A novel spatial heterogeneity decay model for depicting scale-effects in urban land

The variation in geographical feature characteristics with observational scale, known as the scale-effect, presents a fundamental challenge in geography and remote sensing. However, the quantitative characterization of the scale-effect in the spatial heterogeneity of urban land (SHUL) remains underexplored. This study systematically investigates the scale-effect of SHUL using 79 Chinese cities as empirical samples. A semi-variogram function was employed to quantify SHUL across multiple spatial scales, revealing an exponential decay pattern. To model this phenomenon, we propose a scale-effect model that effectively captures the decay dynamics of SHUL. The model demonstrated strong performance, achieving an average goodness-of-fit (R² = 0.944) across the 79 cities. Based on the scale-effect model, we derived characteristic indicators (maximum, minimum, fluctuation, and rate of decay) of the SHUL scale-effect and compared their variation across Chinese cities. Furthermore, we discuss the scale-effect mechanism, potential application pathways, and prospects for global generalization. The proposed scale-effect model offers valuable insights and a methodological reference for the cross-scale transformation of urban data.