2. 10 Under what conditions are mixed cells a problem in raster data models? In what ways may the problem of mixed cells be addressed?

2.10 Under what conditions are mixed cells a problem in raster data models? In what ways may the problem of mixed cells be addressed?

• 2.10 Under what conditions are mixed cells a problem in raster data models? In what ways may the problem of mixed cells be addressed?

2.21 Why do we need to compress data? Which is most commonly compressed, raster data or vector data? Why?

• 2.21 Why do we need to compress data? Which is most commonly compressed, raster data or vector data? Why?

To effectively use GIS, it is important to understand:

• To effectively use GIS, it is important to understand:

• How coordinate systems are established for the surface of the Earth.
• How coordinates are measures on the Earth’s curved surface.
• How these coordinates are converted for use on flat maps

• To understand these things we need some knowledge of geodesy and map projections.

Geodesy is the science of measuring the size and shape of the earth.

• Geodesy is the science of measuring the size and shape of the earth.

• All measurements are relative to some reference, and the best estimates of this reference have changed over time.

• Maps use a two dimensional reference system, but this doesn’t work well for long distances or over the whole Earth.

Every spatial feature needs to be referenced to a location for GIS use

• Every spatial feature needs to be referenced to a location for GIS use

• Spatial reference systems provide a framework to define positions on the Earth‘s surface.

• Steps

• Define the size and shape of the Earth.
• Establish a datum – reference surface from which other points can be measured.
• Develop a spatial reference system:
• Origin
• Orientation of the axes
• Units of measure

Three complicating factors:

• Three complicating factors:

• A flat map must distort geometry in some way.
• The irregular shape of the Earth.
• The imperfections of our measurements.

• Because of these three factors we may have several sets of coordinates for the same location.

Newton reasoned that the Earth was not a sphere.

• Newton reasoned that the Earth was not a sphere.

• Efforts were then focused on measuring the size of the ellipsoid.

A set of points on Earth for which the horizontal and vertical positions have been accurately measured.

• A set of points on Earth for which the horizontal and vertical positions have been accurately measured.

• These form a mathematical surface from which all other points can be measured.

• Many countries have government bodies charged with making these measurements; e.g. National Geodetic Survey

NAD83 (19860

• NAD83 (19860

• NAD83(HARN) – High Accuracy Reference Networks

• NAD83(1996)

• NAD83(2007)

Converting coordinates from one datum to another requires a transformation.

• Converting coordinates from one datum to another requires a transformation.

• Simple formulas do not exist for NAD27 to NAD83 conversions.

Geographic coordinates in decimal degrees:

• Geographic coordinates in decimal degrees:

• Latitude is positive above the equator and negative below.
• Longitude is positive east of the Greenwich meridian and negative west of the Greenwich meridian.

• Two eras of North American datums:

• NAD 27 and NAD 83.
• Must transform from one to the other.

There are many different versions of the NAD83 datum.

• There are many different versions of the NAD83 datum.

• These should not be combined unless you are certain that the errors will be small.

• There are also vertical datums.

• Elevations may be ellipsoidal or orthometric heights.

GIS projects should not mix datums unless you are sure that the datum shifts are small relative to the analysis.

• GIS projects should not mix datums unless you are sure that the datum shifts are small relative to the analysis.

• Datum transformations are estimated relationships that are developed with a specific data sets.

• All datum transformations will introduce error into the data set.

NAD 27 Universal Transverse Mercator – Zone 19N

• NAD 27 Universal Transverse Mercator – Zone 19N

• NAD 27 Maine State Plane (based on the TM projection)

• East Zone
• West Zone

• NAD 83 Universal Transverse Mercator– Zone 19N

• NAD 83 Maine State Plane (based on the TM projection)

• East Zone
• Central Zone
• West Zone

In the tangent case the cone, cylinder or plane just touches the Earth along a single line or at a point.

• In the tangent case the cone, cylinder or plane just touches the Earth along a single line or at a point.

• In the secant case, the cone, or cylinder intersects or cuts through the Earth as two circles.

• Whether tangent or secant, the location of this contact is important because it defines the line or point of least distortion on the map projection.

• This line of true scale is called the standard parallel or standard line.

The line of latitude in a conic or cylindrical projection where the cone or cylinder touches the globe.

• The line of latitude in a conic or cylindrical projection where the cone or cylinder touches the globe.

• A tangent conic or cylindrical projection has one standard parallel.

• A secant conic or cylindrical projection has two standard parallels.

The type of developable surface (e.g., cone)

• The type of developable surface (e.g., cone)

• The size/shape of the Earth (ellipsoid, datum), and size of the surface

• Where the surface intersects the ellipsoid

• The location of the map projection origin on the surface, and the coordinate system units

The LCC requires we specify an upper and lower parallel – 20o & 60o

• The LCC requires we specify an upper and lower parallel – 20o & 60o

• An ellipsoid – GRS 1980

• A central meridian – 96o

• A projection origin – Lat. 40o

Locally preserves angles/shape.

• Locally preserves angles/shape.

• Any two lines on the map follow the same angles as the corresponding original lines on the Earth.

• Projected graticule lines always cross at right angles.

• Area, distance and azimuths change.

A map is equidistant when the distances between points differs from the distances on Earth by the same scale factor.

• A map is equidistant when the distances between points differs from the distances on Earth by the same scale factor.

Equivalent/equal area projections maintain map areas proportional to the same areas of the Earth.

• Equivalent/equal area projections maintain map areas proportional to the same areas of the Earth.

• Shape and scale distortions increase near points 90o from the central line.

A map projections is a systematic rendering from 3-D to 2-D

• A map projections is a systematic rendering from 3-D to 2-D

• Datum transformations are from one datum to another, 3-D to 3-D or 2-D to 2-D

• Changing from one projection to another may require both.

Mercator- A conformal, cylindrical projection tangent to the equator.  Originally created to display accurate compass bearings for sea travel. An additional feature of this projection is that all local shapes are accurate and clearly defined.

• Mercator- A conformal, cylindrical projection tangent to the equator.  Originally created to display accurate compass bearings for sea travel. An additional feature of this projection is that all local shapes are accurate and clearly defined.

• Transverse Mercator - Similar to the Mercator except that the cylinder is tangent along a meridian instead of the equator. The result is a conformal projection that minimizes distortion along a north-south line, but does not maintain true directions.

• Lambert Equal Area - An equidistant, conic projection similar to the Lambert Conformal Conic that preserves areas.

Lambert Conformal Conic – A conic, confromal projection typically intersecting parallels of latitude, standard parallels, in the northern hemisphere.  This projection is one of the best for middle latitudes because distortion is lowest in the band between the standard parallels. It is similar to the Albers Conic Equal Area projection except that the Lambert Conformal Conic projection portrays shape more accurately than area.

• Lambert Conformal Conic – A conic, confromal projection typically intersecting parallels of latitude, standard parallels, in the northern hemisphere.  This projection is one of the best for middle latitudes because distortion is lowest in the band between the standard parallels. It is similar to the Albers Conic Equal Area projection except that the Lambert Conformal Conic projection portrays shape more accurately than area.

• Albers Equal Area Conic - This conic projection uses two standard parallels to reduce some of the distortion of a projection with one standard parallel. Shape and linear scale distortion are minimized between standard parallels.

Projections specify a two-dimensional coordinate system from a 3-D globe

• Projections specify a two-dimensional coordinate system from a 3-D globe

• All projections cause some distortion

• Errors are controlled by choosing the proper projection type, limiting the area applied

• There are standard projections

• Projections differ by datum – know your parameters

Once map data are projected onto a planar surface, features must be referenced by a planar coordinate system.

• Once map data are projected onto a planar surface, features must be referenced by a planar coordinate system.

• Coordinates in the GIS are measured from the origin point. However, false eastings and false northings are frequently used, which effectively offset the origin to a different place on the coordinate plane.

• The three most common systems you will encounter in the USA are:

• State Plane
• Universal Transverse Mercator (UTM)
• Public Land Survey System (PLSS) – non-coordinate systems

Uses Lambert conformal conic (LCC) and Transverse Mercator (TM, cylindrical)

• Uses Lambert conformal conic (LCC) and Transverse Mercator (TM, cylindrical)

• LCC when long dimension East-West

• TM when long dimension N-S

• May be mixed, as many zones used as needed

Each state partitioned into zones

• Each state partitioned into zones

• Each zone has a different projection specified

• Distortion in surface measurement less than 1 part in 10,000 within a zone

UTM define horizontal positions world-wide by dividing the surface of the Earth into 6o zones.

• UTM define horizontal positions world-wide by dividing the surface of the Earth into 6o zones.

• Zone numbers designate the 6o longitudinal strips extending from 80o south to 84o north.

• Each zone has a central meridian in the center of the zone.

Projection: Transverse_Mercator

• Projection: Transverse_Mercator

• False_Easting: 500000.000000

• False_Northing: 0.000000

• Central_Meridian: -69.000000

• Scale_Factor: 0.999600

• Latitude_Of_Origin: 0.000000

• Linear Unit: Meter (1.000000)

• Geographic Coordinate System: GCS_North_American_1983

• Angular Unit: Degree (0.017453292519943295)

• Prime Meridian: Greenwich (0.000000000000000000)

• Datum: D_North_American_1983

• Spheroid: GRS_1980

• Semimajor Axis: 6378137.000000000000000000

• Semiminor Axis: 6356752.314140356100000000

• Inverse Flattening: 298.257222101000020000

False easting – the value added to the x coordinates of a map projection so that none of the values being mapped are negative.

• False easting – the value added to the x coordinates of a map projection so that none of the values being mapped are negative.

• False northing are values added to the y coordinates.

Every projection has a central meridian.

• Every projection has a central meridian.

• The line of longitude that defines the center and often the x origin of the projected coordinate system.

• In most projections, it runs down the middle of the map and the map is symmetrical on either side of it.

• It may or may not be a line of true scale. (True scale means no distance distortion.)

Define

• Define

• Project

• Select a standard projection.
• Create a custom projection.
• Import a projection.

Scale the earth down to a globe whose size is compatible with the size of the map plane. This is called the generating globe.

• Scale the earth down to a globe whose size is compatible with the size of the map plane. This is called the generating globe.

• The radius between the generating globe and the real earth is called the principal scale.

• The representative fraction refers to this scale.

Representative fraction – when the scale value is given as a fraction with a numerator as 1.

• Representative fraction – when the scale value is given as a fraction with a numerator as 1.

• When the representative fraction is relatively large we refer to the map as a large scale map.

• More detail
• Smaller area

0 > scale factor < =1

• 0 > scale factor < =1

• The ratio of the actual scale at a particular place on the map to the stated scale on the map.

• Usually the tangent line or secant lines.

ReadChapter 3.

• ReadChapter 3.

• Problems: 5, 6, 7, 9, 3,10, 22, 28, 29