Inspection of Topographic Distance Measurements within ArcGIS

Steven Rick BradshawPenn State GEOG 596A

Capstone Project ProposalApril, 2013

• In a non-projected global coordinate system, GIS software measures geodetic distances using the surface of a reference ellipsoid.

• Geodetic distance: “…the length of the shortest curve between those two points along the surface of the earth model being used by the spatial reference system. Geodetic distance behaves well for wide areas of coverage, and takes the earth's curvature into account.” The OpenGIS Consortium

Background - Issues with GIS Measurements

• Geodetic distance measurements using a reference ellipsoid, will not consider changes in elevation between two points.

• Compared to geodetic distances, topographic distances can be much longer. • The following scenario will illustrate the need for a tool within GIS software that measures topographical distances.

• Currently, GIS software tools offered by major vendors, do not provide an accurate analysis of topographic distances.

• The results of this study will suggest the need to develop appropriate tools that compute topographic distance within GIS software.

Background - Issues with GIS Measurements

ScenarioConsider two cities (A and B) separated by a mountain range. When traveling from City A to City B, a traveler changes elevation crossing over the summit of the range. When GIS software calculates the distance between City A and B, the resultant distance is calculated using geodetic (or planar) distance but does not include the changes in topography.

Background - Issues with GIS Measurements

Literature Review

Currently, there is little research on topographic distance measurement within a GIS environment.

Previous and current research on GIS based distance measurements can be classified into three categories

1.Methods used in ArcGIS to Measure Geodetic and Euclidean DistancesI. Euclidean DistanceII. Geodetic DistancesIII. Cost-Weighted DistanceIV. Proximity Analysis

Background - Previous Research on Problem

Literature Review Continued …

2. Distance Measurement Algorithm Development I. Meyer’s Topographic Distance Watershed Algorithm

Utilizes watershed lines to calculate geodetic distances. It also uses slope to calculate the topographic distances of water traveling toward the minimum watershed line values from a chosen starting point.

II. Yang’s cell based algorithm for evaluating Directional Distance Identifies the nearest object borderlines to a given point within the map. The

algorithm pre-processes a map into a grid, identifies the nearest object borderline and creates radiating “fetch lines” in multiple directions.

Background - Previous Research on Problem

Literature Review Continued…

3. Research on Issues with Current Distance Measurement Methodology.I. Liu et al. (2007) examined the effects of raster cell resolution on Cost Distance

Modeling.

II. Hunghu et al. (2011) studied on the effects of DEM cell resolution on slope length calculations.

III. Napieralski and Napela (2008) investigated the effect of DEM cell resolution on landform morphology.

Background - Previous Research on Problem

Research ApproachHypothesis- Given the same route, topographic distances would be greater than geodetic distances.

Two sections of Highway 70 that traverses White Sands Missile Range, NM will be mapped with GPS and cast in WGS-84 and NAD27.

1. Organ Mountain Site - a route over a mountain pass with moderate elevation changes.

2. Flats Site – a route across an extinct lakebed with little elevation change.

Proposed Methodology

Proposed Methodology

Research ApproachOrgan Mountain Site-

Highway 70 is a four lane divided, with highrate of traffic. Speed limit ranges from 50 to 75 MPH within study site.

Length- 18 km

Elevation- 3,963 ft. to 5,719 ft at the Pass

Proposed MethodologyResearch ApproachFlats Site-

Is also a four lane divided highway, with high rate of traffic. Speed limit is 75 MPH within study site.

Length- 3 km

Elevation- 3,955 ft. to 3,998 ft

Research Steps – Data Collection

1. Physical survey of study sites

• Relative GPS surveying methods will be used to survey both sites collecting coordinates every 150 meters. These WGS-84 coordinates will be used to generate topographic distances.

• Orthometric heights are determined by calculating the relationship of ellipsoid heights above the reference ellipsoid and the heights of the geoid The results are comparable to the traditional elevation values of a vertical datum.

Proposed Methodology Cont…

Trimble R-8 Receivers

Proposed Methodology Cont…

Research Steps – Data Collection

The Survey at Flat SiteIn addition to the GPS survey, the Flats Site will measure the actual surface distance with a device (measuring wheel). This distance will be used as a baseline of the surface distance to be compared to the measured geodetic distance and the GPS collected Topographic distance.

Research Steps – Data Collection

2. Transform Horizontal Coordinates to NAD27To illustrate how different reference ellipsoids can affect topographic distances, coordinates of both sites will be transformed into the North American Datum of 1927 (NAD27) using survey processing software.

3. Transform Vertical Coordinates to NGVD29NAD27 elevation values collected during the survey will be cast in the National Geodetic Vertical Datum of 1929 (NGVD29).

Proposed Methodology Cont…

Research Steps – Data Collection Continued…

4. Modify Vertical data for Organ Mountain Pass SiteAll vertical data for the Organ Mountain Pass Site will be manipulated to represent extreme elevation changes.

5.Generate Slant Distances of all DatasetsTopographic distances will be calculated with DoD software using 3 dimensional coordinates (x, y, z) of two points on a reference ellipsoid, then calculating the slant distance between those points.

Proposed Methodology Cont…

Proposed MethodologyDataset Workflow

Proposed Methodology Cont..

Organ Mountain Site

WGS-84

Flats Site WGS-84

TransformNAD27

TransformNAD27

Organ Mountain Site

NAD27

Flats Site NAD27

Slant Dist.

Slant Dist.

Flats Site NAD27 Slant Distance

Flats Site WGS-84 Slant Distance

Organ Mountain WGS-84

Slant Distance

Organ Mountain WGS-84 Extreme

Slant Distance

Organ Mountain NAD27 ExtremeSlant Distance

Organ Mountain NAD27

Slant Distance

Elevation Manipulation

Elevation Manipulation

Organ Mountain Site

NAD27/NGVD29

Organ Mountain Site

WGS-84

Organ Mountain Extreme Elevation

WGS-84

Organ Mountain Extreme Elevation

WGS-84

Slant Dist.

Slant Dist.

Slant Dist.

Slant Dist.

TransformNGVD29

Organ Mountain Site

NAD27/NGVD29

Proposed Methodology Cont… Research Steps – Data Analysis6. Comparison of Reference EllipsoidsWGS-84 is a geocentric reference system ellipsoid with an origin at center of Earth’s mass.

• The orientation of the system is oriented and fixed to astronomic observations.

NAD27 is a horizontal control datum that utilizes the Clarke Spheroid of 1866. • The origin is a single survey marker at Meade's Ranch, Kansas. • The origin of NAD27’s reference ellipsoid, Clarke 1866 is approximately 236 meters away from WGS-84 Earth-centered Earth-fixed reference ellipsoid. The orientation of these reference ellipsoids differ by nearly 11 minutes of angle, with NAD27 tilted counter-clockwise to WGS 84. (Roman, 2007)

Ellipsoid Semi-Major Axis Semi-minor Axis Flattening

WGS-84 6,378,137.0 m 6,356,752.314 m 1/298.257223563

NAD27 (Clarke 1866)

6,378,206.4 m 6,356,583.8 m 1/294.9786982

Comparison NAD27 is 69.m wider at equatorial plane

WGS-84 is 168.514m taller between poles

Research Steps – Data Analysis Cont…

7. Comparing DistancesTopographic distance results of all six routes will be compared to the geodetic and actual surface distance. The actual surface distance of the Flats Site will also be compared to the topographic and geodetic distances.

WGS-84 topographic distance will be compared to the NAD27 topographic and actual surface distance data.

8. Explore DataIt is expected any differences in distances will be caused by both the physical distinctions in the dimensions of the reference ellipsoids and the orthometric heights and the NGVD29 elevation values.

Proposed Methodology Cont…

The following results are anticipated.

1. The greater the elevation changes between two locations, the greater the difference between the geodetic and topographic distance. 2. The topographical distance of datasets with extreme elevation changes will be much greater than the geodetic distance. 3. Datasets with smaller elevation changes will have similar topographic and geodetic distances. 4. The differences in the topographic distances between WGS-84 and NAD27 will highlight the importance of selecting the proper reference ellipsoid and its application for a particular geographic region.

The results will illustrate the need for and warrant further study into developing a function within GIS software that measures topographical distances.

Anticipated Results

Project TimelineMay to June 2013 Complete Steps 1, 2, 3• Identify and establish a study area.• GPS the study area and process the data.• Transform WGS-84 horizontal coordinates to NAD27.• Transform WGS-84 orthometric heights to NGVD29 elevation values.

July 2013- Complete Steps 4 and 5• Complete research on WGS-84 and NAD27 and conduct a discussion on the differences between WGS-84 and NAD27 in respect to New Mexico to identify causes of differences in topographic distances.• Create new routes by modifying elevation values.

August 2013- Complete Steps 6, 7 and 8• Calculate slant distances of all routes to create topographic distances.• Analyze all topographic and geodetic distances.• Compare and contrast the differences of topographic and geodetic distances.

September to November 2013- GEOG 596B• Prepare for presentation for formal professional presentation.• Present results of capstone at the North American Cartographic Society Conference in Greenville, South Carolina October, 2013.

A. Defense Mapping Agency. 1984. Geodesy for the Layman. Washington, D.C. Available at http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003A.HTM

B. ESRI. (n.d.). GIS Dictionary. Retrieved from http://support.esri.com/en/knowledgebase/GISDictionary/term/Clarke ellipsoid of 1866

C. Open Geospatial Consortium, T. C. (2007, December 28). Schema for Coverage Geometry and Functions. Retrieved from http://www.opengeospatial.org/standards/as

D. Hoghu, L., Kessel, J., Hormann, G., & Fohrer, N. (2011). Effects of DEM Horizontal Resolution and Methods on Calculating the Slope Length Factor in Gently Rolling Landscapes. Catena, 368-375. Retrieved from http://ac.els-cdn.com.ezaccess.libraries.psu.edu/S0341816211001408/1-s2.0-S0341816211001408-main.pdf?_tid=afdd1c1a-87771-11e2-ba1b-00000aacb35f

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References

Questions and Answers?