Grid, Ground, and a 1998 County System
You are establishing control for a 2,000 ft water main in the Central Valley. Your RTK solution is reduced to NAD83(2011), epoch 2010.00, which is what the state's CORS network serves. The design drawings, however, are on a county "ground" system derived in 1998.4 by taking state plane coordinates of that era and multiplying by 1.000130. The combined factor at the site, referred to NAD83(2011), computes to 0.9999123. Two proposed valve nodes measure 1,520.345 ft apart in current state plane grid distance. Regional crustal motion in the county's adjustment frame is on the order of a few centimeters per year, and the county network has not been readjusted since 1998.
1. Convert the 1,520.345 ft grid distance to ground and to the county system, and state what the difference means for construction.
Read the worked answer
Step 1 - grid to ground:
Ground = grid / combined factor = 1,520.345 / 0.9999123 = 1,520.478 ft
The ground distance is 0.133 ft longer than grid. That is 87.7 ppm - small in absolute terms, but not negligible over a utility run where fittings and stationing must agree.
Step 2 - ground to the county 'ground' system:
The county value was produced by scaling the 1998 grid by 1.000130:
County distance = 1,520.345 × 1.000130 = 1,520.543 ft
Step 3 - compare:
County system minus true ground = 1,520.543 - 1,520.478 = 0.065 ft, about 42 ppm. Over the full 2,000 ft run that grows to roughly 0.084 ft.
The lesson: the county system is called "ground" but it is not ground at this site. It is a particular scale factor applied to a particular realization of state plane. Multiplying a current NAD83(2011) grid distance by the county's 1998 factor produces a number that is close to correct, and close is exactly the condition that lets an error through review.
For construction: compute the design's basis and stay in it. If the drawings are in county coordinates, do all layout math in county coordinates using the county's stated factor, and document the factor; do not mix a county coordinate with a freshly derived ground distance on the same stakeout sheet.
2. What is the epoch and frame problem with the 1998 county coordinates, and how large an error could it create?
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Two separate issues, often confused:
Frame realization. A 1998 county adjustment is on an earlier NAD83 realization (HARN/CORS96-era). Current NAD83(2011) coordinates of the same physical point in California differ from those earlier values by amounts on the order of a meter horizontally - from the realization change, not from the point moving. Holding a 1998 published coordinate as truth and calling it NAD83(2011) puts you about a meter off, which is enormous for control.
Physical motion of the mark. NAD83(2011) is a static frame: the coordinate of a mark does not change with time. The mark itself, however, moves relative to the frame. At a few centimeters per year over roughly 26 years, that is on the order of 0.3 to 1.0 m of accumulated displacement depending on the local rate - and in areas affected by earthquakes, it can be much larger and non-linear. A monument whose 1998 coordinate was good can be a very poor coordinate today even if the disk has not moved in the ground.
Practical consequences:
- Fit your RTK work to the monuments, not to the published 1998 coordinate values, when the deliverable must be in county coordinates. Use the published values only as a check on which monument is which.
- Never constrain an RTK network to a single old published coordinate and assume the rest follows.
- If the county coordinates are the legal basis for anything, the frame and epoch adopted must be stated on the deliverable.
Bottom line: the scale-factor error (0.065 ft) is the smaller problem. The realization/epoch mismatch is roughly a meter, and it will not show up as a misclosure in a loop that is itself constrained to the old coordinate.
3. Your RTK-derived position for a valve differs from a 1998 county coordinate by 1.1 m horizontally. What do you do, and what do you put on the drawing?
Read the worked answer
Diagnose before you act. A 1.1 m offset in a consistent direction across several points is a frame/epoch signature, not a blunder. Check:
- Is the offset consistent in bearing and magnitude from point to point? A systematic vector points to frame/epoch.
- Are you holding a base coordinate from the county system? If yes, the base may be the problem.
- Do the county coordinates fit the found monuments, or do the monuments fit each other better than they fit the coordinates? The monuments are the physical evidence; the numbers are a record of a prior opinion about them.
Then decide by purpose:
- Design/layout in county coordinates: establish your control on the monuments by conventional methods, derive the transformation from current NAD83(2011) to county coordinates from those monument fits, and apply it explicitly. Report the residuals.
- Legal or record deliverable: the coordinate difference does not change the boundary; do not let a coordinate mismatch drive a line position.
On the drawing, state: horizontal datum and realization (NAD83(2011)), epoch (2010.00), the coordinate system and units, whether values are grid or ground and the combined factor used, the transformation parameters or the control held to produce county values, and the residuals. A note that says only "county coordinates" is an invitation to a future dispute you will lose.
Notify the county and the design engineer in writing of the discrepancy. A one-meter systematic offset that everyone quietly absorbs into their own work is how two adjacent projects end up disagreeing at a tie-in.