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Geospatial Mapping


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									                       Geospatial Mapping

GIS Introduction

GIS stands for Geographic Information System

Used by many industries
     - utilities, commerce, law enforcement, transportation,
       health care, agriculture, government
     - particularly good for land use planning, natural resource
       management, demographic analysis, environmental
       assessment, etc.

GIS is basically a system that integrates information about objects
located on the earth’s surface and enables this information to be
retrieved, analyzed, and presented.

Five Components of GIS

     1. People – individuals trained in the use of GIS who define
        problems and tasks to be performed
     2. Data – georeferenced information to be used in the tasks
     3. Hardware – computers, printers, plotters, GPS units,
     4. Software – GIS software, GPS software, conversion
        software, correction software, database software, drawing
        software, statistical software, imaging software, etc.
     5. Procedures – standardized protocols used to generate
        accurate and reproducible results.

Three main components of Geographic Data

     1. Geometry – Geographic features associated with objects
        in the real world are represented in a GIS as lines, points,
        or polygons.

     2. Attributes – data describing the characteristics of
        geographic features, or pertinent information about those
     3. Behavior – refers to the capacity to allow geographic
        features to be edited based on specified attributes or rules.
           E.g. A woodland can be defined as only those groups
           of trees greater than a specified area.
        Often feature behavior is implemented using a

     Geodatabase: A relational database that stores geographic data. More precisely,
     the geodatabase is an object-oriented data model introduced by ESRI that is used
     to store spatial and attribute data and the relationships that exist among them. The
     geodatabase provides tools for creating ―smart‖ geographic features and enforcing
     database integrity. A geodatabase can store feature classes, feature datasets,
     nonspatial tables, and relationship classes.)

Spatial Relationships among Features

Spatial relationships refer to the relative locations of features on a

Topology is the mathematical procedure used to determine spatial
      - connectivity of lines or objects
      - direction of lines
      - length of lines
      - adjacency of areas
      - area definition

Topology is what makes geographic analysis possible. Allows us
to answer questions:
      - What habitat features are within 100m of den sites?
      - What waterways pass through Oak-Hickory Forests?

     - How large is this wetland?
     - How far apart are these nest sites?

A GIS Organizes Geographic Data

A GIS stores information in the form of thematic data layers,
each linked by common geography.

Each layer consists of features that have similar attributes
     E.g. In a map, each of the following could represent a
     separate thematic data layer.
     - Water
     - Forests
     - Scrub
     - Grasslands
     - Farmlands
     - Roads
     - Utilities
     - Soils
     - Elevations

Data Capture and Storage

Ideally, data on geographic features is stored in a Geodatabase.

Creation of a geodatabase is time consuming and costly, therefore,
careful thought must be given to how data are collected, compiled,
organized, and stored.

One must consider what the data will be used for and what form
will make the data most versatile for future analyses.

One must also consider the type of data
    - Geographic data contains coordinates referring to specific
      locations on the earth’s surface.

       - Tabular data contains attributes relevant to the geographic

The GIS must provide means of coordinating both kinds of data

Geographic data are stored either in a vector data format or a
raster data format.

For vector data, geographic features are represented as points,
lines, or polygons
      A graticule or x,y (Cartesian) coordinate system is used to
      georeference these features.

A graphical representation on a map of the network of parallels and meridians (latitude
and longitude lines) that subdivide the earth's surface.

X,Y coordinates

On a map, a location that corresponds to the same location on the earth's spherical
surface, identified by its distance from an origin (0,0) along two axes, a horizontal axis
(x) representing east-west, and a vertical axis (y) representing north-south.

Raster data format is composed of a grid of cells with a pre-defined
georeferenced origin.

     Values are assigned to cells within the grid that correspond to
     the location of a feature or the value of a feature.

     Level of detail depends on the size of the cells.
          E.g. Orthoquad aerial photos (quads) are in raster
          format. Their resolution may be 1.0m or 2.5m. One
          meter quads have cells that are 1.0 m by 1.0 m, whereas
          2.5 m quads have cells that are 2.5 m by 2.5 m.

Raster format is used for data that are collected in grid format.

     1. A data format for storing raster data that defines geographic space as an array
     of equally sized square cells arranged in rows and columns. Each cell stores a
     numeric value that represents a geographic attribute (such as elevation) for that
     unit of space. When the grid is drawn as a map, cells are assigned colors
     according to their numeric values. Each grid cell is referenced by its x,y
     coordinate location.

     2. In cartography, any network of parallel and perpendicular lines superimposed
     on a map and used for reference. These grids are usually named after the map’s
     projection; for example, Lambert grid and transverse Mercator grid.

Querying and Analyzing Data

To be useful a GIS map must allow the user to extract information
from the map or find features or feature attributes on the map

A Query is often a logical expression used to select features and
their records from a map.

     E.g. Highlight all streams with flow rates > 1 m/sec.

A common type of query is to identify attributes of a specific

     - in this case the user knows the location, but want to extract
     information associated with that location.

Alternately, a query might be to determine where particular
attributes exist within the map.
      - in this case the user has a specific attribute in mind and
      wishes to determine where this condition exists on the map.

Analysis of geographic data is more complicated, often requiring
several steps and several sets of geographic data.

Two common types of analysis are Proximity Analysis and
Overlay Analysis.

Proximity analysis is used to analyze the spatial relationship
among features.
     I.e. how many of this feature lie within a specified distance
     of this other feature?

Proximity analysis uses a process known as buffering to determine
the proximity of features.

     - a zone of specified distance is established around a
       feature. Objects within this zone can then be identified.

Overlay Analysis involves the integration of different data layers.

This requires that one or more data layers are joined physically and
combined into a single data layer in the database.

     E.g. Could be used to integrate data on soils, slope,
     vegetation, and land ownership.

Displaying and Outputting Data

A GIS must also provide means of producing maps, graphs, and

In addition, a GIS must provide a means of sharing geographic
      Can be done in the form of:
            Printed Maps
            Image files
            Internet web page files
            Embedded objects within document files

ArcGIS Components and Overview

ArcGIS and its components are produced by the Earth Systems
Research Institute (ESRI)

ArcGIS consists of three desktop GIS components:


In addition, there is a Database management system (ArcSDE) that
allows spatial data to be stored, managed, and retrieved from other
commercial database management systems (DBMS).

ArcView includes ArcCatalog, ArcMap, and ArcToolbox
    - allows you to browse, manage, analyze, edit, and
      document data

ArcEditor has all the functions of ArcView but also includes tools
for editing shapefiles and geodatabases.

ArcInfo has all the capacities of ArcView and ArcEditor and
includes numerous other geoprocessing tools.

ArcView is used for data visualization, query, analysis, and map
      - Tools allow for exploring, selecting, displaying, editing,
         analyzing, symbolizing, and classifying data
      - Allows for creation, updating, and managing metadata.
ArcView is also ―web-enabled‖, meaning that you can write
macros using Visual Basic or create extensions using Visual Basic,
C++, or Delphi.

Optional extensions that can be added to ArcView are:

Spatial Analyst
With Spatial Analyst, you can

      Convert feature themes (point, line, or polygon) to grid themes.
      Create raster buffers based on distance or proximity from feature or grid themes.
      Create density maps from themes containing point features.
      Create continuous surfaces from scattered point features.
      Create contour, slope, and aspect maps and hillshades of these surfaces.
      Perform cell-based map analysis.
      Perform Boolean queries and algebraic calculations on multiple grid themes
      Perform neighborhood and zone analysis.
      Perform grid classification, display, and more.

       ArcView 3D Analyst
With ArcView 3D Analyst, you can

      Generate three-dimensional contours.
      Integrate data from computer-aided design (CAD).
      Perform statistical analysis in three dimensions.
      Create density surfaces from attribute data.
      Perform line-of-sight analysis and create three-dimensional visibility maps.
      Work with most common data formats.
      Build true three-dimensional surface models from any point data source
       (including [GPS]).
      Model real-world surface features, such as buildings as well as subsurface
       features like wells, mines, groundwater, and underground storage facilities.
      Drape two-dimensional features or image data on three-dimensional surfaces and
       have complete access to tabular data via interactive query.

With ArcPress for ArcView, you can

      Convert metafiles into native printer raster languages for many common printing
      Generate raster images from complex raster and vector data.
      Expedite throughput and imaging processes.
      Reduce extraneous overhead costs (e.g., RAM, firmware).
      Enable a unified printing and imaging solution for ESRI products.

       Geostatistical Analyst
With ArcGIS Geostatistical Analyst you can

      Explore data variability, look for data outliers, examine global trends, and
       investigate spatial autocorrelation and the correlation between multiple data sets.
      Create prediction, prediction standard errors, the probability that specified
       threshold was exceeded, and quantile maps using various geostatistical models
       and tools.

With StreetMap you can

      Find addresses anywhere on a street network.
      Quickly create intelligent maps.
      Perform simple point-to-point or optimized routing across nationwide street

Applications: ArcCatalog, ArcMap, and ArcToolbox

ArcCatalog is used to browse and manage geographic data sources
and to create and update metadata

ArcMap is used to display and query maps and to edit and output

ArcToolbox contains tools for performing geographic analyses and
data conversion.


ArcCatalog allows you to view the file structure of you database
and its sources
      - can browse, organize, distribute, and document GIS data
      - contains Database Connections dialogue to help access
         ArcSDE and OLE DB databases
With ArcSDE you can

      Serve spatial data to ArcGIS Desktop (ArcReader, ArcView, ArcEditor, and
       ArcInfo), to Internet clients through ArcIMS, and to applications developed with
       ArcGIS Engine and ArcGIS Server.
      Serve ESRI's file-based data using ArcSDE for Coverages.
      Manage geographic information in one of four commercial databases—IBM's
       DB2 Universal Database and Informix Dynamic Server, Oracle, and Microsoft
       SQL Server.

OLE DB is Microsoft's strategic low-level application program interface (API) for access
to different data sources. OLE DB includes not only the Structured Query Language
(SQL) capabilities of the Microsoft-sponsored standard data interface Open Database
Connectivity (ODBC) but also includes access to data other than SQL data.

       - The connections and file structure in ArcCatalog is
         referred to as your catalogue.
       - It is organized much like Microsoft Windows Explorer
       - Three tabs allow you to view different aspects of a file
             o Contents tab shows you the contents of the selected
             o Preview tab allows you to view the data
             o Metadata tab gives you access to important
                information about the file


ArcMap is used to view and analyze maps

Items can be dragged and dropped into ArcMap from ArcCatalog

Geographic information in ArcMap is displayed as Layers, where
each layer represents a particular type of feature.

The table of contents is displayed in a box on the left side of the
     - it provides a list of layers currently in the map
     - indicates which layers are displayed
     - indicates which layers are active

The order of layers in the catalogue is important
     - layers at the top of the table of contents are drawn over the
        layers below them.
           o Therefore one should put background layers at the
              bottom of the table of contents and foreground layers
              at the top of the table.

ArcMap also allows one to identify features, perform simple
analyses of features, and to present some of these analyses in
graphical format.


ArcToolbox is used to perform advanced GIS analysis tasks and
geographic data processing jobs.
     - map projections and geographic projections
     - creation and integration of various data formats into
       useable GIS databases

ArcToolbox contains many more tools when included with ArcInfo
than it does in ArcView or ArcEditor


ArcGis comes with a desktop help

Accessed separately from the dropdown list in your Start,
Programs directory.

Topical outline with clickable topics.

Also contain a search tab.

              Displaying Data and Georeferencing

A map must accurately display data
    - to do so, must pay attention to how data are displayed and
    how real locations on the earths surface can be accurately
    represented on a map.

Map Document
      - does not store data, stores locations of data files on your
Table of contents in ArcMap lists:
      Data Frame
      Data Layers
            - symbols
Right-clicking on a name in table of contents opens context menus
that can be used to interact with the map.

Status bar on bottom reports the coordinate position of the mouse
pointer in the display window.


Geographic information is displayed as layers.
     - a layer represents a particular type of feature
           o eg. Streams, boundaries, toxic waste sites, nest sites,
     - A layer is not a file in itself.
           o References a set of files that contain the information
              about that layer
Layers can reference several types of data sets:
     - Vector datasets (aka feature layers) in the form of
        coverages, shapefiles, CAD files, geodatabases, and
        ArcSDE databases.
     - Raster datasets (aka raster layers) in the form of grids and

     - Tabular datasets (event layers) in the form of x,y files
       (Cartesian) imported from GPS or field measurements.
     - Triangular Irregular Network (TIN) datasets

Table of Contents

The table of contents lists all of the data frames and layers on the
map and shows the symbology used to display the features in each

A check box beside each layer shows whether that layer is
currently being displayed or not.

Layers on the top of the table of contents draw over layers on the
bottom of the table of contents.

Table of contents is the gateway for many tasks. Right clicking a
name opens a context menu that allows you to access the layer’s
attribute table, its Properties dialogue, and feature labels, among
other things. Clicking on a layer’s symbol opens the Symbol
Selector which allows you to change symbol properties.

Group Layers

Sometimes several layers may share a common feature (eg. They
are all bodies of water, they are all types of roadways)
      - you may want to treat all of these layers the same way. In
         this case a Group Layer can be created by grouping these
         layers together.
      - This will make managing these layers easier
            o all layers in the group can be turned on or off at
               same time
            o properties of all layers can be manipulated

Map Scales

An important component of any map is its scale. The scale
indicates how large objects on the map are in the real world. It can
also be used to measure distances on a map.

Scale affects how features are represented on a map and, therefore,
is an important consideration in map building.

Large-scale maps cover a small area
    Eg. A map of A&M-Commerce campus
          A map of City of Commerce

Small-scale maps cover a large area
    Eg. A map of the Western Hemisphere
          A map of the continental United States

The extent to which real distances are reduced to fit on a map is
expressed as the map’s scale.

Three common ways to express scale:
        1. Linear (aka graphic)
        2. Verbal
        3. Representative Fraction

Linear Scales:
     On most commercial maps, there is a linear or graphic scale
     - these are the scales people tend to be most familiar with
     - they look like:

     With a linear scale, one can compare a distance measured on
     the map with the scale to determine the actual distance.

Verbal Scales

Verbal scales represent scale as an expression. For example, if a
4.8-kilometer road is drawn as a 20-centimeter line on a map, you
can describe the relationship of map units to ground units using the
expression 20cm = 4.8km. Optionally, you can reduce the values to
a single unit, and the expression would read 1cm = .24km.

Representative fractions
Representative fractions express scale as a fraction or ratio of map
distance to ground distance, such as 1:24,000 or 1 / 24,000.

A representative fraction (RF) scale can be derived from a verbal
scale by using the same unit of measure on both sides of the verbal
scale's expression, reducing the expression values, and dropping
the unit designation.

For example:

     20cm = 4.8km (original verbal scale)
     20cm = 480,000cm (convert all units to centimeters)
     1cm = 24,000cm (divide both sides of the expression by 20)
     1 / 24,000 or 1:24,000 (remove the unit designation)

Because the values on either side of the colon represent a
comparison of map distance to ground distance, a representative
fraction can be used with any unit of measure. For example, a
1:24,000 scale (1 map unit represents 24,000 ground units) could
be interpreted as 1cm = 24000cm, 1mm = 24000mm, 1' = 24000',
and so on.

Although all three scales can be displayed on your map document
in ArcMap, only the representative fraction can be used to define a
map's scale. The other scales are derived from the representative

Scale Dependant Display

In ArcMap you can change the maps extent by zooming in or out
or by zooming to a particular feature.

If a map contains numerous features and layers, it may not be
advisable to display all of these features and layers at all scales
      - at small scale there may be too much clutter on the map or
      individual features may be hard to distinguish

ArcMap can allow you to turn features on or off depending on the
scale that you are viewing them at.

Symbolizing Data

The ease to which information in a map can be interpreted depends
strongly on how that information is symbolized on the map.

An important feature of ArcMap is its ability to allow the user to
modify symbology on a map.

When data is added to ArcMap, ArcMap uses a default symbology
to represent the data.
      - this default symbology is rarely acceptable.

The easiest way to change a layer’s symbol is to right click on its
symbol to open the symbol selector.
     - this allows you to choose from a variety of symbol styles
        and colors.
     - Can also load custom symbols

Although ArcMap allows you to choose many symbols and colors,
it is important to remember that the human eye is limited to
deciphering not more than 12 different colors or seven or eight
distinct shades of the same color in one map.

Qualitative Symbology

Used to distinguish differences of type within a feature layer
     - Used for categorical variables
           o Eg. Woodland types: Oak/Elm, Oak/Hickory,
              Ash/Cedar Elm
           o Eg. Soil types
           o Etc.

Three ways to use qualitative symbology:
     1. Unique values
          o Each feature is displayed by a unique symbol based
             on actual category listed in attribute table.
          o traditional method
     2. Unique values, but many fields
          a. each feature is displayed using multiple fields in the
             attribute table
          b. each field must be categorical
     3. Matching Symbols to a style.
          a. Sometimes symbols can be selected from a
             predetermined style.

Quantitative Symbology

Sometime the attributes of a layer vary in a numerical or
quantitative way:
     - eg. Population sizes of urban areas
     - eg. Tree density in particular woodlots
     - eg. Number of nests in breeding colonies

These attributes can be symbolized to facilitate visual comparisons
on a map display

Three ways to symbolized quantitative attributes.

     1. Graduated Colors
     2. Graduated Symbols
     3. Proportional Symbols

Graduated Colors
     - Use a color ramp to represent quantities of an attribute for
       different features within a data layer.
          o Eg. Could shade wooded areas (polygons) different
             colors corresponding to percent overhead cover
          o Eg. Could symbolized bird colonies different colors
             to indicate different numbers of breeding pairs

Graduated Symbols
     - here the symbols (usually circles) vary in size according to
       the relative values of an attribute (values assigned to
       groups or ranges)

     eg. Colony sizes

     0 – 15      16 – 30        > 30

Proportional Symbols
     - here the symbols (again usually circles) vary in size
        relative to their actual values (thus the symbols vary in
        size continuously) – there are no groups or ranges

Multiple attributes can be illustrated for a single feature class
     Eg. Could use a pie chart to display proportions at each
     geographic feature within a layer


Classification is a special type of quantitative symbology whereby
you can display data by grouping features according to their
attribute values
      - this is very similar to graduated symbology, but here the
         user can select from 5 options as to how the data are
1. Equal interval—the range of values within each class is the
2. Quantile—the number of features within each class is the same.
3. Natural Breaks—the gaps within the data are identified and the
intervals defined accordingly. Neither the range of values nor the
number of features within each class may be equal.
4. Standard Deviation—the range of values within each class is
based on the standard deviation of the data.
5. Manual—each class is defined by the user. This method is not
actually a classification method, but rather a way you can define a
custom classification method.

ArcMap can display a histogram to help the user determine where
class breaks should occur. This histogram can be used to move
and rearrange these class breaks.

Labeling Features

Geographic features can frequently be identified by names.
Alternately, the specific value of an attribute can be displayed for
quick reference.

The process of labeling features in an important aspect of a map

In ArcMap, label properties such as position, size, color, font, etc.
are set using the Layer Properties dialog.

Labeling must be done carefully to avoid clutter on the map.
    - one way to do this is to have particular labels display only
    at particular scales.

Another way to avoid clutter is to use Map Tips
    - when map tips are enabled, the label is not displayed until
       the cursor is placed over it.

                        Coordinate Systems

Geographic Coordinate Systems

A geographic coordinate system (GCS) uses a three-dimensional
spherical surface to define locations on earth:
     - sometimes erroneously referred to as a Datum, but a datum
     is really just a component of a GCS.
     - a GCS consists of an angular unit of measurement, a
     prime meridian, and a datum (spheroid)

In a GCS points are referenced by values of longitude and

The values of longitude and latitude are actually measures of
angles from the earth’s center to a point on the surface of the earth.

The angles are typically measured in degrees (or gradians – 100
grads = 90o)

In a spherical system, horizontal lines are lines of equal latitude,
also known as parallels.

The vertical lines are lines of equal longitude, also known as

Together the meridians and parallels form a network known as a

The line of latitude midway between the poles is known as the
      - it usually has a value of 0o and, therefore, can also be
      referred to as the Standard Parallel.

The line of 0o longitude is called the Prime Meridian. In most
GCSs, this line passes through Greenwich, England. In some
GCSs the prime meridian passes through Bern, Bogota, or Paris.

The origin of the graticule (0, 0) is where the prime meridian and
the standard parallel intersect. The globe is then divided into four
quadrants based on their compass bearing from the origin.

Latitude and Longitude are traditionally measured in either
decimal degrees or in degrees, minutes, seconds (DMS).

Latitude is measured relative to the equator
      - ranges from 0 to -90o south of the equator and from 0 to
      +90o north of the equator

Longitude is measured relative to the prime meridian
    - ranges from 0 to -180o west of the prime meridian and from
    0 to +180o east of the prime meridian.

Sometimes, to avoid confusion, verbal designations of latitude and
longitude use cardinal directions rather than + or – signs.

Eg. TAMU-C is located at 33o 14’ 59‖ N, 95o 54’ 22‖ W

Lat and Long can reference specific points on earth, but they are
not uniform units of measurement.
      - only along the equator does 1o of longitude equal 1o of
      - This is because, while all meridians are great circles, the
         equator is the only parallel that is a great circle.
      - Parallels get progressively smaller as one moves away
         from the equator toward the poles.
      - Thus 1o of longitude at the equator is a longer distance
         than 1o of longitude near the poles. (at the poles, 1o of
         longitude is zero)
      - Eg. On the Clarke 1866 spheroid, 1o of longitude at the
         equator is 111.321 km, while at 60o latitude, it is only
         55.802 km.
Because degrees of lat and long don’t have a standard length, they
can’t be used to measure distances or areas accurately.
      - also difficult to display on a flat surface (map or computer

The shape and size of a GCS is defined by the three dimensional
surface that it is based on.

Traditionally, because it is easier to use for mathematical
calculations, the earth was represented as a sphere.
      - this is ok for small-scale maps (smaller than 1:5,000,000).

However, the earth is more accurately represented as a spheroid:

A spheroid is merely an ellipse that has been rotated.
     - the shape of an ellipse is defined by two radii. The longer is
     called the Semimajor Axis, the shorter is the Semiminor

Rotating the ellipse around the semiminor axis creates the

A spheroid is defined by either the semimajor axis, a, and the
semiminor axis, b, or by a and the flattening. The flattening is the
difference in length between the two axes expressed as a fraction
or decimal:

                 f = (a – b) / a

The flattening is a small value, so usually the quantity 1/f is used
instead. The spheroid parameters for the World Geodetic System
of 1984 (WGS 1984 or WGS84) are:

                 a = 6378137.0 meters
                 b = 6356752.31424 meters
                 1/f = 298.257223563

Flattening ranges from zero to 1.0. A flattening of zero indicates
that axes are equal, resulting in a sphere.

The flattening of the earth is approximately 0.003353

Another quantity used to describe the shape of a spheroid is the
square of its eccentricity.

                       e2 = (a2 - b2) / a2

The earth has been surveyed many times and, as a result, many
different spheroids have been described.

     - it turns out that the earth is not a perfect spheroid
     - south pole is closer to the equator than the north pole
     - there are surface and gravitational irregularities that make
       the curvature non-uniform

Because of this, a particular spheroid is usually chosen to fit a
particular country, region, or predefined area.
      - a spheroid that works well in one area may not work well
         in another area

Until recently, North American data used the spheroid defined by
Clarke in 1866. The radii of this spheroid are:
           a = 6378206.4 meters
           b = 6356583.8 meters

This, older spheroid was a ground surveyed spheroid

Satellite technology has revealed hitherto unknown elliptical
deviations, so the spheroid has been revised.
      - the new standard spheroid for North America is the
         Geodetic Reference System of 1980 (GRS 1980)
      - its radii are:
             a = 6378137.0 meters
             b = 6356752.31414 meters
      - parameters were established by the International Union for
      Geodesy and Geophysics

Because changing the spheroid changes all feature coordinates,
many organizations haven’t switched to new (more accurate)


A spheroid approximates the shape of the earth.

A datum defines the position of the spheroid relative to the center
of the earth.
      - provides a frame of reference for measuring locations on
      earth surface.

Because a spheroid has a perfectly curved surface, but the earth
does not, the same spheroid can be fitted to the earth surface in
different ways
      - therefore can have more than one datum for a particular

Changing the GCS will cause all of the coordinates of features on
your map to change.

Eg. Coordinates of a control point in Redlands California (in

North American Datum of 1983 (NAD 1983 or NAD83)
         -117 12 57.75961
         34 01 43.77884

North American Datum of 1927 (NAD 1927 or NAD27)

           -117 12 54.61539
           34 01 43.72995

Longitude differs by about 3 sec (about 92 m), latitude by about
0.05 sec (about 1.5 m).

NAD83 and WGS84 are identical for most applications. Here are
the coordinates for the same control point based on WGS84:

           -117 12 57.75961
           34 01 43.778837

Many modern digital files are based on NAD83, though there is a
movement to convert data to WGS84

All recent GPS data are collected using WGS84

Geocentric Datums

In the last 15 years, satellite technology has provided much more
accurate information to create the best earth-fitting spheroid
relative to the earth’s center of mass.

A Geocentric datum, is earth centered, and based on the earth’s
center of mass as its origin.
     - the most recent and widely used is WGS84.
     - it can be used for local reference world-wide

Local Datums

A local datum’s spheroid is aligned to fit the earth’s surface in a
particular area.
      - the point on the surface of the
       earth where the datum is designed
       to fit the spheroid to is called the
       origin point of the datum.
      - the coordinates of this point are
       fixed and all other coordinates are
       calculated based on their locations
       relative to this point.
The center of a spheroid for a local datum
      is offset from the center of the earth.

NAD27 and the European Datum of 1950
   are local datums.
   - NAD27 is designed to fit North
   America, while ED50 is designed
   to fit Europe.

Local datums are not suitable for use
     outside the areas that they were
     designed for.

North American Datums

The two horizontal datums used almost exclusively in North
America are NAD27 and NAD83.

NAD27 used the Clarke 1866 spheroid
   - Its origin is Meades Ranch in Kansas.

NAD83 was developed from recent technological advances in
surveying and Geodesy.
     - corrects for numerous errors observed at various control
        points established using NAD27
     - NAD83 uses the GRS80 spheroid whose origin is at the
        earth’s center of mass.

The GRS80 spheroid is nearly identical to the WGS84 spheroid.
Thus the WGS84 and NAD83 coordinate systems yield similar

Raw GPS data use the WGS84 coordinate system.

There is an ongoing effort to correct errors in the NAD83 datum at
the state level using more accurate techniques
      - this effort is known as the High Accuracy Reference
         Network (HARN) or High Precision Geodetic Network
      - as a result new grids of coordinates are now being made

Outlying states, parts of Alaska, Hawaii, Puerto Rico, and Virgin
island used datums other than NAD27 in the past.
      - recent maps now utilize NAD83

                         Map Projections

Map projections are also known as Projected Coordinate

- projected coordinates are defined on a flat, two dimensional
      - allows for constant lengths, angles, and areas.

Projected coordinate systems are always based on an underlying
Geographic Coordinate System

                                  In a projected coordinate system
                                  locations are identified by x and
                                  y coordinates.

                                  The origin is at the center of the

                                  Longitude is equated with the x
                                  axis, latitude with the y axis

Map Projections

The principle problem with representing the earth as a map
projection comes from depicting a three-dimensional spheroid as a
two dimensional map.

It is called a map projection, because you are projecting the
spheroid onto a planar surface.
       - actually a mathematical transformation

Trying to represent the earth in two dimensions always results in
     - therefore, all map projections contain one or several of the
     following types of distortion:
            - shape, area, distance, direction.

                 (map projections make cartographers SADD)

Different map projections have been developed to minimize certain
kinds of distortion
     - thus can serve different purposes
     - increases the other types of distortion

Because of the difficulties associated with first selecting an
appropriate spheroid and datum and then deciding what kind of
distortion to minimize, there are innumerable map projections

     - ArcGis supports 65 map projections

Map projections can be classified into four basic categories
depending on their purpose:

1. Conformal Projections:
     Conformal projections preserve local shape. These
     projections must preserve all angles.

     Unfortunately, this preservation of shape greatly distorts

     These projections typically only work on large scales.

     No map projection can preserve shape for small scales.

2. Equal-Area Projections:
     These projections are designed to preserve the area of
     geographic features.

     In doing so, there is increased distortion of shape, angle, and

     For maps of small regions, shapes are not obviously
     distorted, making Equal-Area Projections similar to
     Conformal Projections.

3. Equidistant Projections:
     These projections preserve distances between points on the

     No map projections can maintain scale throughout the map.
     However, in most cases, there are one or more lines on a map
     along which scale is maintained.

     Equidistant projections contain one or more lines in which
     the length of the map is equal to the length of the equivalent
     line on the underlying spheroid
           - regardless of whether those lines are great circles or
           - or whether they are straight or curved.

     Distances measured along these lines are said to be true

     eg. Sinusoidal projection – equator and all parallels are their
     true lengths.

     eg. in other equidistant projections – equator and all
     meridians are true lengths.

     eg. in Two-point equidistant projections – true scale is
     maintained between any point on the map and one or the
     other of two points.

4. True-direction Projections

     The shortest distance between two points on a spheroid
     follows the arc of the great circle on which both points occur.

     True-direction, or Azimuthal projections maintain some of
     the great circle arcs allowing dirctions (or azimuths) of all
     points on the map relative to the center of the map to be

     Some azimuthal projections are also conformal, equal area,
     or equidistant.

Map Projection Types

A map projection must turn a spheroid into a flat surface.

One way to solve this problem is to make a map projection by
using a three dimensional geometric shape that can be easily turned
into a two dimensional shape.

Such shapes are called developable surfaces.
     - these shapes are used to project locations from the surface
     of a spheroid to a flat surface using mathematical algorithms.

Three common types of projection are:
              Conic – based on a cone
              Cylindrical – based on a cylinder
              Planar – based on a plane

Every projection has a defined point, line, or lines of contact with
the spheroid.
      - a planar projection has a single point of contact
      - conic and cylindrical projections can have a single line of
      contact (tangential) or two lines of contact (secant).

The contact lines or points are significant because they represent
locations on the map of zero distortion.

Lines of true scale include the central meridian and standard
      - sometimes called standard lines

In general, distortion increases with the distance from the point or
line of contact.

Common map projections are often classified according to the
projection surface used: conic, cylindrical, or planar.

Conic Projections:

The simplest conic projection is tangential to the globe along a line
of latitude
       - this line then becomes the Standard Parallel

The meridians are projected onto a conical surface such that they
converge at the apex of the cone.

Parallel lines of latitude (parallels) are then drawn onto the cone as
a series of rings.

The cone is then ―cut‖ along a meridian to produce the conic
     - this then has straight convering lines for meridians
            - the meridian directly opposite of the ―cut‖ becomes
            the central meridian.
     - has concentric arcs for parallels

In general, the further you go from the standard parallel the greater
the distortion.

Most conic projections eliminate the top of the cone because the
distortion in this region is unacceptable
      - ie. polar regions are not used

Because of the distortion problem, conic projections are used for
mid-latitude maps and areas in these latitudes that have a
predominantly east-west orientation.

More complex conic projections contact the globe at two locations

These projections are called secant projections and are defined by
two standard parallels, or sometimes a single standard parallel and
a scale factor

In this case distortion between standard parallels is different from
the distortion above and below the standard parallels.
      - eg. distances are compressed between standard parallels
      but are exaggerated above and below them

In general, secant projections have less overall distortion than do
tangential projections

Still more complicated conic projections exist

     - oblique conic projections are based on cones whose axis is
     oblique relative to that of the globe

The representation of geographic features and resultant distortion
depends on the spacing of the parallels.
     - when these are equally spaced, the projection is equidistant
     north to south, but neither conformal nor equal area.

An example of this projection is the Equidistant Conic Projection

     - for small areas the distortion is minimal

On the Lambert Conformal Conic projection, the central parallels
are spaced more closely than the parallels near the edges and small

geographic shapes are maintained for both small-scale and large-
scale maps.
      - see below

On the Albers Equal Area Conic projections, the parallels near the
northern and southern edges are closer together than the central
parallels and the projection displays equivalent areas.

Cylindrical Projections:
(Historical note: Archimedes demonstrated
that the surface area of a sphere is equal to
that of the cylinder that fits exactly around it
and is of the same height as the sphere.)
- thus these projections tend to be equal area
or conformal unless modified to maintain direction.

Like conic projections, cylindrical projections can be tangential or

The Mercator projections is one of the most common cylindrical
projections, and the equator is usually its line of tangency.
     - vertical scale (parallels) modified to maintain direction
     instead of area.

Meridians are geometrically projected onto the cylindrical surface,
and parallels are mathematically projected.

     - results in graticular angles of 90 degrees.

The cylinder is ―cut‖ along any meridian to produce the final

Meridians are equally spaced, while parallels are more widely
separated near the poles.
     This projection is conformal and displays true direction along
     straight lines.

     On a mercator projection, rhumb lines (lines of constant
     bearing) are straight lines whereas most of the great circles
     are not.

There are other, more complex cylindrical projections:

The mercator is a normal cylindrical projection in which the
equator is typically the standard parallel.

A transverse cylindrical projection is rotated by 90 degrees such
that a meridian or meridians serve as the tangent or secants.
      - a commonly used projection is the Transverse Mercator

An oblique cylindrical projection uses a great circle as the tangent
or secant

Neither the Transverse Mercator nor the oblique cylindrical
projection produce meridians or lines of latitude that are straight

In all cylindrical projections the lines of tangency or the secants
have no distortion and therefore are lines of equidistance.

Planar Projections

Planar projections project the surface
of the earth onto a flat surface touching
the surface of the globe.

Also known as Azumuthal projections

Usually tangential to the point of contact, by may also be secant

The point of contact can be any point on the surface of the globe

The point of contact specifies the aspect and is the focus of the

The focus is identified by a central longitude and a central latitude.

Possible aspects are polar, equatorial, and oblique

Polar aspects are the simplest form.
      - in this case parallesl of latitude are concentric circles
      centered on the pole and meridians are straight lines that
      intersect with their true angles of orientation at the pole.

Planar projections tend to preserve distance, since great circles are
typically represented as straight lines.

Some planar projections view surface data relative to a specific
point in a three dimensional space (called the perspective point).
      - this point may be located at the center of the earth, on the
      surface of the earth directly opposite of the focus, or above
      the surface of the earth.

The perspective point affects the extent of distortion observed in
equatorial areas.

Azimuthal (planar) projections are classified by the focus and, if
applicable, the perspective point.

Planar projections are most commonly used for mapping polar

Projection Grids

Map projections all have their problems with distortion.

True direction, distance, area, and shape are only closely
approached near standard lines, especially where these intersect.

Thus to obtain the most accurate possible map of a local area one
needs to choose an appropriate geographic coordinate system for
an area, choose an appropriate map projection, and set the standard
lines to intersect at the center of the area to be mapped

This, of course, requires extensive labor.

One solution is to establish a grid system or a system of zones in
which each cell or zone has a particular geographic coordinate
system and map projection established for it.
     - one then only needs to know which grid cell(s) or zone(s)
     they want to map and apply the appropriate parameters.

Two systems that do this are Universal Transverse Mercator, or
UTM and State Plane Coordinate System (SPCS).
    - both are widely used in GIS applications

State Plane coordinate system is extremely popular among state
and local governments.

Its popularity is primarily due to its accuracy

     -- in terms of linear measurements, it's four times as accurate
     as the Universal Transverse Mercator

However, it achieves this accuracy through the use of relatively
small zones, and these small zones can be quite a problem in
mapping projects covering larger areas.

     - Because of this limitation, the state plane system has never
     really caught on for regional or national mapping tasks.

The state plane coordinate system covers all 50 of the United
States, but it does not extend beyond the borders of the U.S.

The system is designed to have a maximum linear error of 1 in
     - This means that if you use state plane coordinates to
     measure a line as being 10,000 units in length you may be off
     by as much as one unit
     - This is four times as accurate as the UTM system, whose
     maximum linear error is 1 in 2,500.

State plane coordinate system uses about 120 zones to cover the
entire United States.

State plane zones whose long axis run north-to-south (e.g., New
Mexico East) are mapped using a Transverse Mercator projection
(different from the one used by UTM).

State plane zones whose long axis runs east-to-west (e.g., Texas
Central) are mapped using a Lambert Conformal projection.

In either case, the projection's central meridian is generally run
down the approximate center of the zone.

Almost all state plane zones are mapped using the Clarke 1866

A Cartesian coordinate system is associated with each zone by
establishing an origin some distance (usually, but not always,
2,000,000 feet) to the west of the zone's central meridian and some
distance (there is no standard; each zone uses its own unique
distance) to the south of the zone's southernmost point.

This ensures that all coordinates within the zone will be positive.

The X-axis running through this origin runs east-west, and the Y-
axis runs north-south.

Distances from the origin are generally measured in feet

     - X distances are typically called eastings (because they
     measure distances east of the origin)

     - Y distances are typically called northings (because they
     measure distances north of the origin).

The Universal Transverse Mercator, or UTM, spatial coordinate
system has become a favorite among GIS users.

     - Its popularity can be attributed to its nearly worldwide
     coverage (it excludes only small regions around the poles)
     and its ease of use.

     - It is not as accurate as the State Plane Coordinate system,
     but for most uses its accuracy is still quite acceptable.

The UTM system uses 60 zones, each 6 degrees of longitude wide.

Each zone extends from 80°S latitude to 84°N latitude

The zones are numbered, starting with 1 which runs from the 180°
to the 174°W line of longitude, with numbers increasing as you
move west

Collectively, these zones cover almost the entire planet, omitting
only the Arctic Ocean in the north and central Antarctica in the

The UTM system is based on the Transverse Mercator projection

Each UTM zone utilizes a Transverse Mercator map whose central
meridian runs down the line of longitude at the center of the zone

UTM zone maps differ from one another not only in the locations
of their central meridians and lines of tangency, but also in the
spheroids they use.

     Five different spheroids are used in the various zones

     - all the UTM zones in the United States are based on the
     Clarke 1866 spheroid.

For the northern portion of each zone, the origin is located on the
equator, exactly 500,000 meters west of the zone's central

     - this ensures that all coordinates in the zone will be east of
     the origin.

     - placing the origin on the equator ensures that all coordinates
     in the northern hemisphere will be north of the origin.

     Together, these two facts guarantee that all coordinates (in
     both the X and the Y directions) in the northern half of each
     zone will be positive.

The official UTM definition calls for all coordinates within any
given UTM zone to be measured in meters.

The distances east of the origin, which in a Cartesian coordinate
approach would be called the X coordinates, are typically called

Similarly, distances north of the origin, which in a Cartesian
coordinate approach would be called the Y coordinates, are
typically called northings.

Projection Parameters

The map projection itself cannot be used to define a projected
coordinate system

     - one must specify the parameters of the projection in order
     for it to be referenced to a specific location on the earth’s

Each map projection has a set of definable parameters that are used
to fit the projection to the area under study

Angular parameters use the geographic coordinate system units

Linear Parameters use the projected coordinate system units

Angular parameters

Azimuth defines the center line of a projection

Central meridian defines the origin of the x-coordinates

Longitude of origin defines the origin of the x coordinates and is
synonymous with the central meridian

Central parallel defines the origin of the y coordinates

Latitude of origin defines the origin of the y coordinates. In conic
projections this is set to be below the area of interest to ensure that
all y values are positive.

     - no need to set a false northing parameter in this case

Standard Parallel 1 and standard parallel 2 are used with Conic
projections to define the latitude lines where the scale is 1.0

     - in Lambert Conformal Conic projections the first standard
     parallel defines the origin of the y coordinates

Linear Parameters

False easting is a linear value applied to the origin of the x

False northing is a linear value applied to the origin of the y

False easting and false northing values are usually applied to
ensure that all x,y coordinates are positive.

Geographic Transformation Methods

Moving geographic data from one coordinate system to another
requires a geographic transformation

No method is perfect and there are several methods available

                  Basics of GPS – An Overview

Navigation and positioning are crucial to so many activities and yet
the process has always been quite cumbersome.

Over the years all kinds of technologies have tried to simplify the
task but every one has had some disadvantage.

Finally, the U.S. Department of Defense decided that the military
had to have a super precise form of worldwide positioning. And
fortunately they had the kind of money ($12 billion!) it took to
build something really good.

The result is the Global Positioning System, a system that's
changed navigation forever.

These days GPS is finding its way into cars, boats, planes,
construction equipment, movie making gear, farm machinery, even
laptop computers.

The Global Positioning System (GPS) is a worldwide radio-
navigation system formed from a constellation of 24 satellites and
their ground stations.

GPS uses these as reference points to calculate positions accurate
to better than a centimeter!

Here's how GPS works in five logical steps:

   1. The basis of GPS is "triangulation" from satellites.
   2. To "triangulate," a GPS receiver measures distance (range)
      using the travel time of radio signals.
   3. To measure travel time, GPS needs very accurate timing
      which it achieves with some tricks.
   4. Along with distance, you need to know exactly where the
      satellites are in space. High orbits and careful monitoring are
      the secret.
   5. Finally you must correct for any delays the signal
      experiences as it travels through the atmosphere.


Suppose we measure our distance from a satellite and find it to be
11,000 miles.

Knowing that we're 11,000 miles from a particular satellite
narrows down all the possible locations we could be in the whole
universe to the surface of a sphere that is centered on this satellite
and has a radius of 11,000 miles.

Next, say we measure our distance to a second satellite and find
out that it's 12,000 miles away.

That tells us that we're not only on the first sphere but we're also
on a sphere that's 12,000 miles from the second satellite. Or in
other words, we're somewhere on the circle where these two
spheres intersect.

If we then make a measurement from a third satellite and find that
we're 13,000 miles from that one, that narrows our position down
to the two points where the 13,000 mile sphere cuts through the
circle that's the intersection of the first two spheres.

By ranging from three satellites we can narrow our position to just

To decide which one is our true location we could make a fourth
measurement. But usually one of the two points is a ridiculous
answer (either too far from Earth or moving at an impossible
velocity) and can be rejected without a measurement.


We saw that position can be calculated from ranges to at least three

We measure distance by timing how long it takes for a signal to
arrive at our receiver.

The Big Idea Mathematically

Distance = Velocity x Time

If a car goes 60 miles per hour for two hours, how far does it

   Velocity (60 mph) x Time (2 hours) = Distance (120 miles)

In the case of GPS we're measuring a microwave radio signal so
the velocity is close to the speed of light or roughly 186,000 miles
per second.

The problem is measuring the travel time.

First, the times are going to be awfully short.

     If a satellite were right overhead the travel time would be
     something like 0.06 seconds. So we're going to need some
     really precise clocks.

But assuming we have precise clocks, how do we measure travel

The basic idea is to compare the time that a signal is received from
a satellite to the time that it was transmitted.

If we can calculate this delay, we simply multiply this amount of
time by the speed of light to find the distance from the satellite to
the receiver.

Satellites and receivers use something called a "Pseudo Random
Code" (PRC)

     - basically a GPS receiver identifies a satellite (based on it’s
     unique PRC signature) and starts to generate its own
     matching PRC.

     - by lining up the codes to precisely match, the GPS unit can
     determine the amount of delay in the signal coming from the

The PRC is a fundamental part of GPS. Physically it's just a very
complicated digital code, or in other words, a complicated
sequence of "on" and "off" pulses

The signal is so complicated that it almost looks like random
electrical noise. Hence the name "Pseudo-Random."

There are several reasons for that complexity:

     First, it helps make sure that the receiver doesn't accidentally
     sync with some other microwave signal.

     This complexity also allows all the satellites to use the same
     frequency without jamming each other.

     The codes make it possible to use "information theory" to
     "amplify" the GPS signal. And that's why GPS receivers
     don't need big satellite dishes to receive the GPS signals.

Using PRC to determine signal delay assumes that both the
satellite and the receiver have clocks that are perfectly

     If their timing is off by just a thousandth of a second, at the
     speed of light, that translates into almost 200 miles of error!

On the satellite side, timing is almost perfect because they have
incredibly precise atomic clocks on board that are set at Universal
Coordinated Time (UTC).

If our receivers needed atomic clocks (which cost upwards of
$50K to $100K) GPS would be a lame duck technology. Nobody
could afford it.

However, there is a trick that lets us get by with much less accurate
clocks in our receivers.

     The secret to perfect timing is to make an extra satellite

     Using three satellites, a position is calculated based on where
     the three ranges intersect. If there is a time offset between
     the satellites and the receiver, this position will be biased

     However, the range based on a fourth satellite signal will not
     intersect at that point.

     The receiver looks for a single correction factor that it can
     aply to all its timing measurements that would cause them all
     to intersect at a single point.

That correction brings the receiver's clock back into sync with
universal time. This allows for precise positioning.

Because of this, a GPS receiver must be able to receive signals
from at least 4 satellites.

Determining Satellite Locations

For the triangulation to work we not only need to know distance,
we also need to know where the satellites are.

How do we know exactly where they are? After all they're floating
around 11,000 miles up in space.

The Air Force has injected each GPS satellite into a very precise
orbit, according to the GPS master plan.

On the ground the GPS receivers have an almanac sent to them by
the satellites that tell them where in the sky each satellite is,
moment by moment.

The basic orbits are quite exact but just to make things perfect the
GPS satellites are constantly monitored by the Department of

     They use very precise radar to check each satellite's exact
     altitude, position and speed.

The errors they're checking for are called "ephemeris errors"
because they affect the satellite's orbit or "ephemeris." These errors
are caused by gravitational pulls from the moon and sun and by the
pressure of solar radiation on the satellites.

Getting the message out

Once the DoD has measured a satellite's exact position, they relay
that information back up to the satellite itself. The satellite then
includes this new corrected position information in the signals it's

So a GPS signal is more than just pseudo-random code for timing
purposes. It also contains a navigation message with ephemeris
information and almanac data.

Sources of Error

In the real world there are lots of things that can happen to a GPS
signal that will make it less than perfect.

First, as a GPS signal passes through the charged particles of the
ionosphere and then through the water vapor in the troposphere it
gets slowed down a bit, and this can overestimate satellite to
receiver distance, leading to erroneous positions.

When it gets down to the ground the signal may bounce off various
local obstructions before it gets to our receiver.

      This is called multipath error and is similar to the ghosting
      you might see on a TV. Good receivers use sophisticated
      signal rejection techniques to minimize this problem.

The atomic clocks used by satellites are very precise but they're not
perfect. Minute discrepancies can occur, and these translate into
travel time measurement errors.

And even though the satellites positions are constantly monitored,
they can't be watched every second. So slight position or
"ephemeris" errors can sneak in between monitoring times.

Errors caused by Satellite Geometry:

Basic geometry itself can magnify these other errors with a
principle called "Geometric Dilution of Precision" or GDOP. (or
DOP – Dilution of Precision).

There are usually more satellites available than a receiver needs to
fix a position, so the receiver picks a few and ignores the rest.

Basically, if satellites are chosen that are close together, then the
level of accuracy is small. (High DOP)

If the GPS receiver picks satellites that are widely separated then
the level of accuracy is high. (Low DOP).

Good receivers determine which satellites will give the lowest

      GDOP can be divided into three components

            PDOP is Position Dilution of Precision and is a
               measure of three dimensional (x,y,z, error based
               on satellite geometry. (x = long, y = lat, z = alt)

           HDOP is Horizontal Dilution of Precision and measures
              error in latitudinal and longitudinal measures.

           TDOP is Time Dilution of Precision and measures error
              in the precision of estimated UTC.

     Because all three components are highly correlated, most
          GPS units rely on PDOP to measure potential dilution
          of precision (DOP).

           - one standard is to only collect positional information
                 when PDOP is less than or equal to 5.0

Diferential GPS (DGPS)
Differential GPS or "DGPS" is used to eliminate errors caused by
atmospheric conditions, multipath, time differentials, and
ephemeris errors.

Differential GPS involves the use of two receivers, a stationary
reference station and a roving data collection receiver.

If two receivers are fairly close to each other, say within a few
hundred kilometers, the signals that reach both of them will have
traveled through virtually the same slice of atmosphere, and so will
have virtually the same errors.

That's the idea behind differential GPS: We have one receiver
measure the timing errors and then provide correction information
to the other receivers that are roving around. That way virtually all
errors can be eliminated from the system.

The reference receiver is located at a point that's been very
accurately surveyed.

This reference station receives the same GPS signals as the roving
receiver but instead of using timing signals to calculate its position,
it uses its known position to calculate timing. It figures out what
the travel time of the GPS signals should be, and compares it with
what they actually are. The difference is an "error correction"

The receiver can then use this error information to correct the data
collected by the roving receiver.

In the early days of GPS, reference stations were established by
private companies who had big projects demanding high accuracy
- groups like surveyors or oil drilling operations.

Now there are public agencies that provide access to corrections
for free!

Post Processing DGPS

Post processing involves collected positions in the field using a
GPS unit, uploading that information into a database, and using
corrections collected at a reference station to correct (post-process)
the data.

In Texas, access to post-processing data is available from TxDot,
which operates 47 high accuracy base stations distributed across
the state.

Wide Area Augmentation System (WAAS)

More recently the FAA has developed the "Wide Area
Augmentation System" or "WAAS," and it's basically a continental
DGPS system.

The WAAS system is based on 25 high accuracy reference stations
that are networked and scattered across the U.S.

     - each station receives data from GPS satellites and calculates
     the correction parameters.

     - These correction parameters are then sent to a master
     station and uplinked to several geostationary satellites that
     cover the U.S.

     - the geostationary satellites then send a GPS signal that can
     be received by roving GPS units on the ground.

     - the GPs unit can then apply the corrections to their positions
     in real time. (This is sometimes call ―Real-time DGPS).

The WAAS system allows for real-time corrections of positional
information and make the collection of precise data far simpler.


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