### Projections

### Overview

Our earliest and best descriptions of locations on the earth have been presented using angles of latitude and longitude, based in the geographic coordinate system (GCS). Projections are used to transform the spheroidal coordinates of the GCS into planar coordinates. This topic covers the characteristics of projections in general and will look at the Universal Transverse Mercator and the BC Albers Equal-Area projections in particular.

### Learning Outcomes

Upon successful completion of this topic you would be able to:

- Explain the spatial properties affected by different projections
- Describe the properties of the Universal Transverse Mercator (UTM) and the BC Albers projection systems
- Add descriptive projection information to data using ArcCatalog
- Change the coordinate system / projection of a dataset using the coordinate system / projection properties of another dataset in ArcCatalog
- Change the coordinate system / projection of a dataset using the standard coordinate system / projection templates found in ArcCatalog

**Projections**

Map Projections are attempts at accurately representing the geometry of the earth on a flat map. The parallels (lines of latitude) and meridians (lines of longitude) that represent the earth’s spheroidal surface, are manipulated so that they are presented on a flat surface. There are hundreds of different ways of doing this, each mathematically derived.

There are several feature properties that are important to the map user, namely position, direction, distance, shape, and area. Unfortunately, it is impossible to project from a sphere / spheroid onto a plane and retain accuracy in all of these. Decisions must therefore be made regarding the most importance of these and which should be retained for the use at hand, when deciding on the use of a projection.

**Activity 1 – Exploring projection Classes**

Projections are divided into three main classes based on the type of surface used; the plane, the cone and the cylinder. Do an internet search to find information about these projection classes. What is meant when a projection is described as a ‘Tangent Case’ or as a ‘Secant Case’.

**Activity 2 – Exploring projection aspect**

Projections are described as ‘Normal’, ‘Transverse’ or ‘Oblique’. What do these mean?

**Activity 3 – Exploring projection properties**

Please post a short description of the different properties one can find in different types of projections. You should investigate the properties of Conformal projections, Equivalent projections and Equi-distant projections. What geometric properties do they preserve? What kind of use can they be put to? Can we have maps with elements of each or more than one? Name this post “Projection Properties”.

**Universal Transverse Mercator (UTM) projection**

The UTM projection uses the Secant Transverse Mercator Projection (Gauss-Kruger) and is based on concept of dividing the globe using a series of 60 narrow ‘gores’ (zones) which are contiguous at the equator. UTM world coverage is restricted to areas between 80^{o }S to 84^{o} N. The distance unit used is the metre. Measurements taken East of the origin are called *Eastings*. Measurements taken North of the origin are called *Northings*.

**Activity 4 – Exploring the UTM system**

The following link provides information regarding the characteristics and use of the UTM system. Please explore it and search for other sites that may provide additional information.

**Activity 5 – Discussion the UTM System**

Post a blog entry that describes the main characteristics of the UTM system. Your entry should address the following:

- The location of the origin and the axes used
- How does the coordinate zero (0,0) in each zone relate to the origin of the projection in that zone.
- What is the width and height of each zone (metres)
- The scale factors (distortion) expected in different parts of each zone
- Any limitations to the use of this system

Please provide links to any website that you think are particularly helpful.

**Activity 6 – Comments on UTM postings
**

Please post a comment on the posting of at least two other class members.

**BC Albers Equal-Area Projection**

This projection is an adaptation of the standard Albers Equal-Area projection, to meet the requirements of mapping large areas across the province of British Columbia. This projection avoids the problems associated with mapping locations across UTM zones for example. The parameters include a projection centre and standard parallels that best suit mapping in the province of British Columbia.

**Activity 7 – Exploring the BC Albers Equal-Area Projection**

The following link provides information on this projection. Please read this information and do an individual search for further information.