Lambert conformal conic

Description

The Lambert conformal conic map projection is typically based on two standard parallels, but it can also be defined with a single standard parallel and a scale factor. It is best suited for conformal mapping of land masses extending in an east-to-west orientation at mid-latitudes. This projection was rarely used before the First World War but is now commonly used for official topographic mapping around the world. The state plane coordinate system uses it for all zones that have a predominant east-west extent.

Both spherical and ellipsoidal forms of the Lambert conformal conic map projection were developed by Johann H. Lambert in 1772. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.

Projection properties

The subsections below describe the Lambert conformal conic projection properties.

Graticule

Lambert conformal conic is a conic projection. All the meridians are equally spaced straight lines converging to a common point, which is the nearest pole to the standard parallels. The parallels are represented as circular arcs centered on the pole. Their spacing increases away from the standard parallels. The other pole projects to infinity and cannot be shown.

When the standard parallels are set in the northern hemisphere, the fan-shape of the graticule is oriented up and when standard parallels are in the southern hemisphere, the fan-shape of the graticule is oriented down. The graticule is symmetric across the central meridian.

Distortion

Lambert conformal conic is a conformal map projection. Directions, angles, and shapes are maintained at infinitesimal scale. Distances are accurate only along the standard parallels. Scale, area, and distances are increasingly distorted away from the standard parallels, but they are the same along any given parallel and symmetric across the central meridian. The projection is not conformal at the poles.

Usage

The Lambert conformal conic projection is best suited for conformal mapping of land masses in mid-latitudes extending in an east-to-west orientation rather than those trending north-to-south. Typically, the standard parallels are placed at one-sixth of the latitude range below the top and above the bottom of the area to be mapped.

The state plane coordinate system uses the Lambert conformal conic projection for zones that have a predominant east-west extent.

Variants

There are three variants available in ArcGIS:

• Lambert conformal conic variant is a general variant supporting all possible parameters for the projection. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.
• Lambert conformal conic 1SP variant only supports definitions with one standard parallel and scale factor but uses the same algorithm as the Lambert conformal conic variant. It is available in ArcGIS Pro 2.6 and later and in ArcGIS Desktop 10.8.1 and later.
• Lambert conformal conic 2SP variant only supports definitions with two standard parallels but uses the same algorithm as the Lambert conformal conic variant. It is available in ArcGIS Pro 2.6 and later and in ArcGIS Desktop 10.8.1 and later.

Limitations

The implementation of Lambert conformal conic in ArcGIS does not display the whole range of the world. The standard parallels can be at any latitude, except set at opposite poles.

Parameters

Lambert conformal conic parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Standard Parallel 1
• Standard Parallel 2
• Scale Factor
• Latitude Of Origin

To define the projection with two standard parallels (Lambert conformal conic 2SP variant), the scale factor value must be set to 1.0. To define the projection with one standard parallel (Lambert conformal conic 1SP variant), use the same value for the standard parallel 1, the standard parallel 2, and latitude of origin parameters and set an appropriate scale factor.

Lambert conformal conic 1SP parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Scale Factor
• Latitude Of Origin

Lambert conformal conic 2SP parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Standard Parallel 1
• Standard Parallel 2
• Latitude Of Origin

Particular parameter cases

If both standard parallels are set to a pole, the resulting projection is the stereographic projection in polar aspect. If only one standard parallel is set to a pole, the resulting projection is also the stereographic projection in polar aspect, but the second standard parallel presents the circular arc with no scale distortion. When both standard parallels are set symmetrically north and south of the equator or they are set at the equator, the outcome is the Mercator projection.

Sources

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453.Washington, DC: United States Government Printing Office.