Bidirectional yet asymmetric causality between urban systems and traffic dynamics in 30 cities worldwide

Domain: neuroscience
Published: 2026-04-01
Editorial outcome: major_revision

Abstract
Understanding how urban systems and traffic dynamics co-evolve is crucial for advancing sustainable and resilient cities. However, their bidirectional causal relationships remain underexplored due to challenges of simultaneously inferring spatial heterogeneity, temporal variation, and feedback mechanisms. Here we present a spatio-temporal causality framework that bridges correlation and causation by integrating spatio-temporal weighted regression with spatio-temporal convergent cross-mapping. Characterizing cities through urban structure, form, and function, the framework uncovers bidirectional causal patterns between urban systems and traffic dynamics across 30 cities on six continents. Our findings reveal asymmetric bidirectional causality, with urban systems exerting stronger influences on traffic dynamics than the reverse in most cities. Urban form and function shape mobility more profoundly than structure, even though structure often exhibits higher correlations. This does not preclude the reversed causal direction, whereby long-established mobility patterns can also reshape the built environment over time. Finally, we identify three causal archetypes: tightly coupled, pattern-heterogeneous, and workday-attenuated, which support city-to-city learning and inform context-sensitive strategies in sustainable urban and transport planning.

Introduction
Cities function as complex systems where human mobility and the built environment continuously interact1–4. These interactions manifest in diverse ways within urban traffic systems. For example, transit-integrated urban design in Singapore facilitates individual movement through extensive public transport networks, whereas London’s historic and fragmented road layout amplifies congestion-prone traffic patterns. Accordingly, traffic dynamics serve as a tangible indicator of these interactions, reflecting not only how urban systems shape movement patterns but also how human mobility reciprocally influences the built environment5–7. Understanding these bidirectional influences is crucial for designing adaptive transportation policies and promoting sustainable urban development.

Given the complexity and multifaceted nature of cities, comprehensively characterizing urban systems is an important prerequisite for investigating these bidirectional influences4,8. Here, we characterize cities through three interconnected components: urban structure, form, and function, collectively forming the “triple helix” of urban systems. Urban structure establishes the physical backbone of a city, primarily through its road networks9,10. Building on this structural foundation, urban form determines the spatial layout and configuration of the city, while urban function embeds the distribution of land uses and socioeconomic activities across these spatial arrangements11–13. Although closely related, they capture different facets of urban systems that influence traffic dynamics through distinct mechanisms3,14,15. For example, road network topology constrains route choice, whereas district form and function drive the demand for travel orientations and destinations. Together, these three components govern how urban systems interact with human mobility, shaping the spatial and temporal patterns of traffic dynamics.

Existing studies have primarily examined associations among these components, applying such insights to develop analytical models for urban dynamics, traffic forecasting, and public transit systems1,6,16,17. In particular, built-environment factors, ranging from urban morphology indices and land-use types to network structure, have been shown to exert significant influences on traffic states and congestion patterns across diverse metropolitan contexts15,18–20. To investigate these complex interactions between urban systems and traffic dynamics, many methodological approaches have been adopted, including global statistical and econometric models for uncovering macro-level determinants and longitudinal dependencies15,19, local and spatio-temporal varying-coefficient models for characterizing spatiotemporal heterogeneity and dynamic associations21,22, and computational data-driven frameworks for capturing nonlinear dynamics and fine-grained mobility patterns2,3,23. Furthermore, such methodological advances have been deployed in detailed case studies to quantify route diversification capabilities within network topologies24, assess the influence of road functions on localized congestion25, and evaluate the impacts of street design and intersection density on traffic performance18. Collectively, these studies establish important empirical benchmarks on the interplay between urban systems and traffic dynamics, underscoring that both supply-side factors (e.g., network structure) and demand-side factors (e.g., land-use and activity patterns) within the built environment are critical determinants of traffic states. However, the bidirectional feedbacks that govern these interactions and the potential asymmetries in their strength remain underexplored, despite being central to their dynamic and reciprocal nature. For example, while efficient road planning can mitigate traffic congestion, persistent congestion can also reshape urban systems, as seen in cities that expand metro networks in response to traffic pressure26. Without accounting for this feedback, developed models may lead to an underestimation of long-term shifts in mobility and infrastructure demands.

Understanding these feedback mechanisms requires moving beyond statistical associations toward causal modeling that addresses both spatial dependency and temporal variation27,28. Causal inference has proven effective in capturing interactions among diverse elements of urban and traffic systems, ranging from linking individual mobility to health outcomes29, to diagnosing congestion in road networks30, and disentangling complex urban processes31. Among these, convergent cross mapping (CCM) has emerged as a robust tool for detecting nonlinear and bidirectional causal relationships in urban contexts30,32. However, most existing studies focus on investigating causal inference in time-series data to establish temporal causality within the built environment. In contrast, spatial causality modeling remains relatively underexplored, largely due to challenges in modeling spatial dependencies that underlie geographical processes33. A feasible solution is to adapt causal inference models to the spatial domain by integrating spatial dependencies in urban space, as exemplified by the geographical convergent cross mapping (GCCM) framework34. However, GCCM does not explicitly account for temporal changes that are fundamental to urban systems. As features characterizing urban structure, form, and function evolve gradually, movement patterns fluctuate much more rapidly, producing pronounced temporal variations in urban dynamics3. In addition, causal mechanisms are inherently spatially heterogeneous, varying substantially across cities4,35,36. This spatial adaptability of causality complicates the bidirectional interactions between urban systems and traffic dynamics, which highlights the need for an integrated spatio-temporal framework to enhance context-aware understanding of urban dynamics and foster city-to-city learning networks for knowledge exchange.

To address these challenges, we propose a spatio-temporal causality framework that bridges correlation and causation by identifying bidirectional causal relationships between urban systems and traffic dynamics. At its core is a spatio-temporal convergent cross-mapping method (STCCM) developed in this study, which extends CCM and GCCM by jointly embedding spatial dependence and temporal variation into the state-space reconstruction. Intuitively, STCCM uncovers causal relationships by examining whether the spatio-temporal evolution of one process, such as traffic dynamics during congestion periods, embeds information that allows the recovery of another process within the joint state space of interacting urban systems. The framework combines STCCM with spatio-temporal weighted regression (STWR) (see Methods). In detail, STWR first characterizes the spatially heterogeneous and temporally varying relationships between urban systems and traffic dynamics, and then synthesizes these locally estimated effects into composite indicators that capture the combined influence of urban structure, form, and function. Subsequently, STCCM uses these composite indicators to infer nonlinear and bidirectional causal pathways during congestion periods, when mobility-infrastructure mismatches amplify causal signals and make them more detectable and policy-relevant. This integrated pipeline generates comparable causal fingerprints across space and time, converting heterogeneous associations into directional evidence of causality. To ensure broad representativeness, we apply this framework to 30 cities with diverse urban contexts, selected based on data availability, traffic congestion levels, and global distribution (see Methods). These cities encompass major metropolitan capitals in developed countries and economic centers in emerging economies, spanning six continents. Finally, we introduce a causality-driven clustering approach that integrates all three urban system components to reveal underlying similarities and differences in bidirectional causal patterns across cities (see Methods). This analysis identifies distinct causal archetypes and supports city-to-city learning, outlining scalable pathways from causal insights to intervention for advancing sustainable urban and transport planning.

Results
Associating urban systems with traffic dynamics

The three components of urban systems exert distinct influences on traffic dynamics, with varying effects across spatial and temporal dimensions. To assess these effects, we characterize urban systems using distinct yet complementary interpretable feature sets, with urban structure depicted by road network topologies, urban form captured through morphological metrics at the landscape level, and urban function represented by land-use attributes (see Methods). Traffic dynamics are measured using an indicator that captures variations in human mobility across space and time within the road network (see Methods). The STWR model is then employed to quantify these relationships, allowing the strength of association to vary across space and time rather than imposing a single global effect. In Fig. 1(a), we present the R2 values across 30 cities on rest days for urban structure, form, and function, encompassing their average values, as well as the first (Q1) and third (Q3) quartiles. Higher R2 values indicate a better fit of the STWR model. See Supplementary Tables 1 and 3 for model fit (R2), local significance assessment (adjusted α and critical t), and model selection (Akaike Information Criterion corrected, AICc) across 30 cities on rest days. Overall, all three components exhibit strong and significant correlations with traffic dynamics, underscoring their integral roles in shaping individual movement patterns. Among them, urban structure demonstrates the strongest association with traffic dynamics, with an average R2 of 0.94 and Q1 and Q3 values of 0.92 and 0.97, respectively. This outcome is anticipated, as the urban road network serves as the physical framework or “container” of traffic, connecting various parts of the city and facilitating movement10. Its foundational role as the spatial backbone of urban systems accounts for this high degree of correlation. Urban form and function display similar levels of association with traffic dynamics, albeit slightly lower than urban structure. Urban form attains an average R2 of 0.75, closely followed by urban function at 0.73. While urban structure establishes the spatial framework of the city, urban form and function populate this container, providing the spatial layouts and land use configurations that drive human mobility14,37. Together, they influence the traffic system by shaping the patterns and intensity of movement across the city.

Despite the overall significance, the three urban system components display considerable variation in their R2 values across cities, as shown in Fig. 1(b, f). These disparities appear to be partly shaped by underlying socioeconomic conditions and governance context38, and also by the extent to which the globally consistent feature set captures locally salient determinants of traffic patterns. Several high-income cities demonstrate high R2 values across all three components, such as Stockholm, Zurich, and Toronto. Notably, they also exhibit the highest R2 values among the 30 cities for individual components: Berlin records the highest value for urban structure at 0.99, Zurich achieves the highest R2 value for urban form at 0.96, and Stockholm leads in urban function at 0.91. These high R2 values suggest a tighter coupling between urban systems and traffic dynamics, particularly in cities with advanced infrastructure and stable institutional conditions. In contrast, cities in less-developed countries, such as Rio de Janeiro, Riyadh, and Cape Town, exhibit much lower R2 values for all three components. For example, the R2 value between urban form and traffic dynamics in Riyadh is merely 0.26, while Rio de Janeiro shows a low R2 of 0.35 for urban function. In these contexts, the lower R2 indicates that the form and function features used here account for a smaller share of the variance in traffic patterns. This may reflect weaker associations with spatial configurations and land-use distributions, or the influence of latent factors not captured by the current feature set used to construct the composite indicator. However, R2 values do not entirely correspond to local socioeconomic development, as evidenced by exceptions like Manila and Los Angeles. Manilas compact and road-based mobility context tightens the alignment of urban systems with traffic dynamics, whereas Los Angeless polycentric sprawl and extensive boundaries weaken form- and function-traffic links, leaving structure as the dominant correlate.

The variations in R2 values among different cities can be further explained through the STWR coefficient distribution in Fig. 1(c-e). These coefficients highlight regional heterogeneity in the interactions between urban system features and traffic dynamics, measured by traffic congestion levels. Some features exhibit both positive and negative effects across cities, whereas others consistently influence movement patterns in the same direction. Urban structure features in Fig. 1(c) generally present mixed effects on traffic dynamics, which reflects the complex interplay between road network design, topology, and regional characteristics. For example, metrics such as CRS_CT (crossing count, the number of road intersections) and RD_DENS (road density, the total road length per unit area) may have positive or negative impacts depending on whether they enhance connectivity or create bottlenecks in specific regions. For urban form features in Fig. 1(d), NP (number of patches, the total number of land-use patches) and CONTAG (contagion, the degree to which land-use patches are clumped or dispersed) positively correlate with traffic congestion due to increased fragmentation and uneven spatial aggregation, which could hinder connectivity and intensify traffic density. In contrast, TE (total edge, the total length of all patch edges) and ED (edge density, the total length of all patch edges per unit area) generally show negative effects, since more extensive edge configurations can improve spatial connectivity. Most of the other features exhibit mixed effects, with their influence varying across cities. For urban function features in Fig. 1(e), categories such as TRANS (transportation area), SPRT (sports area), and PARK (park area) display predominantly positive effects on traffic dynamics. These land uses are associated with destinations that attract leisure-related mobility on rest days. In contrast, COMM (commercial and business facilities area) presents an overall negative effect, potentially reflecting reduced activity that leads to decreased traffic flows during non-working periods.

When features are considered collectively, their interactions and localized weighting can shift the coefficients between positive and negative values. Within a single city, spatial heterogeneity can also lead to localized variations in effects. Corresponding STWR results for workdays are provided in Supplementary Fig. 1 and Supplementary Tables 2 and 4.

Revealing bidirectional causal patterns

Recognizing that correlation does not imply causation, it is crucial to move beyond statistical associations and identify causal pathways27,39. To capture the bidirectional causal relationships between urban systems and traffic dynamics, we develop the spatio-temporal convergent cross mapping (STCCM) model by incorporating spatial dependency and temporal variation (see Methods). The core principle is to determine whether spatially distributed information that evolves over time in one variable can predict another by reconstructing their state spaces, thereby inferring causality. This bidirectional cross-mapping approach reveals the directional influence and relative strengths. Fig. 2 presents the inferred bidirectional causal patterns between urban systems and traffic dynamics across 30 cities during congested periods on rest days, with detailed performance metrics and significance tests reported in Supplementary Table 5. Each L-ρ plot serves as a diagnostic tool for causal inference, illustrating how predictability evolves with increasing library size L. Here, L represents the number of observations used for state-space reconstruction, while ρ represents the cross-mapping skill of one variable based on another, i.e., how well one variable recovers the state of the other. For each city and each component of the urban system, we generate two L-ρ curves: one for urban systems → traffic dynamics and one for traffic dynamics → urban systems. Crucially, evidence of causality is established not by a static ρ value, but by the property of convergence: a curve that rises and stabilizes at higher ρ values as L grows. This trend indicates a robust causal signal, as additional observations improve coverage of the reconstructed state space and help reveal the underlying deterministic rules of the system34. Furthermore, the shaded regions between the two curves in Fig. 2(a) highlight the magnitude of asymmetry (∆ρ) between the bidirectional influences. Consequently, for a given urban system indicator X and traffic dynamics indicator Y, if the ρ values for X → Y consistently exceed those for Y → X as L increases, X is inferred to be the dominant causal driver of Y, and vice versa.

Fig. 2(b-d) highlights a pronounced bidirectional yet asymmetric causal pattern, exemplified by Singapore, where ρ values reach exceptionally high levels at the largest library size. With increasing L, the L-ρ curves for urban structure, form, and function → traffic dynamics consistently exceed those for the reversed direction, i.e., traffic dynamics → urban structure, form, and function. This indicates a dominant causation from urban systems to traffic dynamics, with spatial layouts and road networks shaping traffic congestion patterns. However, this does not negate the existence of reversed causation. The relatively slower, yet still high, ρ values for traffic dynamics → urban systems reflect feedback processes between mobility and the built environment5,40. In Singapore, urban planning and governance significantly shape human mobility patterns, while these patterns in turn influence urban development through dynamic responses, such as promoting public transport and integrating land-transport planning to mitigate road congestion41. In addition, among the three urban system components, urban form exerts the strongest influence on traffic dynamics. Its L-ρ curve reaches the highest ρ values, highlighting its key role in shaping traffic patterns and driving congestion. This finding diverges from the STWR model results in Fig. 1(f), where urban structure demonstrated the highest R2 value in Singapore. This divergence underscores the critical distinction between association and causation, emphasizing that strong correlations do not necessarily imply causal relationships.

Similar to Singapore, several other cities exhibit comparable bidirectional yet asymmetric causal patterns between urban systems and traffic dynamics during congestion periods. For example, New Delhi, Paris, and London are positioned near Singapore in Fig. 2(b-d), with a stronger causal direction of urban systems → traffic dynamics compared to the reversed direction. Their high ρ values at the largest L reveal that their spatial configurations and structures play a significant role in driving traffic congestion. Meanwhile, cities such as Stockholm, Sydney, and Moscow, positioned toward the left in Fig. 2(b-d), also indicate a stronger causal direction from urban systems to traffic dynamics. However, their ρ values are considerably lower than Singapore’s. This suggests that while urban systems still influence traffic congestion in these cities, the strength of the causal pathway in both directions is relatively weak. The variations in ρ values across cities can be attributed to city-specific urban configurations and how effectively the STCCM model reconstructs their spatial and temporal interactions in the state space. For cities with higher ρ values, the causal model produces more representative state-space reconstructions, effectively incorporating spatially lagged information across the built environment to capture causal interactions between urban systems and traffic dynamics. In contrast, cities with lower ρ values demonstrate less representative state-space reconstructions, influenced by weaker spatial dependencies and increased variability in the built environment and individual movement patterns.

Although some cities near the diagonal might suggest a balanced interaction, statistical tests support the robustness of these relationships. Specifically, the estimated causal strengths (ρ) are statistically significant across all 30 cities (p < 0.001; see Supplementary Table 5). Furthermore, despite the visual proximity to the diagonal, paired t-tests reveal that the asymmetry (∆ρ) remains statistically significant for the majority of cities on rest days, specifically in 26, 29, and 27 out of 30 cities for urban structure, form, and function, respectively (see Supplementary Table 7). Together, these results statistically support the conclusion that urban systems more often exert a dominant influence on traffic dynamics, consistent with the asymmetric nature of the causality.

In addition, rare cases such as Manila and Christchurch reveal distinct bidirectional causal patterns, in which the dominant causal direction runs from traffic dynamics to urban systems. With relatively low ρ values of approximately 0.3, Manila appears below the diagonal line in Fig. 2(c) but lies above the one in Fig. 2(b, d). This pattern highlights its stronger causality directions of urban form → traffic dynamics and traffic dynamics → urban structure/function, as opposed to the reversed directions. Its L-ρ curves show that the relationships are not monotonically increasing with library size (see Fig. 2(a)). Instead, the curves exhibit slight dips before rising, reflecting weak spatial dependencies in capturing the causal-effect relationship between urban systems and traffic dynamics. In contrast, Christchurch consistently displays monotonic L-ρ curves with relatively higher overall ρ values. At the largest library size L, the direction of traffic dynamics → urban function becomes predominant over its reverse, highlighting the significant feedback effect of mobility patterns on urban land uses. This suggests that human mobility patterns in Christchurch influence and shape how urban functions are utilized and experienced within the city.

Overall, the results underscore the bidirectional causal relationship between urban systems and traffic dynamics, yet reveal a clear asymmetry: urban systems exert stronger and more systematic causal effects on traffic dynamics, whereas feedback from traffic dynamics to urban systems is comparatively weaker. This trend is particularly pronounced on rest days, underscoring the role of urban structure, form, and function in shaping travel behavior. The asymmetry persists on workdays (See Supplementary Fig. 2 and Supplementary Tables 6 and 7), but a slight distinction emerges: stronger traffic-to-urban effects occur more frequently, especially for urban structure. This phenomenon appears in cities such as Manila, Christchurch, Sydney, and Hong Kong, where regular commuting rhythms and higher workday volumes provide discernible feedback to urban systems. It also indicates that long-established mobility patterns can reshape land-use patterns and trigger adjustments in the design and capacity of transport infrastructure.

Understanding global cities through bidirectional causality

Urban structure, form, and function, together constituting the “triple helix” of urban systems, provide a cohesive lens for linking the built environment to traffic patterns. Categorizing cities based on these interactions can uncover their commonalities and distinctions, supporting city-to-city learning and cross-regional knowledge exchange. To achieve this, we characterize global cities using the shape and magnitude of their L-ρ bidirectional causality curves across both rest and work days. Specifically, dynamic time warping (DTW) evaluates the shape difference between the bidirectional L-ρ curves of two cities, capturing variations in the temporal patterns of causality. In contrast, the Jaccard distance measures dissimilarity via the intersection-over-union (IoU) of the regions under the bidirectional L-ρ curves (defined as the union of the two directional regions), reflecting differences in the overall magnitude of their causal influence. We then integrate these two measures through hierarchical clustering, grouping the 30 cities into three clusters at a distance threshold of 1.0 (see Methods; Fig. 3(a)). To further illustrate inter-city variation, Fig. 3(b) presents the ρ values at the largest library size L for each city on rest and work days.

Cluster 1 exhibits consistently high ρ values in both causal directions, indicating strong bidirectional causality between urban systems and traffic dynamics. This cluster spans cities from New Delhi to Paris and includes identifiable subgroups such as developing megacities (New Delhi, Mexico City, Mumbai) and global financial hubs (Singapore, Dubai). In these contexts, urban-traffic systems are tightly coupled: landscape morphology, land-use allocation, and road-network topology jointly exert strong influences on traffic dynamics. These robust linkages highlight the strategic value of this cluster for congestion mitigation and sustainable transport planning, as urban system variables already explain a substantial share of spatial and temporal variations in traffic dynamics. Accordingly, practical strategies should prioritize integration of land use and transport planning, coordination across modes and districts through fine-grained street design, and bundling of instruments such as transit provision, pricing schemes, and parking policies41–43.

Cluster 2 is characterized by relatively strong bidirectional causality, albeit slightly weaker than Cluster 1. This pattern is evident in the ρ values at the largest L in Fig. 3(b), spanning cities from Helsinki to Vienna. Within this group, causal patterns are heterogeneous, with several city pairs and triads displaying closely aligned yet distinct causality signatures. For example, Helsinki and Hong Kong show balanced causality magnitudes in both directions for work and rest days; Riyadh and Bangkok are dominated by function- and structure-led patterns, with strong land-use and road-network signals; while Chicago, Toronto, and Vienna share similar rest-day ρ values across components, with consistently lower influence in the reverse direction. This heterogeneity calls for a diagnostic portfolio in planning practice, such as applying the six-direction heatmap to identify component-dominant subareas, including commute corridors shaped by structure and districts influenced by form and function, and then assembling context-specific combinations of network operations, land-use adjustments, and demand management strategies to alleviate congestion43,44.

Comprising only five cities, Cluster 3 presents uniformly low ρ magnitudes compared to the other clusters. A pronounced workday drop is observed in most cases, except for Stockholm, which shows consistently low values across both rest and work days. Overall, rest-day values remain modest, with cities such as Zurich and Sydney exhibiting higher urban system → traffic dynamics than the reverse, while work-day values become consistently lighter in the heatmap, reflecting weaker cross-mapping skill at the largest L. This workday attenuation suggests that policies relying solely on static urban system levers are unlikely to yield substantial congestion relief on workdays unless complemented by operational and demand-side instruments that directly shape daily dynamics45,46. In contrast, rest-day patterns remain more responsive to urban system features, allowing system-based interventions to exert greater influence.

The tendency for higher ρ values on rest days than work days is not limited to Cluster 3, but is broadly observed across most cities, albeit to varying degrees (see Fig. 3(b)). This can be attributed to two potential factors. First, traffic on rest days is largely self-organized, allowing individuals greater flexibility to adjust their travel behavior in response to congestion. This responsiveness reinforces the role of urban systems in shaping movement choices. Second, during peak workday hours, traffic dynamics tend to approach saturation due to fixed commuting schedules, resulting in congestion across various urban regions. This congestion extends over diverse road networks and land-use types, reducing spatial heterogeneity in causality patterns and rendering causal relationships less distinct than those observed on rest days.

Methods
Screening cities and datasets for global reach

To thoroughly investigate how urban systems and traffic dynamics interact, it is crucial to select global cities representing diverse economic, cultural, and administrative contexts. Alongside the rapid urbanization observed worldwide, numerous cities have transitioned beyond their original administrative or industrial functions4,51. Existing studies and international organizations have attempted to classify global cities based on their developmental trajectories, functional characteristics, or international connectivity. Examples include distinguishing between the Global South and North and delineating multi-tier city-regions worldwide35. Based on this, we use three specific criteria to select the cities for exploring their bidirectional causality between urban systems and traffic dynamics: (1) data availability, (2) the extent of traffic congestion, and (3) geographical distribution to ensure global reach.

The first criterion is whether the necessary data sources are accessible. This study mainly relies on three datasets, i.e., traffic datasets for computing traffic dynamics indicators, OpenStreetMap (OSM) datasets for extracting urban system features, and global administrative boundaries (GADM) for defining city limits. In detail, traffic datasets from HERE Technologies provide traffic information in the form of jam factors for road segments, enabling the computation of mobility indicators across global cities52,53. OSM offers detailed datasets on transportation networks, building coverage, points of interest, and land use to derive urban system features54. GADM supplies boundary information to delineate the geographical extents of cities. Although OSM and GADM offer comprehensive global coverage, HERE Technologies imposes certain limitations on cities with available traffic data. Consequently, the initial selection process prioritizes cities where coverage from HERE Technologies is confirmed.

After data availability is confirmed, the second criterion evaluates the congestion levels of traffic dynamics to ensure the representation of diverse human mobility patterns. Drawing on publicly available congestion reports from TomToms 2023 traffic index55, we incorporate both highly congested cities, such as Manila and Lima, in their broader metropolitan areas, as well as London and Toronto in more compact city centers, along with relatively uncongested cities, including Singapore, Zurich, and Stockholm. This selection guarantees a wide spectrum of traffic conditions across diverse transportation and infrastructural settings.

The third criterion emphasizes worldwide representation. To ensure that the findings reflect diverse political and economic contexts, the selected cities should span multiple continents and include major economic centers or national capitals, such as Los Angeles, Moscow, New Delhi, and Cape Town. This global perspective allows for examining spatial causality under varying governance structures, cultural landscapes, and developmental stages.

These three considerations lead to a final selection of 30 cities, ranging from prominent metropolitan capitals in developed nations to mid-sized economic centers in emerging economies. In this study, traffic datasets from HERE Technologies were obtained at 5-minute intervals in two one-month phases: June 1-30, 2024, and September 21-October 20, 2024, owing to data availability. A detailed visualization of their road networks extracted from HERE Technologies and administrative boundaries is presented in Fig. 4.

Delineating traffic dynamics

Identifying appropriate spatial units is critical in delineating residents’ mobility in the urban environment. The commonly used methods include grid-based divisions, traffic analysis zones (TAZs), Voronoi polygons, and buffer areas surrounding road segments5,56. Each method offers distinct advantages while also facing specific limitations. For example, grid-based divisions are straightforward to implement, but they often fail to align with functional boundaries. Voronoi polygons perform well in dense networks by capturing localized traffic dynamics, yet in sparsely populated areas, they tend to generate overly large and less informative units. TAZs capture broader environmental contexts due to their design around traffic flow, but lack fine resolution and strong connections to specific road segments. Buffer areas face challenges with multi-level disparities in buffer sizes across different road segments.

To address these limitations, we employ a hybrid approach that combines Voronoi-based divisions with buffer distances, resulting in Buffered Voronoi Cells (BVCells). The construction of BVCells begins with selecting intersection nodes within the road network. Intersection nodes are chosen as anchor points as they represent critical locations where traffic jams originate, such as those influenced by traffic light controls or congestion spillover effects57. However, many road intersections feature multiple nodes in close proximity, which can lead to an excessively dense computational unit when generating Voronoi polygons. To mitigate this issue, we apply a density-based clustering algorithm to merge nodes within a 20-meter radius. Once the intersection nodes are merged, Voronoi polygons can be generated around these points. A buffer boundary is then applied to limit each polygon with a buffer size of 500 meters5, capturing the surrounding environment relevant to local traffic systems. This process also addresses the issue of sparsely located nodes generating disproportionately large units. A visualization of the BVCell division across the 30 selected cities is presented in Fig. 4.

For each BVCell, we compute a traffic dynamics indicator (TDI) to capture traffic dynamics over time. This indicator is derived from the real-time traffic dataset provided by HERE Technologies, a data source shown to be reliable for measuring and forecasting traffic dynamics across multiple cities52,53,58. Supplementary Table 8 summarizes the dataset for all 30 cities and reports its spatial and temporal representativeness. The traffic dataset was collected every 5 minutes during two one-month windows, either 1 Jun - 30 Jun 2024 or 21 Sept - 20 Oct 2024. For each city, the time-coverage ratio refers to the proportion of 5-minute slots that contain valid traffic records in the one-month window. We present a minimum of 98.40% and a median of 98.60% for all time-coverage ratios, showing high temporal representativeness with near-continuous coverage of both work and rest days. From the spatial perspective, the number of HERE road segments within each city’s boundary ranges from 944 in Manila to 18,788 in Los Angeles. To evaluate spatial representativeness, we overlay a 1 km × 1 km grid on each city and compute the spatial-coverage ratio: for each grid cell that contains OSM roads for motor-vehicle traffic, i.e., classified as motorway, trunk, primary, secondary, tertiary, or their links, we check whether the grid cell also contains HERE road segments. The resulting spatial-coverage ratios exceed 70% in 28 out of 30 cities and reach about 95% in Buenos Aires, Sydney, and Paris. Although Mexico City and Riyadh achieve lower city-wide ratios, their central districts are still well covered by HERE road segments, as shown by the blue grids in the accompanying heatmaps. Overall, the HERE traffic dataset exhibits high spatial and temporal representativeness, supporting its use for TDI computation.

Given the traffic dataset, we use the jam factor, representing real-time traffic dynamics for each road segment, to compute the TDI. The jam factor is a dimensionless congestion index, ranging from 0.0 as free flow to 10.0 as blocked, which is obtained by applying a piecewise-linear mapping to the ratio between the current traffic speed and the expected default traffic speed16. Since each BVCell encompasses multiple road segments and time slots, we account for both spatial and temporal variability by applying separate weighting strategies. First, temporal weighting smooths the short-term fluctuations in traffic conditions over a month to generate the hourly traffic dynamics series. Each road segment r is associated with a jam factor JF(r,d,h,i), where d ∈ {1,...,30} is the day in the one-month window, h ∈ {0,...,23} is the hour of the day, and i indexes the 5-minute snapshots within each hour. We apply temporal weighting to aggregate jam factors in two steps, i.e., hourly aggregation and daily aggregation. We start with obtaining the hourly average JF(r,d,h):

JF(r,d,h) = 1/m(d,h) ∑_{i=1}^{m(d,h)} JF(r,d,h,i), 0 < m(d,h) ⩽ 12, (1)

where m(d,h) is the number of valid 5-minute observations in hour (d,h). To obtain a typical diurnal profile, we then average the hourly values across work and rest days separately:

JF(r,h)work = 1/Dwork ∑_{d ∈ workdays} JF(r,d,h), JF(r,h)rest = 1/Drest ∑_{d ∈ restdays} JF(r,d,h), (2)

with Dwork and Drest denoting the numbers of work and rest days in the month, respectively. For simplicity, we denote either of them as JFt. Second, spatial weighting recognizes the relative importance of each road segment within a BVCell by assigning weights proportional to its length. Given hour t, the TDI for BVCell s is the length-weighted average of the hourly jam factor values of all road segments within s. Any segment that spans multiple BVCells is clipped at the cell boundaries. Let Rs represent the set of road segments in BVCell s. Then, the spatially weighted TDI is defined as:

TDIt s = ∑_{r ∈ Rs} JFt r × Lr / ∑_{r ∈ Rs} Lr, (3)

where TDIt s denotes the TDI value for BVCell s at hour t and Lr is its length. The same calculation is performed separately for work and rest days, yielding two hourly TDI series for each BVCell.

Delineating urban systems

Urban systems are complex and can be characterized by three interconnected components: structure, form, and function8,13,59. These components constitute the “triple helix” of urban systems, involving their physical, morphological, and functional dimensions. Note that this differs from the “triple helix” model, often referred to as describing university-industry-government relations in innovation systems60, as our framework focuses specifically on the interplay among structure, form, and function of the urban environment. Here, urban structure constitutes the physical framework and network backbone of a city, primarily shaped by its transportation networks9. Then, urban form captures its morphological characteristics, such as spatial layouts, while urban function describes the roles and utilization of these spatial configurations11. To ensure cross-city comparability, we compute these urban system features from globally available OSM data and select variables based on three criteria: (i) representing complementary aspects of the three components; (ii) established interpretability in existing urban and transport studies; and (iii) consistent computability at the BVCell scale across cities.

Urban structure is a multifaceted concept, encompassing polycentricity, topological organization of road networks, and other related aspects61,62. This study focuses on the spatial structure of road networks derived from OSM data as the foundation for calculating topological features. To comprehensively characterize the road networks within each BVCell, we define urban structure metrics from three perspectives: (1) node-related metrics quantify the properties of intersections and junctions in the network, including node count (NODE_CT), node density (NODE_DENS), crossing count (CRS_CT), and average node degree (K_AVG); (2) edge-related metrics depict the properties of road segments in the network, including total length (EDGE_LEN), road density (RD_DENS), and network intensity (NET_INT); and (3) centrality-related metrics assess the importance and connectivity of road segments in the network, including average betweenness centrality (BTW_CEN), average closeness centrality (CLS_CEN), and average degree centrality (DEG_CEN).

Urban form defines the spatial layout and arrangements of the built environment, commonly measured through morphological metrics11,63. This study employs a comprehensive set of metrics at the landscape level to delineate urban form for each BVCell, categorized into four dimensions: (1) area-edge metrics quantify the size and edge characteristics of spatial units, including total area (TA), number of patches (NP), patch density (PD), total edge (TE), and edge density (ED); (2) shape metrics capture shape properties from the geometric perspective, such as landscape shape index (LSI), perimeter-area ratio (PARA), shape index (SHAPE), and fractal dimension (FRAC); (3) aggregation metrics describe the spatial cohesion or dispersion of patches, including contagion (CONTAG), aggregation index (AI), cohesion (COHES), and splitting index (SPLIT); and (4) diversity metrics reflect the variety and evenness of spatial patterns, using measures such as patch richness (PR), Shannons diversity index (SHDI), and Shannons evenness index (SHEI).

Urban function represents the socioeconomic and land-use attributes of urban space64. In this study, the functional features of each BVCell are quantified using the area percentage of various land-use types. The land-use classification system is established based on OSM datasets through a hierarchical computational framework65, with modifications to better align with human mobility patterns. The following land-use categories are used to depict urban functions: transportation area (TRNS), commercial and business facilities area (COMM), industrial area (IND), residential area (RES), farmland and forest area (FRST), education and science area (EDU), sports area (SPRT), park area (PARK), recreation area (RECR), water area (WATR), health care area (HLTH), cultural facilities area (CULT), and administration area (ADMIN).

Descriptions of the features characterizing urban structure, form, and function are provided in Supplementary Table 9. Interdependent by nature, these three dimensions represent distinct facets of urban systems, each influencing human mobility in different yet complementary ways. Essentially, urban structure provides the spatial framework that enables connectivity and accessibility, while urban form and function co-evolve to shape activity distribution and influence travel behavior. By differentiating these components, we can more comprehensively disentangle their unique contributions to traffic dynamics.

Spatio-temporal causality framework

We propose a spatio-temporal causality framework to investigate the bidirectional causal patterns between urban systems and traffic dynamics, comprising two complementary components: spatio-temporal weighted regression (STWR) and spatio-temporal convergent cross mapping (STCCM). The first step involves applying the STWR model to quantify the relationship between traffic dynamics and urban structure, form, and function. Throughout this process, the STWR model accounts for temporal variations while generating geographically weighted coefficients for urban system features at each location. To integrate insights from multiple metrics within each component of urban systems, such as the 16 metrics representing urban form, their geographically weighted coefficients are utilized to construct composite indicators for urban structure, form, and function, respectively. Then, the composite indicators serve as input to the STCCM model, which explores the bidirectional causal patterns between urban systems and traffic dynamics during congestion periods. Following this, a clustering approach grounded in bidirectional causality synthesizes the three urban system components to uncover patterns of similarity and differences across global cities.

Spatio-temporal weighted regression. To address spatial nonstationarity in geographical processes, the geographically weighted regression (GWR) model was introduced to account for spatial variability by estimating local parameters66. However, it struggles with temporal variations in dynamic systems, which prompted the development of spatio-temporal extensions that capture evolving patterns over space and time, such as spatio-temporal weighted regression (STWR) and geographically and temporally weighted regression (GTWR)21,67. Here, we adopt STWR for its ability to update spatio-temporal kernel functions and adjust temporal bandwidths dynamically, thereby better capturing complex spatio-temporal interactions and aligning with the rapidly changing nature of traffic dynamics.

When examining the relationship between urban systems and traffic dynamics, urban structure, form, and function features are assumed to remain constant over the one-month study period, as their temporal variations are expected to be negligible. However, the relationship between these static features and traffic dynamics can vary over time, capturing dynamic patterns inherent to traffic systems. To address multicollinearity, we employ the variance inflation factor (VIF) to iteratively identify and remove urban system features with VIF values above 10 before applying the STWR model (see Supplementary Fig. 3)68. Given k dependent variables from each component of urban systems, the formulation of STWR can be expressed as:

y(s,t) = β0(s,t) + ∑_{k=1}^{p} βk(s,t)xk(s) + ε(s,t), (4)

where y(s,t) is the dependent variable TDI for BVCell s at time t, xk(s) are the p independent variables for BVCell s, βk(s,t) are the coefficients that vary across both space and time, and ε(s,t) is the error term. During the estimation process, we employ a spatio-temporal bi-square kernel function to adaptively assign weights based on spatial and temporal proximity67. In addition, when implementing the STWR model, we include TDI from 06:00 to 23:00 to account for active human behavior while excluding non-service hours of urban infrastructure21. The performance comparisons of GWR and STWR are reported in Supplementary Tables 3 and 4 for rest and work days, respectively.

After deriving the spatially and temporally weighted coefficients from the STWR model, a bandwidth-based smoothing approach was employed to construct composite indicators for each component of urban systems. Given that βk(s,t) varies across spatial and temporal dimensions, a bi-square kernel function was applied to derive the smoothed coefficient β˜k(s,t) for feature k at location s and time t. Using the smoothed coefficients, the composite indicator for each BVCell was computed as a weighted sum of the input variables, incorporating both the intercept term and the contributions of each feature. The composite indicator CI(s,t) for BVCell s at time t was computed as:

CI(s,t) = β0(s,t) + ∑_{k=1}^{p} β˜k(s,t)xk(s), (5)

where xk(s) represents the standardized values of the independent variables. This composite indicator captures the aggregated impact of each urban system component on traffic dynamics, which retains critical spatial heterogeneity while reflecting the localized interactions between urban systems and mobility patterns. However, since these composite indicators are derived from a globally consistent feature set, cross-city differences in STWR model fit may reflect not only heterogeneous urban-traffic interactions but also the degree to which the selected variables capture locally salient determinants of traffic patterns.

In urban systems, strict stationarity is rarely plausible due to the inherent spatial heterogeneity and temporal non-stationarity of interactions between the built environment and traffic dynamics21,22,66. Consequently, our framework relaxes the stationarity requirement by first estimating spatially and temporally varying coefficients with STWR and then smoothing these coefficients with a bi-square kernel to construct composite indicators CI(s,t)67,69. This procedure yields quasi-stationary neighborhoods in which the association structure is approximately stable within the local support defined by the STWR kernel and the BVCell aggregation. Practically, the STWR bandwidth controls the bias-variance trade-off: narrower bandwidths preserve fine-grained heterogeneity but may retain more local noise, while wider bandwidths improve stability but may blend distinct local regimes. In addition, the BVCell buffer size determines the spatial support over which traffic and surrounding urban contexts are aggregated, thereby affecting the homogeneity of each cell. The choice of a 500-meter buffer is consistent with prior evidence on the scale of local traffic impacts5,16. Increasing this size would likely increase signal stability through aggregation but decrease the sensitivity to micro-scale urban system variations.

Spatio-temporal convergent cross mapping. Establishing causation, rather than merely identifying correlation, determines whether and how changes in one variable drive changes in another. So far, many methods have been developed to address this issue, such as structural causal models and causal graphical models70. Among them, convergent cross mapping (CCM) stands out for its capacity to infer both the presence and direction of causality in complex dynamical systems71. Building on CCM, the geographical convergent cross mapping (GCCM) model was introduced for spatial causal inference by utilizing spatial cross-sectional data and reconstructing state spaces34. Although GCCM effectively integrates geographical information, the lack of temporal dynamics makes it less suited for rapidly changing processes, such as traffic dynamics. To address this limitation and align with the STSWR model, we propose a customized temporal period selection model, i.e., spatio-temporal convergent cross mapping (STCCM), to capture the bidirectional causal pattern between urban systems and traffic dynamics under time-varying conditions.

STCCM builds upon the STWR-based composite indicator CI(s,t) to represent each component of urban systems, denoted as X(s,t) for BVCell s at time t, while the TDI is treated as Y(s,t). The objective of STCCM is to determine whether X can reconstruct Y and vice versa, thus elucidating the direction and strength of causal influences. Following Takens’ embedding theorem, the shadow manifolds MX and MY can be reconstructed from X and Y to preserve the topological equivalence of the original dynamical system30. Cross-mapping then leverages the correspondence between these shadow manifolds to infer causality. If X causes Y, information about X is encoded in MY, enabling predictions of X using MY; conversely, Y causing X allows predictions of Y using MX. In detail, the STCCM model is implemented in three steps: state space reconstruction, simplex projection, and bidirectional cross mapping.

State space reconstruction. We first reconstruct the state spaces MX and MY based on X and Y, respectively. Recognizing that congestion periods vary across locations and are spatially propagated57, we focus on the most congested period for each BVCell. This ensures that the reconstructed state space captures local spatial interactions under specific temporal conditions. In addition, as traffic patterns differ significantly between workdays and rest days, we separately consider these two scenarios. For BVCell s, we identify its most congested time ts and reconstruct its state space under this period. Given an embedding dimension E, the embedding vector for X(s,ts) is defined as:

X(s,ts) = [x(s,ts), x(s1,ts), ..., x(sE-1,ts)], (6)

where x(si,ts) represents the value of a lagged spatial unit si with order i at time ts. Here, the first-order spatial lag includes all adjacent BVCells to s, while second-order lags are derived from the first-order neighbors, and so forth34. Thus, the embedding dimension E determines how many spatial-lagged neighbors are included in the reconstructed state space, where a larger E corresponds to higher-order spatial neighborhoods. The sensitivity analysis of STCCM with varying E is reported in Supplementary Figs. 4 and 5. Fig. 5 provides a schematic illustration of spatial lags across different orders and time periods. Similarly, the embedding vector for Y(s,ts) that encapsulates local traffic patterns at time ts is constructed as:

Y(s,ts) = [y(s,ts), y(s1,ts), ..., y(sE-1,ts)]. (7)

Since each order of the spatial lag encompasses multiple BVCells, we apply a weighted averaging method to aggregate CI and TDI values across all BVCells within the order Si. The construction of x(si,ts) employs the BVCell area as the weighting coefficient for CI, while the road length within each BVCell serves as the weighting coefficient for TDI when constructing y(si,ts).

Simplex projection. Once the embeddings in the reconstructed state space are generated, STCCM employs a simplex projection scheme to quantify the causal influence between X(s,ts) and Y(s,ts). Simplex projection estimates the target variable by locating its nearest reconstructed states and forming a distance-weighted average of their observed values71. For BVCell s, we use a specific library size L to define a library set of BVCells, which are determined based on spatial proximity to s. Then, given x(s,ts), the value of y(s,ts) can be predicted according to its nearest neighbors identified from MX in this library set. Here, we set the number of nearest neighbors as E+171. Each neighbor contributes to the prediction through a weighted average of its corresponding target values, where the weights decrease with distance to prioritize closer neighbors. The predicted value for a target BVCell s at time ts is computed as:

yˆ(s,ts)|MX = ∑_{i=1}^{E+1} wsi y(si,ts) / ∑_{i=1}^{E+1} wsi, (8)

where wsi is the weight for the i-th nearest neighbor of s34.

Bidirectional cross mapping. To assess bidirectional causality, we can reverse the roles of X and Y in cross-mapping. The cross-mapping skill is quantified by the Pearson correlation coefficient ρ between the observed and the predicted values. A higher ρ indicates greater predictive skill and serves as a measure of causal strength. Specifically, X → Y uses X as the predictor variable to reconstruct the state space and predict Y, whereas Y → X uses Y as the predictor variable to reconstruct the state space and predict X. We vary the library size L in increments of 5, ranging from 5 to 500, to observe how ρ evolves as more BVCells are incorporated. For cities with a maximum library size smaller than 500, we use the largest library size permissible by the data, such as Manila. The causal influence is determined by comparing the cross-mapping skills ρX→Y and ρY→X. If ρX→Y converges with increasing library size and surpasses ρY→X, X is inferred to have a dominant causal influence on Y. Conversely, if ρY→X is higher, Y is inferred to dominate the causal relationship.

Since STCCM inputs are derived from locally fitted and smoothed STWR models, key scale parameters can influence the convergence behavior of the cross-mapping skill ρ with increasing library size L. Intuitively, a narrower STWR bandwidth (or finer BVCell partition) yields more localized and potentially more heterogeneous composite-indicator fields67,69, which can reduce the effective signal-to-noise ratio and lead to slower or less stable convergence in L-ρ curves. Conversely, overly large bandwidths (or coarse spatial aggregation) may blur distinct sub-regimes and attenuate causality signals by mixing mechanisms, producing flatter L-ρ curves and weaker separations between ρX→Y and ρY→X. Therefore, the selected bandwidth and BVCell buffer size should be interpreted as defining the operative scale of quasi-stationarity, within which the local causal diagnostics are valid.

To assess parameter robustness, we conducted a sensitivity analysis of the STCCM model by varying E at the largest L for both rest and work days across 30 cities, with results reported in Supplementary Figs. 4 and 5. In addition, we performed statistical significance tests on the cross-mapping skill derived from the STCCM model. As our analysis covers the full study area partitioned into BVCells, we utilize the distribution across these spatial units as a standardized basis for statistical testing. First, the statistical significance of ρ at each library size was evaluated using a one-sample Student’s t-test across all BVCells (see Supplementary Tables 5 and 6). Second, to verify the observed asymmetry, we assessed the significance of the difference between directional causal strengths (∆ρ = ρX→Y - ρY→X) at the largest library size. This was conducted using a paired Student’s t-test comparing the distributions of causal strengths in both directions across all BVCells for each city (see Supplementary Table 7). All tests reported are two-sided with a significance threshold of 0.05.

Bidirectional causality clustering for global cities. After deriving the bidirectional causal patterns between urban systems and traffic dynamics, we categorize global cities to explore their similarities and differences by analyzing the shape characteristics of the ρ-L curves. We employ two distinct distance measures to characterize the ρ-L curves for urban systems and their causal relationships with traffic dynamics across both work and rest days. The first measure, dynamic time warping (DTW), assesses the similarity of ρ-L curves by non-linearly aligning them to capture shape variations in bidirectional causal patterns72. The second measure, the Jaccard index, quantifies the overlap of areas under the curves to reflect the overall magnitude and distribution of causality influences across cities73.

Given the bidirectional causality results from STCCM for all library sizes within a city m, the two ρ-L curves are denoted as PmX→Y and PmY→X. The DTW distance DTW(m,n,r) between cities m and n for urban systems X ∈ {Xstr, Xfrm, Xfun} and traffic dynamics Y on rest days r is computed as follows:

DTW(m,n,r) = ∑_{X ∈ {Xstr, Xfrm, Xfun}} [DTW(PmX→Y, PnX→Y) + DTW(PmY→X, PnY→X)], (9)

where Xstr, Xfrm, and Xfun refer to structure, form, and function, respectively.

Similarly, we quantify magnitude differences using a Jaccard distance defined on regions under the bidirectional L-ρ curves over L ∈ [Lmin, Lmax], where [Lmin, Lmax] denotes the library-size range considered in STCCM. For each city m and dimension X ∈ {Xstr, Xfrm, Xfun} on rest days r, we define each directional region as the area between the curve and the L-axis (i.e., u=0):

A(m,r)X→Y = {(L,u): L ∈ [Lmin, Lmax], 0 ≤ u ≤ P(m,r)X→Y(L)}, (10)

A(m,r)Y→X = {(L,u): L ∈ [Lmin, Lmax], 0 ≤ u ≤ P(m,r)Y→X(L)}. (11)

In practice, each directional region is represented as a polygon by connecting sampled points (Li, ρ(Li)) and closing the boundary with u=0. The bidirectional region is then defined as A(m,r)X = A(m,r)X→Y ∪ A(m,r)Y→X. (12)

Given two cities m and n, the Jaccard index J(·) is computed as the intersection-over-union of these bidirectional regions:

J(A(m,r)X, A(n,r)X) = |A(m,r)X ∩ A(n,r)X| / |A(m,r)X ∪ A(n,r)X|, (13)

and the Jaccard distance is JaccardDist = 1 - J(·). Accordingly, the overall Jaccard distance between cities m and n on rest days r is computed as follows:

Jaccard(m,n,r) = ∑_{X ∈ {Xstr, Xfrm, Xfun}} JaccardDist(A(m,r)X, A(n,r)X). (14)

The overall distance D(m,n) between cities m and n is determined by a weighted combination of the normalized DTW and Jaccard distances, formulated as follows:

D(m,n) = λ(DTW′(m,n,r) + DTW′(m,n,w)) + (1 - λ)(Jaccard′(m,n,r) + Jaccard′(m,n,w)), (15)

where DTW′ and Jaccard′ represent the normalized DTW and Jaccard distances to ensure unit consistency. The parameter λ, set to 0.5, assigns equal weight to both measures. The subscripts r and w denote rest and work days, respectively. Then, hierarchical clustering is applied to the overall city-to-city distances D(m,n) to categorize global cities, enabling a multi-level exploration of urban similarities.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper introduces STCCM (spatio-temporal convergent cross mapping) to investigate bidirectional causal relationships between urban systems and traffic dynamics. The topic is timely and relevant: uncovering causal dependencies in urban processes remains a central yet underexplored challenge in urban science. The proposed approach has the potential to advance our understanding of how urban structure and traffic mutually influence each other. However, the presentation of the methodology and the results requires substantial improvement before the contribution can be properly assessed.\nDetailed comments\n1) Several key concepts are fully delegated to the Methods section. While technical details can indeed be confined there, the main text should still provide intuitive explanations of the central ideas. This is particularly true for STCCM, which represents the core methodological innovation of the paper. Without a conceptual introduction in the main text, readers cannot grasp the novelty or rationale of the method.\n2) The discussion would benefit from stronger engagement with recent studies on the interplay between urban form and traffic dynamics (e.g., https://arxiv.org/abs/2510.02582 , https://onlinelibrary.wiley.com/doi/10.1155/2023/6144048 , https://www.sciencedirect.com/science/article/abs/pii/S0966692321002532 ). These works provide useful benchmarks and could help position the proposed approach within the broader literature. The authors should systematically collect and discuss similar studies, emphasizing what STCCM adds conceptually or empirically.\n3) Some figures are difficult to interpret (e.g., Fig. 1f and Fig. 2a). Displaying all cities on a world map adds little to the understanding of the results. It would be clearer to present the graphs or scatter plots as standalone figures, perhaps selecting a subset of representative cities. This would considerably improve readability and allow the reader to focus on the patterns conveyed by the plots.\n4) The meaning of some features is not immediately intuitive. For instance, SPRT (sports area) is self-explanatory, but CONTAG (contagion) is not. The main text should briefly describe each feature the first time it is mentioned, so that the discussion can be followed without repeatedly consulting the Supplementary Information.\n5) Significance of ρ values in L–ρ analysis (Fig. 2b–d). In Figs. 2b-d, most cities appear close to the diagonal, suggesting that the estimated ρ values may not be statistically significant. The authors should clarify whether a threshold for the significance of ρ exists, how it is computed, and whether the reported relationships pass such a test. This is an important aspect for assessing the robustness of the findings.\n6) At line 202, the paper mentions the “Jaccard similarity” but does not specify what entities are being compared. This issue occurs in several instances: key technical aspects are mentioned without sufficient explanation, making the paper difficult to follow for readers unfamiliar with the specific computational pipeline.\nIn summary, the paper tackles an important and underexplored topic with a potentially valuable methodological contribution, but the clarity, contextualization, and interpretability of both the methods and results must be significantly improved.", "reviewer_3": "The current landscape of urban simulations, predictive, and optimization models is largely fragmented, with a predominant presence of solutions tailored to a specific cities or regions. Significant differences in urban layouts and traffic dynamics hamper the easy transfer of models between the cities. In modern conditions, when the pace of change in city infrastructure and mobility patterns can be compared to the pace of model development itself, the ability to accelerate the process by exploiting and fine-tuning results from similar cities becomes crucial. How can such similarity be defined and empirically evaluated so that cities can be meaningfully partitioned into clusters with similar traffic dynamics, and, moreover, similar types of interventions to reduce congestion?\nThe work answers this question for the first time by considering not only a single aspect (e.g. topology of the road network) but the interplay between structure, form, function and dynamics. This makes it highly significant not only for urban studies and geospatial science, but also for Urban AI applications, suggesting a set of interpretable variables that can serve as a context which conditions decision-making policies and facilitates transfer learning between cities. The latter is also supported by the city causal archetypes revealed in the analysis, which enable the identification of cities with similar coupling between urban systems and traffic dynamics. A second aspect defining the significance of the study is its focus on causation rather than correlation. This provides a foundation for scientifically justified transportation policies and interventions, as well as for designing assumptions and induction biases for intelligent transportation models which both are highly relevant and challenging problems in the field of intelligent transportation systems. In summary, this work is highly significant for several research fields including urban studies, geospatial science, intelligent transportation systems and data-driven traffic simulation.\nThe work is grounded in well-established literature on causal inference, spatio-temporal prediction models, geospatial information science and urban mobility studies. The application of Convergent Cross Mapping (CCM) to detect (potentially bidirectional) causalities is methodologically sound. The original CCM method assumes that the underlying dynamical system is stationary, so that the functional relationships between observables remain constant over time. However, this assumption may not hold for the systems under study which are characterized by spatial heterogeneity and temporal variability. The authors relax the strict stationarity assumption (similarly to GCCM but extending to both spatial and temporal dimensions) and propose novel ST-CCM method for bidirectional causal estimation in spatio-temporal systems. ST-CCM combines spatio-temporal CCM with spatio-temporal weighted regression (STWR) that smooths the original data into quasi-stationary, piecewise regions. The approach appears both methodologically innovative and practically sound, as it denoises the data and transforms them into a set of interpretable composite indicators which tend to be more stationary across space-time cells than the original variables. Since the data points to calculate the estimates of ρ are derived from locally fitted STWR regression models, a brief discussion on the theoretical and practical implications of relaxing the stationarity assumption (e.g. how the bandwidth of the STWR kernel or buffer size of Voronoi cells influence the convergence of ST-CCM, or how to interpret the results for the cities comprising sub-regions with highly heterogeneous structure, form or function), would further strengthen the methodological contribution of the study.\nIn the study, STWR models are estimated for three groups of variables representing urban structure, form, and function, and a single response variable related to traffic congestion. This enables a comparative evaluation of how well congestion can be explained by the composite indicators across cities worldwide. The results demonstrate that the proposed indicators have strong and significant correlation with traffic dynamics, with urban structure contributing more than form or function. A short discussion of the variable selection for composite indicators would further strengthen this result. For example, if the chosen variables primarily reflect certain types of cities, the regression model may exhibit lower explanatory power not only because the underlying processes differ, but also because the feature set is less representative for other urban contexts.\nThe third important result of the study is the development of hierarchical clustering approach that groups the cities according to the direction and strength of causality between urban structure, form, and function, and traffic dynamics), using ST-CCM outputs (L-ρ curves) as input data. The clustering results reveal the existence of three distinct causal archetypes of cities. This finding is highly relevant for scientifically grounded design of transportation policies and interventions, as the identified direction and strength of causality in a city highlights specific groups of measures that could be the most effective in mitigating congestion.\nThe work supports all its conclusions and claims, and no additional evidence is needed. In particular, the goodness of fit of the STWR regression for modelling the traffic indicator is supported by consistently high R^2 and AICc values compared to the GWR model. The authors evaluate the significance of ρ values for two library sizes, which aligns with standard CCM validation practice (see, e.g., Gao, B., Yang, J., Chen, Z. et al. Causal inference from cross-sectional earth system data with geographical convergent cross mapping. Nat Commun 14, 5875 (2023)). The general conclusions regarding the causal interplay between urban systems and traffic dynamics, as well as the explanatory power of the urban structure, form, and function composite indicators, are well supported by the extensive dataset covering 30 cities on multiple continents. Moreover, the uniformity of the traffic congestion data which are sourced from the same provider and tested for spatial and temporal representativeness, adds credibility to the reported findings.\nThe study provides enough details in the methods to ensure reproducibility. As a minor suggestion, in Figure 1c-e, the zero reference line in the violin plots is difficult to distinguish due to the grey dotted style. Enhancing its visibility would help readers interpret whether the distributions lie above or below the mean.\nIn summary, the study is methodologically sound, meets the expected standards of the field, and has substantial potential impact across several research domains, as well as practical implications for the development of more efficient transportation policies and models. The work can therefore be recommended for a publication after minor revision."}, "author_response": "Response to Reviewers\nReviewer #1 (Remarks to the Author):\nThis paper introduces STCCM (spatio-temporal convergent cross mapping) to investigate\nbidirectional causal relationships between urban systems and traffic dynamics. The topic is timely\nand relevant: uncovering causal dependencies in urban processes remains a central yet\nunderexplored challenge in urban science. The proposed approach has the potential to advance our\nunderstanding of how urban structure and traffic mutually influence each other. However, the\npresentation of the methodology and the results requires substantial improvement before the\ncontribution can be properly assessed.\nResponse: We would like to express our sincere gratitude for your constructive assessment of\nour work, especially regarding the timeliness of the problem and the potential of STCCM. We also\nacknowledge your central concern that, in the original manuscript, key methodological ideas and\nparts of the computational pipeline were not presented intuitively enough in the main text, making\nit difficult for readers to assess the novelty and interpret the results.\nIn the revised manuscript, we substantially strengthened the presentation and interpretability\nof the manuscript. In detail, we (i) added a clear non-technical conceptual introduction of STCCM\nin the main text and clarified how it integrates with STWR; (ii) expanded and better positioned our\nwork within the recent literature on urban systems and traffic dynamics; (iii) redesigned figures that\nwere hard to interpret (most notably Fig. 1f and Fig. 2a) by separating city-level plots from the\nworld map and improving legibility; (iv) added brief and intuitive definitions for non-obvious\nfeatures at first mention; (v) made the statistical validation of cross-mapping skill (𝜌) and directional\nasymmetry (∆𝜌) explicit and easy to follow; and (vi) clarified previously under-specified technical\nelements (e.g., Jaccard similarity, DTW, embedding dimension, simplex projection) at their first\nappearance.\nWe believe these revisions have fundamentally improved the clarity and accessibility of the\nmanuscript. We provide a point-by-point response to your detailed comments below.\nDetailed comments\n1) Several key concepts are fully delegated to the Methods section. While technical details can\nindeed be confined there, the main text should still provide intuitive explanations of the central ideas.\nThis is particularly true for STCCM, which represents the core methodological innovation of the\npaper. Without a conceptual introduction in the main text, readers cannot grasp the novelty or\nrationale of the method.\nResponse: Thank you very much for this insightful comment! We fully agree that the main text\nshould include intuitive explanations of the key methodological concepts so that readers can better\nunderstand their novelty and rationale. In the revised manuscript, we have made several changes to\naddress this concern.\nIn the Introduction section, we have added an intuitive description of STCCM that conveys its\n1\ncore idea in non-technical terms. This complements the formal methodological exposition and\nmakes the underlying rationale accessible to readers unfamiliar with CCM-based approaches. We\nalso clarify the respective roles of STWR and STCCM in the spatio-temporal causality framework,\nexplaining how the two components jointly bridge correlation and causation. These changes can be\nfound in Lines 63-72 on Page 3: “Intuitively, STCCM uncovers causal relationships by examining\nwhether the spatio-temporal evolution of one process, such as traffic dynamics during congestion\nperiods, embeds information that allows the recovery of another process within the joint state space\nof interacting urban systems. The framework combines STCCM with spatio-temporal weighted\nregression (STWR) (see Methods). In detail, STWR first characterizes the spatially heterogeneous\nand temporally varying relationships between urban systems and traffic dynamics, and then\nsynthesizes these locally estimated effects into composite indicators that capture the combined\ninfluence of urban structure, form, and function. Subsequently, STCCM uses these composite\nindicators to infer nonlinear and bidirectional causal pathways during congestion periods, when\nmobility-infrastructure mismatches amplify causal signals and make them more detectable and\npolicy-relevant.”\nIn the Result section for STWR, we revised the description of STWR to make the notions of\nspatial heterogeneity and temporal variation more transparent to readers in Lines 89-90 on Page 4:\n“The STWR model is then employed to quantify these relationships, allowing the strength of\nassociation to vary across space and time rather than imposing a single global effect.”\nIn the Result section for STCCM, before introducing Fig. 2, we now explicitly explain how to\ninterpret the L-𝜌 plots and why the convergence of 𝜌 with increasing library size 𝐿 is regarded as\nevidence of causality, which provides the basis for understanding the strength and direction of causal\neffects. The revisions are in Lines 158-170 on Pages 7-8: “Each L-𝜌 plot serves as a diagnostic tool\nfor causal inference, illustrating how predictability evolves with increasing library size L. Here, L\nrepresents the number of observations used for state-space reconstruction, while 𝜌 represents the\ncross-mapping skill of one variable based on another, i.e., how well one variable recovers the state\nof the other. For each city and each component of the urban system, we generate two L-𝜌 curves:\none for urban systems → traffic dynamics and one for traffic dynamics → urban systems.\nCrucially, evidence of causality is established not by a static 𝜌 value, but by the property of\nconvergence: a curve that rises and stabilizes at higher 𝜌 values as L grows. This trend indicates a\nrobust causal signal, as additional observations improve coverage of the reconstructed state space\nand help reveal the underlying deterministic rules of the system [34]. Furthermore, the shaded\nregions between the two curves in Fig. 2(a) highlight the magnitude of asymmetry (∆𝜌) between the\nbidirectional influences. Consequently, for a given urban system indicator X and traffic dynamics\nindicator Y, if the 𝜌 values for X → Y consistently exceed those for Y → X as L increases, X is\ninferred to be the dominant causal driver of Y, and vice versa.”\nTaken together, these additions provide readers with intuitive and high-level explanations of\nSTCCM and its integration with STWR directly in the main text, while leaving the mathematical\n2\ndetails in the Methods section. We believe these revisions address your concern and make the core\nmethodological innovation of the paper much more transparent and interpretable.\n2) The discussion would benefit from stronger engagement with recent studies on the interplay\nbetween urban form and traffic dynamics (e.g., https://arxiv.org/abs/2510.02582\n, https://onlinelibrary.wiley.com/doi/10.1155/2023/6144048\n, https://www.sciencedirect.com/science/article/abs/pii/S0966692321002532\n). These works provide useful benchmarks and could help position the proposed approach within\nthe broader literature. The authors should systematically collect and discuss similar studies,\nemphasizing what STCCM adds conceptually or empirically.\nResponse: Thank you very much for this helpful suggestion! In the revised version, we have\nstrengthened the manuscript’s engagement with recent work on the interplay between urban systems\nand traffic dynamics. We expanded the literature coverage by incorporating the three benchmark\nstudies you suggested and adding several closely related studies, and we revised the main text to\nsummarize how these studies typically model urban systems and traffic dynamics. Building on this\nexpanded context, we also clarified the conceptual and empirical contributions of STCCM,\nparticularly its ability to provide bidirectional and asymmetric causal diagnostics that are\ncomparable across cities and day types.\nIn the Introduction section, we have reframed the paragraph that reviews previous evidence\nlinking built-environment factors to traffic dynamics, and we also briefly organize the commonly\nused modelling approaches. In addition, we explicitly incorporated the three benchmark studies (i.e.,\nroute diversification in road networks, POI-based road-function analysis, and street-network design\neffects), alongside other closely related studies, to provide a more systematic context. The revised\ncontent is shown in Lines 21-35 on Page 2: “In particular, built-environment factors, ranging from\nurban morphology indices and land-use types to network structure, have been shown to exert\nsignificant influences on traffic states and congestion patterns across diverse metropolitan contexts\n[15, 18-20]. To investigate these complex interactions between urban systems and traffic dynamics,\nmany methodological approaches have been adopted, including global statistical and econometric\nmodels for uncovering macro-level determinants and longitudinal dependencies [15, 19], local and\nspatio-temporal varying-coefficient models for characterizing spatiotemporal heterogeneity and\ndynamic associations [21, 22], and computational data-driven frameworks for capturing nonlinear\ndynamics and fine-grained mobility patterns [2, 3, 23]. Furthermore, such methodological advances\nhave been deployed in detailed case studies to quantify route diversification capabilities within\nnetwork topologies [24], assess the influence of road functions on localized congestion [25], and\nevaluate the impacts of street design and intersection density on traffic performance [18].\nCollectively, these studies establish important empirical benchmarks on the interplay between urban\nsystems and traffic dynamics, underscoring that both supply-side factors (e.g., network structure)\nand demand-side factors (e.g., land-use and activity patterns) within the built environment are\n3\ncritical determinants of traffic states.”\nIn the Discussion section, we have added a new paragraph to connect our findings with these\nbenchmarks and to position STCCM within the broader literature. We highlight that most prior\nevidence remains association-based, whereas STCCM provides bidirectional and potentially\nasymmetric causal diagnostics and yields comparable causal fingerprints across cities and between\nrest and work days. Then, we also discuss the implications of these fingerprints for context-sensitive\ncongestion mitigation strategies that coordinate land-use configuration, activity distribution, and\nnetwork operations. The added paragraph is shown in Lines 334-345 on Page 14: “Our empirical\nfindings are broadly consistent with, yet also extend, previous evidence on the links between urban\nsystems and traffic dynamics [18-20, 24, 25]. By moving from correlations to explicit causal\ninference, our spatio-temporal causality framework complements this literature in two ways.\nConceptually, a large share of existing work relies on global or locally varying associations [15,\n22], which are valuable for explanation and prediction but do not directly resolve directionality or\nfeedback. In contrast, the STCCM model provides bidirectional and potentially asymmetric causal\ndiagnostics, enabling a comparable assessment of how urban structure, form, and function exert\ndirectional influence on traffic dynamics across cities and between rest and work days. Empirically,\nthe resulting causal fingerprints reveal recurring causal patterns and cross-city regularities, while\nalso highlighting substantial context dependence. These findings suggest that interventions focusing\nsolely on network supply may overlook critical demand-side mechanisms embedded in urban form\nand function. Consequently, effective mitigation requires a synergistic approach that coordinates\nland-use configuration and activity distribution with network operations, tailored to local causal\npathways.”\nWe believe these revisions provide a clearer and more up-to-date positioning of our study and\nstrengthen the discussion of what STCCM adds beyond existing benchmark approaches.\nReferences:\n[2] L. Pappalardo, E. Manley, V. Sekara, L. Alessandretti, Future directions in human mobility\nscience, Nature Computational Science 3 (2023) 588–600. doi: 10.1038/s43588-023-00469-4.\n[3] J. Cao, W. Tu, R. Cao, Q. Gao, G. Chen, Q. Li, Untangling the association between urban\nmobility and urban elements, Geo-spatial Information Science 27 (2024) 1071–1089. doi:\n10.1080/10095020.2022.2157761.\n[15] M. Wang, N. Debbage, Urban morphology and traffic congestion: Longitudinal evidence from\nus cities, Computers, Environment and Urban Systems 89 (2021) 101676. doi:\n10.1016/j.compenvurbsys.2021.101676.\n[18] D.-a. Choi, R. Ewing, Effect of street network design on traffic congestion and traffic safety,\nJournal of Transport Geography 96 (2021) 103200. doi: 10.1016/j.jtrangeo.2021.103200.\n[19] M. M. Rahman, P. Najaf, M. G. Fields, J.-C. Thill, Traffic congestion and its urban scale factors:\nEmpirical evidence from American urban areas, International Journal of Sustainable\nTransportation 16 (2022) 406–421. doi: 10.1080/15568318.2021.1885085.\n[20] D. Xiao, I. Kim, N. Zheng, Does built environment have impact on traffic congestion?—a\nbootstrap mediation analysis on a case study of Melbourne, Transportation Research Part A: Policy\nand Practice 190 (2024) 104297. doi: 10.1016/j.tra.2024.104297.\n[21] X. Ma, J. Zhang, C. Ding, Y. Wang, A geographically and temporally weighted regression\nmodel to explore the spatiotemporal influence of built environment on transit ridership, Computers,\nEnvironment and Urban Systems 70 (2018) 113–124. doi: 10.1016/j.compenvurbsys.2018.03.001.\n[22] H. Liu, W. Zhang, S. Wang, Z. Cheng, L. Wei, W. Huang, Exploring the effect of built\nenvironment on spatiotemporal evolution of traffic congestion using a novel GTWR model: a case\nstudy of Hefei, China, Transportation Letters 17 (2025) 869–880. doi:\n10.1080/19427867.2024.2396773.\n[23] Z. Kan, D. Liu, X. Yang, J. Lee, Measuring exposure and contribution of different types of\nactivity travels to traffic congestion using GPS trajectory data, Journal of Transport Geography 117\n(2024) 103896. doi: 10.1016/j.jtrangeo.2024.103896.\n[24] G. Cornacchia, L. Pappalardo, M. Nanni, D. Pedreschi, M. C. González, A computational\nframework for quantifying route diversification in road networks, arXiv preprint arXiv:2510.02582\n(2025). doi: 10.48550/arXiv.2510.02582.\n[25] H. Zhu, K. Zhang, C. Wang, L. Jia, S. Song, The impact of road functions on road congestions\nbased on POI clustering: An empirical analysis in Xi’an, China, Journal of Advanced Transportation\n2023 (2023) 6144048. doi: 10.1155/2023/6144048.\n3) Some figures are difficult to interpret (e.g., Fig. 1f and Fig. 2a). Displaying all cities on a world\nmap adds little to the understanding of the results. It would be clearer to present the graphs or scatter\nplots as standalone figures, perhaps selecting a subset of representative cities. This would\nconsiderably improve readability and allow the reader to focus on the patterns conveyed by the plots.\nResponse: Thank you for highlighting the readability issue. We agree that embedding many\nsmall plots within a global map made the original figures difficult to interpret, particularly for\nregions with dense cities (e.g., Europe and Southeast Asia). The combination of highly compressed\npanels and connecting leader lines also introduced visual clutter that obscured city-specific patterns.\nTo address this, we redesigned Fig. 1f and Fig. 2a by presenting the city-level results as\nstandalone small-multiple panels arranged in a clean grid, rather than placing the plots on the world\nmap. This redesign allows each panel to be substantially enlarged, making the STWR fingerprints\nin Fig. 1f and the L-𝜌 convergence curves in Fig. 2a clearly legible. To retain the worldwide context\nwithout sacrificing readability, we now include a simplified world map only as a spatial locator,\nshowing the geographic distribution of the 30 cities without embedding any analytical plots. Cities\nare grouped by region using color-coded boxes, and the same colors are applied on the locator map,\nallowing immediate cross-referencing between the map and the corresponding panel groups. We\nalso removed the crowded leader lines and labeled each city directly beneath its panel.\nIn addition, we have redrawn the individual L-𝜌 plots for each city in Fig. 2a, increasing the\n5\nfont size and clarity of the x- and y-axis labels to ensure they are easily readable. Fig. 2a now also\nincludes visual annotations (zoom-in indicators and ∆𝜌 shading cues) to clarify how the plotted\nelements should be interpreted. We also clarified this in the revised caption: “The enlarged view on\nthe right magnifies the trends at large library sizes to clearly reveal the directional difference in\ncausal strength, while the shaded regions between the curves highlight the magnitude of asymmetry\n(∆𝜌) between the bidirectional causal influences.”\nWe considered showing only a subset of representative cities. However, this study discusses\npatterns across all 30 cities and is framed from a worldwide perspective. Since the new grid layout\nresolves the crowding problem while maintaining clarity, we retained the complete set of cities to\nprovide a comprehensive view and to avoid any perception of selective presentation. This also\nallows readers to directly verify results for any city referenced in the main text without repeatedly\nconsulting the Supplementary Information. The locator map remains intentionally minimal and is\nincluded solely for geographical context.\nWe believe these revisions directly address the concern about interpretability and enable\nreaders to focus on the patterns conveyed by the plots. We implemented the same redesign principles\nfor Extended Data Figs 1 and 2. The revised figures of Fig. 1f and Fig. 2a are as follows.\n6\n4) The meaning of some features is not immediately intuitive. For instance, SPRT (sports area) is\nself-explanatory, but CONTAG (contagion) is not. The main text should briefly describe each\nfeature the first time it is mentioned, so that the discussion can be followed without repeatedly\nconsulting the Supplementary Information.\nResponse: We appreciate your insightful suggestion to provide brief descriptions for features\nin the main text. Following this, we have revised the main text and added intuitive explanations for\nfeatures that are not self-explanatory when they first appear, including CRS_CT, RD_DENS, NP,\nCONTAG, TE, ED, and SHEI. These revisions are primarily located in the Results section (Pages\n5-7). For clarity, the brief explanations are summarized below:\n CRS_CT: crossing count, the number of road intersections (Line 131, Page 5).\n RD_DENS: road density, the total road length per unit area (Line 131, Page 5).\n NP: number of patches, the total number of land-use patches (Line 133, Page 5).\n CONTAG: contagion, the degree to which land-use patches are clumped or dispersed (Line\n134, Page 5).\n TE: total edge, the total length of all patch edges (Line 137, Page 7).\n ED: edge density, the total length of all patch edges per unit area (Line 137, Page 7).\n SHEI: Shannon’s evenness index, the evenness of area distribution among patch types (Fig. 1,\nPage 6).\nTo further support readability, we have also added Supplementary Table 9, which provides\nconcise descriptions for all features used to characterize urban structure, form, and function.\nSupplementary Table 9. Descriptions of features characterizing urban structure, form, and function\nAbbreviation Full Name Definition\nNODE_CT Node Count The number of nodes in the road network.\nNODE_DENS Node Density The number of nodes per unit area.\nCRS_CT Crossing Count The number of road intersections.\nK_AVG Average Node Degree The average degree of nodes in the road network.\nEDGE_LEN Total Length The total length of road segments.\nRD_DENS Road Density The total road length per unit area.\nThe total length of road segments normalized by the cell\nNET_INT Network Intensity\nperimeter.\nAverage Betweenness The average of the fraction of shortest paths that pass\nBTW_CEN\nCentrality through each node.\nAverage Closeness The average reciprocal of the sum of the shortest path\nCLS_CEN\nCentrality distances from a node to all other nodes.\nAverage Degree\nDEG_CEN The average normalized degree of nodes within the cell.\nCentrality\nTA Total Area The total area of land-use patches.\nNP Number of Patches The total number of land-use patches.\nPD Patch Density The number of land-use patches per unit area.\nTE Total Edge The total length of all patch edges.\nED Edge Density The total length of all patch edges per unit area.\nThe average perimeter-area ratio across all patches\nPARA Perimeter-Area Ratio\nwithin the cell.\nThe average shape index across all patches, quantifying\nSHAPE Shape Index\nhow much patch shapes deviate from compact forms.\nThe average fractal dimension of all patches, describing\nFRAC Fractal Dimension\nhow perimeter complexity scales with patch size.\nThe degree to which land-use patches are clumped or\nCONTAG Contagion\ndispersed.\nThe measure indicating how closely land-use patches\nAI Aggregation Index\nare clustered together.\nThe physical connectedness of land-use patches within\nCOHES Cohesion\nthe cell.\nThe fragmentation reflecting the degree of landscape\nSPLIT Splitting Index\nsubdivision.\nPR Patch Richness The total number of distinct patch types.\nShannon’s Diversity\nSHDI The diversity of area distribution among patch types.\nIndex\nShannon’s Evenness\nSHEI The evenness of area distribution among patch types.\nIndex\nThe percentage of land designated for transport\nTRNS Transportation Area\ninfrastructure.\nCommercial and The percentage of land used for commerce, finance,\nCOMM\nBusiness Facilities Area hospitality, and retail.\nThe percentage of land used for industrial production\nIND Industrial Area\nand extraction.\nThe percentage of land designated for housing and\nRES Residential Area\nliving quarters.\nFarmland and Forest The percentage of natural, semi-natural, and productive\nFRST\nArea rural land.\nEducation and Science The percentage of land dedicated to educational and\nEDU\nArea research institutions.\nThe percentage of land used for physical sports and\nSPRT Sports Area\nathletic activities.\nThe percentage of public green spaces and manicured\nPARK Park Area\nvegetation.\nThe percentage of land used for leisure, tourism, and\nRECR Recreation Area\nentertainment.\nWATR Water Area The percentage of land covered by water bodies.\nThe percentage of land used for medical and care\nHLTH Health Care Area\nservices.\nThe percentage of land used for cultural arts and public\nCULT Cultural Facilities Area\ngatherings.\nADMIN Administration Area\nadministration.\nThese additions ensure that key features are understandable directly within the main text, while\nthe Supplementary Information offers a reference for readers who wish to explore all features in\ndetail.\n5) Significance of ρ values in L-ρ analysis (Fig. 2b-d). In Figs. 2b-d, most cities appear close to the\ndiagonal, suggesting that the estimated ρ values may not be statistically significant. The authors\nshould clarify whether a threshold for the significance of ρ exists, how it is computed, and whether\nthe reported relationships pass such a test. This is an important aspect for assessing the robustness\nof the findings.\nResponse: Thank you for this important observation! We note that proximity to the 45°\ndiagonal in Fig. 2b-d indicates that the two directional cross-mapping skills are similar in magnitude\n(i.e., weak asymmetry), rather than implying that the 𝜌 values themselves are close to zero or\nstatistically non-significant. To explicitly address statistical significance and robustness, we\nconducted formal tests for (i) the significance of 𝜌 and (ii) the significance of directional asymmetry\n(∆𝜌). All tests are two-sided with a significance threshold of 0.05.\nFirst, regarding the significance of 𝜌, our statistical validation was originally detailed only in\nthe Supplementary Information and not sufficiently highlighted in the main text. We appreciate you\npointing this out, as it is indeed crucial for assessing robustness. To clarify whether a threshold for\nthe significance of 𝜌 exists, we conducted a two-sided one-sample t-test on the distribution of 𝜌\nvalues across all BVCells. We find that the estimated 𝜌 values for all 30 cities (across urban structure,\nform, and function) are statistically significant (p < 0.001; see Supplementary Tables 5 and 6).\nSecond, to address the concern that points near the diagonal might imply indistinguishable\nbidirectional effects, we explicitly tested the significance of the asymmetry using the difference in\ntheir 𝜌 values, i.e., ∆𝜌 =𝜌 −𝜌 . We\nurban systems→traffic dynamics traffic dynamics→urban systems\nperformed two-sided paired Student’s t-tests to compare BVCell-wise 𝜌 values in both directions\nfor each city. As detailed in the newly added Supplementary Table 7, the asymmetry is statistically\nsignificant for the majority of cities, even those visually close to the diagonal. For example, on rest\ndays, significant asymmetry was observed in 26, 29, and 27 out of 30 cities for urban structure,\nform, and function, respectively. Notably, among these significant cases, the majority surpass the high\nsignificance threshold of p < 0.001.\nThe revisions in the manuscript are summarized as follows:\nIn the Methods section, we explicitly described the one-sample and paired Student's t-tests in\nLines 656-664 on Pages 26-27: “In addition, we performed statistical significance tests on the cross-\nmapping skill derived from the STCCM model. As our analysis covers the full study area partitioned\ninto BVCells, we utilize the distribution across these spatial units as a standardized basis for\nstatistical testing. First, the statistical significance of 𝜌 at each library size was evaluated using a\none-sample Student’s t-test across all BVCells (see Supplementary Tables 5 and 6). Second, to verify\n9\nthe observed asymmetry, we assessed the significance of the difference between directional causal\nstrengths (∆𝜌 =𝜌 −𝜌 ) at the largest library size. This was conducted using a paired\n𝑋→𝑌 𝑌→𝑋\nStudent’s t-test comparing the distributions of causal strengths in both directions across all BVCells\nfor each city (see Supplementary Table 7). All tests reported are two-sided with a significance\nthreshold of 0.05.”\nIn the Results section, we discussed the statistical significance of both 𝜌 and ∆𝜌 to support\nthe interpretation of Fig. 2 in Lines 201-208 on Pages 9-10: “Although some cities near the diagonal\nmight suggest a balanced interaction, statistical tests support the robustness of these relationships.\nSpecifically, the estimated causal strengths (𝜌) are statistically significant across all 30 cities (p <\n0.001; see Supplementary Table 5). Furthermore, despite the visual proximity to the diagonal,\npaired t-tests reveal that the asymmetry (∆𝜌) remains statistically significant for the majority of\ncities on rest days, specifically in 26, 29, and 27 out of 30 cities for urban structure, form, and\nfunction, respectively (see Supplementary Table 7). Together, these results statistically support the\nconclusion that urban systems more often exert a dominant influence on traffic dynamics, consistent\nwith the asymmetric nature of the causality.”\nWe also added Supplementary Table 7 reporting the ∆𝜌 values and their significance.\nSupplementary Table 7. Statistical assessment of the causal asymmetry (∆𝜌) between urban systems\nand traffic dynamics across 30 cities. The table reports the mean difference in cross-mapping skill\nat the largest library size, defined as ∆𝜌 =𝜌 −\nurban systems→traffic dynamics\n𝜌 . A positive value indicates that urban systems exert a stronger causal\ntraffic dynamics→urban systems\ninfluence on traffic dynamics, while a negative value implies the reverse. Statistical significance\nwas evaluated using a paired Student’s t-test comparing the distributions of causal strengths in both\ndirections across all BVCells for each city, with two-sided p-values reported.”\nRest days Work days\nCity\nStructure ∆𝜌 Form ∆𝜌 Function ∆𝜌 Structure ∆𝜌 Form ∆𝜌 Function ∆𝜌\nLondon 0.011*** 0.071*** 0.054*** -0.002 0.052*** 0.013***\nParis 0.013*** 0.046*** 0.076*** 0.016*** 0.048*** 0.063***\nZurich -0.011 0.047*** 0.059*** -0.045*** -0.096*** -0.030***\nRome 0.052*** 0.077*** 0.090*** 0.084*** 0.031*** 0.110***\nVienna 0.004 -0.004 0.014*** 0.011** 0.040*** 0.024***\nBerlin 0.010*** 0.028*** 0.042*** -0.019*** 0.063*** 0.021***\nStockholm 0.039*** 0.049*** 0.033*** 0.004 0.028*** 0.030***\nHelsinki 0.019*** 0.031*** 0.018*** 0.016*** 0.005* 0.018***\nSt. Petersburg 0.048*** 0.079*** 0.086*** 0.054*** 0.109*** 0.079***\nMoscow 0.033*** 0.109*** 0.065*** 0.030*** 0.076*** 0.058***\nRiyadh 0.063*** 0.132*** 0.101*** 0.062*** 0.119*** 0.134***\nDubai 0.019*** 0.044*** 0.043*** 0.021*** 0.043*** 0.015***\nNew Delhi 0.054*** 0.122*** 0.120*** 0.073*** 0.165*** 0.133***\nMumbai 0.015*** -0.023*** 0.097*** 0.005* -0.053*** 0.072***\nBangkok 0.055*** 0.024*** 0.067*** 0.043*** 0.033*** 0.068***\nHong Kong -0.010*** 0.018*** 0.000 -0.061*** -0.011*** -0.023***\nKuala Lumpur 0.063*** 0.055*** 0.132*** 0.093*** 0.105*** 0.123***\nSingapore 0.043*** 0.090*** 0.063*** 0.071*** 0.122*** 0.087***\nJakarta 0.056*** 0.030*** -0.001 0.054*** 0.046*** -0.003ns\nSydney 0.157*** 0.139*** 0.186*** -0.037*** -0.059*** -0.054***\nChristchurch -0.054*** 0.020*** -0.005 -0.081*** -0.037*** 0.028***\nLos Angeles 0.005*** 0.042*** -0.014*** -0.021*** 0.026*** -0.019***\nChicago 0.023*** 0.078*** 0.087*** 0.020*** 0.040*** 0.031***\nToronto 0.015*** 0.041*** 0.025*** -0.015*** 0.016*** 0.030***\nMexico City -0.005** 0.009*** 0.023*** 0.060*** 0.056*** 0.225***\nLima 0.001 -0.004* 0.015*** 0.019*** -0.008*** 0.029***\nBuenos Aires 0.049*** 0.093*** 0.116*** -0.007** 0.034*** 0.036***\nRio de Janeiro -0.002 -0.017*** 0.044*** -0.006** 0.027*** -0.035***\nCape Town -0.013*** 0.069*** 0.055*** 0.019*** 0.023*** -0.025***\nFinally, we updated the captions for Fig. 2 and Supplementary Tables 5 and 6 to reflect the\nstatistical method. In Fig. 2, we added the statement: “Note that all plotted cities exhibit statistically\nsignificant causal relationships (𝜌) at the p < 0.001 level. Detailed significance tests for both 𝜌 and\nthe directional asymmetry (∆𝜌) are provided in Supplementary Tables 5 and 7.” In Supplementary\nTables 5 and 6, we specified: “Statistical significance was evaluated using a one-sample Student's\nt-test on the distribution of 𝜌 values across all BVCells at each library size, with two-sided p-values\nreported.”\nThese tests clarify that although cities appear close to the diagonal, the estimated 𝜌 values are\nstatistically significant. Furthermore, these results validate the existence of the bidirectional yet\nasymmetric causality between urban systems and traffic dynamics reported in our study.\n6) At line 202, the paper mentions the “Jaccard similarity” but does not specify what entities are\nbeing compared. This issue occurs in several instances: key technical aspects are mentioned without\nsufficient explanation, making the paper difficult to follow for readers unfamiliar with the specific\ncomputational pipeline.\nResponse: Thank you very much for pointing out this critical issue. We have revised the main\ntext to clarify how the Jaccard-based measure is used in our framework. Specifically, we now state\nthat the Jaccard distance measures the dissimilarity between the enclosed areas under the\nbidirectional L-𝜌 causality curves of two cities, thereby reflecting differences in the overall\nmagnitude of their causal influence. We also carefully reviewed the manuscript to identify similar\ncases where key technical aspects were mentioned without sufficient explanation. Following your\nsuggestion, we now provide brief descriptions at the first appearance of the following concepts in\nthe main text:\n Jaccard similarity: “In contrast, the Jaccard distance quantifies the dissimilarity in the\nenclosed areas of these bidirectional L-𝜌 curves, reflecting differences in the overall magnitude\nof their causal influence.” (Lines 238-240, Pages 10-11).\n Dynamic time warping: “Specifically, dynamic time warping (DTW) evaluates the shape\ndifference between the bidirectional L-𝜌 curves of two cities, capturing variations in the\ntemporal patterns of causality.” (Lines 236-238, Page 10).\n Embedding dimension: “Thus, the embedding dimension E determines how many spatial-\nlagged neighbors are included in the reconstructed state space, where a larger E corresponds\nto higher-order spatial neighborhoods. The sensitivity analysis of STCCM with varying E is\nreported in Supplementary Figs. 2 and 3.” (Lines 614-617, Pages 24-25).\n Simplex projection: “Simplex projection estimates the target variable by locating its nearest\nreconstructed states and forming a distance-weighted average of their observed values.”\n(Lines 624-626, Page 25).\nTogether with the revisions made in response to Comments 1 and 4, we believe that the revised\nmanuscript now allows readers who are less familiar with the computational pipeline to follow the\nmethodological logic directly from the main text.\nIn summary, the paper tackles an important and underexplored topic with a potentially valuable\nmethodological contribution, but the clarity, contextualization, and interpretability of both the\nmethods and results must be significantly improved.\nResponse: Thank you very much for this concluding remark. We appreciate your recognition\nof the study’s potential value, and we have focused our revision on the three areas you highlighted:\nclarity (via intuitive conceptual explanations), contextualization (via benchmarking with recent\nliterature), and interpretability (via figure redesign and rigorous statistical validation). We believe\nthese improvements now allow readers to assess methodological contribution and the results more\nclearly.\nReviewer #1 (Remarks on code availability):\nThe repository's README file describes the code structure, data organization, and system\nrequirements necessary to replicate the study. Although I did not attempt a full replication, the\nrepository appears to provide sufficient information and resources to enable reproducibility.\nResponse: Thank you for your remarks on code availability and reproducibility. We appreciate\nyour careful check of the repository documentation and your assessment that the README provides\nsufficient details to support replication.\nReviewer #3 (Remarks to the Author):\nThe current landscape of urban simulations, predictive, and optimization models is largely\nfragmented, with a predominant presence of solutions tailored to a specific cities or regions.\nSignificant differences in urban layouts and traffic dynamics hamper the easy transfer of models\nbetween the cities. In modern conditions, when the pace of change in city infrastructure and mobility\npatterns can be compared to the pace of model development itself, the ability to accelerate the\nprocess by exploiting and fine-tuning results from similar cities becomes crucial. How can such\nsimilarity be defined and empirically evaluated so that cities can be meaningfully partitioned into\nclusters with similar traffic dynamics, and, moreover, similar types of interventions to reduce\ncongestion?\nThe work answers this question for the first time by considering not only a single aspect (e.g.\ntopology of the road network) but the interplay between structure, form, function and dynamics.\nThis makes it highly significant not only for urban studies and geospatial science, but also for Urban\nAI applications, suggesting a set of interpretable variables that can serve as a context which\nconditions decision-making policies and facilitates transfer learning between cities. The latter is also\nsupported by the city causal archetypes revealed in the analysis, which enable the identification of\ncities with similar coupling between urban systems and traffic dynamics. A second aspect defining\nthe significance of the study is its focus on causation rather than correlation. This provides a\nfoundation for scientifically justified transportation policies and interventions, as well as for\ndesigning assumptions and induction biases for intelligent transportation models which both are\nhighly relevant and challenging problems in the field of intelligent transportation systems. In\nsummary, this work is highly significant for several research fields including urban studies,\ngeospatial science, intelligent transportation systems and data-driven traffic simulation.\nResponse: Thank you very much for this thoughtful and encouraging assessment! We really\nappreciate your recognition that advancing transferable urban modelling requires defining similarity\nacross cities in a way that moves beyond single aspects of the built environment. In line with your\nremarks, our work integrates urban structure, form, and function with traffic dynamics to derive\ncross-city causal archetypes.\nWe also appreciate your emphasis on the importance of moving from correlation to causation.\nBy providing bidirectional and potentially asymmetric causal diagnostics that are comparable across\ncities and day types, we aim to offer a more robust foundation for scientifically justified congestion\nmitigation and for the development of transferable Urban AI and intelligent transportation models.\nThe work is grounded in well-established literature on causal inference, spatio-temporal prediction\nmodels, geospatial information science and urban mobility studies. The application of Convergent\nCross Mapping (CCM) to detect (potentially bidirectional) causalities is methodologically sound.\nThe original CCM method assumes that the underlying dynamical system is stationary, so that the\nfunctional relationships between observables remain constant over time. However, this assumption\nmay not hold for the systems under study which are characterized by spatial heterogeneity and\ntemporal variability. The authors relax the strict stationarity assumption (similarly to GCCM but\nextending to both spatial and temporal dimensions) and propose novel ST-CCM method for\nbidirectional causal estimation in spatio-temporal systems. ST-CCM combines spatio-temporal\nCCM with spatio-temporal weighted regression (STWR) that smooths the original data into quasi-\nstationary, piecewise regions. The approach appears both methodologically innovative and\n13\npractically sound, as it denoises the data and transforms them into a set of interpretable composite\nindicators which tend to be more stationary across space-time cells than the original variables. Since\nthe data points to calculate the estimates of ρ are derived from locally fitted STWR regression\nmodels, a brief discussion on the theoretical and practical implications of relaxing the stationarity\nassumption (e.g. how the bandwidth of the STWR kernel or buffer size of Voronoi cells influence\nthe convergence of ST-CCM, or how to interpret the results for the cities comprising sub-regions\nwith highly heterogeneous structure, form or function), would further strengthen the methodological\ncontribution of the study.\nResponse: Thank you very much for this insightful comment! We agree that a discussion on\nthe theoretical and practical implications of relaxing the stationarity assumption would significantly\nstrengthen the manuscript. In the revised manuscript, we added a concise discussion to clarify how\nour framework relaxes strict stationarity through STWR-based smoothing and what this implies for\nthe interpretation of STCCM results.\nFirst, after constructing the STWR-based composite indicators, we now explicitly describe the\nresulting quasi-stationary approximation and clarify that STCCM should be interpreted as a BVCell-\nlevel causal diagnostic defined within the local support of the spatio-temporal kernel and the BVCell\naggregation (Lines 572-584 on Page 23): “In urban systems, strict stationarity is rarely plausible\ndue to the inherent spatial heterogeneity and temporal non-stationarity of interactions between the\nbuilt environment and traffic dynamics [21, 22, 66]. Consequently, our framework relaxes the\nstationarity requirement by first estimating spatially and temporally varying coefficients with STWR\nand then smoothing these coefficients with a bi-square kernel to construct composite indicators\nCI(s,t) [67, 69]. This procedure yields quasi-stationary neighborhoods in which the association\nstructure is approximately stable within the local support defined by the STWR kernel and the\nBVCell aggregation. Practically, the STWR bandwidth controls the bias-variance trade-off:\nnarrower bandwidths preserve fine-grained heterogeneity but may retain more local noise, while\nwider bandwidths improve stability but may blend distinct local regimes. In addition, the BVCell\nbuffer size determines the spatial support over which traffic and surrounding urban contexts are\naggregated, thereby affecting the homogeneity of each cell. The choice of a 500-meter buffer is\nconsistent with prior evidence on the scale of local traffic impacts [5, 16]. Increasing this size would\nlikely increase signal stability through aggregation but decrease the sensitivity to micro-scale urban\nsystem variations.”\nSecond, after introducing the L-𝜌 convergence criterion and the library-size design, we added\na short paragraph discussing how STWR bandwidths and BVCell buffer sizes can affect the stability\nand convergence of L-𝜌 curves by trading off local heterogeneity against denoising and regime\nmixing (Lines 645-653, Page 26): “Since STCCM inputs are derived from locally fitted and\nsmoothed STWR models, key scale parameters can influence the convergence behavior of the cross-\nmapping skill 𝜌 with increasing library size L. Intuitively, a narrower STWR bandwidth (or finer\nBVCell partition) yields more localized and potentially more heterogeneous composite-indicator\n14\nfields [67, 69], which can reduce the effective signal-to-noise ratio and lead to slower or less stable\nconvergence in L-𝜌 curves. Conversely, overly large bandwidths (or coarse spatial aggregation)\nmay blur distinct sub-regimes and attenuate causality signals by mixing mechanisms, producing\nflatter L-𝜌 curves and weaker separations between 𝜌 and 𝜌 . Therefore, the selected\n𝑋→𝑌 𝑌→𝑋\nbandwidth and BVCell buffer size should be interpreted as defining the operative scale of quasi-\nstationarity, within which the local causal diagnostics are valid.”\nThird, in the Discussion section, we clarified how to interpret city-level causal fingerprints for\ncities comprising highly heterogeneous sub-regions, emphasizing that the reported patterns\nsummarise mixtures of BVCell-level regimes and motivating stratified extensions for sub-regional\ndiagnosis (Lines 325-334, Page 14): “In this context, it is important to note that our STCCM causal\nfingerprints aggregate local causal diagnostics, computed over within-city spatial units, into city-\nlevel L-𝜌 patterns. For cities with strongly heterogeneous sub-regions, such as pronounced core-\nperiphery contrasts or polycentric structures, the city-level curves may reflect a mixture of distinct\nlocal regimes rather than a single dominant mechanism. In these instances, weaker separations\nbetween bidirectional cross-mapping skills or less pronounced convergence should be interpreted\ncautiously, as they may arise from offsetting local causal pathways. This motivates future stratified\nextensions in which STCCM is applied separately across spatial-unit groups defined by congestion\nintensity, centrality, or urban form archetypes. Such an approach would better reveal sub-regional\ncausal heterogeneity while maintaining cross-city comparability through a consistent spatial\nsupport and kernel design.”\nWe believe these additions strengthen the methodological contribution by making the quasi-\nstationarity assumption, its scale dependence, and its interpretive implications explicit in the main\ntext.\nIn the study, STWR models are estimated for three groups of variables representing urban structure,\nform, and function, and a single response variable related to traffic congestion. This enables a\ncomparative evaluation of how well congestion can be explained by the composite indicators across\ncities worldwide. The results demonstrate that the proposed indicators have strong and significant\ncorrelation with traffic dynamics, with urban structure contributing more than form or function. A\nshort discussion of the variable selection for composite indicators would further strengthen this\nresult. For example, if the chosen variables primarily reflect certain types of cities, the regression\nmodel may exhibit lower explanatory power not only because the underlying processes differ, but\nalso because the feature set is less representative for other urban contexts.\nResponse: We sincerely appreciate your valuable suggestion! We agree that cross-city\ndifferences in STWR explanatory power can be influenced not only by heterogeneous underlying\nprocesses, but also by how representative the selected feature sets are for different urban contexts.\nTo address this, we have strengthened the manuscript in three places.\nFirst, in the Methods section, we added a concise rationale for the variable selection used to\n15\ngenerating the composite indicators for urban systems, emphasizing global comparability,\ninterpretability, and consistent computability from OSM data, while also clarifying the potential\nrepresentativeness boundary of a fixed feature library: “To ensure cross-city comparability, we\ncompute these urban system features from globally available OSM data and select variables based\non three criteria: (i) representing complementary aspects of the three components; (ii) established\ninterpretability in existing urban and transport studies; and (iii) consistent computability at the\nBVCell scale across cities.” (Lines 481-484, Page 20) and “However, since these composite\nindicators are derived from a globally consistent feature set, cross-city differences in STWR model\nfit may reflect not only heterogeneous urban-traffic interactions but also the degree to which the\nselected variables capture locally salient determinants of traffic patterns.” (Lines 569-571, Page\n23).\nSecond, in the Results section, we have refined our interpretation of cross-city differences in\nR². We now explicitly acknowledge that lower R² values may arise not only from weaker couplings\nbetween form/function and traffic dynamics, but also from the extent to which the globally\nconsistent feature set captures locally salient determinants of traffic patterns. The revised text states\n“These disparities appear to be partly shaped by underlying socioeconomic conditions and\ngovernance context [38], and also by the extent to which the globally consistent feature set captures\nlocally salient determinants of traffic patterns.” (Lines 108-109, Page 5) and “In these contexts, the\nlower R² indicates that the form and function features used here account for a smaller share of the\nvariance in traffic patterns. This may reflect weaker associations with spatial configurations and\nland-use distributions, or the influence of latent factors not captured by the current feature set used\nto construct the composite indicator.” (Lines 117-121, Page 5).\nThird, in the Discussion, we explicitly stated this representativeness issue as a limitation and\noutlined future directions to expand the feature library and consider more context-sensitive\nspecifications (Lines 354-360, Page 15): “Second, the composite indicators for each urban system\ncomponent are constructed from a fixed set of globally available features to ensure cross-city\ncomparability. While this design facilitates consistent benchmarking, it may underrepresent context-\nspecific determinants of congestion in some cities (e.g., multimodal supply, demand-management\npolicies, or informal transport), which can lower the explanatory power of the association models\neven when strong urban-traffic coupling exists. Future work could expand the feature set and\nexplore hierarchical specifications or models tailored to specific city clusters to obtain more\nrepresentative composite indicators across diverse urban contexts.”\nThese additions strengthen the interpretation of the composite indicators and clarify the sources\nof cross-city variation in model fit. We believe the revised discussion better situates our framework\nwithin diverse global urban contexts and addresses your concern.\nThe third important result of the study is the development of hierarchical clustering approach that\ngroups the cities according to the direction and strength of causality between urban structure, form,\nand function, and traffic dynamics), using ST-CCM outputs (L-ρ curves) as input data. The\nclustering results reveal the existence of three distinct causal archetypes of cities. This finding is\nhighly relevant for scientifically grounded design of transportation policies and interventions, as the\nidentified direction and strength of causality in a city highlights specific groups of measures that\ncould be the most effective in mitigating congestion.\nThe work supports all its conclusions and claims, and no additional evidence is needed. In particular,\nthe goodness of fit of the STWR regression for modelling the traffic indicator is supported by\nconsistently high R^2 and AICc values compared to the GWR model. The authors evaluate the\nsignificance of ρ values for two library sizes, which aligns with standard CCM validation practice\n(see, e.g., Gao, B., Yang, J., Chen, Z. et al. Causal inference from cross-sectional earth system data\nwith geographical convergent cross mapping. Nat Commun 14, 5875 (2023)). The general\nconclusions regarding the causal interplay between urban systems and traffic dynamics, as well as\nthe explanatory power of the urban structure, form, and function composite indicators, are well\nsupported by the extensive dataset covering 30 cities on multiple continents. Moreover, the\nuniformity of the traffic congestion data which are sourced from the same provider and tested for\nspatial and temporal representativeness, adds credibility to the reported findings.\nResponse: We sincerely thank you for your positive assessment! We are really encouraged by\nyour recognition that these findings are highly relevant for the scientifically grounded design of\ntransportation policies and interventions. We also appreciate your note that the main claims are well\nsupported by the STWR & GWR performance comparisons, standard CCM significance validation\npractice (e.g., Gao et al., 2023), and the credibility of the cross-city findings.\nThe study provides enough details in the methods to ensure reproducibility. As a minor suggestion,\nin Figure 1c-e, the zero reference line in the violin plots is difficult to distinguish due to the grey\ndotted style. Enhancing its visibility would help readers interpret whether the distributions lie above\nor below the mean.\nResponse: We appreciate this valuable feedback regarding visual clarity. In the revised Figure\n1c-e, we have enhanced the visibility of the zero reference line by changing it to a bold black line.\nIn addition, to prevent any visual confusion between this reference line and the internal data markers,\nwe have updated the inner quartile lines within the violin plots to white. These adjustments ensure\nhigh contrast against the background, allowing readers to effortlessly distinguish whether the\ncoefficient distributions lie above or below the mean.\nThe revised figure is shown as follows:\nsubstantial potential impact across several research domains, as well as practical implications for\nthe development of more efficient transportation policies and models. The work can therefore be\nrecommended for a publication after minor revision.\nResponse: Thank you very much for this positive overall assessment! Your endorsement\nreinforces our confidence in the validity and impact of this work. We have carefully addressed all\nthe minor revisions suggested to further strengthen the manuscript.\nReviewer #3 (Remarks on code availability):\nThe code package consists of four Python scripts accompanied by a folder containing all necessary\ndata. It also includes a README file with installation instructions, dependency specifications, and\na clear description of how each script corresponds to the methods presented in the paper. Overall,\nthe provided code fully covers all methodological components of the study, and the complete dataset\nfor the 30 evaluated cities is included. The code is well-structured, readable, and sufficiently\ndocumented. I was able to launch the code successfully after installing the necessary dependencies\non a system with Windows 11 and Anaconda.\nResponse: Thank you very much for your detailed remarks on code availability. We appreciate\nyour assessment that the package is well structured and sufficiently documented, and we are grateful\nthat you were able to install the dependencies and successfully launch the workflow on your system,\nwhich further supports the reproducibility of our study.\n18"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I would like to thank the authors for the substantial effort put into revising the manuscript. Nearly all of the concerns I raised in my previous review have been carefully addressed. I only ask the authors to consider two remaining minor points:\n1) Figures 1 and 2 (readability). Regarding Figure 1, I wonder whether the geographic map is strictly necessary in the main text; it could be moved to the Supplementary Material without any loss of essential information. Even if the authors decide to keep the map in Figure 1, it seems redundant in Figure 2, as it is identical to that in Figure 1. Moreover, while the overall trends of the curves in Figure 2 are visible, the individual curves and numerical values are difficult to read because the plots are too small. Removing the map would free space to enlarge the city-specific plots and substantially improve their readability. In general, Figure 2 should be revised to make the panels larger and more legible.\n2) Clarification of the Jaccard distance. It is still unclear how the Jaccard distance is computed in this work. The Jaccard measure is defined on two sets (as the ratio between their intersection and their union), but the manuscript does not clearly specify what the two sets are in this context. More generally, I believe that the procedure described in point 6 of the rebuttal should be explained in greater detail (either in the main text or in the Supplementary Material) to ensure full clarity and reproducibility.", "reviewer_3": "The revised manuscript adequately addresses all points raised during review. The authors’ responses are clear, and the changes made resolve the previous concerns. Specifically:\n- the authors discuss the implications of relaxing the stationarity requirement in the proposed method, as well as the choice of parameters influencing the size of quasi-stationary neighborhoods;\n- the authors discuss the influence of latent factors not included in the current feature set on the interpretation of the results;\n- the proposed modifications improve the readability and completeness of the manuscript.\nI therefore recommend acceptance of the manuscript for publication."}, "author_response": "Response to Reviewers\nReviewer #1 (Remarks to the Author):\nI would like to thank the authors for the substantial effort put into revising the manuscript. Nearly\nall of the concerns I raised in my previous review have been carefully addressed. I only ask the\nauthors to consider two remaining minor points:\n1) Figures 1 and 2 (readability). Regarding Figure 1, I wonder whether the geographic map is strictly\nnecessary in the main text; it could be moved to the Supplementary Material without any loss of\nessential information. Even if the authors decide to keep the map in Figure 1, it seems redundant in\nFigure 2, as it is identical to that in Figure 1. Moreover, while the overall trends of the curves in\nFigure 2 are visible, the individual curves and numerical values are difficult to read because the\nplots are too small. Removing the map would free space to enlarge the city-specific plots and\nsubstantially improve their readability. In general, Figure 2 should be revised to make the panels\nlarger and more legible.\nResponse: Thank you for this helpful follow-up. We agree that repeating the geographic map\nin Fig. 2 was redundant and that it constrained the readability of the city-level 𝐿-𝜌 panels. We\ntherefore revised the figure design to enhance legibility.\nIn the revised manuscript, we removed the world map from Fig. 2 and reorganized the 𝐿-𝜌\ncurves into a larger grid (with fewer panels per row), which substantially increases the panel size\nand allows a larger font for axis and tick labels. To further improve readability, we increased the\nline weights of the individual curves and added subtle gridlines to facilitate reading numerical values.\nThe geographic locator map is now shown only in Fig. 1 to avoid duplication.\nThese changes make both the individual curves and their numerical scales clearly interpretable.\nWe applied the same redesign to Extended Data Fig. 2. The revised Fig. 2a is provided below.\n1\n2) Clarification of the Jaccard distance. It is still unclear how the Jaccard distance is computed in\nthis work. The Jaccard measure is defined on two sets (as the ratio between their intersection and\ntheir union), but the manuscript does not clearly specify what the two sets are in this context. More\ngenerally, I believe that the procedure described in point 6 of the rebuttal should be explained in\ngreater detail (either in the main text or in the Supplementary Material) to ensure full clarity and\nreproducibility.\nResponse: Thank you for this suggestion. We revisited our description and agreed that it did\nnot explicitly define the two sets used in the Jaccard computation. In the revised manuscript, we\nnow clarify that the Jaccard distance is computed on the 2D regions under the bidirectional 𝐿-𝜌\ncurves, where the bidirectional region for each city is constructed as the union of the two directional\nregions (𝑋→𝑌 and 𝑌→𝑋). We then compute the Jaccard index as the intersection-over-union (IoU)\nof these regions and define the Jaccard distance as 1−𝐽(⋅).\nAccordingly, we added a concise clarification in the Results stating that the Jaccard distance is\nbased on the IoU of the bidirectional regions (Lines 238-240, Page 11): “In contrast, the Jaccard\ndistance measures dissimilarity via the intersection-over-union (IoU) of the regions under the\nbidirectional 𝐿–𝜌 curves (defined as the union of the two directional regions), reflecting differences\nin the overall magnitude of their causal influence.”\nWe also added a detailed definition in the Methods that explicitly specifies the two sets, their\nunion construction, and the IoU formula, together with a description of the practical implementation\n(Lines 679-689, Pages 27-28): “Similarly, we quantify magnitude differences using a Jaccard\ndistance defined on regions under the bidirectional 𝐿 –𝜌 curves over 𝐿 ∈[𝐿 ,𝐿 ] , where\nmin max\n[𝐿 ,𝐿 ] denotes the library-size range considered in STCCM. For each city 𝑚 and dimension\nmin max\n𝑋 ∈{𝑋 ,𝑋 ,𝑋 } on rest days 𝑟, we define each directional region as the area between the curve\nstr frm fun\nand the 𝐿-axis (i.e., 𝑢 =0):\n𝐴 (𝑚,𝑟) ={(𝐿,𝑢):𝐿 ∈[𝐿 ,𝐿 ], 0≤𝑢 ≤𝑃 (𝑚,𝑟)(𝐿)},\n𝑋→𝑌 min max 𝑋→𝑌\n(𝑚,𝑟) (𝑚,𝑟)\n𝐴 ={(𝐿,𝑢):𝐿 ∈[𝐿 ,𝐿 ], 0≤𝑢 ≤𝑃 (𝐿)}.\n𝑌→𝑋 min max 𝑌→𝑋\nIn practice, each directional region is represented as a polygon by connecting sampled points\n(𝐿 ,𝜌(𝐿 )) and closing the boundary with 𝑢 =0. The bidirectional region is then defined as\n𝑖 𝑖\n(𝑚,𝑟) (𝑚,𝑟) (𝑚,𝑟)\n𝐴 =𝐴 ∪𝐴 .\n𝑋 𝑋→𝑌 𝑌→𝑋\nGiven two cities 𝑚 and 𝑛, the Jaccard index 𝐽(⋅) is computed as the intersection-over-union of\nthese bidirectional regions:\n(𝑚,𝑟) (𝑛,𝑟)\n|𝐴 ∩𝐴 |\n(𝑚,𝑟) (𝑛,𝑟) 𝑋 𝑋\n𝐽(𝐴 ,𝐴 )= ,\n𝑋 𝑋 (𝑚,𝑟) (𝑛,𝑟)\n|𝐴 ∪𝐴 |\n𝑋 𝑋\nand the Jaccard distance is 𝐽𝑎𝑐𝑐𝑎𝑟𝑑𝐷𝑖𝑠𝑡 =1−𝐽(⋅) . cccordingly, the overall Jaccard distance\nbetween cities 𝑚 and 𝑛 on rest days 𝑟 is computed as follows:\n𝐽𝑎𝑐𝑐𝑎𝑟𝑑 =∑ 𝐽𝑎𝑐𝑐𝑎𝑟𝑑𝐷𝑖𝑠𝑡 (𝐴 (𝑚,𝑟) ,𝐴 (𝑛,𝑟) ).”\n(𝑚,𝑛,𝑟) 𝑋∈{𝑋str,𝑋frm,𝑋fun} 𝑋 𝑋\nJaccard computation and ensuring clarity and reproducibility.\nReviewer #3 (Remarks to the Author):\nThe revised manuscript adequately addresses all points raised during review. The authors’ responses\nare clear, and the changes made resolve the previous concerns. Specifically:\n- the authors discuss the implications of relaxing the stationarity requirement in the proposed method,\nas well as the choice of parameters influencing the size of quasi-stationary neighborhoods;\n- the authors discuss the influence of latent factors not included in the current feature set on the\ninterpretation of the results;\n- the proposed modifications improve the readability and completeness of the manuscript.\nI therefore recommend acceptance of the manuscript for publication.\nResponse: We sincerely thank you for your supportive evaluation and recommendation for\nacceptance. We are very pleased that the revisions have addressed the concerns and enhanced the\nmanuscript’s clarity and completeness.\n3"}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have thoroughly addressed all of my concerns. I appreciate the diligence and care taken in the revision."}, "author_response": ""}]

Decision letter