Analyzing the relationship between three-dimensional architectural landscapes and urban carbon emissions using machine learning approaches

2.1 Study area

Qingdao located in the southern part of Shandong province, China, and covers an area of 11293 km². The city has undergone rapid urbanization and includes seven municipal districts (Shinan, Shibei, Licang, Laoshan, West Coast, Chengyang, and Jimo) and three county-level cities (Jiaozhou, Pingdu, and Laixi). Plains and basins make up approximately 59.4% of the city. In comparison, mountains comprise 17.6% of the area, mainly in the southeast and northern regions (Fig. 1). From 2010 to 2020, construction land increased by 56.6 km², while energy consumption per unit of GDP and carbon emissions decreased by 21.5% and 27%, respectively. Therefore, investigating the relationship between architectural landscapes and carbon emissions is essential for promoting low-carbon cities and guiding the design of energy-efficient buildings. However, rapid urban growth has driven up energy consumption and carbon emissions annually, the architectural landscape significantly influences urban carbon emissions. Therefore, investigating the relationship between architectural landscapes and urban carbon emissions is essential for promoting low-carbon cities.

Close

Fig. 1.

Study area and buildings’ three-dimensional information.

Export to PPT

2.2 Data and processing

The buildings’ 3D information (height and contour) was extracted from high-resolution satellite images of Qingdao in 2020 using Barista software (Fig. 1). The Open-Data Inventory for Anthropogenic Carbon dioxide (ODIAC) data (Fig. 2) was obtained from the Center for Global Environmental Research (CGER) at https://db.cger.nies.go.jp/dataset/ODIAC/. This dataset provides monthly carbon emission estimates at a spatial resolution of 1km × 1km (Oda et al., 2018), making it highly reliable for scientific purposes, and widely used for analyzing urban carbon emission assessments and carbon flux inversion (Dissanayake et al., 2018).

Close

Fig. 2.

Carbon emissions and fishnet in Qingdao City.

Export to PPT

The size of rectangular grids was optimized through iterative testing to balance spatial resolution with data completeness. A coarse grid size resulted in a loss of important spatial detail, while overly small grids may lead to a high proportion of empty building grids, particularly in rural areas. So, a grid of size 5km × 5km was selected, yielding 424 spatial units across Qingdao City (Fig. 2). Various architectural landscape indices, as well as carbon emissions, were calculated for each grid using Fragstats and ArcGIS software. Finally, the relationships between architectural landscapes and carbon emissions were analyzed, and a regression model was developed at the grid scale utilizing RF, SVR, and PSO algorithm.

2.3. Methods

2.3.2 Random forest

Random forest (RF), developed by (Breiman, 2001) as an improvement over the classification and regression tree algorithm, has been further developed and analyzed in subsequent studies (Scornet et al., 2015; Biau and Scornet, 2016). RF enhances prediction accuracy and effectively manages complex relationships within data due to its strong classification capabilities (Zheng and Zhang, 2023). RF is an ensemble algorithm that constructs multiple decision trees using bootstrap aggregating of the training dataset and combines their outputs. During training, bootstrap re-sampling randomly selects k samples to build k decision trees, each grown without pruning. Each tree is trained on a random vector that is independently and identically distributed. The final prediction is obtained by averaging or majority voting (Fig. 3). RF is particularly effective in handling nonlinear relationship between input and output variables, making it suitable for regression tasks with strong generalization ability and feature importance evaluation. In this study, RF was implemented in Python to explore the contribution of architectural landscapes to carbon emissions.

Close

Fig. 3.

Workflow of RF.

Export to PPT

2.3.3 Support vector regression

Support vector regression (SVR) is a machine learning algorithm based on statistical learning theory, proposed by Vapnik. SVR has proven highly capable of capturing nonlinear data patterns and effectively addresses challenges posed by small sample sizes, multifactor scenarios, high dimensionality, and nonlinear regression. It is resistant to overfitting and high predictive accuracy and stability, and widely used in energy prediction, where kernel functions are critical for modeling nonlinear relationships in high-dimensional feature spaces. The linear, Gaussian, and polynomial kernels are commonly applied in nonlinear regression, the Gaussian kernel’s free parameter allows SVR to approximate a broader range of nonlinear responses than the polynomial kernel (Roy and Chakraborty, 2023). The SVR model’s vector field structure is shown in Fig. 4 (Zhong et al., 2019). So, this study built a regression model of the key factors and carbon emissions using support vector regression in Python. SVR hyperparameters, such as penalty coefficient, degree of the polynomial kernel function, and kernel function parameters are crucial to defining support vectors in the regression model.

Close

Fig. 4.

Structure of the vector field-based SVR (Zhong et al., 2019).

Export to PPT

2.3.4 Particle swarm optimization algorithm

The Particle swarm optimization (PSO) algorithm is an intelligent optimization method inspired by birds’ foraging behavior. PSO randomly initializes a population of particles that iteratively seeks individual and global optima to update their position and locate the optimal solution (Eberhart and Kennedy, 1995). In each iteration, each particle’s objective function is evaluated, recording the optimal solution (Pbest) and the optimal solution (Gbest) of the current population. The particle’s velocity and position are then updated based on these two optima, with the fitness calculated for each particle to determine the individual and global optimal values (Zeng et al., 2023). PSO effectively identifies optimal parameter combinations in high-dimensional spaces without being constrained by local optima. By balancing computational efficiency, global search capability, and implementation simplicity, POS is well-suited for optimizing SVR models in capturing the complex relationship between architectural landscapes and carbon emissions.

This study identified the key factors of architectural landscapes on carbon emissions using RF, then built a regression model of the key factors and carbon emissions using Support Vector Regression, and optimized the SVR model using Particle Swarm Optimization in Python. During these processes, we applied standardized normalization and outlier detection procedures for the dataset prior to model training. And a 10-fold cross-validation strategy and incorporated a grid-search mechanism for hyperparameter optimization were implemented to enhance the model’s generalization capability and prevent overfitting. The model framework is shown in Fig. 5.

Close

Fig. 5.

Model framework for architectural landscape indices and urban carbon emissions.

Export to PPT

To evaluate the accuracy of the SVR and POS-SVR regression model, the coefficient of determination (R²), mean absolute error (MAE) (Eq. 1), and mean relative error (MRE) (Equation 2) were used. A higher R², lower MAE, and MRE indicate a better fit and greater prediction accuracy.

(1)

$MAE=\frac{1}{n}\sum _{i=1}^n\left|{\hat{y}}_i-y_i\right|$

(2)

$MRE=\frac{1}{n}\sum _{i=1}^n\left|\frac{{\hat{y}}_i-y_i}{y_i}\right|$

where n is the sample size; y_i and ${\hat{y}}_{\text{i}}$are the actual and predicted carbon emissions for the i-th grid, respectively.

2.4 Indices

In this study, 10 2D and 5 3D architectural landscape indicators were selected (Table 1) to examine their relationship with urban carbon emissions. These indicators represent aspects of building number, area, shape, connectivity, aggregation, and diversity. The values of these indices were calculated within a 5km × 5km grid using Fragstats 4.2 (Liu et al., 2017) and ArcGIS.

Where B is the total number of buildings; H_i, V_i and A_i denote the height (m), volume (m³), and footprint area (m²) of the i-th building, respectively; A is the area of the grid cell (m²); F_i is the number of floors in the i-th building; P_i is the perimeter of the i-th building (m); β is the slope of the regression line obtained from a log-transformed regression of building area and perimeter; p_k is the frequency of occurrence of patch type k in the landscape; n is the number of patch types in the landscape; E is the total boundary length of all building patches (m); A_b is the total area of the building landscape (m²); g_i is the number of like adjacencies between pixels of patch type i, calculated using the single-count method; B_j is the number of buildings in the j-th grid; g_ii is the number of adjacencies within patch category i; and g_ik is the number of adjacencies between patch categories i and k.

3.1 Pearson correlation between architectural landscapes and carbon emissions

Pearson linear correlation was calculated for architectural landscapes and carbon emissions (Fig. 6). All the architectural landscape indicators were significantly associated with carbon emissions at the 0.01 significance level. Indicators such as largest patch index (LPI), proportion of like adjacency (PLADJ), patch cohesion index (COHESION), and aggregation index (AI) showed a negative correlation with carbon emissions, while the other indicators exhibited positive correlations. A correlation coefficient with an absolute value greater than 0.6 indicates a strong correlation. Several indicators, including landscape shape index (LSI), building number (BN), building coverage ratio (BCR), mean building height (MBH), standard deviation of building height (SDBH), and floor area ratio (FAR), meet this threshold. Indicators such as SHDI, perimeter area fractal dimension (PAFRAC), landscape division index (DIVISION), building shape coefficient (BSC), PLADJ, COHESION, LPI, and AI, with correlation coefficients between 0.2 and 0.6, demonstrated moderate relevance to carbon emissions. Indicators with values below 0.2, such as SCD, showed a weak correlation and were excluded from further analysis.

Close

Fig. 6.

Correlation coefficients between architectural landscape indices and carbon emissions.

Export to PPT

The linear relationship indicates that carbon emissions have a strong correlation with building number, density, shape, and height, while showing moderate relevance to building aggregation, diversity, and boundary complexity.

3.2 Factor contributions to carbon emissions by RF

The contribution of architectural landscape indices to carbon emissions has been shown in Fig. 7. It presents the importance ranking of variables from highest to lowest, a higher importance indicates a greater influence on carbon emissions. FAR exerted the most influence, contributing 45.5% to carbon emissions. This predominance suggests that an increase in FAR directly escalates energy consumption and population concentration, thereby amplifying carbon emissions. BN (18.4%) and LSI (13.3%) constituted secondary critical factors, with denser building clusters and complex geometric forms further intensifying emissions. Moderately influential parameters included BCR, SHDI, and BSC, each exceeding 2.8% contributions, while remaining indicators ranged from 0.7% to 2.5%. Cumulatively, these six metrics (FAR, BN, LSI, BCR, SHDI, and BSC) explained 86% of emissions, highlighting the critical interplay between architectural landscapes (building density, number, shape, and diversity) and carbon emissions. Consequently, these six indices were selected as predictors in the SVR model to quantify architectural landscapes impacts on carbon emissions.

Close

Fig. 7.

Variable importance ranking for urban carbon emissions from the RF model.

Export to PPT

3.3 Regression model of architectural landscapes and carbon emissions by SVR

The relationship model of architectural landscapes (FAR, BN, LSI, BCR, SHDI, and BSC) and carbon emissions was built using SVR in Python. The dataset was partitioned into training and test sets through randomized sampling, with 90% for training and 10% for testing. Three kernel configurations of linear, polynomial, and Gaussian kernels were systematically evaluated in the SVR model. The regression model was selected according to the prediction accuracy (Fig. 8) of three kernel configurations.

Close

Fig. 8.

Comparison of accuracy for different kernel functions in SVR models.

Export to PPT

The polynomial kernel function achieved the highest coefficient of determination (R²) for both training and test sets, with values of 70% and 68.58%, respectively. The polynomial kernel function also exhibited the lowest MRE and MAE values across both sets, at 44.75% and 40.82%, 325.47 and 456.7, respectively, outperforming the linear and Gaussian kernel functions. These results indicated that the polynomial kernel function exhibited superior predictive performance in the SVR model.

Therefore, the SVR model with a polynomial kernel function was selected for further analysis, as shown in Eq. (3):

Where C is the total carbon emissions (unit: t); k is the coefficient (with k=±10); n is the number of grids; $K(X_i,X)$ is a kernel function that satisfies Mercer’s condition; $X_i$ represents the architectural landscape index in the i-th grid, X_i∈(FAR, BN, LSI, BCR, SHDI, BSC).

3.4 Optimization of the SVR model by PSO

PSO was applied to optimize the hyperparameters of the SVR model with a polynomial kernel, using the same random sampling approach. The optimization process iteratively adjusted the penalty coefficient, kernel coefficient, and kernel function degree to maximize prediction accuracy. The initial PSO parameters were carefully determined based on a combination of prior empirical studies and sensitivity analysis (Table 2).

The optimal parameters of the PSO-SVR model, obtained through iterative computation in Python, were a penalty factor (c) of 2.17, a kernel function degree of 3, and a kernel function parameter gamma of 5.4. Then optimized regression model (PSO-SVR), which captures the relationship between architectural landscape indices and urban carbon emissions, is presented in Eq. (4):

Where $C$ represents total carbon emissions (unit: t); k is the coefficient (with k=±2.1); n is the number of grids; $K(X_i,X)$ is a kernel function satisfying Mercer’s condition; and $X_i$ represents the architectural landscapes index in the i-th grid, where X _i∈(FAR, BN, LSI, BCR, SHDI, BSC).

3.5 Prediction accuracy of SVR and PSO-SVR models

Fig. 9 displays the observed and predicted carbon emissions for each model across training and test datasets, with absolute errors shown in blue. Each dataset is presented separately in sub-graphs. Error analysis revealed that the variance of prediction error was higher in the training dataset than in the test dataset. Specifically, both R² and MRE values were higher for the training dataset, while MAE was lower for both SVR and PSO-SVR models (Table 3). These results indicated that the models are reliable for predicting urban carbon emissions.

Close

Fig. 9.

Observed and predicted carbon emissions using SVR and POS-SVR models.

Export to PPT

As shown in Table 3, the PSO-SVR model achieved an R² of 77.32% on the training dataset and 76.14% on the test dataset, representing improvements of 7.32% and 11.56%, respectively, over the standard SVR model. In addition, the PSO-SVR model reduced MAE by 60.27 on the training dataset and 51.78 on the test dataset. It also lowered MRE by 2.16% and 4.58%, respectively. These results collectively demonstrated that the PSO-SVR model significantly outperforms the SVR model in predicting carbon emissions based on architectural landscape indices. Therefore, optimizing the SVR model with PSO notably enhances model accuracy and generalization capability.

3.6 Relative errors of carbon emissions predictions

The relative errors (RE) between observed and predicted carbon emissions from the SVR and PSO-SVR models were categorized into seven levels. Fig. 10 compares the proportion of grid cells at each RE level for both models. For the SVR model, the distribution was as follows: RE≤5% (25.4%), 5%<RE≤10% (6.5%), 10%<RE≤20% (12.6%), 20%<RE ≤30% (11.7%), 30%<RE≤40% (13.9%), 40%<RE≤50% (5.0%), and RE>50% (25%). In comparison, the PSO-SVR model showed a 2.22% increase in the proportion of grids with RE≤5%, a 0.9% reduction in RE levels between 5% and 30%, and a 1.3% reduction in RE>30%, including a 1.67% decline in the RE>50% category. These results indicated that the PSO optimization effectively improved the predictive accuracy of the SVR model.

Close

Fig.10.

RE comparison for carbon emissions prediction between SVR and POS-SVR models.

Export to PPT

Fig. 11 illustrates the spatial distribution and variation in RE for carbon emissions predictions generated by the SVR and PSO-SVR models using ArcGIS. In both models (Figs. 11a and b), RE values below 30% were mainly concentrated in central urban grids with high building density. In contrast, RE values exceeding 30% were mainly distributed in suburban, rural, and green areas characterized by sparse building coverage, which negatively affected prediction accuracy.

Close

Fig. 11a.

RE of carbon emissions using the SVR model.

Export to PPT

Close

Fig. 11b.

RE of carbon emissions using the POS-SVR model.

Export to PPT

Fig. 11(c) compares the changes in RE between the two models. Specifically, 40.7% of grid cells were unchanged, 31.7% experienced reduced errors, and 27.6% exhibited increased errors. Grids with unchanged or improved accuracy were primarily located in city centers, while those with increased errors were predominantly found in suburban, rural, and green areas. These findings suggested that PSO effectively enhanced the SVR model by reducing errors in dense urban zones. The PSO-SVR model provides more accurate and spatially stable estimates of carbon emissions in Qingdao City.

Close

Fig. 11c.

RE changes from SVR to POS-SVR.

Export to PPT

4.1 The correlation between architectural landscapes and urban carbon emissions

Compact urban development is generally more sustainable than urban sprawl. However, unchecked vertical expansion of buildings has led to environmental challenges, including the urban heat island effect (Lin et al., 2021), poor pollutant dispersion, and increased carbon emissions. Unlike previous studies, this research emphasized the role of both 2D and 3D architectural landscape indices in explaining urban carbon emissions. The findings revealed significant correlations between urban carbon emissions and architectural landscape indicators, including FAR, BN, LSI, BCR, and building height. These findings align with previous studies: Higher FAR is linked to increased energy, water, and gas consumption, greater waste production (Pu et al., 2022), and higher carbon emissions. Higher BN and BCR reduce carbon sequestration in green areas and amplify emissions (Xu et al., 2021). LSI and SHDI impacted carbon emissions by altering energy efficiency (Nutkiewicz et al., 2018; Quan et al., 2020) and modifying block-level wind and thermal environment (Wei et al., 2022). These findings underscore the importance of optimizing FAR, BN, LSI, BCR, SHDI, and BSC in urban planning and building design to enhance energy efficiency and support low-carbon city development.

4.2 Comparison of SVR and PSO-SVR models

A comparative analysis of the SVR and PSO-SVR models revealed that the PSO effectively optimized the SVR model. The PSO-SVR model significantly improved the forecasting accuracy of carbon emissions across all test cases, indicating its superior generalization capacity and enhanced capability to capture complex nonlinear dependencies in emission patterns. These improvements could have tangible implications for urban carbon management. The enhanced prediction accuracy enables more reliable identification of high-emission zones, supports targeted mitigation interventions, and strengthens data-driven decision-making for localized policy development.

While this study focuses on SVR and PSO-SVR due to their proven effectiveness in modeling spatially heterogeneous and nonlinear emission data, alternative machine learning models such as XGBoost and artificial neural networks (ANNs) also show promise. XGBoost has been recognized for its high predictive accuracy and efficiency, particularly for structured datasets with moderate sample sizes. However, its performance depends heavily on hyperparameter tuning, and its decision rules can lack interpretability. ANNs offer strong capabilities in capturing complex nonlinear interactions and are well-suited for large-scale, high-dimensional datasets. However, their reliance on extensive data preprocessing and computational demands may limit their practical deployment in urban planning. Future studies could integrate a broader model comparison to enhance model selection rigor and robustness of conclusions.

4.3 Limitations

While the PSO-SVR model effectively demonstrated the relationship between three-dimensional architectural landscapes and urban carbon emissions in Qingdao City, three limitations require attention:

(1) Dataset limitations: The urban carbon emissions data from ODIAC may underrepresent the impact of architectural landscape indices (Gao et al., 2022; Sun et al., 2024), potentially affecting the prediction accuracy of both the SVR and PSO-SVR models. Future studies should use detailed building-level carbon emission data to improve model precision.

This study relies solely on 2020 data for Qingdao, which limits the generalizability of findings. Architectural styles, industrial structures, and social-economic conditions vary across cities, potentially altering the observed relationships. Although our results are valid for Qingdao and similar Chinese cities, multi-city analysis with longitudinal dataset would provide more comprehensive insights.

(2) Computational scale limitation: This study employed a 5 x 5 km² grid resolution determined through iterative testing to balance data density and emission variability. While this approach ensured computational feasibility, finer-scale differences in carbon emissions may be masked, especially in heterogeneous urban environments. Coarse grid size introduced spatial averaging effects, resulting in a loss of detail important spatial detail. Future studies should consider using the adaptive mesh methods or multi-resolution spatial frameworks that dynamically adjust grid sizes based on urban density or functional zoning. Such approaches may help capture spatial heterogeneity more precisely while maintaining computational feasibility.

(3) Limitations of Machine Learning Methods: Although we applied standardized normalization and 10-fold cross-validation strategy for model training and hyperparameter optimization to enhance generalization capability and prevent overfitting. The PSO-SVR model outperformed the conventional SVR in terms of prediction accuracy of carbon emissions. It is essential to recognize the inherent limitations of such machine learning approaches. Such as the necessity for comprehensive data pretreatment, overfitting, and overlook complex causal relationships. Future studies should consider incorporating advanced preprocessing frameworks, such as principal component analysis or mutual information-based filtering to improve model, and integrate machine learning with domain knowledge for more comprehensive insights.