Geographically weighted regression (GWR) introduces the distance weighted kernel function to examine the non-stationarity of geographical phenomena and improve the performance of global regression. However, GWR calibration becomes critical when using a serial computing mode to process large volumes of data. To address this problem, an improved approach based on the compute unified device architecture (CUDA) parallel architecture fast-parallel-GWR (FPGWR) is proposed in this paper to efficiently handle the computational demands of performing GWR over millions of data points. FPGWR is capable of decomposing the serial process into parallel atomic modules and optimizing the memory usage. To verify the computing capability of FPGWR, we designed simulation datasets and performed corresponding testing experiments. We also compared the performance of FPGWR and other GWR software packages using open datasets. The results show that the runtime of FPGWR is negatively correlated with the CUDA core number, and the calculation efficiency of FPGWR achieves a rate of thousands or even tens of thousands times faster than the traditional GWR algorithms. FPGWR provides an effective tool for exploring spatial heterogeneity for large-scale geographic data (geodata).

Land use/land cover change (LUCC) analysis is a fundamental issue in regional and global geography that can accurately reflect the diversity of landscapes and detect the differences or changes on the earth’s surface. However, a very heavy computational load is often unavoidable, especially when processing multi-temporal land cover data with fine spatial resolution using more complicated procedures, which often takes a long time when performing the LUCC analysis over large areas. This paper employs a graph-based spatial decomposition that represents the computational loads as graph vertices and edges and then uses a balanced graph partitioning to decompose the LUCC analysis on spatial big data. For the decomposing tasks, a stream scheduling method is developed to exploit the parallelism in data moving, clipping, overlay analysis, area calculation and transition matrix building. Finally, a change analysis is performed on the land cover data from 2015 to 2016 in China, with each piece of temporal data containing approximately 260 million complex polygons. It took less than 6 h in a cluster with 15 workstations, which was an indispensable task that may surpass two weeks without any optimization.

In spatiotemporal applications, geographically weighted principal component analysis (GWPCA) is commonly adopted to describe spatial heterogeneity. However, time effects are ignored in GWPCA. In this study, the temporal effect was incorporated into GWPCA . Thus, an extended model, geographically and temporally weighted principal component analysis (GTWPCA), was developed to simultaneously explore spatial and temporal non-stationarity. The GTWPCA was implemented using a case study of air pollution in China. The results mainly show that GTWPC1 (the local component one in GTWPCA) corresponds to a ‘winning group’ with constantly varying ‘winning’ variables adapted to the spatiotemporal non-stationary characteristics of air pollution in China.

Cultivated land concentration and contiguity, as a core element of agricultural modernization development, holds strategic significance for enhancing agricultural production efficiency and ensuring national food security. This study employs vector patches as research units and classifies spatial connections between patches into direct and indirect connections. We quantify six types of spatial relationships between patches using binary encoding, enabling precise delineation of concentrated contiguous cultivated land. A Patch Connectivity Index is proposed. Combined with the Patch Area Index and Patch Shape Index, an evaluation system for cultivated land concentration and contiguity is established. Using Suixi County as a case study, we investigate the spatiotemporal evolution of its cultivated land concentration and contiguity from 2019 to 2023. Overall, patch connectivity exhibits a “single-element dominant, multi-element complementary” structural pattern, while the evaluation grading of cultivated land concentration and contiguity follows a normal distribution. Between 2019 and 2023, the average patch area decreased while the average number of connections between patches increased, indicating significant improvement in cultivated land concentration and contiguity levels. By adjusting spatial relationships between patches, the effective integration and utilization of cultivated land resources can provide theoretical foundations and practical references for agricultural modernization development.