Scale-dependent cooling effects of urban green spaces based on multi-satellite data in Penang, Malaysia

Urban green spaces (UGS) have been increasingly recognized as effective nature-based solutions for mitigating urban heat island effects. However, the scale-dependent cooling efficiency of UGS remains insufficiently explored in tropical cities. This study investigated the scale-dependent cooling mechanisms and dominant landscape factors of 1,892 UGS patches on Penang Island, Malaysia, using multi-satellite data from Landsat-9, Sentinel-2, and ASTER. Cooling intensity (CI) and per-unit-area cooling efficiency (CE = CI/Area) were derived using power-law scaling relationships to examine size-dependent thermal regulation patterns. Results revealed that 851 (44.98%) UGS patches exhibited cooling island effects, with a mean CI of 0.46 ± 0.63°C. The size distribution reflected highly fragmented green infrastructure: small patches (≤0.1 ha) comprised 30.9% of cooling patches but only 2.9% of the total cooling area, while 21 large patches (>4 ha, 2.5%) accounted for 50.0%. The CI-area relationship followed a sub-linear power law (CI = 0.29 × Area^0.17, p < 0.001), with absolute CI increasing across scales (small: 0.39°C; medium: 0.48°C; large: 0.72°C), representing an 88% increase from small to large patches. In contrast, per-unit-area CE exhibited a pronounced declining trend (small: 7.66°C/ha; large: 0.08°C/ha), reflecting diminishing marginal returns consistent with the sub-linear scaling exponent (β = 0.17 < 1). The significant between-scale differences (Kruskal–Wallis p < 0.001) coupled with universally non-significant within-bin slopes (all p > 0.05) indicated that cooling gains arise primarily from crossing scale thresholds rather than incremental area expansion. Multivariate regression revealed that Vegetation density (NDVI_in) was the dominant factor for green space surface temperature (27.69% contribution, R² = 0.521), while landscape shape complexity (LSI) was the primary driver of CI (3.98%, R² = 0.079). Urbanization factors showed increasing importance for larger patches, indicating greater susceptibility to surrounding thermal stress. These findings support differentiated planning strategies: small patches should prioritize vegetation density, medium patches benefit from shape complexity optimization, and large patches require buffer zones to mitigate urbanization impacts.