# Improper Projection Definitions: Common Mistakes And How To Avoid Them

## Defining Projection Systems Properly

A map projection flattens the three-dimensional Earth into a two-dimensional map by mathematically transforming geographic coordinates of latitude, longitude, and elevation into planar coordinates of x, y, and z. Defining map projections properly is crucial for accurate geospatial analysis and visualization. Mistakes in projection definitions can lead to distorted measurements, inaccurate analysis, and misaligned data layers.

### Common Mistakes with Projection Definitions

Some common mistakes made when defining projection systems include:

- Not specifying a datum along with the projection
- Using the wrong datum for a particular region or country
- Not fully specifying projection parameters like standard parallels or central meridian
- Assuming default projection values without checking
- Using outdated projection systems

### Consequences of Improper Projection Definitions

#### Inaccurate Measurements and Analysis

The most direct impact of improperly defined projections is distorted measurements and calculations in the projected map. Some projections preserve areas accurately but distort distances and angles. Other projections preserve shapes but distort scale. Without proper parameters, projections can distort both areas and shapes.

For example, using the Web Mercator projection with alocalize scale factor for a region like Alaska can alter area measurements by up to 20%. Even at mid-latitudes, errors above 5% are common. Similarly, not specifying standard parallels for conic projections can cause uneven distortion across a map.

#### Data Misalignment Issues

The second major issue is incorrect alignment of data layers aligned to different projections or datums. Modern geospatial datasets often combine data from multiple sources that use different projection systems. Aligning such data requires transforming these sources to one common projection.

If projections are improperly defined, this transformation will align the layers incorrectly and introduce positional errors of hundreds or even thousands of meters in some cases. Such misaligned maps are unsuitable for analysis until data is correctly reprojected to a shared projection system.

### Best Practices for Defining Projections

Following best practices helps avoid most common mistakes related to projection definition:

#### Understand Projection Terminology

It is essential to understand the basic terminology of projections before working with projected data:

**Geodetic Datum:**Mathematical model of the earth’s shape and orientation in space, defines coordinate system origin**Spheroid/Ellipsoid:**Geometric approximation of earth’s surface, defines size and shape**Coordinate Systems:**Latitude/longitude coordinates based on datum and ellipsoid

#### Know Your Area of Interest and Select Appropriate Projections

No single projection works equally well for all regions across the earth. Before projecting geographic data, determine the appropriate projection for your continents or countries of interest based on standard practices and guidelines.

For example, a conic projection with two standard parallels is better suited for countries like the United States that span multiple climate zones and have varying latitudes. An azimuthal equidistant projection centered on the north pole is a common choice for artic regions like Alaska and Northern Canada.

#### Define Parameters Fully and Precisely

Fully specify all relevant projection parameters like datum, standard parallels, central meridians, and false eastings/northings. Use parameter values tailored for your specific country or region when possible rather than global defaults.

For example, the Europe Africa Lambert Conformal Conic projection uses a central meridian of 10°E with standard parallels at 35°N and 65°N. This minimizes distortion over Western Europe and Central Africa but is not appropriate globally.

#### Use Established Projection Systems When Possible

When working with specific countries, states, or provinces, use established projection standards for that area instead of creating custom projections. Such standards have well-tested parameters designed to minimize error and distortion locally.

For example, State Plane Coordinate System projections standardized by the US National Geodetic Survey provide optimized projections for US territories with precisely defined parameters tailored to individual state needs.

#### Validate Projected Data Visually and Empirically

Always visually inspect projected maps to ensure shapes, distances and relative area appear as expected without distortion. Further validation should test actual geometry measurements against known good baselines at multiple test points across each map.

Statistical summaries of residual measurement errors can quantify projection distortion numerically. For example, the mean, max, min, and standard deviation of length or area differences highlighted outliers and systemic distortion issues.

### Example Projection Definition Code Snippets

Implementing projections properly in GIS environments requires precisely defined projection strings with all parameters fully specified. Below are examples in Well-Known Text format:

#### WGS84 Web Mercator

PROJCS["WGS 84 / Pseudo-Mercator", GEOGCS["WGS 84", DATUM["WGS_1984", SPHEROID["WGS 84",6378137,298.257223563, AUTHORITY["EPSG","7030"]], AUTHORITY["EPSG","6326"]], PRIMEM["Greenwich",0, AUTHORITY["EPSG","8901"]], UNIT["degree",0.0174532925199433, AUTHORITY["EPSG","9122"]], AUTHORITY["EPSG","4326"]], PROJECTION["Mercator_1SP"], PARAMETER["central_meridian",0], PARAMETER["scale_factor",1], PARAMETER["false_easting",0], PARAMETER["false_northing",0], UNIT["metre",1, AUTHORITY["EPSG","9001"]], AXIS["X",EAST], AXIS["Y",NORTH], EXTENSION["PROJ4","+proj=merc +a=6378137 +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null +wktext +no_defs"], AUTHORITY["EPSG","3857"]]

#### USA Contiguous Albers Equal Area Conic

PROJCS["USA_Contiguous_Albers_Equal_Area_Conic", GEOGCS["GCS_North_American_1983", DATUM["D_North_American_1983", SPHEROID["GRS_1980",6378137.0,298.257222101]], PRIMEM["Greenwich",0.0], UNIT["Degree",0.0174532925199433]], PROJECTION["Albers"], PARAMETER["False_Easting",0.0], PARAMETER["False_Northing",0.0], PARAMETER["Central_Meridian",-96.0], PARAMETER["Standard_Parallel_1",29.5], PARAMETER["Standard_Parallel_2",45.5], PARAMETER["Latitude_Of_Origin",37.5], UNIT["Meter",1.0]]

#### British National Grid

PROJCS["OSGB 1936 / British National Grid", GEOGCS["OSGB 1936", DATUM["OSGB_1936", SPHEROID["Airy 1830",6377563.396,299.3249646, AUTHORITY["EPSG","7001"]], TOWGS84[375,-111,431,0,0,0,0], AUTHORITY["EPSG","6277"]], PRIMEM["Greenwich",0, AUTHORITY["EPSG","8901"]], UNIT["degree",0.0174532925199433, AUTHORITY["EPSG","9122"]], AUTHORITY["EPSG","4277"]], PROJECTION["Transverse_Mercator"], PARAMETER["latitude_of_origin",49], PARAMETER["central_meridian",-2], PARAMETER["scale_factor",0.999601272], PARAMETER["false_easting",400000], PARAMETER["false_northing",-100000], UNIT["metre",1, AUTHORITY["EPSG","9001"]], AXIS["Easting",EAST], AXIS["Northing",NORTH], AUTHORITY["EPSG","27700"]]