A transparent constrained stochastic framework for urban expansion forecasting and future service-network screening: Cape Town demonstration using annual building evidence, empirical land constraints, spatial hindcasting, and multi-horizon ensembles

Jaco Moolman

Spatial forecasts of urban expansion require separate, auditable answers to two questions: how much built area is assumed to appear, and where it is allocated. This study presents a constrained stochastic workflow and demonstrates it for metropolitan Cape Town, South Africa. Annual Open Buildings Temporal building-presence surfaces for 2016–2023 are harmonised to a 10 m grid and cleaned with a temporal median and a suffix-persistence rule. A binned logistic model ranks unbuilt cells on distance to the built edge, local and neighbourhood built fractions, and direct adjacency, with the distance and neighbourhood curves projected onto monotone ones after fitting. Terrain, flood and water enter as a separate multiplier rather than inside that fit, and a weak directional term and a detached-growth pool modify the allocation. Demand is supplied independently of location potential, and weighted sampling without replacement updates the urban state at every step across twelve replicates.

A spatially blocked classifier diagnostic returned ROC-AUC 0.880 and PR-AUC 0.307; its best-threshold F1 of 0.456 is optimistic, because that threshold was chosen on the same held-out cells. The end-to-end 2016–2023 hindcast, supplied with observed annual quantities, achieved a 29.02% pixel hit rate and 16.97% Figure of Merit, 7.9 times the uniform-random value. It is an in-period reconstruction rather than an independent forecast test, because location, direction, detached share and terrain strength are all calibrated on the interval it is scored over. The hindcast reproduced dominant edge expansion, overpredicted infill, almost eliminated fringe growth, and missed the observed north-easterly growth bearing by about 35°. The aggregate hit rate also conceals a strong asymmetry: recall falls from 39.2% for change immediately adjacent to the built edge to under 1% beyond about 40 m, and from 36.6% for change in patches under 0.1 ha to 0.9% for patches larger than 50 ha, so the workflow reproduces incremental thickening of an existing perimeter and not the appearance of new districts. Under the central scenario, new built area after a modelled 2026 baseline is 54.9 km² by 2036, 249.7 km² by 2076 and 441.3 km² by 2126. A downstream screen combines forecast growth pressure, straight-line distance from an existing bank network, and developability to rank neighbourhood-scale ATM and branch opportunities. All of these are conditional scenarios and screening hypotheses, not parcel, timing, demographic, or investment predictions.