# BC Environment Standard Projection

BC Environment GIS Working Group has chosen a standard projection and datum for all spatial data stored in ARC/INFO.

The projection is Albers Equal Area Conic, with parameters of :

• Central meridian: -126.0 (126:00:00 West longitude)
• First standard parallel: 50.0 (50:00:00 North latitude)
• Second standard parallel: 58.5 (58:30:00 North latitude)
• Latitude of projection origin: 45.0 (45:00:00 North latitude)
• False northing: 0.0
• False easting: 1000000.0 (one million metres)

The datum is NAD83, based on the GRS80 ellipsoid.

# ARC/INFO data

ARC/INFO data stored in geographics (ie coordinates are in Longitude/Latitude) may need extra processing when converting Long/Lat to Albers.

# Tutorial

This tutorial explains some of the issues involved in choosing a map projection, and characteristics of the commonly-used ones.

# Projection choice

The Albers Equal Area Conic projection was chosen because :
• It is appropriate for representing the whole province on one projection plane, while maintaining sufficient accuracy for all BC Environment's analysis needs.

• Latitude lines are represented by simple curves, and longitude lines by straight lines. This makes tiling on mapsheet boundaries reliable and straightforward.

• As its name implies, it distorts area very little.

• Its area representation is very close to Universal Transverse Mercator, the standard projection used by Ministry of Forests. We found the average difference to be 0.05 %, and the maximum difference to be 0.08 % within the province.

• Its distance representation is also very close to Universal Transverse Mercator. We found the average difference in latitude to be 0.15 %, and the maximum difference to be 0.30 % within the province. The average difference in longitude is 0.17 %, and the maximum difference is 0.32 %.

## Parameter choice

• The latitudes of the standard parallels were chosen to minimize the total distortion of area across the province as a whole from Victoria (at about 48:15 N) to the Yukon border (at 60:00 N). Albers distorts much more outside the standard parallels than between them.

• The longitude of the central meridian was chosen to approximately bisect the area of the province. BC has a longer E-W dimension than N-S.

• The latitude of projection origin and false easting were chosen to ensure positive coordinate values across the province.

• The range of coordinates can be stored in single precision with metre accuracy.

## Datum choice

The NAD83 datum is preferable to NAD27 in British Columbia, and is also used as the base for Terrain Resources Inventory Mapping (TRIM) by Surveys and Resource Mapping Branch of BC Lands. As NAD27 data is added to the corporate spatial database, it is NAD-shifted to NAD83 using the Canadian National Transformation Matrix.

# Justification

A subcommittee of the GIS Working Group was formed to decide on a standard projection. Its findings are summarized below.

## References

Snyder, and the ARC/INFO 'User's Guide to Map Projections and Coordinate Management' were used.

## Other agencies

A survey of other provincial ministries and agencies found no clear standard.

## ARC/INFO limitations

Most of ARC/INFO's analysis functions (eg UNION, the polygon overlay function) do not work across map projections (ie both layers must be stored in the same projection). This made it important that one projection plane be used for all provincial data.

## Projection choices

The projections considered and rejected were:
• Longitude/Latitude. BC Environment had been storing its spatial data in Genasys in degrees of Longitude/Latitude, partly due to limitations of its map tiling/indexing scheme. However, Genamap calculates polygon areas only when it builds topology. This meant that it calculated areas using an equivalent to a Mercator projection plane, which introduced significant distortion (up to 15 %) of area calculations in maps of large areas.

It is theoretically possible to store data this way in ARC/INFO also, but analysis cannot be done unless the data is projected, and duplicated, in a better projection. This is impractical.

Also, no GIS can yet store or process raster data in Long/Lat. Therefore, a true projection must be chosen for generation and storage of raster data. Once this is done, it is more convenient if all data (including vector) is stored in the same projection.

For both of these reasons, Long/Lat storage was rejected.

• Universal Transverse Mercator. This projection represents area, distance, and shape well. However, BC contains 5 UTM zones, and most of the management regions contain two or more zones. This means that data must be projected between zones to do analysis across a zone boundary. ARC/INFO must copy data to do this transformation, so UTM was rejected.

• Polyconic. This projection represents the province well on paper, but all its lines (longitudes and latitudes) are complex curves. It preserves neither area nor shape. Also, Snyder recommends against using Polyconic for large, tiled datasets, so Polyconic was rejected.

## Projection testing

Both Lambert Conformal Conic (two parallels), and Albers Equal Area were tested statistically for distortion of area and distance.

A polygon coverage of the entire province was created, composed of rectangular areas (The 1:20,000 BCGS mapsheet neatlines) in longitude/latitude. This coverage was projected into UTM, Lambert, Polyconic, and Albers. The areas, latitudinal (horizontal) widths, and longitudinal (vertical) heights of the polygons in each projection were calculated. These measurements in each of the three projections were then compared with the corresponding measurements in UTM.

These tables show:

These images illustrate : As the tables and images show, the representation of both area and distance in Albers is much closer to UTM than either Polyconic or Lambert are to UTM.

## Shape distortion

The Queen Charlotte Islands and Haines Triangle were plotted at similar scale in both UTM and Albers. The Albers conic projection rotates the data, because it is so far from the central meridian. However, there are no visible differences in the shapes of the features.