Two surveys of the same site never match exactly. Each has its own reference frame, flight-line offsets, density and classification. Difference them as delivered and the map shows change everywhere, much of it in the surveys rather than the ground.
Alignment on stable ground
Co-registration measures the offset between surveys on stable ground, such as roads, roofs and open ground, and removes it from the whole survey before any change is measured. Published methods for elevation data take the same approach, using stable terrain to remove shifts and biases first (Nuth and Kääb, 2011).
The correction is measured, not assumed: a single shift, a tilt where a survey leans, or a separate shift for each flight line. The Hobart showcase used all three to align the 2008 and 2011 surveys to the 2024 survey.
A threshold from the surveys
After alignment, the surveys still scatter slightly on stable ground. That scatter is the floor: a smaller difference cannot be told apart from survey error.
For change maps and volumes, GroundMap measures the scatter of each pair of surveys, separately on stable open ground and under forest, and adds each surface’s interpolation uncertainty, which grows with distance from the nearest measured point and with slope. The threshold is set at 95 % confidence, from the pair's scatter for each area and each cell's own uncertainty; only contiguous patches above it count as change. The Change detected class of a confidence layer is a separate, fixed flag: passes more than 15 cm apart.
Published practice for repeat surveys is the same: change is thresholded at a stated confidence (Wheaton et al., 2010), and each measurement can carry its own confidence interval (Lague et al., 2013). The threshold changes the answer. Over five years of surveys of a braided river reach in Scotland, thresholding at 95 % confidence excluded between 24 % and 59 % of volumetric change from the budget, depending on the year.
Why averaging hides change
Averaging surveys into one surface fails exactly where change matters. Where a stockpile was removed between surveys, the average sits halfway: a surface that existed on neither date, holding half the volume. The difference is spread through the model, and no layer records it.
GroundMap keeps change out of the fused surface. Where surveys differ by more than the per-cell threshold, the newest survey describes the site and the earlier one becomes its history, kept as a change layer. The LAS specification provides a class for such points: 22, Temporal Exclusion, for features excluded because of changes over time between data sources.
Cut and fill, with confidence
A volume is only as defensible as the threshold behind it. For each area GroundMap reports cut and fill above the threshold, the threshold, the area left out (where either survey had no measured ground close by, or water) and the surveys, dates and alignment used. A reviewer can repeat the calculation and reach the same figure.
Change and volumes, with the method and confidence behind every figure.
Sources
- Nuth, C. and Kääb, A. (2011). Co-registration and bias corrections of satellite elevation data sets for quantifying glacier thickness change. The Cryosphere 5, 271–290.
- Wheaton, J. M., Brasington, J., Darby, S. E. and Sear, D. A. (2010). Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets. Earth Surface Processes and Landforms 35(2), 135–156.
- Lague, D., Brodu, N. and Leroux, J. (2013). Accurate 3D comparison of complex topography with terrestrial laser scanner: application to the Rangitikei canyon (N-Z). arXiv:1302.1183.
- ASPRS. LAS Specification 1.4 R15 (2019): point classes.