Probabilistic Modelling of Parcel Area Uncertainty: Implications for Land Administration and Urban Planning

Parcel area sits at the intersection of urban planning, land administration and land surveying. It underpins development intensity, floor area allocation, minimum lot thresholds, land readjustment and value capture mechanisms. Yet discrepancies between modern measurements and ownership titles are usually evaluated through fixed tolerance formulas rather than quantified confidence intervals. While coordinate precision is routinely specified, the uncertainty of the derived parcel area is seldom expressed explicitly, limiting the traceability of planning calculations based on cadastral geometry. This paper presents a variance-based formulation for estimating parcel area uncertainty from boundary coordinates. Using the Gauss area function and first-order propagation, vertex precision is translated into parcel-level confidence intervals based on horizontal RMS parameters commonly reported in cadastral practice, including documented transformation accuracy. The Greek cadastre provides an illustrative case combining a national GNSS infrastructure, a unified reference system and formula-based area screening embedded in statutory workflows. Illustrative examples show how area uncertainty varies with parcel geometry and measurement origin. Absolute uncertainty increases with parcel size and boundary elongation, while relative uncertainty decreases with parcel size. A Monte Carlo analysis of the error-correlation structure shows that the diagonal, independent model is not a universal bound: depending on the structure of the transformation error and on parcel geometry it may either overstate or understate the true area uncertainty, by factors between about 0.4 and 3.5 in the cases examined. The results clarify how coordinate precision propagates into regulatory-relevant area values and support more transparent interpretation of area discrepancies in planning and land administration contexts.