GEOG 380 - Topic 06 - Coordinate systems

Coordinate Systems

What is a coordinate system?

A coordinate system is a way to describe the location of features on Earth or on a map.

What is the difference between a coordinate system, a datum, and a projection?

A coordinate system tells how to locate something, a datum defines the Earth model being used, and a projection defines how Earth is flattened onto a map.

What is a Geographic Coordinate System (GCS)?

A GCS uses a 3D Earth model and angular coordinates, usually latitude and longitude, to define locations.

What is a Projected Coordinate System (PCS)?

A PCS uses a flat 2D surface and Cartesian coordinates, usually eastings and northings in metres, to define location.

What is latitude?

Latitude is the angular distance north or south of the equator.

What is the origin of latitude?

The equator, which is 0° latitude.

What is the range of latitude?

0° to 90° north and 0° to 90° south.

What is longitude?

Longitude is the angular distance east or west of the prime meridian.

What is the origin of longitude?

The prime meridian at Greenwich, England, which is 0° longitude.

What is the range of longitude?

0° to 180° east and 0° to 180° west.

What are parallels?

Parallels are latitude lines.

What are meridians?

Meridians are longitude lines.

Which latitude line is a great circle?

The equator.

Are all meridians great circles?

Yes

What is a great circle?

A circle on Earth whose center is the same as Earth’s center.

What is a small circle?

A circle on Earth whose center is not the same as Earth’s center.

What are the three common ways to write latitude and longitude?

Degrees-minutes-seconds, degrees and decimal minutes, and decimal degrees.

In signed coordinates, which directions are positive?

North and east are positive.

In signed coordinates, which directions are negative?

South and west are negative.

How do you convert DMS to decimal degrees?

Decimal degrees = degrees + minutes/60 + seconds/3600.

What is a datum?

A datum is the reference framework that defines the size, position, and orientation of the Earth model used for coordinates.

Why is datum important?

Because the same coordinates can refer to different actual locations if different datums are used.

What is the geoid?

The geoid is an irregular gravity-based surface that approximates mean sea level.

What is the ellipsoid?

The ellipsoid is a smooth mathematical surface used to approximate the geoid.

Why do we use an ellipsoid instead of the geoid for many calculations?

Because it is regular, smooth, and mathematically easier to work with.

What does flattening describe in an ellipsoid?

It describes how much the Earth is squashed at the poles compared with the equator.

What is NAD27?

A North American datum from 1927 based on the Clarke 1866 ellipsoid.

What is NAD83?

A North American datum from 1983 based on the GRS80 ellipsoid.

What is WGS84?

A global Earth-centered datum widely used in GPS and GNSS.

What does ECEF mean?

Earth-Centered, Earth-Fixed.

What is meant by a plate-fixed datum?

A datum whose coordinates remain fixed relative to a tectonic plate, such as North America.

Why can ECEF and plate-fixed datums differ over time?

Because tectonic plates move over time.

What is a vertical datum?

A vertical datum defines what is considered zero elevation.

What is orthometric height?

Height above the geoid, usually thought of as elevation above sea level.

What is ellipsoidal height?

Height above the ellipsoid, often given directly by GNSS/GPS.

What is geoid height?

The separation between the ellipsoid and the geoid.

What is the relationship between orthometric height, ellipsoidal height, and geoid height?

H = h - N

Why doesn’t GPS directly give true sea-level elevation?

Because GPS measures height relative to the ellipsoid, not the geoid.

What is a map projection?

A map projection is a method for representing Earth’s curved surface on a flat map.

Why must distortion occur in a map projection?

Because a curved 3D surface is being transformed to a flat 2D surface.

What four key properties of maps are affected by projection?

Shape, area, distance, and direction.

What does a conformal projection preserve?

Local shape and angles.

What does an equal-area projection preserve?

Relative area.

What does an equidistant projection preserve?

True distance from certain points or along certain lines only.

What does a direction-preserving projection preserve?

Accurate direction in certain or all directions, depending on the projection.

Why can’t a flat map preserve all four projection properties everywhere?

Because flattening Earth always introduces distortion.

What type of projection is Mercator?

A conformal cylindrical projection.

What is Mercator especially known for preserving?

Local shape and direction.

What is Mercator especially bad at preserving?

Area, especially near the poles.

What is Plate Carrée?

A simple cylindrical projection where x = longitude and y = latitude.

What is an azimuthal projection?

A projection made using a plane as the developable surface.

What is a cylindrical projection?

A projection made using a cylinder as the developable surface.

What is a conic projection?

A projection made using a cone as the developable surface.

What does tangent mean in projections?

The projection surface touches the globe at one line or point.

What does secant mean in projections?

The projection surface cuts through the globe and intersects it in two lines.

Why are secant projections often useful?

Because they spread distortion more evenly and reduce maximum error over the map area.

What is Orthographic projection meant to resemble?

The Earth viewed from far away in space.

What is Stereographic projection based on?

A light source on the far side of the globe.

What is Gnomonic projection based on?

A light source at the center of the Earth.

What kind of region is often best for a conic projection?

A mid-latitude region that is wider east-west than north-south.

What kind of region is often best for a polar azimuthal projection?

A region centred on the poles or containing a lot of polar area.

What kind of projection is often best for comparing statistical regions?

An equal-area projection.

What kind of projection is often best when shape is most important?

A conformal projection.

What kind of projection is often good for long north-south regions?

A projection like UTM or another transverse Mercator-based system.

What is UTM?

Universal Transverse Mercator, a projected coordinate system based on the Transverse Mercator projection.

How wide is each UTM zone?

6 degrees of longitude.

How many UTM zones cover the world?

60 main zones.

Why is UTM divided into zones?

To keep distortion low within each narrow strip.

What units are used in UTM coordinates?

Meters

What are the two coordinate values in UTM?

Easting and northing.

What is an easting?

The east-west coordinate in a projected system.

What is a northing?

The north-south coordinate in a projected system.

In UTM, what is the coordinate order?

Easting first, northing second.

What is false easting in UTM?

A value added so easting coordinates stay positive within a zone.

What is the central meridian in UTM commonly assigned?

500,000 metres easting.

What do northings in UTM measure from?

Which UTM zones cover Alberta?

What major longitude separates Alberta’s two UTM zones?

114°W.

Why is UTM commonly used in GIS and topographic mapping?

Because it provides precise metric coordinates with relatively low distortion within each zone.

What is the Canadian Spatial Reference System (CSRS)?

A Canadian framework of standards and models for spatial positioning, height, and gravity reference systems.

What is the simplest way to distinguish GCS from PCS?

GCS uses angular coordinates on a 3D Earth model; PCS uses linear coordinates on a flat map.

What should you always check before combining two spatial datasets?

Their coordinate system, datum, and projection.

What is the main question to ask when choosing a projection?

What kind of distortion can be tolerated for the purpose of the map?

What is the “best” projection?

The one whose distortion properties best match the purpose of the map.

What does DLS stand for?

Dominion Land Survey.

What is the Dominion Land Survey used for?

It is used for legal land description and land ownership.

What is another common name for DLS?

Township and Range.

What is the main purpose of a legal land description?

To describe an exact parcel of land for ownership and legal reference.

What is the basic hierarchy of DLS from largest to smallest?

Meridian → Range → Township → Section → Quarter section or Legal Subdivision (LSD)

What is a meridian in DLS?

A north-south reference line used to count ranges east or west from it. The lecture map shows numbered meridians such as the 3rd, 4th, 5th, 6th, and 7th meridians.

In Alberta, why do you often see W4, W5, or W6 in legal descriptions?

They mean the land is west of the 4th, 5th, or 6th meridian. The meridian used is part of the legal description.

What is a township in DLS?

A township is a large square block of land made up of 36 sections. The lecture’s DLS hierarchy diagram shows a township divided into sections numbered 1 to 36.

How many sections are in one township?

36 sections

How are sections numbered inside a township?

They are numbered in a back-and-forth “snake” pattern from 1 to 36, not simply left to right on every row. The lecture diagram shows 1 in the southeast corner, 6 in the southwest, then numbering reverses on the next row.

What is a quarter section?

A section divided into four parts: NW, NE, SW, SE.

What is a Legal Subdivision (LSD)?

A smaller subdivision within a section used for more precise legal description. The lecture shows a section divided into 16 legal subdivisions.

How many legal subdivisions are in a section?

16

What does this legal description mean: NE ¼ - Sec 1 - Twp 17 - Rge 8 - W3?

It means the northeast quarter of Section 1, Township 17, Range 8, west of the 3rd meridian.

What does this legal description mean: LSD 15 - Sec 1 - Twp 17 - Rge 8 - W3?

It means Legal Subdivision 15 of Section 1, Township 17, Range 8, west of the 3rd meridian.

What is the difference between a quarter section and an LSD?

A quarter section divides a section into 4 larger parts, while LSD divides it into 16 smaller parts.