FZStats v1.0: a raster statistics toolbox for simultaneous management of spatial stratified heterogeneity and positional dependence in Python

Abstract. Focal and zonal statistics are fundamental tools in geographic information systems (GISs) for characterizing spatial patterns, yet they have traditionally addressed spatial stratified heterogeneity (SSH) and spatial positional dependence (SPD) in isolation. To overcome this limitation, we introduce FZStats v1.0, a Python 3/QT5–based toolbox that not only integrates conventional focal and zonal statistics, but also implements a novel focal–zonal mixed statistics approach capable of jointly capturing both SSH and SPD. First, we formally develop the focal–zonal mixed statistics model to address stratified heterogeneity, spatial dependence, and their interactions within a unified framework – filling a key methodological gap left by traditional approaches that cannot accommodate their co-occurrence in real-world spatial data. Second, FZStats v1.0 provides a user-friendly graphical interface for flexible configuration of neighborhood window shapes (e.g., rectangular, circular, elliptical), sizes, and statistical operations (e.g., mean, percentiles). It also supports multiprocessing and batch operations, enabling scalable computation across diverse spatial analysis tasks. Third, we validate the effectiveness and robustness of the new method through a geothermal anomaly detection case study. Across multiple years, seasons, representative target sizes, and local window radii, the focal–zonal mixed statistics consistently outperforms both focal and zonal statistics, demonstrating its superior capability in enhancing anomaly signals under complex spatial conditions. In summary, FZStats v1.0 is not only a theoretically grounded and methodologically novel tool, but also a highly adaptable and practical solution for spatial data analysis in diverse application domains.