ENV103 Chap.2 Map Projections, Datums and Coordinate Systems
Map Projections, Datums and Coordinate Systems
Every flat map distorts the curved Earth, so this chapter explains what each family of projections keeps and gives up, how geodesy, datums and projections fit together, and how New Zealand fixes its coordinates with NZTM2000, EPSG 2193. It ends with reading real easting and northing values, the skill behind every distance and area you calculate in the labs.
The worked examples read real Lab 1 coordinates for the Māngere and Oneroa treatment plants, so the numbers you meet in the labs stop looking arbitrary.
What this chapter covers
- 01
Why all flat maps distort
- 02
Conformal and equal-area projections
- 03
Planar, conical and cylindrical surfaces
- 04
Projections matched to country shape
- 05
Geodesy, datums and projections
- 06
NZTM2000 parameters and EPSG 2193
- 07
Geographic versus projected coordinates
Worked example · free
Read the Oneroa treatment plant's NZTM2000 easting and northing
- +1NZTM2000 gives the central meridian an easting of 1,600,000 m, so the offset east = 1,778,490.68 − 1,600,000 = 178,490.68 m, about 178.5 km.
- +1The equator carries the false northing of 10,000,000 m, so the distance south = 10,000,000 − 5,927,764.55 = 4,072,235.45 m, about 4,072 km.
- +1Both offsets are positive metres because the false easting and false northing were chosen to keep New Zealand coordinates positive.
Key terms
- Map projection
- A map projection is a method of representing part of Earth's curved surface on a flat plane.
- Conformal projection
- A conformal projection preserves the shapes of small areas while distorting their relative sizes.
- Equal-area projection
- An equal-area projection preserves the relative sizes of areas while distorting shape and direction.
- Datum
- A datum fixes coordinates to a chosen spheroid so that positions, including height, are referenced consistently.
- False easting
- A false easting is a constant added to x coordinates so that values across a mapped region stay positive.
- EPSG code
- An EPSG code is a numeric identifier for a coordinate reference system, such as 2193 for NZTM2000.
- Great circle route
- A great circle route is the shortest path between two points on the globe's surface.
- Central meridian
- The central meridian is the line of longitude at the centre of a Transverse Mercator projection, 173 degrees east for NZTM2000.
Map Projections, Datums and Coordinate Systems FAQ
Why does Greenland look as big as Africa on many maps?
Those maps use Mercator or Web Mercator, which preserve direction but enlarge areas increasingly with distance from the equator. Greenland lies far north, so it is drawn far larger than its true size relative to Africa, which straddles the equator. Equal-area projections such as Gall-Peters remove that inflation at the cost of shape.
Which coordinate system should a New Zealand project use in QGIS?
The labs set the project CRS to NZTM2000, EPSG 2193, a Transverse Mercator projection on the NZGD2000 datum. It suits the country's long north-south shape and expresses positions in metres, so distances and areas calculated in QGIS come out in sensible units.
What happens if two layers use different coordinate systems?
They may not line up, and measurements taken across them can be wrong. The Week 5 seabird example had points in WGS 84 and rasters in NZTM2000, so the points were reprojected first. Always check each layer's CRS before overlaying or measuring.
What is the difference between a datum and a projection?
A datum fixes coordinates to a chosen model of the Earth's shape, a spheroid, so that positions and heights are referenced consistently. A projection then flattens that curved surface onto a plane using a coordinate system. NZTM2000 combines the NZGD2000 datum with a Transverse Mercator projection, so both parts are needed to place a point correctly.
Assessment move
Learn projections as trade-offs rather than as a list of names. Draw a two-row table: the top row lists the four properties a map can distort, shape, area, distance and direction, and the bottom row names a projection that protects each one, with a sentence on what it sacrifices.
Then add the country-shape rule from the lecture: Transverse Mercator for long north-south countries such as New Zealand, Chile and Norway, and conic projections for wide countries such as Australia and the United States. Spend at least one session on NZTM2000 itself.
Memorise that the central meridian is 173° E with a false easting of 1,600,000 m and that the equator carries a false northing of 10,000,000 m, then practise reading eastings and northings from the Lab 1 and Lab 3 data as distances east of the meridian and south of the equator.
In QGIS, make checking the Project CRS in the bottom-right corner the first thing you do in every session, and the first thing you check when layers refuse to line up. Finally, try the True Size tool from the online lecture with a country you know well; seeing the distortion with your own eyes makes the explanation far easier to write.