A novel metric to assess the accuracy of land use change modeling

The integration of the first law of geography into land use change simulation models has attracted considerable attention, aiming to improve model accuracy through the enhanced representation of spatial heterogeneity. However, existing evaluation metrics, which primarily focus on cell-to-cell agreements, inadequately capture the models' ability to represent spatial heterogeneity. Consequently, there is a pressing need for updated evaluation metrics that accurately reflect the models' capability to depict spatial features. To address this issue, the Fuzzy Figure of Merit (Fuzzy FoM) grounded in fuzzy theory was proposed. This metric effectively quantifies and visualizes a model's ability to capture spatial features by introducing the notion of degree of membership, facilitating a comprehensive analysis of model accuracy from both statistical and spatial perspectives. This paper demonstrates the metric's utility in the validation process, illustrating four land use change models that incorporate the spatial heterogeneity.