Urban Trails and Demand Response to Weather Variations

0 0 0 Urban Trails and Demand Response to Weather Variations Alireza Ermagun, Ph.D. (Corresponding) Urban and Regional Planning Humphrey School of Public Affairs University of Minnesota, Twin Cities Tel: + () 0-00 Email: ermag00@umn.edu Greg Lindsey, Ph.D. Professor Humphrey School of Public Affairs University of Minnesota, Twin Cities Email: linds0@umn.edu Tel: + () - Tracy Hadden Loh, Ph.D. Senior Data Scientist Center for Real Estate and Urban Analysis George Washington University Email: thloh@gwu.edu Tel: +(0) - Paper submitted for: Presentation at th Annual Transportation Research Board Meeting, January 0 Bicycle and Pedestrian Data Subcommittee (ABJ()) Word Count (excluded references option):, +,00 =, words (Text) ( Tables + Figure)

Ermagun, Lindsey, and Hadden Loh ABSTRACT This paper makes three contributions to the literature on non-motorized traffic monitoring and trail management. First, we summarize trail traffic monitoring results for monitoring stations on multiuse trails in cities in the United States, including locations across climate regions and zones classified by the U.S. Department of Energy. The monitoring results include estimates of average daily bicyclists (ADB) and average daily pedestrians (ADP) for the period, January, 0 through February, 0. Second, we present a set of econometric models that summarize the effects of variation in temperature, precipitation, wind speed, dew point, and hours of daylight on daily bicycle and pedestrian trail traffic volumes. We compare regional elasticities for each weather variable for both bicyclists and pedestrians. Third, we introduce the concept of demand returns to scale by testing the parabola form of the weather factors in the models, and measuring the vertex points of demand functions. Our results show that bicyclists and pedestrians respond differently to variations in weather and that the responses of both bicyclists and pedestrians to these variations also vary regionally. Transportation planners and trail managers can use these results to assess the effects of weather on trail traffic throughout the United States. Keywords: Trail traffic; Return to scale; Average daily bicyclists; Average daily pedestrians; Negative binomial regression

Ermagun, Lindsey, and Hadden Loh 0 0 0 INTRODUCTION Since passage of The Intermodal Surface Transportation Efficiency Act in, the federal government has allocated more than US$ billion to trail projects. These investments have been supported by hundreds of millions of additional investments by state and local governments, private foundations, and nonprofit organizations (). During the same period, demand for access to trails has grown disproportionately to other urban recreational facilities. Off-street, multiuse trails have been integrated into local and regional transportation infrastructure networks for both bicyclists and pedestrians. The Rails to Trails Conservancy (RTC) estimates that % of Americans currently live within miles of a multiuse trail that is at least 0. miles long. RTC also notes that these trails are not evenly distributed: populations within of the Censusdesignated Metropolitan Statistical Areas (MSAs) on average are closer to trails than populations elsewhere in the United States (). The research studying factors associated with trail use has grown over the past years, gaining momentum during the growth in demand for using trails. Trail managers and funding agencies need this information to plan systems and facilities, optimize investments, and increase efficiency of trail operations and maintenance. Among the influential factors on trail use, climate has aroused the interest of planners and practitioners for certain reasons. For example, understanding the demand response to variations in weather during the year enables managers to make efficient operational decisions about whether to maintain trails in winter or when to resurface or mow in summer. Information about demand response to weather also may affect the design of facilities, including the need for traffic controls. Our contribution to the existing body of knowledge is threefold: () Much of the previous research has been limited to a single mode, population group, facility, network, or city. Little is known about weather factors associated with trail demand for both pedestrian and bicyclists over different climate regions. This deficiency stems from the lack of comprehensive data. The present study overcomes this challenge by using the daily demand of multiuse trails in urban areas across the United States for periods of at least one year at each site. () We present a set of econometric models that summarize the effects of variation in temperature, precipitation, wind speed, dew point, and hours of daylight on daily bicycle and pedestrian trail traffic volumes. We compare regional elasticities for each weather variable for both bicyclists and pedestrians. () Many studies assume a linear relationship between weather factors and trail use, and few studies explicitly model this complex relationship to capture the more realistic weather effects. We test the parabola form of weather factors to explore the realistic relationship between weather factors and trail use. Under the umbrella of our modeling approach, we introduce the concept of demand returns to scale. This approach enables us to capture the more realistic response of trail users to weather variations across climate regions. Having this introduction, the rest of the paper is organized as follows. First, we comprehensively synthesize the existing literature studying the effects of weather on biking, walking, and trail use. We discuss the both weather and trail demand data used in detail, followed the data analysis. We then introduce the concept of Demand Returns to Scale by measuring the vertex point of parabola functions. In the penultimate section, we present the results of the elasticity measurements, and we conclude the paper with unpacking the remarkable findings and suggesting the potential pathways for the future research.

Ermagun, Lindsey, and Hadden Loh 0 0 0 THE EFFECTS OF WEATHER ON BICYCLING, WALKING, AND TRAIL USE Researchers have published many papers on the effects of weather on bicycling and walking, including some papers specifically about the effects of weather on trail use. These papers have been published in the transportation, health, recreation, geography, planning, and meteorological journals. Not surprisingly, these studies have confirmed casual observations and intuitive hypotheses: people bicycle and walk more when the weather is pleasantly warm and sunny and less when it rains, snows, is very hot or very cold, very humid, and very windy. These findings generally are consistent regardless of the measures of cycling and walking (e.g., traffic counts, travel diaries), trip purpose (e.g., commuting, recreation), season, and geographic region. However, the magnitude of the marginal effects of weather on mode and trips made for different purposes in different seasons in different places varies within and across regions. Variations in weather generally have been shown to have greater effects on cycling than on walking. Weather and Trail Use Studies of the effect of weather on use of multiuse trails or shared-use paths are of greatest relevance to this study (-). Most of these studies have analyzed traffic counts from automated monitoring devices, either infrared devices that cannot distinguish between cyclists and pedestrians (,,,, ) or pneumatic tubes (). Some have relied on manual counts from video or field observations (, ) or on survey data (, ). Most have used regression analysis to analyze counts; different modeling techniques, including OLS, log-linear models, and negative binomial models, have been used. Temperature and precipitation have been analyzed more frequently than wind speed and humidity; daylight has been modeled less frequently. These variables have been operationalized in a variety of ways. For example, temperature has been represented as degrees (Fahrenheit or Celsius), as categorical variables (e.g., days in temperature ranges), or as deviations from long-term or seasonal averages. Similarly, in models of the effects of precipitation, researchers have used both measures of depth and categorical variables (e.g., zero, trace, < inch, etc.) based on depth. Researchers have found that trail use increases with temperature, but only up to a point: trail use levels or drops off at higher temperatures (e.g., above ). Deviations from expected temperature also are correlated with variation in trail use, and this effect may vary seasonally. For example, in cold climates, unexpectedly high temperatures in winter months (e.g., ) may be associated with spikes in use, while the same temperatures in summer may be associated with dips in use. Collectively, studies of trails in Chicago IL (), Indianapolis IN (, ), Knoxville TN (, ), Spartanburg S.C. (), Vienna, Austria (), and cities in the Netherlands () show that trail use is positively associated with temperature and hours of sunshine and inversely associated with precipitation and wind speed. Weather and Bicycling Researchers have used a variety of approaches to analyze the effects of weather on cycling. Some researchers have used survey-based discrete choice modeling to assess the effects of weather on propensity to bicycle or for different trip purposes (-). Other researchers have developed count-based, facility demand models of hourly or daily traffic that control for the effects of weather (, -). These models have become increasingly common as new technologies for distinguishing cyclists from vehicles on streets have been developed. Other researchers have used sample surveys to model the effects of weather () or focus groups and interviews to assess why cyclists respond to variations in particular ways (). Most of these studies of been general population surveys or counts on public facilities, but some studies have

Ermagun, Lindsey, and Hadden Loh 0 0 0 been limited to special facilities or populations of interest, including bike share stations (), university students, faculty, and staff (). Studies have been reported for a variety of facilities, cities, and regions around the world: Ithaca, NY (); Vermont (), Auckland, New Zealand (); Brisbane, Australia (), Madrid, Spain (), Melbourne, Australia (), Montreal, Canada (), the Rotterdam region in Netherlands (), Toronto, Canada (), and in cities and regions of Sweden (, ). With few exceptions, the findings are consistent: cyclists are less likely to bicycle on colder, rainier, and windier days or when there is snow accumulation, and these effects are larger for recreational cyclists than for commuters. Weather and Walking Travel diaries generally show that walking accounts for a larger percentage of trips than bicycling, but fewer studies seem to have explored the effects of weather on walking than on bicycling. Automated counts of pedestrians are less common than counts of bicyclists, partly because devices for monitoring pedestrians on sidewalks are not as widely available as devices for monitoring cyclists on roads, and partly because pedestrian behaviors are more complex. In some cases, researchers have relied on manual field observations or counts of pedestrians from video (e.g., peak-hour, intersection counts; ()). One study focused on Montreal, Quebec; another compared patterns in nine cities across the world (). Both discrete choice models of walking estimated from travel diaries and counts of pedestrians indicate: () walking fluctuates less seasonally than bicycling and () daily variations within seasons are less than for cycling. Summary Researchers have produced quantitative information about the marginal effects of specific elements of weather on cycling and walking, including their effects on mixed-mode trail use. In general, bicycling has been shown to be more elastic than walking: both models of propensity to bicycle and models of traffic counts of bicyclists show bicycling generally is characterized by greater seasonality and variation in response to differences in daily weather than walking. While our understanding of these effects has grown, it is not complete. None of the studies cited here has separately analyzed counts of both cyclists and pedestrians taken with automated sensors over long sampling periods in regions with different climates. More systematic inquiries into the marginal effects of weather on bicycling and walking on trails are needed. THE TRAIL MODELING AND ASSESSMENT PLATFORM The Trail Modeling and Assessment Platform (T-MAP) is a multi-year national data collection and research effort focused on urban trail use in the United States. The goal of the project is to understand American trail use in the urban context, establish baseline volumes of trail use and identify correlates of trail use, including weather that can be used to predict trail use. This paper presents the first results from this initiative, specifically, from a network of trail traffic monitoring stations on trails in urban areas across all climate zones in the continental US. These volume data will be complemented in the future with additional geo-spatial data and with measurements from an intercept survey of trail users conducted on a sample of trails from the traffic monitoring network.

Ermagun, Lindsey, and Hadden Loh 0 0 0 T-MAP Monitoring Locations The T-MAP study area includes urban areas in nine National Oceanic and Atmospheric Administration (NOAA) climatically-consistent reporting regions in the contiguous U.S. (0). These regions encompass seven continental climate zones identified by the U.S. Department Energy (): very cold, cold, marine, mixed-dry, mixed-humid, hot-dry, and hot-humid. We use the DOE zones to group sites because the zones cross state boundaries and generally are descriptive of climate factors that affect how people use trails. The sample includes only larger cities with Census-designated urbanized areas of over 0,000 people. Specific cities were recruited to the study based on Rails-to-Trails Conservancy staff knowledge of the existence and maturity of an area s trail facilities and interest and willingness on the part of local trail managers to permit the permanent installation of traffic monitoring equipment on local trails. In each study area, a minimum of two distinct trail facilities were selected by local partners for monitoring. The exact station locations were sited based on safety, security, suitability, and minimization of proximate features that might affect the performance of the monitoring equipment. In addition, several locations where traffic monitoring equipment already had been installed as part of a local initiative are included in the sample. However, only stations of the same make and model as the traffic monitoring equipment used elsewhere in this study are included. All locations were subject to the same data validation protocol. Our final sample includes stations in the following cities: Portland, ME; Arlington, VA; Miami, FL; New Orleans, LA; Indianapolis, IN; Minneapolis, MN; Duluth, MN; Fort Worth, TX; Houston, TX; Albuquerque, NM; Colorado Springs, CO; Billings, MT; Seattle, WA; and San Diego, CA (Figure ). Each traffic monitoring station consists of a combination inductive loop and passive infrared sensor. Recent NCHRP Project 0- found that inductive loops provide accurate counts of cyclists with less than % average percentage deviation from true volumes, while passive infrared sensors are accurate, on average, within % (). Although it is possible to adjust for occlusion and other error (), the analysis presented in this paper is based on unadjusted data. The original T-MAP traffic monitoring network included 0 station locations. Following procedures used in NCHRP Project 0- (), we conducted a four-hour manual validation count at each location. We examined the absolute percentage deviation from true volumes on an hourly basis by mode and in total for each location, and we then excluded from this analysis any location that had over 0% deviation for any one hour for either mode. We did not apply this criterion to hours in which volumes per mode were under, because at extremely low volumes, very small errors in absolute volumes produce large percentage deviations that do not reflect the order of magnitude of the significance of the error. With this approach, station locations were excluded from the study. We inspected visualizations of all counts and followed standard procedures for quality assurance, quality control, eliminating days in the record when non data were recorded or only one sensor was functioning. Both visual inspection and statistical procedures were used to identify and censor outliers. Because events can result in atypical volumes, we searched the web to determine whether events have may occurred on days with high readings.

Ermagun, Lindsey, and Hadden Loh FIGURE Trail traffic monitoring locations Trail Traffic and Weather Data Trail traffic volumes recorded at -minute intervals from January, 0 through February, 0 form the basis of this analysis. These data then were aggregated to the daily level for purposes of estimation of average daily bicyclists (ADB) and average daily pedestrians (ADP). Based on findings of previous studies, the research team selected six weather variables for analysis: temperature, precipitation, snow, dew point, average daily wind speed, and hours of daylight. All weather data were downloaded from two electronic archives maintained by the National Oceanic and Atmospheric Administration: the Global Historical Climatology Network () and the Quality Controlled Local Climatological Data (). The closest weather station with a complete record of data for the variables of interest was selected for each trail site. Descriptive statistics for the weather and temporal variables are summarized in Table.

Ermagun, Lindsey, and Hadden Loh TABLE Descriptive of data and parameters used in the analysis Variable Definition Average St. Dev. Min Max 0 Weekend : If the counting day is weekend/ 0: Otherwise 0. 0. 0 Holiday : If the counting day is Holiday/ 0: Otherwise 0.0 0. 0 Winter : If the counting month is winter/ 0: Otherwise 0. 0. 0 Fall : If the counting month is fall/ 0: Otherwise 0. 0. 0 Spring : If the counting month is spring/ 0: Otherwise 0. 0. 0 Precip Precipitation in tenths of mm.. 0,0 D_Precip : If Precipitation is zero/ 0: Otherwise 0. 0. 0,.,. 0,,0 Snow Depth Snow depth..0 0 0 D_ Snow : If Snow depth is zero/ 0: Otherwise 0. 0. 0 Average daily temperature (Fahrenheit) 0..,.,. 0, Dew point Dew point (Fahrenheit).0. -,.,. 0,0 Day light The natural light of the day (Hour).... Avg. Speed Average daily wind speed (miles/hour).. Pedestrian The counted number of pedestrians.0. 0,0 Bike The counted number of bicyclists.. 0,0 DATA ANALYSIS Bicycle and Pedestrian Volumes on Urban Trails Across the sites, ADB and ADP each spanned three orders of magnitude. ADB ranged from a low of 0 cyclists to a high of, cyclists. ADP ranged from to,. Table summarizes descriptive statistics for ADB and ADP for all trail sites by climate regions. These numbers represent traffic volumes users that passed through the counters and not individual visits of each trail. Because some users likely make round-trips, the actual number of user-visits would be lower. The relative magnitudes of ADB and ADP varied substantially across the monitoring sties. ADB exceeded ADP at sites. ADB and ADP were approximately equivalent at some locations, but there were large differences at many locations, indicating that different trails attract different types of users. Within climate zones, ADB and ADP also varied. Many of these variations likely are associated with geo-spatial characteristics of the built environment and neighborhood socio-demographic factors that are beyond the scope of this inquiry and not analyzed here. At each site, variation in both bicycle and pedestrian traffic volumes is affected by temporal factors such as day of week and season. These factors are addressed in our trail traffic weather models.

Ermagun, Lindsey, and Hadden Loh TABLE Descriptive statistics for ADB and ADP for all trail sites by climate regions Daily Bicyclists Daily Pedestrians Region Trail Site Location Average Min Max Average Min Max Very Cold Duluth Lake Walk Duluth, MN. 0. Cold Marine Mixed Dry Mixed Humid Hot Dry Hot Humid Descro Billings, MT. 0. Kiwanis Billings, MT 0. 0. Pikes Peak Greenway Colorado Springs, CO.0. Portland Trails A Portland, ME. 0. 0 Portland Trails B Portland, ME. 0. Rock Island Colorado Springs, CO. 0. 0 W. River Greenway Minneapolis, MN..0 BGT Seattle, WA. 0 0 0. 0 Elliott Bay Seattle, WA. 0 MTS Washington Seattle, WA. 0. 0 Paseo del Nordeste Albuquerque, NM 0.0. Paseo del Norte Albuquerque, NM.. Ballston Connector Arlington, VA. 0. 0 0 Bluemont Connector Arlington, VA 0. 0. 0 CC Connector Arlington, VA. 0. 0 Custis Bon Air Arlington, VA.. TR Island Arlington, VA.. WOD Bon Air West Arlington, VA 0.. WOD Columbia Pike Arlington, VA 0. 0 0. Chula Vista San Diego, CA.0. Coronado Bayshore San Diego, CA.0. Escondido Inland San Diego, CA.0. Imperial Beach San Diego, CA.0. 0 Oceanside SLR River San Diego, CA.. SD Harbor San Diego, CA. 0. 0 FW Clear Fork A Fort Worth, TX 0. 0. FW Clear Fork B Fort Worth, TX. 0. Miami Dade A Miami, FL.. Miami Dade B Miami, FL.. Tammany Trace New Orleans, LA.0. White Oak Houston, TX.. Regional Weather Models To examine the effects of weather variables on trail demand, we develop a set of negative binomial regression models, one for bicyclists and one for pedestrians for each of the seven climate regions. Across regions, the number of monitoring stations included in each regional model varies, ranging from one location in the very cold region to seven in both the cold and the mixed-humid regions. We use count outcome modeling as our dependent variable (daily traffic) is count data. We selected negative binomial regression among all approaches for modeling counts in light of two basic criteria. First, we checked the distribution of our count variable and confirmed it is overdispersed and follows the negative binomial distribution. Second, we applied the Akaike

Ermagun, Lindsey, and Hadden Loh 0 0 0 Information Criterion (AIC) that confirm the negative binomial modeling approach has a better fit on our data sample. We present negative binomial regression models that summarize the effects of variations in weather and temporal factors on bicyclists and pedestrians demand for each climate region, while controlling for holiday, weekend, and seasonality. We depict the results in Table. The purpose of estimating the climate zone models is to explore the feasibility of developing general models that can be used to characterize the effects of weather in areas with mostly homogeneous climates. We employ the stepwise modeling approach to specify the model, choosing variables that were significant at the 0% confidence interval. The student's t-statistic is used to check the level of significance in hypothesis testing. We judge the overall fit of the models by measuring the Nagelkerke Pseudo. This measurement fluctuates between 0 and : values closer to indicates a better fit but cannot be interpreted as percentages as in standard OLS regression. As shown in Table, the Nagelkerke Pseudo ranges from 0.0 to 0. for different models. The bicyclists demand models have better fit than the pedestrian models, indicating bicyclists are more responsive to changes in weather, season, and day-of-week. Across the seven climate regions, five of the bicyclist models have the overall fit greater than 0.0. Only one pedestrian model has a fit greater than 0.0. These differences in the explanatory models demonstrate that bicyclists and pedestrians respond differently to weather and seasonality, and weather variables apparently are not major factors contributing to variations in daily use of either bicyclists or pedestrians. From the response to weather factors, we draw the following observations: Bicyclists and pedestrians in the same climate region respond differently to variations in weather. Bicyclists and pedestrians in different climate regions respond differently to variations in weather. Although the direction of the effects of specific weather elements generally is the same, the magnitude of correlations of weather variables with bicyclists and pedestrians demand differs across climate regions. With respect to specific variables, we tested the daily average temperature, precipitation, dew point, average daily wind speed, and snow depth in both modes across all climate regions. For the bicycling models, the daily average temperature, precipitation, and average wind speed are significant in all the models. Dew point and snow depth are significant in seven out of eight models. For the pedestrian models, the results are similar but differ in a few cases. The daily average temperature is significant in all climate regions, while precipitation, average wind speed, and dew point are significant in seven out of eight models. Noteworthy is that the snow depth dummy variable is insignificant in five out of eight models. This reveals bicyclists demand is more sensitive to snow than pedestrians demand. We also controlled the models by seasonal, weekend, and holiday variables. For the bicycling models, we found Winter is significant in five out of eight models. However, Fall and Spring are significant in only 0% of models. Weekend is significant in more models than Holiday. For the pedestrian models, Winter, Fall, and Spring are found significant in three, five, and two models, respectively. While weekend is significant in all models, the Holiday is found significant in 0% of models.

Ermagun, Lindsey, and Hadden Loh TABLE Results of negative binomial regression models for both bicyclists and pedestrians Climate regions Variables Very Cold Cold Marine Mix Dry Mix Humid Hot dry Hot Humid All Regions Bicycle Models Day Light 0. Insignificant 0.0 0.0 0.0 0.0 0. 0. Winter Insignificant -0. Insignificant 0.0 0. -0. Insignificant -0.0 Fall Insignificant 0. Insignificant Insignificant 0. -0. 0. Insignificant Spring -0. 0. Insignificant Insignificant Insignificant -0. Insignificant -0.0 Holiday -0. Insignificant Insignificant Insignificant Insignificant 0. 0. 0. Weekend Insignificant 0. Insignificant 0. Insignificant 0. 0. 0. 0.0 0.0 0. 0. 0. 0. 0. 0.0 Insignificant -0.000-0.000-0.000-0.000-0.000-0.000-0.000 D_Precip 0. 0. 0. 0. 0. 0. 0. 0. Precip -0.00-0.00-0.00-0.00-0.00-0.00-0.00-0.00 Dew Point -0.0 Insignificant -0.0-0.0-0.0-0.0 0.0 0.0 Insignificant 0.000 Insignificant 0.000 Insignificant 0.000-0.000-0.000 Avg Speed -0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0 D_ Snow 0. 0.. 0.. Insignificant.. Constant.. -0.0 0. -0..0 -..0 Pseudo 0. 0. 0. 0. 0. 0. 0. 0. Pedestrian Models Day Light Insignificant 0.0 0.0 0.0 0.0 Insignificant 0. 0. Winter Insignificant Insignificant Insignificant Insignificant 0. -0. Insignificant -0. Fall -0. Insignificant Insignificant 0. 0.0-0. 0. Insignificant Spring Insignificant 0. Insignificant Insignificant Insignificant Insignificant Insignificant -0. Holiday Insignificant 0. Insignificant Insignificant 0. Insignificant 0. 0. Weekend 0. 0. 0. -0. 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 0. 0.0 0.0 Insignificant -0.000-0.000-0.000-0.000-0.00-0.000-0.000 D_Precip 0. 0. 0. 0. 0. 0. 0. 0. Precip -0.00-0.00-0.00 Insignificant -0.00-0.00-0.000-0.00 Insignificant Insignificant Insignificant Insignificant Dew Point -0.0-0.0-0.0-0.0-0.0 Insignificant 0.0 0.0-0.000 0.000 Insignificant Insignificant Insignificant Insignificant -0.000-0.000 Avg Speed -0.0-0.0 Insignificant -0.0-0.0-0.0 0.00-0.00 D_ Snow Insignificant Insignificant Insignificant Insignificant 0. Insignificant.0 0. Constant..... -0. -0.. Pseudo 0. 0. 0. 0.0 0. 0.0 0. 0.0 DEMAND RETURNS TO SCALE In this section, we introduce the concept of the demand returns to scale, as it is fundamental to understand how trail demand responds to variations in weather. In its basic usage, this concept represents three distinct forms: () Constant returns to scale: The trail demand changes by the same proportion as the change in weather variables. () Increasing returns to scale: The trail demand changes by a larger proportion than the change in weather variables. () Diminishing returns to scale: The trail demand changes by a lesser proportion than the change in weather variables.

Ermagun, Lindsey, and Hadden Loh To measure the demand returns to scale, we tested the quadratic form of weather variables in the models as shown in Table. The U- and -shape of quadratic function enable us to measure the response of demand to weather changes. Using a mathematical notation, the returning forms are formulated as per equation, where is the trail demand, is the specific weather variable, and,, and stand for the coefficients of the function. () { (.a) 0 0 0 { (.b) (.c) Simply speaking, if there is a significant quadratic correlation between the demand and a weather variable of interest, the demand is either increasing or decreasing returns to scale in response to the interest weather variable. It is increasing if the correlation forms an upward parabola. It is decreasing if the correlation forms a downward parabola. There is a constant returns to scale, if the quadratic correlation between the demand and the interest weather variable is insignificant. It is useful to illustrate the method of examining demand returns to scale for an example in detail. An Example: Demand Response to Daily Average Temperature In this example, we represent the response of trail users to daily average temperature. In very cold climate region, is statistically significant in both bicyclist and pedestrian models with a positive value. However, is not significant in either of the models. This indicates has a constant return to scale in very cold regions. That is, increasing the daily average temperature increases the trail demand with the approximately the same proportion. Looking at the both and variables in marine climate regions, we find the coefficients of both variables are significant. In the bicycle model, the coefficient of is negative indicating the parabola opens downward. It means the daily average temperature has a decreasing return to scale. We substitute the parameters of equation with the coefficients estimated by the model as follows: () We then derive the first derivative of Equation to find the vertex point or absolute maximum in this specific case. The results are presented in Equation. ()

Ermagun, Lindsey, and Hadden Loh 0 0 This illustrates that the bicyclists demand in the marine climate zone is characterized by decreasing returns to scale up to a daily average temperature of. It is inferred when the daily average temperature approaches, the bicyclists demand increases with a deceleration rate. Likewise, the pedestrians demand increases with a deceleration rate followed by an increase in daily average temperature to the estimated vertex point of, after which the demand starts diminishing. This indicates pedestrians are more tolerant than bicyclists in responding to temperature in marine regions. We summarize the demand returns to scale form of daily average temperature, precipitation, and dew point along with their vertex point value for all climate regions in Table. The constant term in this table means the weather variable has constant returns to scale. This is happened when the squared form of the interest variable is not significant. The increasing term in this table means the weather variable is increasingly returned to scale all the time. A strong point of emphasis is that for illustration of the demand returns to scale, the range of interest variable should be considered. For example, although the dew point variable exhibits increasing returns to scale among bicyclists, the demand would never approach infinity due to the maximum possible temperature in cold regions. As for, the coefficient of is negative for both modes in all climate regions, but very cold where it is insignificant. This shows in all but the very cold region, there is an inflection point above which decreasing returns to scale occur. Only in the very cold region the demand is characterized by constant returns to scale. In mixed-dry regions, the bicyclists demand is characterized by increasing returns to scale up to a daily average temperature of. Above this temperature, the bicyclists demand begins diminishing. This change is occurred above for pedestrians demand. This indicates pedestrians are less tolerant than bicyclists in responding to temperature in mixed-dry regions, unlike marine and hot-dry climate regions. The results indicate that the trail demand falls after the absolute maximum. We accentuate the vertex points reported in Table are derived from the negative binomial regression models, where we controlled for various weather variables, seasonality, and day light. The vertex points may change if the demand model embeds only the interest weather variables. TABLE Vertex point of weather variables in different climate regions classified by mode Variable Mode Climate Regions Very Cold Cold Marine Mix Dry Mix Humid Hot Dry Hot Humid Bicycle Constant 0. 0. 0 Walk Constant.. 0 0 Precipitation Bicycle 0.0 00 00 00 00 00 Walk. Constant - Constant 0 Constant Dew Point Bicycle Constant Increasing Constant Constant 0. Walk 0. Constant Constant Constant - ELASTICITY ANALYSIS To quantify the effects of independent variables used in the models of trail demand, we calculated the elasticity of continuous variables and marginal effects of dummy variables. We outline the results in Table. The elasticity represents the percent change in the dependent variable when one of the independent variables changes by one percent, while other independent

Ermagun, Lindsey, and Hadden Loh variables are fixed. For dummy variables, the marginal effects measurement shows the demand deference between two conditions in percentage. Two main methods of elasticity calculation are the arc elasticity method and the point elasticity method. In this study, we used the arc elasticity method, which measures the elasticity at the average. In elasticity interpretation it should be kept in mind that elasticities are estimated for marginal changes, so they are meaningful for small changes around the average. TABLE Results of elasticity and marginal effects for both bicyclist and pedestrian models Climate regions Variables Very Cold Cold Marine Mix Dry Mix Humid Hot dry Hot Humid All Regions Bicycle Models Day Light. Insignificant 0. 0. 0. 0.0..0 Winter Insignificant -0. Insignificant.. -. Insignificant -. Fall Insignificant 0. Insignificant Insignificant 0. -0.. Insignificant Spring -..0 Insignificant Insignificant Insignificant -. Insignificant -. Holiday -. Insignificant Insignificant Insignificant Insignificant... Weekend Insignificant 0. Insignificant. Insignificant 0. 0.0... Insignificant..... Insignificant -0. -. -.0 -.0 -. -. -0. D_Precip...0...00.. Precip -0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0 0.0 0.00 0.0 0.00 0.0 0.0 0.0 0.00 Dew Point -. Insignificant -0. -0. -. -...0 Insignificant 0. Insignificant 0. Insignificant 0. -. -0. Avg Speed -0. -0. -0.0-0. -0. -0. -0. -0. D_ Snow.0...0. Insignificant 0.. Pedestrian Models Day Light Insignificant 0. 0. 0..0 Insignificant..0 Winter Insignificant Insignificant Insignificant. -. Insignificant -. Fall -. Insignificant Insignificant.. -..0 Insignificant Spring Insignificant.0 Insignificant Insignificant Insignificant Insignificant Insignificant -. Holiday Insignificant 0. Insignificant Insignificant. Insignificant.. Weekend 0... -..0. 0.0........0. Insignificant -. -. -. -. -. -. -. D_Precip.0. 0.0 0...0..0 Precip -0.0-0.0-0.0 Insignificant -0.0-0.0-0.0-0.0 0.0 0.00 Insignificant Insignificant Insignificant 0.0 Insignificant 0.00 Dew Point -0. -. -0. -0. -0. Insignificant.0. -0..0 Insignificant Insignificant Insignificant Insignificant -. -0.0 Avg Speed -0. -0. Insignificant -0. -0. -0. 0.0-0.0 D_ Snow Insignificant Insignificant Insignificant Insignificant. Insignificant.0. The marginal effects of the dummy variables for seasonality vary across the regions. In cold regions, bicyclists demand is 0.% lower in Winter than in Summer. Likewise, the bicyclists demand in Winter is.% lower than Summer in hot dry regions. In marine regions, we found no seasonal effects on demand for bicycling. In mixed dry and mixed humid regions, the bicyclists demand in winter is significantly more than other seasons. The seasonal effect on pedestrians demand is fairly low, and, like demand for cycling, varies across regions. Although

Ermagun, Lindsey, and Hadden Loh 0 0 0 there are no seasonal effects in cold and marine regions, the demand of pedestrians is high in mixed humid regions and low in hot dry regions for both Winter and Fall. As far as the day of week and holidays are concerned, the bicyclists demand is two to three times higher in hot dry and hot humid regions. Interestingly, the bicyclists demand in very cold regions is.% lower on holidays than other days of the year when controlling for seasonality and other factors. There is no significant effect in other climate regions. The marginal effects of weekend are fairly significant on pedestrians demand over all climate regions, although the direction and magnitude of effect are mixed. As far as the weather effects are concerned, daily average temperature is the most effective variable on trail demand. The results highlight that the bicyclists are more sensitive to daily average temperature than pedestrian in five of climate regions. For instance, a % increase in the average daily temperature in very cold regions constantly increases the bicyclists and pedestrians demand by.% and.%, respectively. These are in line with the constant returns to scale nature of average daily temperature in very cold regions. As alluded to previously, the daily average temperature in mixed humid regions has increasing returns to scale for both the bicyclists and pedestrians demand below the 0 and 0, respectively. The elasticity results demonstrate that a % increase in the average daily temperature below the 0 and 0 is followed by.% and.% increase in bicyclists and pedestrians demand, respectively. Above the 0 and 0, the demand begins diminishing with the same rate, on average. SUMMARY, CONCLUSIONS, AND IMPLICATIONS We obtained separate daily bicycle and pedestrian counts from automated monitors on urban multiuse trails in cities, including at least one monitoring station in each of seven US DOE regional climate zones. Average daily bicycle and pedestrian traffic both vary over three orders of magnitude across monitoring locations. We used negative binomial regression models to estimate the effects of weather on daily bicycle and pedestrian trail traffic. We explicitly modeled the complex relationship between the weather factors and both bicyclists and pedestrians demand by testing the parabola form of weather factors. We introduced the concept of demand returns to scale and calculated the vertex point of parabola functions. The results disclosed that the weather effects exhibit constant, increasing, or decreasing returns to scale. To quantify the magnitude of the effects, we estimated elasticities and marginal effects of continuous and dummy variables. The weather variables in our models included average temperature, precipitation, snow, dew point, and average wind speed. We controlled for seasons, weekends, and holidays. Our results both confirm and extend findings reported previously in the literature. We showed that the effects of temperature, precipitation, snow, dew point, and wind speed generally are consistent and significant in the expected direction for both bicycle and pedestrian demand, but that the magnitude of the effect varies. In addition, on some trails in some zones, the variables have no significant effects. We also showed that vertex points exist for temperature and precipitation at which point demand moves from increasing to decreasing returns to scale, or vice-versa. These effects, and the specific values at which vertex points occur, also vary by region. Relatively few variables have constant returns to scale. Our estimates of the elasticity of demand in response to specific variables vary by mode and region. To summarize: Bicyclists and pedestrians in the same climate region respond differently to variations in weather.

Ermagun, Lindsey, and Hadden Loh 0 0 0 Bicyclists in different climate regions respond differently to variations in weather. Pedestrians in different climate regions respond differently to variations in weather. These results have implications for trail management. Most importantly, they underscore the fact that demand and user patterns vary across the U.S. and that these factors need to be considered when analyzing use. Understanding of traffic magnitudes and seasonal and weekend-weekday differences in traffic can inform decisions about investment, marketing, maintenance, and traffic patrols. More generally, data about trail use collected with technologies analogous to those used for motorized traffic on road and street networks can inform transportation planning and ensure that the evidence base for all transportation modes is similar. A very practical use of these models is to use them (or models like them) for estimating traffic volumes on days when counts are not available. These results also have implications for trail monitoring and reflect both its potential and the challenges inherent in establishing comprehensive monitoring networks. With the increased availability of comparatively low-cost automated monitoring devices, many new initiatives to monitor bicycle and pedestrian traffic have been launched. As illustrated here, these initiatives can generate information about both traffic volumes and, with additional analyses, the effects of weather and other variables on patterns of use. Yet these newer devices are not without limitations. As noted, we excluded many potential sites from these analyses because on-site manual validation of totals indicated potential problems with accuracy. We elected not to adjust measurements for observed error (mainly undercounts associated with occlusion) because our decision criteria were consistent across sites and adjustment mainly is a scaling exercise that should not affect these modeling results significantly. More generally, the problems that prevented inclusion of all data underscore the need for managers launching new monitoring programs to validate counts. ACKNOWELDGEMENTS This research was conducted with funding from the members and supporters of the Rails-to-Trails Conservancy. The authors would like to thank the Trail Modeling and Assessment Platform Advisory Committee for their guidance and insight: Jack Wells, formerly of USDOT; Joan Dorn, City University of New York; Jeff Riegner, Whitman, Requardt, & Associates LLP; Peter Furth, Northeastern University; Sean Co, Toole Design; Andy Dannenberg, University of Washington; Spencer Finch; Langan Engineering & Environmental Services; and Jean-Francois Rheault, Eco-Counter. The authors would also like to thank Erik Anderson of the University of Minnesota; Sherry Ryan of San Diego State University; David Patton and Arlington County, VA; Kara Wooldrik, Jaime Parks, and Portland Trails; David Henderson and the Miami-Dade Metropolitan Planning Organization; Sue Burow of Indiana University- Purdue University Indianapolis, Andre Denman, and the City of Indianapolis, IN; Tara Tolford of the University of New Orleans, Lisa Maddox, and the Tammany Trace Foundation; Kevin Kokes, Daniel Snyder, and the North Central Texas Council of Governments; Robert Benz and the Houston-Galveston Area Council; Julie Luna and the Mid-Region Council of Governments; Jeff Webb and the City of Colorado Springs, CO; Susan Davies and the Trails and Open Space Coalition; Scott Walker and the City of Billings, MT; Craig Moore and the City of Seattle, WA. Erik Anderson at the University of Minnesota assisted with data management and extraction.

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