# Presentation: 819292

## Using Maps with GPS

**Using Maps with GPS**

**GPS for Fire Management & ICS - 2006**

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**Notes:**
Using Maps with GPS

## Using Maps with GPS

**Unit objectives:**
- Identify two datums common to the U.S..
- Identify the two “global” coordinate systems most commonly used with GPS receivers.
- Describe “datum shift,” and the relevance it has when using GPS in the field.
- Describe the four components that make up UTM coordinates.
- Identify the three ways that lat/long coordinates can be expressed.

**Notes:**
Using Maps with GPS

Unit objectives:
Identify two datums common to the U.S..
Identify the two “global” coordinate systems most commonly used with GPS receivers.
Describe “datum shift,” and the relevance it has when using GPS in the field.
Describe the four components that make up UTM coordinates.
Identify the three ways that lat/long coordinates can be expressed.

## Projecting a Sphere Onto a Plane

**Three-dimensional sphere to two-dimensional flat map.**

**Notes:**
Projecting a Sphere Onto a Plane

	The Earth is a three-dimensional sphere that can be portrayed on two-dimensional paper maps using a process called “projection.” To project something literally means to “throw forward” (as in projecting a movie from a camera onto a screen – hence the name movie “projector”). Whenever a three-dimensional object (such as a sphere) is projected onto a flat surface a certain amount of distortion occurs. This is because displaying three-dimensional objects in two-dimensional form is very difficult to do without introducing a certain amount of distortion.
	To demonstrate this, try peeling an orange, keeping the rind in one piece. Press the rind onto a flat surface, noticing how the rind “splays” outward when pressed flat. It loses its original shape and dimensions, with the center of the peel exhibiting the least amount of shape and linear distortion, while the outer edges exhibiting the greatest distortion.
	The same thing occurs when projecting the round Earth onto flat maps. This is one reason why map many projections tend to be regional in scope, covering only a portion of the Earth’s surface (though there are also global projections depicting the entire Earth). In the example above, the Earth is projected using the Mollweide projection, which is a common global projection. In the graphic above notice that the Mollweide projection tends to depict land masses most realistically for area, and is called an “equal-area” projection. Land masses depicted on a Mollweide map are proportional to land masses on the Earth for area. Unfortunately, the Mollweide projection distorts distance, shape and direction (notice Antarctica).

## Examples of Several Projections

**Depending on the projection, a certain amount of distortion occurs when portraying the Earth on paper.**

**Notes:**
Examples of Several Projections

	All projections include some form of spatial distortion. Map projection distortion can affect shape, area, distance, and direction, either individually or combination of all four, may be present in a single map projection. Mapmakers over the years have created many different projections to suit their particular cartographic needs. For example, a mapmaker creating a road map will probably not want to select a projection that distorts distance and direction.
	Projection distortion becomes less important on maps covering very small areas (so-called “large scale” maps), such as USGS 7.5 minute quadrangle maps of the United States. This is because the area covered by the map is not large enough for projection distortion to become noticeable (or even measurable). But maps covering large regions of the Earth (called “small scale” maps), and maps of the entire Earth, do present very noticeable distortion (as seen in the examples on the next slide). Universal Transverse Mercator is a very good projection for USGS 7.5 minute maps because the large scale of these maps exhibit almost no spatial distortion, thus producing maps that are nearly distortion-free in every respect. (More about Universal Transverse Mercator (UTM) later in this lesson.)
	Projection becomes important to the GPS user through the datum (more about datums later). The next slide shows examples of distortion among several projections. 

## Projections and Datums

**Notes:**
Projections and Datums
	In this diagram the continental United States is represented in two different projections, and un-projected latitude and longitude. This map is depicted using the Clarke 1866 Ellipsoid model for the Earth (named after English geodesist A.R. Clarke), which was designated the official ellipsoid model for the United States. A triangulation station located at Meade Ranch in Kansas was selected in 1927 as the origin for the United States official horizontal datum, based on the Clarke 1866 Ellipsoid model. 
	Notice that the projections and latitude longitude are most equal around the Kansas area, closest to Meade Ranch. Kansas, Oklahoma, Nebraska and Missouri are all defined rather equally among the three models. But as the distance from Kansas increases, so too does the distortion among the three models. This is because distortion in any projection is least when closest to its geographic point of origin.
	Basic users of the Global Positioning System need not worry about projections. However, datums are very important to the GPS user. A datum is a function of a projection, and can be summarized as “the mathematical model for the shape of the Earth that gives coordinate system values their Earth-tie or link to the physical world.” In other words, a datum allows a set of coordinates to reference the same feature, whether that feature is represented as a dot on a map, or the knob of a hill on the ground. A datum forms the reference frame for a selected map coordinate system. Combined, projection and datum form a mathematical model of the Earth used to plot the coordinates of a geographic point on any map, chart, or survey system. Maps are drawn so that every point (whether on a map or on the ground) is a known distance and height from a standard reference point (the datum’s point of origin). Depending on the datum chosen, one point on the Earth can have different sets of coordinates.

## Projections and Datums

**Notes:**
	Since a datum describes the mathematical model that is used to match the location of physical features on the ground to locations on a map, maps can be drawn so that every point is a known distance and height from a standard reference point (the datum’s point of origin). Different datums may be chosen to represent the same geographic area. Because of this, it’s important for the GPS user to know which datum the coordinates for a location were derived in. Without knowing the correct datum, a GPS user may be directed to the wrong location, even though the coordinate values for the desired location are the same. This is due to what’s known as “datum shift.”
	Datum shift means that a single point on a map, or on the ground, can have different coordinate values based on different datums. For example, two commonly used datums in North America are North American Datum 1927 (NAD27) and North American Datum 1983 (NAD83). Between those two datums, a single point on a map, or a physical point on the ground, will have two different sets of coordinates, one for each datum. Sometimes two datums are very similar, and coordinates will be nearly identical. For example, the datum used by the Global Positioning System is WGS84 (see explanation below), and this datum resembles NAD83 very closely. For most navigation purposes, NAD83 and WGS84 can be interchanged with negligible datum shift occurring. 

## Projections and Datums

**Notes:**
	There are several datums commonly used in North America. The most common datum used on U.S. Geological Survey maps is currently North American 	Datum 1927 (NAD27), which has many variations:
	NAD27 Caribbean
	NAD27 Canada
	NAD27 Alaska
	NAD27 CONUS (for “continental U.S.”)
	NAD27 Cuba
	NAD27 Mexico
	These variations of NAD27 are available in any GPS receiver, so it’s important to pay attention when selecting a datum in a GPS receiver to make sure that the correct one is selected.
	The Global Positioning System uses its own unique datum, WGS84, or World Geodetic System 1984. Most GPS receivers use this datum for processing information regardless of the datum selected by the user. Position information in the GPS receiver is presented to the user in whatever datum the user selects. The datum chosen by the user is for display purposes only, and is not used by the receiver for internal processing. It’s up to the GPS user to find out what datum and coordinate system data should be collected in prior to using a GPS receiver. 

## Datum Shift

**Notes:**
Datum Shift Example

	When there is a datum change, coordinate values change for all points on the ground.
“The coordinate system grid moves, while the ground remains stationary.”
	Switching from one datum to another, whether in a GPS receiver or on a map, results in different coordinate values for the same location on the ground. This is because the point of origin for each datum may be slightly different.
	The graphic example above uses Universal Transverse Mercator (UTM) coordinate system (described later) to demonstrate datum shift. Each UTM grid square is one kilometer (1,000 meters) on a side, and its position on the map is defined by the numbers along the left and bottom edges of the map. In the example, the Highlands School is 700 meters to the east of the UTM gridline nearest to it on the left, and 275 meters north of the nearest UTM gridline below the school (as shown by the arrows and numbers).
	Recalling that different datums can change the coordinate system values for points and features on the ground, the distances from the grid lines west and south of the school will correspondingly change. This is because the grid, not the map features or points on the ground, moves when a switch in datums occurs. Introducing a new datum to the map gives every feature on that map a new set of coordinates. Using the school as an example, and NAD27 as the map’s datum, the school’s coordinates are: 700 meters east of grid line 541, and 275 meters north of grid line 4789.
The next slide shows how those coordinates for the school change when datum NAD83 is used on the map instead of NAD27. 

## Datum Shift

**Datum Shift**

**Notes:**
Datum Shift Example

	In the graphic example above, the features on the map remain stationary, just as they do on the ground (the school has not moved). By switching the UTM grid from datum NAD27 to NAD83 has shifted the coordinate system grid on the map resulting in a new set of coordinates tied to NAD83, not NAD27: 600 meters east of grid line 541, and 350 meters north of grid line 4789.
	Compare that to the NAD27 coordinates for the school on the previous page.
	Since UTM is based on the metric system, the amount of offset between NAD27 and NAD83 can be easily measured. The difference between NAD27 and NAD83 is 100 meters (700 – 600), or 328 feet from the new NAD83 grid line to the west of the school. The difference is 75 meters (350 – 275), or about 230 feet for the NAD83 grid line to the south of the school. A person navigating by GPS using NAD27 coordinates programmed into a receiver that has its datum incorrectly set to NAD83 will end up at a point 100 meters east and 75 meters south of the desired destination. While this difference isn’t much, the difference between other datums can be much greater.

## Datum Shift

**Datum Shift**

**Notes:**
	On an incident, datum shift can create a potentially dangerous situation if the coordinates refer to a safety zone, drop point, medivac point, helispot, or other such point. To ensure correct datum matching, the GPS user should always verify the datum for any coordinates prior to inputting those coordinates into a GPS receiver. It’s best if all GPS users on an incident should operate with one datum and coordinate system standard on the ground (air operations may have to use another datum).
	To alleviate potential datum errors, the GPS user should follow these guidelines:
The National Wildfire Coordinating Group (NWCG) GPS datum standard is NAD83 (same as WGS84). Unless directed otherwise, set GPS receiver datum to NAD83. 
When receiving coordinates provided by another person, always obtain the datum used to derive those coordinates, and use that datum as well.
When plotting coordinates from any map, determine the datum used on the map from the map’s legend.
When passing on coordinates to other GPS users, provide them with the datum those coordinates were derived in.
Always set a GPS receiver to the correct datum before entering coordinates into the receiver.

## Datum Shift

**Datum Shift**

**A set of coordinates can yield different positions due to different datums.**

**NAD27 (true position)**

**NAD83/WGS84**

**WGS72**

**Bermuda 1957**

**NAD27 Greenland**

**Notes:**
Datum Shift

	The example above graphically shows how the same set of coordinates can have different locations on the ground due to different datums assigned to those coordinates. The school’s coordinates were derived using datum NAD27. Those same coordinates were then shifted by switching to the other datums shown above. The greatest shift is with datum Bermuda 1957, which places the school’s coordinates approximately 1⁄2 mile from where it should be.
	* Always set a GPS receiver to the correct datum before entering coordinates into a GPS receiver.

## GPS Operates in WGS84 & ECEF

**GPS Operates in WGS84 & ECEF**

- The receiver’s processor _always_ works in datum WGS84 and coordinate system ECEF. The user cannot change this.

- The user can only change the way  coordinates are _displayed_ by selecting the datum and coordinate system.

**Datum Displays**

**Coordinate System Displays**

**Notes:**
GPS Uses  Datum WGS84 and Coordinate System ECEF

	All GPS receivers process information internally using only one datum and one coordinate system. That datum is World Geodetic System 1984 (WGS84), and since 1987 has been the default datum used by the Global Positioning System. All calculations in a GPS receiver, including storing waypoint coordinates, are performed using the WGS84 datum. When a GPS user changes the datum in the receiver’s setup page, only the way coordinates are displayed on the GPS receiver screen changes. The receiver continues to execute all functions and calculations in WGS84 invisible to the user.
	The Global Positioning System also has its own coordinate system, called Earth Centered Earth Fixed (ECEF). Unlike the datum WGS84, which is found outside of the GPS, the coordinate system ECEF is unique to the Global Positioning System, and is not found outside of GPS. It resides only in the processors of GPS computers and receivers. There is no selection for ECEF in a receiver’s list of coordinate systems. And, like a datum, whenever a user changes the coordinate system in a receiver, only the way coordinates are displayed on the receiver screen changes. The receiver continues to perform all calculations in ECEF regardless of the coordinate system selected by the user. 

## GPS Uses WGS84 & ECEF

- User selects the datum and coordinate system _for display only_.

- GPS receiver’s processor _always_ performs calculations in WGS84 and Earth Centered Earth Fixed (ECEF) coordinate system.

**Datum**

**Coordinate System**

## 
A map is a two-dimensional representation of the Earth.
Maps incorporate projections and datums to provide a way to reference locations on the map to features on the ground (via coordinate systems).
All maps distort the Earth to some extent.
Many different types of maps can be used with GPS.
When using a GPS receiver with a map, the datum and coordinate system in the receiver must match the map datum.

- A map is a two-dimensional representation of the Earth.
- Maps incorporate projections and datums to provide a way to reference locations on the map to features on the ground (via coordinate systems).
- All maps distort the Earth to some extent.
- Many different types of maps can be used with GPS.
- When using a GPS receiver with a map, the datum and coordinate system in the receiver must match the map datum.

- Maps

**Notes:**
Maps

A map is a two-dimensional representation of the Earth.
Maps incorporate projections and datums to provide a way to reference locations on the map to physical features on the ground.
All maps distort the Earth to some extent (due to the projection).
Many different types of maps can be used with GPS.
When using a GPS receiver with a map, the datum and coordinate system in the receiver must match the map’s datum.

## Mapped, edited, and published by the Geological Survey
Control by USGS USC&GS
Topography from aerial photographs by multiplex methods
and by plane-table surveys 1953. Aerial photographs taken 1951
Polyconic projection.     1927 North American Datum
10,000 foot grid based on Idaho coordinate system, west zone
1000-meter Universal Transverse Mercator grid ticks,
1000-meter Universal Transverse Mercator grid ticks, zone 11, shown in blue
To place on the predicted North American Datum 1983 move the projection lines 15 meters north and 77 meters east as shown by dashed corner ticks

**Control by USGS USC&GS**
**Topography from aerial photographs by multiplex methods**
**and by plane-table surveys 1953. Aerial photographs taken 1951**
**Polyconic projection.     1927 North American Datum**
**10,000 foot grid based on Idaho coordinate system, west zone**
**1000-meter Universal Transverse Mercator grid ticks,**
**1000-meter Universal Transverse Mercator grid ticks, zone 11, shown in blue**
**To place on the predicted North American Datum 1983 move the projection lines 15 meters north and 77 meters east as shown by dashed corner ticks**

**UTM GRID AND 1971 MAGNETIC NORTH**
**DECLINATION AT CENTER OF SHEET**

**Example of a USGS Map Legend**

**Notes:**
Example of a USGS Map Legend

	This diagram shows only that portion of the map legend pertaining to datum, coordinate system, and north reference. U.S. Geological Survey topographic maps are drawn with information gathered by surveys, ground observations, and aerial photography.
	The datum currently used for most USGS 7 1/2 minute maps is NAD27 (see graphic above), although some new maps are being drawn using datum NAD83. Grid ticks in the lower left and right corners of the map (not shown on all maps) presents the NAD83 projection (as shown in the example). The legend may also describe the datum shift in meters from NAD27 to NAD83 (see graphic).
	Latitude and longitude forms the basis for the map. That’s why this type of map is referred to as “7 1/2 minute quadrangle,” because it’s printed using a 7.5 minute lat/long grid.
Universal Transverse Mercator (UTM), another coordinate system, is represented on USGS quadrangle maps by 1,000 meter ticks (blue on older maps), or a fine black grid (on newer maps). The UTM zone for the map is shown in the legend (see middle text box in the graphic). (More about UTM later.)
True north, compass and magnetic declination information is presented at the bottom of the legend. True north is represented by the vertical line with the star at the top. Magnetic north is shown by “MN.” Declination is shown in degrees and mils (there are 6400 mils in a circle, just as there are 360 degrees in a circle). In the graphic, grid north is 0o 28’ (also 8 mils). Magnetic north is shown as 18 1/2o (329 mils).

## Mapped, edited, and published by the Geological Survey
Control by USGS USC&GS
Topography from aerial photographs by multiplex methods
and by plane-table surveys 1953. Aerial photographs taken 1951
Polyconic projection.     1927 North American Datum
10,000 foot grid based on Idaho coordinate system, west zone
1000-meter Universal Transverse Mercator grid ticks,
1000-meter Universal Transverse Mercator grid ticks, zone 11, shown in blue
To place on the predicted North American Datum 1983 move the projection lines 15 meters north and 77 meters east as shown by dashed corner ticks

**Control by USGS USC&GS**
**Topography from aerial photographs by multiplex methods**
**and by plane-table surveys 1953. Aerial photographs taken 1951**
**Polyconic projection.     1927 North American Datum**
**10,000 foot grid based on Idaho coordinate system, west zone**
**1000-meter Universal Transverse Mercator grid ticks,**
**1000-meter Universal Transverse Mercator grid ticks, zone 11, shown in blue**
**To place on the predicted North American Datum 1983 move the projection lines 15 meters north and 77 meters east as shown by dashed corner ticks**

**UTM GRID AND 1971 MAGNETIC NORTH**
**DECLINATION AT CENTER OF SHEET**

**Example of a USGS Map Legend**

**Notes:**

	All rectangular grids are afflicted to some extent with direction distortion. Grid North (represented by “GN” in the compass and declination graphic) is shown as east or west of true north by x number of degrees. Grid north is the direction that a north-south grid line points on a rectangular coordinate system. Grid north refers to the declination angle (relative to true north) of a vertical grid line in a rectangular coordinate system. The grid declination varies in relation to the grid’s point of origin. In the case of the UTM coordinate system, grid declination is always zero along the central meridian of each UTM zone. To the east of the Central Meridian, grid declination will be east (the vertical grid lines point east of true north). To the west of the meridian, grid declination will be west (the vertical grid lines point west of true north). A point to note, in the UTM coordinate system grid north can never deviate more than 3o from true north on any map (refer to UTM section). 

## All coordinate systems reference some particular set of numbers for the size and shape of the Earth (the datum).
Coordinate systems are used to designate locations within a datum.
There are two types of coordinate systems:
Angular coordinate system (lat/long is one)
Rectangular (Cartesian) coordinate system (UTM is one)
Latitude and longitude, and Universal Transverse Mercator are two global coordinate systems commonly used with GPS.
Many other coordinate systems exist worldwide.

- All coordinate systems reference some particular set of numbers for the size and shape of the Earth (the datum).
- Coordinate systems are used to designate locations within a datum.
- There are two types of coordinate systems:
- Angular coordinate system (lat/long is one)
- Rectangular (Cartesian) coordinate system (UTM is one)
- Latitude and longitude, and Universal Transverse Mercator are two global coordinate systems commonly used with GPS.
- Many other coordinate systems exist worldwide.

**Coordinate Systems**

**Notes:**
Coordinate Systems

	Coordinate systems provide unique descriptions of geographic locations using numeric or alphanumeric characters. Think of coordinates as addresses similar to street addresses. For example, the location “1234 S. Main St” can also be described with map coordinates, such as “11T 565700E  4756500N.” A key component for any coordinate system is the datum. 
Recall that datums provide coordinate systems with an Earth tie (a geographic reference point), and that without a datum, coordinate values cannot reference geographic points on the ground, and therefore will have no meaning. Datums and coordinate systems work in conjunction with each other to provide a link between maps and the physical world. 
Two common types of global coordinate systems are:
Angular (geographic) Coordinates (such as latitude and longitude)
Rectangular (Cartesian) Coordinates (such as Universal Transverse Mercator)
Other coordinate systems are also available in GPS receivers. 

## Coordinate Systems

**hddd****0**** mm’ ss.s”: N 43****0 ****40’  **_**55.8”**_**  X  W 116****0 ****17’ 14.1”**
**(**_**55.8”**_** ****/ 60 =**** ****.93’****)**

**Different coordinates representing the same location:**

**UTM:****	****	****	****11T  0557442m E     4836621m N**

## Latitude & Longitude

**Latitude & Longitude**

**Notes:**
Latitude and Longitude

## A geographic (spherical) coordinate system.
Coordinates are angular, perfectly suited to the round shape of the Earth.
Coordinates are expressed in degrees, minutes and seconds (and two other variations of that).
Position coordinates are based on an angular distance from a known reference point.
That reference point is where the Prime Meridian and equator intersect in the Atlantic Ocean near Africa.
Lat/long is the predominant coordinate system used for nautical and aeronautical navigation.

- A geographic (spherical) coordinate system.
- Coordinates are angular, perfectly suited to the round shape of the Earth.
- Coordinates are expressed in degrees, minutes and seconds (and two other variations of that).
- Position coordinates are based on an angular distance from a known reference point.
- That reference point is where the Prime Meridian and equator intersect in the Atlantic Ocean near Africa.
- Lat/long is the predominant coordinate system used for nautical and aeronautical navigation.

- Latitude & Longitude

**Notes:**
Latitude & Longitude

	Latitude and longitude (lat/long) is a spherical, or angular, coordinate system perfectly suited to the three-dimensional shape of the Earth. Points or locations are based on an angular distance from a known reference point. That reference point is where the Prime Meridian and the equator meet in the South Atlantic Ocean. In lat/long the Earth is divided into 360 degrees east and west. Each degree is divided into 60 minutes, and each minute into 60 seconds. Each second can be further divided into fractions (or decimals) of a second. Latitude and longitude is the predominant coordinate system used for marine and aeronautical navigation. Aircraft use degrees and decimal minutes for expressing lat/long coordinates. Mariners prefer degrees, minutes and seconds.
	* The NWCG coordinate system standard is latitude and longitude (degrees, minutes and seconds). Unless directed otherwise, set GPS receiver coordinate system to lat/long, degrees, minutes and seconds (hddd mm ss.s). 

## Latitude & Longitude

**Latitude & Longitude**

**Notes:**
Latitude & Longitude (cont.)

	The point of origin for latitude and longitude on the Earth’s surface is where the Prime Meridian and the equator intersect. Geographically that point is just west of Africa in the South Atlantic Ocean. Lines of latitude (known as “parallels”) slice through the Earth horizontally. Lines of longitude (known as “meridians”) slice through the Earth vertically. 

## Latitude & Longitude

**Notes:**
Latitude & Longitude (cont.)

	The Prime Meridian runs north to south through Greenwich, England (specifically through the Royal Naval Observatory located in the town of Greenwich). The equator runs east to west around the Earth’s mid section. Where the two intersect is expressed as “0 degrees north latitude, 0 degrees east longitude.” Everything west of the Prime Meridian is defined as “west longitude,” and everything east is defined as “east longitude.” Similarly, everything north of the equator is defined as “north,” and everything south of the equator is defined as “south.” 

## Latitude is comprised of parallels, which are equally spaced circles around the Earth paralleling the equator.
Parallels are designated by their angle north or south of the equator (10o, 20o, etc) .
The equator is 0o latitude, and the North and South Poles are at 90o angles from the equator.
The linear distance between parallel (latitude) lines never changes, regardless of their position on the Earth.

- Latitude is comprised of parallels, which are equally spaced circles around the Earth paralleling the equator.
- Parallels are designated by their angle north or south of the equator (10o, 20o, etc) .
- The equator is 0o latitude, and the North and South Poles are at 90o angles from the equator.
- The linear distance between parallel (latitude) lines never changes, regardless of their position on the Earth.

- Latitude

**Notes:**
Latitude & Longitude (cont.)

	Latitude is comprised of parallels, which are equally spaced circles around the Earth paralleling the equator. Parallels are designated by their angle north or south of the equator (10o, 20o, etc.). The equator is zero degrees latitude, and the North and South Poles are at 90 degree angles from the equator. The linear distance between parallel (latitude) lines never changes, regardless of their position on the Earth. The distance between parallels one degree apart is approximately 69 miles, whether measured at the equator, or at the North or South Poles. In other words, parallels are always equidistant from each other. 

## Parallels of Latitude

**10o**

**10o**

**10o**

**690 miles**

**690 miles**

**690 miles**

**10o S**

**0o N**

**10o N**

**20o N**

**Notes:**
Parallels of Latitude

	The distance between each degree of latitude does not change, regardless of where it lies in relation to the equator. This differs from longitude where lines converge as they approach the North and South Poles. 

## Longitude is comprised of meridians that form one-half of a circle, or plane.
Meridians are designated by their angle west or east of the prime meridian.
The Prime Meridian is designated 0o and extends from the North Pole to the South Pole through Greenwich, England.
Meridians are angled, and so are not equidistant from each other at different points. 
The linear distance between one degree of longitude at the equator is approximately 69 statute miles.
The linear distance between one degree of longitude at the arctic circle is only about 26 statute miles.

- Longitude is comprised of meridians that form one-half of a circle, or plane.
- Meridians are designated by their angle west or east of the prime meridian.
- The Prime Meridian is designated 0o and extends from the North Pole to the South Pole through Greenwich, England.
- Meridians are angled, and so are not equidistant from each other at different points.
- The linear distance between one degree of longitude at the equator is approximately 69 statute miles.
- The linear distance between one degree of longitude at the arctic circle is only about 26 statute miles.

- Longitude

**Notes:**
Longitude

	Longitude lines are a bit different from latitude lines. Longitude is comprised of meridians that form one-half of a circle, or plane that slices through the Earth. A meridian actually splits the Earth in half from top to bottom (Pole to Pole). Meridians originate at the center of the Earth and radiate outward into space at specific angles. Those angles designated by their angle west or east of the Prime Meridian. The Prime Meridian is designated 0o and extends from the North Pole to the South Pole through Greenwich, England. Meridians do not parallel each other at an equal distance, which is the primary difference they have with lines of latitude.
	The linear distance of one degree of longitude at the equator is approximately 69 statute miles (same as latitude). However, the linear distance of one degree of longitude at the Arctic Circle is only about 26 statute miles. This is because longitude lines converge as they get closer to the North and South Poles, and diverge as they get closer to the equator. 

## Meridians of Longitude

**10o**

**10o**

**110o W**

**120o W**

**690 miles**

**460 miles**

**240 mi**

**10o**

**Equator**

**To North Pole**

**To South Pole**

**Notes:**
Meridians of Longitude

	Longitude lines (meridians) run north to south, but partition the Earth into east and west halves. Unlike latitude, the distance between each degree of longitude narrows as the distance away from the equator increases. 

## Determining Latitude & Longitude

**Determining Latitude & Longitude**

**50o W**

**30oN, 50oW**

**Notes:**
Determining Latitude & Longitude

	The location defined as latitude 30o degrees north, and longitude 50o west is derived simply by counting the parallels (latitude lines) north from the equator, and the meridians (longitude lines) west from the Prime Meridian. In the example above, where the parallel and the meridian meet is described as 30o N and 50o W. The coordinates are defined as “north” because the point lies north of the equator. The coordinates are defined as “west” because the point lies west of the Prime Meridian. 

## Determining Latitude

**Determining Latitude**

**Each tick mark = 5 seconds**

**Notes:**
Determining Latitude on a Map

	To determine the coordinates in latitude and longitude for the square in the example above requires a two step process: determine latitude first, then longitude (the steps can be reversed). The grid lines represent lines of latitude and lines of longitude. These lines must be drawn on a USGS 7 1⁄2 minute quad map. Since 7 1⁄2 minute quad maps are created based on latitude and longitude, then the lines that form the border of the printed edge of the map are also lines of latitude and longitude (called the “neat line”).
	The first step to determine the square’s location in latitude is to locate the two latitude lines above and below the square (represented by the heavy lines in the example). Along the neat lines printed on the map are coordinate values for the two lines above and below the square to be plotted. In the example above these lines are identified as 44o 15’ 00” and 17’ 30”.
	Next, slide the lat/long ruler next to the point to be plotted, making sure to line up the top and bottom tick marks on the ruler with the lines of latitude as shown by the arrows pointing at the ruler. The ruler may have to skewed (rotated) slightly to get the ruler to line up precisely with the latitude lines.
Once the ruler is in place as shown in the example, count the tick marks from the lower latitude line upward until you reach the one closest to the square. Depending on the ruler being used, the ruler tick marks may be in seconds, or tenths of a minute. In the example, the number of tick marks counted equals one minute and 30 seconds (the ruler in the graphic is for representation only, and is not drawn to scale). Recalling that the map gave the location of the lower latitude line as 44o 15’ 00”, simply add the 1’ 30” counted between the latitude line and the square being plotted to the 44o 15’ 00”. This gives a position of 44o 16’ 30”. (Remember, there are 60 seconds in a minute, and 60 minutes in a degree.) 

## Determining Longitude

**Determining Longitude**

**Longitude of red square =**
**115o 19’ 00”**

**Each tick mark = 5 seconds**

**Notes:**
Determining Longitude on a Map

	The process for determining longitude is similar to that for determining latitude. First, find the two meridians on either side of the point you want to plot (the square in the example above). Skew the ruler so that the end tick marks on either side of the ruler line up with the two meridians on either side of the point being plotted as shown. Slide the ruler up or down until it is adjacent to the point to be plotted.
	In the example, the longitude line to the east of the square is identified with the coordinate 115o 17’ 30.” This is the value to add the counted ruler tick marks to. If the point being plotted lies in the western hemisphere, count degrees, minutes and seconds from right to left (east to west).
	Remember that counting minutes and seconds in lat/long is the same as counting minutes and seconds on a clock. When the seconds count reaches 60, carry over and add 1 minute to the minute’s number in the coordinates, then start counting seconds again from zero. When the minutes count reaches 60, carry 1 degree over and add it to the degrees number, and start counting minutes again from zero. Using the example in the slide, see how this is done.
	The longitude location of the square in the example (the ruler tick marks equal 5” each) is 1 1⁄2 minutes west of the longitude line, so that value is added to 115o 17’ 30” to come up with 115o 19’ 00.”
The complete location of the square expressed in both latitude and longitude is: N 44o 16’ 30” X W 115o 19’ 00.” 

## Is a rectangular coordinate system based on the latitude and longitude coordinate system.
The Earth is divided into 60 UTM zones.
Sixty zones allows the Earth to be projected onto maps with minimal distortion.
UTM uses “false” values (easting and northing) to express coordinates.
Coordinates are expressed in meters.

- Is a rectangular coordinate system based on the latitude and longitude coordinate system.
- The Earth is divided into 60 UTM zones.
- Sixty zones allows the Earth to be projected onto maps with minimal distortion.
- UTM uses “false” values (easting and northing) to express coordinates.
- Coordinates are expressed in meters.

- Universal Transverse Mercator

**Notes:**
Universal Transverse Mercator (UTM)

	The Mercator projection was created by Gerardus Mercator in 1569 as a navigation aid for mariners. In the 1700’s Johann Lambert modified Mercator’s projection to create what eventually came to be known as “Universal Transverse Mercator,” in common use today. A modified version of UTM is used by the U.S. military, and is referred to as the Military Grid Reference System (MGRS).
	UTM is a rectangular (or “Cartesian”) coordinate system, but is actually based on the angular coordinate system of latitude & longitude. It’s a grid that allows the Earth’s spherical surface to be projected onto paper with a minimal amount of distortion, which makes it nearly perfect as a coordinate system for maps.
UTM divides the Earth into 60 zones. Each zone is 6o of longitude wide and extends from 84o N latitude to 80o S latitude. (Above those latitudes Universal Polar Stereographic, or UPS, is used.) Each zone’s central meridian is centered exactly on a line of longitude. UTM uses false values (called “easting” and “northing”). All UTM coordinates are expressed in meters. 

## UTM Coordinates

**4789650**

**UTM Coordinates**

**Notes:**
Universal Transverse Mercator Coordinates - What They Mean

	Universal Transverse Mercator uses coordinates that can be divided into four parts. The UTM zone number refers to the particular zone of the Earth the rest of the coordinates reference. There are 60 UTM zones covering the Earth, beginning with number one at 180o west longitude, and ending with number 60 at 180° east longitude. By slicing the Earth into 60 zones, projection distortion is kept to a minimum.
Each zone is independent of the other zones. Because of this every UTM zone can have the same coordinate values for different points on the ground. A set of coordinates without a specified UTM zone can define 60 different points, one in each zone, around the world in the northern hemisphere alone. There are another 60 possible points for those same coordinates in the southern hemisphere as well. The latitude band letter defines which hemisphere (southern or northern) a set of coordinates lies in.
	So how does a GPS receiver know which hemisphere it’s in? Usually it knows from two pieces of information: its last known position, and a downloaded satellite almanac. If a user turns on a GPS receiver in Boise, Idaho, the receiver will download an almanac from the GPS satellite constellation, and will know it’s in the northern hemisphere. However, if the user takes that receiver to Sydney, Australia, then turns the receiver on, the receiver will have to download a new almanac, and then will know that it’s now in the southern hemisphere. 
	When manually inputting UTM coordinates into a GPS receiver, the receiver can select the correct latitude band letter based on the northing coordinate value entered by the user along with almanac information collected the last time the receiver was used.

## UTM Coordinates

**4789650**

**UTM Coordinates**

**Notes:**
	The easting coordinate refers to a “false” value defining a zone’s central meridian, which is given a default value of 500,000 meters. The central meridian does not reference any geographical point on the ground, hence the “false” designation. An easting number below 500,000 will be west of that zone’s central meridian (zone 11 in the example above), and a value higher than 500,000 meters will be east of that zone’s central meridian. The central meridian in each zone is directly tied to a meridian of longitude. Each half of a zone is equal to three degrees of longitude. By keeping zones to only three degrees of total width on each side of a central meridian, projection distortion is kept to a minimum even on a global scale.
	The northing coordinate refers to a position in relation to the equator. In the northern hemisphere the equator is given a northing value of zero meters north. The higher the northing number, the farther north the point is from the equator. In the above example, the northing value 4789650  means 4,789,650 meters north of the equator (or 4,789 kilometers and 650 meters north of the equator).
	In the southern hemisphere northing coordinates start at a false value of 10,000,000 meters at the equator. Coordinates in the southern hemisphere decrease the farther south one travels from the equator. 

## UTM Coordinates

**9****650**

**11T**

**05**
**47**

**4**
**8**

**UTM Coordinates**

**You need only plot the black numbers on the map. The rest of the coordinate values are provided for you by the map.**

**Notes:**
UTM Coordinates

	Since UTM coordinates are based on the metric system, it’s easy to determine distances based on UTM coordinates. Easting coordinates can never exceed 999,999 meters in any one zone, so the value will never exceed six digits (though some GPS receivers require a preceding “0” to be entered in the coordinate value – as shown in the example). Northing coordinate values can exceed seven digits, and are based on the distance a point is from the equator.
	A UTM zone is comprised first of 100,000 meter squares forming a grid. These squares are broken into 10,000 meter squares, which are broken into 1,000 meter squares (one square kilometers). A 7 1⁄2 minute USGS map will have UTM tick marks printed along the neat line at 1,000 meter (one kilometer) intervals. The coordinate values for those tick marks are also printed on the map. For easting coordinates those values will be the first three digits in the coordinate (“541” in the example above), and for northing values they will be the first four digits (“4789” in the example above). The map legend will also provide the zone number, but not the latitude band letter. 

## UTM Grid Overlay

**1**

**60**

**UTM Grid Overlay**

**60 Zones, and 20 Latitude Bands**

**Zones**

- Equator

**Notes:**
Universal Transverse Mercator

Note: The grid shown in the example is not drawn to scale.
	There are 60 UTM zones, extending north-south and covering all of the Earth, beginning with zone 1 located at 180o W longitude. Twenty latitude bands, extending east-west, cover most of the Earth from 80o S latitude to 84o N latitude. The polar regions above and below those latitudes are covered by the Universal Polar Stereographic coordinate system, which is similar to the UTM coordinate system. Notice that the letters “I” and “O” are not used to designate latitude bands. This is to prevent confusion with the numbers “one” and “zero.” The equator separates latitude bands N (north of the equator), and M (south of the equator). If a GPS receiver is showing a UTM position with a latitude band letter of C through M, then it’s in the southern hemisphere. If the latitude band letter shown on a GPS receiver display is N through X then the receiver is in the northern hemisphere.
	Each UTM zone is 6° of longitude wide. By knowing the correct zone number and latitude band letter, you can narrow your location from the entire surface of the Earth down to a rectangle 6° x 8°, as shown in the example above with zone 21, latitude band T (21T). The easting and northing numbers refine the position to a single point somewhere inside that rectangle. 
	Try this test with your GPS receiver. Set your receiver coordinate system to UTM. Get a UTM position of your present location, and save it as a waypoint. Remember the UTM zone number. Now change the coordinate system in the receiver to latitude and longitude (it doesn't matter which format you select). Next edit the waypoint in lat/long by changing just the longitude to a new value. For example, if the original waypoint longitude shows 115° 10' 30", change the degrees from 115° to 80°. Save the modified waypoint, and change the lat/long coordinate system back to UTM in the receiver's setup page. Now look at the saved waypoint once again in UTM. Notice how the UTM zone number has changed to reflect the new coordinates edited in lat/long. Try the same test again, only this time leave the coordinates in UTM. Change only the northing coordinate by a large amount (for example, more than a million) and notice how the latitude band changes automatically the moment you save the edited waypoint. 

## UTM Zones in the Contiguous U.S.

**Notes:**
UTM Zones Covering the Contiguous U.S.

The continental United States lies within ten UTM zones. UTM zone boundaries are determined by longitude meridians six degrees apart.

## UTM Zones - Side by Side

**Zones:  11****	**** 12****	****13****	****14      15      16**

**Notes:**
UTM Zones - Side by Side

	The 60 zones that make up the UTM coordinate system are independent of each other, and have no association with each other. The North and South Poles are covered by the Universal Polar Stereographic (UPS) coordinate system above 84o degrees north, and 80o south latitudes. In the northern hemisphere the UTM grid ends at 84o north latitude, and in the southern hemisphere it ends at 80o south latitude. At the equator each UTM zone is less than a million meters wide, so no UTM zone exceeds one million meters in width (hence only six digits are required in easting coordinate values). At 84o N latitude, each UTM zone is less than 200,000 meters wide. 

## UTM Uses a Cartesian Grid

**Notes:**
UTM Uses a Cartesian Grid

	Universal Transverse Mercator is a grid system made up of perfectly shaped squares. Each square has a starting point just like an x and y grid. Coordinate values increase along the x axis as they move to the right (to the east), and increase along the y axis as they move up (to the north). By thinking of each square in the UTM grid drawn on a map in this way can help minimize errors when plotting coordinates on the map.

## Plotting UTM Coordinates

**House coordinates = 0541450mE**
**4789650mN**

**UTM grid reader**

**Place the corner of the UTM grid reader on the point to be plotted**

**542**

**543**

**4790**

**4791**

**1,000 m**

**Each tic = 100 meters**
**on this grid reader (your****grid reader has 20 meter tics)**

**Notes:**
Plotting UTM Coordinates on a Map

	First, match the scale of the UTM grid reader device to the scale of the map (for example, 1:24,000). Both scales must match. Place the UTM grid reader so that the “0” corner mark is over the point you want to determine the coordinates of. Read the easting value from the point where the grid overlaps the first UTM grid line to the west (left) of the point being plotted. Add the numeric value derived from the grid reader to the three digit easting value for that grid line printed on the map (outside the neatline). In the example above, the first three digits for the easting value for the house are found on the map for the grid line identified as “541.” The gird reader in the example shows that the house is 450 meters east of the first grid line to the left of the house. Append (don’t add the two together) 450 to the end of 541 to establish the easting coordinate for the house: 541450E. (Some GPS receivers require a preceding zero in front of easting coordinates, but this is not required when expressing easting coordinates.)
	Do the same for the northing coordinate, using the UTM grid line found just below the point being plotted. In the example that grid line is identified as “4789.” The grid reader shows that the house is about 650 meters to the north of grid line 4789. Put the two numbers together to get 4789650N. Add the zone number found in the map legend and the complete coordinates for house are: 11T 541450E  4789650N.

## Precision and accuracy are not the same.
Precision refers to how small an area coordinates can be defined or plotted.
GPS lat/long coordinates can be defined to 1/10 of a second.
UTM coordinates can be defined down to one meter.
Accuracy refers to how closely a GPS receiver can determine its position relative to its true location on the ground.
GPS accuracy can vary from a few millimeters to several kilometers.

- Precision and accuracy are not the same.
- Precision refers to how small an area coordinates can be defined or plotted.
- GPS lat/long coordinates can be defined to 1/10 of a second.
- UTM coordinates can be defined down to one meter.
- Accuracy refers to how closely a GPS receiver can determine its position relative to its _true_ location on the ground.
- GPS accuracy can vary from a few millimeters to several kilometers.

- A Final Word:Precision vs Accuracy

**Notes:**
Precision vs. Accuracy

	Precision refers to how close coordinates for a location can be defined on the Earth or on a map. In the field, coordinates for a point on a USGS 7 1/2 minute quadrangle map can usually be defined to within 10 or 20 meters. For example, if you are plotting coordinates on a map in UTM, and your grid reader has ticks 20 meters apart, then your precision will probably be around 20 meters, maybe a little closer.
	UTM coordinates in GPS receivers are expressed to one meter. But users generally cannot define a point to that level of precision when plotting UTM coordinates on a map. Most of the time the user need only round off those coordinate numbers to around ten or twenty meters. 
	Accuracy refers to how close a GPS receiver can pinpoint a user’s true location on the ground. Accuracy has nothing to do with how precisely a position can be defined. Because of errors inherent in the Global Positioning System most GPS receivers cannot provide a position with the accuracy of one meter to match the one meter precision of the GPS coordinates entered into the receiver.
	So, even though a GPS receiver can define UTM coordinates down to one meter (or similarly close in other coordinate systems) does not mean that the receiver is accurate to one meter. The receiver is merely expressing the coordinates of where it thinks it is, or a waypoint, down to one meter. But where the receiver thinks it is, and where it actually is, may be different by hundreds of meters or more. 

## Using GPS with Maps

**Objectives revisited:**
-  Identify two datums common to the U.S.
-  Identify the two “global” coordinate systems most commonly used with GPS receivers.
-  Describe “datum shift,” and the relevance it has when using GPS in the field.
-  Describe the four components that make up UTM coordinates.
-  Identify the three ways that lat/long coordinates can be expressed.

**Notes:**
Using GPS with Maps
Lesson Objectives:
Identify two datums common to the U.S:
North American Datum 1927 (NAD27) and North American Datum 1983 (NAD83).
Identify the two “global” coordinate systems most commonly used with GPS:
Latitude and longitude, and UTM.
Describe “datum shift,” and the relevance it has when using GPS in the field:
When there is a change in datums, coordinate values change for all points on the ground. You must know the datum that any coordinates were derived in to be able to accurately use those coordinates.
Describe the four components that make up UTM coordinates:
Zone number, latitude band letter, easting and northing
Identify the three ways that lat/long coordinates can be expressed:
Degrees, minutes and seconds; degrees, decimal minutes; and decimal degrees