Datums and Projections:How to fit a globe onto a 2-dimensional surface

Overview

Ellipsoid

Spheroid

Geoid

Datum

Projection

Coordinate System

Definitions: EllipsoidAlso referred to as Spheroid, although Earth is not a sphere but is bulging at the equator and flattened at the polesFlattening is about 21.5 km difference between polar radius and equatorial radiusEllipsoid model necessary for accurate range and bearing calculation over long distances GPS navigationBest models represent shape of the earth over a smoothed surface to within 100 meters

Geoid: the true 3-D shape of the earth considered as a mean sea level extended continuously through the continents

Approximates mean sea level

WGS 84 Geoid defines geoid heights for the entire earth

Definition: DatumA mathematical model that describes the shape of the ellipsoidCan be described as a reference mapping surfaceDefines the size and shape of the earth and the origin and orientation of the coordinate system used.There are datums for different parts of the earth based on different measurementsDatums are the basis for coordinate systemsLarge diversity of datums due to high precision of GPSAssigning the wrong datum to a coordinate system may result in errors of hundreds of meters

Commonly used datums

Datum Spheroid Region of use

NAD 27 Clark 1866Canada, US, Atlantic/Pacific Islands,

Central America

NAD 83 GRS 1980 Canada, US, Central America

WGS 84 WGS 84 Worldwide

GPS is based on WGS 84 system

GRS 1980 and WGS 84 define the earth’s shape by measuring and triangulating from an outside perspective, origin is earth’s center of mass

ProjectionMethod of representing data located on a curved surface onto a flat planeAll projections involve some degree of distortion of:

DistanceDirectionScaleAreaShape

Determine which parameter is importantProjections can be used with different datums

Projections

The earth is “projected” from an imaginary light source in its center onto a surface, typically a plate, cone, or cylinder.

Planar or azimuthal Conic Cylindrical

Other Projections

Pseudocylindrical

Unprojected or Geographic projection: Latitude/Longitude

There are over 250 different projections!

Cylindrical:

used for entire world

parallels and meridians form straight lines

Tangency: only one point touches surface

Secancy: projection surface cuts through globe, this reduces distortion of larger land areas

Cylindrical projection

Shapes and angles within small areas are true (7.5’ Quad)

Distances only true along equator

Conical:

can only represent one hemisphere

often used to represent areas with east-west extent (US)

Secant at 2 standard parallels

Distorts scale and distance, except along standard parallels

Areas are proportional

Directions are true in limited areas

Albers is used by USGS for state maps and all US maps of 1:2,500,000 or smaller

96 degrees W is central meridian

Lambert is used in State Plane Coordinate System

Azimuthal:

Often used to show air route distances

Distances measured from center are true

Distortion of other properties increases away from the center point

Lambert:

Specific purpose of maintaining equal area

Useful for areas extending equally in all directions from center (Asia, Atlantic Ocean)

Areas are in true proportion

Direction true only from center point

Scale decreases from center point

Orthographic:

Used for perspective views of hemispheres

Area and shape are distorted

Distances true along equator and parallels

Pseudocylindrical:

Used for world maps

Straight and parallel latitude lines, equally spaced meridians

Other meridians are curves

Scale only true along standard parallel of

40:44 N and 40:44 S

Robinson is compromise between conformality, equivalence and equidistance

Mathematical RelationshipsConformality

Scale is the same in every directionParallels and meridians intersect at right anglesShapes and angles are preservedUseful for large scale mappingExamples: Mercator, Lambert Conformal Conic

EquivalenceMap area proportional to area on the earthShapes are distortedIdeal for showing regional distribution of geographic phenomena (population density, per capita income)Examples: Albers Conic Equal Area, Lambert Azimuthal Equal Area, Peters, Mollweide)

Mathematical RelationshipsEquidistance

Scale is preserved Parallels are equidistantly placedUsed for measuring bearings and distances and for representing small areas without scale distortionLittle angular distortionGood compromise between conformality and equivalenceUsed in atlases as base for reference maps of countriesExamples: Equidistant Conic, Azimuthal Equidistant

CompromiseCompromise between conformality, equivalence and equidistanceExample: Robinson

Projections and Datums

Projections and datums are linked

The datum forms the reference for the projection, so...

Maps in the same projection but different datums will not overlay correctly

• Tens to hundreds of meters

Maps in the same datum but different projections will not overlay correctly

• Hundreds to thousands of meters.

Coordinate System

A system that represents points in 2- and 3- dimensional spaceNeeded to measure distance and area on a mapRectangular grid systems were used as early as 270 ADCan be divided into global and local systems

Geographic coordinate system

Global system

Prime meridian and equator are the reference planes to define spherical coordinates measured in latitude and longitude

Measured in either degrees, minutes, seconds, or decimal degrees (dd)

Often used over large areas of the globe

Distance between degrees latitude is fairly constant over the earth

1 degree longitude is 111 km at equator, and 19 km at 80 degrees North

Universal Transverse Mercator

Global system

Mostly used between 80 degrees south to 84 degrees north latitude

Divided into UTM zones, which are 6 degrees wide (longitudinal strips)

Units are meters

Eastings are measured from central meridian (with 500 km false easting for positive coordinates) Northing measured from the equator (with 10,000 km false northing)

Easting 447825 (6 digits) Northing 5432953 (7 digits)

State Plane Coordinate System

Local systemDeveloped in the ’30s, based on NAD27Provide local reference systems tied to a national datumUnits are feetSome larger states have several zonesProjections used vary depending on east-west or north-south extent of state

Each of the three coordinate systems (Lat/Long, UTM, and SPCS) have their own set of tick marks on 7½ minute quads:

Lat/Long tics are black and extend in from the map collarUTM tic marks are blue and 1000 m apartSPCS tics are black, extend out beyond the map collar, and are 10,000 ft apart

Which tic marks belong to which grid?

Other systems

Global systemsMilitary grid reference system (MGRS)World geographic reference system (GEOREF)

Local systems Universal polar stereographic (UPS) National grid systems Public land rectangular surveys (township and sections)

Determining datum or projection for existing data

MetadataData about dataMay be missing

HeaderOpened with text editor

SoftwareSome allow it, some don’t

ComparisonOverlay may show discrepanciesIf locations are approx. 200 m apart N-S and slightly E-W, southern data is in NAD27 and northern in NAD83

Selecting Datums and Projections

Consider the following:Extent: world, continent, regionLocation: polar, equatorialAxis: N-S, E-W

Select Lambert Conformal Conic for conformal accuracy and Albers Equal Area for areal accuracy for E-W axis in temperate zonesSelect UTM for conformal accuracy for N-S axisSelect Lambert Azimuthal for areal accuracy for areas with equal extent in all directions Often the base layer determines your projections

Summary

There are very significant differences between datums, coordinate systems and projections,

The correct datum, coordinate system and projection is especially crucial when matching one spatial dataset with another spatial dataset.