# Understanding Coordinates

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Understanding Coordinates
NJDEP & ESRI: Understanding Map Projections & Coordinate Systems

Department Standards Spheroid GRS80 Datum NAD83
Projection New Jersey State Plane (based on Transverse Mercator) Units Feet

Parameters for Mapping
A mathematical model of the earth must be selected. Spheroid The mathematical model must be related to real-world features. Datum Real-world features must be projected with minimum distortion from a round earth to a flat map; and given a grid system of coordinates. Projection These factors are part of the process in the creation of each projection.

A mathematical model of the earth must be selected.
Spheroid A mathematical model of the earth must be selected. Simplistic - A round ball having a radius big enough to approximate the size of the earth. Reality - Spinning planets bulge at the equator with reciprocal flattening at the poles. e.g. The mathematical model is an ellipsoid not a sphere. The earth is a bit like a tangerine, not perfectly round like a tennis ball.

Different Spheroids

Why use different spheroids?
The earth's surface is not perfectly symmetrical, so the semi-major and semi-minor axes that fit one geographical region do not necessarily fit another. Satellite technology has revealed several elliptical deviations. For one thing, the most southerly point on the minor axis (the South Pole) is closer to the major axis (the equator) than is the most northerly point on the minor axis (the North Pole).

The earth's spheroid deviates slightly for different regions of the earth.
Ignoring deviations and using the same spheroid for all locations on the earth could lead to errors of several meters, or in extreme cases hundreds of meters, in measurements on a regional scale. GRS80 (North America) Clark 1866 (North America WGS84 (GPS World-wide) International 1924 (Europe) Bessel 1841 (Europe)

A mathematical model must be related to real-world features.
Datum A mathematical model must be related to real-world features. A smooth mathematical surface that fits closely to the mean sea level surface throughout the area of interest. The surface to which the ground control measurements are referred. Provides a frame of reference for measuring locations on the surface of the earth.

How do I get a Datum? To determine latitude and longitude, surveyors level their measurements down to a surface called a geoid. The geoid is the shape that the earth would have if all its topography were removed. Or more accurately, the shape the earth would have if every point on the earth's surface had the value of mean sea level.

Geoid vs Spheroid Coordinate systems are applied to the simpler model of a spheroid. The problem is that actual measurements of location conform to the geoid surface and have to be mathematically recalculated to positions on the spheroid. This process changes the measured positions of many point. Sometimes by a few feet, sometimes by hundreds of feet. Different datums use a different orientation of the spheroid to the geoid to determine which parts of the world keep accurate coordinates on the spheroid. For an area of interest, the surface of the spheroid can arbitrarily be made to coincide with the surface of the geoid; for this area, measurements can be accurately transferred from the geoid to the spheroid.

Earth Centered Datums Satellite technology has made earth-centered datums possible. In an earth-centered datum, the spheroid is no longer aligned with the geoid at a point on the earth's surface. Instead, the center of the spheroid is aligned with the center of mass of the earth—a location that satellite technology has made it possible to determine. In an earth-centered datum, the spheroid and geoid still don't match up perfectly, but the separations are more evenly distributed.

Changes to the values of any datum parameters can result in changes to coordinate values of points.
If you have two different datums, in practive you have two different geographic coordinate systems.

World Geodetic System - 1984
WGS 84 World Geodetic System The datum on which GPS coordinates are based and probably the most common datum for GIS data sets with global extent.

Horizontal vs Vertical Datums
Horizontal datums are the reference values for a system of location measurements. Vertical datums are the reference values for a system of elevation measurements. The job of a vertical datum is to define where zero elevation is, this is usually done by determining mean sea level, a project that involves measuring tides over a cycle of many years.

Graticules Latitude/Longitude Lines of latitude Longitude lines   N or S of Equator E or W of Prime Meridian Also called parallels and meridians. Latitude lines are parallel, run east and west around the earth's surface, and measure distances north and south of the equator.

Longitude lines run north and south around the earth's surface, intersect at the poles, and measure distances east and west of the prime meridian. Based on 360 degrees. Each degree is divided into 60 minutes and each minute into 60 seconds.

Projection Real-world features must be projected with minimum distortion from a round earth to a flat map; and given a grid system of coordinates. You cannot flatten out features on an ellipsoid without distorting them. (Imagine viewing a tennis ball in its natural round state, now imagine putting a slit into it and trying to spread it out flat. It cannot be done without stretching, tearing, and altering its appearance substantially. A map projection transforms latitude and longitude locations to x,y coordinates.

What is a Projection? If you could project light from a source through the earth's surface onto a two-dimensional surface, you could then trace the shapes of the surface features onto the two-dimensional surface. This two-dimensional surface would be the basis for your map.

Why use a Projection? Can only see half the earth’s surface at a time.
Unless a globe is very large it will lack detail and accuracy. Harder to represent features on a flat computer screen. Doesn’t fold, roll or transport easily.

Map Projection & Distortion
Converting a sphere to a flat surface results in distortion. Shape (conformal) - If a map preserves shape, then feature outlines (like county boundaries) look the same on the map as they do on the earth. Area (equal-area) - If a map preserves area, then the size of a feature on a map is the same relative to its size on the earth. On an equal-area map each county would take up the same percentage of map space that actual county takes up on the earth. Distance (equidistant) - An equidistant map is one that preserves true scale for all straight lines passing through a single, specified point. If a line from a to b on a map is the same distance that it is on the earth, then the map line has true scale. No map has true scale everywhere.

Direction/Azimuth (azimuthal) – An azimuthal projection is one that preserves direction for all straight lines passing through a single, specified point. Direction is measured in degrees of angle from the north. This means that the direction from a to b is the angle between the meridian on which a lies and the great circle arc connecting a to b. If the azimuth value from a to b is the same on a map as on the earth, then the map preserves direction from a to b. No map has true direction everywhere.

Imagine capturing the world in a net
Imagine capturing the world in a net. The net divides the larger earth into sections, all contained in squares of the same size. Suddenly order is imposed on chaos. Finally we have the means to describe a location as so many squares to the left, so many to the right, so many up, or so many down, and at last we have its number. Watts, 1966

Planar Coordinate Systems
Coordinate systems identify locations by making measurements on a framework of intersecting lines that resemble a net. On a map, the lines are straight and the measurements are made in terms of distance. On a round surface (like the earth) the lines become circles and the measurements are made in terms of angle.

Any projected data that you add to ArcMap, or that you project within ArcMap, is associated with a projected coordinate system (PCS) in addition to its underlying Geographic Coordinate System (GCS).

Cartesian Coordinate System
Planar coordinate systems are based on Cartesian coordinates.

The origin of the coordinate system is made to coincide with the intersection of the central meridian and central parallel of the map. But this conflicts with the desire to keep all their map coordinates positive (within the first quadrant) and unique numbers. This conflict can be resolved with false easting and false northing. Adding a number to the Y axis origin (false easting) and another number to the X axis origin (false northing) is equivalent to moving the origin of the system.

The projected coordinate system is a Cartesian coordinate system with an origin, a unit of measure (map unit), and usually a false easting or false northing. The main value of Cartesian coordinates is for making measurements on maps. Before the age of computers formulas for converting latitude and longitude were too cumbersome to be done quickly, but Cartesian coordinates offered a satisfactory solution.

NJ State Plane Coordinates

Universal Transverse Mercator (UTM)
A comprehensive system for identifying locations and making measurements over most of the earth's surface. Divide the world into sixty vertical strips, each spanning six degrees of longitude. Apply a custom Transverse Mercator projection to each strip and use false eastings and northings to make all projected coordinates positive. Data that crosses zones is subject to distortion.

State Plane Coordinate System
StatePlane NJ FIPS 2900 (Feet).prj Divides the US into 120 sections, referred to as zones. Each zone is assigned a code number that defines the projection parameters for the region. Zones that lie north-south (New Jersey) use the Transverse Mercator projection; zones that lie east-west (Tennessee) use the Lambert Conformal Conic.

Developed in the 1930s by the US Coast and Geodetic Survey to provide a common references system for highway engineering, survey marker location, and other high-precision needs. Goal was to design a conformal (preserve shapes) mapping system for the country with a maximum scale distortion of one part in 10,000, then considered the limit of surveying accuracy. Four times more accurate than UTM.

Common Transformations
Latitude/Longitude to State Plane Feet Lat/Long DMS to Lat/Long Decimal Degrees Universal Transverse Mercator (UTM) Zone 18 to NJ State Plane Feet NAD27 to NAD83

Geographic Coordinate System
New Jersey State Plane Coordinate System

Decimal Degrees Minutes and seconds are expressed as decimal values. Used to store digital coordinate information. Example coordinate is 37° 36' 30" (DMS) Divide each value by the number of minutes or seconds in a degree: 36 minutes = .60 degrees (36/60) 30 seconds = degrees (30/3600) 2. Add up the degrees to get the answer: 37° + .60° ° = DD LAT DD = Latd +(Latm/60)+(Lats.s/3600) LONG DD = -(-Longd+(Longm/60)+(Longs.s/3600))

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