, by time of day and access point a 1998 and 2007. Time of day X1 2007 X4 2007 X5 2007 Total 2007 Total 1998 7:00 AM 8:00 AM 8 0 4 12 25 8:00 AM 8:30 AM 4 0 2 6 13 8:30 AM 9:00 AM 18 0 10 28 59 9:00 AM 9:30 AM 65 1 37 103 211 9:30 AM 10:00 AM 39 1 22 62 128 10:00 AM 10:30 AM 57 1 32 90 185 10:30 AM 11:00 AM 96 2 44 142 203 11:00 AM 11:30 AM 169 2 79 250 282 11:30 AM 12:00 PM 154 3 90 247 243 12:00 PM 12:30 PM 140 1 101 242 336 12:30 PM 1:00 PM 163 1 93 257 295 1:00 PM 1:30 PM 202 1 106 309 270 1:30 PM 2:00 PM 200 2 70 272 354 2:00 PM 2:30 PM 177 1 68 246 375 2:30 PM 3:00 PM 217 2 90 309 470 3:00 PM 3:30 PM 174 2 81 257 252 3:30 PM 4:00 PM 146 2 81 229 320 4:00 PM 4:30 PM 150 2 62 214 304 4:30 PM 5:00 PM 144 3 63 210 258 5:00 PM 5:30 PM 137 3 60 200 245 5:30 PM 6:00 PM 105 3 46 154 188 6:00 PM 6:30 PM 75 2 33 110 134 6:30 PM 7:00 PM 48 1 21 70 86 7:00 PM 7:30 PM 42 1 18 61 75 7:30 PM 8:00 PM 31 1 14 46 56 Total 2,761 38 1,327 4,126 5,367 Note: Numbers in italics denote estimated arrivals. a Refer to the schematic diagram of Yosemite Falls (P. 12) for the locations of access points. It should be noted there was only one access point to Yosemite Falls during the 1998 study, there are now three access points due to changes in the design of the site. 48

Once mean visitor arrivals were summarized into 30 minute intervals, they were used to compute interarrival times (i.e., the average amount of time, in minutes, between visitor arrivals) for each 30 minute time interval using the following equation: where: IT (7:00 AM 7:30 AM) = 30 minutes / MVA (7:00 AM 7:30 AM) (3) IT (7:00 AM 7:30 AM) = mean interarrival time for the 7:00 AM to 7:30 AM time period MVA (7:00 AM 7:30 AM) = mean visitor arrivals for the 7:00 AM to 7:30 AM time period Thus, the unit of measurement for interarrival times is minutes per visitor arrival. Next, individual interarrival times (as computed in Equation 3) were converted to group interarrival times. To do this, a groups per people factor was computed using the group size frequency distributions reported early, where the number of groups contained within the frequency distribution was divided by the number of people contained within the groups. For example, the dummy data presented in Table 37 include 73 groups (sum of column 2) and 190 individuals (sum of the products of columns 1 and 2). Thus, the groups per people factor for the dummy data in Table 37 equals 73 divided by 190, or 0.38 groups per people. Next, the individual interarrival times were divided by the groups per people factor to compute group interarrival times for each 30 minute time interval. The results of these computations were used to generate group interarrival distributions, by access point. In the case of El Capitan Meadow, group interarrivals were computed by access point and by arrival mode of transportation, while at Mirror Lake, group interarrival distributions were computed separately for visitor groups arriving on foot and bicycle at each access point. 49

Table 37. Group size distribution dummy data Group Size Frequency 1 10 2 32 3 15 4 9 5 7 The group interarrival distributions were used to specify the number of simulated visitor group arrivals, by time of day, within the computer simulation models. Thus, the models are designed to simulate the temporal pattern of visitor arrivals as observed through the visitor counts conducted at the study sites during the summer of 2007. Furthermore, group interarrival multipliers were included in the models to allow the user to ramp up or ramp down the number of simulated visitor group arrivals by specified percentages in order to simulate increases or decreases in visitor use at the study sites. Model Algorithm and Programming The computer simulation models of visitor use at the five study sites were developed using Extend v.6 (2002) discrete-event systems simulation software. The structure of the models consists of hierarchical blocks (H-blocks) that: 1) simulate visitor use and behavior of the study sites, including arriving at access points, hiking on trails, lingering at attraction sites, and exiting to the valley shuttle service or other mode of transportation; and 2) monitor crowding-related indicators of quality (i.e., PAOT at attractions and PPV on selected sections of trail) throughout the course of simulated visitor use days. Each type of hierarchical block contained within the study models are described in the following paragraphs. Access Point H-blocks are used within the study models to generate simulated visitor groups (Figure 8). The rate at which simulated visitor groups are generated within an access 50

point is determined by the corresponding group interarrival distribution computed following procedures described earlier in this chapter. The rate of visitor arrivals can be ramped up or ramped down by changing the value of the multiplier contained within the Access Point H- blocks to simulate increases or decreases in daily visitation. 2773 Total use MultiplierIn Eqn t y Interarrivals V 1 2 3 Generator Figure 8. Sample Access Point H-block After being generated within Access Point H-blocks, simulated visitor groups are routed within the study models to Attribute H-blocks (Figure 9). Attribute H-blocks are designed to assign attribute values to simulated visitor groups, including values that define a simulated group s size and the amount of time they spend hiking on trails and lingering at attractions during their simulated visit to the study site. Distributions of attribute values used in the models to assign group sizes, hiking times, and lingering times are based on the visitor survey data analysis results presented earlier in this chapter. For example, results of statistical tests conducted with the visitor survey data suggest that, on average, large groups spend a longer time hiking on the trail to Bridalveil Fall and lingering at the base of the fall than small groups. Thus, separate distributions were specified within the Bridalveil Fall model, with group size-specific means and standard deviations of lingering times, and these distributions were used to assign hiking and lingering times separately to small and large simulated visitor groups (Figure 9). 51

Set A(5) Set A(5) Rand Rand Rand Rand Rand Rand Rand 1 2 3 TTU_X1-PPV 1 2 3 TTU_PPV 1 2 3 TTU_PPV-X2 1 2 3 Base Delay 1 2 3 TTD_X2-PPV 1 2 3 TTD_PPV 1 2 3 TTD_PPV-X1 Set Travel Times and Base Delay, Small Groups Set A(5) Set A(5) Rand Rand Rand Rand Rand Rand Rand 1 2 3 TTU_X1-PPV 1 2 3 TTU_PPV 1 2 3 TTU_PPV-X2 1 2 3 Base Delay 1 2 3 TTD_X2-PPV 1 2 3 TTD_PPV 1 2 3 TTD_PPV-X1 Set Travel Times and Base Delay, Large Groups Figure 9. Sample Attribute H-block After receiving attribute values within Attribute H-blocks, the simulated visitor groups are directed to the trail(s) and/or attractions within the study site. Trail Section H-blocks simulate visitor use and travel along the study sites trails (Figure 10). The Trail Section H-blocks are designed to hold each simulated visitor group as they pass along the trail section on their simulated visit. The amount of time each simulated visitor group is held within a Trail Section H-block is determined by the value of the group s hiking time attribute that was assigned within the Attribute H-block. 52

Get F U A Δ TTU_PPV D C L W 50m of Trail Figure 10. Sample Trail Section H-block Attraction Area H-blocks simulate visitor use at attraction areas (e.g., the base of Bridalveil Fall) within the study sites, and operate similarly to Trail Section H-blocks. When simulated visitor groups enter Attraction Area H-blocks, they are held within the block for an amount of time determined by the value of the group s lingering time attribute that was assigned within the Attribute H-block (Figure 11). Get F U Δ A D C L W Base of Fall Figure 11. Sample Attraction Area H-block Within the study models, PPV Calculator H-blocks and PAOT Calculator H-blocks are connected to Trail Section H-blocks and Attraction Area H-blocks, respectively (Figure 12). The PPV Calculator H-blocks and PAOT Calculator H-blocks are designed to monitor the number of people on trails and at attractions at one minute intervals throughout the course of each simulated visitor use day. The PPV Calculator H-blocks and PAOT Calculator H-blocks contain File Output blocks that report to an ASCII text file the percentage of time within a simulated visitor use day user-specified standards of quality for PPV and PAOT are exceeded. Thus, the PPV Calculator H-blocks and PAOT Calculator H-blocks are key components of the simulation 53

analyses conducted within this study to estimate user capacities for the study sites and Yosemite Valley. Figure 12. Sample PAOT Calculator H-block To summarize, the sequence of processes that occurs within the study models is as follows: 1. Access point H-blocks generate simulated visitor groups based on group interarrival distributions and route them to Attribute H-blocks. 2. Attribute H-blocks assign each simulated visitor group a group size and transportation mode of arrival based on group size and mode frequency distributions constructed from the visitor survey data. Subsequently, the Attribute H-blocks assign each simulated visitor group hiking and/or lingering times (depending on whether the study site has trails, an attraction, or trails and an attraction). The hiking and lingering times are drawn from distributions that account for group size and transportation mode of arrival in cases where statistically significant differences where found within the analysis of visitor survey data. 54