Megacities are causal pacemakers of extreme heatwaves

Urbanization concentrates population, energy use, and emissions in cities, making them central to climate impacts such as heatwaves. Heatwaves have increased in duration, intensity, and frequency across the contiguous United States since the mid-1960s. Both natural drivers (e.g., synoptic high-pressure systems, soil moisture memory, ENSO, PDO) and anthropogenic forcings (greenhouse gas emissions, waste heat) contribute to extreme heat. Anthropogenic emissions have accounted for a large share of observed warming and are projected to intensify heat extremes in the U.S. Urban environments are interconnected and can exhibit similar thermal behaviors and long-range teleconnections, forming clusters under environmental stressors. This study asks how causal interactions among U.S. urban areas structure the propagation of extreme heatwaves, whether megacities function as causal mediators or pacemakers, and how human activity (proxied by population) relates to causality strength. A complex network framework with causal inference is adopted to uncover teleconnections, mediating nodes, and hub-periphery structures in urban heatwave dynamics during the warm season.

Recent climate studies increasingly use complex network approaches to represent the climate system as interacting nodes (spatial variables like temperature or precipitation) connected by edges defined by interaction strength. Traditional teleconnection detection commonly relies on linear correlations (Pearson, Spearman), which may miss nonlinear dependencies and underlying processes. Nonlinear methods—event synchronization, mutual information, distance metrics, and causality—provide richer insights. Causality networks are particularly valuable for distinguishing direct interactions from common drivers in complex climate systems and are comparatively robust to measurement errors and model initial/boundary conditions. Prior work has applied network methods to extremes (heatwaves, rainfall) and early warning of large-scale climate phenomena. Building on these advances, this study uses causal network reconstruction to analyze urban heatwave propagation, addressing gaps in understanding the roles of human activity and megacities in shaping extreme heat teleconnections.

Study scope and periods: The analysis focuses on warm-season (May–September) heatwaves over the contiguous U.S. (CONUS), examining 12 major events between 1998 and 2021 and causal connections among 520 urban sites.

Heatwave detection: Daily maximum temperature data (1979–2021) were obtained from NOAA Climate Prediction Center (CPC) Global Unified Temperature, described in the text as 5° × 5° spatial grids. A heatwave is defined as at least 3 consecutive days when the daily maximum temperature exceeds the 90th percentile computed using a 15‑day moving window for each warm season and location. Major events with comparatively higher intensity, longer duration, and/or larger spatial coverage were selected; 12 events from 1998–2021 were used.

Urban temperature data: Hourly air temperatures for urban areas were compiled from the Historical Comprehensive Hourly Urban Weather Database (CHUVD-H) for 1998–2021. A set of 390 weather stations within urban areas (within 15 km) and 130 additional stations near urban boundaries (selected by inspection) were used to represent 520 urban sites with populations typically ≥50,000 (per TIGER-defined urban areas). Data underwent gap filling and quality control following prior work. To reduce seasonal/annual cycles and adjacency effects on causality, long-term hourly means were removed to form temperature anomalies for each urban area.

Causal inference (CCM): Convergent Cross Mapping (CCM) based on Takens’ embedding reconstructs shadow manifolds from temperature anomaly time series to infer causality between city pairs. For each pair (X,Y), cross-mapping estimates Y from the manifold of X using E+1 nearest neighbors with exponentially weighted distances. Predictability is quantified by the correlation between estimated and observed Y, ρ_XY; positive larger values imply stronger causal influence. Embedding parameters (delay τ and dimension E) were chosen using correlation integral/dimension analysis. The slope of log C(r) versus r plateaued for embedding dimension >10, supporting E=10. Sensitivity tests on library size L during two long events showed stabilization at ~4.5 days, indicating that events ≥4 days suffice for reliable CCM estimation.

Network construction and metrics: Each urban site is a node (n=520). A directed edge from node j to i is set (A_ij=1) when CCM-derived causality strength exceeds a statistically determined threshold (based on causality distribution; details in supplementary). The resulting directed network is characterized by in-degree (number of incoming edges), out-degree (outgoing edges), and PageRank centrality (with α=0.85, β=1e-6). Spatial visualization by subregions highlights hubs and long-range links. Population metrics (totals and densities from U.S. Census/WorldPop) for large cities (>200,000 population) were correlated with causality (out-degree) to evaluate anthropogenic influence.

Data and resources: CPC temperature data, TIGER urban boundaries, and WorldPop population data were used; code available on request.

• Urban causal heatwave networks exhibit pronounced teleconnections and regional mediators across CONUS during heatwaves.
• Megacities emerge as dominant hubs (supernodes), being causally connected with most other cities and shaping network structure during extreme events.
• Indegree hubs (heat sinks): Cities such as New York City (NY), Chicago (IL), and San Jose (CA) show indegree values above 450 during a representative event, implying influence from roughly 90% of the 520 sites.
• Outdegree hubs (heat sources): Large cities including Detroit (MI), New York City (NY), San Jose (CA), Portland (OR), and Columbus (OH) show outgoing influence to approximately 400 other urban areas in a representative event.
• PageRank centrality highlights large metropolitan areas (e.g., Chicago, Seattle, New York City, San Jose) as highly influential in network-level heatwave propagation.
• Positive association between human activity and causality: For large cities (>200,000 population), most exhibit more than 230 outgoing links during the July 18–22, 2020 heatwave, indicating influence on over half of the 520 sites. Causal outdegree shows significantly positive correlations with both population totals and population density (consistent patterns across other heatwaves).
• Long-range links connect geographically distant cities, evidencing teleconnections that can inform prediction and understanding of heatwave spread.
• Examples of region clusters and adjacency effects include New York and neighboring areas, as well as influence on more isolated cities like Denver (CO) and Phoenix (AZ).

The causal network approach reveals that extreme heat conditions in U.S. urban areas are interconnected through directed teleconnections, with hub cities—especially megacities—acting as pacemakers of heatwave evolution. These hubs both absorb and disseminate thermal stress, reflecting combined effects of large-scale climatic drivers and concentrated anthropogenic activities (e.g., waste heat, GHG emissions, increased air-conditioning use during heatwaves). The topology (in/out-degree, PageRank) provides interpretable metrics of vulnerability (incoming influence) and influence (outgoing impact) useful to urban planners and policymakers. The uncovered long-range teleconnections are analogous to precursors used for predicting climate phenomena (e.g., ENSO) and may aid in early detection and forecasting of extreme heat events as such teleconnections become more prominent with continued warming. The study offers a data-driven framework for understanding inter-urban dynamics of heat stress and guiding targeted mitigation and adaptation strategies based on network roles of cities.

This study integrates complex network analysis with causal inference (CCM) to map and quantify how extreme heatwaves propagate across 520 U.S. urban areas. It identifies megacities as causal pacemakers and mediators, reveals widespread teleconnections, and demonstrates a positive relationship between urban population metrics and causal influence during heatwaves. The network metrics (indegree, outdegree, PageRank) provide actionable insights into city vulnerability and influence, informing heat mitigation and adaptation strategies, and supporting predictive efforts for extreme events under ongoing climate change. The findings also contribute new perspectives on inter-municipal and inter-urban dynamics of extreme heat.