GIS CH4 - Coordinate Systems and Map Projections

What is a coordinate system?

a reference system used to represent the location of geographic features

Two types of coordinate systems

1. global or spherical CS such as lat-long (geographic coordinate systems)
2. Projected CS based on a map projection

A CS may be __ or __

projected or unprojected

A feature class has a ___ documenting CS parameters

label

Different CS have same __ different __

point, x-ys

What is the most common method of providing spatial referencing?

through geographic coordinate systems

What is a spatial reference?

a complete description of the GIS data coordinate system

Components of spatial reference:

1. geographic coordinate system (datum)
2. project method (if one is used)
3. Unit (degrees, meters, feet, etc)
4. Domain (max x and y)
5. Resolution (precision of x, y values)

Unprojected data are stored in

degrees

What is the shape of earth?

Geoid

What shape is a geoid?

the shape measured at constant gravity of sea level

The distance from the geoid surface is the

elevation

Details on ellipsoids:

since the earth is irregular, comparing to the size of the earth, the gravity change is minimal, so that earth can be represented by an ellipsoid object

Most used ellipsoid models

CLARKE 1866, WGS84, GRS80

What does the datum definition include and what do the components make up

1. the particular ellipsoid (major and minor axis) and the adjustment or fit (translation of center)
2. together these define the Geographic coordinate system

Datums in North America

NAD1927 (based on Clarke1866 spheroid), NAD1983 (based on GRS80 spheroid), WGS84, NAD1983 HARN

What was the first attempt at a truly 3D system

NAD 1983 HARN

What is the most popular datum used in NA?

NAD1983

What are the ways to transform datums?

1. three parameter method
2. seven parameter method
3. grid based method (most accurate)

What is a WKID?

Well known ID, unqiue ID assigned for each coordinate system

Map Projection concept

1. A systematic transformation of the 3D spherical surface onto a 2D plane surface of a flat map
2. A map is made by transforming the spherical surface to a plane

Map projection goes from ___ with these coordinates __ to __ with these coordinates __

Curved earth, geographic coordinates (lat and lon)
Flat map, cartesian coordinates (easting and northing)

The process of 'flattening' the spherical surface involves:

stretching, shrinking, or tearing

Projection process inevitably distorts at least one of these properties:

shape, area, direction, distance (SADD)

What are developable projection surfaces?

Cylindrical and conic

Types of projections:

cylindrical, conic, and azimuthal

Azimuthal Projection details

can either be polar (pane on top), equatorial (pane on side), or oblique (pane tilted)

Cylindrical projection details

Mercator (flat map cylinder upright, pretty standard), or transverse mercator (transverse cylindrical on side, more of a strip)

Conic Projection details:

Tangent (one standard parallel) or secant (two standard parallels)

What is the central meridian?

the longitude which serves as the x = 0 origin of the map, x values to the right of the CM are pos, x value to the left of CM are neg

What is the reference latitude?

the latitude which serves as the y=0 origin for the map, y values above are pos, y values below are neg, often the equator is used

Tangent Projections

1. cylinder/cone is tangent to the globe
2. single standard parallel
3. no distortion along parallel, increases with distance from it

Secant Projections

1. cylinder/cone is secant to the globe
2. has two standard parallels
3. no distortion along parallels, increases with distance from them

False Easting and Northing

Projected, flat map w cartesian coordinates (x,y), arbitrary values added to x and y values, usually used to ensure that all x-y coordinates are positive

Coordinate Units after projecting?

projecting changes the x-y values from degrees (GCS, lat lon, curved earth) to meters or feet (flat map, cartesian, xy)

Four types of distortion:

shape, area, distance, direction

Mercator Projection Distortions

conformal, so it preserves shape and local direction
distorts distance and area

Sinusoidal preserves:

area

Azimuthal equidistant preserves:

direction and area

Robinson projection distortion:

compromises all distortions

Equidistant conic projection distortions:

distorts direction and shape
preserves distance and area

Projections commonly used in the US:

Albers Equal area conic projection, LAMBERT CONFORMAL CONIC PROJECTION, TRANSVERSE MERCATOR PROJECTION

Albert Equal Area Conic details

1. equal area (equivalent) projection = shapes directions, angles, and distances are generally distorted
2. well suited for large countries that are mainly east-west in extent
3. most maps in US use this
4. standard parallels 29.5N and 45.5N

One sixth rule (albert equal area conic)

use 1/6 of the latitude range to define the first and second standard parallels

Lambert Conformal Conic

1. conformal = preserves angle (direction) and shape
2. used for aeronautical charts and portion of state plane CS
3. distortions of shape and areas minimal at standard lines (distances are only true along standard lines)
- good for east west (Turkey)

Transverse Mercator

1. horizontal cylinder
2. intersects ellipsoid along a single north-south tangent or two secant lines
3. has a band of low distortion, runs in a north south direction

Commonly used coordinate systems in the US:

Universal Transverse Mercator (world widely used, meters, UTM zone 15N)
State Plane (only used in US, foot, FIPS zone number, zone names north or south since states split into several zones

Universal Transverse Mercator (UTM) Grid System:

area between 84N and 60S lat divided into N-S columns of 6 degrees wide (UTM zones), numbered from 1 - 60 eastward beginning at 180th meridian, mapped on Transverse Mercator projection, Meridian in the zones center is given a false easting of 500,000 and equator is given a false northing value of 0 m for the northern hemi and 10 mil in the southern

State Plane Coordinate System (SPC)

based on the transverse mercator or the lambert conformal conic, the (FIPS 5001 Alaska zone) uses hotline oblique mercator, feet or meters , FIPS (federal information processing system) codes used to identify each zone, Louisiana zones 1701, 1702

FIPS?

Federal Information Processing system, State Plane Coordinate System (transverse mercator or lambert conformal projection), they are codes used to identify each zone

States with their own special coordinate systems:

Oregon Lambert CS, NAD 1983 Texas Centric Mapping System Albers

What is the spatial reference:

label that records the complete coordinate system parameters for proper display and analysis

Spatial reference components:

1. Geographic coordinate system/datum
2. Projection (if one is used)
3. Storage units used to store the x-y values (degrees, feet, meters)
4. Domain (max x y values)
5. Resolution (x y precison)

Difference between projected and unprojected coordinate systems

projected is in meters or something like that and has a table for the projection type and the GCS, unprojected is in degrees and only has a table for the GCS

Extent?

the extent of a spatial data set indicates the range of x-y values present in the data, can tell the stored map units from here

On the Fly Projection details

all data sets are transferred to the map coordinate system automatically, on the fly projection doesnt affect the orginal coord system of the data, if the label (spatial reference info) is wrong, OTFP will not work

If the spatial reference label is missing:

a. on the fly projection will not transfer the layer to the selected data coordinate system
b. on the fly projection will only display the data by its original coordinate numbers

If the spatial reference label exists but is wrong:

a. projection labels is wrong: on the fly projection will place the data into a strange location thousands kilometers away
b. datum label is wrong: the displacement is usually 10s or 100s meters

All spatial reference labels of the data used in a research projection are correct but in different parameters

a. it is better to project all data into the same coordinate system before using them in the project

Use "project" tool to:

permanently convert data from one coordinate system to another
a. create new data set
b. transformation must be specified if the new CS has a different datum than the original CS
- equivalent to export features

Define Projection:

a. creates or changes only the CS label (spatial reference info)
b. does not change the coordinates in the file
c. keeps the original data set
d. use only when CS is missing or incorrect
e. most CS problems are caused by the misuse of this tool

Solving Coordinate System Problems

1. Change map projection by Project
a. project
b. project raster
c. datum transformation
2. For data sets with missing spatial reference information, use DEFINE PROJECTION to label them
3. For data sets with wrong labels, identify the correct labels and define it

I want to display ROADS (GCS NAD 1983, latlon) and STATE (UTM zone 13) in UTM 13. I need to define the ROAD data set as the UTM zone 123 sso that these two layers are in the same coordinate system. Is that decision correct?

NO! You will create a dataset with a mislabeled CS. ArcGIS will see the label and say "I don't have to reproject it to UTM on the fly (coordinates are the same as before still bc define only changes the LABEL)

CORRECT REASONING:
Just let Arc-GIS do on the fly, or use the Project Tool to convert roads to UTM, creating a new file

Three Types of units in ArcGis

1. Map Frame Unit
2. Display Unit
3. Stored Data Unit

Map Frame Unit

determined by the map frame coordinate system setting

Display Unit

user selected unit to display coordinates in the map interface

Stored Data Unit

x-y values saved in the GIS data file

Always create maps with a __ system

projected coordinate

Projections for large scale maps

Local, city, county maps, smaller states; projection systems virtually eliminate distortion, UTM or state plane zone should lie in single zone

Remember: large scale = detailed

Projections for Small Scale Maps

Continents and countries, distortion is inevitable

- equidistant maps when distances are important
- equal area maps when area is important
- conformal or compromise for general purpose maps

For maps where there's no special state projection defined that you can simply use

use the UTM zone parameters but adjust the central meridian of the zone

The RMS Error

gives you an idea of the average accuracy (in map units) as long as you have more control points than the minimum needed

RMSE = SQRT(sum(error^2)/n)

Transformation Method

1. First order rotates and shifts images (requires fewest links)
2. Second order allows for the bending of the image (requires more links)
3. Third order (rarely used) like a second order but allows greater curvature

- used the lowest order that produces a reasonable fit

If a data set's features have x coordinates between -180 and +180, what is the coordinate system likely to be? In what units are the coordinates?

GCS, in degrees latitude

Explain why the UTM projection would not be a good choice for making a map of the contiguous United States.

Contiguous US spans multiple UTM zones, so using UTM projection would result in significant distortion, esp along the east west direction

What is the difference between a central meridian and the Prime Meridian?

The central meridian is the center of a map projection where x=0 and may be any longitude line, the prime meridian is the longitude line on earth defined as zero and it runs through Greenwich, England

A shapefile has an Unknown coordinate system, but a file on the web site says that the coordinate system is UTM Zone 13 NAD 1983. What is the next step?

Use the define projection tool to set the coordinate system to UTM Zone 13 NAD 1983.

A shapefile has a UTM Zone 10 NAD 1983 coordinate system and must be brought into a state database that uses the Oregon Statewide Lambert coordinate system. What is the next step?

Use the project tool to convert the shapefile to the Oregon Statewide Coordinate System

What is the difference between a spheroid and a geoid?

A geoid is the theoretical surface of earth that is affect by topographic and gravitational factors. It is too complex and irregular to map with. The spheroid is a mathematical model of the earth. It is simplistic and realistic.

True or False: A shapefile of the US with a GCS coordinate system would have an x-y extent that contains entirely pos values

FALSE. North of the equator will have pos values but neg numbers of longitude bc its west of the prime meridian