Network RTK Heighting for a Floodplain Corridor: Does the Error Budget Close?
A district survey office must map a 14 km × 9 km floodplain corridor for a 1:1000 topographic model with 0.10 m contours. The contract defines this as vertical RMSE ≤ 25 mm at 95% confidence. Fieldwork uses network RTK through a VRS service: the nearest continuously operating reference station is 38 km away and the VRS is synthesised about 4 km from the rover, with four constellations tracked. On the first day, 92% of shots fixed in the morning (Kp = 3) but only 41% fixed in the afternoon (Kp = 6). Twelve independent checkpoints were then observed by 20-minute static sessions and processed against three reference stations; residuals against the RTK heights gave a mean of +0.041 m and a standard deviation of 0.028 m. Two of the six published benchmarks used as control lie inside the floodplain, carry a published subsidence rate of 8 mm/yr and were last levelled in 2011. The client wants the full corridor delivered in three weeks.
1. Determine whether the RTK heighting meets the 25 mm specification. Support the conclusion with numbers.
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Verdict: the heights fail the specification, and they fail it twice over.
Compute the total error of a single RTK height from both components, not from the scatter alone:
- RMSE = sqrt(bias² + SD²) = sqrt(0.041² + 0.028²) = sqrt(0.001681 + 0.000784) ≈ 0.0496 m
- The 25 mm allowance is a total budget. Scatter alone (0.028 m) already exceeds it before any bias is considered.
- At 95%, a single height carries an interval of about ±1.96 × 0.028 ≈ ±0.055 m about a mean that is itself displaced by 41 mm, so the end-to-end spread is roughly 0.10 m - four times the requirement.
A useful sanity check: to achieve RMSE ≤ 25 mm with 28 mm of scatter is impossible regardless of how well the bias is removed; the observation strategy, not the adjustment, has to change.
There is a second, quieter failure. A 41% afternoon fix rate means the afternoon sample is a selected subset - only the strongest geometry and lowest-multipath shots fix - so production data are worse than the checkpoint statistics suggest. Float solutions misreported as fixed, a known VRS failure mode under disturbed ionosphere, would pass a casual check because their scatter looks small while their bias does not.
2. The +41 mm mean residual is systematic. Identify the most probable causes and state how you would test between them.
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Three candidates, distinguishable by a simple experiment.
- Datum/epoch mismatch (most likely). The reference stations are constrained in a stable global frame; the two floodplain benchmarks are subsiding at 8 mm/yr and were last levelled in 2011. Over 13 years that is about 104 mm of movement, so those published heights are stale. If any part of the solution is pulled toward them, a bias of tens of millimetres appears. The observed +41 mm is the right sign but smaller than 104 mm, which is consistent with only partial influence - or with a subsidence rate that is not uniform across the floodplain.
- Geoid/height-system mismatch. Mixing ellipsoidal and orthometric values, or using a geoid model of the wrong epoch or resolution, produces a smooth regional bias of exactly this kind.
- Antenna or rod error. A 41 mm constant is not typical of a rod misreading (usually a round 10–50 mm) but is small enough to be a phase-centre or slant-height error.
Decisive test: establish one bedrock monument well outside the subsidence zone, observe it statically for 60+ minutes alongside two floodplain benchmarks, and connect all three by spirit levelling. If the bedrock monument agrees with GNSS but the floodplain monuments do not, cause 1 is proven. If all three carry the same offset, cause 2 is proven. Repeat with two different rod heights to eliminate cause 3.
3. Propose the survey design and quality-control regime that would actually deliver the corridor to specification in the available time.
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Separate the control problem from the detail problem.
Control (the part that must be right):
- Establish 5–6 stable monuments on bedrock or deep-set pillars outside the subsidence zone; 30–45 minute static sessions, processed in a single least-squares network adjustment, with loop closures reported.
- Tie the network to a declared reference epoch and state it in the deliverable. Do not silently mix epochs.
- Validate the geoid model locally by spirit-levelling between two GNSS-derived points.
Detail (the part that can be fast):
- Use RTK only with baselines ≤ 5 km from a locally established base, never 38 km from a network station, and re-observe during low Kp windows (morning).
- Two independent occupations per point, at least 60 s apart, rejecting any pair differing by more than 30 mm in height.
- Occupy 5% of all points as independent checkpoints and plot residuals against northing and against distance from the base; a trend means the base is wrong.
- Where the vertical is critical (embankment crests, drainage inverts), derive heights by total station or leveling from control - RTK is a horizontal tool here.
Reporting: publish the checkpoint RMSE, the bias and the number of rejected points. A deliverable with 0.0496 m RMSE and three weeks of schedule pressure should be renegotiated, not quietly accepted.