5.1 Horizontal Datums and Assumed Systems

5.1 Horizontal Datums and Assumed Systems

Quick Answer: A horizontal datum is the origin, orientation, and scale you use to assign northing and easting. The 2022 Civil Engineering Surveying (CES) test plan lists horizontal and vertical datums with the parenthetical assumed non-geodetic—so a small-site assumed system is in scope, not a footnote. Hold one documented system. Do not paste Google/GIS World Geodetic System 1984 (WGS 84) into an assumed CAD file, and do not rotate a job to "true north" after design has started.

What a Horizontal Datum Is

Every northing and easting on a grading plan is measured from an origin, along an azimuth, at a scale. That triple—origin, orientation, scale—is the horizontal datum of the job. It may be a named geodetic or mapped system such as the North American Datum of 1983 (NAD 83) expressed as California Coordinate System of 1983 (CCS83) State Plane coordinates, or it may be a project (assumed) system that never claims to be geodetic.

Geodetic systems are tied to a reference ellipsoid and a national or state network. Mapped systems (State Plane / CCS83) project that ellipsoid onto a plane so civil drawings can use northing and easting in feet or meters. Assumed (non-geodetic) systems are local: you pick Hub A, assign convenient numbers, and hold a site azimuth. The assumed system is still a datum. It is just not NAD 83.

The CES exam is a civil-engineering surveying exam. It tests whether you can pick a system that matches the project, document it, and keep it. It is not a Professional Land Surveyor (PLS) course in National Spatial Reference System (NSRS) modernization, map-projection series, or crustal-velocity models.

When an Assumed System Is Appropriate

Assumed coordinates are appropriate when all of the following are true:

1. The work is geometrically local—an isolated pad, a private parking lot, a small detention basin, or a short on-site utility that does not have to overlay a city GIS to a tenth of a foot.
2. Design, mapping, and construction will all live in the same coordinate file and the same field book.
3. You do not need to match an adjacent mapped-datum contract or a city requirement to submit CCS83.

If any of those fail, either start on the named datum or plan a documented transformation from assumed to mapped (Section 5.3).

A 380 ft by 260 ft grading pad behind a warehouse is a classic assumed-system job. The longest diagonal is about 460 ft; construction tolerances of a few hundredths to a tenth of a foot dominate any geodetic refinement. A street widening that must overlay the city's storm GIS, or a channel that must match an adjacent Caltrans contract on CCS83, is not an assumed-only job—unless you also budget the transformation and the checks.

Holding a Local Origin and Azimuth

Hold means: once you publish the origin and the azimuth, you do not "improve" them mid-job. Every later topographic shot, design coordinate, and construction stake refers to that same pair.

Worked example: assumed origin on a small pad

Hub A is a mag nail in the south-west walk. Assign:

• N = 10,000.00 ft
• E = 20,000.00 ft

Occupy A, backsight the north face of the existing warehouse, and hold that face as project north: azimuth A–B = 0°00'00" project. Measured horizontal distance A to Hub B (a nail at the north-west corner of the same wall) is 248.60 ft.

Hub B:

• N = 10,000.00 + 248.60 = 10,248.60 ft
• E = 20,000.00 ft

A design catch basin 85.00 ft project-north and 40.00 ft project-east of A is N = 10,085.00, E = 20,040.00. Construction stakes that same pair. The warehouse did not have to sit on geodetic north. Project north is a documented axis, and 248.60 ft along that axis is a field measurement, not a published CCS83 inverse.

A GNSS check later shows true north (geodetic or grid, depending on the receiver setting) is 14°18' east of the warehouse face. That is useful metadata. It is not a command to rotate the CAD file.

Worked example: inconsistent true-north rotation

If a second crew rotates every assumed coordinate about Hub A by 14°18' to "put the job on true north," but the grading plan, the earthwork surface, and the contractor's stakes still use the original numbers, the physical warehouse wall and the coordinates stop matching.

A point 300.00 ft project-north of A was N = 10,300.00, E = 20,000.00. After a 14°18' rotation about A:

• ΔN′ = 300.00 × cos(14°18′) = 300.00 × 0.96902 = 290.70 ft
• ΔE′ = 300.00 × sin(14°18′) = 300.00 × 0.24702 = 74.11 ft
• New coordinates: N = 10,290.70, E = 20,074.11

The same physical point has moved 74.7 ft in the coordinate file: √(9.30² + 74.11²) = √(86.49 + 5,492.29) = √5,578.78 = 74.7 ft. Nothing in the dirt moved. That is a datum break, not a layout tolerance. Rotating only the field book, or only the GIS overlay, produces the same class of error at a smaller scale: two datasets that look like the same site and are not.

Mixing Google/GIS WGS 84 with Assumed Coordinates

Consumer GIS and Google Earth commonly store positions on WGS 84 geographic coordinates or in Web Mercator (EPSG:3857). NAD 83 (the basis of CCS83) and WGS 84 differ on the order of about one meter (a few feet) in the contiguous United States. That difference is not zero, and it is not a California constant you should memorize as 3.28 ft everywhere. Web Mercator additionally scales distances by about 1 / cos(latitude)—near latitude 37°, that factor is about 1.25—so a Google-measured 80 ft curb return is not 80 ft on the ground.

Pasting a shapefile hydrant into an assumed site plan without a documented transformation is how a water easement gets drawn to the wrong physical object. The field crew then looks like the bust. The bust was the datum mix. A 3 ft GIS-versus-field disagreement on a hydrant is the size of the NAD 83 / WGS 84 mismatch plus geolocation error; it is not a reason to average the two and call it project control.

Treat GIS as a reference overlay until it is transformed onto the project datum and checked to surveyed features. Domain I.G (GIS) is a later planning topic; the datum rule is already here: do not mix.

California Coordinate System of 1983 (CCS83)

When a job must live on a mapped datum in California, the usual plane system is CCS83: the California implementation of NAD 83 State Plane, defined in Public Resources Code (PRC) beginning at § 8801.

Facts that matter on a civil job:

Zone 4 includes Fresno, Inyo, Kings, Monterey, San Benito, and Tulare. Zone 3 includes the San Francisco Bay counties listed in PRC § 8802 (Alameda, San Francisco, Santa Clara, and others). Zone 6 includes Imperial, Orange, Riverside, San Diego, and named Channel Islands. You do not need to recite every county on the exam, but you must not put Los Angeles in "Zone 7" on a CCS83 deliverable. Zone 7 exists in CCS27 only. PRC § 8802 folded Los Angeles County into CCS83 Zone 5.

PRC § 8815 requires the suffix CCS83 (not a bare "State Plane") when that system is named on a map. PRC § 8815.1 requires the datum realization tag in parentheses and the epoch date in decimal-year form to two places; the statute’s own examples are CCS83 (2011) epoch 2010.00 and CCS83 (NSRS) epoch 2007.00. Omitting the epoch is how two NAD 83 files in the same zone still fail to overlay after an adjustment or a crustal-motion epoch change.

Linear units are part of the datum statement: meters, or U.S. survey feet as commonly used on California engineering drawings. Write the unit. The statute origin is in meters; converting to feet does not create a new zone, but mixing meter files with foot files will look like a 3.28× scale bust.

Grid vs ground (conceptual)

CCS83 coordinates are grid. Distances computed from those northings and eastings are grid distances. A tape or EDM on the ground, reduced to horizontal, is a ground distance. They differ by the combined factor:

combined factor ≈ (grid scale factor) × (elevation factor)

The elevation factor is the usual civil approximation R / (R + h), with R ≈ 20,906,000 ft as a mean-earth-radius stand-in and h a height above the ellipsoid (orthometric height is often used as a stand-in on municipal jobs). Example composition, not a zone constant: at h = 850 ft, elevation factor = 20,906,000 / 20,906,850 = 0.9999593. If a published grid factor is 0.9999728, combined factor ≈ 0.9999728 × 0.9999593 = 0.999932. Near a standard parallel the grid factor is close to 1, and the product still matters on a long street.

This chapter does not teach zone-constant computation, distortion isograms, or a full geodesy workflow. Know that grid ≠ ground, know the combined-factor multiply/divide, and put the factor on the control diagram when you are on CCS83.

Worked example: combined factor 0.999932

A control sheet lists combined factor 0.999932. A measured ground (horizontal) distance is 500.00 ft.

Grid distance = 500.00 × 0.999932 = 499.966 ft
Difference = 0.034 ft

At 1,250.00 ft ground: grid = 1,250.00 × 0.999932 = 1,249.915 ft (difference 0.085 ft).
At 3,000.00 ft ground: grid = 3,000.00 × 0.999932 = 2,999.796 ft (difference 0.204 ft).

Direction: D_grid = D_ground × CF and D_ground = D_grid / CF. Dividing when you should multiply—or ignoring the factor on a mapped-datum job—is the exam trap. On a 400-ft assumed pad, 0.03 ft is noise compared with construction tolerances. On a 3,000-ft mapped corridor, 0.20 ft is a real stationing error. Section 5.3 treats changing the factor mid-job as a separate trap.

NSRS modernization: a short note, not a course

The National Geodetic Survey (NGS) is modernizing the NSRS. NATRF2022 (North American Terrestrial Reference Frame of 2022) is the planned replacement for NAD 83, and NAPGD2022 (North American-Pacific Geopotential Datum of 2022) is the planned replacement for the North American Vertical Datum of 1988 (NAVD 88). California statute now also names a California Coordinate System of 2022 (CCS2022) as the California portion of State Plane 2022. As of 2026 this remains a phased NGS/federal change; NAD 83 / CCS83 and NAVD 88 are still what most California civil projects actually use. The CES exam still tests datums as used on projects, including assumed non-geodetic systems. Do not spend study hours on transformation parameters that the 2022 test plan does not emphasize.

Exam traps

• Treating assumed northings as CCS83 because the numbers have six digits.
• Pasting WGS 84 / Google Earth into an assumed file.
• Rotating to true north after design, or rotating only the field book.
• Using CCS27 Zone 7 language on a CCS83 Los Angeles job.
• Reporting CCS83 without zone, epoch, or linear unit.
• Using grid distances as ground distances (or the reverse) without the combined factor.