In the study of spatiotemporal geographical phenomena, the space–time interpolation method is widely applied, and the demands for computing speed and accuracy are increasing. For nonprofessional modelers, utilizing the space–time interpolation method quickly is a challenge. To solve this problem, the classical ordinary kriging algorithm was selected and expanded to a spatiotemporal kriging algorithm. Using the OpenCL framework to integrate central processing unit (CPU) and graphic processing unit (GPU) computing resources, a parallel spatiotemporal kriging algorithm was implemented, and three experiments were conducted in this work to verify the results. The results indicated the following: (1) when the size of the prediction point dataset is consistent, the performance of the method is robust with the increasing size of the observation point dataset; (2) the acceleration effect of the parallel method increases with an increased number of predicted points. Compared with the original sequential program, the implementation of the improved parallel framework showed a 3.23 speedup, which obviously shortens the interpolation time; (3) when cross-validating the temperature data in the Beijing Tianjin Hebei region, the space–time acceleration model provides a better fit than traditional pure space interpolation.

The scientific measurement of land use in space is an essential task in urban agglomeration studies, and the fractal feature is one of the most powerful tools for describing the phenomenon of space. However, previous research on the fractal feature of land use has mostly been conducted in urban space, and examines the fractal feature of different land use types, respectively; thus, the measurement of the relationship between different land use types was not realized. Meanwhile, previous prediction methods used for spatial land use mostly relied on subjective abstraction of the evolution, theoretically, regardless of whether they were calibrated, so that complete coverage of all the mechanisms could not be guaranteed. Based on this, here, we treat the land use structure in urban agglomeration space as the research object, and attempt to establish a fractal measure method for the relationship between different land use types in the space of urban agglomeration. At the same time, we use the allometric relationship between “entirety” and “local” to establish an objective forecast model for the land use structure in urban agglomeration space based on gray prediction theory, to achieve a predictive measurement of the structure of land use in urban agglomeration space. Finally, this study applied the methods on the Beijing–Tianjin–Hebei urban agglomeration to analyze the evolution of the stability of the structure of land use and achieve predictive measurement of the structure of land use. The results of the case study show that the methods proposed in this study can obtain the measurement of the relationship between different land use types and the land use prediction that does not depend on the subjective exploration of the evolution law. Compared with the measurement methods that analyzed the fractal feature of different land types, respectively, and the prediction methods that rely on subjective choice, the methods presented in this study recaps some innovations and reference values for relevant future research.

The evolution of the urban agglomeration is a significant development in urban geography. Determining its spatial range for effective measurement remains a challenge for researchers. In previous studies, determining spatial range has primarily been done through distinguishing the cities that should belong to urban agglomerations from among other cities by using various indicators. Both the selection of indicators and the standards used for calculation and identification have been based on subjective choices, and have not considered spatial distribution or morphology. The urban agglomeration can be regarded as a self-organized space, and spatial features of the fractal can be regarded as one of the morphological characterizations of spatial self-organization. From the perspective of the assumption that the space of urban agglomerations is molecule like assembled, and through the extraction and analysis of spatial fractals, we present an objective method to determine the “spatially contiguous zone” of urban agglomeration, particularly the spatial range in which the urban agglomeration is able to exercise jurisdiction within the radius of its capacity, rather than in the administrative division. Our method is applied in this paper to the Beijing–Tianjin–Hebei urban agglomeration and produced the following results: (1) the existence of spatial fractals and the theory of space unit molecule like self-organization or assembly in the morphology of urban agglomerations has been proved; and (2) a spatially contiguous zone could be identified for the urban agglomeration has been confirmed. Compared with previous methods used for determining space, this method is centered on the spatial morphology of urban agglomerations; the recognition of a spatially contiguous zone liberates the geographical limits of the result from city boundary restrictions. Concurrently, by considering the linkages within the city as a self-organizing black box, we can circumvent the one-sidedness involved with the selection of indicators that has biased previous studies, thereby avoiding having to focus on the specific mechanism of urban dynamics, and coming much closer to its self-organizing dynamic inner nature. This approach will prove to be a useful reference for the identification of spatial ranges in future studies.