Enhancing Land Use Efficiency Assessment Through Built-Up Area–Built-Up Volume Trajectories: Integrating Vertical Urban Growth into SDG 11.3.1 Monitoring

SDG Indicator 11.3.1 assesses urban land use efficiency (LUE) through the ratio of the land consumption rate (LCR) to the population growth rate (PGR), or LCRPGR. However, its methodology is restricted to two-dimensional built-up area expansion, excluding vertical development and limiting insight into the structural mechanisms underlying efficiency outcomes. This study aims to integrate vertical urban growth into SDG 11.3.1 monitoring to improve the interpretation of efficiency outcomes. We introduce the Built-up Area–Built-up Volume (BUA–BUV) trajectory framework, which embeds vertical growth into LUE monitoring. The framework represents urban growth as trajectories in normalized BUA–BUV space and classifies them by prevailing built form (horizontal, balanced, vertical) and growth modality (expansion or intensification). This classification is then coupled with LCRPGR to link efficiency outcomes with spatial structure. We apply the framework to 10,856 urban centres worldwide using Global Human Settlement Urban Centre Database (GHS-UCDB 2025) data from 1980 to 2020. Results show that inefficient growth (LCRPGR > 1) dominated, affecting 69% of centres during 1980–2000 and 52% during 2000–2020, while inefficiency linked to demographic decline (LCRPGR ≤ 0) rose from 9% to 20%. Efficient centres (0 < LCRPGR ≤ 1) increased from 22% to 29%. Across all efficiency classes, BUA–BUV trajectories revealed a prevailing pattern of horizontal expansion, with similar LCRPGR values associated with structurally divergent growth paths. Vertically intensifying development was rare, even among efficient centres. The BUA–BUV framework embeds structural context into efficiency assessments, thereby strengthening SDG 11.3.1 monitoring and informing policies for compact and sustainable urbanization.