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Cycling in three dimensions : developing road grade information for bicycle travel analysis El Masri, Omar 2018

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CYCLING IN THREE DIMENSIONS: DEVELOPING ROAD GRADE INFORMATION FOR BICYCLE TRAVEL ANALYSIS by  Omar El Masri  B.Eng., American University of Beirut, 2016  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2018  © Omar El Masri, 2018  ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled:  CYCLING IN THREE DIMENSIONS: DEVELOPING ROAD GRADE INFORMATION FOR BICYCLE TRAVEL ANALYSIS  submitted by Omar El Masri  in partial fulfillment of the requirements for the degree of Master of Applied Science in Civil Engineering  Examining Committee: Dr. Alexander York Bigazzi Supervisor  Dr. Steven Weijs Supervisory Committee Member   Supervisory Committee Member  Additional Examiner     Additional Supervisory Committee Members:  Supervisory Committee Member  Supervisory Committee Member   iii  Abstract  Road grade is a major factor influencing cyclist physiology and travel decisions. Research studying cycling and other non-motorized transportation modes often use coarse elevation data sources to obtain the necessary grade information. In addition, routing applications such as Google Maps, Strava and RideWithGPS append the GPS data collected with elevation data from the coarse elevation datasets which can be inaccurate and inadequate. The objective of this research is to determine the best methods of obtaining road grade information on a network scale for bicycle travel analysis and to understand the limitations of the coarse data sources.   Multiple elevation data sources, high resolution and coarse, are collected for the city of Vancouver, BC Canada. Different road grade estimation algorithms are then applied to the data sources at eight locations in the city where ground truth elevation data were surveyed using a total station. Different cycling performance measures were used to compare the elevation and road grade estimates of the locations to identify the data sources that accurately represent the true ground elevation for cycling analysis. Finally, the elevated structures in the City of Vancouver are characterized to help infer grade information in the absence of high resolution data sources.  Results show that elevation data collected from Light Detection and Ranging (LiDAR) are the most accurate for elevated and non-elevated roads with mean absolute error in the elevation not exceeding 0.6 meters. Additionally, road grades derived from LiDAR data sources were closest to measured grade data. In the absence of LiDAR, coarse data sources can provide adequate grade estimates for cycling analysis on non-elevated structures. However, on elevated structures, iv  especially ones without a single dominant grade, coarse datasets can only provide estimates of total elevation change or mean grade. Overall, the results show that it is vital to understand the accuracy and limitations of elevation data sources used in analysis and modeling of active travel. v  Lay Summary  The objective of this research is to determine the best methods of obtaining road grade information for bicycle travel studies. Common sources of road grade data are compared with ground surveying data and applied to cyclist power estimation. Results show that standard approaches are inaccurate and inadequate, and an improvement is proposed. The findings of this research will improve road grade estimates in future cycling studies, which is a major factor influencing cyclist physiology and travel decisions. vi  Preface  This dissertation is original, unpublished, independent work by the author, Omar El Masri, under the supervision of Dr. Alexander Bigazzi. vii  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ........................................................................................................................ vii List of Tables ................................................................................................................................ ix List of Figures ............................................................................................................................... xi List of Abbreviations ................................................................................................................. xiii Acknowledgements ......................................................................................................................xv Dedication ................................................................................................................................... xvi Chapter 1: Introduction ................................................................................................................1 1.1 Context and Motivation .................................................................................................. 1 1.2 Literature Review............................................................................................................ 5 1.3 Research Question ........................................................................................................ 20 Chapter 2: Methodology..............................................................................................................21 2.1 Overview ....................................................................................................................... 21 2.2 Elevation Data Sources ................................................................................................. 22 2.3 Ground Truth Data Collection ...................................................................................... 25 2.4 Road Grade Estimation Methods .................................................................................. 27 2.5 Evaluation Comparison Measures ................................................................................ 29 2.6 Characterization of Elevated Structures........................................................................ 33 Chapter 3: Results........................................................................................................................35 viii  3.1 Elevation and Grade Profiles ........................................................................................ 35 3.2 Performance Measures .................................................................................................. 46 3.3 Characterization of Elevated Structures........................................................................ 55 3.4 Inferring Grades on Elevated Structures ....................................................................... 59 Chapter 4: Recommendations ....................................................................................................62 Chapter 5: Conclusion .................................................................................................................65 Chapter 6: Limitations and Future Work .................................................................................67 References .....................................................................................................................................69 Appendices ....................................................................................................................................78 Appendix A Elevation Profiles of All Ground Truth Locations ............................................... 79 Appendix B Grade Profiles of All Ground Truth Locations ..................................................... 87 Appendix C Performance Measure Estimates per location ...................................................... 95 C.1 400 Smithe Street ...................................................................................................... 95 C.2 1200 1500 Island Park Walk ..................................................................................... 96 C.3 2500 Trafalgar Street ................................................................................................ 97 C.4 2500 W 10th Street ................................................................................................... 98 C.5 Burrard Bridge .......................................................................................................... 99 C.6 1000 Beach Street ................................................................................................... 100 C.7 Main Street over Waterfront Street ......................................................................... 101 C.8 Cambie Street North Ramp ..................................................................................... 102 Appendix D Slope Distributions of Elevated Structures in the City of Vancouver................ 103  ix  List of Tables  Table 1 Summary of elevation data sources adopted from (Nelson et al., 2009; Wilson, 2012) . 12 Table 2 Collected elevation data source details (accuracy based on (Nelson et al., 2009; Wilson, 2012)) ............................................................................................................................................ 22 Table 3 Ground truth location site details ..................................................................................... 26 Table 4 Performance measures used to compare elevation and road grade estimates.................. 30 Table 5 Coincidence ratio of grade distribution compared to ground truth for all locations from all elevation sources ...................................................................................................................... 39 Table 6 Mean absolute error (m) in elevation at each location from available sources compared to ground truth. Presented as Mean Absolute Error (m) (Standard deviation of Mean Absolute Error (m)) ...................................................................................................................................... 41 Table 7 Worst performing elevation sources for each location and performance measure .......... 47 Table 8 Best performing elevation sources for each location and performance measure ............ 48 Table 9 Total energy calculated from each elevation data source at each ground truth location Presented as Energy (J) (Percent Absolute Error) ........................................................................ 53 Table 10 Average power calculated at each location Presented as Power (W) (Percent Absolute Error) ............................................................................................................................................. 54 Table 11 Summary of the characteristics of the classified elevated structures in the City of Vancouver Presented as mean (standard deviation)] .................................................................... 56 Table 12 Estimated Parameters from the normal fit at unimodal locations .................................. 57 Table 13 Characteristics of the bimodal distributions of the elevated structures in class 2 (grades are in %) ........................................................................................................................................ 58 x  Table 14 Percent error in total energy compared to Boyko (J) ..................................................... 60  xi  List of Figures  Figure 1 Canadian Digital Elevation Model in British Columbia, Canada .................................... 2 Figure 2 Example of elevation data in Google Earth ...................................................................... 3 Figure 3 Burrard Bridge elevation profile as depicted by Google Maps ........................................ 4 Figure 4 Example of cloud point data from Airborne Laser Scanning ........................................... 9 Figure 5 Simple illustration of how LiDAR cloud points are collected (Zhang & Frey, 2006) ..... 9 Figure 6 Example of multiple returns over a tree ......................................................................... 10 Figure 7 Diagram representing the projection of 2D map into 3D line (Boyko & Funkhouser, 2011) ............................................................................................................................................. 17 Figure 8 Diagram representing the different methods to calculate road grade from elevation data sources........................................................................................................................................... 19 Figure 9 Map of the ground truth measurement sites ................................................................... 25 Figure 10 Bilinear interpolation versus simple extraction from the Canadian DSM on 400 Smithe Street ............................................................................................................................................. 28 Figure 11 Elevation profiles of 2500 Trafalgar Street using DEMs (without interpolation) compared to Ground Truth............................................................................................................ 35 Figure 12 Elevation profiles of 400 Smithe Street from LiDAR data sources compared to ground truth ............................................................................................................................................... 37 Figure 13 Elevation profiles of 1000 Beach Street from LiDAR data sources compared to ground truth ............................................................................................................................................... 38 Figure 14 Elevation profiles of 400 Smithe Street from DEMs compared to ground truth .......... 40 Figure 15 Elevation profiles of Burrard Bridge from DEMs compared to ground truth .............. 42 xii  Figure 16 Histogram of the grade distribution of the measured ground truth on Burrard Bridge 44 Figure 17 Elevation profiles Cambie Street North Ramp from all sources compared to ground truth ............................................................................................................................................... 45 Figure 18 Cumulative Elevation Gain, loss and Absolute Elevation Change estimates from all the data sources on 2500 Trafalgar Street ........................................................................................... 49 Figure 19 Descriptive statistics of road grade distribution from all the data sources on 2500 Trafalgar Street ............................................................................................................................. 50 Figure 20 Cumulative Elevation Gain, loss and Absolute Elevation Change estimates from all the data sources on Burrard Bridge..................................................................................................... 51 Figure 21 Decision tree to identify the elevation profile of a road ............................................... 64  xiii  List of Abbreviations  Kinematic abbreviations sec  Second  m  Meter  Km Kilometer G  Grade  W  Watt  hr Hour  Elevation dataset related abbreviations DEM Digital Elevation Model DSM Digital Surface Model LiDAR Light Detection And Ranging SRTM Shuttle Radar Topography Mission ASTER Advanced Spaceborne Thermal Emission and Reflection Radiometer CDSM Canadian Digital Surface Model CDEM Canadian Sigital Elevation Model    xiv  Elevation file formats LAS An industry-standard binary format for storing airborne lidar data. raster A matrix of cells (or pixels) organized into a grid where each cell contains a value representing elevation information GeoTIFF A standard which allows georeferencing information ina TIFF file TIFF or TIF Tagged Image File Format  Statistics abbreviations sd Standard Deviation CR Coincidence Ratio  Other abbreviations VSP Vehicle specific Power GPS Global Positioning System  xv  Acknowledgements  First and foremost, I must thank my parents for their great support and understanding to pursue higher education. Attending the best university in Lebanon with high financial restrictions is something I cannot thank them enough for. It allowed me to consider graduate studies at the best universities in the world. The support I got from my parents and sisters is priceless.  I would like to also thank fellow REACT Lab members here at the University of British Columbia for their help and support, especially their patience when helping me collect ground truth data. They are Amr Mohamed, Xugang Zhong, Hossameldin Mohammed and Elmira Berjisian. Special thanks goes to my advisor Dr. Alex Bigazzi whose guidance kept me on the right track forward. The values and principles he taught me are invaluable.   I would also like to thank all the staff member in the Civil Engineering Department for their help and support. They have made my path smoother and always greeted me with positivity.  I would finally like to thank Dan Campbell at the City of Vancouver for providing the LiDAR cloud point data along with the design drawings of Burrard Bridge.  xvi  Dedication  To My Family  1  Chapter 1: Introduction  1.1 Context and Motivation  Non-motorized travel models rely on precise road grade information. The sensitivity of pedestrians and cyclists to road grade is greater than that of motorized modes. Route choice models for pedestrians and cyclists will depend on road grade given that they try to avoid hills (Hood, Sall, & Charlton, 2011; Menghini, Carrasco, Schüssler, & Axhausen, 2010). Furthermore, cycling performance models depend on road grade as a parameter in their empirical or physical forms (Olds et al., 1995). In his model estimates, Parkins showed that a 1% change in grade going uphill will vary speed by approximately 1.4 km/h (Parkin & Rotheram, 2010). Additionally, vehicle specific power (VSP) estimation depends on road grades based on the empirical formula provided by the U.S Environmental Protection Agency (Environmental Protection Agency, 2002). Assuming an acceleration of zero and a speed of 100 km/h a change in 1% grade causes the VSP to change by approximately 4 kw/ton, which will greatly vary the emission estimate (Zhang & Frey, 2006). Thus, the importance of road grade estimates for non-motorized and motorized travel models cannot be simply overlooked. Yet, elevation data with the required precision are not readily available for public use.  2   Figure 1 Canadian Digital Elevation Model in British Columbia, Canada  The elevation and road grade datasets available are coarse and inaccurate. Most elevation datasets are in the form of a square-grid Digital Elevation Model (DEM) (Wilson, 2012) (See example in Figure 1). The past two decades have shown a rapid growth in mass produced higher resolution DEMs such as the DEMs from the Shuttle Radar Topographic Mission (SRTM) and remote sensing like Light Detection And Ranging (LiDAR). At the continental and global scale the SRTM DEM developed in 2000 shows great improvements. The three arc-second (90m) grid spacing is much better than the previously adopted 1 km spacing  of the world wide GTOPO30 DEM, but such a resolution is still not fine enough for the required applications. This problem was also not addressed by the Advanced Spaceborne Thermal Emission and Reflectance Radiometer Global Digital Elevation Model (ASTER G-DEM) that was released in 2009.  The resolution improved to 1 arc-second compared to 3 arc-seconds with similar accuracies 7-20 m 3  vertically and 30 m horizontally compared to  16 and 20m respectively for SRTM (Hirano, Welch, & Lang, 2003; Nelson, Reuter, & Gessler, 2009; Slater et al., 2011; Wilson, 2012). But this resolution is still not sufficient to support network wide road grade calculation. Moreover, these datasets lack information on elevated roads, bridges and tunnels. Numerous applications, such as Google Earth, currently use SRTM as their elevation dataset so at elevated structures the data misrepresents reality. The figure below shows how a bridge can be depicted by Google Earth.    Figure 2 Example of elevation data in Google Earth  The elevation profile shows unrealistic elevation gains and losses which requires additional processing to better represent locations like bridges, especially in non-motorized routing and performance models. Furthermore, routing applications such as Google maps, Strava or RideWthGPS to name a few, have adopted SRTM as their elevation dataset which raises concerns about the accuracy of the elevation estimates produced by these applications. Figure 3 shows that Google Maps can identify the presence of an elevated road by connecting the start and end of the road with a straight line. The straight line approximation is inaccurate when 4  considering cumulative elevation gain and loss but these inaccuracies are less severe than when considering only the output of the SRTM elevation models similar to Figure 2.    Figure 3 Burrard Bridge elevation profile as depicted by Google Maps  Routing applications would append detailed tracked coordinates with elevation information which requires the presence of an accurate extensive elevation dataset which can provide the necessary detailed elevation information. Some of the applications allow the user to review and manually fix the elevation profile of their tracked ride, by replacing unrealistic drops in elevation with straight lines, which shows that the developer of the applications understand that the elevation data source referred to are not perfectly adequate.  Since most motorized travel models make little use of road grade or are less sensitive to resolution and accuracy of the elevation data, precise elevation datasets are rare. Most available 5  Geographic Information Systems (GIS) dataset like street network shape files lack elevation information (Wang et al., 2017). Thus most papers that study non-motorized travel and applications that append elevation to large GPS datasets, resort to coarse and inadequately accurate elevation data sources (Menghini et al., 2010; Teschke, Chinn, & Brauer, 2017; Ziemke, Metzler, & Nagel, 2017). Ultimately, the errors in the elevation models used will propagate to the model estimates. Thus this research provides a better understanding of the effect of different elevation sources on bike performance measures and recommends different elevation data sources based on different situations. The elevation sources will be evaluated by comparing their elevation profiles and grade distributions to those of surveyed ground truth data collected in Vancouver, BC, Canada.  1.2 Literature Review  Roadway elevation data play an important role in a wide range of transportation analysis, design and modeling (Wang et al., 2017). Applications range from road geometry, road safety analysis, fuel and environmental impact, and behavioral modeling for active travelers (pedestrians and cyclists). Previous research has shown how cyclist route choice and performance can be a function of road grade. The physical model representing cyclist power consumption depends on grade (Olds et al., 1995). Likewise, empirical models also show speed and acceleration of cyclists as linear functions of road grade (Parkin & Rotheram, 2010). Previous research has also identified the effect of grade on cyclist route choice since most cyclists tend to avoid steep uphill paths (Broach, Dill, & Gliebe, 2012; Hood et al., 2011; Menghini et al., 2010; Winters, Davidson, Kao, & Teschke, 2011). Ziemke et al. (2017) incorporated road grade as a parameter 6  in their agent-based simulations to model bicycle traffic. Additionally, cyclists’ perception of comfort is influenced by the road geometry at a significant level (Z. Li, Wang, Liu, & Ragland, 2012). Hence, bike mode share can also be affected by the road geometry in addition to the bike infrastructure (Teschke et al., 2017; Winters, Teschke, Brauer, & Fuller, 2016). Relationships between road grade and performance and behavior of active travelers indicates the importance of the availability and quality of road grade information for developing new behavioral models for active travelers especially with their increasing mode share (Z. Li et al., 2012; Menghini et al., 2010; Milakis & Athanasopoulos, 2014) and increasing need for transport models for effective planning (Ziemke et al., 2017). Most of the studies that model some behavior that is affected by road grade get their elevation information from inadequate and inaccurate elevation data sources.  With the lack of elevation information in traditional roadway GIS data, elevation data must be sought for from other sources. With the new data collection and processing methods that emerged in the past two decades, there is no longer a need to manually survey and draw elevation profiles of roads. Currently available datasets include the global 30 arc-second (~1 km) grid spacing elevation dataset (GTOPO30) (Becker et al., 2009), the three arc-second (90 m) grid spacing SRTM DEM (Farr et al., 2007), the 1 arc-second grid spacing ASTER G-DEM (Tachikawa, Hato, Kaku, & Iwasaki, 2011), the 25 m grid spacing Canadian DEM (Ministry of Natural Resources, Canada, 2014a), Digital Surface Model (DSM) (Ministry of Natural Resources, Canada, 2014b) and LiDAR data (Reutebuch, Andersen, & McGaughey, 2005).  The different elevation datasets vary in quality and applicability to road grade estimation based on the source and acquisition technology (Wang et al., 2017). The approximately 1 km grid 7  spacing of GTOPO30 is not applicable to derive elevation profiles of roads when taking into account the variable vertical accuracy of the dataset. The three arc-second (90 m) grid spacing SRTM is a much better source due to its higher resolution and consistent vertical accuracy of about 10m (Rodríguez, Morris, & Belz, 2006). SRTM was collected as part of a collaborative effort between NASA and the National Geospatial Intelligence Agency (NGA). Data were collected over an 11-day mission in February 2000 (Farr et al., 2007; Robinson, Regetz, & Guralnick, 2014). The data were presented as a Digital Surface Model (DSM) which captures above ground structures like buildings and trees compared to bare-earth DEMs. Nevertheless, the 90 m resolution might not be enough for road profile extraction. Conversely, ASTER G-DEM has a resolution of 1 arc-second (30 m) and a coverage of 99% of the world compared to 80% of SRTM (Tachikawa et al., 2011). ASTER also has similar accuracy as that of SRTM (Wilson, 2012). The joint Japanese-US ASTER G-DEM version 2 (latest version) was released in 2011 three years after the initial release of version 1. ASTER G-DEM v2 will be used in this research.   SRTM had some voids and errors in version 1. NGA applied several post-processing procedures to fix some of the issues and released version 2.1 (finished version) in 2009 on the USGS website as SRTM2.1. The resolution was still three arc-second but was later resampled and released in 2014 at one arc-second resolution (Jarihani, Callow, McVicar, Van Niel, & Larsen, 2015). Both versions were used in this research. After SRTM2 was released the Consortium for Spatial Information of the Consultative Group of International Agricultural Research (CGIAR-CSI), further processed the data to obtain the most quality controlled version of SRTM: CGIAR-CSI SRTM v4.1 (Jarvis, Reuter, Nelson, & Guevara, 2008).   8  The Canadian Digital Surface Model (CDSM) is derived from the SRTM in 2010 (Ministry of Natural Resources, Canada, 2014a). Original SRTM elevation data at one arc second step were reprocessed to improve the product. Gaps were filled, the vertical datum changed, data were filtered for noise and aligned with the grid resolution of 0.75 arc seconds, and water surfaces were leveled. CDSM products feature 0.75 arc-seconds spacing (20 m) harmonized with the Canadian Digital Elevation Model (CDEM) to facilitate combined use where needed. The Canadian DEM is based on the elevation contours and hydrographic data of Natural Resources Canada’s (NRCan) Geospatial Data Base at the scale of 1:50,000, or data at various scales provided by provinces and territories. Both the CDSM and CDEM were used in the comparison in this research.  LiDAR is a type of mobile mapping based on remote sensing technology. The system integrates data from multiple sensors to position the ground in three dimensions (Grejner-Brzezinska, 2002). LiDAR is capable of producing DEMs with vertical accuracies of about 30cm (Keqi Zhang et al., 2003). LiDAR is mainly composed of three components that work together to produce a cloud point of everything visible from the mobile platform the sensors are on. Airborne Laser Scanning refers to when the LiDAR system is placed on an aircraft to collect ground elevation data (Example in Figure below).  9   Figure 4 Example of cloud point data from Airborne Laser Scanning   The basic components of a LiDAR system include an airborne GPS, LiDAR sensor, and inertial measurement unit (IMU) as shown in Figure 5.   Figure 5 Simple illustration of how LiDAR cloud points are collected (Zhang & Frey, 2006) The LiDAR sensor scatters laser pulses that reflect off the earth and measures the return time which is representative of the distance from the airplane to the ground. The GPS measures the position of the plane in x, y, z coordinates and the IMU establishes the angular orientation of the 10  LiDAR sensor. The system combines this data to produce accurate dense cloud points of the ground (J. Li, Lee, & Cho, 2008; Zhang & Frey, 2006). In locations with dense vegetation, a bridge or overpass, the laser might not reach ground level and thus might not be representative of the elevation of the earth. Yet, some of the scattered laser will go through the tree canopy and reflect off the earth later than the pulse that hit the tree. In such a scenario, the ground points will be registered as Last Returns (based on time) and the point scattering off the tree canopy as First Returns (Figure 6). LiDAR technology can have up to five returns (Hu, 2003). Thus obstructions will produce voids when trying to obtain bare earth elevation data. Yet, LiDAR DEM benefits from better accuracy, more dense point spacing (3m compared to 10-30m of traditional sources) and lower cost (Zhang & Frey, 2006). LiDAR data are not as widely available as SRTM and ASTER and it does not have a spatial extent as great as SRTM and ASTER based DEM. It is used in a more local context.   Figure 6 Example of multiple returns over a tree  (from:http://home.iitk.ac.in/~blohani/LiDAR_Tutorial/Multiple%20return%20LiDAR.htm)  11  The City of Vancouver collected LiDAR data over three days in February 2013 (The City of Vancouver, 2013). This data were made available online in a cloud point format and a DEM raster. A DSM raster was later created from the LiDAR data and used in this study in conjunction with the RAW cloud point in LAS classified point data format.  Zhang and Frey (2006) identified three sources of road elevation that are not based on remote sensing or photogrammetry : [1] design drawing data, [2] traditional surveying, such as direct on-road measurement, [3] measurement and analysis of GPS data.  Design Drawing Data. Road grade estimates can be inferred from design drawings especially for major roadway construction projects. However, design drawings may not be representative of the as-built roadway since the as-built drawings may not have been updated or created (Zhang & Frey, 2006). Also, modifications to the roadway are not usually included in the drawings. Nevertheless, and in the absence of road grade measurements, design drawings are the most accurate source of road grade data (Zhang & Frey, 2006). Road grades can directly be extracted from the drawing and assigned to a roadway segment. It is a time-consuming process, since most drawings are not digitized, but it is the best available source for interstates (Zhang & Frey, 2006).  Direct On-Road Measurement. Direct measurement of road grade can be done using a digital level, grade meter, or data log vehicle (Zhang & Frey, 2006). However, road grade measurement using all three methods is time-consuming and expensive, and measurements can be affected by imperfections in the asphalt. 12   GPS Data. Accurate elevation data estimates from GPS require a receiver with high accuracy and precision, in addition to data correction and post-processing. Reliable road grade estimates necessitate several GPS runs. If one of the requirements are not met “the accuracy of GPS-estimated elevation can vary by up to twice as much as the two-dimensional estimates”(Hughes, 2014; Wood, Burton, Duran, & Gonder, 2014). Due to the need for repeated runs and high cost of accurate GPS receivers, this method is not very viable.  Table 1shows the characteristics of relevant elevation data sources  as adopted from Nelson et al. (2009).  Table 1 Summary of elevation data sources adopted from (Nelson et al., 2009; Wilson, 2012) Source Resolution (m) Accuracy Footprint (km2) Post-processing requirements Elevation/surface Ground survey Variable but usually <5 m Very high vertical and horizontal Variable, but usually small Low Elevation GPS Variable but usually <5 m Medium vertical and horizontal Variable,  but usually small Low Elevation Table digitizing Depends on map scale and contour interval Medium vertical and horizontal Depends on map footprint Medium Elevation Ortho-photography <1 Very high vertical and horizontal – High Surface LiDAR 1–3 0.15–1 m vertical, 1 m horizontal 30–50/h High Surface SRTM  Band C 90 (30) 16 m vertical, 20 m horizontal Almost global,  60° N to 58° S Potentially high Surface ASTER 30 7–50 m vertical, 7–50 m horizontal 3,600 Medium Surface  The literature identifies numerous methods to calculate road elevation profile and grade distribution from the different elevation sources. Souleyrette et al. (2003) used LiDAR based 13  surface models to estimate road grade by following this method: [1] Triangulated irregular network (TIN) surface models including a particular type of data format for GIS were used to delineate the needed road segments. [2] A rectangle defined the edges of the roadway segment. The midpoint of the shorter sides of the rectangle helped estimate the center line. A local origin is defined and used as a basis to calculate distances for LiDAR data points from and along the center line. [3] The calculated distances and observed elevations were used for regression to estimate the grade and banking. This method did not account for the effect of vertical curvature on road grade estimation. Additionally, delineating a street network from a TIN surface model is not practical for large networks (Zhang & Frey, 2006).   Zhang and Frey fit a plane to elevations for segments of roadways using regression techniques to obtain road grades from LiDAR data, thus accounting for vertical curves. The LiDAR based method for road grade estimation includes five major steps: [1] Select LiDAR data within a buffer zone for the roadway. [2] Define the roadway center line. [3] Compute distances. [4] Segment the roadway to eliminate the effect of vertical curvature by creating segments that are approximately piecewise linear. [5] Fit a plane to the roadway surface for each roadway segment using bivariate linear regression. Segmenting the roadway was done following these steps: [1] Specify the end points of a roadway link and identify its local extremums by elevation to generate candidate segments. [2] Divide each candidate segment into two equal length sub segments. [3] Check the difference of estimated road grade between the candidate segment and its sub segments. If it is > 0.1% further divide the segment. The estimates of road grade are affected only by elevation and distance along the center line of the roadway segment. The estimates of banking are affected only by elevation and distance from the center line of the 14  roadway segment. Locations where voids in the LiDAR data occur (near bridges, overpasses and dense vegetation) were modeled as vertical curves connecting adjacent roadway links. To evaluate the accuracy of the LiDAR estimates, the LiDAR-based road grade estimates were compared with design drawing data for selected portions of the studied roadways.  Regression and fitting were not the only methods identified in the literature where road grade estimates were obtained from elevation datasets. Wood et al. (2014) appended elevation data to two-dimensional GPS data by using the GPS coordinates to look up the U.S. Geological Survey (USGS) 1/3 arc second DEM to obtain elevations of these points. This DEM is a bare-earth dataset, which returns the lowest elevation at a given point. Thus, at overpasses and bridges, it shows a sudden drop in elevation of tens of feet. Elevation data were down sampled into uniformly spaced intervals and passed through a combined Savitzky-Golay (Savitzky & Golay, 1964) and binomial filter. Points where elevation difference exceeds a threshold were discarded and replaced with interpolated points. The new elevation points are passed through the filter again to eliminate noise. The results were then validated against the Navteq/Nokia/HERE ADAS (“Navteq Advanced Driver Assistance Systems,” n.d.) height/grade database of elevation and road grade values for approximately five million points in the contiguous United States.  Similarly, Payne and Dror (2017) utilized the 1/3-arc second DEM available from the USGS to create smart maps that incorporated road grade and elevation data. The street network was initially represented as a graph containing nodes and edges, followed by adding nodes at 10m intervals to the graph using a navigation algorithm. Nodes at intersections were not modified. The DEM was queried using the coordinates at the nodes to obtain the elevation at each node. 15  Grades were calculated as the change in height over the change in distance traveled. The nodes that mark a grade change or intersection were conserved in the final graph.  LiDAR data in cloud point format would require a different approach than that in raster format. Cai and Rasdorf (2008) compared two methods for obtaining road grade from a LiDAR point cloud data. The first method included using two elevation points (within a buffer of the road) at opposite sides of the road centerline to interpolate the elevation of the centerline. The other more preferred method included snapping points (within a buffer) to the road centerline. This method results in the same elevation at the points identified by the interpolation method, but also adds more elevation points to the roadway.  To obtain better estimates of road grade from LiDAR cloud point data, one can classify and filter the data as road points (Boyko & Funkhouser, 2011; Choi, Jang, Lee, & Cho, 2007; Clode, Kootsookos, & Rottensteiner, 2004; J. Li et al., 2008) and then apply the methods by Cai and Rasdorf (2008) or Zhang and Frey (2006). Classifying points as road points is achieved by considering the intensity data collected with the LiDAR data collection (Kashani, Olsen, Parrish, & Wilson, 2015) along with the elevation. Most of these methods are computationally intensive, as they require processing of a large set of points. Also, these methods do not account for the confounding factors that affect the intensity measurements when intensity is being used as a proxy for the type of material. This is based on the fact that reflectivity is a function of intensity (Hu, 2003). Kashani et al. (2015) identify multiple factors that might affect the recorded intensity in a LiDAR system including surface characteristics, acquisition geometry, and instrumental and environmental effects. For intensity values to be able to represent target surface characteristics 16  accurately all other effects must be accounted for. Kashani et al (2015) identify four levels of processing intensity data and two general models followed: empirical and theoretical. Most theoretical models are based on the LiDAR range equation.   Equation 1 LiDAR power received 𝑃𝑟 =𝑃𝑡𝐷𝑟2𝜂𝑎𝑡𝑚𝜂𝑠𝑦𝑠𝜎4𝜋𝑅4𝛽𝑡2   where Pr = received optical power (watts), Pt = transmitted power (watts), Dr = receiver aperture diameter (meters), σ = effective target cross section (square meters), ηatm = atmospheric transmission factor (dimensionless), ηsys = system transmission factor (dimensionless), R = range (meters), and βt = transmit beam width (radians).  Empirical models are based on collecting the LiDAR data with different conditions and creating a quadratic or exponential model based on that data. In both cases, obtaining a value of intensity that would more accurately represent the target surface characteristics requires range information of each data point that is missing in the data set supplied by the city of Vancouver.  On the other hand, Boyko and Funkhouser (2011), while detecting road points from a dense LiDAR cloud point data , used the LiDAR data to create 3D lines out of 2D polylines from a network shapefile. This method relies exclusively on the elevation information within the LiDAR data by optimizing the elevations of cardinal spline control vertices at 15m along the 17  line. The steps are as follows: [1] place spline control points at 15m along the 2D lines of the network, [2] solve for the elevations of the control vertices by minimizing the error:  Equation 2 Error value in Boyko Method 𝐸(𝑉) = ∑ (𝑤(𝑠) ∑ (𝑠𝑧 − 𝑝𝑧)2𝑃∈𝑁(𝑠))𝑠 ∈𝑆(𝑉)  where V is the set of control vertices, s is a set of points sampled at 1 m intervals along the Cardinal spline S defined by V, sz is the elevation of s, p is a LiDAR point in the set of points N(s) within 15 cm of s in 2D, w(s) is a weight computed as the inverse of the variance of the elevations within N(s), and pz is the elevation of p (Figure 7).   Figure 7 Diagram representing the projection of 2D map into 3D line (Boyko & Funkhouser, 2011)  [3] fit smooth spline to the LiDAR points, [4] snap the elevation of every point s to a LiDAR point closest to spline curve position, Finally [5], visit each point in order and assign the elevation of that point to be that of the previous one if the incline on that point exceeds 0.35. 18   Wang et al. (Wang et al., 2017), on the other hand, found the methods to obtain road elevation on the available elevation sources lacking, so they extracted Google Earth (GE) elevation data to use it in transportation applications. The steps to incorporate elevation data from GE are as follows: [1] Determine GE viewbox parameters based on the start/end points and geometric information of the segment of interest. [2] Convert the latitude and longitude coordinates (widely used in roadway GIS) of sampling points into the GE form relative coordinates and extract the raw elevation data. [3] Eliminate errors induced by surface sheltering using multi-layered roadway recognition and data correction, and estimate the elevation for the roadways that cannot be directly acquired. [4] Segment the extracted route by recognizing roadway grade changes and calculate the grade length and grade. Two datasets were utilized as ground truth data to examine the accuracy of the elevation data extracted from the GE. The first is the GPS on Bench Markers dataset of geodetic control points from the National Geodetic Survey (NGS)(“GPS On Bench Marks for GEOID09,” n.d.). The second source of ground truth data is roadway monuments directly adjacent to the roadways of interest.  A few methods that are independent of elevation datasets can be mentioned. These methods cannot be used with an existing GPS dataset (Wood et al., 2014).   Kalman filters integrated with powertrain models and signals from the controller area network bus to simultaneously estimate vehicle mass and road grade (Kim, Kim, Bang, & Huh, 2013; McIntyre, Ghotikar, Vahidi, Xubin Song, & Dawson, 2009; Vincent Winstead & Ilya V. Kolmanovsky, 2005) 19   Filtered differential GPS velocity signals used as vectors to directly calculate instantaneous road grade (potentially requiring multiple runs over a given segment for estimates to converge) (Bae & Gerdes, 2004; Ryan, Bevly, & Lu, 2009; Sahlholm & Henrik Johansson, 2010; Sahlholm & Johansson, 2010)  The graph below summarizes the methods considered in this paper.    Figure 8 Diagram representing the different methods to calculate road grade from elevation data sources   Raster File DEM/DSMLiDAR Cloud Point DataGPS 3D DataDesign DrawingsExtract Elevations based on Point Locations Filtering/ SmoothingRoad Grade EstimatesNetwork ShapefileCardinal Spline Interpolation OptimizationMeasurementRoad Point ClassificationFitting/InterpolationDATA SOURCES20  1.3 Research Question  The objective of this research is to determine the best methods of obtaining road grade information for bicycle travel analysis. Common sources of elevation data are compared with ground surveying data and applied to cyclist power estimation. A detailed recommendation of what elevation data sources are most suitable to calculate the road grades of elevated and non-elevated roads in the network is made based upon the results of the comparison. The research provides insight on the limitations of the elevation data sources available and how to best utilize them. 21  Chapter 2: Methodology  2.1 Overview  In this research, multiple elevation data sources were collected for the city of Vancouver, BC Canada. Different road grade estimation algorithms were then applied to the data sources at locations in the city where ground truth elevation data were surveyed using a total station. Different cycling performance measures were used to compare the elevation and road grade estimates of the locations to identify the data sources that mostly represent the true ground elevation. Finally, the best algorithm based on overall percent error is used to calculate elevations of all the elevated structures in the city of Vancouver to characterize the elevated structures and understand how to approach them when conducting a study.  22  2.2 Elevation Data Sources Table 2 Collected elevation data source details (accuracy based on (Nelson et al., 2009; Wilson, 2012)) Source Name Vancouver DEM (from LiDAR)  Vancouver DSM (from LiDAR First Return)  LiDAR Cloud Point Canadian DSM  Canadian DEM  SRTM 1arcs DEM  SRTM 3arcs DEM  CGIAR SRTM DEM  ASTER DEM  Format Raster File (GeoTIFF) Raster File (GeoTIFF) Cloud Points (LAS) Raster File (GeoTIFF) Raster File (GeoTIFF) Raster File (GeoTIFF) Raster File (GeoTIFF) Raster File (GeoTIFF) Raster File (GeoTIFF) Grid Spacing 0.5m 0.5m 1-3m ~20m ~20m 30m (1 arc second) 90m (3 arc second) 90m (3 arc second) 30m (1 arc second) Extent City of Vancouver City of Vancouver City of Vancouver Canada Canada 80% of world 80% of world 80% of world 99% of world Base Data Source/ Acquisition Technology Vancouver LiDAR (2013) Vancouver LiDAR (2013)) Vancouver LiDAR (2013) SRTM Elevation contours and hydrographic data of Natural Resources Canada’s (NRCan) Geospatial Data Base SRTM SRTM SRTM ASTER Reported Accuracy   0.15–1 m vertical, 1 m horizontal 0.15–1 m vertical, 1 m horizontal 0.15–1 m vertical, 1 m horizontal 16 m vertical, 20 m horizontal Not Available 16 m vertical, 20 m horizontal 16 m vertical, 20 m horizontal 16 m vertical, 20 m horizontal 7–50 m vertical 7–50 m horizontal Vertical units meters meters meters meters meters meters meters meters meters  23  The different elevation datasets (Table 2) vary in quality and applicability to road grade estimation based on the source and acquisition technology (Wang et al., 2017). The three arc-second (90 m) grid spacing SRTM has a consistent vertical accuracy of about 10m (Rodríguez et al., 2006). The data are presented as a Digital Surface Model (DSM) which captures above ground structures like buildings and trees compared to bare-earth DEMs. Nevertheless, the 90 m resolution might not be enough for road profile extraction. Conversely, ASTER G-DEM has a resolution of 1 arc-second (30 m) and a coverage of 99% of the world compared to 80% of SRTM (Tachikawa et al., 2011). ASTER also has similar accuracy as that of SRTM (Wilson, 2012). The joint Japanese-US ASTER G-DEM version 2 (latest version) was released in 2011 three years after the initial release of version 1. ASTER G-DEM v2 will be used in this research in its raster format.   SRTM had some voids and errors in version 1. NGA applied several post-processing procedures to fix some of the issues and released version 2.1 (finished version) in 2009 on the USGS website as SRTM2.1. The resolution was still three arc-second but was later resampled and released in 2014 at one arc-second resolution (Jarihani et al., 2015). Both the 1 arc second and 3 arc second SRTM V2.1 were used in this research. After SRTM2 was released the Consortium for Spatial Information of the Consultative Group of International Agricultural Research (CGIAR-CSI), further processed the data to obtain the most quality controlled version of SRTM: CGIAR-CSI SRTM v4.1 (Jarvis et al., 2008) which is included in this research in its raster format.   24  The Canadian Digital Surface Model (CDSM) is derived from the SRTM in 2010 (Ministry of Natural Resources, Canada, 2014a). Original SRTM elevation data at one arc second step were reprocessed to improve the product. Gaps were filled, the vertical datum changed, data were filtered for noise and aligned with the grid resolution of 0.75 arc seconds, and water surfaces were leveled. CDSM products feature 0.75 arc-seconds spacing (20 m) harmonized with the Canadian Digital Elevation Model (CDEM) to facilitate combined use where needed. The Canadian DEM is based on the elevation contours and hydrographic data of Natural Resources Canada’s (NRCan) Geospatial Data Base at the scale of 1:50,000, or data at various scales provided by provinces and territories. Both the CDSM and CDEM in a raster format were used in the comparison in this research.  LiDAR is a type of mobile mapping based on remote sensing technology. The system integrates data from multiple sensors to position the ground in three dimensions (Grejner-Brzezinska, 2002). LiDAR is capable of producing DEMs with vertical accuracies of about 30cm (Keqi Zhang et al., 2003). The City of Vancouver collected LiDAR data over three days in February 2013 (The City of Vancouver, 2013) and made it available online in a cloud point LAS format and a DEM raster file format. A DSM raster of grid spacing of 0.5m, to match the LiDAR DEM raster, was created from the LiDAR last return cloud points using the binning approach for determining each output cell using the average of the points that fall within its extent, along with a linear interpolation for determining the value of cells that do not contain any LAS points. The LiDAR DSM created was used in this study in conjunction with the cloud point data in LAS classified point data format and the DEM in a raster format. 25  2.3 Ground Truth Data Collection  To obtain ground truth road grades to compare the implemented methods to, the elevation profiles of 8 sample locations were measured. The figure below shows the locations in the city of Vancouver and Table 3 includes further detailed information.    Figure 9 Map of the ground truth measurement sites   26  Table 3 Ground truth location site details Location Name 400 Smithe Street 1200 1500 Island Park Walk 2500 Trafalgar Street 2500 W 10th Street Burrard Bridge 1000 Beach St Main Street Over Waterfront Street Cambie Street North Bike Ramp Description Steep Street in Downtown Off road bike Path Steep Residential Street Residential Street Bridge Crossing Water Body City Street Bridge Not Crossing Water Body Two Story Bike Ramp Bike Path On Street Separated Separated Shared Shared On Street Separated Shared Shared Ramp Elevated  No No No No Yes No Yes Yes Under a Bridge No Yes No No No Yes No No Length 75m 75m 60m 120m 1010m 90m 255m 135m Data Extraction Interval (m) 5m 5m 5m 5m 10m 5m 5m 5m  The 8 locations were chosen to be have different bike facility types, conditions and grades (see details in Table 3). The locations were contingent to having a Vancouver Surveying Monument (Tyson Altenhoff, 2017) nearby to allow for correct elevation referencing. Two of the locations were elevated structures: one over land (Main Street) and the Burrard Bridge over a water body. Two other locations were under a bridge: Beach St and Island Park Walk. They have different facility types where Beach St is a shared road and Island Park Walk is an off road bike path. They help understand the robustness of the methods to sizable obstructions above the ground. The rest of the locations are ground locations with mostly open sky with some trees on the side walk that can obstruct LiDAR. One expectedly challenging location is the bike ramp North of Cambie Bridge which a two story bike ramp that leads to an elevated bike path on the Cambie Bridge.  27  Measurements were taken using a Leica TCR700 total station, with an angle accuracy of 5 seconds and a distance accuracy of +/-3m, and a standard reflector prism. At each site, the total station was initially set up on the surveying monument closest to the site and the coordinate system and reference horizontal angle were set. Distance and angle measurements of the target prism were taken from the start of the road (at the intersection) to the end of the road (at the next intersection). The total station was moved when the target prism was occluded or farther than 100m. When the total station was moved the coordinates and reference horizontal angle were maintained.   The target prism was moved at predetermined intervals (using a measuring tape) along the length of the road at a fixed distance parallel to the curb. Measurements were taken at 5m intervals in locations with a length less than 300m and at 10m intervals otherwise due to time constraints. Six measurements were taken at each location to account for human and instrument inaccuracies. The mean coordinates at each location were used as the ground truth. The maximum standard deviation of the measurements at each target location across all the sites was 6mm, with an average standard deviation of 1mm.  2.4 Road Grade Estimation Methods  Two main types of elevation datasets (raster files and LAS cloud point data) were used in the evaluation to find the most appropriate method to estimate road grade data. The DEMs and DSMs collected in raster format were utilized to calculate road grade using two different methods. The first is the simple extraction of elevation from the coordinates of points (target 28  points) along the road with 5 or 10 m intervals in each site. The elevation values form the elevation profile of the road. The second method involves bilinear interpolation (Press, 1992) for the extraction of elevations, which determines elevation values from interpolating between the four nearest cells, instead of simple extraction. Figure 10 shows the difference in interpolated and non-interpolated elevations from the Canadian DSM.   Figure 10 Bilinear interpolation versus simple extraction from the Canadian DSM on 400 Smithe Street  In addition, the Boyko and Funkhouser (2011) method was applied to the LiDAR cloud point data to produce the elevation profiles and road grades of roads and bridges in the network (discussed in Section 1.2). The method involves placing spline control vertices at 15m along the road line. Then optimizing for the elevation of these vertices by minimizing the error of spline 29  points at 1m intervals along the line. Then the elevation of the spline points will be updated with that of the closest LiDAR point. Finally, all points are visited in order and assigned the elevation of the previous point in case the grade exceeds a threshold of 0.35 which is the maximum road grade in the world (Boyko & Funkhouser, 2011). The method is illustrated in Figure 7.  Some applications like Google Maps provide a straight line approximation of the elevation profile along roads with missing information. Thus a straight line approximation was also calculated from the ground truth elevations at the end points of the roads in the 8 locations.  Road grade was calculated from the elevation profiles by differencing at each interval (5m or 10m) and dividing by the interval length.  2.5 Evaluation Comparison Measures   The elevation profiles obtained from the different datasets identified above were evaluated based on the absolute error of the elevation at each interval (at 5m or 10m intervals) along the profile.  The mean and standard deviation of the absolute error of the elevation at each location for each dataset was calculated to evaluate the accuracy of the elevation profile from the dataset compared to ground truth. The standard deviation of the percent error will provide insight on the grade distribution from each dataset. If the standard deviation was very small then the elevation profiles run parallel.  30  Grade distributions do not contain the serial correlation of the grades along the length of the road but they contain essential information about the elevation variability along a road. For cycling applications, road grade is the key elevation measure that influences cycling performance and behavior. Grade distributions of each ground truth location from each dataset were further evaluated based on the coincidence ratio compared to the grade distribution of the ground truth. The coincidence ratio is used to identify the similarity of two distributions. It is the ratio of the intersection of two distributions over the union of the two distributions. Mathematically, it is calculated as the sum of the lower frequency of the two grade distributions at each increment of 0.005 or 0.5% divided by the sum of the higher frequency of the two grade distributions at each increment of 0.005.  Table 4 Performance measures used to compare elevation and road grade estimates Performance Metric1 Cumulative Elevation Gain Cumulative Elevation Loss Absolute Elevation Change Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Calculation Formula Sum of every elevation change where grade>0 Sum of every elevation change where grade<0 Absolute value of the difference in elevation between the start and end of a road  Average of the absolute grades on the road  Percentage of positive grades out of all of  the grades on the road  Percentage of negative grades out of all of  the grades on the road  Average of the grades greater than or equal to zero Average of the grades less than zero 1 The Calculation interval for all performance measures is 10m for Burrard Bridge and 5m in all other locations  In addition, the performance measures in Table 4 were calculated for each location from each dataset and the percent error of each performance measure from each elevation dataset was used to evaluate the elevation datasets. The performance measures include Average Absolute Grade (AAG), Percent Positive Grade, Absolute Elevation Change, Percent Positive Grade, Percent 31  Negative Grade, Average Positive Grade, Average Negative Grade, Cumulative Elevation Gain, and Cumulative Elevation Loss which are descriptive measures that can depict the intricacies of the elevation profile and grade distribution, inspired by the information provided by routing applications like google maps.  Descriptive statistics of the grade distribution such as minimum, maximum, mean, median, interquartile range and standard deviation were also used as performance measures to evaluate the different elevation datasets. Performance measures along with the length and descriptive statistics of the grade distribution of the road can provide enough context to help understand the power exerted and the possible time and speed to cross the road given the strength of the cyclist.  Estimated power (in watts) of a cyclist traversing a road was used as an applied performance measure to further evaluate the elevation datasets. Equation 3 shows how power can be calculated from road grade (𝐺, unit-less), constant speed relative to wind (𝑣 in m/s) and cyclist characteristics (Bigazzi & Figliozzi, 2015):  Equation 3 Power consumption of a cyclist (Bigazzi & Figliozzi, 2015) 𝑃 = 𝑚𝑔(𝐶𝑟 + 𝐺)𝑣 + 0.5ρ𝐴𝑓𝐶𝑑𝑣3   where 𝑃 is power (watts), 𝑚𝑔 is the total weight (N) of the cyclist, bicycle, and cargo, 𝐶𝑟  (unitless) is the rolling resistance coefficient, 𝜌 is the air density (assumed to be 1.225 kg/m3) and 𝐴𝑓𝐶𝑑   is the effective frontal area (m2). Assumed values of 𝐶𝑟 = 0.0077, 𝐴𝑓𝐶𝑑 = 0.559m2 and 𝑚𝑔 = 105 kg for urban cyclists in Vancouver are taken from (Tengattini & Bigazzi, 2018). 32  Speed was assumed to be a constant 𝑣 = 4 m/s as an average cyclist speed (15 km/h) as per  Bernardi & Rupi (2015). Cyclist energy to traverse each interval of length 𝐿 (5 m or 10 m) was calculated as 𝐸 = 𝑃𝐿𝑣, and summed for all the intervals at each location to estimate total energy.  All the performance measures were compared to their corresponding ground truth estimates using absolute percent error, as per Equation 4.  Equation 4 Absolute percent error equation 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =  |#𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 − #𝑡𝑟𝑢𝑡ℎ#𝑡𝑟𝑢𝑡ℎ| × 100    33  2.6 Characterization of Elevated Structures  In areas where only coarse bare-earth elevation datasets are available, elevation of structures above the ground will not be attainable. Thus, with the best available dataset from the ones identified above, the elevated structures in the City of Vancouver are characterized.  Using the Open Street Maps (OSM) Vancouver network shape file (OpenStreetMap contributors, 2017), elevated structures in the City of Vancouver were identified based on the binary bridge attribute associated with each road in the network and its length which were assumed to be greater than 30m to exclude short stairways and pathways. The bridge attribute takes a value of 1 if the road is elevated and a value of 0 if it is not. The elevated roads were then visually inspected and duplicates of the same road but with different directions or facility type were excluded. The total number of elevated roads identified, which will also be referred to as locations, is 35.  The elevation dataset that performed best on elevated roads (according to the evaluation criteria described in the previous section) was used to obtain elevation profiles of the identified elevated roads. Grade distribution and performance measures of the elevated roads were then calculated in comparison to the best-performing elevation dataset.  To classify the elevated roads, the modality of the grade distributions was calculated using the Kernel Density Estimate (KDE) (Hall & York, 2001; Ling Xu, Bedrick, Hanson, & Restrepo, 2014; Silverman, 1981). The bandwidth of the KDE was set to (0.5%) and the modes were 34  identified by locating local maxima in the KDE (Silverman, 1981) which minimized the effect of any noise in the elevation profile.  Roads were then grouped according to their modality unimodal and bimodal locations in their respective groups and the locations with greater modality in their own group. The unimodal locations were fitted with a parametric distribution using maximum likelihood estimation (Scholz, 2006).  To simulate a situation where only the coarse elevation dataset are available, measures calculated from the best performing coarse elevation dataset were used to infer the road grade distribution according to the parametrized distribution and the straight line approximation of the profile. Total energy as an applied performance measure was then calculated using the approximations to compare them to the best performing dataset. 35  Chapter 3: Results   3.1 Elevation and Grade Profiles   Figure 11 Elevation profiles of 2500 Trafalgar Street using DEMs (without interpolation) compared to Ground Truth.  Figure 11 shows the elevation profile of 2500 Trafalgar Street from the elevation sources without interpolation. DEMs that are based on SRTM or ASTER have resolutions of 1 or 3 arc seconds which is too coarse for roads of length around 100m. The 30 – 90 m grid spacing will render a road of 100m length to have 3~4 or 1~2 points maximum from these elevation datasets respectively. A low number of elevation points across a road profile cannot help detail its 36  elevation profile and accurately estimate its grade distribution given that elevation changes occur a max of 2~3 times along the road which can be clearly seen in Figure 11 where the 3 arc second dataset, (CGIAR SRTM and SRTM 3arcs DEM) have basically two unique elevation values and the 1 arc second DEMs, (Canadian DEM, Canadian DSM, ASTER and SRTM 1 arcs DEM) have around 3 elevation values. The use of bilinear interpolation is thus important to try and depict detailed elevation profiles compared to simple extraction (Figure 11) based on the 2D coordinates of the lines and points in the shapefile. In denser raster files with grid spacing of about half a meter (LiDAR based DEMs: Vancouver DEM and Vancouver DSM), the issue is not present since a simple extraction at 5m intervals provides unique elevation values at each location along the line. For the rest of the discussion, the values and calculations are made from the elevation profiles extracted from DEMs using the bilinear interpolation (all the elevation and grade profiles are found in the appendix).   37   Figure 12 Elevation profiles of 400 Smithe Street from LiDAR data sources compared to ground truth  Figure 12 shows the elevation profile of 400 Smithe Street and Figure 13 shows the profile of 1000 Beach Street running under Burrard Bridge. The Vancouver DSM has a noisy elevation profile (Figure 12) due to the objects above the ground level since the raster was made from first return LiDAR cloud points which capture all the objects above street/ground level. In addition, Figure 12 shows that the elevation profile from Boyko also has some inaccuracies due to the mechanics of the algorithm that relate to those in Vancouver DSM. The algorithm considers all LiDAR cloud points and in locations, where all the LiDAR points are blocked from reaching the ground, the elevation from the Boyko algorithm with be greater than that of the ground truth. Boyko behaves similarly and more obviously when a road crosses under a ramp or bridge as seen 38  in Figure 13. Yet, other DEMs are not affected by the objects above the ground due to the way they are measured or constructed (discussed in Section 1.2).   Figure 13 Elevation profiles of 1000 Beach Street from LiDAR data sources compared to ground truth   39  Table 5 Coincidence ratio of grade distribution compared to ground truth for all locations from all elevation sources Source 400 Smithe Street 1200-1500 Island Park Walk 2500 Trafalgar Street 2500 W 10th Street Burrard Bridge 1000 Beach St Main Street Over Waterfront Street Cambie Street North Bike Ramp Straight Line 0.250 0.000 0.043 0.116 0.000 0.333 0.000 0.019 Vancouver DEM (from LiDAR) 0.364 0.200 0.600 0.333 0.135 0.565 0.325 0.080 Vancouver DSM (from LiDAR First Return) 0.250 0.250 0.263 0.091 0.603 0.385 0.342 0.200 Boyko Method 0.250 0.200 0.333 0.455 0.616 0.125 0.342 0.125 Canadian DSM 0.000 0.154 0.200 0.263 0.098 0.000 0.259 0.149 Canadian DEM 0.071 0.000 0.091 0.143 0.128 0.125 0.259 0.200 SRTM 1arcs DEM 0.000 0.034 0.091 0.000 0.086 0.029 0.275 0.125 SRTM 3arcs DEM 0.000 0.071 0.043 0.067 0.058 0.000 0.342 0.038 CGIAR SRTM DEM 0.000 0.071 0.043 0.091 0.041 0.000 0.325 0.125 ASTER DEM 0.111 0.111 0.091 0.067 0.104 0.029 0.214 0.102  Table 5 gives the coincidence ratio for the slope distributions for each location from available data sources compared to the slope distribution of the ground truth. Vancouver DSM as a noisy elevation profile has a misrepresentative grade distribution. Excessive elevation changes can result in unrealistically high grades which is found in the profiles of the Vancouver DSM across all elevated or non-elevated roads. The grade outliers skew the grade distribution estimates and reduce the usability of the elevation source. However, the coincidence ratio of the grade distribution from the Vancouver DSM compared to that of the ground truth is not as affected (Table 5) since the extreme grade values occurred at a very low frequency.  40   Figure 14 Elevation profiles of 400 Smithe Street from DEMs compared to ground truth  Figure 14 shows the elevation profile of 400 Smithe Street. Non-LiDAR based profiles on non-elevated structures can sometimes show an uphill road on a downhill road as seen in Figure 14. The reversed dominant grade can be attributed to the coarseness of the elevation source and the error contained in the elevation data. The mean absolute error (Table 6) of the SRTM 1 arcs DEM at 400 Smithe Street is the greatest compared to other elevation sources. Moreover, the grade distributions along with other estimates will contain major errors due to the reversed dominant grade. Even with interpolation, some elevation sources have fundamental errors that would completely reduce their usability and increases the propagated error in estimating certain measures (will be discussed in 3.2).   41  Table 6 Mean absolute error (m) in elevation at each location from available sources compared to ground truth. Presented as Mean Absolute Error (m) (Standard deviation of Mean Absolute Error (m)) Source 400 Smithe Street 2500 Trafalgar Street 2500 W 10th Street 1200 1500 Island Park Walk 1000 Beach St Burrard Bridge Main Street Over Waterfront Street Cambie Street North Bike Ramp Straight Line 0.013 (0.014) 0.124 (0.068) 0.191 (0.11) 0.468 (0.303) 0.09 (0.062) 6.584 (3.779) 3.409 (2.117) 0.207 (0.157) Vancouver DEM (from LiDAR) 0.339 (0.055) 0.038 (0.034) 0.295 (0.108) 0.382 (0.323) 0.302 (0.066) 17.293 (10.493) 3.394 (3.929) 3.936 (1.932) Vancouver DSM (from LiDAR First Return) 1.342 (3.035) 0.788 (1.617) 5.823 (5.25) 9.709 (11.975) 6.385 (8.251) 0.497 (1.89) 0.227 (0.121) 2.388 (1.737) Boyko Method 0.612 (0.353) 0.129 (0.072) 0.404 (0.121) 0.391 (0.251) 0.529 (0.208) 0.127 (0.054) 0.274 (0.134) 2.74 (1.615) Canadian DSM 8.488 (2.872) 2.227 (0.143) 3.694 (0.396) 4.581 (0.675) 2.652 (2.243) 17.363 (10.574) 4.692 (2.159) 4.202 (1.466) Canadian DEM 3.492 (0.304) 1.585 (0.22) 1.821 (0.265) 7.375 (2.307) 3.435 (0.349) 16.19 (10.754) 2.535 (1.528) 1.443 (1.044) SRTM 1arcs DEM 10.178 (6.141) 2.419 (0.334) 4.398 (0.628) 6.353 (1.29) 4.622 (2.706) 17.255 (10.481) 4.194 (1.904) 3.447 (1.435) SRTM 3arcs DEM 7.788 (3.442) 3.127 (0.212) 3.659 (0.282) 5.31 (0.754) 5.667 (2.87) 16.462 (10.724) 4.301 (2.08) 3.063 (1.469) CGIAR SRTM DEM 8.085 (2.381) 2.969 (0.332) 3.338 (0.786) 5.422 (0.722) 4.75 (1.916) 16.367 (10.684) 3.858 (2.006) 3.185 (1.459) ASTER DEM 0.743 (0.51) 3.905 (0.514) 9.992 (2.054) 9.077 (0.987) 5.166 (1.553) 12.391 (8.631) 2.792 (1.622) 6.696 (1.726)  Table 6 gives the mean absolute error in elevation at each location as calculated from the available source compared to ground truth. On non-elevated structures, Vancouver DEM and the straight line estimates have the least errors with the least standard deviation of the error. A low standard deviation shows that the profiles from Vancouver DEM and Straight line estimates are mostly parallel if not overlapping with the ground truth profile. Straight lines are not the best estimate in locations with greater variations in grades like (Island Park Walk) and are only 42  practically used as a gap filling estimate which is not required in all non-elevated locations. Despite their low errors in elevation, they were the least representative of the grade distribution when looking at the coincidence ratio with the measured truth (Table 6). A single value of grade is not representative of the grade distribution in non-elevated structures. Thus, Vancouver DEM produces the most accurate elevation profile estimates after the straight line profile estimates on non-elevated locations. And, the grade distributions from the Vancouver DEM have high coincidence ratio with ground truth data. When LiDAR data are not available, the least errors are present in the Canadian DEM and DSM as seen in both Table 6 and Table 5.   Figure 15 Elevation profiles of Burrard Bridge from DEMs compared to ground truth    43  Figure 15 shows the elevation profile of the Burrard Bridge. DEMs in general do not capture objects above the ground which is advantageous on non-elevated structures but is the main disadvantage of using DEMs on elevated structures. All elevation sources except LiDAR DSM and Boyko fail to represent the elevated structure when the structure starts to divert from the ground level Figure 15. Boyko and Vancouver DSM also perform the best with the least cumulative errors in the elevation profile and a low standard deviation of the error which shows that their resulting profiles run parallel to the ground truth elevation profile. The accurate elevation profile is also represented in a high coincidence ratio of the grade distributions compared to measured truth were highest for Boyko. As an additional verification, Figure 16 shows the histogram of the grade from the measured ground truth which matches the information in the design drawings of Burrard Bridge with two main slopes of 3% and -3%. In comparison to a specified +/-3% slope in the Burrard Bridge design drawings, the Boyko method generated average road grade estimates of 3.03% (standard deviation 0.69%) and –2.90% (standard deviation 0.53%) for the up and down slopes, respectively.  44   Figure 16 Histogram of the grade distribution of the measured ground truth on Burrard Bridge  In a situation without LiDAR data, the highest coincidence ratio is 0.128 in bridges crossing a water body (Burrard Bridge) and 0.34 in bridges over ground (Main Street) as seen in Table 5. The small coincidence ratios are only due to some variation in elevation present in the profiles of the DEMs in elevated structures. Thus results may vary depending on the profile of the ground below the bridge. For example an increase in the coincidence ratio of the grade distribution is expected in locations where the ground truth is an almost exact mirroring of the elevated structure profile along the length of the profile. Clearly the lack of LiDAR data on elevated structures do not allow for an accurate representation of the grade distribution.  45   Figure 17 Elevation profiles Cambie Street North Ramp from all sources compared to ground truth  Figure 17 contains the elevation profiles of the bike ramp North of Cambie Bridge. In general all sources are not able to represent profiles of multistory structures like the ramp at North Cambie Bridge (Figure 17). Locations visible from a top view will be captured by at least the LiDAR dataset due to its dense cloud point and its accuracy. The profile from the Vancouver DSM is parallel to that of the ground truth at the later stages of the ramp (after ~90m) and Boyko follows ground truth shortly the first 10 m and then continues as a straight line when the LiDAR data are obstructed by the ramp structure due to its algorithm. Ramps such as the North Cambie Bridge ramp are locations that are difficult for most sources to represent well and thus should have special care when dealing with GPS data or studying cyclists going through this route.  46  3.2 Performance Measures  The performance measures calculated help describe the road elevation changes and the grade distribution. Table 7 & Table 8 give the best and worst performing data sources across all locations based on the percent error from ground truth. All measure estimates for each location from all the data sources are included in the appendix.  47  Table 7 Worst performing elevation sources for each location and performance measure Performance Measure 400 Smithe Street 2500 Trafalgar Street 2500 W 10th Street 1200-1500 Island Park Walk 1000 Beach St Burrard Bridge Main Street Over Waterfront Street Cambie St Ramp Cumulative Elevation Gain SRTM 1arcs DEM   Vancouver DSM Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Straight Line Estimate Vancouver DSM Cumulative Elevation Loss Vancouver DSM     Vancouver DSM Vancouver DSM     Vancouver DSM     Vancouver DSM     ASTER DEM   Straight Line Estimate Vancouver DSM Absolute Elevation Change SRTM 1arcs DEM   CGIAR SRTM DEM   Vancouver DSM     SRTM 1arcs DEM   SRTM 1arcs DEM   Canadian DEM   SRTM 1arcs DEM   Boyko Method Average Absolute Grade Vancouver DSM     Vancouver DSM  Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Straight Line Estimate Vancouver DSM Percent Positive Grade Canadian DSM   Vancouver DSM  SRTM 1arcs DEM   Straight Line Estimate ASTER DEM   Straight Line Estimate Straight Line Estimate Vancouver DEM Percent Negative Grade Canadian DSM   Vancouver DSM  SRTM 1arcs DEM   Straight Line Estimate ASTER DEM   Straight Line Estimate Straight Line Estimate Vancouver DEM Average Positive Grade Vancouver DSM     Vancouver DSM   Vancouver DSM     Vancouver DSM     Vancouver DSM     ASTER DEM   Canadian DSM   Vancouver DSM Average Negative Grade Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM  Vancouver DSM Straight Line Estimate Vancouver DSM Grade Standard Deviation Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM Vancouver DSM  Vancouver DEM     Vancouver DSM Grade Interquartile Range SRTM 1arcs DEM   ASTER DEM   Vancouver DSM     Canadian DEM   Canadian DEM   Straight Line Estimate Straight Line Estimate ASTER DEM   Min. Grade Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DEM     Vancouver DSM 1st Qu. Grade SRTM 1arcs DEM   SRTM 1arcs DEM   Vancouver DSM     Canadian DEM   SRTM 1arcs DEM   ASTER DEM   Straight Line Estimate ASTER DEM   Median Grade SRTM 1arcs DEM   CGIAR SRTM DEM   SRTM 1arcs DEM   SRTM 1arcs DEM   SRTM 1arcs DEM   ASTER DEM   Canadian DEM   Vancouver DEM     Mean Grade SRTM 1arcs DEM   CGIAR SRTM DEM   Vancouver DSM     Canadian DEM   SRTM 1arcs DEM   ASTER DEM   SRTM 1arcs DEM   Vancouver DEM     3rd Qu. Grade SRTM 1arcs DEM   ASTER DEM   Vancouver DSM     Canadian DEM   SRTM 1arcs DEM   SRTM 3arcs DEM   SRTM 3arcs DEM   Boyko Method Max. Grade Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM     Vancouver DSM  Vancouver DEM  Vancouver DSM 48  Table 8 Best performing elevation sources for each location and performance measure Performance Measure 400 Smithe Street 2500 Trafalgar Street 2500 W 10th Street 1200-1500 Island Park Walk 1000 Beach St Burrard Bridge Main Street Over Waterfront Street Cambie St Ramp Cumulative Elevation Gain Vancouver DEM    Vancouver DEM    Vancouver DEM    SRTM 3arcs DEM  Straight Line Estimate Boyko Method Canadian DEM  Straight Line Estimate Cumulative Elevation Loss Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate SRTM 1arcs DEM  Boyko Method Boyko Method Boyko Method Absolute Elevation Change Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Average Absolute Grade Straight Line Estimate Straight Line Estimate Straight Line Estimate Boyko Method Straight Line Estimate Boyko Method Vancouver DSM   Straight Line Estimate Percent Positive Grade Vancouver DEM    Vancouver DEM    Vancouver DEM    Vancouver DEM    SRTM 1arcs DEM  Vancouver DSM   ASTER DEM  Boyko Method Percent Negative Grade Vancouver DEM    Vancouver DEM    Vancouver DEM    Vancouver DEM    SRTM 1arcs DEM  Vancouver DSM   ASTER DEM  Boyko Method Average Positive Grade ASTER DEM  Vancouver DSM   SRTM 3arcs DEM  Boyko Method ASTER DEM  Boyko Method Vancouver DSM   Canadian DSM  Average Negative Grade Straight Line Estimate Straight Line Estimate Straight Line Estimate CGIAR SRTM DEM  Vancouver DEM    Boyko Method Vancouver DSM   Boyko Method Grade Standard Deviation Straight Line Estimate Canadian DSM  CGIAR SRTM DEM  SRTM 3arcs DEM  Straight Line Estimate Boyko Method Vancouver DSM   Vancouver DEM    Grade Interquartile Range Straight Line Estimate Canadian DSM  Canadian DSM  Boyko Method Straight Line Estimate Canadian DEM  Vancouver DEM    Vancouver DEM    Min. Grade Straight Line Estimate Vancouver DEM    SRTM 3arcs DEM  Vancouver DEM    SRTM 1arcs DEM  Boyko Method SRTM 3arcs DEM  Boyko Method 1st Qu. Grade Vancouver DSM Vancouver DEM    ASTER DEM  Boyko Method Straight Line Estimate Vancouver DSM   Vancouver DSM   Boyko Method Median Grade Straight Line Estimate Vancouver DEM    Vancouver DEM    CGIAR SRTM DEM  Straight Line Estimate Vancouver DSM   CGIAR SRTM DEM  CGIAR SRTM DEM  Mean Grade Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate Straight Line Estimate 3rd Qu. Grade Straight Line Estimate SRTM 3arcs DEM  Straight Line Estimate Boyko Method Vancouver DSM   Vancouver DSM   ASTER DEM  SRTM 1arcs DEM  Max. Grade Straight Line Estimate Canadian DSM  CGIAR SRTM DEM  SRTM 3arcs DEM  ASTER DEM  Boyko Method Vancouver DSM   Canadian DSM  49  The noise found in the Vancouver DSM negatively impacted the performance measure estimates derived from it. The Vancouver DSM had the highest error in almost all the measures and across almost all the locations. Particularly, Vancouver DSM is the worst estimate of more than 8 performance measure across the non-elevated structures where noise in the elevation was a product of objects above the ground in a relatively flat ground. The performance measures that were most impacted from the noisy elevation profile are cumulative elevation gain/loss, average absolute grade, average positive grade and average negative grade, Min and Max grade.   Figure 18 Cumulative Elevation Gain, loss and Absolute Elevation Change estimates from all the data sources on 2500 Trafalgar Street   02468101214Cumulative Elevation Gain Cumulative Elevation Loss Absolute Elevation Change2500 Trafalgar StreetMeasured Ground Truth Straight Line EstimateVancouver DEM (from LiDAR) Vancouver DSM (from LiDAR First Return)Boyko Method Canadian DSMCanadian DEM SRTM 1arcs DEMSRTM 3arcs DEM CGIAR SRTM DEMASTER DEM50  Figure 18 shows the value of 18 Cumulative Elevation Gain, loss and Absolute Elevation Change estimates from all the data sources on 2500 Trafalgar Street. Trafalgar Street is a strictly downhill street with a total elevation loss of 5.3m based on the ground truth data. Yet, an unrepresentative cumulative elevation gain of 6 m was estimated from the Vancouver DSM due to the noise in the data.   Figure 19 Descriptive statistics of road grade distribution from all the data sources on 2500 Trafalgar Street  Figure 19 is an example of some descriptive statistics of the grade distribution on a non-elevated road, it is clear that the Vancouver DSM has the highest variability and that is due to the extreme values that come from capturing objects that are above ground. Erroneous elevation datasets may contain high variability but in most cases are able to estimate average grade with low errors. Yet, -0.4-0.200.20.40.60.81Average Positive Grade Average NegativeGradeGrade StandardDeviationGrade Inter QuantileRangeMean Grade2500 Trafalgar StreetMeasured Ground Truth Straight Line EstimateVancouver DEM (from LiDAR) Vancouver DSM (from LiDAR First Return)Boyko Method Canadian DSMCanadian DEM SRTM 1arcs DEMSRTM 3arcs DEM CGIAR SRTM DEMASTER DEM51  across all performance measures, the Vancouver DEM had least errors along with the straight line estimate.   Figure 20 shows the value of 18 Cumulative Elevation Gain, loss and Absolute Elevation Change estimates from all the data sources on Burrard Bridge. Looking at the performance measures on Burrard Bridge (Figure 20), since all DEMs follow the bare earth rather than the bridge, the cumulative elevation gain and loss are over estimated. Yet, the absolute elevation change is similar over all the sources and that is because the road starts and ends at locations that meet bare earth.    Figure 20 Cumulative Elevation Gain, loss and Absolute Elevation Change estimates from all the data sources on Burrard Bridge 0102030405060Cumulative Elevation Gain Cumulative Elevation Loss Absolute Elevation ChangeBurrard BridgeMeasured Ground Truth Straight Line EstimateVancouver DEM (from LiDAR) Vancouver DSM (from LiDAR First Return)Boyko Method Canadian DSMCanadian DEM SRTM 1arcs DEMSRTM 3arcs DEM CGIAR SRTM DEMASTER DEM52   Straight line profile estimates produced highly erroneous performance measures over elevated structures especially in estimating the cumulative elevation gain and loss. They were also particularly erroneous in estimating the percent positive and negative grades and the average positive and negative grade. Yet, absolute elevation change and mean grade estimates from the straight line profile were consistently of least errors which can be attributed to the fact that the straight lines were derived from the measured truth. Yet, it shows that if the end points of the road have accurate elevations or even if the absolute elevation change with the correct sign was accurate, then assuming a straight line to connect the end points of the elevation profile can provide accurate estimates of the mean grade despite the elevation changes throughout the road.  At non-elevated structures, Vancouver DEM and straight line estimates provide the least erroneous estimates of all the performance measures (Table 8). Whereas in elevated structures, both Boyko and Vancouver DSM provide the best estimates of almost all the performance measures with the least errors (Table 8). In the absence of LiDAR data, on elevated and non-elevated structures the Canadian DEM and DSM give the least error estimates across almost all the performance measures. Yet, there no performance measure that is consistently accurately estimated by a specific elevation source across all locations. Thus it is difficult to recommend one method that can be an overall best performer across the performance measures due to the different errors in the LiDAR elevation sources not based on LiDAR data.   53  Table 9 Total energy calculated from each elevation data source at each ground truth location Presented as Energy (J) (Percent Absolute Error) Source 400 Smithe Street 2500 Trafalgar Street 2500 W 10th Street 1200 1500 Island Park Walk 1000 Beach St Burrard Bridge Main Street Over Waterfront Street Cambie Street North Bike Ramp Measured Ground Truth 5291.427 (0) 6239.651 (0) 5092.261 (0) 2834.079 (0) 1095.31 (0) 13332.863 (0) 11897.68 (0) 550.755 (0) Straight Line 5291.556 (0) 6242.076 (0) 5092.394 (0) 2843.879 (0) 1096.312 (0) 1667.953 (87) 7685.107 (35) 0.000 (100) Vancouver DEM (from LiDAR) 5333.383 (1) 6203.476 (1) 5310.463 (4) 3551.866 (25) 1259.179 (15) 31616.102 (137) 15145.585 (27) 4117.399 (648) Vancouver DSM (from LiDAR First Return) 18006.457 (240) 13432.635 (115) 74340.649 (1360) 27364.306 (866) 20237.453 (1748) 48285.022 (262) 11877.415 (0) 7546.759 (1270) Boyko Method 4290.267 (19) 6144.151 (2) 5332.889 (5) 2338.116 (17) 1529.94 (40) 13158.304 (1) 11874.022 (0) 1807.956 (228) Canadian DSM 0.000 (100) 5741.711 (8) 4129.389 (19) 3530.879 (25) 303.811 (72) 27513.217 (106) 11053.025 (7) 3406.257 (518) Canadian DEM 4392.613 (17) 5672.629 (9) 4777.954 (6) 14563.171 (414) 2078.571 (90) 29414.574 (121) 12071.677 (1) 2354.762 (328) SRTM 1arcs DEM 0.000 (100) 7240.235 (16) 3794.445 (25) 6249.155 (121) 434.13 (60) 34104.863 (156) 13125.206 (10) 3667.918 (566) SRTM 3arcs DEM 0.000 (100) 5410.594 (13) 3925.444 (23) 4237.473 (50) 0.000 (100) 31907.083 (139) 11792.469 (1) 2753.898 (400) CGIAR SRTM DEM 30.783 (99) 5019.788 (20) 3073.105 (40) 1893.869 (33) 0.000 (100) 29320.867 (120) 11765.716 (1) 3102.967 (463) ASTER DEM 6189.484 (17) 6529.693 (5) 3510.435 (31) 5605.139 (98) 5486.998 (401) 57170.513 (329) 14546.912 (22) 7688.983 (1296)  Total energy as an applied performance measure was calculated across all locations using all the available elevation datasets. Table 9 shows the calculated total energy along with the absolute percent error for each dataset at each location. Similar to other measures, on non-elevated structures, Vancouver DEM and straight line estimate produced the least erroneous total energy estimate. The worst performing across all locations was Vancouver DSM due to the noise in the elevation profile which leads to unrealistic grades that provoke major spikes in power.  54   Table 10 shows the average power estimates along with their percent absolute error compared to ground truth average power estimate. As seen in Table 10, the average power calculated by Vancouver DSM is high which corresponds with the unrealistic grade estimates. In addition, elevation sources that had the wrong dominant grade show 100% error since their power estimates are zero which emphasizes the propagation of such fundamental errors in the road profile estimates.  Table 10 Average power calculated at each location Presented as Power (W) (Percent Absolute Error) Source 400 Smithe Street 2500 Trafalgar Street 2500 W 10th Street 1200 1500 Island Park Walk 1000 Beach St Burrard Bridge Main Street Over Waterfront Street Cambie Street North Bike Ramp Measured Ground Truth 282.44 (0) 411.06 (0) 174.379 (0) 145.853 (0) 48.775 (0) 52.277 (0) 186.777 (0) 16.946 (0) Straight Line 282.216 (0) 416.138 (1) 169.746 (3) 151.674 (4) 48.725 (0) 6.606 (87) 120.551 (35) 0.000 (100) Vancouver DEM (from LiDAR) 281.098 (0) 418.696 (2) 178.447 (2) 176.949 (21) 56.697 (16) 126.464 (142) 238.989 (28) 126.689 (648) Vancouver DSM (from LiDAR First Return) 924.339 (227) 577.21 (40) 2472.83 (1318) 1535.821 (953) 948.743 (1845) 192.675 (269) 186.46 (0) 232.208 (1270) Boyko Method 245.158 (13) 413.871 (1) 180.648 (4) 106.961 (27) 68.837 (41) 51.354 (2) 187.674 (0) 53.563 (216) Canadian DSM 0.000 (100) 382.933 (7) 135.815 (22) 184.134 (26) 14.297 (71) 110.053 (111) 176.848 (5) 93.705 (453) Canadian DEM 237.71 (16) 391.502 (5) 164.274 (6) 627.386 (330) 87.054 (78) 117.658 (125) 192.072 (3) 67.673 (299) SRTM 1arcs DEM 0.000 (100) 472.377 (15) 120.514 (31) 320.467 (120) 20.43 (58) 136.419 (161) 210.003 (12) 103.093 (508) SRTM 3arcs DEM 0.000 (100) 357.583 (13) 133.519 (23) 220.753 (51) 0.000 (100) 127.628 (144) 188.68 (1) 76.318 (350) CGIAR SRTM DEM 1.759 (99) 331.658 (19) 100.866 (42) 108.221 (26) 0.000 (100) 117.283 (124) 188.251 (1) 85.773 (406) ASTER DEM 311.224 (10) 457.768 (11) 114.189 (35) 279.883 (92) 251.324 (415) 228.682 (337) 229.582 (23) 221.128 (1205)  55  On the other hand, Boyko method shows least error estimate of total energy on elevated structures if not right after Vancouver DSM (Table 9). This can be expected with the high coincidence ratios in the grade distribution between the two estimates and that of the ground truth (Table 5).  The straight line estimate has a close to zero percent absolute error on all non-elevated locations for both average power and total energy (Table 9 & Table 10). Its worst total energy estimates are on elevated structures but its energy estimate on the Cambie ramp has the least error compared to all other data sources even though the error is still substantial (100%). Thus in locations that have a dominant constant grade uphill or downhill, or in other words that do not have substantially high cumulative elevation gains and losses compared to the absolute elevation change, the straight line profile assumption can minimize the errors in energy and power estimation. This further emphasizes elevation models that can produce accurate absolute elevation change with the correct sign (positive or negative). Sources that produce accurate elevation changes over the length of a road can help produce accurate power estimates in locations with a mostly dominant grade.   3.3 Characterization of Elevated Structures  Elevated structures in the City of Vancouver were characterized based on the modality of their grade distributions, calculated using the Boyko method which is considered the closest data source to ground truth since there are no ground truth measurements at these locations. Table 11 summarizes the relevant characteristics of the different classes that the elevated structures were 56  characterized into. Thirteen locations were identified as having a unimodal grade distribution (class 1), 9 locations had a bimodal grade distribution (class 2) and 11 other locations with a grade distribution of three or more modes were placed in class 3. The slope distribution of all the locations is in the appendix.  Table 11 Summary of the characteristics of the classified elevated structures in the City of Vancouver Presented as mean (standard deviation)] Class (Number of Modes) 1 2 3 Number of locations 13 9 11 Number crossing water 0 1 4 Length  63.00 (16.54) 517.33 (356.86) 482.15 (565.34) Absolute Elevation Change  1.07 (0.91) 5.85 (5.39) 3.60 (2.70) Cumulative Elevation Gain 0.91 (1.00) 2.98 (5.74) 6.33 (7.28) Cumulative Elevation Loss 0.22 (0.38) 6.01 (5.36) 5.87 (6.98) Percent Positive Grade (%) 68.74 (41.12) 31.46 (30.22) 52.50 (24.67) Absolute Average Grade (%) 1.69 (1.16) 1.02 (0.56) 1.55 (1.29) Mean Grade (%) 1.02 (1.82) -0.67 (0.99) 0.20 (2.05) Median Grade (%) 1.06 (1.78) -0.01 (1.25) 0.28 (2.09) Grade Interquartile Range (%) 0.54 (0.42) 2.25 (1.65) 5.24 (3.20) Grade Standard Deviation (%) 0.42 (0.27) 1.59 (0.61) 3.08 (1.38)  The unimodal locations can be characterized as locations that do not cross a water body (100%) with a length of around 63m and an elevation difference of around 1m and a tight grade distribution with a standard deviation of 0.5%. The locations within class 1 were tightly distributed around the average values of the three performance measures according to the standard deviation. Thus these performance measures can be used in reverse to characterize a location as being unimodal.  The grade distributions of unimodal locations can be approximated as either a single value which corresponds to a straight line profile or a normal distribution centered on the mean grade. 57  Approximating the grade distribution as a normal distribution or a single value (straight line profile) can help reduce the errors induced by the additional elevation losses and gains in a ground profile below a bridge which may contain unrealistic road grades.  Table 12 Estimated Parameters from the normal fit at unimodal locations Location Elevation Difference (m) Cumulative Elevation loss (m) Cumulative Elevation Gain (m) Median Grade (%) Mean Grade (%) Normal fit Mean Grade (%) Normal fit Grade Standard Deviation (%) AIC Log Likelihood 1 0.44 0.04 0.48 0.60 0.86 0.86 1.05 153.68 -74.84 2 0.06 0.25 0.31 0.33 0.07 0.07 0.68 191.25 -93.62 3 1.45 0.00 1.45 1.87 1.88 1.88 0.44 95.53 -45.77 4 -0.80 0.80 0.00 -1.38 -1.56 -1.56 0.41 57.19 -26.60 5 0.29 0.08 0.37 0.72 0.55 0.55 0.84 132.94 -64.47 6 0.19 0.02 0.21 0.28 0.29 0.29 0.33 44.70 -20.35 7 1.26 0.00 1.26 2.87 2.92 2.92 0.28 16.60 -6.30 8 2.15 0.00 2.15 3.43 3.41 3.41 0.26 12.13 -4.06 9 -0.45 0.45 0.00 -0.79 -0.96 -0.96 0.30 23.98 -9.99 10 0.97 0.00 0.97 1.48 1.38 1.38 0.26 11.40 -3.70 11 -1.22 1.22 0.00 -1.84 -1.80 -1.80 0.20 -19.73 11.87 12 3.38 0.00 3.38 3.57 3.56 3.56 0.24 5.71 -0.86 13 1.32 0.00 1.32 2.70 2.69 2.69 0.18 -23.12 13.56  Table 12 shows the normal distribution fit estimates, Akaike information criterion (AIC) (Akaike, 1974) and log-likelihood calculated using maximum likelihood estimation. Yet, the normal distribution is representative given that grades are mainly centered on the mean grade. The mean of the distribution is the same as the mean of the grade at each location and the mean standard deviation is 0.42%.  58  Bimodal locations on the other hand, can be observed as two groups: locations with same sign grades and locations with opposite sign grades. The locations with the same sign grade can be locations similar to the Georgia Viaduct and those of opposite sign grades can be bridges with two main straight line segments in their profile connected with a short vertical curve like Burrard Street Bridge. Within each of these groups there is still high variability in length and all performance measures as seen in the variability with the class itself. It is then difficult to specify a certain performance measure and a certain value to be able to classify a location as bimodal.  Table 13 Characteristics of the bimodal distributions of the elevated structures in class 2 (grades are in %) Location Minimum Maximum Median Mean Standard Deviation Skewness Kurtosis First Mode Second Mode Mode Spacing 1 -3.92 1.58 -0.54 -0.68 0.88 -0.97 4.74 -3.17 -0.52 2.66 2 -4.85 1.13 -0.44 -1.39 2.12 -0.27 1.31 -3.91 0.63 4.54 3 -2.31 0.11 -0.24 -0.64 0.81 -1.21 2.87 -2.03 -0.20 1.83 4 -5.59 2.01 -1.21 -1.94 1.70 -0.48 2.26 -4.39 -0.99 3.40 5 -5.71 1.77 -1.06 -1.59 1.42 -1.50 4.23 -4.79 -0.94 3.86 6 -5.04 2.93 0.45 -0.15 2.10 -0.78 2.63 -3.62 0.78 4.40 7 -3.72 0.05 -0.76 -1.24 1.22 -1.06 2.62 -3.38 -0.52 2.86 8 -3.82 4.48 0.90 0.59 1.44 -0.70 3.93 -1.81 1.09 2.90 9 -3.39 3.92 2.80 0.99 2.65 -0.68 1.60 -2.98 2.95 5.93  The characteristics of the bimodal distributions of the 9 locations are summarized in the table above (Table 13). The distributions are not centered on the mean and the mode with the greater value always has a much larger density and is thus closer to the mean. There is no clear pattern in the distributions of the locations. Thus there is no one clear method of identifying the distribution of these locations given a certain measure.  59  Finally, the profiles of locations with modes greater than or equal to 3 can be described as one of three types: an S-shaped profile, a profile made of 3 linear segments, and a location with a wide vertical curvature. There is also high variability in length and other measures that they cannot be clearly identified (Table 11).  3.4 Inferring Grades on Elevated Structures  Grade distributions of unimodal locations can be approximated as a constant value corresponding to a straight line profile or as normal distributions around the mean with a standard deviation of 0.42%. Assuming that LiDAR data are not available, the mean grade will be estimated from the Canadian DSM which is the best available after LiDAR since it performed the best across the majority of the performance measures. Particularly, out of all the performance measures studied in Chapter 3, the Canadian DSM performed best when approximating the absolute elevation change and mean grade on elevated structures.  With the mean grade from the Canadian DSM, the total energy was calculated (with the same assumptions as section 3.2 but with an interval of 1m) to provide a measure to test the performance of the approximations of the unimodal locations.   60  Table 14 Total energy calculated by approximations Presented as Total Energy (J) (Percent Absolute Error) Location Boyko Canadian DSM Constant Grade Normal Distribution 1 1136.78 (0.00) 1432.56 (26.02) 1432.56 (26.02) 1455.55 (28.04) 2 1271.01 (0.00) 1513.44 (19.07) 1257.49 (1.06) 1250.08 (1.65) 3 2526.61 (0.00) 1333.41 (47.23) 1156.38 (54.23) 1165.59 (53.87) 4 9.56 (0.00) 885.16 (9154.25) 885.16 (9154.25) 894.17 (9248.42) 5 1016.67 (0.00) 1946.92 (91.5) 1946.92 (91.5) 1949.97 (91.8) 6 1037.45 (0.00) 846.01 (18.45) 846.01 (18.45) 859.64 (17.14) 7 1872.21 (0.00) 2255.18 (20.46) 2255.18 (20.46) 2363.25 (26.23) 8 3060.44 (0.00) 1255.42 (58.98) 1255.42 (58.98) 1255.66 (58.97) 9 187.12 (0.00) 382.9 (104.63) 352.73 (88.5) 350.06 (87.08) 10 1936.61 (0.00) 1396.05 (27.91) 1396.05 (27.91) 1398.61 (27.78) 11 4.12 (0.00) 1510.24 (36576.94) 1499.87 (36324.98) 1516.51 (36729.11) 12 4756.19 (0.00) 6257.02 (31.56) 6257.02 (31.56) 6258.9 (31.59) 13 2016.91 (0.00) 2387.75 (18.39) 2387.75 (18.39) 2380.92 (18.05)  The table of the percent error in cumulative power from the Boyko method (Table 14) shows that the constant grade approximation slightly reduce the error in the cumulative power estimate from the Canadian DSM except for one location where both the constant grade and the normal fit increased the error. The normal distribution approximation increased the error in multiple locations where the constant grade approximation maintained the same error as the CDSM profiles. This, further emphasizes what has been previously discussed in section 3.2 which is the 61  dependence of the accuracy of the energy estimate, as calculated here, on the accuracy of the absolute elevation change.   Using the constant grade approximation reduced or maintained the error in the CDSM cumulative power estimate. To further reduce the error in the estimated cumulative power, improvement in the estimate of the absolute elevation change is required.  Both approximations then show the importance of understanding the limitations of each elevation dataset and approximating the correct measures from the appropriate elevation dataset and understanding that there are errors in all the elevation datasets that have to be accounted for especially when modeling a particular behavior or appending elevation data to bicycle GPS data used in later studies.  62  Chapter 4: Recommendations  Initially, coarse raster file DEMs lack detailed information in locations of length around 100m (see Figure 11) since they would only provide up to 3 unique elevation values due to their grid spacing of 30 or 90 m (1 or 3 arc seconds). Thus, it is not recommended to apply simple extraction from coarse elevation datasets since that would result in unrealistic grades and high frequency of zero grades depending on the interval of extraction. LiDAR data collection is the only method to provide data that allow for denser DEM raster files of 0.5m grid spacing. High resolution raster files do not require post processing since the resolution is high. Additionally, the grades of noisy elevation data as seen in Vancouver DSM can affect estimates of all measures and offset the calculations due to unrealistic grades which further emphasizes the need for smoothing. It is recommended to avoid the use of the noisy raster files if for example it’s based on LiDAR data and can be avoided.  On non-elevated roads, even ones passing under a bridge or a ramp, the Vancouver DEM, a LiDAR based raster file produced from last returns, performed best in all performance measures and in depicting accurate elevation and grade estimates along a road. When LiDAR cloud point data are not available, the Canadian DSM was most representative of the elevation profile and grade distribution. Lower errors in the performance measures and grade distribution, compared to other SRTM or ASTER based DEMs, are expected since the Canadian DSM is a locally calibrated dataset sourced from SRTM. It is then recommended to used raster files based on LiDAR last returns for GPS data and routing studies on non-elevated structures or the most 63  locally calibrated highest resolution (<=30m) raster file based on SRTM in case LiDAR data are not available.  On elevated structures, applying the Boyko algorithm on raw LiDAR cloud point data provided the best elevation profile estimates with the least error and the grade distribution with the highest coincidence ratio (see Chapter 3). Without LiDAR data on elevated structures, no elevation dataset produced the profiles of the elevated structures since they followed the bare earth elevation. Estimates of absolute elevation change and mean grade had the lowest errors when estimated from non-LiDAR datasets compared to other measures due to the better accuracies in estimating the elevations at the start and end of a structure where the structure meets bare earth. It recommended to use LiDAR cloud point data on elevated structures when it is available but without the LiDAR data estimates, only the absolute elevation change and the mean grade should be extracted from the most locally calibrated raster based on SRTM.  Elevated structures can be characterized based on the modes in their grade distribution. Unimodal locations can be identified as locations that do not cross water bodies and have a length of around 60m and an elevation change of around 1m while bimodal and multimodal locations had no distinct features that helped identify them. Approximating profiles of unimodal elevated structures as constant grade straight line profiles, only propagated the errors of the elevation dataset, which produced the mean grade for the constant grade, when approximating the power estimates. Yet, it improved other aspects of the grade distribution like removal of unrealistically high grades from bare earth. When estimating power, a straight line estimate of 64  the elevation profile is a marginal improvement at unimodal elevated structures. In most cases it is recommended to seek further information (like LiDAR) to better describe elevated structures.  It should be noted that the Open Street Maps shape file of the network help identify whether a structure is elevated or non-elevated based on the attributes of the roads in the file. This will then help guide the decision of elevation data or measures to be calculated per road based on whether it is elevated or not.  Figure 21 shows the decision tree that should be followed to obtain the elevation profile of a road. Road coordinatesRoad Within Extent of LiDAR Data?NORoad Elevated?NOYESUse Boyko MethodYESUse LiDAR Last Return DEMRoad Elevated?NOYESUse Local SRTM based DEM/DSMObtain all Elevation/Grade MeasuresUse Local SRTM based DEM/DSMObtain all Elevation/Grade MeasuresObtain ONLY Average Grade and Total Elevation Change Figure 21 Decision tree to identify the elevation profile of a road 65  Chapter 5: Conclusion  The state of the art and practice is to use coarse elevation datasets mainly products of SRTM when elevation data are required. In applications like Google Maps or Google Earth or even sports tracking applications like RideWithGPS, SRTM products are utilized to add elevation information. The use of SRTM datasets especially in literature should be cautiously approached with clear understanding of the limitations the datasets. The datasets entail errors that need to be accounted for when estimating physical models or routing with the main gap in the datasets being the complete lack of information on elevated structures. The study at hand provided comparisons of different data sources on different locations (elevated and non-elevated) to seek better understanding of how to use the available datasets.  Products of LiDAR cloud point data were the best elevation sources to use whether it were on elevated or non-elevated structures. Whereas in the absence of LiDAR data, the coarse DEMs based on SRTM and ASTER provide the best estimates of elevation and grade distribution on non-elevated structures when they have been calibrated with local conditions just like the case of the Canadian DSM.  In locations without LiDAR data, detailed elevation profiles of elevated structures are difficult to obtain except for a couple of aggregate measures (absolute elevation change and mean grade). It is important to understand that no bare earth DEM was capable of estimating profiles of elevated structures and that absolute elevation change and mean grade are the most accurate measures obtained from the coarse elevation datasets compared to other performance measures.  66   When using DEMs whether LiDAR based or SRTM based, consideration should be given to the errors embedded in them and special consideration should be given to their limitations, mainly considering the almost lack of information about elevated structures, when doing routing or appending elevation to GPS data. Errors from these dataset will propagate to other estimates that depend on them. 67  Chapter 6: Limitations and Future Work  The study provided great insight into the available elevation datasets and the effect of their accuracy on different cycling performance measures, but further work is needed to provide more detailed and more exhaustive recommendations. The recommendations for elevated structures in locations without LiDAR data are still limited and thus can be expanded. The locations with ground truth data were not fully exhaustive of all possible bike paths for example paths running under the length of a bridge were not considered. As an attempt to provide insight about errors in elevation datasets used in active transportation studies and how to mitigate them, further work can be done to better reduce the errors in these datasets.  The following is proposed for further research: 1. Studying the effect of the error in the elevation datasets on walking measures and models. 2. Combining other non-photogrammetric and aerial data sources to the ones identified in the study as a possible method of reducing the errors in the elevation datasets. 3. Developing a model to estimate the elevation profile with detail of elevated structures based on SRTM based elevation datasets. 4. Exploring novel measures that can be estimated from SRTM data sources that can help better describe elevated structures without additional information. 5. Obtaining a large database of elevation profiles of elevated structures to help produce look up tables for reference that may help mitigate errors in elevation data sets. 6. In this study, interpolation was used to smooth elevation profiles from coarse elevation dataset. Exploring other smoothing techniques is proposed for future work. 68  7. Understanding how other data sources, like crowd sourced GPS data, can be better alternatives to elevation datasets for certain active transportation measures. 8. Ground truth data were extracted at 8 locations at an interval of 5 m on locations less than 300m and at 10m at locations longer than 300m. It is proposed to study the effect of the extraction interval on the estimated measures. 9. Studying the effect of the error in the elevation datasets on electric bicycles as opposed to normal bicycles. 69  References  Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.org/10.1109/TAC.1974.1100705 Bae, H. S., & Gerdes, J. C. (2004). Command Modification Using Input Shaping for Automated Highway Systems with Heavy Trucks. California Partners for Advanced Transit and Highways (PATH). Retrieved from http://escholarship.org/uc/item/1tv3z496 Becker, J. J., Sandwell, D. T., Smith, W. H. F., Braud, J., Binder, B., Depner, J., … Weatherall, P. (2009). Global Bathymetry and Elevation Data at 30 Arc Seconds Resolution: SRTM30_PLUS. Marine Geodesy, 32(4), 355–371. https://doi.org/10.1080/01490410903297766 Bernardi, S., & Rupi, F. (2015). An Analysis of Bicycle Travel Speed and Disturbances on Off-street and On-street Facilities. Transportation Research Procedia, 5, 82–94. https://doi.org/10.1016/j.trpro.2015.01.004 Bigazzi, A. Y., & Figliozzi, M. A. (2015). Dynamic Ventilation and Power Output of Urban Bicyclists. Transportation Research Record: Journal of the Transportation Research Board, 2520, 52–60. https://doi.org/10.3141/2520-07 Boyko, A., & Funkhouser, T. (2011). Extracting roads from dense point clouds in large scale urban environment. ISPRS Journal of Photogrammetry and Remote Sensing, 66(6), S2–S12. https://doi.org/10.1016/j.isprsjprs.2011.09.009 Broach, J., Dill, J., & Gliebe, J. (2012). Where do cyclists ride? A route choice model developed with revealed preference GPS data. Transportation Research Part A: Policy and Practice, 46(10), 1730–1740. https://doi.org/10.1016/j.tra.2012.07.005 70  Cai, H., & Rasdorf, W. (2008). Modeling Road Centerlines and Predicting Lengths in 3-D Using LIDAR Point Cloud and Planimetric Road Centerline Data. Computer-Aided Civil and Infrastructure Engineering, 23(3), 157–173. https://doi.org/10.1111/j.1467-8667.2008.00518.x Choi, Y.-W., Jang, Y. W., Lee, H. J., & Cho, G.-S. (2007). Heuristic Road Extraction (pp. 338–342). IEEE. https://doi.org/10.1109/ISITC.2007.63 Clode, S., Kootsookos, P. J., & Rottensteiner, F. (2004). The automatic extraction of roads from LIDAR data. In The International Society for Photogrammetry and Remote Sensing’s Twentieth Annual Congress (Vol. 35, pp. 231–236). ISPRS. Environmental Protection Agency. (2002). EPA’s Onboard Analysis Shootout: Overview and Results (No. EPA/420/R-02/026;). Oct 2002. Farr, T. G., Rosen, P. A., Caro, E., Crippen, R., Duren, R., Hensley, S., … Alsdorf, D. (2007). The Shuttle Radar Topography Mission. Reviews of Geophysics, 45(2). https://doi.org/10.1029/2005RG000183 GPS On Bench Marks for GEOID09. (n.d.). Retrieved from https://www.ngs.noaa.gov/GEOID/GPSonBM09/ Grejner-Brzezinska, D. A. (2002). Direct georeferencing at the Ohio State University: A historical perspective. Photogrammetric Engineering and Remote Sensing, 68, 557–560. Hall, P., & York, M. (2001). ON THE CALIBRATION OF SILVERMAN’S TEST FOR MULTIMODALITY. Statistica Sinica, 11(2), 515–536. Hirano, A., Welch, R., & Lang, H. (2003). Mapping from ASTER stereo image data: DEM validation and accuracy assessment. ISPRS Journal of Photogrammetry and Remote Sensing, 57(5–6), 356–370. https://doi.org/10.1016/S0924-2716(02)00164-8 71  Hood, J., Sall, E., & Charlton, B. (2011). A GPS-based bicycle route choice model for San Francisco, California. Transportation Letters, 3(1), 63–75. https://doi.org/10.3328/TL.2011.03.01.63-75 Hu, Y. (2003). Automated extraction of digital terrain models, roads and buildings using airborne lidar data. Hughes, W. J. (2014). Global positioning system (GPS) standard positioning service (SPS) performance analysis report. Retrieved from http://www.nstb.tc.faa.gov/REPORTS/PAN77_0412.pdf Jarihani, A. A., Callow, J. N., McVicar, T. R., Van Niel, T. G., & Larsen, J. R. (2015). Satellite-derived Digital Elevation Model (DEM) selection, preparation and correction for hydrodynamic modelling in large, low-gradient and data-sparse catchments. Journal of Hydrology, 524, 489–506. https://doi.org/10.1016/j.jhydrol.2015.02.049 Jarvis, A., Reuter, H., Nelson, A., & Guevara, E. (2008). Hole-filled seamless SRTM data v4. International Centre for Tropical Agriculture (CIAT). Kashani, A., Olsen, M., Parrish, C., & Wilson, N. (2015). A Review of LIDAR Radiometric Processing: From Ad Hoc Intensity Correction to Rigorous Radiometric Calibration. Sensors, 15(12), 28099–28128. https://doi.org/10.3390/s151128099 Keqi Zhang, Shu-Ching Chen, Whitman, D., Mei-Ling Shyu, Jianhua Yan, & Chengcui Zhang. (2003). A progressive morphological filter for removing nonground measurements from airborne LIDAR data. IEEE Transactions on Geoscience and Remote Sensing, 41(4), 872–882. https://doi.org/10.1109/TGRS.2003.810682 72  Kim, I., Kim, H., Bang, J., & Huh, K. (2013). Development of estimation algorithms for vehicle’s mass and road grade. International Journal of Automotive Technology, 14(6), 889–895. https://doi.org/10.1007/s12239-013-0097-9 Li, J., Lee, H. J., & Cho, G. S. (2008). Parallel Algorithm for Road Points Extraction from Massive LiDAR Data (pp. 308–315). IEEE. https://doi.org/10.1109/ISPA.2008.60 Li, Z., Wang, W., Liu, P., & Ragland, D. R. (2012). Physical environments influencing bicyclists’ perception of comfort on separated and on-street bicycle facilities. Transportation Research Part D: Transport and Environment, 17(3), 256–261. https://doi.org/10.1016/j.trd.2011.12.001 Ling Xu, Bedrick, E. J., Hanson, T., & Restrepo, C. (2014). A Comparison of Statistical Tools for Identifying Modality in Body Mass Distributions. Journal of Data Science, 12, 175–196. McIntyre, M. L., Ghotikar, T. J., Vahidi, A., Xubin Song, & Dawson, D. M. (2009). A Two-Stage Lyapunov-Based Estimator for Estimation of Vehicle Mass and Road Grade. IEEE Transactions on Vehicular Technology, 58(7), 3177–3185. https://doi.org/10.1109/TVT.2009.2014385 Menghini, G., Carrasco, N., Schüssler, N., & Axhausen, K. W. (2010). Route choice of cyclists in Zurich. Transportation Research Part A: Policy and Practice, 44(9), 754–765. https://doi.org/10.1016/j.tra.2010.07.008 Milakis, D., & Athanasopoulos, K. (2014). What about people in cycle network planning? applying participative multicriteria GIS analysis in the case of the Athens metropolitan cycle network. Journal of Transport Geography, 35, 120–129. https://doi.org/10.1016/j.jtrangeo.2014.01.009 73  Ministry of Natural Resources, Canada. (2014a). Canadian Digital Elevation Model. DEM. Retrieved from https://open.canada.ca/data/en/dataset/7f245e4d-76c2-4caa-951a-45d1d2051333 Ministry of Natural Resources, Canada. (2014b). Canadian Digital Surface Model. DEM. Retrieved from https://open.canada.ca/data/en/dataset/768570f8-5761-498a-bd6a-315eb6cc023d Navteq Advanced Driver Assistance Systems. (n.d.). Retrieved from http://www.navteq.com/industries_automotive.htm Nelson, A., Reuter, H. I., & Gessler, P. (2009). Chapter 3 DEM Production Methods and Sources. In Developments in Soil Science (Vol. 33, pp. 65–85). Elsevier. https://doi.org/10.1016/S0166-2481(08)00003-2 Olds, T. S., Norton, K. I., Lowe, E. L., Olive, S., Reay, F., & Ly, S. (1995). Modeling road-cycling performance. Journal of Applied Physiology, 78(4), 1596–1611. https://doi.org/10.1152/jappl.1995.78.4.1596 OpenStreetMap contributors. (2017). Planet dump. Retrieved from https://planet.osm.org Parkin, J., & Rotheram, J. (2010). Design speeds and acceleration characteristics of bicycle traffic for use in planning, design and appraisal. Transport Policy, 17(5), 335–341. https://doi.org/10.1016/j.tranpol.2010.03.001 Payne, K. C., & Dror, M. (2017). The Development of a Smart Map for Minimum “Exertion” Routing Applications. https://doi.org/10.24251/HICSS.2017.142 Press, W. H. (Ed.). (1992). Numerical recipes in C: the art of scientific computing (2nd ed). Cambridge ; New York: Cambridge University Press. 74  Reutebuch, S. E., Andersen, H.-E., & McGaughey, R. J. (2005). Light detection and ranging (LIDAR): an emerging tool for multiple resource inventory. Journal of Forestry, 103(6), 286–292. Robinson, N., Regetz, J., & Guralnick, R. P. (2014). EarthEnv-DEM90: A nearly-global, void-free, multi-scale smoothed, 90m digital elevation model from fused ASTER and SRTM data. ISPRS Journal of Photogrammetry and Remote Sensing, 87, 57–67. https://doi.org/10.1016/j.isprsjprs.2013.11.002 Rodríguez, E., Morris, C. S., & Belz, J. E. (2006). A Global Assessment of the SRTM Performance. Photogrammetric Engineering & Remote Sensing, 72(3), 249–260. https://doi.org/10.14358/PERS.72.3.249 Ryan, J., Bevly, D., & Lu, J. (2009). Robust sideslip estimation using GPS road grade sensing to replace a pitch rate sensor (pp. 2026–2031). IEEE. https://doi.org/10.1109/ICSMC.2009.5346320 Sahlholm, P., & Henrik Johansson, K. (2010). Road grade estimation for look-ahead vehicle control using multiple measurement runs. Control Engineering Practice, 18(11), 1328–1341. https://doi.org/10.1016/j.conengprac.2009.09.007 Sahlholm, P., & Johansson, K. H. (2010). Segmented road grade estimation for fuel efficient heavy duty vehicles (pp. 1045–1050). IEEE. https://doi.org/10.1109/CDC.2010.5717298 Savitzky, A., & Golay, M. J. E. (1964). Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36(8), 1627–1639. https://doi.org/10.1021/ac60214a047 75  Scholz, F. W. (2006). Maximum Likelihood Estimation. In S. Kotz, C. B. Read, N. Balakrishnan, B. Vidakovic, & N. L. Johnson (Eds.), Encyclopedia of Statistical Sciences. Hoboken, NJ, USA: John Wiley & Sons, Inc. https://doi.org/10.1002/0471667196.ess1571.pub2 Silverman, B. W. (1981). Using Kernel Density Estimates to Investigate Multimodality. Journal of the Royal Statistical Society. Series B (Methodological), 43(1), 97–99. Slater, J. A., Heady, B., Kroenung, G., Curtis, W., Haase, J., Hoegemann, D., … Tracy, K. (2011). Global Assessment of the New ASTER Global Digital Elevation Model. Photogrammetric Engineering & Remote Sensing, 77(4), 335–349. https://doi.org/10.14358/PERS.77.4.335 Souleyrette, R., Hallmark, S., Pattnaik, S., O’Brien, M., & Veneziano, D. (2003). Grade and cross slope estimation from LiDAR-based surface models. Tachikawa, T., Hato, M., Kaku, M., & Iwasaki, A. (2011). Characteristics of ASTER GDEM version 2 (pp. 3657–3660). IEEE. https://doi.org/10.1109/IGARSS.2011.6050017 Tengattini, S., & Bigazzi, A. Y. (2018). Physical characteristics and resistance parameters of typical urban cyclists. Journal of Sports Sciences, 1–9. https://doi.org/10.1080/02640414.2018.1458587 Teschke, K., Chinn, A., & Brauer, M. (2017). Proximity to four bikeway types and neighbourhood-level cycling mode share of male and female commuters. Journal of Transport and Land Use, 10(1). https://doi.org/10.5198/jtlu.2017.943 The City of Vancouver. (2013). LiDAR 2013 - Open Data. Retrieved April 3, 2018, from http://data.vancouver.ca/datacatalogue/LiDAR2013.htm Tyson Altenhoff. (2017). MASCOT - Management of Survey Control Operations and Tasks. Retrieved April 22, 2018, from http://a100.gov.bc.ca/pub/mascotw/ 76  Vincent Winstead, & Ilya V. Kolmanovsky. (2005). Estimation of road grade and vehicle mass via model predictive control (pp. 1588–1593). IEEE. https://doi.org/10.1109/CCA.2005.1507359 Wang, Y., Zou, Y., Henrickson, K., Wang, Y., Tang, J., & Park, B.-J. (2017). Google Earth elevation data extraction and accuracy assessment for transportation applications. PLOS ONE, 12(4), e0175756. https://doi.org/10.1371/journal.pone.0175756 Wilson, J. P. (2012). Digital terrain modeling. Geomorphology, 137(1), 107–121. https://doi.org/10.1016/j.geomorph.2011.03.012 Winters, M., Davidson, G., Kao, D., & Teschke, K. (2011). Motivators and deterrents of bicycling: comparing influences on decisions to ride. Transportation, 38(1), 153–168. https://doi.org/10.1007/s11116-010-9284-y Winters, M., Teschke, K., Brauer, M., & Fuller, D. (2016). Bike Score®: Associations between urban bikeability and cycling behavior in 24 cities. International Journal of Behavioral Nutrition and Physical Activity, 13(1). https://doi.org/10.1186/s12966-016-0339-0 Wood, E., Burton, E., Duran, A., & Gonder, J. (2014). Appending High-Resolution Elevation Data to GPS Speed Traces for Vehicle Energy Modeling and Simulation. National Renewable Energy Laboratory (NREL), Golden, CO. Zhang, K., & Frey, H. C. (2006). Road Grade Estimation for On-Road Vehicle Emissions Modeling Using Light Detection and Ranging Data. Journal of the Air & Waste Management Association, 56(6), 777–788. https://doi.org/10.1080/10473289.2006.10464500 77  Ziemke, D., Metzler, S., & Nagel, K. (2017). Modeling bicycle traffic in an agent-based transport simulation. Procedia Computer Science, 109, 923–928. https://doi.org/10.1016/j.procs.2017.05.424 78  Appendices  The appendix contains graphs of the elevation and grade profiles of the roads at the ground truth locations in addition to their performance measure estimates from each data source. The appendix also contains the slope distribution of the elevated roads identified in the City of Vancouver.  79  Appendix A  Elevation Profiles of All Ground Truth Locations  80  81  82  83  84  85  86    87  Appendix B  Grade Profiles of All Ground Truth Locations   88  89  90  91  92  93  94    95  Appendix C  Performance Measure Estimates per location C.1 400 Smithe Street  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 0.000 4.221 4.221 0.055 0.000 100.000 #N/A -0.055 0.005 0.005 -0.064 -0.058 -0.055 -0.055 -0.053 -0.046 Straight Line Estimate 0.000 4.221 4.221 0.055 0.000 100.000 #N/A -0.055 0.000 0.000 -0.055 -0.055 -0.055 -0.055 -0.055 -0.055 Vancouver DEM (from LiDAR)  0.000 4.258 4.258 0.056 0.000 100.000 #N/A -0.056 0.016 0.017 -0.093 -0.065 -0.057 -0.056 -0.048 -0.032 Vancouver DSM (from LiDAR First Return)  12.750 16.996 4.247 0.393 20.000 80.000 0.850 -0.278 0.926 0.034 -2.492 -0.061 -0.052 -0.053 -0.027 2.382 Boyko Method 0.240 3.250 3.010 0.048 13.333 86.667 0.026 -0.051 0.033 0.027 -0.074 -0.062 -0.051 -0.041 -0.035 0.034 Canadian DSM  4.766 0.000 4.766 0.062 100.000 0.000 0.062 #N/A 0.018 0.019 0.025 0.054 0.068 0.062 0.072 0.091 Canadian DEM  0.000 3.314 3.314 0.044 0.000 100.000 #N/A -0.044 0.020 0.025 -0.082 -0.056 -0.039 -0.044 -0.030 -0.013 SRTM 1arcs DEM  13.035 0.000 13.035 0.174 100.000 0.000 0.174 #N/A 0.092 0.170 0.025 0.078 0.204 0.174 0.248 0.284 SRTM 3arcs DEM  6.228 0.000 6.228 0.082 100.000 0.000 0.082 #N/A 0.038 0.033 0.015 0.073 0.099 0.082 0.105 0.112 CGIAR SRTM DEM  3.054 0.000 3.054 0.040 100.000 0.000 0.040 #N/A 0.016 0.013 0.011 0.038 0.047 0.040 0.050 0.053 ASTER DEM  0.328 5.317 4.988 0.074 26.667 73.333 0.016 -0.095 0.063 0.105 -0.152 -0.126 -0.053 -0.065 -0.021 0.037 96  C.2 1200 1500 Island Park Walk  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 0.123 1.880 1.757 0.027 33.333 66.667 0.005 -0.038 0.031 0.047 -0.080 -0.045 -0.009 -0.024 0.002 0.010 Straight Line Estimate 0.000 1.757 1.757 0.024 0.000 100.000 #N/A -0.024 0.000 0.000 -0.024 -0.024 -0.024 -0.024 -0.024 -0.024 Vancouver DEM (from LiDAR)  1.310 2.639 1.329 0.054 33.333 66.667 0.052 -0.054 0.072 0.067 -0.081 -0.062 -0.044 -0.019 0.005 0.208 Vancouver DSM (from LiDAR First Return)  24.472 25.796 1.324 0.671 46.667 53.333 0.699 -0.647 1.685 0.074 -3.904 -0.068 -0.002 -0.019 0.006 4.839 Boyko Method 0.320 1.450 1.130 0.025 60.000 40.000 0.008 -0.051 0.035 0.047 -0.078 -0.043 0.000 -0.016 0.004 0.030 Canadian DSM  0.710 2.622 1.913 0.045 26.667 73.333 0.035 -0.048 0.044 0.048 -0.089 -0.052 -0.042 -0.026 -0.004 0.060 Canadian DEM  8.652 13.093 4.441 0.299 60.000 40.000 0.192 -0.458 0.405 0.461 -0.809 -0.239 0.029 -0.068 0.222 0.416 SRTM 1arcs DEM  0.181 5.047 4.866 0.071 6.667 93.333 0.036 -0.074 0.044 0.049 -0.111 -0.096 -0.086 -0.066 -0.046 0.036 SRTM 3arcs DEM  0.141 3.175 3.035 0.045 20.000 80.000 0.009 -0.054 0.029 0.028 -0.074 -0.059 -0.054 -0.041 -0.031 0.022 CGIAR SRTM DEM  1.008 1.304 0.296 0.031 46.667 53.333 0.030 -0.033 0.035 0.059 -0.059 -0.030 -0.005 -0.004 0.029 0.044 ASTER DEM  1.313 4.475 3.162 0.079 13.333 86.667 0.131 -0.071 0.084 0.086 -0.128 -0.100 -0.050 -0.044 -0.015 0.169  97  C.3 2500 Trafalgar Street  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 0.000 5.280 5.280 0.088 0.000 100.000 #N/A -0.088 0.011 0.008 -0.101 -0.093 -0.091 -0.088 -0.085 -0.059 Straight Line Estimate 0.000 5.280 5.280 0.088 0.000 100.000 #N/A -0.088 0.000 0.000 -0.088 -0.088 -0.088 -0.088 -0.088 -0.088 Vancouver DEM (from LiDAR)  0.000 5.240 5.240 0.087 0.000 100.000 #N/A -0.087 0.014 0.015 -0.104 -0.095 -0.092 -0.087 -0.080 -0.054 Vancouver DSM (from LiDAR First Return)  7.542 12.389 4.847 0.332 16.667 83.333 0.754 -0.248 0.505 0.058 -1.054 -0.116 -0.088 -0.081 -0.058 0.921 Boyko Method 0.000 5.060 5.060 0.086 0.000 100.000 #N/A -0.086 0.019 0.019 -0.116 -0.098 -0.086 -0.086 -0.079 -0.047 Canadian DSM  0.000 4.792 4.792 0.080 0.000 100.000 #N/A -0.080 0.009 0.005 -0.086 -0.086 -0.081 -0.080 -0.081 -0.059 Canadian DEM  0.000 4.725 4.725 0.079 0.000 100.000 #N/A -0.079 0.013 0.014 -0.088 -0.088 -0.084 -0.079 -0.074 -0.043 SRTM 1arcs DEM  0.000 6.247 6.247 0.104 0.000 100.000 #N/A -0.104 0.023 0.035 -0.132 -0.132 -0.098 -0.104 -0.097 -0.063 SRTM 3arcs DEM  0.000 4.470 4.470 0.075 0.000 100.000 #N/A -0.075 0.021 0.001 -0.084 -0.084 -0.083 -0.075 -0.083 -0.021 CGIAR SRTM DEM  0.000 4.091 4.091 0.068 0.000 100.000 #N/A -0.068 0.020 0.001 -0.077 -0.077 -0.077 -0.068 -0.076 -0.018 ASTER DEM  0.000 5.557 5.557 0.093 0.000 100.000 #N/A -0.093 0.060 0.065 -0.219 -0.097 -0.097 -0.093 -0.033 -0.032  98  C.4 2500 W 10th Street  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 0.000 3.380 3.380 0.028 0.000 100.000 #N/A -0.028 0.008 0.007 -0.038 -0.033 -0.030 -0.028 -0.026 -0.002 Straight Line Estimate 0.000 3.380 3.380 0.028 0.000 100.000 #N/A -0.028 0.000 0.000 -0.028 -0.028 -0.028 -0.028 -0.028 -0.028 Vancouver DEM (from LiDAR)  0.000 3.591 3.591 0.030 0.000 100.000 #N/A -0.030 0.010 0.013 -0.051 -0.036 -0.029 -0.030 -0.023 -0.006 Vancouver DSM (from LiDAR First Return)  57.909 71.194 13.284 1.076 37.500 62.500 1.287 -0.949 1.450 1.734 -2.658 -0.762 -0.032 -0.111 0.971 2.654 Boyko Method 0.000 3.600 3.600 0.030 0.000 100.000 #N/A -0.030 0.011 0.014 -0.052 -0.036 -0.032 -0.030 -0.022 -0.012 Canadian DSM  0.000 2.444 2.444 0.020 0.000 100.000 #N/A -0.020 0.006 0.006 -0.031 -0.024 -0.020 -0.020 -0.017 -0.011 Canadian DEM  0.070 3.144 3.074 0.027 29.167 70.833 0.002 -0.037 0.027 0.048 -0.066 -0.047 -0.018 -0.026 0.001 0.002 SRTM 1arcs DEM  0.221 2.340 2.119 0.021 54.167 45.833 0.003 -0.043 0.025 0.049 -0.051 -0.046 0.003 -0.018 0.004 0.004 SRTM 3arcs DEM  0.034 2.280 2.246 0.019 20.833 79.167 0.001 -0.024 0.018 0.033 -0.036 -0.036 -0.020 -0.019 -0.003 0.002 CGIAR SRTM DEM  0.000 1.419 1.419 0.012 0.000 100.000 #N/A -0.012 0.009 0.017 -0.021 -0.021 -0.011 -0.012 -0.003 -0.003 ASTER DEM  3.051 2.403 0.647 0.045 50.000 50.000 0.051 -0.040 0.058 0.086 -0.094 -0.035 -0.003 0.005 0.051 0.100  99  C.5 Burrard Bridge  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 20.253 8.710 11.543 0.029 69.307 30.693 0.029 -0.028 0.027 0.056 -0.034 -0.025 0.029 0.011 0.031 0.038 Straight Line Estimate 11.543 0.000 11.543 0.011 100.000 0.000 0.011 #N/A 0.000 0.000 0.011 0.011 0.011 0.011 0.011 0.011 Vancouver DEM (from LiDAR)  32.914 22.417 10.498 0.055 44.554 55.446 0.073 -0.040 0.107 0.047 -0.354 -0.013 -0.004 0.010 0.034 0.668 Vancouver DSM (from LiDAR First Return)  54.638 42.721 11.917 0.096 69.307 30.693 0.078 -0.138 0.268 0.058 -1.293 -0.027 0.029 0.012 0.032 1.339 Boyko Method 20.320 8.540 11.780 0.029 68.317 31.683 0.029 -0.027 0.027 0.052 -0.041 -0.020 0.027 0.012 0.032 0.051 Canadian DSM  29.385 17.734 11.651 0.047 57.426 42.574 0.051 -0.041 0.070 0.072 -0.083 -0.034 0.000 0.012 0.038 0.228 Canadian DEM  29.535 20.467 9.068 0.050 63.366 36.634 0.046 -0.055 0.074 0.057 -0.159 -0.022 0.000 0.009 0.035 0.310 SRTM 1arcs DEM  37.671 24.037 13.634 0.061 60.396 39.604 0.062 -0.060 0.095 0.070 -0.209 -0.034 0.000 0.013 0.036 0.345 SRTM 3arcs DEM  35.382 22.909 12.473 0.058 61.386 38.614 0.057 -0.059 0.077 0.103 -0.133 -0.036 0.000 0.012 0.067 0.207 CGIAR SRTM DEM  31.760 19.875 11.885 0.051 65.347 34.653 0.048 -0.057 0.098 0.070 -0.550 -0.009 0.000 0.012 0.061 0.553 ASTER DEM  36.724 47.230 10.505 0.083 44.554 55.446 0.082 -0.084 0.121 0.107 -0.444 -0.071 -0.010 -0.010 0.036 0.298  100  C.6 1000 Beach Street  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 0.256 0.147 0.109 0.004 72.222 27.778 0.004 -0.006 0.006 0.005 -0.013 0.000 0.002 0.001 0.005 0.008 Straight Line Estimate 0.109 0.000 0.109 0.001 100.000 0.000 0.001 #N/A 0.000 0.000 0.001 0.001 0.001 0.001 0.001 0.001 Vancouver DEM (from LiDAR)  0.464 0.340 0.125 0.009 55.556 44.444 0.009 -0.008 0.014 0.010 -0.020 -0.005 0.001 0.001 0.005 0.042 Vancouver DSM (from LiDAR First Return)  18.831 18.749 0.082 0.418 50.000 50.000 0.418 -0.417 0.939 0.024 -2.278 -0.020 0.000 0.001 0.004 2.668 Boyko Method 0.735 0.625 0.110 0.015 61.111 38.889 0.013 -0.019 0.024 0.015 -0.038 -0.005 0.000 0.001 0.010 0.058 Canadian DSM  7.555 0.230 7.325 0.086 94.444 5.556 0.089 -0.046 0.040 0.050 -0.046 0.058 0.100 0.081 0.108 0.115 Canadian DEM  1.170 1.329 0.158 0.028 44.444 55.556 0.029 -0.027 0.031 0.070 -0.039 -0.036 -0.005 -0.002 0.035 0.036 SRTM 1arcs DEM  15.583 0.226 15.357 0.176 83.333 16.667 0.208 -0.015 0.087 0.028 -0.019 0.188 0.204 0.171 0.216 0.242 SRTM 3arcs DEM  9.181 0.000 9.181 0.102 100.000 0.000 0.102 #N/A 0.019 0.027 0.061 0.089 0.108 0.102 0.116 0.127 CGIAR SRTM DEM  6.186 0.000 6.186 0.069 100.000 0.000 0.069 #N/A 0.015 0.024 0.037 0.056 0.075 0.069 0.080 0.087 ASTER DEM  0.007 4.160 4.153 0.046 5.556 94.444 0.001 -0.049 0.026 0.046 -0.080 -0.073 -0.043 -0.046 -0.026 0.001  101  C.7 Main Street over Waterfront Street  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 4.943 9.074 4.131 0.055 27.451 72.549 0.071 -0.049 0.059 0.069 -0.071 -0.060 -0.045 -0.016 0.009 0.115 Straight Line Estimate 0.000 4.131 4.131 0.016 0.000 100.000 #N/A -0.016 0.000 0.000 -0.016 -0.016 -0.016 -0.016 -0.016 -0.016 Vancouver DEM (from LiDAR)  8.260 12.176 3.916 0.080 31.373 68.627 0.103 -0.070 0.120 0.068 -0.261 -0.065 -0.043 -0.015 0.003 0.379 Vancouver DSM (from LiDAR First Return)  5.295 9.184 3.889 0.057 29.412 70.588 0.071 -0.051 0.061 0.084 -0.079 -0.062 -0.042 -0.015 0.021 0.123 Boyko Method 5.410 9.180 3.770 0.058 31.373 68.627 0.069 -0.053 0.064 0.084 -0.098 -0.063 -0.039 -0.014 0.021 0.126 Canadian DSM  1.706 8.018 6.312 0.038 21.569 78.431 0.031 -0.040 0.033 0.034 -0.058 -0.048 -0.040 -0.025 -0.014 0.061 Canadian DEM  5.211 9.607 4.396 0.058 49.020 50.980 0.042 -0.074 0.076 0.091 -0.188 -0.057 -0.015 -0.017 0.034 0.132 SRTM 1arcs DEM  2.634 10.409 7.775 0.051 31.373 68.627 0.033 -0.059 0.050 0.090 -0.108 -0.074 -0.037 -0.030 0.016 0.071 SRTM 3arcs DEM  1.876 8.514 6.638 0.041 11.765 88.235 0.063 -0.038 0.037 0.024 -0.069 -0.049 -0.033 -0.026 -0.024 0.079 CGIAR SRTM DEM  1.794 8.495 6.702 0.040 13.725 86.275 0.051 -0.039 0.038 0.052 -0.061 -0.054 -0.044 -0.026 -0.002 0.072 ASTER DEM  5.364 11.603 6.238 0.067 27.451 72.549 0.077 -0.063 0.079 0.081 -0.172 -0.077 -0.020 -0.024 0.004 0.136  102  C.8 Cambie Street North Ramp  Cumulative Elevation Gain (m) Cumulative Elevation Loss (m) Absolute Elevation Change (m) Average Absolute Grade Percent Positive Grade Percent Negative Grade Average Positive Grade Average Negative Grade Grade Standard Deviation Grade Inter Quantile Range Min. Grade 1st Qu. Grade Median Grade Mean Grade 3rd Qu. Grade Max. Grade Measured Ground Truth 5.736 0.052 5.683 0.043 81.481 18.519 0.052 -0.002 0.034 0.065 -0.005 0.007 0.056 0.042 0.071 0.089 Straight Line Estimate 5.683 0.000 5.683 0.042 100.000 0.000 0.042 #N/A 0.000 0.000 0.042 0.042 0.042 0.042 0.042 0.042 Vancouver DEM (from LiDAR)  1.502 2.756 1.254 0.032 33.333 66.667 0.033 -0.031 0.037 0.058 -0.065 -0.037 -0.008 -0.009 0.022 0.056 Vancouver DSM (from LiDAR First Return)  12.694 6.670 6.024 0.143 66.667 33.333 0.141 -0.148 0.257 0.102 -0.599 -0.010 0.044 0.045 0.092 0.711 Boyko Method 0.275 0.065 0.210 0.003 88.889 11.111 0.002 -0.004 0.011 0.000 -0.011 0.000 0.000 0.002 0.000 0.054 Canadian DSM  4.165 2.590 1.576 0.050 59.259 40.741 0.052 -0.047 0.051 0.106 -0.058 -0.049 0.040 0.012 0.057 0.070 Canadian DEM  1.693 1.292 0.401 0.022 59.259 40.741 0.021 -0.023 0.029 0.035 -0.057 -0.018 0.003 0.003 0.017 0.061 SRTM 1arcs DEM  5.101 2.844 2.257 0.059 59.259 40.741 0.064 -0.052 0.064 0.111 -0.106 -0.039 0.031 0.017 0.073 0.111 SRTM 3arcs DEM  3.311 1.956 1.354 0.039 59.259 40.741 0.041 -0.036 0.039 0.083 -0.042 -0.039 0.040 0.010 0.044 0.053 CGIAR SRTM DEM  3.870 2.295 1.575 0.046 59.259 40.741 0.048 -0.042 0.047 0.101 -0.048 -0.048 0.046 0.012 0.053 0.063 ASTER DEM  8.877 6.617 2.260 0.115 51.852 48.148 0.127 -0.102 0.126 0.217 -0.191 -0.084 0.040 0.017 0.132 0.191  103  Appendix D  Slope Distributions of Elevated Structures in the City of Vancouver  104   105   106   107   108  109  110  111  112  113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128  129  130  131  132  133  134  135  136  137   

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