GNSS Baseline, Level Loop, and Grid-to-Ground Control for a Sewer Extension
You are establishing control for a 2.5-mile sanitary-sewer extension in Washtenaw County. Three published MCS NAD83(2011) control points in the Michigan Oblique Mercator zone are available, with NAVD88 elevations. Your static GNSS baseline between CP-1 and CP-2 gives a grid length of 1,842.335 m; the published grid distance is 1,842.379 m. The ellipsoid height difference is -3.216 m, and the geoid undulation at CP-1 is -34.12 m. You run a differential level loop from BM-1 to BM-2, 1.80 mi, and close with +0.08 ft. The design engineer wants ground coordinates and elevations for pipe layout, with a construction tolerance of plus or minus 0.05 ft in elevation. The contractor's machine-control model uses the county's GIS surface, which differs from your check shots by a consistent 0.10 ft.
1. Evaluate the GNSS baseline result. Is the 0.044 m difference acceptable for this project?
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Convert: 0.044 m equals 0.144 ft, or about 24 ppm over 1,842 m. That ratio is better than 1:10,000, so it does not by itself fail a typical horizontal-control standard. But the inconsistency with the published control must be explained before the network is used. Check: (1) the published coordinates are NAD83(2011) and the same realization and epoch; (2) antenna heights and base-station coordinates; (3) multipath or obstructions; (4) whether the published value is grid or ground; (5) the projection and combined factor. Reobserve the baseline or occupy a third point and perform a least-squares adjustment. Do not simply average the two values. If the difference persists, use the published control and document the discrepancy. For construction layout, a consistent network matters more than a single ratio; a 24-ppm scale error over 2.5 miles is about 0.32 ft of horizontal displacement.
2. Evaluate the level loop misclosure against NGS standards and the project tolerance. What should you do with the elevations?
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M equals 1.80 mi. Second-order Class II allowable misclosure is 0.05 times the square root of M: 0.05 times 1.342 equals 0.067 ft. Third-order is 0.10 times the square root of M: 0.134 ft. The +0.08 ft closure fails second-order Class II but passes third-order. Because the construction tolerance is plus or minus 0.05 ft, third-order is not adequate for final pipe grades. Reobserve the loop and check for systematic error: collimation, rod calibration, turning points, and closure on a known benchmark. If reobservation closes within 0.067 ft, adjust the elevations by distributing the misclosure proportionally to distance. Do not use the unadjusted 0.08 ft closure for layout.
3. Explain grid versus ground and recommend how to provide coordinates and elevations for construction, including the 0.10 ft GIS difference.
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MCS grid distances are on the ellipsoid and projection; ground distances are at the site elevation. The relationship is ground equals grid divided by the combined factor, where combined factor equals ellipsoid scale times projection scale. At this site the factor is near unity but must be computed, not assumed. For pipe layout, provide a site calibration or a low-distortion projection so that grid and ground differ by less than about 10 ppm; otherwise the contractor's machine control will lay out slightly wrong distances. Also resolve the 0.10-ft vertical discrepancy between the county GIS surface and your check shots. GIS surfaces are often derived from different sources and are not survey control. Verify with a level loop and a known NAVD88 benchmark; do not adopt the GIS surface for grade. Provide the contractor with a control table, datum statement, and check point.