Geog 258: Maps and GIS

January 30, 2006

Grid Coordinate Systems

Reading: Chapter 4

Outlines

 

Making measurement in the round earth is not quite straightforward (for example, distance of one degree longitude is not constant, but rather it is a function of latitude). We looked at how the round earth can be transformed into flat map (i.e. map projection). With map projection, it is possible to locate things in 2-dimensional (i.e. projected) coordinate system. Grid coordinate system is convenient because things can be located by using a simple two-axis reference system (x, y) value. Beside, we can make measurement (distance, direction and area) between any points by applying simple geometry in grid coordinate systems.

 

Two commonly used grid coordinate systems will be introduced, that is State Plane Coordinate (SPC) System and Universal Transverse Mercator (UTM) System. They can be commonly seen in USGS topographic maps (see labels at the edge of maps). Not knowing about how these coordinate systems are defined can easily perplex beginner map readers.

 

Demo:

Go to Terraserver

Explore Seattle area

Click info tab, which will give you (x, y) coordinates at the edge of maps

Find out what a world file is when you download images

Check cursor location (x, y value reported in status bar for instance in ArcGIS) when the image is displayed with world file and without world file. How are they different?

 

State Plane Coordinate (SPC) System

 

Many map uses arise from municipal needs (e.g. land record), so it may be practical to have coordinate systems defined within administrative units.

 

Divide the country into zones, where zone boundaries follow state and county boundaries

 

Make a separate grid for each zone. Each zone has its own projection surface based on the Clarke 1866 ellipsoid (for SPC 27).

 

 

For each zone, appropriate map projection will be employed given the following rules: If zones have greater east-west extent (e.g. Washington N, S zones), secant-case Lambert conformal conic projections will be used such that overall distortion can be minimized within a zone. (See below; standard parallels are lines of tangency of generating globe to developable surface; scale factor is 1 along standard parallels).

 

 

If zones have greater north-south extent (e.g. NY W, C, E zones), secant-case Transverse Mercator projections will be used such that overall distortion can be minimized within a zone. (See below; grid is converged into central meridian)

 

Which map projection should be used for zones in Texas? Where (approximately) would standard parallels lie?

Which map projection should be used for zones in Idaho? Where (approximately) would central meridian lie?

 

To make coordinate values positive, it is common to use false northing and easting. For instance, false easting is usually located 2,000,000 feet west of the central meridian for Lambert conformal conic.

 

Until 20 years ago, NAD27 had been used as datum for State Plane Coordinate system. In 1983, a new geodetic model GRS80 was adopted.

 

SPC27 is based on Clark 1866, and its measurement unit is feet

SPC83 is based on GRS80, and its measurement unit is meter

 

Universal Transverse Mercator (UTM) System

 

It may be convenient to have grid coordinate systems that can be recognized in international scope. Of course we have looked at many map projections that simply portray the world (e.g. Mercator, Mollweide, Robinson). Are they good enough for giving accurate measurement of location? What’s the problem with using those map projections?

 

They use one developable surface, which necessarily involves too much distortion particularly in the area further from a line of tangency (mostly equator). Why if we use small developable surfaces? It can minimize distortion because areas further from a line of tangency are reduced. UTM divide the world into 60 strip-like zones for every 6 degree longitude as you can see below.

 

 

For each zone (numbered 1 to 60 from west to east), secant-case Transverse Mercator projection centered on the zone’s central meridian is used.

 

False origin is located 500,000 meters west of the central meridian.

 

Washington portrayed in UTM zone 10 relative to graticule

 

 

See where a line of tangency (between generating globe and developable surface) lies in the following figure. What would be the consequence of making contact there? Why is this projection called “Transverse” Mercator?

Let’s compare UTM with SPC

 

 

UTM

SPC

Boundary

Latitude & longitude

Administrative boundary

Projection type

Transverse Mercator

Lambert conformal conic

Transverse Mercator

Geographic scope

International

U.S. only

Measurement unit

Meter

Feet (for SPC27)

Meter (for SPC83)

 

Review questions

 

The text below is taken from a USGS topographic map. Read the text below and answer the followings.

 

 

·       What is the source of this map?

·       If you imagine light source in the transparent globe being projected onto plane to make this map, what would be the shape of the developable surface?

·       Which geodetic model is used in this map? In other word, coordinates are measured relative to what?

·       What grid coordinate system is used in this map?