Cadastral Migration: Scale Factor, Area and a Conflicting Monument
A municipality is migrating 4,800 cadastral parcels (mean 0.80 ha, total 3,840 ha) from a local Transverse Mercator grid into a national UTM zone. The parcels lie up to 42 km from the central meridian at a mean orthometric height of 620 m. The local grid used k0 = 0.9996 but never applied a combined factor to parcel areas, so all recorded areas are grid areas. Take R = 6,371 km. Meanwhile a boundary dispute has arisen on a 25.6 ha parcel: the record bearing and distance from the 1974 survey close on an original stone monument that is found in place and undisturbed, but the 2019 survey set a new iron pin 0.35 m away from it. The 2019 survey closed its control traverse through a point that has since been shown to be disturbed. The assessor wants a single area figure for the tax roll.
1. Compute the combined factor and quantify the area effect at both parcel and municipal scale. Which area should be published?
Read the worked answer
Elevation factor: R/(R+h) = 6,371,000 / 6,371,620 = 0.9999027
Point scale at x = 42 km: k = k0 (1 + x²/2R²) = 0.9996 × (1 + 42,000² / (2 × 6,371,000²))
- x²/2R² = 1.764 × 10⁹ / 8.118 × 10¹³ = 2.173 × 10⁻⁵
- k = 0.9996 × 1.00002173 = 0.9996217
Combined factor = 0.9996217 × 0.9999027 = 0.999524; area factor = 0.999524² = 0.999048
Effect:
- 25.6 ha ground → 25.6 × 0.999048 = 25.576 ha grid, a difference of 0.024 ha (≈244 m²).
- 3,840 ha → 3,836.3 ha grid, a difference of ≈3.7 ha.
Judgement. Per parcel the difference is trivial - far inside the usual cadastral tolerance of about 0.1√A (≈0.5 ha for this parcel). But it is systematic and one-signed, so it does not average away across 4,800 parcels; it appears as a 3.7 ha hole in the tax base. Publish ground areas, computed per parcel rather than with the single municipal factor, because point scale varies from 0.9996 to 0.99962 across 42 km and elevation varies between parcels. Keep grid coordinates for GIS, mapping and any spatial join; state the method and the factor set in the metadata so the two figures are never confused again.
2. Resolve the boundary dispute and state what evidence governs the location of the parcel line.
Read the worked answer
The monument governs, not the pin and not the bearing/distance.
Reasons, in order of weight:
- An original, undisturbed monument found in place is the best evidence of the boundary. It is contemporaneous with the 1974 survey and was set by the surveyor who created the parcel. Recorded bearings and distances, and any coordinates computed from them, are secondary - they describe where the line should be, and are used only to identify or reinstate a monument.
- The 2019 pin was set from disturbed control. A 0.35 m displacement of a control point propagates directly into every point set from it. The pin is therefore not evidence; it is an artefact of a broken survey. The 0.35 m offset between pin and monument is almost exactly the scale of error a disturbed control point produces, which corroborates the explanation.
- Occupation and long possession may support the pin in equity, but that is a legal question decided on evidence of the parties' intent and duration of use - not a survey decision. The surveyor's job is to reinstate the 1974 line, not to arbitrate the ownership.
Action: reject the 2019 pin as boundary evidence, re-establish the 2019 survey from undisturbed original control (or re-observe the disturbed point), recompute the parcel from the found monument, and record the reinstatement with a sketch showing both the monument and the pin and the 0.35 m separation. Notify both parties and, if they still disagree, hand the file to the adjudicating authority with the survey evidence clearly separated from the legal question. Recompute the parcel area only after the line is fixed - the 25.6 ha figure is the grid value and needs the area factor applied before it goes on the roll.