# Presentation: 532199

**Using GPS with Maps**

## GPS’ Own Internal System

**GPS Ellipsoid: GRS-80**
**(Geodetic Reference System 1980)**

**GPS Datum: WGS-84**
**(World Geodetic System 1984)**
**(equivalent to NAD-83)**

**GPS Coordinate System: ECEF**
**(Earth Centered Earth Fixed)**

## Modeling the Earth

**Ellipsoids and Geoids**

## Both are mathematical formulas used to represent the earth’s surface so that it can be projected onto maps.
An ellipsoid treats the earth as a smooth, featureless sphere, and approximates the shape of the earth at sea level without regard to land masses. GPS uses ellipsoid.
A geoid is an imaginary representation of the earth characterized by constant gravity, which corresponds to the average level of the oceans (mean sea level), and to vertical locations on land masses that have the same constant gravity as mean sea level. USGS maps use geoid to generate height above MSL.

- Both are mathematical formulas used to represent the earth’s surface so that it can be projected onto maps.
- An ellipsoid treats the earth as a smooth, featureless sphere, and approximates the shape of the earth at sea level without regard to land masses. GPS uses ellipsoid.
- A geoid is an imaginary representation of the earth characterized by constant gravity, which corresponds to the average level of the oceans (mean sea level), and to vertical locations on land masses that have the same constant gravity as mean sea level. USGS maps use geoid to generate height above MSL.

**Ellipsoid & Geoid**

## Ellipsoid & Geoid

**Geoid (USGS Maps)**

**Ellipsoid (GPS)**

**Topographic Surface**

**Earth**

## Projecting a Sphere Onto a Plane

## Types of Projections

## Two Different Projections of the U.S.

**Two Different Projections of the U.S.**

**Maps Datums,****& Coordinate Systems**

## A datum specifies the earth-model (ellipsoid), and the origin associated with a particular set of coordinates.
It’s a function of a projection. 
Datums provide the link between the earth and coordinate systems.
Without a datum, coordinates have no meaning.
There are many datums used worldwide.
Only one datum, WGS-84, is global, the rest are regional.

- A datum specifies the earth-model (ellipsoid), and the origin associated with a particular set of coordinates.
- It’s a function of a projection.
- Datums provide the link between the earth and coordinate systems.
- Without a datum, coordinates have no meaning.
- There are many datums used worldwide.
- Only one datum, WGS-84, is global, the rest are regional.

**Datum**

## NAD27 CONUS (Continental US)
NAD27 Alaska
NAD27 Canada
NAD83 CONUS (Continental US)
NAD83 Alaska
NAD83 Canada
WGS72
WGS84 (GPS internal datum)

- NAD27 CONUS (Continental US)
- NAD27 Alaska
- NAD27 Canada
- NAD83 CONUS (Continental US)
- NAD83 Alaska
- NAD83 Canada
- WGS72
- WGS84 (GPS internal datum)

**North American Datums**

## Datum Shift

**541**

**Map Corner**

**NAD83**

**610m**

**150m**

**Datum Shift**

**4790**

**542**

## 2 Datums = 2 Sets of Coordinates

## 
A map is a two-dimensional representation of the earth.
Maps incorporate projections and datums for accuracy.
All maps distort the earth to some extent.
Many different types of maps can be used with GPS.
When using a map with a GPS receiver, the datum and coordinate system must match.

- A map is a two-dimensional representation of the earth.
- Maps incorporate projections and datums for accuracy.
- All maps distort the earth to some extent.
- Many different types of maps can be used with GPS.
- When using a map with a GPS receiver, the datum and coordinate system must match.

**Maps**

## 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**

**Map Legend**

## All coordinate systems reference some particular set of numbers for the size and shape of the earth (the datum).
Coordinates designate locations within a spatial reference system (datum).
There are two types of global coordinate systems:
Angular Coordinates
Rectangular (Cartesian) Coordinates
Latitude and longitude, and Universal Transverse Mercator are two global coordinate systems used by 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).
- Coordinates designate locations within a spatial reference system (datum).
- There are two types of global coordinate systems:
- Angular Coordinates
- Rectangular (Cartesian) Coordinates
- Latitude and longitude, and Universal Transverse Mercator are two global coordinate systems used by GPS.
- Many other coordinate systems exist worldwide.

**Coordinate Systems**

## Coordinate Systems

**(**_**55.8”**_** ****/ 60 =**** ****.93’****)**
**hddd****0**** mm.mmm’:  N 43****0   **_**40.93’**_**  X  W 116****0  ****17.235’**
**(**_**40.93’**_** ****/ 60 =**** ****.68216****0****)**
**hddd.ddddd****0 ****:**** ****	****N 43.68216****0****  X  W 116.28725****0**
**UTM/UPS:****	****	****11T  0557442m E     4836621m N**

**Different coordinates representing the same location:**

**Coordinate Systems**

## Precision and accuracy are not the same.
Precision refers to how small an area coordinates can be defined.
GPS lat/long coordinates can be defined to 1/10 of a second on most C/A Code, GPS receivers.
UTM coordinates can be defined down to one meter.
Accuracy refers to how close GPS can place a receiver to its true location.
Accuracy can vary from a few centimeters to several kilometers.

- Precision and accuracy are not the same.
- Precision refers to how small an area coordinates can be defined.
- GPS lat/long coordinates can be defined to 1/10 of a second on most C/A Code, GPS receivers.
- UTM coordinates can be defined down to one meter.
- Accuracy refers to how close GPS can place a receiver to its true location.
- Accuracy can vary from a few centimeters to several kilometers.

**Precision vs Accuracy**

## Latitude & Longitude

**Latitude & Longitude**

## A spherical coordinate system that is unprojected.
Angular coordinates are perfectly suited to the spherical surface of the earth.
Coordinates are expressed in degrees, minutes and seconds (and 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.
Lat/long is the predominant coordinate system used for nautical and aeronautical navigation.

- A spherical coordinate system that is unprojected.
- Angular coordinates are perfectly suited to the spherical surface of the earth.
- Coordinates are expressed in degrees, minutes and seconds (and 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.
- Lat/long is the predominant coordinate system used for nautical and aeronautical navigation.

**Latitude & Longitude**

## Latitude & Longitude

**0o**

**0o**

**Point of Origin**

**Prime Meridian**

**Equator**

**(Longitude)**

**(Latitude)**

**10o N**

**30o N**

**10o S**

## Latitude & Longitude

**0o, 0o**

**Prime Meridian**

**Equator**

**10o**

**20o**

**W   30o**

**10o**

**20o**

**30o E**

**10o**

**20o**

**30o**

**10o**

**20o**

**30o**

**S**

**N**

**+**

## Latitude is comprised of parallels, which are circles around the earth paralleling the equator.
Parallels are rays that originate at the center of the earth. They are designated by their angle north or south of the equator.
The equator is 0o latitude, and the north and south poles are at 90o angles from the equator.
The linear distance between parallel lines never changes, regardless of their position on earth. That distance is approximately 69 miles per degree anywhere on earth.

- Latitude is comprised of parallels, which are circles around the earth paralleling the equator.
- Parallels are rays that originate at the center of the earth. They are designated by their angle north or south of the equator.
- The equator is 0o latitude, and the north and south poles are at 90o angles from the equator.
- The linear distance between parallel lines never changes, regardless of their position on earth. That distance is approximately 69 miles per degree anywhere on earth.

**Latitude**

## Parallels of Latitude

**Parallels of Latitude**

**10o**

## Parallels of Latitude

**10o**

**10o**

**10o**

**690 miles**

**690 miles**

**690 miles**

**10o S**

**0o N**

**10o N**

**20o N**

## Longitude is comprised of meridians that form one-half of a circle, or plane.
Meridians are rays which originate at the center of the earth.
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 do not parallel each other.
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 about 26 statute miles.

- Longitude is comprised of meridians that form one-half of a circle, or plane.
- Meridians are rays which originate at the center of the earth.
- 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 do not parallel each other.
- 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 about 26 statute miles.

**Longitude**

## Meridians of Longitude

**Meridians of Longitude**

**10o**

## Meridians of Longitude

**10o**

**10o**

**110o W**

**120o W**

**690 miles**

**460 miles**

**240 mi**

**10o**

## Determining Latitude & Longitude

**Determining Latitude & Longitude**

**50o W**

## Is a rectangular coordinate system derived from latitude and longitude.
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 derive coordinates.
Coordinates are expressed in meters.

- Is a rectangular coordinate system derived from latitude and longitude.
- 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 derive coordinates.
- Coordinates are expressed in meters.

**Universal Transverse Mercator**

## UTM Grid Overlay

**1**

**60**

**UTM Grid Overlay**

**60 Zones, and 20 Latitude Bands**

**Zones**

## UTM Zones Covering the Contiguous U.S.

**120****0**

**114****0**

**108****0**

**102****0**

**96****0**

**90****0**

**84****0**

**78****0**

**72****0**

**66****0**

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

**UTM Zones**

**Longitude**

## UTM Zones - Side by Side

**Equator**

**84****0 ****N**

**80****0 ****S**

**6****0**

**UTM Zones - Side by Side**

**6****0**

**6****0**

**6****0**

**6****0**

**6****0**

## UTM Zone Grid Overlay

**UTM Zone Grid Overlay**

**Central**
**Meridian**

**6o of Longitude**

**Zero East**

**500,000m E**

**<1,000,000 m E**

## Anatomy of a UTM Zone

**6****0**

**0000000 m N**

**increasing**

**10000000 m N**

**central meridian**

**Equator**

**decreasing**

**84****0 ****N**

**80****0 ****S**

**500000 m E**

**increasing**

**decreasing**

**Anatomy of a UTM Zone**

## UTM Coordinates

**0000000 m N**

**increasing**

**10000000 m N**

**Equator**

**decreasing**

**84****0 ****N**

**80****0 ****S**

**UTM Coordinates**

**Similar coordinates, but two different locations.**

**S 260500 7100500**

**N 260500 7100500**

## Zone to Zone Easting Changes

**East Edge of Zone 11**

**West Edge of Zone 12**

**750000m E**

**265000m E**

**600000m E**

**140000m E**

## UTM Coordinates

**4789650**

**UTM Coordinates**

## UTM Coordinates

**9650**

**11T**

**05**
**47**

**4**
**8**

**UTM Coordinates**

## UTM Coordinates

**400000**

**500000**

**600000**

**4500000**

**4600000**

**4700000**

**4800000**

**4900000**

**100,000 Meter Grid**

**10,000 Meter Grid**

**500000E**

**4750000**

**550000**

**600000**

**4700000N**

**(Red square = 10,000 sq m)**

**4800000**

**Red square is located at 54 E, and 478 N**

**UTM Coordinates**

## UTM Coordinates

**1,000 meter square**

**4785000**

**545000**

**550000**

**4790000**

**Red square is located at 541 E, and 4789 N**

**540000E**

**4780000**

**10,000 meter square**

**UTM Coordinates**

## UTM Coordinates

**541**

**542**

**543**

**4789**

**4790**

**4791**

**UTM Coordinates**

**Red house coordinates = 0541450mE**
**4789650mN**

## UTM uses a Cartesian Grid

**542**

**543**

**4790**

**4791**

**UTM uses a Cartesian Grid**

***x***

***y***

- Coordinates are calculated from lower left corner.

- Increasing

- Increasing

## UTM Principle Digits

**Map Corner**

**(Neatline)**

**Principle Digits**

**650m**

**350m**

**UTM Principle Digits**

## Using UTM to Determine Direction

**“****I am at 565400E, 4500500N”**

**W**

**E**

**S**

**N**

**+**

**decreasing**

**increasing**

**“****You are at 564900E, 4500200N”**

## Slide 46

## Determining Latitude

**44o 15’ 00”**

**17’ 30”**

**2.5 min**

**Latitude of red square =**
**44o 16’ 30”**

**Parallel**
**Lines**

## Determining Longitude

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

**115o 17’ 30”**

**20’**

**2.5 min**

**Meridian**
**Lines**