Coordinate Systems, Heights, and Low Distortion Projections

Coordinate Systems Overview

A coordinate system defines how positions on Earth are expressed. There are three primary categories:

• Geodetic (geographic): Latitude, longitude, and ellipsoidal height referenced to an ellipsoid (e.g., WGS84).
• Projected: Two-dimensional coordinates derived by mathematically projecting the curved Earth surface onto a plane (e.g., UTM, State Plane).

  

• Local: Custom, site-specific systems defined by a known point, orientation, and scale factor for construction or engineering projects.

Geodetic Coordinates and the GNSS Ellipsoid

GNSS computes positions on a mathematical model of the Earth called an ellipsoid. Common ellipsoids include WGS84 and GRS80. Geodetic coordinates are expressed as:

• Latitude: angle north or south of the equator
• Longitude: angle east or west of the prime meridian
• Ellipsoidal height: distance above or below the ellipsoid

These are the fundamental outputs of GNSS receivers and serve as the basis for all transformations to projected or local coordinates.

Projected Coordinate Systems

A map projection converts the curved Earth to a flat plane for 2D mapping. The projection introduces controlled distortion of scale, area, or shape depending on how it's defined.

• UTM (Universal Transverse Mercator): Divides the world into 6° longitudinal zones, good for narrow north–south regions.
• State Plane Coordinate System (SPCS): Used in the United States; uses Transverse Mercator, Lambert Conformal Conic, or Oblique Mercator projections depending on state geometry.

Each projection is defined by parameters such as a central meridian, scale factor, and false easting/northing. These must be known or provided through an EPSG code to ensure consistency.

Local Coordinate Systems (Site Grids)

Local grids are project-based systems tied to a known base point and oriented to match site plans. They simplify field operations by reducing coordinate magnitudes and aligning northing/easting to project orientation.

Localization or calibration processes define a mathematical transformation between GNSS-derived coordinates and the site grid using surveyed control points.

Vertical References: Ellipsoid, Geoid, and Orthometric Heights

GNSS determines positions relative to an ellipsoid, but engineers and mappers often require heights relative to mean sea level (the geoid). The relationship between these three surfaces is:

H = h − N

• h = Ellipsoidal height (from GNSS)
• N = Geoid undulation (separation between ellipsoid and geoid)
• H = Orthometric height (above mean sea level)

Using a geoid model (e.g., GEOID18, EGM2008) allows conversion from ellipsoidal to orthometric height for consistency with leveling data and engineering standards.

Low Distortion Projections (LDPs)

A Low Distortion Projection (LDP) is a specially designed map projection that minimizes the combined distortion between ground distances and grid distances across a limited area - typically a county, region, or state.

Purpose and Concept

Traditional map projections (like UTM or State Plane zones) are optimized for broad regions, meaning that local projects often experience measurable differences between grid and ground distances due to projection scale factors and elevation.

An LDP is optimized for a specific elevation (mean project height) and region extent so that the grid-to-ground scale factor is close to 1.000000 - i.e., grid coordinates can be used directly for engineering, construction, and surveying without significant scale corrections.

Mathematical Basis

The design of an LDP typically involves:

• Choosing a base projection (Transverse Mercator or Lambert Conformal Conic).
• Setting the projection's central meridian and latitude to minimize convergence and distortion over the region.
• Applying a custom scale factor at the origin to match the mean ellipsoid-to-ground scale for that area's average elevation.

Advantages of LDPs

• Minimized ground-to-grid corrections: Reduces or eliminates the need for applying combined scale factors during construction layout or coordinate computation.
• Improved consistency: All users in the region work in the same projection, reducing confusion and data misalignment.
• Simplified workflows: Field software and CAD packages can use grid coordinates directly for layout and design.
• Better integration with GNSS: GNSS data transformed through an LDP matches ground distances more closely, minimizing apparent discrepancies between measured and mapped features.

Why NGS is adopting LDPs

The U.S. National Geodetic Survey (NGS) is incorporating Low Distortion Projections as part of its modernization of the National Spatial Reference System (NSRS), which will replace NAD 83 and NAVD 88 with new reference frames (North American Terrestrial Reference Frame 2022 (NATRF2022) and corresponding geopotential datum).

NGS's goals for LDP adoption include:

• Uniform, modern standards: LDPs will replace legacy State Plane zones with better accuracy and reduced distortion.
• Regional optimization: Each LDP is tuned for local topography and elevation to ensure less than 20 ppm (0.002%) distortion over its extent.
• Ease of transition: Surveyors and engineers can continue to work in familiar plane coordinates while benefiting from precise geodetic foundations.
• Compatibility with GNSS and geoid models: The new system integrates ellipsoid-based GNSS positioning directly with geoid-based height systems, reducing the need for multiple transformations.

Implementation and Use

NGS publishes LDP parameters through official EPSG codes and tools such as NCAT and NOAA VDatum. Survey software vendors are integrating these definitions so that users can work seamlessly in the new zones without manual setup.

Field takeaway: When using NATRF2022 or newer frames, choose the LDP that covers your county or region - it gives nearly one-to-one correspondence between measured ground distances and grid coordinates.