Inferring Carbon Emissions from Human Mobility Data

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Inferring Carbon Emissions from Human Mobility Data

https://doi.org/10.21203/rs.3.rs-3657266/v1

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Accurate identification, quantification, and continual monitoring of carbon emissions constitute pivotal elements for proactive climate interventions. Conventional methodologies like direct measurement, including point-source assessments or remote sensing, often face challenges related to high costs or limited accuracy. Especially in low- and middle-income nations experiencing escalating emissions, carbon monitoring heavily relies on the administrative capabilities of local governments, which frequently lack adequate monitoring infrastructures. Addressing this predicament, our study introduces a computational framework to forecast CO₂ emissions by leveraging comprehensive observable human activity data from third-party sources. Our findings elucidate a robust correlation between multi-origin CO₂ emissions and human mobility (r = 0.89). Notably, machine learning models adeptly predict these emissions by integrating characteristics extracted from temporally aggregated, anonymized mobility networks (R²≈1.0). We demonstrate that the model effectively captures the notable reduction in CO₂ emissions during the COVID-19 lockdown, with both human mobility and CO₂ emissions in China decreasing by 56.97% and 32.45%, respectively. The prediction accuracy remains high for countries with varying social economic development, such as the U.S., Italy and Mexico. This study presents an inexpensive, real-time, and robust method of quantifying CO₂ emissions on a large scale with high precision, and it could facilitate tailored CO₂ emission reduction strategies, grounded in robust scientific evidence derived from the dynamics of human mobility.

Earth and environmental sciences/Climate sciences/Climate change/Projection and prediction

Scientific community and society/Social sciences/Climate change/Projection and prediction

Carbon dioxide (CO₂) emissions have been driving long-term climate change ^1-3, posing huge threats to human health ⁴, economic activities ⁵, and agriculture ⁶. While top-down approaches to CO₂ mitigation, such as national policies and SDGs, encounter delays due to lock-ins of energy infrastructure and resistance from stakeholders, bottom-up approaches centered on behavioral shifts in human activities offer promising avenues for comprehensive decarbonization ⁷ as transportation-derived CO₂ emissions emerged as the predominant source of greenhouse gases by 2017 ⁸. The international community has set ambitious targets under the United Nation’s Pairs Agreement to bring global emissions to net-zero by the mid-21st century. This commitment necessitates each signatory country to articulate its emissions targets for the forthcoming decades. Accurate and effective carbon monitoring is a central requirement of the Pairs Agreement, anchored on periodic assessments of countries’ commitments and advancements at five-year intervals. The agreement mandates the improvement and innovation of carbon monitoring techniques, a constant theme at the United Nations Framework Convention on Climate Change’s (UNFCCC) annual Conference of the Parties ⁹.

Considerable efforts have been made to accurately quantify CO₂ emissions using different methodologies. Countries such as Japan, the United States, and China have utilized satellites to monitor CO₂ concentration. However, financial limitations often prevent many low- and middle-income countries (LMICs) from implementing similar practices. Alternatively, scientists infer emissions indirectly using methods like mass balance approach ¹⁰, emission factors-based measurements ¹¹, life cycle carbon emissions assessment ¹², and input-output analysis ¹³. Despite their utility, these methods, however, require significant time, resources, human effort, and remain susceptible to unexpected errors. For example, life-cycle analysis, a comprehensive and intricate method, assesses emissions throughout the entire life cycle of a product, process, or service, encompassing emissions from production, utilization, and disposal phases, but there are challenges in determining responsibility for emissions. Another avenue involves leveraging mathematical or machine learning models to predict CO₂ emissions from various sources, such as marine fleets ¹⁴, intercity freight ¹⁵, commercial activities ¹⁶, cement industry ¹⁷, and residential ¹⁸ sectors. These models often integrate annually updated factors such as GDP ^19,20, energy usage ²¹, and population ²². However, their primary emphasis on yearly forecasting of CO₂ emissions might constrain the timeliness for effective governmental oversight and policy formulation. As we navigate toward the global emission target, the effort to real-time monitoring and prompt trend detection of CO₂ emissions become evident, underscoring the need for nuanced strategies attuned to both temporal and spatial considerations.

In this study, we propose a computational framework (Extended Data Fig. 1 and Methods) to predict CO₂ emissions by harnessing insights from human mobility patterns. Human mobility, with its abundance of geolocated details, provides a valuable lens through which to understand various social phenomena. It also has been demonstrated to be pivotal in urban planning ²³, traffic forecasting ²⁴, epidemic modeling ^25,26, disaster analysis ²⁷, and social-economic development estimation ²⁸. Drawing from China’s national level Cellular Signaling Data (CSD) as a proxy for human mobility, the unparalleled resolution and dependable quality of the human mobility data enable us to analyze and predict CO₂ emissions from an independent and novel perspective. Moreover, leveraging human mobility data to infer CO₂ emissions can greatly enhance the efficiency of CO₂ emissions data collection, analysis, and reporting. The developed computational framework could automate this process, reduce human errors and time costs, and improve the efficiency of carbon emissions management.

Spatio-temporal synchronization between population mobility and multi-source CO₂emissions

High synchronization exists between population mobility and CO₂ emissions. The correlation between daily national multi-source CO₂ emissions, encompassing emissions from seven sources (power, industry, residential consumption, ground transportation, domestic aviation, international aviation, and international shipping), and the total population mobility was Pearson’s r=0.89 during the study period from January 1 to February 29, 2020 (Fig. 1a). Notably, the first two months of 2020 witnessed human mobility being quickly and drastically changed by the COVID-19 lockdowns. Despite these perturbations, the temporal synchronization between CO₂ emissions and population mobility remained stable. Daily intercity population movement increased from an average of 53.53 million to a peak of 68.74 million during the Lunar New Year travel season (starting on January 10), subsequently dropping by 71.30% due to travel restrictions. This decline was followed by a gradual recovery as restrictions were lifted. Correspondingly, multi-source CO₂ emissions, which averaged 356.52 million kgC/d from January 1 to January 17, experienced a sharp drop to their lowest levels of 209.64 million kgC/d on February 13, marking a 41.20% decrease. Emissions then embarked on a recovery with intermittent fluctuations. This pattern of variation was also mirrored in the CO₂ emissions specifically associated with domestic aviation and ground transportation (Fig. 1b, c).

Furthermore, the spatial distribution of multi-source CO₂ emissions in China is of significant heterogeneity and unevenly distributed among cities (Fig. 1d). The analysis of regions sharing the same latitude reveals that cities on the east coast exhibit substantially higher CO₂ emissions compared to their western counterparts, Longitudinally, CO₂ emissions are notably more concentrated in the northern cities. A parallel trend is observed in the distribution of population mobility across cities. These observations demonstrate a spatial consistency between multi-source CO₂ emissions and population mobility, with Pearson’s r= 0.49.

These findings confirm that changes in intercity population movements and CO₂ emissions exhibit temporal and spatial consistency. Furthermore, the discrepancies in CO₂ emissions between cities correspond with the varying connectivity of intercity mobility. Consequently, the large-scale population mobility data illustrated in this study is deemed a reliable predictor of CO₂ emissions.

Correlations between mobility network features and CO₂ emissions

In this investigation, we focused on examining the complex connection between human mobility and CO₂ emissions by analyzing network topology. To achieve this, we created temporal directed mobility networks using both unweighted and weighted approaches (see Methods). From these networks, we extracted different node characteristics to access the activity features of cities and global characteristics for each network snapshot, allowing us to gain a comprehensive understanding of population movement over various time periods. Detailed descriptions of network features analyzed in this study can be found in Supplementary Table 1, which are further categorized into unweighted and weighted node and global features.

Our analysis revealed positive correlations between node features and CO₂ emissions, indicating cities with higher transportation accessibility and extensive connections to other cities tend to have increased CO₂ emissions (Fig. 1e). Furthermore, all global features demonstrated strong correlations with CO₂ emissions, with the majority of |r| values surpassing 0.80. Notably, the number of edges (NE) had a strong positive correlation with CO₂ emissions, reaching r=0.86. In contrast, the Strength Assortativity coefficient (SA) had a pronounced negative correlation, quantified at . Further insights into the correlation analysis can be found in Extended Data Table 1, Supplementary Figs. 1 and 2, and Extended Data Fig 2.

More surprisingly, node characteristics derived from unweighted mobility networks showed a stronger correlation with CO₂emissions when compared to their weighted counterparts (Fig. 1e). For example, the correlation values for Inward Closeness Centrality (ICC), Eigenvector Centrality (EC), and Betweenness Centrality (BC) were 0.50, 0.46, 0.38, respectively. In contrast, the correlation of Weighted Inward Closeness Centrality (WICC), Weighted Eigenvector Centrality (WEC), and Weighted Betweenness Centrality (WBC) were 0.31, 0.07, 0.27. This suggests that the network topology features, even without the detailed edge flow information, play a significant role in understanding spatio-temporal variation in CO₂ emissions.

Predicting CO₂ emissions with mobility network features

In this section, we combined the selected network features from the preceding step with the corresponding geographic and demographical information to predict CO₂ emissions. The integration yields a complete dataset with a sample size of 60 (days) × 366 (cities) =21,960. Subsequently, we employed eight distinct machine learning models and two different data split strategies to predict CO₂ emissions. Split Strategy 1 involved randomly partitioned all the 21,960 samples, whereas split Strategy 2 entailed partitioning based on days, ensuring that, samples from the same day were simultaneously allocated to either the training or test set (Extended Data Fig. 3).

Among the models tested, the LGBM demonstrated the best performance, achieving R² value near 1.0 in predicting multi-source CO₂ emissions under both data split strategies. The performance of all other models varied slightly depending on the data split strategies, with Strategy 1 generally performing better (Extended Data Table 2).

Fig. 2 shows the agreement between the predicted and observed CO₂ in mainland China during the turbulent period of Chinese Spring Festival Travel Rush and strict lockdown measures, indicating that LGBM accurately models the relationship between human mobility and CO₂ emissions. Despite the substantial fluctuations in both human mobility and CO₂ emissions throughout the study period, the predictions remained satisfactory (R²≥0.98). For split Strategy 1, LGBM outperforms all the rest models with R²=1.00, 0.99, 0.98 for predicting CO₂ from multi-source, domestic aviation, and ground transportation, respectively; and for split Strategy 2, LGBM remains the best performed model with R²=1, 0.97 and 0.94 for the three types of CO₂. XGB runs next to LGBM as the second-best model in both scenarios, with slightly decreased R² (0%~1%) and higher RMSE (7%~17%) and MAE (2%~18%). The significant superiority of LGBM and XGB indicates that, the gradient boosting frameworks for ensemble learning are powerful in predicting spatio-temporal carbon emission with high precision, such that there is a great potential of extrapolating the approach to other settings with either missing observable emission data for some places, or for forecasting future trend of emission with human activity data.

Feature importance and robustness analysis

The importance of geographic and demographic information in predicting CO₂ emissions was confirmed by SHapley Additive exPlanations (SHAP) values ²⁹ (Methods). This analysis identified latitude (LAT), longitude (LON), and population (POP) as the three most crucial features (Fig. 3a, b, and Supplementary Fig. 3), which consistent with previous studies ^30,31. Notably, the substantial difference in winter temperature across different latitudes in China contributes to divergent heating demands. The northern region, characterized by its heavy industrial base, requires more heating compared to the southern region, which is predominantly developed in light industry. This climatic and industrial disparity significantly influences the regional CO₂ emissions.

Connectivity and population flow, as represented by network features such as WDAC, WICC, OCC and IS, were found to be crucial for predicting CO₂ emissions. To further investigate the contribution of network information to the prediction, an ablation experiment was executed. A null model was built using LGBM trained solely on latitude, longitude and population. The model’s predictions were repeated 200 times with independent random splits to mitigate potential biases from data splitting (Supplementary Figs. 4, 5). Notably, when network features were incorporated, there was a marked improvement in prediction accuracy compared to the null model. For multi-source CO₂ emissions, the R² value increased from 0.93 to 0.98. Additionally, an increase of over 60% was observed across other evaluation settings, such as RMSE and MAE (Fig. 3c, Extended Data Table 3).

To further evaluated the prediction performance, we conducted analysis that involved gradually extending the study period and increasing the time span of training data. Specifically, at each timestep, the model was trained using all historical data, meaning that for prediction the outcome on the nth day, the training set consisted of data accumulated from the preceding n-1 days. The results demonstrate that an increase in the quantity of historical data led to significant improvements in all three prediction performance metrics (Fig. 3d-e). Notably, there was a distinct turning point observed on the seventh day, indicating that even with just one week’s worth of historical data, the method could generate predictions with satisfactory accuracy. This resilience was evident despite substantial fluctuations in population mobility. Moreover, we conducted sensitivity analyses by considering segmentation and scaling in the training and test sets, reaffirming the robustness of our model and ensuring accurate predictions across diverse conditions (Extended Data Fig. 4).

Generalization and extrapolation of the method to Italy, the U.S. and Mexico

To validate the generalizability and practicality of the proposed method, we utilized open-source mobility data from Italy ³², the U.S. ³³, and Mexico ³⁴ as a basis for predicting their respective CO₂ emissions (Fig. 4a-c). Surprisingly, despite the distinct socio-economic landscapes of these countries, our method consistently demonstrated commendable forecasting accuracy across all the three countries. In the case of Italy, outflows of each province were normalized on a daily basis, leading to the exclusion of weighted network features in our predictive model. Despite this constraint, we achieved an impressive R² value of 0.91. Similarly, our method demonstrated success in predicting CO₂ emissions for the U.S. and Mexico, yielding R² values of 0.96 and 0.99, respectively (Fig. 4d-f, and in Supplementary Fig. 6). These results demonstrate the generalizability and efficacy of the computational framework across diverse countries, highlighting its considerable potential for monitoring and forecasting carbon emission in LMICs where reliable emission measurements are often deficient.

Delineating CO₂ emissions in city clusters through human mobility

Given the notable carbon footprint of city areas, it is imperative to establish specialized carbon mitigation units, tailored to city clusters, for effective monitoring and reduction of carbon emissions. The previous finding of close association between CO₂ emissions and human mobility (Figs. 1 and 2), suggests the latter as a promising objective means of delineating city clusters. Therefore, we utilized Louvain algorithm ³⁵ (Methods) to detect communities in mobility networks during the period unaffected by Chunyun and COVID-19 lockdowns (Supplementary Table 2). The study period coincided with the run-up to the annual Chunyun mass migration and COVID-19 epidemic, which was divided into four distinct periods: normal times (January 1-9), Chunyun (January 10-23), stringent travel restrictions (January 24 - February 10), and recovery times (February 11-29).

During the normal times, significant geographical disparities in CO₂ emissions across city clusters were observed. Notably, the Beijing-Tianjin-Hebei (62.75 million kgC/d), the Northwest (Ordos) (60.24 million kgC/d), and the Yangtze River Delta (49.71 million kgC/d) were identified as leading emitters, primarily due to their dense population and industrial development activities (Fig. 5a-c). In addition, our findings indicate that polycentric city clusters are associated with higher CO₂ emission efficiency compared to city clusters with a concentric structure centered around a single unban core. For example, the Northwest (Changji) city cluster records emissions at 15.32 million kgC/d, significantly lower than 60.24 million kgC/d observed in the Northwest (Ordos).

A detailed examination of CO₂ emissions across different time periods reveals a dispersion of emissions throughout China. During the Chunyun period, characterized by high variability in mobility patterns, emissions were more dispersed throughout China (Fig. 5d). Stringent travel restrictions imposed during the COVID-19 pandemic substantially reduced CO₂ emissions in all city clusters (Fig. 5e). In the subsequent recovery period, strengthened local interactions within the mobility network resulted in lower CO₂ emissions compared to normal levels (Fig. 5f). These investigations, which delve into the examination of CO₂ emissions within city clusters, have significant implications for designing of customized CO₂ emissions policies. Such an approach can contribute to effective governance of CO₂ emissions at an aggregated level.

This study underscores the potential of utilizing human mobility data to make accurate CO₂ emissions prediction. Common transportation modes such as airplanes, high-speed trains, and long-distance buses play a crucial role in shaping intercity connections, and it follows that network features derived from human mobility networks demonstrate significant potential in predicting CO₂ emissions from domestic aviation and ground transportation. More notably, these same network features have shown considerable efficacy in forecasting multi-source CO₂ emissions across seven distinct carbon sources. Also, this study offers an inexpensive method for predicting CO₂ emissions, which could be particularly valuable for implementation in economically disadvantaged nations. Our approach leverages existing data, unlike carbon monitoring satellites that have restricted coverage in LMICs, making scaling across countries simple and nearly cost-free. Particular noteworthy is the resilience of our method in face of fluctuating human mobility patterns observed during the study period, ranging from the Chunyun—the largest annual human migration in the world ³⁶—to the exceptional calm of COVID-19 lockdowns. Despite these variances, the approach consistently yielded reliable predictions.

It is imperative to develop innovative and cost-effective solutions for monitoring CO₂ emissions, as they play a vital role in attaining emissions targets set forth by the Paris Agreement. Our research employed community detection methods of human mobility networks to categorize cities into city clusters. This analysis revealed considerable variations in CO₂ across different clusters, highlighting the need to pinpoint specific characteristics of carbon-intensive cities. City clusters can serve as effective units for monitoring and coordinating efforts to reduce CO₂ emissions, enabling collaborative planning to achieve emission reduction goals. It has the potential to lower the cost of CO₂emissions mitigation, which is particularly valuable for LMICs where detailed mapping of city clusters is limited. Despite the continuous growth of cities, there are steps that city planners can take into mitigate carbon emissions. These measures include promoting the adoption of cleaner sources of industrial and domestic energy, implementing energy-efficient ground transportation technologies, and improving rail transportation systems as a viable to domestic aviation. However, it is often perceived that these solutions are unpredictable and costly. Therefore, it is crucial to implement scalable policies that can effectively achieve these objectives and significantly reduce carbon emissions from city clusters.

Our research findings align with the previous studies that have established a correlation between CO₂emissions and various factors such as socio-economic development ³⁷, energy consumption ^38,39, and nighttime stable light ⁴⁰. Additionally, it is important to note that an accurate and efficient carbon monitoring approach plays a pivotal role in fostering international agreements and collaborations on climate change, as demonstrated by the Paris Agreement. Our proposed solutions not only deepen our understanding of the relationship between human activity and CO₂ emissions but also provide practical tools and strategies for effectively managing carbon emissions in the face of ongoing socio-economic and environmental challenges. These efforts are crucial for achieving development goals in a post-climate change era.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this paper.

Data Availability

The aggregated mobility matrices from China analyzed in this study are available on GitHub (https://github.com/wangmengning/MobilityForCO2Prediction). To facilitate the review process, an encrypted version of the data is accessible, requiring the password XGUTZH to decompress the data.

The weighted daily origin-destination matrices for Italy are available at https://data.humdata.org/dataset/covid-19-mobility-italy.

The multiscale dynamic human mobility flow dataset for the U.S. can be accessed at https://github.com/GeoDS/COVID19USFlows.

The daily intermunicipal travel networks of Mexico are available at https://osf.io/42xqz/.

The Global Gridded Daily CO₂ Emissions Dataset (GRACED) is available at https://carbonmonitor-graced.com/.

Code availability

All the code to reproduce the results are available on GitHub (https://github.com/wangmengning/MobilityForCO2Prediction). To facilitate the review process, the same code XGUTZH can be used to download and extract the code files.

Acknowledgments

We great appreciate Professor Maribel Hernández Rosales and Guillermo de Anda-Jáuregui for providing the mobility data in Mexico and for further data clarifications. This work was supported by the National Nature Science Foundation of China (72025405, 72088101, 72001211), the Innovation Team Project of Colleges in Guangdong Province (2020KCXTD040), and the Hunan Science and Technology Plan Project (2020TP1013).

Inclusion & Ethics statement

We declare that all individuals who contributed significantly to this work have been appropriately acknowledged. The accountability of authorship strictly complies with relevant national and international regulations and guidelines regarding research ethics, such as those listed by the Committee on Publication Ethics (COPE) and the International Council of Medical Journal Editors (ICMJE).

Author Contributions

X.L. conceived the research. M.N.W., X.L.Z., S.Y.T., and Z.Q. performed the research. M.N.W. and Z.Q. collected and cleaned the data. M.N.W., Z.Q., B.S., M.S.C., and S.H.G. analyzed the data. M.N.W., X.L.Z. wrote the paper. X.L., M.N.W., X.L.Z., S.Y.T., D.W., M.O., M.J.L., Z.L. and X.H.C revised the paper.

Declaration of interests

All authors declare no competing interests.

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Peer review information.

Reprints and permissions information is available at http://www.nature.com/reprints.

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Mobility data

China. The dataset was provided by one of China’s largest national mobile operators, China Unicom, which had 318 million active users as of 2019 ⁴¹. The mobility data used in this study was derived from Cellular Signaling Data (CSD), and was aggregated into city-level mobility matrices on a daily basis. To exclude population flow resulting from brief stays in a city, users who spent less than 30 minutes in a city were filtered out. The dataset encompasses the period from January 1, 2020, to February 29, 2020, a critical period during the COVID-19 pandemic outbreak.

Italy. The dataset captures aggregated movements between different Italian provinces, utilizing location data derived from a large-scale dataset of anonymously shared positions of about 170,000 de-identified smartphone users and a total of about 200 million data points at the sub-national scale ³². The mobility data is recorded in the form of OD (origin-destination) matrix, which was normalized by row, with each entry (i, j) in the matrix representing the proportion of user movements to province j out of those from province i. The dataset spans from January 18, 2020, to June 26, 2020.

The U.S. The dataset was sourced from anonymous mobile phone user visits to various locations provided by SafeGraph ³³. The mobility patterns were aggregated at two geographical scales: county and state. The reliability of this dataset was confirmed through a high correlation with openly available data sources. The dataset covers the period from January 1, 2020, to February 29, 2020.

Mexico. The dataset is a collection of human mobility networks which depict travel patterns between municipalities in Mexico ³⁴. These networks were constructed based on geolocation data obtained from mobile devices. In the network, each municipality was represented as a node, and the weight of an edge (i, j) corresponded to the total number of observed trips from municipality i to municipality j, and was normalized by the varying number of mobile devices recorded on a given day. The dataset covers the period from January 1, 2020, to December 31, 2020.

Details of the mobility datasets can be found in Supplementary Information.

CO₂ emissions data

The CO₂ emissions data comes from the Global Gridded Daily CO₂ Emissions Dataset (GRACED) ⁴². GRACED offers a daily spatial resolution of 0.1°×0.1°, encompassing CO₂ emissions from seven sectors: power, industry, residential consumption, ground transportation, domestic aviation, international aviation, and international shipping. GRACED is derived by Carbon Monitor national-level daily emissions, which are also allocated to finer-grid cells using spatial patterns from the Global Carbon Grid (GID) and the Emission Database for Global Atmospheric Research (EDGAR), as well as sub-national proxy based on TROPOMI NO2 retrievals. Rasterizing the global map at a resolution of 0.1°×0.1° results in matrix of 1800×3600 grids. GRACED is recorded in the form of an 1800×3600 matrix, with each element representing CO₂ emissions that correspond to a grid in the rasterized map.

Network construction

Computational framework

Based on the large-scale, third-party, and non-intrusive mobility data, our study introduces a comprehensive computational framework for predicting CO₂ emissions. This framework initiates with the acquisition of mobility data and the subsequent construction of mobility networks. These networks facilitate the extraction of predictor features. Next, network features (X) are integrated with the additional data, such as population and geographical coordinates (X’), to fine-tune a machine learning model on the training data. The fine-tuned model is then capable of being applied to predict the CO₂ emissions (Y) in scenarios where specific time-location pair of CO₂ emissions data are unavailable.

To perform the prediction, we divided the dataset into training and testing sets using two different strategies (Strategy 1 and Strategy 2, Extended Data Fig. 2). We then applied eight supervised learning algorithms (Multiple Linear Regression (MLR), Polynomial Regression (PR), Least Absolute Shrinkage and Selection Operator (LASSO) ⁴³, Ridge Regression (RR) ⁴⁴, K-Nearest Neighbors Regression (KNNR) ⁴⁵, Support Vector Regression (SVR) ⁴⁶, Artificial Neural Network (ANN), Random Forest (RF) ⁴⁷, eXtreme Gradient Boosting (XGB) ⁴⁸, Light Gradient Boosting Machine (LGBM) ⁴⁹ ) to make a crosswise comparison of their ability to predict CO₂ emissions. In conducting these experiments, stratified 10-fold cross-validation was employed on the training set using the above eight prediction models.

To optimize the training process, we employed z-score normalization during data preprocessing. This step involved normalizing the labels of the training set prior to model training and then de-normalizing the prediction results for final output. The effectiveness of the out-of-sample forecast capability was then evaluated using three key metrics: coefficient of determination (R²), root mean square error (RMSE) and mean absolute error (MAE).

SHapley Additive exPlanations (SHAP) values

SHAP is an additive method to overhaul each feature contribution to the prediction results in the learning model ⁵⁰ . SHAP actually attributes the output value to the shapely value of each feature ⁵¹. The output value is given as

Louvain algorithm

The Louvain algorithm utilizes multi-level modularity optimization to extract the community structure of large networks, and consists of two iteratively repeated phases. In the first phase, the algorithm computes a partition of the given network through modularity optimization. This phase stops when the modularity reaches a local maximum, indicating that no individual movement can improve it. In the second phase, the same community is folded to create a new weighted network. The first phase is then reapplied to the resulting weighted network and iterated. The algorithm aims to maximize modularity, defined as follows:

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There is NO Competing Interest.

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Inferring Carbon Emissions from Human Mobility Data (SI)

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