1 Introduction
In pursuit of Sustainable Development Goals, the International Geo-Biosphere Program (IGBP) and the International Human Dimensions Program (IHDP) (GLP,
2005) launched a plan of “Land Use/Cover Change (LUCC)” in 1995, regarding LUCC as the core content of global environmental change research. In 2012, the International Council for Science (ICSU) and the International Social Science Council (ISSC) subsequently launched the “Future Earth” research program, signifying the increasing focus on researching the monitoring and simulation of LUCC (Verburg
et al.,
2016). Given the uncertainty about land-use futures and their environmental consequences, spatiotemporal LUCC simulations have become efficient and essential tools for characterizing landscape dynamics, integrating a diverse array of socioeconomic and physio-geographical factors (Li
et al.,
2018; Wu
et al.,
2021; Kang
et al.,
2024). For example, over the past two decades, cellular automata (CA) models have significantly advanced LUCC simulations (Aburas
et al.,
2016). During the iterative modeling operation, the status of each cell is updated according to its initial state, the surrounding neighborhood effects, and a set of transition rules (White
et al.,
1997). By properly defining the neighborhood effect on the basis of the land uses in all cells within the neighborhood and their distances from the location of interest, CA models have strong capabilities for simulating complex interactions between different land-use types. This capability is crucial for developing strategies that promote sustainable land use and guide urban development. Notable examples include the LUMOCAP (van Delden
et al.,
2010), LANDSCAPE (Verburg and Overmars,
2009; Ke
et al.,
2017; Sheng
et al.,
2022), and Dyna-CLUE (Sakayarote and Shrestha,
2019).
Concerns have arisen regarding the spatial homogeneity of these methods. Most studies have assumed “spatial neighborhood stationarity,” suggesting that the neighborhood effect remains consistent across the entire study area (Couclelis,
1985). For example, the enrichment factor is frequently employed to quantify neighborhood effects regarding the over- or underrepresentation of land-use types on the basis of their quantitative proportions within the neighborhood (Verburg
et al.,
2004). However, this assumption appears to contradict the inherent spatial heterogeneity of geographic dynamics, as the spatial distribution of land use is oversimplified or disregarded. To address this limitation, recent studies have modified the enrichment factor by incorporating additional parameters through expert knowledge and manual calibration to better reflect spatial heterogeneities (Liao
et al.,
2016; Karimi
et al.,
2017). However, these approaches are subjective, lack repeatability and are highly dependent on the knowledge and skills of the experts. In seeking alternative solutions, researchers have also employed zoning scenarios (Yin
et al.,
2018; Xu
et al.,
2021) and size-adaptive strategies (Zhang
et al.,
2023; Li
et al.,
2024) to enhance the representation of neighborhood effects. However, this has somewhat increased the complexity and uncertainty of the simulation process. Several other studies have utilized distance-decay rules to delineate the correlation between the intensity of neighborhood effects and distance factors (Zhao
et al.,
2011; Feng and Tong,
2018). However, these studies have often focused exclusively on individual land-use types, neglecting the complex interactions between different land uses that collectively contribute to the final distribution (Roodposhti
et al.,
2020). On the other hand, the distance-decay function can cover only limited variations in neighborhood effect changes. For example, the intensity of neighborhood effects may initially increase with distance followed by a subsequent decrease. Therefore, considering the complexity, subjectivity, and hard repeatability of the above solutions, indicators adhering to the “spatial neighborhood stationarity” hypothesis continue to be widely used. This usage limits the ability to investigate intricate neighborhood effects and hampers the effectiveness of CA models. Furthermore, the insufficient consideration of macroscale landscape dynamics, such as urban sprawl, in the formulation of transition rules neglects their impact on long-term land-use patterns.
Urban sprawl, defined as the expansion of urban areas into rural land, is driven mainly by population growth and large-scale migration (Song
et al.,
2024). Urban sprawl has enduring effects on the spatial pattern of LUCC, combined with subsequent impacts on temperature variation (Xiong and Zhang,
2021; Wang
et al.,
2022b), air pollution (Valencia
et al.,
2023; Wang
et al.,
2023), food risk (Abu Hatab
et al.,
2019), and more; moreover, urban sprawl threatens both urban and social sustainability. Thus, it is necessary to consider urban sprawl as a macroscale demand that shapes land-use patterns (Wang
et al.,
2022a). Earlier studies combined top-down models, such as Markov chains (Sang
et al.,
2011; Shafizadeh-Moghadam and Helbich,
2013; Halmy
et al.,
2015), system dynamics models (Luo
et al.
, 2010), and agent-based models (Filatova
et al.
, 2013; Filatova, 2015), to quantify macroscale demand as the number of cells for each land-use type at the end of the study period. Simultaneously, bottom-up CA models are combined to identify locations for land-use transitions. However, despite the macroscale demand directing the trajectory of microscale allocation in iterative modeling, the interactions and feedback loops between these two subcomponents have been overlooked (Liu
et al.,
2017; Xu
et al.,
2019). This oversight leads to a disparity between the evolution of land use in simulations and reality, thereby increasing uncertainty in long-term LUCC simulations. An exception to this trend is the S-CMM-CA model proposed by Wang, which uses the inverse S-shaped function to deduce the urban land demand within each concentric ring of the study area, guiding land-use transitions accordingly (Wang
et al.,
2019). Although this model altered the combination process between macroscale demand and microlevel allocation, the characterization of urban sprawl remains tethered to a static target rather than a dynamic trend with temporal dependence, posing a challenge in capturing its true spatiotemporal signatures. In summary, there is an urgent need to incorporate the concept of a time step into urban sprawl measurement. To combine the regularity of urban sprawl and neighborhood effects during the construction of CA models, adopting the classic Gaussian function becomes imperative. On the one hand, describing various fluctuating trends, which are described in Section 2.3.2, is efficient and intuitive. On the other hand, a comparative analysis conducted by Yang
et al. (
2022) on urban sprawl patterns in 27 representative Chinese cities revealed that the Gaussian function accurately depicts the trends of urban land sprawl within a specific period.
In addition, the inclusion of a calibration module is an essential prerequisite for model applications, as it enables the adjustment of parameters that govern the model’s behavior on the basis of an assessment of output accuracy (Brown
et al.,
2013; Blecic
et al.,
2015). This module has the ability to increase the accuracy of models in representing real-world conditions and to evaluate their performance. However, longstanding challenges for calibrating CA models have been identified owing to the spatiotemporal heterogeneity and path dependence of LUCC (Yu
et al.
, 2021). Nevertheless, the neighborhood effect is dynamic during LUCC simulation, adding complexity to the calibration process. As a result, previous studies for calibrating CA parameters have heavily relied on manual or expert knowledge (van Vliet
et al.,
2016); however, these studies potentially fall short in capturing the complexities of LUCC while also meeting the requirements for objectivity and reliability of simulation results (Jafarnezhad
et al.,
2016). More recently, researchers have increasingly shown interest in the self-calibration process (Newland
et al.,
2020; Roodposhti
et al.,
2020). To further maximize the performance of LUCC models on the basis of multiple accuracy assessment metrics, multiobjective optimization (MOO) algorithms, such as particle swarm optimization (Zhang and Wang,
2021) and the nondominated sorting genetic algorithm (Liu
et al.,
2022), have been considered accordingly. Through the MOO algorithm, parameters related to neighborhood effects and urban sprawl can be calibrated to improve the performance of the CA model.
In this paper, we present a self-calibrated convolutional neural network-based cellular automata (SC-CNN-CA) model to capture the macroscale urban sprawl and microscale neighborhood effects of LUCC. To formulate the transition rule of the CA, we incorporated a lightweight convolutional neural network (CNN) to estimate the growth probabilities of different land-use types. Additionally, the Gaussian function is employed to measure the spatiotemporal characteristics of both urban sprawl and neighborhood effects. Finally, the multiobjective optimization (MOO) algorithm is utilized to automatically adjust the Gaussian function and improve the simulation accuracy of the CA model in the calibration process. The efficacy of our proposed model is demonstrated through simulations of LUCC from 2005 to 2015, with a specific focus on a case study of Wuhan, China.
2 Data and methods
This section provides a concise overview of our framework, integrating the MOO algorithm into the CA model to explore the micro- and macrolevel characteristics of land-system behaviors. Within the CA model, we incorporate the neighborhood effect and sprawl trend to capture complex interactions among various land-use types. The MOO model is used to facilitate the calibration of these two components and improve the accuracy of simulation outputs from the CA model. The details of the model framework are shown in
Figure 1.
Figure 1 Framework for the SC-CNN-CA model with multiple dynamic land-use classes |
Full size|PPT slide
2.1 Study area
Wuhan (29°58′-31°22′N, 113°41′-115°05′E) is the capital of Hubei province in China and has a strategic position in the rise of central China (
Figure 2) because of its comprehensive geographical and talent advantages. The city has a total area of approximately 8569.15 km
2, with a water surface area of 2117.6 km
2, accounting for nearly 25% of the city. In addition to its ideal geographic location and environmental advantages, Wuhan had a total registered population of 9,341,016, but a resident population of 13,648,900, with a resident population density of 1593/km
2 in 2021. As a result, Wuhan plays a dominant role in the Yangtze River Economic Belt and the “1+8” city circle. Wuhan has undergone rapid urbanization in the last 10 years, as construction land has increased by 133.43% compared with that in 2020 (658.64 km2). There are 13 districts in Wuhan, 11 of which were selected for this study, including the seven central districts of Jianghan, Jiang’an, Qiaokou, Wuchang, Hongshan, Qingshan, and Hanyang, and the four distances of Jiangxia, Caidian, Hannan and East West Lake.
Figure 2 Location of the study area (Wuhan, Hubei province, central China) and the land-use pattern in 2005 (upper- right) |
Full size|PPT slide
2.2 Data sources
The data sources of this study are listed in
Table 1, including a historical land-use map and socioeconomic and physio-geographic drivers in Wuhan. The land-use data were collected via the 30 m annual China land-cover dataset (CLCD), which has an overall accuracy of approximately 79.31% (Yang and Huang,
2021). The model developed for Wuhan has six land-use classes, including agricultural land, forest land, grassland, water area, urban land, and unused land. The land expansion map was generated by extracting cells with changed states from the target land-use maps through overlay analysis of the initial and target land-use maps (Liang
et al.,
2021). Consequently, fourteen driving factors involving physio-geographic and socioeconomic features were chosen to evaluate the conversion probability of CA transition rules after thoroughly reviewing literature reviews and the urban development trajectory in Wuhan (Li
et al.,
2016; Wu
et al.,
2021). To represent socioeconomic influences, we primarily utilized the road network to calculate proximity effects and generated seven distance-based variables via Euclidean distance. As city centers were identified as central business districts (CBDs) in 1990 (Jiao,
2015; Yang
et al.,
2022), we divided the research region in Wuhan into 50 concentric rings (each 1 km wide) that ran from city centers outward to rural areas to analyze the macrotrend of urban sprawl (
Figure 3). Given the study’s aims and the model’s effectiveness, all the spatial data used in this study were resampled to a common resolution of 100 m via majority aggregation.
Table 1 List of data used in this study |
| Category | Data | Resolution | Year | Data source |
| Historical land use | Land-use data | 30 m | 2005-2015 | http://irsip.whu.edu.cn/resources/CLCD |
Physio-geographic
driver | Annual precipitation | 100 m | 1970-2000 | WorldClim v2.0
(http://www.worldclim.org/) |
| Annual mean temperature | | |
| DEM | 30 m | 2016 | SRTM1 (https://glovis.usgs.gov/app) |
| Slope | | |
| Dist_water | 30 m | 2005 | |
Socio-economic
driver | Dist_highway | 30 m | 2015 | https://lbsyun.baidu.com/ |
| Dist_railway | | | https://www.openstreetmap.org/ |
| Dist_arterial road |
| Dist_primary road |
| Dist_secondary road |
| Dist_teriary road |
| Dist_governments | 30 m | 2013 | https://lbsyun.baidu.com/ |
| Population | 1000 m | 2010 | http://www.geodoi.ac.cn/WebCn/Default.aspx |
| GDP | | |
Figure 3 City centers and concentric rings of Wuhan in 2005 and 2015 |
Full size|PPT slide
2.3 Land-use change simulation via the CA model
The CA model was developed to simulate the spatial pattern of LUCC under the given parameters of neighborhood effect and sprawl trend calibrated by the MOO model. The CA simulation consists of three steps: 1) use a convolutional neural network to train and estimate the growth probability of each land-use type, 2) employ multiobjective optimization to calibrate the parameters of the neighborhood effect and urban sprawl trend, and 3) utilize roulette selection to describe land-use competition and determine the final land-use allocation. During CA iterations, a specific land grid either retains the current land-use type or transforms into another depending on the combined probabilities of growth probability, neighborhood effect, and sprawl trend as well as the roulette selection.
2.3.1 Growth probability estimation via a convolutional neural network
Convolutional neural networks (CNNs) have been widely adopted to reveal the driving mechanisms of LUCC while considering various factors, such as slope, urbanization policy, and traffic networks. In general, CNNs comprise input layers, convolutional layers, pooling layers, fully connected layers, and output layers. The convolutional layer, which serves as a feature extractor, plays a pivotal role in processing the neighborhood characteristics of input data into outputs with high-level features (Rawat and Wang,
2017). Given the CNN’s ability to account for the dynamics of drivers and neighborhood effects over time (Pan
et al.,
2021;
2022), it has been successfully applied in diverse nonlinear geographical tasks, including knowledge discovery, feature classification, and spatial pattern modeling (Qian
et al.,
2020; Chen
et al.,
2021; Wu
et al.,
2023). To calculate the growth probability of different land-use types, this study employed a lightweight CNN adapted from LeNet-5, which is known for its simplicity and computational efficiency, enabling faster training and inference times (Lecun
et al.,
1998). Two small convolutional kernels 3×3 were used instead of LeNet’s 5×5 convolutional kernels to construct the network. This mini-network has the same detection area as 5×5 convolutions do, reducing the geometric size and making training less computationally demanding. Additionally, it prevents overfitting issues while extracting more nonlinear features. The architecture of the CNN proposed in this study is illustrated in
Figure 4.
Figure 4 Illustration of the architecture of the CNN |
Full size|PPT slide
The CNN model was built from a series of shared layers (
Figure 4): one input layer, five convolutional layers, and two maximum pooling layers followed by three fully connected layers and one output layer. The input layer, which includes the driving factors (N=14) and the initial land-use map, within the neighborhood of each sample cell was constructed with a 21×21 sampling window. Then, a convolution operation with a filter size of 24×3×3 was applied to the input, resulting in an equal-sized feature map of 24×21×21 with edge padding. The second layer was defined by the same convolutional size (3×3) and forty-eight filters to obtain a feature map of size 48×19×19. The max pooling layer with a 2×2 kernel was then used, resulting in the 48×9×9 output image. The fourth and fifth layers were similar to the first two convolutional layers with a 3×3 kernel to explore additional nonlinear factors influencing land-use evolution, whereas the 96×7×7 and 128×5×5 feature maps were output. Then, the maximum value within the 2×2 kernel neighborhood was extracted, reshaping the input into 128×2×2. To further enhance the network’s ability to extract nonlinear features, the seventh layer consisted of two hundred and fifty-six 1×1 convolution kernels followed by a scaled exponential linear unit (SELU) as the nonlinear activation function (Klambauer
et al.,
2017), resulting in an output of 256×2×2. Finally, the input became 6×1 feature vectors via three fully connected layers followed by softmax regression. Each vector in the output layer indicates the growth probability for each land-use type at the corresponding cell.
The driving factor dataset, initial land-use map, and land expansion map were input into the CNN model for training. After several training and feedback cycles, an optimal CNN model was chosen, which can efficiently extract the complicated neighborhood-scope properties of the driving factors and calculate the growth probability for each land-use type.
2.3.2 Neighborhood effect
The neighborhood effect was employed to estimate the probability that a grid cell will either retain its original land-use type or convert to a potential target type, influenced by the spatial distribution of land use in the surrounding neighborhood. Typically, the neighborhood effect is defined as follows:
where denotes the neighborhood transition potential for the status of cell i converted to k as the future state, which reflects the force of attraction between initial and target land-use types in V(i), which contains a set of cells surrounding the center cell i; K(i°,t) returns the present cell state for i°; D(i,i°) is the Euclidean distance between i and i°; and indicates the conversion probability of k with the influence of i°. According to the formula, the computational complexity of Ni,k is influenced by the neighborhood size and the number of land-use types. To explain the computational cost specifically, we made a few simplifying assumptions that apply to this study. If the neighborhood radius is 5 and there are 6 land-use categories, there will be 36 potential land conversions within the neighborhood distance of 1 to 5. Consequently, the modeling process required the consideration of a total of 108 (6×6×5) parameters, significantly increasing complexity. Therefore, a more efficient calculation was needed.
This study employed the Gaussian function to quantify the neighborhood effect to simplify the parameterization process, which is initially defined as:
where y(x) represents the effect exerted by the target cell on the center at a distance of x; a, b and c are both Gaussian function control variables; when 0<x≤xc, there is an attraction between the central and target cells, showing distance-dependent neighborhood interactions through a Gaussian function; and when x>xc, the effect on the central cell by cells beyond neighborhood range xc equals zero.
To enhance the comprehensive description of micro land-use interactions, we divided the neighborhood effect into two components, the inertial point and the conversion curve, utilizing the Gaussian function mentioned above. As shown in
Figure 5, the red dot on the conversion curve illustrates the conversion probabilities of the central cell (from type 1 to type 2), influenced by a neighboring cell located 2 units away. The inertial point is fundamentally distinct from the conversion curve; it is disconnected. Depicted as a hollow dot in
Figure 5, the inertial point illustrates the inherent characteristics of land-use types and indicates how effectively cells maintain their original land-use categories (persisting as type 1). This parameter is defined exclusively by specific land-use categories; thus, the number of inertial points corresponds to the number of land-use types in the modeling process. This configuration mitigates challenges associated with land-use conversions by constraining the overexpansion of dominant land-use types. Accordingly, the final neighborhood effect is defined as follows:
where denotes the neighborhood transition potential for the target land-use type k, which can also be expressed as K(i,t+1); K(i,t) returns the present cell state of cell ; and K(i,t) = K(i,t+1) denotes that cell i contains the initial land-use type or the land-use type of cell i. d is the inertial probability of cell i; the opposite describes the land-use conversion. a, b and c shape a Gaussian function to describe attractions related to the initial land-use type K(i,t) and target type, and d(i,i°) is the distance between i° and the nearest cell with the initial type K(i,t). Using the Gaussian function described above, various types of land conversions in the neighborhood can be represented by a set of parameters (a, b, c and d). This reduction in the total number of parameters for describing neighborhood effects from 180 (6×6×5) to 96 becomes more advantageous as neighborhood sizes and the number of land-use classes increase. It enriches the application scenarios across various spatial scales and multiple land-use types.
Figure 5 Parameterization of the neighborhood effect via the Gaussian function. The values on the x-axis indicate the distance to a land-use change location (the central cell), whereas the values on the y-axis represent the force between the central cell and its surrounding cells |
Full size|PPT slide
2.3.3 Urban sprawl trend
To capture the macroprocesses of LUCC, we incorporated the urban sprawl trend into the CA model, which also uses the Gaussian function. The urban sprawl trend encapsulates land urbanization, reflecting the trend in the expansion of new urban land and its evolving pattern over time. The sprawl trend is defined as follows:
where is the urban sprawl probability of a cell i within concentric ring r and denotes the radius of a concentric circle from the city center. For a given urban sprawl process, a, b and c shape the Gaussian function (i.e., amplitude, mean, and standard deviation): a indicates the height of the crest; b shows the peak of the crest, which describes the hotspots of urban sprawl; c denotes the width of the function curve, which approximates the spatial compactness of the urban sprawl; and d • t describes the variation in the Gaussian function along the horizontal axis under the assumption that the macroscopic probability of urban sprawl moves uniformly toward the urban periphery over time. By parameterizing the urban sprawl trend via the Gaussian function, we can explain the generation of urban patterns in distant areas and the urban voids in the central areas. The urban sprawl trend also characterized the dynamics and complexity of LUCC, offering opportunities for setting flexible transition rules and more precision in simulating and predicting urban development.
2.3.4 Roulette selection
By considering the growth probability, neighborhood effect, and urban sprawl trend, the overall probability can be expressed as follows:
where describes the growth probability of k (future cell state of cell i), which is obtained via the LeNet-based network in this study; and are obtained via the self-calibration module; denotes the neighborhood effect of land-use type k; and denotes the probability of urban sprawl, which effectively eliminates the overconcentration of urban land in the center area and thus improves the ability to simulate the macro-urban sprawl pattern. Specifically, the iterative operation of the CA model is the calculation process of . A preliminary land-use transition probability is obtained via network and parameter correction before adding random perturbations, which is defined as:
After the above factors are considered and each cell’s combined probability is calculated, roulette selection is utilized to determine the final land-use type of cell i. This method depicts land-use competition, as it allows for the spread of the disadvantaged land-use type with the lowest total probability. After the iteration, the winning land-use type is allocated. The CA iteration ends if the land-use types reach their quantitative demand in the target year, and if not, the next iteration is performed.
2.4 Land-use change calibration via multiobjective optimization
To implement an auto calibration module, the MOO method was utilized to identify several potential CA parameter sets that reveal the best possible trade-off between the calibration objectives, illustrated in
Figure 1 by the curved blue line. The nondominated sorting genetic algorithm III (NSGA-III), a population-based MOO algorithm proposed by Deb and Jain (
2014), was adopted on the basis of its ability to train and correct CA model parameters. This algorithm contains a fast nondominated sorting technique, an implicit elitist selection mechanism based on Pareto dominance rank, and a secondary selection method based on target distance, greatly enhancing its performance on challenging multiobjective problems. For the calibration objectives, the locational agreement between the actual and simulated land-use maps via CA was measured via the figure of merit (FOM) (Pontius
et al.,
2007) and overall accuracy (OA). The FOM index can be expressed as follows:
where
B represents the total number of pixels that represent the hit (i.e., the observed change in LUCC consistent with the model predicted as change);
A represents the total number of pixels that are inconsistent with the prediction of persistence;
C represents the total number of pixels that are inconsistent with the prediction of an incorrect land-use type; and
D represents the total number of pixels that are inconsistent with the prediction of a change. Both the OA and FOM range from 0 to 1, where a higher FOM demonstrates a higher simulation accuracy within changed areas (most of the values are lower than 0.3) (Pontius
et al.,
2008b).
3 Results
3.1 Implementation
NSGA-III retained an exceptional population of individuals on the basis of reference points of idealized simulation output, resulting in a high-performance LUCC model with superior simulation accuracy. This study applied the
Moore neighborhood configuration considering the time consumption of the modeling process. On the basis of an analysis of historical land-use data in the study area and insights from regional experts, we specifically selected primary land-use transitions when calculating neighborhood effects for faster convergence. Thus, the overall number of calibration parameters decreased from 360 (6×6×10) to 40 (10×3+6+4) as a consequence (
Table 2). Since the final land-use allocation depends on the relative magnitude of the conversion probability rather than its absolute value, the threshold for all decision factors, including conversion curves (num = 30) and inertial points (num = 6) of the neighborhood effect, was set between 0 and 10. The thresholds of
a,
b,
c and
d for shaping the Gaussian function (num = 4) to modify the urban sprawl trend were set to (0–1), (10–20), (5–10), and (0.001–5) considering the actual spatial processes of urban expansion in Wuhan (Yang
et al.,
2022). To ensure the discovery of nondominated solutions for large problems, where the population size must exceed the number of decision variables (num=40), we configured the population size and maximum number of evolutionary generations for NSGA-III to 100 and 200, respectively. Given that the NSGA-III objectives no longer improve significantly after approximately 150 iterations, we considered 200 iterations a reasonable maximum limit. In addition, the crossover and variance probabilities were 0.9 and 0.009, respectively, as recommended by Wang
et al. (
2015) to prevent excessive exploration of the optimization algorithm and to avoid becoming trapped in local optima. The proposed SC-CNN-CA model was coded in Python and implemented via libraries such as keras, geatpy, cupy, rasterio, and multiprocessing. Vectorization computing technology, as introduced by Xia
et al. (
2018), was employed, which converts scalar operations of CA into vector operations (
Figure 6). This approach is especially effective for reducing computational costs, as the auto calibration module is time-consuming.
Table 2 Main neighborhood effects in Wuhan |
| Land-use type | Agricultural land | Forest land | Grassland | Water area | Urban land | Unused land |
| Agricultural land | 1 | 1 | 0 | 1 | 1 | 0 |
| Forest land | 1 | 1 | 0 | 0 | 1 | 0 |
| Grassland | 0 | 0 | 1 | 0 | 1 | 0 |
| Water area | 1 | 0 | 0 | 1 | 1 | 0 |
| Urban land | 0 | 0 | 0 | 1 | 1 | 0 |
| Unused land | 0 | 0 | 0 | 1 | 0 | 1 |
Figure 6 Vectorization process of the SC-CNN-CA model |
Full size|PPT slide
3.2 Validation of CNN performance
The effectiveness of the LeNet-based network was assessed on the basis of the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) (Elith
et al.,
2011; Mas
et al.,
2013). The true positive rate and the false-positive coordinate generated the ROC curves. Consequently, intermediate states in the classification results were created, leading to multiple classifications. While the ROC curve has a broader scope of application, it cannot quantify the effectiveness of categorization; therefore, an AUC was needed. Generally, a completely random model has an AUC value of 0.5, whereas the AUC value of the perfect model is 1.0.
Figure 7 shows the ROC curves of the six land-use types in orange and the random guess curves in black. Although the limited sample size resulted in nonsmooth ROC curves for grassland and unused land, all the AUC values surpassed 0.85. In particular, the AUC values of agricultural land, forest land, water area, and urban land were all above 0.9, approaching 1.0. These results indicate that the proposed network achieved satisfactory performance in capturing the driving mechanism of LUCC via the gathered drivers.
Figure 7 ROC curves and AUC values of individual land-use types fitted by the LeNet-based network |
Full size|PPT slide
3.3 Calibration of CA parameters
The NSGA-III-based calibration model employs 200 population optimizations, yielding approximately 20,000 optimal solutions during the calibration process (
Figure 8). Each solution corresponds to a group of parameters and is colored to identify the number of population optimization rounds to which it belongs. The last population optimization is given a dark blue color, which constitutes the final Pareto front. As shown in
Figure 8, the range of OA was 0.790 to 0.847, whereas the FOM values ranged between 0.173 and 0.222. At the Pareto front, the overall accuracy (OA) and figure-of-merit (FOM) values exhibit a negative correlation, possibly attributable to the large study area in relation to the relatively small proportion of actual LUCC. As a result, the capacity of NSGA-III to acquire high OA values through optimization is weak.
Figure 8 Pareto front of NSGA-III after self-calibration |
Full size|PPT slide
Finally, we obtained three types of parameters through the peak of the Pareto front: (1) the inertial points of the neighborhood effect for each land-use type; (2) the conversion curves of the neighborhood effect for land-use transitions; and (3) the conversion curve of the urban sprawl trend.
3.3.1 Inertia points of neighborhood effects
Figure 9 shows the violin plot of the values of inertial points (the
d value in Eq. 3), which are colored and sorted by land-use type and parameter distribution characteristics. According to
Figure 9, the values of the inertial points varied considerably between categories. The largest values of inertial points were found for agricultural land and water areas, with median values of 8.94 and 8.67, respectively. This result indicates that agricultural land and water area were most likely to maintain their original land-use types during the study period. Effective local ecological protection policies prevent agricultural land and water area from transitioning, thus protecting them against urbanization. The inertial points for urban land were relatively small and were more concentrated than the other points were, with a median value of 2.91. This finding indicates that urban areas, while less resistant to land-use change than agricultural land and water area, still demonstrate a degree of stability. This stability is reinforced by the identification of primary urban conversion types detailed in
Table 2, suggesting that urban land does not necessitate excessively high inertial values to prevent undesirable conversions. Conversely, unused land has the lowest inertial points among all categories, with a median value of only 1.28. This low inertia underscores the heightened susceptibility of unused land to conversion into other land-use types. However, it is important to note that the calibration of inertial points for grassland and unused land may not fully reflect real-world dynamics because of the limited number of grid cells available for these categories.
Figure 9 Violin plot of inertial points for each land-use type |
Full size|PPT slide
3.3.2 Conversion curves of neighborhood effects
By adopting Gaussian-based conversion curves in this study, the analysis of micro land-use interactions achieved a higher level of clarity than previous approaches. Unlike earlier CA models that relied on enrichment factors and distance-decay rules, as well as the calibration of numerous parameters, our approach can better capture the spatial heterogeneity and temporal dependencies of LUCC. For example, a previous CA model based on distance-decay rules calibrated 136 parameters to identify the neighborhood effect (Newland
et al.,
2020). However, this approach may have inadvertently overlooked other significant trends in land-use interactions. In contrast, the Gaussian-based approach used here offers the ability to capture a broader range of trends in neighborhood effects, as demonstrated in
Figure 10.
Figure 10 Different neighborhood effects ordered by land-use conversion types: (a) the conversion parameters between agricultural land and forest land; (b) the conversion parameters between agricultural land and water area; (c) the conversion parameters between agricultural land and urban land; (d) the conversion parameters between grassland and urban land; (e) the conversion parameters between water area and agricultural land; (f) the conversion parameters between water area and urban land; (g) the conversion parameters between urban and water; and (h) the conversion parameters between unused land and water area |
Full size|PPT slide
Specifically, all the conversion curves of neighborhood effects (8 in total) were divided into three categories: continuous increase, continuous decrease, increase, and then decrease. The subsequent analysis did not consider transfers from forests to agricultural and urban land, considering limited neighborhood effects. The “continuous increase,” the main characteristic of the neighborhood effect, indicates that initial land has the largest conversion probability to the target land at the far end of the neighborhood. The conversion curves of “agricultural land-forest land” and “grassland-urban land” reached peaks of 5.185 and 7.043, respectively, when the distance between the cells was 500 m (Figures 10a and 10d). Compared with these relationships, the other three relationships were less powerful, with fewer than 4 peaks. The conversion probability from water to urban land increased slowly when the distance was less than 300 m, then rose rapidly and reached a peak of 3.366 (
Figure 10f). The curve of “unused land-water area” initially had the highest attraction from the water area, decreasing slowly with distance (
Figure 10h). Furthermore, the neighborhood effects of “agricultural land-water area” and “agricultural land-urban land” increased and then decreased (Figures 10b and 10c). At a distance of 300 m, the conversion probability from agricultural land to water reached a maximum of 8.960. At distances less than 300 m or greater than 300 m, this attraction soon decreased nearly to zero. There was a tremendous attraction between urban land and agriculture. Initially, the conversion probability was relatively high and slowly reached a peak of 8.322 at a distance of 200 m. As the distance from urban areas continuously increased, this attraction gradually decreased to 6.967.
3.3.3 Urban sprawl trend
By incorporating the time variable into the Gaussian function, our model can capture the temporal dependency of urban sprawl within the study area. This adjustment allows for a more precise representation of how urban growth evolves over time, thereby improving the accuracy and realism of our simulation results. According to
Figure 11,
b in the Gaussian function reflects the hotspot areas of urban sprawl, with a value of 18.20. The values of
a and
c, which determine the macroscopic sprawl probability of urban land, were 0.015 and 6.24, respectively. Using Gaussian function curves, one can approximate the spatial compactness of new urban developments. Applying urban zoning theory (Yang
et al.,
2022), Wuhan was separated into four circular zones on the basis of the distance to urban centers: the urban core, inner urban area, suburban area, and urban fringe. As shown in
Figure 11, the urban core in this study encompassed concentric rings with distances of fewer than 11.96 km (
b-
c). It was the most densely distributed urban area with finite expandable space; therefore, the probability of macro-expansion was low, at less than 0.009. The inner and suburban areas were within a distance from 11.96 km to 24.44 km (
b-
c→
b+c). In particular, the probability of urban sprawl increased rapidly with distance in the inner city and reached a maximum of 0.015 at 18.20 km. The expansion of suburbs occurred mainly at the intersection of urban and suburban areas, and the probability soon decreased as the distance from the urban centers increased. The sprawl probability of urban development at the urban fringe had a similar variation to that of the suburbs. When the distance exceeded 30.68 km (
b+2·
c), the probability of decline decreased until it tended to zero at the end. Since
d, which describes the variation in the Gaussian function along the horizontal axis, was only 0.0102, the urban development hot zones exhibited a limited outward migration trend. This may have been caused by the fact that most of the potential urban land had already been allocated by early iterations of the CA model.
Figure 11 Urban sprawl trend based on the Gaussian function |
Full size|PPT slide
4 Discussion
4.1 Improving the accuracy through self-calibration
To highlight the strengths of the SC-CNN-CA model, we conducted a comparative analysis with the CNN-CA model and a patch-generating land-use simulation (PLUS) model (Liang
et al.,
2021) as references. The CNN-CA model employs the enrichment factor to identify neighborhood effects and considers only land-use demands at the end of the study period for model evolution. The PLUS model uses land spreading mechanisms and patch-generation strategies to describe the generation of distant urban patches effectively and has seen widespread usage in ecosystem service studies (Shi
et al.,
2021) and carbon sequestration projections (Wang
et al.,
2022) with diverse land-use scenarios. The study examined the impact of Gaussian-based descriptions of neighborhood effects and urban sprawl on the simulation results, demonstrating the effectiveness of the SC-CNN-CA model. The confusion matrix was also intended to quantitatively assess the simulation results of our proposed model (
Table 3). We found that simulation errors were observed in the conversion process between agricultural land and forest land. This was partly due to the extensive presence of agriculture in the study area, where its natural geographical distribution overlaps with that of forests, resulting in the model converting a significant portion of forest land into agricultural areas. Conversely, the sparse distribution of forest land in the southeastern part of Wuhan makes it challenging to capture using neighborhood effects. Nonetheless, we maintain that the model remains effective. According to local protection policies, designating forest land as a restricted area can mitigate these land conversion errors in future simulations.
Table 3 Confusion matrix of the simulation results of the SC-CNN-CA model versus the actual pattern in 2015 |
| Land-use type | Agricultural land | Fore st land | Grassland | Water area | Urban land | Unused land | Total |
| Agricultural land | 49761 | 1366 | 9 | 2679 | 3152 | 2 | 56969 |
| Forest land | 1280 | 2208 | 1 | 14 | 26 | 0 | 3529 |
| Grassland | 3 | 4 | 0 | 1 | 1 | 10 | 16 |
| Water area | 3030 | 4 | 0 | 15117 | 200 | 1 | 18352 |
| Urban land | 2911 | 1 | 3 | 399 | 12846 | 0 | 16160 |
| Unused land | 0 | 0 | 0 | 2 | 0 | 0 | 2 |
| Total | 56986 | 3579 | 14 | 18212 | 16234 | 3 | 95028 |
Table 4 shows an overview of model performance on the basis of the OA, FOM, and producer accuracy (PA) (Pontius
et al.,
2008b) derived from the confusion matrix. Among the three models evaluated, the SC-CNN-CA model yielded the best simulation results among all three models tested. Specifically, its OA and FOM were 84.12% and 20.20%, respectively, which were notably higher than those of the CNN-CA (OA = 79.91%, FOM = 16.72%) and PLUS model (OA = 83.59%, FOM = 14.54%). Among the three models in the experiments, the SC-CNN-CA model performed better for agricultural land, water, and urban land, with PAs improved by 0.71%, 1.57%, and 2.24%, respectively, compared with those of the PLUS model. Furthermore, the SC-CNN-CA model had a significant advantage in simulating urban sprawl (PA = 79.13%), indicating that the SC-CNN-CA model can effectively extract urban evolution. While our model’s simulation accuracy for water areas was slightly lower than that of the PLUS model, the PA decreased by 2.18%. This issue can be addressed by restricting the transition from water to other land-use types.
Table 4 The overall accuracy (OA), figure of merit (FOM), and producer accuracy (PA) in 2015 of six classifiers with simulation results of the SC-CNN-CA model and PLUS model |
Accuracy
assessment
indexes | OA | FOM | PA |
| Agricultural land | Forest land | Grassland | Water area | Urban land | Unused land |
SC-CNN-CA
CNN-CA | 84.12%
79.91% | 20.20%
16.72% | 87.32%
84.07% | 61.69%
51.35% | 7.14%
2.08% | 83.01%
76.96% | 79.13%
75.14% | 0.00%
0.00% |
| PLUS | 83.59% | 14.54% | 86.61% | 60.12% | 13.04% | 84.86% | 76.89% | 0.00% |
Furthermore,
Figure 12 compares the actual maps in 2015 with the simulated outputs of the three models in 2015. Additionally, three regional zooms provide details about incorrect patches among these models. Both the CNN-CA and SC-CNN-CA models exhibited a high degree of consistency between the simulated and actual results in 2015, particularly along the urban periphery (
Figure 12, A2, B2, A4, B4). The experimental results demonstrate the effectiveness of CNN in exploring the driving mechanisms of urban development. However, compared with the SC-CNN-CA model, the CNN-CA model resulted in more evenly distributed simulation errors across urban areas (
Figure 12, A2_Erro, B2_Erro). This difference arose because the use of the enrichment factor in the CNN-CA model enforced the spatial homogeneity of the simulation results, whereas Gaussian-based descriptions of the neighborhood effect and urban sprawl in the SC-CNN-CA model enabled the extraction of the spatial heterogeneity of landscape dynamics, resulting in higher accuracy. Furthermore, the urban sprawl boundaries simulated by the proposed SC-CNN-CA model closely approximated the actual situation, with urban growth dominated by infilling growth and fringe growth (Sun
et al.,
2013; Huang
et al.,
2022). In contrast, simulation errors of the PLUS were scattered far from the urban core (
Figure 12, A3_Erro, B3_Erro), with the urban transformation pattern being mainly fringe and outlying, contrary to reality. This finding indicates that our model better captures the macroprocess of urban sprawl considering its temporal dependency. Although the spatial distributions of forest land simulated by all three models differed significantly from reality (
Figure 12, C2_Erro, C3_Erro, C4_Erro), the SC-CNN-CA model still performed well, as newly added forest land did not exhibit excessive clustering.
Figure 12 Comparison of the simulated land-use maps via the CNN-CA, PLUS, and SC-CNN-CA models. Panels A1, B1, and C1 show the observed land-use patches of a subregion. The A2, B2, C2, A3, B3, C3, A4, B4, and C4 panels show the simulated land-use patches. A2_Erro, B2_Erro, C2_ Erro, A3_Erro, B3_Erro, C3_ Erro, A4_Erro, B4_Erro, and C4_ Erro show incorrect patches compared with the actual map |
Full size|PPT slide
4.2 Broader policy implications
In the realm of sustainable urban management and planning, the advancing coordinated development of the Wuhan metropolitan area will increase the undertaking of economic development functions. This poses new challenges for sustainable land use. Given the significant impact of government policies on urban development, our findings about the potential macro- and microspatial characteristics of LUCC may inform sustainable land-system design. Specifically, our study results highlight that agricultural land and water area transformations are constrained and less prone to conversion. This suggests that regional policies positively affect the protection of agricultural and water areas. However, forests and grasses are more vulnerable than agricultural land and water areas are, as shown by the lower inertial points. Urban planners and policy-makers should be cautious in protecting and managing urban green space, as the spatial distribution of forest and grass is closely related to various socioeconomic and environmental phenomena, including urban heat islands (Zhang
et al.,
2017), carbon emissions (Zhou
et al.,
2021), and mental health (Ha
et al.,
2022).
Furthermore, a potential application of the SC-CNN-CA model is the spatial optimization and prediction of land use based on scenarios designed in a more micro way. Optimizing urban patterns for cropland protection involves meticulous adjustments to the inertial points and conversion curves of the neighborhood effect. A higher value of the inertial point for agricultural land increases the possibility of maintenance. Afterward, to prevent transitions from agricultural to urban land, the amplitude of the Gaussian-based conversion curve should be designed to have a lower value. Additionally, the MOO module offers a platform for exploring trade-off scenarios among different ecosystem services. Researchers can incorporate diverse indicator systems into MOO’s calibration objectives to investigate optimal spatial land-use distributions combined with CA models. Consequently, this approach expands the horizons for scenario-based studies on future sustainable land use.
4.3 Limitations
Although the SC-CNN-CA model has high-accuracy results in the spatial allocation of LUCC in Wuhan, the estimation of the amount of LUCC is also important (Seto
et al.,
2011; Hou
et al.,
2023). While the model currently focuses on simulating land-use changes in specific regions, extending its application to simulate land use in other regions is crucial to fully demonstrate its spatial transferability and generalization capabilities. In a future study, we will couple future LUCC scenarios supporting land resource allocation and urban management. Moreover, there is still much to be done to increase the conversion of agricultural land to forest land. The forested land in Wuhan had a homogeneous rather than aggregated spatial configuration during the study period, which was difficult to simulate by neighborhood effects. Accordingly, in subsequent studies, the stochastic mechanisms of the model should be improved so that it can also be applied to uniformly dispersed land expansion patterns. In addition, increasing the midterm calibration may result in a more natural land evolutionary process and make the model more suitable for future land-use predictions in long time series. In conclusion, the model proposed in this study needs to be further optimized for different regions or applications by adding midterm correction and optimizing stochastic mechanisms, making the model more reliable for a wider range of applications.
5 Conclusion
This study presented the novel SC-CNN-CA model, which aims to capture both macroscale urban sprawl and microscale neighborhood effects in the dynamics of LUCC. A CNN with small convolutional kernels was employed to capture the driving mechanisms of LUCC, incorporating multiple socioeconomic and physio-geographical factors. An SC process incorporating the MOO algorithm into the CA model was employed to calibrate the neighborhood effect and urban sprawl trend via a Gaussian function. Four major findings were found: (1) Agricultural land and water area transformations were constrained and less likely to be converted between them than others (such as grassland and forest land). (2) Neighborhood effects of land-use conversions were divided into three categories: continuous increase, continuous decrease, and increase, then decrease. Among them, the neighborhood effect of “agricultural land-urban land” tended to “increase then decrease.” Specifically, agricultural land had the highest conversion probability at 200 m from urban land. (3) The early urban sprawl in Wuhan occurred mainly in the core and inner urban areas, while the expansion pattern was mostly infill and edge-like. The hot zones of urban sprawl subsequently moved to the urban periphery, and the new urban patterns were located mainly in inner and suburban areas, followed by edge expansion and outlying patterns of expansion. Our results revealed that the proposed SC-CNN-CA model obtained the highest simulation accuracy and generated a more realistic land-use pattern. The proposed model will serve as an empirical case for high-precision land-use simulation models to analyze historical trajectories and predict future LUCC.
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
PDF(6575 KB)
({{custom_author.role_en}}), {{javascript:window.custom_author_en_index++;}}
Figure 1 Framework for the SC-CNN-CA model with multiple dynamic land-use classes
Table 1 List of data used in this study
