Grid Systems

Transverse Mercator Projection

Copyright © 2009 by Maribeth H. Price 3-3

South Dakota

Zone 16

Universal Transverse Mercator

• Based on Transverse Mercator (cylindrical) projection• World divided into 60 zones 6 degrees wide• Distortion is minimal within each zone• Maps of different areas use best zone• Best for maps covering small area in one zone

UTM Zones

UTM Pole to Pole

Halfway to the Pole

Using UTM

Using UTM

Using UTM

Three Kinds of North

• True North – Along Meridians• Magnetic North – What a compass detects– Important in field– Not important in most GIS

• Grid North – Along N-S grid lines– Minor importance for compass work– Be aware there’s a difference!– Military uses exclusively

Cautions About UTM• Military maps use two letter codes for each

100-km square, but maps will have information to enable conventional UTM

• With military grid references, number of digits indicates level of precision

• Older maps will sometimes have obsolete grids

• Datum, datum, datum!

Military Grid System

• 45N 89 W = E 342,369, N 4,984,896 Zone 16T• Digraph = CQ• 1 km accuracy = 16T CQ 42 84• 100 m accuracy = 16T CQ 423 848• 10 m accuracy = 16T CQ 4236 8489• 1 m accuracy = 16T CQ 42369 84896

• Ticks on USGS topo map = 342,000, 4,984,000

Where Zones Meet

Why a Grid?Latitude /Longitude Grid System

North varies from place to place on the map

Grid north is always the same direction

Angular units differ in scale between N-S and E-W

Grid scale the same in all directions

E-W angular units vary in scale with latitude

Grid squares are always the same size and shape

Hexadecimal Scale Decimal Scale

Copyright © 2009 by Maribeth H. Price 3-15

State Plane System• States divided into

one or more zones identified by a unique FIPS number

• Uses several types of projections

• E-W zones generally Conic, N-S zones generally UTM

Copyright © 2009 by Maribeth H. Price 3-16

Projections for large scale maps

• Local, city, county maps, smaller states– Projection systems virtually eliminate distortion– Choose appropriate UTM or State Plane zone

Wisconsin State Plane Zones

Wisconsin Grid

Systems

Copyright © 2009 by Maribeth H. Price 3-19

Projections for smaller scales• Distortion is inevitable, so

purpose drives the choice– Equidistant maps when

distances are important– Equal area maps when areas

are important– Conformal or compromise

projections for general purpose maps

Coordinate system names generally indicate the locale and purpose it is optimized for. Use for clues to choice.

Metes and Bounds System

Public Land Survey System• AKA Congressional System• Established 1785• Does not apply to:– 13 Original Colonies– Derivative States (VT, KY, TN, ME, WV)– Texas (Former independent country)– Hawaii (Uses Kingdom of Hawaii system)

• Land Division– 6 x 6 mile townships, 36 sections, quarter sections

USA Public Land Surveys

Non-Congressional

Grids

Before Greenwich

Arbitrary Geography

More Arbitrary Geography

Grid vs. No Grid

Gridded Landscape

Where Wisconsin’s Grid Starts

Where California’s Grid Starts

Section Numbering

Wisconsin Townships

Township Labels

Section Descriptions

Limitations of the

Congressional Land Survey

System

Congressional Land Survey System• Not an accurate grid!• Locations within subdivisions may be

imprecise• Data points used in GIS may be tied to system• Authoritative surveys are forever– French strips in LA, MO, WI– Spanish and Mexican land grants

French Long Lot System

French Long Lot System

California: PLSS and Land Grants

California: PLSS and Land Grants

Oh, Canada• Eastern Canada: Metes and Bounds, Long Lot• Northern Ontario: 6 and 10-mile townships• Western Canada: Dominion Land Survey– Modeled on PLSS– 6-mile townships– Townships numbered N-S with Arabic numerals– Ranges numbered E-W with Arabic or Roman numerals– Road allowances between sections– Sections zigzag from 1 in SE to 36 in NE (Opposite US)– ¼-1/4 sections numbered from 1 in SE to 16 in NE

Dangers of Cheap Work

Missed It By That Much