15.2 Grid versus Ground, Datums, and Heights

Chapter 6 introduced Public Resources Code sections 8801–8819: named plane systems, zones, the U.S. Survey foot versus the international foot, realization and epoch, and a preview of PRC 8815.5. Independent OpenExamPrep teaching in this section is Domain IV analysis of grid versus ground (knowledge W), projections, datums, realizations, and epochs (knowledge U), geoid, ellipsoid, and orthometric heights (knowledge V), and bearings or azimuths related to geodetic, magnetic, grid, or astronomic north (knowledge BB). The job is to convert a length and to print what 8815.5 actually names.

Two different lengths of the same line

A ground distance is the horizontal distance between two marks at the topographic surface after slope reduction. A grid distance is the distance between the same two points after their positions have been projected onto the California Coordinate System plane. Construction staking on ground, a CCS83 inverse on a Record of Survey, and a GIS length on a Lambert web map are three different numbers until you convert them.

NOAA Manual NOS NGS 5, State Plane Coordinate System of 1983, is the published National Geodetic Survey (NGS) procedure used here. It is not a BPELSG exam specification. The manual's approximate elevation factor reduces a horizontal ground distance to the ellipsoid:

elevation factor = R / (R + h)

where R = 6,372,000 m (the approximate radius NGS states served NAD 27 and serves NAD 83 equally well; 20,906,000 ft in foot working) and h is ellipsoid height. On NAD 83, h = H + N, with H the orthometric height and N the geoid height. The working height equation remains H = h − N.

The grid scale factor k is the Lambert (or, if used, SPCS2022) point scale at the location—the ratio of grid distance to geodetic distance on the ellipsoid. PRC 8803–8808 publish standard parallels, central meridians, and origin latitudes. They do not publish a k you can memorize for a county. Compute k from the projection at the point, or take it from NGS or California Spatial Reference Center software for that latitude and longitude.

Combined factor CF = k × elevation factor

NGS multiplies the horizontal ground distance by the combined factor to obtain the grid distance. Divide a CCS83 inverse by CF (or multiply by 1/CF) to recover ground. Parcel area computed from grid coordinates is ground area only after you divide by CF².

Worked combined-factor example (stated assumptions)

Representative point P on a San Bernardino County project, CCS83 Zone 5, NAD83(2011) epoch 2010.00. These values are a teaching set. They are not an NGS station datasheet and not a Board-published factor.

• Grid scale factor k = 0.99994820 (Lambert point scale at P; not a PRC zone constant)
• Orthometric height H = 1,800.000 m NAVD88
• Geoid height N = −32.000 m (assumed GEOID18 interpolation at P; in production you interpolate the published model, you do not invent a county-wide N)
• Mean radius R = 6,372,000 m (NGS NOS NGS 5 approximate radius)

Ellipsoid height h = H + N = 1,800.000 + (−32.000) = 1,768.000 m.

Elevation factor = 6,372,000 / (6,372,000 + 1,768.000) = 6,372,000 / 6,373,768 = 0.999722614.

Combined factor CF = 0.99994820 × 0.999722614 = 0.99967083 (eight decimal places in this example).

A horizontal ground distance measured along the project, 400.000 m, becomes

grid = 400.000 × 0.99967083 = 399.868 m.

The same line, inversed from CCS83 coordinates as 399.868 m, returns

ground = 399.868 / 0.99967083 = 400.000 m.

The difference is 0.132 m in 400 m, about 329 ppm. Using k alone (0.99994820) would have given 399.979 m and left 0.111 m of elevation reduction unapplied. Using the elevation factor alone would have given 399.889 m and missed the projection. PRC 8815.5 names the combined grid factor, not "scale factor" and not a sea-level factor from NAD 27 literature.

If the 400.000 m had been a slope electronic distance, you would still reduce to horizontal at the marks before applying CF. Combined factor is not a slope correction. Applying CF as a scale on coordinates from an arbitrary origin can create a local ground coordinate system. That product is not CCS83 and must not be labeled State Plane under PRC 8801(e).

PRC 8815.5 in full, deeper than Chapter 6

The Legislative Counsel display of PRC 8815.5, and FindLaw's text current as of January 1, 2026, both print the SB 566 sentence (Stats. 2023, Ch. 111, effective January 1, 2024):

When CCS83 or CCS2022 coordinates are shown on any map, corner record, or record of survey, a mapping angle, combined grid factor, and the elevation used to determine the combined grid factor shall be shown on that document for at least one representative point.

Read it as a reporting statute, not as a calculation recipe:

1. Trigger. CCS83 or CCS2022 coordinates on a map, corner record, or record of survey. A CCS27-only plat is outside this sentence. Coordinates on a private working sketch that is not one of those three documents are outside this sentence; coordinates on the filed Record of Survey are not.
2. Three quantities, not one. Mapping angle. Combined grid factor. Elevation used to compute that factor. A note that says only "CSF = 0.99967" fails. A note that omits the elevation used to build CF fails. A note that omits mapping angle fails.
3. Representative point. One point that represents the survey is the statutory floor. A Continuously Operating Reference Station thirty miles away, or the zone origin at northing 500,000 m and easting 2,000,000 m, is not representative of a mountain site at H = 1,800 m. Los Angeles County's 2025 Record of Survey / Corner Record guide repeats the 8815.5 list and still expects the control scheme under PRC 8813.1. Use a point on the project whose elevation you actually know.
4. Elevation used. Report the height that entered R/(R+h). If you used ellipsoid height, say h and the realization and epoch. If you used H and N, say H, N, and the geoid model. Printing H = 1,800.000 m NAVD88 without N is an incomplete derivation even if the number 1,800 appears.
5. One point is a floor. CF changes with k (latitude, longitude) and with h. A project that drops 1,000 m of elevation does not honestly share one CF everywhere. The statute does not require a factor at every lot corner. Professional analysis still asks whether one representative value misleads the next surveyor by more than the work can tolerate. That judgment is yours; it is not a published Board part-per-million.
6. Mapping angle is the convergence between geodetic north and grid north at the point. It is not a substitute for a basis of bearings statement, and it is not a magnetic declination. If the map's bearings are already CCS83 grid bearings, 8815.5 still wants the mapping angle when coordinates are shown, because the next surveyor must relate those grid bearings to a geodetic or astronomic observation. For this teaching point P, a stated mapping angle of 0°12'32" (from (λ − λ0) sin φ with P east of the Zone 5 central meridian 118°00' W) is an assumption to show the form of the note, not a datasheet value.

North is not one direction, and heights stay in families

A grid bearing from a CCS83 inverse is not a geodetic azimuth. A magnetic bearing from a 1960 deed is not grid. An astronomic observation on a mountain is not geodetic until you account for the deflection of the vertical. Mixing them in one basis-of-bearings note is an analysis failure.

Heights stay in families. NAD83 (with a realization and epoch) carries horizontal position and ellipsoid height h. NAVD88 carries orthometric height H. GEOID18 is the current NGS hybrid model that pairs NAD 83 (2011) epoch 2010.0 ellipsoid heights with NAVD 88 in the conterminous United States. Feeding an ITRF ellipsoid height into GEOID18, or reporting h as H, corrupts the h that entered the elevation factor. Chapter 11 treated that blunder on the occupation; this section treats it as a grid-to-ground input error.

CCS83 k is not a license to call projected WGS 84 coordinates State Plane. PRC 8801(e) still limits that name to CCS27, CCS83, and CCS2022.