ABSTRACT Time underpins analysis across the natural and social sciences, yet representing and computing it across extreme temporal scales and multiform expressions remains challenging, particularly in cross‐disciplinary data integration and discovery in the geosciences. Textual forms are difficult to compute, numerical forms often suffer from unit inconsistencies and symbolic complexity, and existing temporal models remain limited in cross‐scale continuity and flexibility. To address these issues, this study conducts a systematic analysis of the distinct characteristics of time and proposes a novel time‐coding framework—Variable‐length Ultra‐scale Time Segmented Coding (VUTSC). This method encodes time as three components: a Base reference, a Level indicator, and a variable‐length sequence of Codes, which together enable consistent and scalable representation across ultra‐wide temporal scales within a unified structural framework. Using the geosciences as a case study, we build a Deep‐Time Digital Earth Timeline System based on VUTSC. Experiments on multi‐scale and interdisciplinary time expressions validate the feasibility, breadth, simplicity, flexibility, and efficiency of VUTSC. Results indicate that this model can effectively express geoscientific time across a wide range of scales, while its coding efficiency is significantly higher than that of timestamp‐based methods. The encoding and decoding strategies are stable and support hierarchical traversal, neighborhood search, and time‐relationship calculations. For time‐centric scientific disciplines, including the Earth sciences, this approach provides a promising pathway for multi‐source, multi‐scale data mining and knowledge discovery.
ABSTRACT Detecting spatial heterogeneity boundaries from irregular point observations is important for understanding abrupt changes in spatial processes and producing interpretable boundary maps. However, irregularly sampled spatial data lack a natural ordering, making conventional one‐dimensional change point detection difficult to apply directly. We develop a modular two‐stage spatial analysis framework that connects spatial interpolation with established change point detection procedures. First, interpolation reconstructs a gridded representation of the underlying spatial field. Second, the interpolated surface is decomposed into geographically ordered one‐dimensional spatial profiles, where change point detection is used to identify boundaries between heterogeneous regions. Simulation experiments under different boundary configurations, spatial error structures, interpolation settings, and detection methods show that the framework can recover major boundary patterns, especially when appropriate interpolation smoothing is combined with stable detection methods. An application to January 2025 PM 2.5 monitoring data in China demonstrates its usefulness for extracting interpretable boundary structures from irregular environmental monitoring networks.
ABSTRACT Rapid urbanization in semi‐arid regions with complex geomorphological settings poses significant environmental and territorial challenges, particularly in developing countries where planning frameworks struggle to keep pace with spatial dynamics. This study investigates the spatiotemporal dynamics, geo‐environmental drivers, and future trajectories of urban expansion in the Wilaya of Constantine, northeastern Algeria, from 1985 to 2050. We used multi‐temporal land‐cover data from the GLC_FCS30D dataset (30 m resolution; 1985–2022) to quantify land‐use/land‐cover (LULC) change and urban growth. We extracted built‐up areas from the impervious surface class and analyzed areal expansion, growth rate, and spatial trajectory. To identify the geo‐environmental determinants of urbanization, 49,878 stratified sample points (24,939 urban and 24,939 non‐urban pixels) were generated, and eight predictor variables slope, elevation, topographic wetness index, drainage density, distance to streams, seismic hazard, geology, and soil type were incorporated into four machine‐learning algorithms. Model performance was assessed through five‐fold cross‐validation, and predictor contributions were interpreted via SHAP (SHapley Additive exPlanations) analysis. Future urban expansion for 2030, 2040, and 2050 was projected under a business‐as‐usual scenario using a Cellular Automata–Markov Chain (CA–Markov) model calibrated using LULC maps for 2000 and 2010, validated by simulating the 2020 land‐cover map and comparing it with the observed GLC_FCS30D 2020 map (Overall Accuracy = 95.7%, Kappa = 0.926, K_no = 0.994). Future projections used a transition matrix derived from the 2010 to 2020 period. Results reveal a near‐fourfold increase in urban area between 1985 and 2022 (+303%; Compound Annual Growth Rate (CAGR) ≈3.84%), with the most intense expansion phase occurring between 1995 and 2000. Random Forest (RF) achieved the highest predictive accuracy (AUC‐ROC = 0.906), with soil type, elevation, and seismic hazard identified as the dominant geo‐environmental predictors of urbanization. Under a business‐as‐usual scenario, the urban area is projected to expand from 113.8 km 2 in 2020 to 205.9 km 2 by 2050, with a plausible range of 124–243 km 2 across low, BAU, and high growth scenarios. The integrated ML/CA‐Markov framework proposed here constitutes a robust, transferable, and policy‐relevant approach for evidence‐based urban planning in rapidly urbanizing Mediterranean cities.
ABSTRACT As the primary spatial data format in geographic information systems (GIS), vector maps demand exact coordinate reversibility for copyright protection. However, vector maps encode geographic features as irregularly distributed floating‐point coordinates with limited redundancy. This lack of redundancy forces algorithms to perturb coordinates, creating a trade‐off among capacity, geometric robustness, and exact reversibility. We propose CFPG‐RW, a Coarse‐to‐Fine Polar Grid Reversible Watermarking method built on three mechanisms. First, a triplet‐defined local polar coordinate system provides embedding carriers invariant to rotation, scaling, and translation (RST): differential angle and distance ratio. Second, a coarse‐to‐fine polar grid encodes multi‐bit watermarks per‐vertex, lifting capacity beyond 1–2 bpv schemes. Third, a center‐referenced offset contraction strategy guarantees exact reversibility by shrinking and inverting vertex offsets. On real‐world OpenStreetMap‐derived datasets, CFPG‐RW achieves 6.99 bpv, recovers coordinates with errors at the degree level, and remains robust against RST attacks, cropping, and vertex‐editing attacks, outperforming existing methods.
ABSTRACT With the rapid acceleration of urbanization, understanding the coordination between urban expansion (UE) and urban resilience (UR) has become critical for achieving sustainable urban development. However, the spatial patterns and driving mechanisms of the coupling coordination between UE and UR remain insufficiently understood. This study develops a multi‐source geospatial analysis framework by integrating remote sensing data and socioeconomic statistics to investigate the spatiotemporal evolution, spatial correlation, and influencing factors of UE‐UR coupling coordination in Shandong Province, China, from 2002 to 2022. Urban built‐up areas were extracted using a modified lighting index integrating nighttime light, vegetation, and thermal information, while a multidimensional indicator system was established to evaluate UR. The coupling coordination degree (CCD) model and random‐effects Tobit model were further applied to reveal the spatial characteristics and driving mechanisms of UE‐UR coordination. The results showed that: (1) The built‐up area of Shandong Province expanded by 3821 km 2 during 2002–2022, while the expansion rate and intensity gradually declined, with the center of gravity of built‐up areas shifting southwestward. (2) UR exhibited an overall increasing trend, although significant spatial disparities remained among cities. (3) The CCD between UE and UR continuously improved, with Qingdao reaching 0.616 in 2022. Spatial correlation analysis revealed increasingly strengthened linkages among cities, while urbanization level, industrial structure, and government regulation significantly promoted UE‐UR coordination. This study provides new insights into understanding the spatial interaction between urban growth and resilience enhancement and offers practical implications for sustainable urban planning and resilient city development.
