Spatial time series (STS), which refers to time-series data collected at fixed spatial locations, is crucial for understanding the spatiotemporal dynamics of geographical phenomena. Measuring the spatial association based on STS similarity provides valuable insights into the exploratory analysis of spatiotemporal data. However, existing methods are not effective in accurately quantifying such spatial association. To address this gap, this study proposes a conceptual model and a statistical method for identifying spatial clusters that exhibit significantly similar time-varying characteristics within a set of STS data. Conceptually, three representative patterns are defined: positive, negative, and no associations. A positive pattern occurs when spatially adjacent STSs show similar time-varying characteristics, while a negative pattern occurs when they show dissimilar ones. Technically, this study introduces a distance metric to measure similarities among STSs. The spatial association of STS at global and local scales is quantified according to the spatial concentration of these similarities. The validity and applicability of the proposed statistics are verified through synthetic and real-world examples, demonstrating their potential as effective tools for understanding spatiotemporal dynamics from a new perspective.

Intercity human dynamics has involved increasing interactions between the physical world and cyberspace with the boom of the Internet and social media, expanding traditional intercity activities from a single dimension of physical space to a multidimensional hybrid space. Revealing the dynamics of intercity activities in a hybrid physical–virtual space requires considering interactions between human activities in both the physical world and cyberspace. However, existing studies often overlook cross-space interactions, failing to adequately model interactions between virtual and physical spaces in terms of the network structure and spatial effects. To address these gaps, this study investigates intercity human dynamics through travel movement–intention interactions. A multilayer network framework is proposed to represent the hybrid space, where travel movement–intention interactions can be conceptualized and measured. Using travel and search flows in China during the ‘Labor Day’ holiday periods in a three-year period of the pandemic, we demonstrate the proposed approach’s utility through an analysis of city centrality of multilayer networks. Results find that travel movement–intention interactions exhibit dynamic patterns that vary with city size and geographic distance. This approach is broadly applicable to studies of hybrid physical–virtual spaces, aiding the evaluation of human dynamics beyond intercity activities.

The evaluation of urban open spaces plays an important role in landscape design, urban management and public security. However, few three-dimensional openness approaches with high accuracy and applicability to multiple data models have been developed. A method has been developed to measure the openness of an arbitrary location in an urban space accurately. This method is based mainly on the geometric subdivision of 3D space. First, a complete visual sphere was constructed with the viewpoint as the centre. The visual sphere was subsequently uniformly subdivided by multiple lines of sight at certain horizontal and vertical angle intervals, generating multiple discrete visual difference elements (VDEs). Finally, the specific visible volumes in each VDE were calculated separately to accumulate the all-visible volumes. The visible space index (VSI) was defined as the ratio of all visible space volumes to the visual sphere. The results indicate that the proposed method can accurately calculate the volume of visible space at any location, and the corresponding VSI reflects the difference of visible space in urban environments under different terrain conditions. The proposed method is expected to provide technical support for large-scale urban openness mapping, consequently contributing to the unified evaluation of urban space.

Terrain models are widely used to depict the shape of the Earth’s surface. With the development of photogrammetric methods, point cloud data have become one of the most popular data sources for terrain modelling. However, the obtained point clouds are of high density, which often increases redundancy rather than improving accuracy. Therefore, point cloud simplification should be a core component of terrain modelling. This paper proposes a point cloud simplification method by integrating topographic knowledge into terrain modelling (TKPCS). The method contains two steps: (1) topographic knowledge recognition and construction and (2) point cloud simplification using this topographic knowledge for terrain modelling. The proposed approach is benchmarked against improved versions of existing methods to validate its capability and accuracy in digital elevation model construction and terrain derivative extraction. The results show that the simplified points of the TKPCS method can generate finer resolution terrain models with higher accuracy and greater information entropy. The good performance of the TKPCS method is also stable at different scales. This work endeavours to transform perceptive topographic knowledge into a process of point cloud simplification and can benefit future research related to terrain modelling.

Viewshed computation is a central component for visibility analysis. The majority of existing viewshed computation methods use regular square grid digital elevation models (DEMs) and have limitations in considering spatial relationships among observers, targets and line-of-sight (LOS). Therefore, considering that the visibility is dominated by LOS between observers and targets, this study proposes a method to compute viewsheds using a new type of tree structure, the ‘view-tree’, that can efficiently extract LOS from DEMs for viewshed computation. The proposed method first constructs a view-tree using cells in regular square grid DEM according to the spatial occlusion relationships among cells. Then, the method traverses the view-tree to judge the visibility of each tree node and derives the viewshed. The results show that the view-tree method is 40% faster than the traditional R2 method. The view-tree method also reduces the error and omission rates by approximately 60% compared with the popular XDraw method.

Terrain derivative calculations from triangulated irregular network (TIN)-based digital elevation models (DEMs) have been extensively explored in geomorphometry. However, most calculation methods focus on the triangulation facets of TIN-based DEMs and ignore the vertices. In fact, these vertices are the original sampling points from the terrain surface and serve as the basis for triangulation. In this study, we argue that terrain derivative calculations using TIN-based DEMs should focus on the vertices. Employing examples with slope and aspect, we applied the TIN vertex-based method to a mathematical surface and a real topography using TIN-based DEMs with a range of sampling point densities. We performed a comparative analysis of the TIN vertex-based, TIN facet-based, and grid-based methods. Assessments on the mathematical surface showed that the TIN vertex-based method achieved the highest accuracy among the three methods. Error analysis for the real landform case indicated that the TIN vertex-based method performed slightly better than the grid-based method for slope calculation and slightly worse than the grid-based method for aspect calculation. Among the three methods, the TIN facet-based method was most sensitive to error. The TIN vertex-based method can provide a reference for the slope and aspect calculation based on point clouds.

Agricultural terraces are important for agricultural production and soil-and-water conservation. They comprise treads and risers that require manual construction and maintenance. If managed improperly, risers will collapse, causing soil loss, gully erosion, and cultivation threats. However, mapping terrace risers remains a challenge. This study presents a novel approach to automatically map terrace risers by combining remote sensing images and digital elevation models (DEMs). First, a terraced hillslope was extracted via a hill-shading method and edges in the image were detected using a Canny edge detector. Next, the DEM was used to generate the contour direction, and edges along this direction were searched and coded as candidate terrace risers via directional detection. Finally, the results of directional detection and the edge image obtained from the Canny detector were overlaid to backtrack complete terrace risers. The approach was validated using four study areas with different topographic characteristics in the Loess Plateau, China. The results verify that the approach achieves outstanding performance and robustness in mapping terrace risers. The precision, recall, and F-measure were 90.81%–97.57%, 88.53%–94.10%, and 90.13%–95.80%, respectively. This approach is flexible and applicable with freely available images and DEM sources.

Residual upland planation surfaces serve as strong evidence of peneplains during long intervals of base-level stability in the peneplanation process. Multi-stage planation surfaces could aid the calculation of uplift rates and the reconstruction of upland plateau evolution. However, most planation surfaces have been damaged by crustal uplift, tectonic deformation, and surface erosion, thus increasing the difficulty in automatically identifying residual planation surfaces. This study proposes a peak-cluster assessment method for the automatic identification of potential upland planation surfaces. It consists of two steps: peak extraction and peak-cluster characterization. Three critical parameters, namely, landform planation index (LPI), peak elevation standard deviation, and peak density, are employed to assess peak clusters. The proposed method is applied and validated in five case areas in the Tibetan Plateau using a Shuttle Radar Topography Mission digital elevation model (SRTM DEM) with 3 arc-second resolution. Results show that the proposed method can effectively extract potential planation surfaces, which are found to be stable with different resolutions of DEM data. A significant planation characteristic can be obtained in the relatively flat areas of the Gangdise–Nyainqentanglha Mountains and Qaidam Basin. Several vestiges of potential former planation areas are also extracted in the hilly-gully areas of the western part of the Himalaya Mountains, the northern part of the Tangula–Hengduan Mountains, and the northeastern part of the Kunlun–Qinling Mountains despite the absence of significant topographical features characterized by low slope angles or low terrain reliefs. Vestiges of planation surfaces are also identified in these hilly-gully upland areas. Hence, the proposed method can be effectively used to extract potential upland planation surfaces not only in flat areas but also in hilly-gully areas.

Selecting the set of candidate viewpoints (CVs) is one of the most important procedures in multiple viewshed analysis. However, the quantity of CVs remains excessive even when only terrain feature points are selected. Here we propose the Region Partitioning for Filtering (RPF) algorithm, which uses a region partitioning method to filter CVs of a multiple viewshed. The region partitioning method is used to decompose an entire area into several regions. The quality of CVs can be evaluated by summarizing the viewshed area of each CV in each region. First, the RPF algorithm apportions each CV to a region wherein the CV has a larger viewshed than that in other regions. Then, CVs with relatively small viewshed areas are removed from their original regions or reassigned to another region in each iterative step. In this way, a set of high-quality CVs can be preserved, and the size of the preserved CVs can be controlled by the RPF algorithm. To evaluate the computational efficiency of the RPF algorithm, its performance was compared with simple random (SR), simulated annealing (SA), and ant colony optimization (ACO) algorithms. Experimental results indicate that the RPF algorithm provides more than a 20% improvement over the SR algorithm, and that, on average, the computation time of the RPF algorithm is 63% that of the ACO algorithm.

This paper presents an intelligent approach to discover transition rules for cellular automata (CA) by using cuckoo search (CS) algorithm. CS algorithm is a novel evolutionary search algorithm for solving optimization problems by simulating breeding behavior of parasitic cuckoos. Each cuckoo searches the best upper and lower thresholds for each attribute as a zone. When the zones of all attributes are connected by the operator ‘And’ and linked with a cell status value, one CS-based transition rule is formed by using the explicit expression of ‘if-then’. With two distinct advantages of efficient random walk of Lévy flights and balanced mixing, CS algorithm performs well in both local search and guaranteed global convergence. Furthermore, the CA model with transition rules derived by CS algorithm (CS-CA) has been applied to simulate the urban expansion of Nanjing City, China. The simulation produces encouraging results, in terms of numeric accuracy and spatial distribution, in agreement with the actual patterns. Preliminary results suggest that this CS approach is well suitable for discovering reliable transition rules. The model validation and comparison show that the CS-CA model gets a higher accuracy than NULL, BCO-CA, PSO-CA, and ACO-CA models. Simulation results demonstrate the feasibility and practicability of applying CS algorithm to discover transition rules of CA for simulating geographical systems.

Traveling salesman problem (TSP) and its quasi problem (Quasi-TSP) are typical problems in path optimization, and ant colony optimization (ACO) algorithm is considered as an effective way to solve TSP. However, when the problems come to high dimensions, the classic algorithm works with low efficiency and accuracy, and usually cannot obtain an ideal solution. To overcome the shortcoming of the classic algorithm, this paper proposes an improved ant colony optimization (I-ACO) algorithm which combines swarm intelligence with local search to improve the efficiency and accuracy of the algorithm. Experiments are carried out to verify the availability and analyze the performance of I-ACO algorithm, which cites a Quasi-TSP based on a practical problem in a tourist area. The results illustrate the higher accuracy and efficiency of the I-ACO algorithm to solve Quasi-TSP, comparing with greedy algorithm, simulated annealing, classic ant colony algorithm and particle swarm optimization algorithm, and prove that the I-ACO algorithm is a positive effective way to tackle Quasi-TSP.

Cellular automata (CA) have been used increasingly to simulate complex geographical phenomena. This paper proposes a CA model for simulating the evolution of dynamic positive and negative (P–N) terrains in a small loess watershed. The CA model involves a large number of attributes, including the state of P–N terrains, distance to the shoulder-line, neighbourhood condition and topographic factors. Topographic factors include the slope gradient, aspect, slope length, slope variation, aspect variation, plan curvature, profile curvature, relief amplitude and flow accumulation. The CA model was applied to simulate the evolution of P–N terrains in an indoor, small loess watershed under artificial rainfall. The transition rules for CA were constructed automatically using a decision-tree algorithm. The derived transition rules are explicit for decision-makers and helpful for generating more reliable terrains. The simulation produces encouraging results in terms of numeric accuracy and spatial distribution, in agreement with natural P–N terrains. The iterative processes show that loess negative terrains continuously erode positive terrains. The development of a loess sinkhole near the centre gully head was reproduced as well, which shows the function of loess sinkholes in the formation of loess channel systems.

This paper presents a new, intelligent approach to discover transition rules for geographical cellular automata (CA) based on bee colony optimisation (BCO–CA) that can perform complex tasks through the cooperation and interaction of bees. The artificial bee colony miner algorithm is used to discover transition rules. In BCO–CA, a food source position is defined by its upper and lower thresholds for each attribute, and each bee searches the best upper and lower thresholds in each attribute as a zone. A transition rule is organised when the zone in each attribute is connected to another node by the operator ‘And’ and is linked to a cell status value. The transition rules are expressed by the logical structure statement ‘IF-Then’, which is explicit and easy to understand. Bee colony optimisation could better avoid the tendency to be vulnerable to local optimisation through local and global searching in the iterative process, and it does not require the discretisation of attribute values. Finally, The BCO–CA model is employed to simulate urban development in the Xi’an-Xian Yang urban area in China. Preliminary results suggest that this BCO approach is effective in capturing complex relationships between spatial variables and urban dynamics. Experimental results indicate that the BCO–CA model achieves a higher accuracy than the NULL and ACO–CA models, which demonstrates the feasibility and availability of the model in the simulation of complex urban dynamic change.