## Projections

#### Projections used in State Plane Coordinate Systems

• "To convert geodetic positions of a portion of the Earth's surface to plane rectangular coordinates, points are projected mathematically from the ellipsoid to some imaginary developable surface -a surface that can conceptually be developed or 'unrolled and laid out flat' without distortion of shape or size. A rectangular grid can be superimposed on the developed plane surface and the positions of points in the plane specified with respect to X and Y grid axes. A plane grid developed using this mathematical process is called a map projection.... Today, two of the most commonly used mapping projections are the Lambert conformal conic and the Transverse Mercator projections." (Elementary Surveying, 12th Edition by Ghilani and Wolf, p. 580)

#### State Plane Coordinate System (SPCS)

• "...points couldn't be projected from the ellipsoid to developable surfaces without introducing distortions in the lengths of lines or the shapes of areas. However, these distortions are held to a minimum by selected placement of the cone or cylinder secant to the ellipsoid, by choosing a conformal projection (one that preserves true angular relationships around points in a small region), and also by limiting the zone size or extent of coverage on the Earth's surface for any particular map projection. If the width of zones is held to a maximum of 158 mi (254 km), and if two-thirds of this zone width is between the secant lines, distortions (differences in line lengths on the two surfaces) are kept to 1 part in 10,000 or less. The NGS intended this accuracy in its development of the state plane coordinate systems." (Elementary Surveying, 12th Edition by Ghilani and Wolf, p. 581-2)
• Clark County uses StatePlane Coordinate- Nevada East Zone (NV-E) along with other local agencies (e.g. City of Las Vegas, Henderson, North Las Vegas, and so on)
• Map of all Stateplane coordinate zones is included with ArcMap, depending upon where you installed the program, e.g. C:\Program Files\ArcGIS\Reference Systems\usstpln83.shp (download zip of shapefiles from UNLV, usstpln83.zip - Geographic Coordinate System - GCS_WGS_1984)
• State Plane Coordinate System of 1983 NOAA Manual NOS NGS 5 by James E. Stem
• "A new figure of the Earth, the Geodetic Reference System of 1980 (GRS 80), which approximates the Earth's true size and shape, supplied a better fit than the Clarke 1866 spheroid, the reference surface used with NAD 27." (ibid p. 2)
• "The ellipsoid that forms the basis of NAD 83, and consequently the SPCS 83, is identified as the Geodetic Reference System of 1980 (GRS 80). GRS 80 provides an excellent global approximation of the Earth's surface. The Clarke spheroid of 1866, as used for NAD 27 approximated only the conterminous United States. Because the geoid separation at point MEADES RANCH was assumed equal to zero, a translation exists between ellipsoids. The ellipsoid change is the major contributor of the coordinate shift from NAD 27 to NAD 83." (ibid p. 12)
• NAD 27 - U.S. coast and Geodetic Survey (USC&GS) Special Publication 235 - The State Coordinate Systems
• Fundamentals of the State Plane Coordinate Systems
• U.S. Coast and Geodetic Survey. Manual of Traverse Computation on the Transverse Mercator Grid by Oscar S. Adams, Senior Mathematician and Charles N. Claire, Associate Mathematician. GPO, Washington, DC, 1935. 199 pages. Special Publication No. 195.
• Publication of North American Datum of 1983 State Plane Coordinates in Feet in Nevada
• State Plane Coordinates Presentation by Dr. Ghilani
• National Geospatial-Intelligence Agency Geodesy and Geophysics
• Fundamentals of the State Plane Coordinate Systems by Joseph F. Dracup, Sept 1974. National Geodetic Survey
• Map Projections: A Working Manual by John P. Snyder. USGS Professional Paper 1395. Washington, D.C.: USGS, 1993.
• GRS 80
• Equatorial Radius/Semiaxis, a = 6,378,137 meters
• Polar Radius/Semiaxis, b = 6,356,752.3 meters
• Flattening, f = 1/298.257
• "in computations if the ellipsoid is assumed a sphere, its radius is usually taken such that its volume is the same as the reference ellipsoid. It is computed from (a2b)1/3. For the GRS80 ellipsoid, its rounded value is 6,371,000 meters." (Elementary Surveying, 12th Ed, Ghilani and Wolf, p. 523)
• WGS 84
• Equatorial Radius, a = 6,378,135 meters
• Polar Radius, b = 6,356,750.5 meters
• Flattening, f = 1/298.26
• Nevada East Zone Map Projectsion: A Working Manual, p. 53 and 374
• Transverse Mercator Projection
• Central meridian = 115°35' West
• ESRI uses -115.583333333333300000 decimal degrees = -115°35'
• Scale reduction = 1:10,000
• ESRI uses a scale factor of 0.999900000000000010
• "Lines of contact. Any single meridian for the tangent project. For the secant projection, two almost parallel lines equidistant from the central meridian...Accurate scale along the central meridian if the scale factor is 1.0. If it is less than 1.0, there are two straight lines with accurate scale equidistant from and on each side of the central meridian." (ESRI ArcGIS Transerve Mercator)
• Origin (latitude) = 34°45' North
• ESRI uses 34.7500 decimal degrees = 34°45'
• Coordinates of Origin (meters): False Easting x=200,000 and False Northing y=8,000,000
• "State plane coordinate systems are generally designed to have a scale error maximum of about 1 unit in 10,000. Suppose you calculated the Cartesian distance (using the Pythagorean theorem) between two points represented in a state plane coordinate system to be exactly 10,000 meters. Then, with a perfect tape measure, pulled tightly across an idealized planet, you would be assured that the measured result would differ by no more than 1 meter from the calculated one. The possible error with the UTM coordinate system may be larger: 1 in 2500." (Introducing Geographic Information Systems with ArcGIS, 2nd Edition by Michael Kennedy, p. 18)
• Datum: NAD 1983 (Conus) (Mol) is used on the Trimble TSC2
• GPS Course Lesson 6: Two-Coordinate Systems and Heights by Jan Van Sickle, Senior Lecturer
• "...the projection of points from the Earth's surface onto a reference ellipsoid and finally onto flat maps..." (ibid)
• Stateplane Coordinates in USA use Secant Projections to minimize distortion by providing 2 lines of intersection instead of one line with the Tangent case. Secant Projection intersect the ellipsoid at two areas and these two lines are of exact scale (also known as standard lines) to the ellipsoid.
• Ellipsoidal lengths = geodetic distances
• Lengths on the map projection surface = grid distances
• Grid North is parallel to the Central Meridian. Convergence is the angle between Grid North and Geodetic North
• False Easting and Northing
• False easting is a linear value applied to the origin of the x coordinates.
• False northing is a linear value applied to the origin of the y coordinates.
• False easting and northing values are usually applied to ensure that all x and y values are positive.
• False easting and false northing adjustments by Margaret M. Maher
• "False easting and false northing values are sometimes inserted into a projection file in order to make all the x- and y-coordinate values across the area of the data positive numbers. False easting and false northing values can also be used to adjust the position of the data in either the east-west or north-south direction in order to align the data.
Making the false easting value in the projection file larger will adjust the position of the data to the west, moving the data to the left in the ArcMap display. Making the false easting value in the project file smaller will adjust the position of the data east, to the right in the ArcMap display.
Adjustments to the false northing value in the projection file will move the data display north or south, though they are not as intuitive as the false easting adjustments. Making the false northing value in the projection file larger will move the data display south in the ArcMap window. Making the false northing value smaller will move the data display north in the ArcMap window.
Keep these adjustments in mind while creating the custom projection file to align your data in ArcMap." (Lining Up Data in ArcGIS by Margaret M. Maher, p. 55, ISBN 978-1-58948-249-4)
• "A constant E0 is adopted to offset the N grid axis from the central meridian and make E coordinates of all points positive. Similarly, a constant Nb can be adopted to offset the E grid axis from the southern edge of the projection." (Elementary Surveying, 12th Edition by Ghilani and Wolf, p. 587)
• You can also use the false easting and northing parameters to reduce the range of the x or y coordinate values. For example, if you know all y values are greater than 5,000,000 meters, you could apply a false northing of -5,000,000.
• ESRI ArcGIS Desktop 10 - Projection parameters
• According to David Doyle with NGS, metadata is hard to obtain on current surveying work but was extremely difficult in the 1980s. So, the State of Nevada wanted to ensure when surveyors where working with the two different Datums (NAD27 and NAD83) that a surveyor could easily tell from the coordinate values, which Datum is being used. So the NAD83 coordinates have a 8,000,000 meters added to the Northing (Y) coordinate values.
• NAD27 - Nevada East Zone uses a False Northing of 0 ft
• NAD83 - Nevada East Zone uses a False Northing of 8,000,000 meters (26,246,666.66666666 feet)
• Notice how the same data (city boundaries in Clark County NV) do not overlay, that is the NAD83 is shifted 8,000,000 meters north of the NAD27 layer
• Conversion from NAD83/27 to Geodetic/Geographic
• Central Meridian (Longitude)
• Notes from Earl F. Burkholder, PS, PE with Global COGO, Inc., Las Cruces NM 88003
• Central Meridian (Longitude) is a north/south line and secant lines in a transverse Mercator projection are parallel to the central meridian. Problem is Longitude lines are not parallel because the all converge at the poles.
• The easting of a secant line will vary slightly from the south end of the state to the north end.
• secant line in state plane coordinates is always a constant distance from the central meridian.
• UTM

#### How to draw the SPCS origin

• Step 1: Identify the SPCS Defining Parameters
• If you have ArcGIS installed on your computer, view the projection file (.prg)
• Elementary Surveying, 12th Edition by Ghilani and Wolf, Appendix F (and definitions on p. 586) U.S. State Plane Coordinate System Defining Parameters
• Step 2: Create a shapefile using WGS84 geographic coordinates (e.g. GCS_WGS_1984)
• Use ArcCatalog to create a new shapefile. Assign it the GCS_WGS_1984 projection
• Step 3: create gratitcules
• Using an ArcMap edit session, add the line features using Absolute X,Y to enter the latitude and longitude values

#### Scale Factors

• scale factors move distances from the stateplane grid to the ellipsoid
• "After a distance has been reduced to its ellipsoidal equivalent, it must then be scaled to its grid equivalent. This is accomplished by multiplying the ellipsoidal length of the line by an appropriate scale factor." (Elementary Surveying, 12th Ed, Ghilani and Wolf, p. 599)
• Scale, Elevation, Grid, and Combined Factors Used in Instrumentation. Professional Surveyor Magazine - Feb 2006

### Coordinate Systems (Geographic and Projected) in ArcMap

#### When adding data to ArcMap, will sometimes get a warning message "One or more layers is missing spatial reference information, Data from those layers cannot be projected"

• "If you add a layer that is in a projected coordinate system to ArcMap, and the coordinate system information is missing" will get that message. Much of the time this is not a problem. You can still display and work with this data as long as ArcMap does not need to project it on the fly. ArcMap will not be able, however, to align this data with data in a different coordinate system." [Ormsby 01, p. 340]

#### Map Projections

• Mathematical transformation of a model of the earth's shape (i.e. Oblate Spheroid) to a flat surface (grid). [Ormsby 01, p. 324]
• Can distort shape, area, distance, and direction
• Geographic Coordinates System (GCS)
• based on a curved surface
• Sphere - less accurate approximation of the shape of the earth
• Spheroid - more accurate approximation of the shape of the earth (most widely used)
• Geoid - most accurate model of the shape of the earth
• a measurement of a location on the earth's surface expressed in degrees of latitude and longitude. Tend to have a "taffy-pull appearance" when displaying [Ormsby 01, p. 331]
• GCS includes: angular unit of measure (e.g. degrees), prime meridian (i.e. line of zero longitude which passes through Greenwich England), and a datum (e.g. position of spheroid relative to the center of earth, typically use North American Datum of 1983 a.k.a. NAD83)
• Latitude: horizontal lines (e.g. equator) and also known as parallels. Measurement values range from -90 to 90 degrees
• Longitude: vertical lines, also known as merdians. Measurement values range from -180 to 180 degrees.
• Degrees - 1/360th of a cirle
• Minutes - 1/60th of a degree, or 60 minutes = 1 degree
• Seconds - 1/60th of a minute, or 60 seconds = 1 minute
• See ESRI Virutal Campus - Learning ArcGIS 9, Module 3 for more details
• Projected Coordinates
• based on a flat surface
• does NOT use spheriods, spheres, or geoids since these are approximations of the shape of the earth
• also known as planar coordinates
• a measurement of a location on the earth's surface expressed in a two-dimensional system that locates features based on their distance from an origin (0,0) along two axes.
• Map projections transform latitude and longitude to x,y coordinates in a projected coordinate system.
• Latitude and Longitude can located exact locations on the earth, but no uniform units of measurement (see figure on [Ormsby 01, p. 326])
• If all your GIS data is using the same coordinate system, don't have to worry about projections
• Empty data frames inherit the projection of the first layer added to it. [Ormsby 01, p. 333]
• On-the-fly Projections, [Ormsby 01, p. 328, 336]
• ArcMap determines if the coordinate system is geographic or projected by comparing the coordinates. Lat/Long values will be in the tens (Lat=36 degrees) and hundreds (Long=-115 degrees), where as Stateplane coordinates hundred thousand (e.g. x=800,000) and tens of million (y=26,750,000)[Ormsby 01, p. 340]
• On-the-fly projections are less mathematically rigorous than permanent projections done using the ArcToolbox Projection Wizard. [Ormsby 01, p. 330]
• On-the-fly projections are defined by the Layer Properties. Note this doesn't change the actual file. Projection only applied to data frame. [Ormsby 01, p. 330]
• "... a coordinate system is a framework for locating features on the earth's surface using either latitude-longitude or x,y values."
• Works well when the data has the same geographic coordinate system (GCS). [Ormsby 01, p. 329]
• To transform the coordinate location of a CAD file using coordinate values in ArcMap, see ESRI Article Number 20860
• Projection info is assigned to the feature dataset, not the geodatabase. Note all feature classes in a feature dataset must have the same projection. Doesn't appear that all feature datasets need to have the same projection in a geodatabase. Remember a feature class can be contained in a feature dataset, which will ensure it has the same projection info, or can be a standalone feature class.
• ESRI software does not support vertical datums. Only reads the z-value as is, you must perform any pre-processing/corrections to the vertical data before entering into ArcGIS. Appears the projection metadata doesn't allow you to enter any additional z-value related data (for example NAVD88 datum, elevation units of feet, and so on).fs

#### How to Project Geodatabases and Shapefiles

• Projections in ArcMap
• Can project the data frame, not the actual feature class, shapefile, or coverage.
• Can export the layer with the same projection as the data frame, so in a sense your actually reprojecting the layer.
• ArcMap will not project data on the fly if the coordinate system for the data set has not been defined.
• Additional info, see ESRI Article ID 24893, How to identify an unknown coordinate system using ArcMap.
• ESRI Article ID 20837, how to align vector data in ArcMap
• Projections in ArcCatalog
• Can only define a projection for a layer, not reproject it.
• Data frame will inherit the projection of the first layer added to it.
• ArcCatalog: select a geodatabase feature, right mouse click to bring up the context menu, Properties -> Fields tab, select Shape, then at the bottom of that window, click the ellispe (...) and either Select or Import.
• Projections in ArcToolbox
• Will reproject the layer permentently
• ArcToolbox: Data Management -> Projections -> Project Wizard (shapefiles, geodatabase)
• Reference: see ESRI Article ID 21447 how to project shapefiles or geodatabase feature classes with the ArcToolbox Project wizard

#### Define a Shapefile's Projection

• Using ArcCatalog
• Problem: metadata, spatial reference property says "unknown" or "assumed geographic" projection.
• File -> Properties -> Fields tab: click Shape column. In Properties list below, select ellipses button to open the Spatial Reference Properties window. Click Select... button. Browse through Projected Coordinate Systems folder -> State Plane folder -> NAD 1983 (Feet) folder -> NAD 1983 StatePlane Nevada East FIPS 2701 (Feet).prj
• Metadata should now say the projected coordinate system name.
• Shapefile's coordinate system parameters are stored in the same location and name as the shapefile but with a .prj extension
• see ArcGIS Desktop Help -> ArcCatalog -> Working with shapefiles -> Defining a shapefile's coordinate system
• Using ArcToolbox
• ArcToolbox -> Data Management Tools -> Projections -> Define Projection Wizard (shapefiles, geodatabase). Then give same inputs as the "Using ArcCatalog" solution above.
• see [Ormsby 01, p. 341-346]

#### Common Coordinate Systems used in Clark County NV

• StatePlane Coordinate System (SPCS)
• Projection used by local agencies (e.g. Clark County, City of Las Vegas, Henderson, North Las Vegas, and so on)
• Map of all Stateplane coordinate zones is included with ArcMap, depending upon where you installed the program, c:\arcgis\arcexe83\Reference Systems\usstpln83.shp or C:\Program Files\ArcGIS\Reference Systems\usstpln83.shp (download shapefiles from UNLV, usstpln83.zip - Geographic Coordinate System - GCS_WGS_1984)
• Clark County uses StatePlane Coordinate- Nevada East Zone (NV-E)
• ArcGIS Resource Center - view of USSTPLN83.shp
• Universal Transverse Mercator, UTM
• Earth is divided into 60 zones (each zone 6 degrees of longitude)
• Origin for each zone is the Equator and its central meridian (3 degrees west and 3 degrees east). To eliminate negative coordinates, a false easting of 500,000 is applied
• Typically used for statewide datasets
• Map of all UTM zones is included with ArcMap, depending upon where you installed the program, c:\arcgis\arcexe83\Reference Systems\utm.shp or c:\Program Files\ArcGIS\Reference Systems\utm.shp (download shapefiles from UNLV, utm.zip - Geographic Coordinate System - GCS_WGS_1984) and overlay with the USA Counties Layer countyp020.zip from the National Atlas
• Best way to show two datasets that are in different UTM zones, is to project one into the other zone.
• State of Nevada uses UTM Zone 11
• Margaret Maher (mmaher@esri.com) with ESRI Tech Support - specialize in Map Projections and Symbology
• Local/Surface Coordinates
• Used extensively for small development projects by surveyors
• referred to as ground distances by surveyors
• different origin for each design project
• To project into another coordinate system, need 2 points and have coordinate values in both systems.

#### Define Local/Surface Coordinate Projection in ArcMap

• Objective is to create a projection file so ArcMap can project on the fly from local/surface coordinates to stateplance coordinates. The projection file (.prj) will be similar to a shapefile file .prj file but for the AutoCAD .dwg, example anyfilename.dwg and anyfilename.prj (note cannot have any spaces in the filename for the .dwg and .prj files). Then ArcMap will automatically project the dwg.
• Most difficult step is determining the local/surface coordinate parameters
• ArcMap Data Frame Properties -> New -> Projected Coordinate System
• Projection name cannot contain spaces
• Custom Projection File options for 7 local/surface projections
• Local
• Parameters
• False_Easting
• False_Northing
• Scale_Factor
• Azimuth
• Longitude_Of_Center
• Latitude_Of_Center
• Linear Unit = Foot_US
• Datum is defined by Select... button under Geographic Coordinate System, select North America folder
• North American Datum 1983.prj
• North American 1983 HARN.prj (use if survey done to HARN accuracy)
• North American 1983 (CSRS98).prj is for Canada
• Hotine_Oblique_Mercator_Azimuth_Center
• Hotine_Oblique_Mercator_Azimuth_Natural
• Hotine_Oblique_Mercator_Two_Point_Center
• Hotine_Oblique_Mercator_Two_Point_Natural
• Rectified_Skew_Orthomorphic_Center
• Rectified_Skew_Orthomorphic_Natural_O (has a rotation parameter)
• Alternative method is to Define a Projection using ArcToolbox