California Coordinate System and Geodetic Surveying
The system
California Coordinate System of 1983 (CCS83) is based on NAD83 and consists of six Lambert conformal conic zones numbered 1 through 6 (for example, Zone 3, Mount Diablo, and Zone 6, San Diego). The Lambert projection keeps scale distortion small across an east-west zone. Within a zone, scale factor is smallest near the central meridian (slightly below 1.0) and increases toward the zone boundaries; a point on the central meridian is not at scale factor exactly 1.0 unless the projection convention makes it so.
The elevation factor accounts for being above the ellipsoid: elevation factor = R / (R + h), using mean Earth radius (about 20,906,000 ft). The combined factor is scale factor times elevation factor. Grid distance = ground distance x combined factor; ground distance = grid distance / combined factor. Convergence is the angle between grid north and geodetic north and must be applied when converting geodetic azimuths to grid azimuths (or the reverse).
Traps
- Using only the scale factor and ignoring elevation.
- Multiplying when you should divide (or the reverse) when converting ground to grid.
- Reversing the sign of convergence.
- Mixing datums or epochs (NAD83(2011), modernized NATRF2022) or assuming CCS83 coordinates are themselves a boundary description rather than a reference system.
Worked example
Ground distance 1,000.000 ft at h = 1,000 ft. Elevation factor = 20,906,000 / 20,907,000 = 0.999952. Scale factor = 0.99990. Combined factor = 0.999852. Grid distance = 1,000.000 x 0.999852 = 999.852 ft - a 0.148 ft difference, about 1:6,760, which matters when comparing to record monument positions.
Rule of thumb
Grid is always shorter than ground in a normal zone/elevation setting; combined factor is less than 1.