The Traverse That Closed Well but Did Not Agree With Control
A surveyor closes a seven-point traverse around a 40-acre parcel in Litchfield, Connecticut. Total traverse length is 3,860 ft; the unadjusted misclosure is 0.11 ft north and 0.08 ft east, for a linear misclosure of 0.136 ft. Angles were turned in two sets, the EDM prism constant was checked, and the instrument was calibrated. The traverse was computed in ground coordinates. A static GNSS session tied two points to published Connecticut state plane coordinates (NAD83(2011)) and showed a 0.9-ft horizontal difference from the traverse positions. The parcel lies at about 640 ft elevation. A colleague suggests that the state plane combined factor explains the difference. The client wants lot corners set next week, and the town wants the map in state plane coordinates. The surveyor must decide whether to adjust the traverse to the GNSS control or to hold the traverse and investigate.
1. Evaluate the traverse precision and compare it with the agreement to control.
Read the worked answer
Linear misclosure = sqrt(0.11² + 0.08²) = sqrt(0.0121 + 0.0064) = sqrt(0.0185) = 0.136 ft. Relative precision = 0.136 / 3,860 = 1:28,400. That is good for a boundary traverse and would normally satisfy a 1:10,000 or 1:15,000 standard, assuming angle closure and repeated observations are also acceptable.
However, the comparison with the GNSS control is 0.9 ft over 3,860 ft = 1:4,300, or about 233 ppm, which is far worse. Internal precision does not prove absolute accuracy. A traverse can close well and still be systematically displaced by an orientation error, an incorrect backsight, a prism constant, or an occupying-point error.
The discrepancy is between two independent determinations of the same points, so at least one has a problem. The traverse should not be assumed correct merely because it closes well, and the GNSS control should not be assumed correct merely because it is on state plane coordinates.
2. Test the colleague's claim that the state plane combined factor explains the 0.9-ft difference.
Read the worked answer
Combined factor = grid scale factor × elevation factor. Elevation factor ≈ R / (R + h) = 20,906,000 / (20,906,000 + 640) ≈ 0.999969. In Connecticut the Lambert grid scale factor is near unity, typically within about ±20 ppm in developed areas. The combined factor is therefore roughly 0.99995 to 1.00000, within about 50 ppm. Over 3,860 ft, 50 ppm is at most about 0.19 ft, and more likely 0.02 to 0.05 ft. The observed difference is 0.9 ft, or 233 ppm, several times larger. The colleague's explanation fails.
Check units (meters versus U.S. survey feet), because a unit mistake would produce a much larger error, but a 0.9-ft offset is not explained by the state plane factor. Potential causes include a wrong published coordinate, a different datum or epoch, a base-station coordinate error, an antenna-height blunder, poor GNSS geometry, or a traverse orientation blunder. Also verify that the GNSS points are the same physical points and that the control is authoritative.
3. What should the surveyor do before setting corners, and what should the map show?
Read the worked answer
Do not set corners until the discrepancy is resolved. Reobserve the GNSS session with an independent base or a second occupation; check the published control data and the datum/epoch; verify antenna heights and point identifiers; run a closed loop through the two control points; and compare the traverse's angle closure and bearing base. If the GNSS control is sound, adjust the traverse to it by least squares with realistic weights, or hold the control and reobserve the traverse. If the control is suspect, use the traverse for relative boundary positions and document why the control was rejected.
On the map, show boundary lines with ground distances and bearings, plus state plane coordinates for the corners with a note giving the combined factor and datum. Do not distort boundary distances to grid. Report the 0.9-ft discrepancy, its resolution, and the final coordinates. The town's coordinate requirement does not override the need for correct boundary positions, and a premature adjustment could move every corner by nearly a foot.