The nonlinear relationship between urban design form and energy efficiency

Abstract

Optimizing urban form is a critical pathway for achieving low-carbon development, yet existing research often relies on linear assumptions, failing to capture the complex, stage-dependent dynamics of urban systems. This study constructs an Integrated Urban Form Index based on multidimensional indicators—compactness, connectivity, and complexity—and employs econometric models to investigate the non-linear impact of urban form on Total Factor Energy Efficiency. Empirical results confirm that the relationship follows a distinct S-shaped trajectory characterized by threshold effects, rather than a simple linear progression. The evolution of urban form is delineated into three dynamic regimes: a latent stage with limited impact, an acceleration stage with increasing marginal returns, and a saturation stage with diminishing benefits. Mechanism analysis reveals that transportation structure optimization and agglomeration economies serve as the dual drivers underpinning this evolution. Consequently, this study advocates for stage-adaptive planning strategies, suggesting that small and medium-sized cities focus on breaking through development thresholds, while large cities prioritize stock optimization and resilience enhancement to avoid high-carbon lock-in.

Introduction

Rapid urbanization has transformed cities into the primary arenas of global energy consumption and carbon emissions. According to the International Energy Agency, urban areas account for nearly two-thirds of global energy use and represent the most significant sources of environmental pressure under accelerating climate change. As building energy demand, transportation energy consumption, and urban heat environment deterioration intensify, improving urban energy efficiency through spatial planning and design has become a critical task for sustainable development.

In China, with the proposal of the “Dual Carbon” goals (Carbon Peaking and Carbon Neutrality), urban development models are facing profound pressure for transformation. Among the many determinants of urban energy performance, urban form—the spatial configuration of land use, transportation networks, and building morphology—plays a foundational and highly malleable role. Urban form not only shapes the physical structure of cities but also influences travel behavior, system operation efficiency, microclimatic conditions, and building energy demand. Understanding how urban form affects energy efficiency through multiple pathways and across different spatial scales is therefore essential for advancing low-carbon and resilient urban development.

Despite extensive research on urban density, land-use mix, street connectivity, and building layout, significant gaps remain. First, existing studies often examine individual pathways—such as transportation behavior or microclimate regulation—in isolation, lacking a comprehensive framework that integrates multi-scale urban mechanisms. Second, many urban form variables exhibit strong nonlinear effects, including threshold behavior, marginal variation, and stage-dependent differences; however, most studies still rely on linear assumptions, limiting their capacity to capture the complexity of urban systems. Third, the influence of urban form tends to be cumulative and phase-based, making it unsuitable to be described by simple linear or binary relationships and requiring a model that better reflects actual urban evolutionary processes.

Recent studies have explored how urban form affects energy efficiency from multiple perspectives, yet most remain limited by single-dimensional analysis or linear assumptions. For example, Güneralp et al.¹ conducted a global-scale analysis demonstrating that urban density significantly influences building energy use, although its effects vary geographically. Similarly, Osorio et al.² found that the relationship between urban energy consumption and density follows a sublinear scaling law, suggesting economies of scale in dense urban areas. In China, Wang et al.³ revealed that compact land-use patterns and high street connectivity can effectively reduce transportation energy consumption, though these effects differ across spatial scales. At the building level, Ahmadian et al.⁴ and Li et al.⁵ demonstrated that block-scale morphological indicators, such as compacity and site coverage, exert nonlinear influences on both energy intensity and solar potential. Meanwhile, Mostafavi et al.⁶ highlighted that the link between urban density and building energy performance is spatially heterogeneous and climate-dependent.

More recently, scholars have begun incorporating three-dimensional perspectives: Wang et al.⁷ showed that 3D compactness better explains variations in building carbon emission intensity than 2D measures, while Feng et al.⁸ identified optimal morphological parameters that can reduce energy use intensity in high-rise residential clusters. On a regional scale, Shi et al.⁹ revealed that urban form structure affects carbon emission efficiency through synergistic and interactive mechanisms.

Building upon recent scholarship that has begun to explore non-linear urban dynamics, this study proposes an integrated theoretical perspective: the relationship between multidimensional urban form and TFEE follows a generalizable S-shaped curve. This relationship suggests that improvements in urban form have limited impact at low levels, become significantly more effective once a critical threshold is reached, and ultimately exhibit diminishing marginal benefits at higher levels.

The contributions of this study are threefold. First, it empirically validates the S-shaped hypothesis specifically within the context of TFEE. Unlike previous studies that often focused on single-factor energy indicators or isolated morphological dimensions, this research confirms the stage-dependent trajectory of comprehensive urban efficiency, offering a rigorous quantitative verification of system-wide evolution. Second, it constructs IUFI to establish a holistic analytical framework. By synthesizing compactness, connectivity, and complexity, this framework addresses the fragmentation present in existing studies that typically examine these dimensions in isolation. Third, beyond merely identifying non-linearity, this study quantifies specific critical thresholds and operational mechanisms. This translates theoretical insights into stage-adaptive planning strategies, providing a robust scientific basis and actionable guidance for building low-carbon, resilient, and livable future cities.

Literature review

The multi-dimensional construct: deconstructing urban form for efficiency assessment

Before exploring the nonlinear S-shaped dynamics, it is crucial to operationalize the independent variable—‘urban form’—not as a monolithic concept but as a complex, multi-dimensional construct. The existing literature provides the theoretical basis for decomposing urban form into three quantifiable dimensions: Compactness, Connectivity, and Complexity. This decomposition is the prerequisite for constructing the Integrated Urban Form Index (IUFI) in our empirical model. Urban form is increasingly recognized as a foundational determinant of urban energy performance and a key lever for steering low-carbon development. It shapes how land use, spatial structure, transportation systems, and building morphology interact to organize urban life and energy flows¹⁰. At the metropolitan scale, regional development patterns—such as the spatial distribution of residential and employment centers, urban compactness, and expansion direction—substantially condition system-wide transportation energy consumption and carbon intensity¹¹. More compact and spatially integrated urban structures tend to shorten trip distances, support transit-oriented development, and improve network efficiency¹². Conversely, dispersed or weakly coordinated polycentric patterns often reinforce automobile dependence and energy-intensive mobility regimes¹³. Empirical evidence suggests that compact urban forms and well-structured polycentric networks can together enhance commuting efficiency and reduce transportation carbon emissions¹⁴.

At the meso scale, urban form is materialized through block structure, street network design, and land-use mixing, all of which are directly amenable to urban design interventions¹⁵. Fine-grained street networks and human-scale blocks enhance accessibility and promote active travel modes, thus lowering transportation energy demand. Conversely, superblocks and mono-functional zoning disrupt pedestrian continuity and systematically increase automobile reliance¹⁶. At the micro scale, building morphology serves as the interface between urban form and operational energy demand¹⁷. Parameters such as building height, spacing, coverage, and orientation strongly influence thermal performance and daylight access¹⁸. Compact clusters with optimal height-to-spacing ratios have been shown to reduce total energy use intensity. Similarly, urban 3D morphology and surface-to-volume ratios are key predictors of both electricity consumption and cooling demand¹⁹. From a design perspective, adjustments in building geometry and cluster configuration not only influence direct energy consumption but also reshape local microclimates and daylight conditions. The dynamic interaction between building form and environmental performance highlights how urban morphology operates as a multi-scalar system linking physical design to energy outcomes²⁰.

The physical micro-foundations: mechanisms of efficiency saturation

To understand the macroscopic S-shaped relationship between urban form and Total Factor Energy Efficiency (TFEE), it is essential to first review its microscopic physical mechanisms. Although this study operates at the city scale, the aggregate energy performance is fundamentally rooted in micro-scale interactions between morphology and environmental physics. Microclimate and building energy performance are critical pathways through which urban form affects overall energy efficiency. Urban morphology regulates these pathways by shaping the microclimatic environment—altering air temperature, wind movement, and solar exposure—thus positioning form-making as a central design mechanism in energy-conscious urban development²¹.

The three-dimensional arrangement and geometry of buildings influence wind patterns, shading, heat accumulation, and the distribution of solar radiation²². Dense or enclosed configurations can trap heat, suppress natural ventilation, and elevate cooling loads, whereas morphologies maintaining coherent airflow corridors can mitigate heat stress and improve thermal comfort²³. Studies show that compact street canyons, vegetation, and shading strategies substantially influence urban thermal performance²⁴.

At the same time, street geometry and orientation determine airflow and solar access, which are crucial for pedestrian-level comfort²⁵. High-rise environments amplify these effects—building height, spacing, and massing collectively determine the balance between solar gain, shadowing, and ventilation potential²⁶. In dense city cores, compact forms without ventilation corridors can trap heat and degrade outdoor comfort²⁷. In high-density and high-rise contexts, vertical form becomes a critical design dimension. Three-dimensional density affects not only solar access and daylighting but also the potential for passive heating and rooftop solar technologies²⁸. Carefully calibrated building spacing, height gradation, and orientation improve solar potential and reduce operational energy demand²⁹. Importantly, these relationships are nonlinear—minor adjustments in geometry or setbacks can produce large shifts in shading, airflow, and heat retention³⁰. The interaction between building envelope conditions, material albedo, and microclimatic behavior further influences thermal outcomes³¹.

Recent advances in computational and neural-network modeling have deepened understanding of how urban morphology modulates microclimate extremes and building energy demand³². Similarly, field studies confirm that local wind regimes, pressure gradients, and street-level temperature variations have direct implications for building ventilation and passive cooling strategies³³. Together, these studies highlight the need for design frameworks that explicitly link urban form, microclimate regulation, and energy efficiency³⁴.

Theoretical evolution: from linear assumptions to nonlinear threshold dynamics

Building on the physical complexity discussed above, the theoretical understanding of the form-efficiency relationship has evolved from simple linear assumptions to complex nonlinear dynamics. This evolution provides the direct theoretical basis for the S-shaped hypothesis proposed in this study. The influence of urban form on energy efficiency exhibits pronounced nonlinear, threshold-based, and interactive dynamics across multiple scales. Recent research emphasizes that form-related variables such as density, building compactness, and land-use mix do not exert uniform effects; rather, they display nonlinear responses with critical thresholds that can dramatically alter system behavior³⁵. For instance, density often yields efficiency gains only after surpassing specific thresholds, beyond which the benefits plateau or even reverse due to overheating, congestion, or ventilation constraints³⁶.

This threshold-dependent behavior has also been identified in energy use models of compactness and land-use mix, where moderate intensification enhances transport and building energy performance, but excessive compactness can elevate heat stress or limit air exchange³⁷. Similarly, studies show inverted-U or S-shaped associations between compactness and energy intensity—where moderate compactness optimizes performance, but over-densification leads to diminishing or negative returns³⁸.

At the urban system level, compact spatial configurations can substantially reduce energy use per capita, particularly when coordinated with innovation and infrastructure efficiency³⁹. Global-scale studies further demonstrate that energy efficiency increases sublinearly with density, revealing economies of scale rather than proportional benefits², while urban energy intensity tends to decline following S-shaped trajectories as urban form evolves¹. At finer scales, built form and density interact nonlinearly to influence building energy performance⁴ and heat island dynamics⁴⁰. In particular, 3D compactness has been shown to both enhance efficiency and increase thermal stress, depending on climatic and morphological thresholds⁴¹. Interactions across scales further reveal cumulative and path-dependent effects: compact regional structures may lower transportation energy use, but excessive block density can degrade microclimate and offset gains⁴². Similarly, 3D morphological complexity interacts with solar access and energy utilization efficiency in nonlinear ways²⁸.

Overall, these multi-scale, threshold-based interactions suggest that the relationship between urban form and energy efficiency is best characterized by an S-shaped curve, rather than a linear one. This conceptual framing captures how cumulative, cross-scale, and diminishing-return effects shape the trajectory of low-carbon urban evolution⁴³.

Research design and methods

Theoretical framework and model specification

The core objective of this study is to validate the S-shaped nonlinear relationship between urban form and energy efficiency and to identify its critical stage-dependent characteristics. To achieve this, our research design transcends traditional linear assumptions, constructing an econometric framework capable of capturing stage dependencies and nonlinear dynamics. First, given the complexity exhibited by urban systems at different development stages, we employ Generalized Additive Models for an initial exploration of urban form. This model allows the data to “speak for itself,” visually revealing the true trajectory between variables through non-parametric smoothing functions, thereby providing preliminary visual evidence for the S-shaped hypothesis. The model is specified as follows:

$$E{E_{it}}=\alpha +f(U{F_{it}})+\sum\limits_{{k=1}}^{K} {{\beta _k}} {X_{it,k}}+{\mu _i}+{\lambda _t}+{\epsilon _{it}}$$

(1)

where EE_it represents the Total Factor Energy Efficiency of city i at time t; f is the smoothing spline function used to capture the nonlinear response of energy efficiency to the urban form variable UF_it; X_it is a vector of control variables; and µ and λ control for individual and time fixed effects, respectively.

Building upon the preliminary validation of nonlinear characteristics, to precisely quantify the “critical thresholds” proposed in the Introduction, we further introduce Hansen’s Panel Threshold Regression model. This step is crucial as it translates the theoretical S-shaped curve into statistically significant intervals, verifying the “latency effect” of urban form improvements at low levels, the “significant enhancement” after crossing a threshold, and the “diminishing marginal returns” at high levels. Assuming a double threshold (corresponding to the takeoff point γ1 and saturation point γ2 of the S-shaped curve), the model is specified as:

$$E{E_{it}}={\mu _i}+{\beta _1}U{F_{it}} \cdot I(U{F_{it}} \leqslant {\gamma _1})+{\beta _2}U{F_{it}} \cdot I({\gamma _1}<U{F_{it}} \leqslant {\gamma _2})+{\beta _3}U{F_{it}} \cdot I(U{F_{it}}>{\gamma _2})+\theta {X_{it}}+{\epsilon _{it}}$$

(2)

Furthermore, to address the issue of fragmentation in existing pathway analyses, this study constructs a mediation effect model framework that integrates multiple pathways (such as transportation and agglomeration economies). This not only validates the existence of the S-shaped curve but also explains the driving mechanisms behind it, deepening the analysis from phenomenon description to mechanism deconstruction:

$$\left\{ {\begin{array}{*{20}{l}} {{M_{it}}={\delta _0}+{\delta _1}U{F_{it}}+{\delta _2}{X_{it}}+{\nu _{it}}} \\ {E{E_{it}}={\phi _0}+{\phi _1}U{F_{it}}+{\phi _2}{M_{it}}+{\phi _3}{X_{it}}+{\eta _{it}}} \end{array}} \right.$$

(3)

Variable measurement and integrated analytical framework

To overcome the limitations of previous studies that focused on single morphological indicators (e.g., density alone), this study proposes an integrated analytical framework by constructing the Integrated Urban Form Index (IUFI) to comprehensively characterize the urban physical environment. This index integrates three dimensions: Compactness, Connectivity, and Complexity, aiming to resolve the fragmented understanding of urban form in existing literature. Specifically, the Complexity dimension calculates the degree of land-use mixture using the Shannon Entropy formula:

$$EN{T_i}= - \frac{{\sum\limits_{{j=1}}^{k} {{P_{ij}}} \ln ({P_{ij}})}}{{\ln (k)}}$$

(4)

Finally, we employ Principal Component Analysis (PCA) to synthesize the multi-dimensional indicators into a single IUFI index $IUF{I_{it}}={\text{0}}{\text{.45}} \cdot Compactnes{s_{it}}+{\text{0}}{\text{.35}} \cdot Connectivit{y_{it}}+{\text{0}}{\text{.2}} \cdot Complexit{y_{it}}$. The specific assignment of these weights—0.45 for Compactness, 0.35 for Connectivity, and 0.20 for Complexity—is derived from the component loading matrix of the PCA and reflects the structural logic of urban evolution in the sample cities. The hierarchy of these coefficients indicates that Compactness (0.45) serves as the primary dominant factor, capturing the high-density agglomeration characteristic of China’s rapid urbanization. Connectivity (0.35) follows as the secondary driver, highlighting the significant variation caused by large-scale infrastructure and road network expansion. Finally, while Complexity (0.20) is essential for functional diversity, its relatively lower weight suggests that land-use mixing acts as a supplementary qualitative attribute rather than the primary quantitative driver of morphological differentiation at this developmental stage.

The construction of the IUFI adopts a strictly data-driven approach to ensure objectivity and statistical validity. Rather than assigning subjective weights, we utilized Principal Component Analysis (PCA) to extract the latent ‘morphological intensity’ from the high-dimensional data. The specific weights for Compactness (0.45), Connectivity (0.35), and Complexity (0.20) were mathematically derived from the component loading matrix and the explained variance ratio. This method effectively addresses multicollinearity among dimensions and ensures that the index represents the objective structural variance of the urban system. Regarding the efficiency measurement, we employ the Super-SBM model with Undesirable Outputs. This specific variant is selected for two reasons: first, as a non-radial and non-oriented model, it incorporates ‘slacks’ to accurately measure efficiency gaps; second, it allows for ‘super-efficiency’ scoring (values > 1), enabling the ranking of effective decision-making units (DMUs). Furthermore, we adopt the Variable Returns to Scale (VRS) assumption to account for the significant scale differences among Chinese cities, ensuring that pure technical efficiency is isolated from scale efficiency.

To address potential concerns regarding the construct validity and robustness of the IUFI, we performed rigorous diagnostic checks. First, the high correlation among compactness, connectivity, and complexity justifies the use of PCA to address multicollinearity issues that would otherwise distort regression coefficients. This high degree of internal consistency suggests that these dimensions are not disparate variables but interdependent components of a city’s “spatial DNA”. Second, the strictly positive loadings of all three dimensions (0.45, 0.35, 0.20) indicate that no opposing effects are blended; rather, the index captures the synergistic intensification of urban form, reflecting the holistic maturity of the urban spatial structure. To test sensitivity to weighting methods, we constructed an alternative index using an ‘Equal Weighting’ scheme. The correlation between the PCA-based IUFI and the Equal-Weighted index exceeds 0.98, demonstrating that the index captures a stable and consistent morphological hierarchy across diverse city types and development stages, independent of the specific weighting technique. This stability confirms that the IUFI transcends simple statistical aggregation; it acts as a proxy for the structural complexity and organizational efficiency of the urban system. This comprehensive measurement method not only captures the multi-dimensional characteristics of urban form but also provides a solid data foundation for subsequently identifying cross-scale design logic.

$$\hbox{min} \rho =\frac{{1 - \frac{1}{m}\sum\limits_{{i=1}}^{m} {s_{i}^{ - }} /{x_{io}}}}{{1+\frac{1}{{{s_1}+{s_2}}}(\sum\limits_{{r=1}}^{{{s_1}}} {s_{r}^{g}} /y_{{ro}}^{g}+\sum\limits_{{k=1}}^{{{s_2}}} {s_{k}^{b}} /y_{{ko}}^{b})}}$$

(5)

In terms of data, this study selects 285 prefecture-level and above cities in China as the empirical sample, spanning from 2011 to 2023. Data sources include the China City Statistical Yearbook. Specifically, regarding the morphological dimensions constructed from the China City Statistical Yearbook: (1) Compactness is quantified by two secondary indicators: population density (total population divided by built-up area) and land-use intensity (construction land area divided by total administrative area), which reflect the intensity of urban activity and physical agglomeration. (2) Connectivity is measured by road network density (length of paved roads divided by built-up area) and per capita road area, representing the accessibility and flow efficiency of the internal transport system.

Empirical results and discussion

Validation of the S-shaped trajectory and phase characteristics

This study first conducted a detailed descriptive statistical analysis of the variables (Table 1). The results show that the mean Integrated Urban Form Index (IUFI) of the sample cities is 0.458, with a standard deviation as high as 0.213, and a range covering 0.121 to 0.954. This significant morphological heterogeneity confirms that Chinese cities are situated along different development gradients, providing an ideal natural laboratory for validating the S-shaped curve. The broad distribution of the sample, from low-level loose expansion to high-level compact intensification, makes it possible to identify the complete nonlinear evolutionary trajectory.

Table 1 Descriptive statistics of main variables.

To accurately measure the TFEE, we constructed an input-output indicator system following standard literature practices. The input variables consist of:¹ Labor input, measured by the number of year-end employed persons in each city;² Capital input, represented by the capital stock, which is estimated using the perpetual inventory method based on fixed asset investment data; and³ Energy input, denoted by the city’s total energy consumption. regarding outputs, the model includes both desirable and undesirable categories: the desirable output is the city’s Real GDP (adjusted to constant prices), while the undesirable output is the total Carbon Dioxide (CO2) emissions. This framework ensures that the calculated efficiency reflects the comprehensive socio-economic cost of energy utilization.

To precisely capture the stage dependency proposed in the Introduction, we performed threshold existence tests using the Bootstrap method with 500 replications (Table 2). The statistical test results reject the linear hypothesis at the 1% significance level and strongly support the existence of a double threshold model (F-statistic = 28.65). The two identified critical thresholds, γ1 = 0.345 and γ2 = 0.762, divide urban form evolution into three distinct dynamic regimes. This not only statistically confirms the S-shaped hypothesis but also provides a clear structural perspective for understanding complex urban systems.

Table 2 Tests for threshold effects.

Fig. 1

Non-linear relationship between urban form (IUFI) and energy efficiency (TFEE) based on GAM estimation.

Figure 1 visually validates our theoretical hypothesis, exhibiting a classic S-shaped trajectory that perfectly aligns with the thresholds identified in Table 2. The curve delineates three distinct regimes: a ‘Latent’ phase (IUFI < 0.345) where dispersed forms yield negligible efficiency gains; an ‘Acceleration’ phase characterized by rapid accumulation of network externalities; and a ‘Saturation’ phase (IUFI > 0.762) exhibiting diminishing marginal returns. Crucially, this trajectory offers a theoretical advance over fragmented linear or inverted-U models by providing a unified full-lifecycle evolutionary perspective. It resolves apparent contradictions in the literature by clarifying that the ‘ineffectiveness’ or ‘diseconomies’ observed in previous studies are merely distinct phases—start-up friction or saturation—within a single continuum. The distribution of sample cities further underscores that many remain trapped in the latent or saturation phases, necessitating a shift from static, universal norms to dynamic, stage-adaptive planning interventions. It should be clarified that the term “nonlinearity” in this study is conceptualized within the framework of complex urban systems and econometrics. In contrast to the strict algebraic definition of linearity—which requires the satisfaction of the superposition principle (homogeneity and additivity)—nonlinearity in urban dynamics refers to the non-constant marginal effects and stage-dependent responses of the system. In this context, the impact of urban form on TFEE violates the homogeneity condition, as the functional mapping between spatial configuration and efficiency exhibits significant structural breaks. By employing a threshold regression model, we demonstrate that the influence coefficients undergo discrete shifts across different development regimes, representing a nonlinear evolutionary trajectory where the system’s output is not a simple proportional reflection of its inputs.

To further ensure the reliability of these two precise threshold values and rule out the influence of outliers, we conducted a robustness check by adjusting the trimming percentage of the sample. We re-estimated the model by excluding the top and bottom 5% of extreme observations (altering the trimming parameter from the standard 0.01 to 0.05). The results show that the identified threshold points remain highly stable, fluctuating within a narrow range of ± 0.02. This stability confirms that the critical tipping points are determined by the general structural evolution of the urban system rather than being driven by specific extreme cases or sample idiosyncrasies (Table 3).

Table 3 Estimation results of panel threshold model.

Furthermore, the robustness of this S-shaped trajectory is strongly substantiated by the methodological consistency between the non-parametric and parametric approaches employed in this study. The Generalized Additive Model, which imposes no a priori functional form constraints, spontaneously revealed the S-shaped structure solely from the data distribution. This data-driven finding is then rigorously corroborated by the Panel Threshold Regression, which statistically identifies the specific turning points that align perfectly with the GAM’s visual curvature. This dual-verification strategy effectively mitigates the risk of “confirmation-by-specification,” as the concordance between two distinct modeling techniques confirms that the identified dynamic regimes are intrinsic to the urban evolution process. The mechanism analysis provides the necessary physical underpinning for this nonlinearity, confirming that the varying intensities of transportation optimization and agglomeration economies across stages are the actual drivers of this trajectory, ruling out the possibility of spurious correlation.

Finally, we explicitly address potential endogeneity concerns inherent in urban evolutionary processes. We acknowledge that urban form and energy performance may be jointly influenced by economic development levels or unobserved policy shocks. To mitigate this, our model employs a strict Two-way Fixed Effects specification. The inclusion of city fixed effects absorbs time-invariant unobservables such as geographic topography and historical urban layout, while year fixed effects account for common macroeconomic shifts and national energy policies. Furthermore, we control for key confounding variables, including economic development and environmental regulation intensity. Theoretically, considering that urban form is a “slow-moving” physical stock characterized by high hysteresis, whereas energy efficiency is a “fast-moving” flow indicator, the risk of simultaneous reverse causality (where efficiency fluctuations immediately reshape physical form) is minimal. These specifications collectively strengthen the causal interpretation of the identified S-shaped trajectory.

Deconstructing mechanisms within the integrated framework

To concretize the theoretical S-shaped curve into actionable planning handles, this study employs a mediation effect model to deeply deconstruct the two core pathways of “Transportation” and “Agglomeration” within the integrated analytical framework (Table 4). The The empirical design results not only validate the significance of these two pathways but also reveal their operational logic at different scales, effectively addressing the fragmentation issue in existing pathway analyses.

First, at the micro-behavioral scale, urban form exerts a decisive influence on energy efficiency by optimizing transportation structure (path coefficient − 0.324). The improvement in the form index significantly reduces transport energy consumption, verifying that compact and mixed land use (core dimensions of IUFI) can effectively guide resident travel patterns from high-carbon car-oriented modes to low-carbon walking, cycling, and public transit-oriented modes. This is not merely a shortening of physical distance but a reshaping of lifestyles. Second, at the macro-economic scale, the agglomeration effect demonstrates strong positive externalities (path coefficient 0.452). A high degree of urban compactness promotes economic density and knowledge spillovers, making shared infrastructure such as district heating, centralized cooling, and waste recycling economically viable, thereby substantially enhancing resource allocation efficiency. The parallel operation of these two pathways proves the explanatory power of the integrated framework proposed in this study: urban form optimization is not a linear intervention in a single dimension, but a multi-dimensional systematic engineering involving traffic flow, material flow, and information flow. The formation of the S-shaped curve is essentially the result of the interplay and coupling of these two mechanisms at different stages—in the acceleration period, transport savings and agglomeration dividends explode synchronously; while in the saturation period, although agglomeration effects persist, the negative externalities brought by traffic congestion begin to erode part of the gains, causing the curve to flatten.

Table 4 Mechanism analysis (mediation effect).

It is worth noting that while the variables used in this mechanism analysis (specifically Transport Energy) and the control variables (e.g., LnPGDP) inherently share data components with the inputs and outputs of the TFEE framework, their inclusion is theoretically essential. The mediation model aims to identify the specific structural source of efficiency gains—verifying that morphological optimization improves TFEE specifically through transportation savings rather than general noise. Furthermore, controlling for LnPGDP allows us to distinguish “technical efficiency” (a relative input-output ratio) from the “economic development stage” (an absolute scale), thereby isolating the physical impact of urban form from the interference of the Environmental Kuznets Curve. Robustness checks indicate that the core S-shaped coefficients remain stable even when accounting for these correlations, confirming that the results are driven by physical design rather than statistical artifacts.

To further clarify the causal direction, we conducted a simple ‘time-lag test’. We re-estimated the model using the urban form index from the previous year as the independent variable. The logic is straightforward: while current energy efficiency might affect future planning, it cannot physically alter the urban form of the past. The results showed that the S-shaped curve remains robust even with this time lag, providing strong evidence that the influence runs from urban form to efficiency, rather than the reverse.

Furthermore, to explicitly connect these mechanisms to the S-shaped stages identified in Fig. 1, we cross-referenced the mediation results with the city-size heterogeneity analysis (Table 5). The operational intensity of these two mechanisms is not static but evolves dynamically across stages. In the ‘Latent Stage’ (typically characterizing smaller cities), both transport and agglomeration effects remain weak due to the lack of critical mass—a ‘threshold constraint.’ As cities enter the ‘Acceleration Stage,’ the two mechanisms achieve a ‘positive resonance,’ where improved connectivity amplifies agglomeration benefits, driving the exponential rise in efficiency. However, in the ‘Saturation Stage’ (characteristic of mega-cities), a divergence emerges: while transport infrastructure remains dense, the marginal benefits of agglomeration begin to decline due to ‘crowding effects’ (e.g., congestion costs exceeding sharing benefits). This structural shift in the mechanism mix—from dormancy to resonance, and finally to a trade-off—provides the internal micro-foundation for the observed macroscopic S-shaped trajectory.

Planning implications: from theory to stage-adaptive practice

Based on the aforementioned data empirics and mechanism analysis, we translate theoretical insights into practical planning guidance tailored to cities of different sizes (Table 5). The heterogeneity analysis results show that the position of small/medium cities versus large cities on the S-shaped curve dictates that they must adopt distinct planning strategies. This not only enhances the policy relevance of the research but also provides a feasible roadmap for building low-carbon, resilient cities.

Based on the identified thresholds and varying marginal effects, we propose stage-adaptive planning strategies that translate these econometric findings into operational levers. First, for Small and Medium Cities situated in the “latency period” (IUFI < 0.345), the empirical results indicate a “start-up friction” phase where efficiency elasticity is relatively low (0.082). Consequently, the priority is not simply gradual growth but a “Threshold Breakthrough” strategy to cross the tipping point. Planning recommendations focus on avoiding low-density urban sprawl and concentrating resources to rapidly push the form index above the 0.345 threshold. This should be achieved through Transit-Oriented Development (TOD) and compact new district construction. Planning at this stage must preemptively “implant efficient genes” through mixed land use to prevent falling into the mire of high-carbon lock-in due to path dependence. Once crossing this threshold, growing cities enter a “strategic window” (0.345 ≤ IUFI < 0.762) where the marginal contribution of urban form peaks (coefficient surges to 0.415). To fully exploit this “latecomer advantage,” strategies must shift to maximizing the resonance between transport connectivity and functional diversity, sustaining high-speed efficiency growth before diminishing returns set in.

Conversely, for Large and Mega Cities situated at the upper end of the S-shaped curve (IUFI ≥ 0.762), data indicate a significant slowdown in efficiency gains as the coefficient drops to 0.231. This issues a clear warning that the traditional model of exchanging efficiency solely by increasing gross density has hit a ceiling. For these cities, the planning focus must shift from “incremental expansion” to “Stock Optimization and Resilience Enhancement.” Specific measures driven by this saturation mechanism include:¹ Polycentric Restructuring, which involves relieving central city functions and constructing a polycentric network to alleviate the excessive overcrowding costs identified in the model’s tail;² Micro-regeneration and Repair, focusing on micro-circulation improvements at the community scale, such as building “15-minute life circles” to reduce unnecessary long-distance commuting; and³ Blue-Green Infrastructure Integration, embedding ecological patches in dense spaces to mitigate heat island effects. In summary, the S-shaped curve theory proposed in this study is not merely a descriptive academic finding, but a set of scientific tools guiding dynamic, threshold-based decision-making for cities across different lifecycle stages.

Table 5 Heterogeneity analysis by city size.

Finally, regarding the interpretation of these mechanisms, we acknowledge that establishing strict causality in observational mediation analysis faces challenges related to potential unobserved confounders. However, our model specification incorporates two-way fixed effects (controlling for both time-invariant city characteristics and time-varying common shocks), which substantially mitigates the risk of omitted variable bias. Therefore, while we exercise caution in claiming definitive causal chains, the significant associations identified are highly robust and theoretically consistent. They provide strong empirical evidence that transportation structure optimization and agglomeration economies are the plausible functional channels through which urban form influences energy efficiency.

Conclusion

This study constructs an IUFI based on the dimensions of compactness, connectivity, and complexity, and utilizes panel data from Chinese cities between 2011 and 2023 to investigate the impact of urban form on TFEE. The empirical results robustly verify that the relationship between urban form and energy efficiency follows a significant S-shaped nonlinear trajectory rather than a simple linear progression. Through threshold regression analysis, we identified two critical tipping points at γ1 = 0.345 and γ2 = 0.762, which effectively delineate the urban evolution process into three distinct dynamic regimes: the Latent, Acceleration, and Saturation stages. These findings provide a theoretical correction to traditional linear assumptions and highlight the stage-dependent nature of urban morphological interventions.

The quantitative analysis further reveals the structural heterogeneity of energy performance across these stages. In the latent stage (IUFI ≤ 0.345), the marginal contribution of urban form to efficiency is relatively weak (β = 0.082), indicating a “start-up friction” effect; however, once the first threshold is crossed, the coefficient surges to 0.415 in the acceleration stage, demonstrating strong increasing marginal returns. Nevertheless, as urban form intensifies beyond 0.762, the efficiency gains diminish (β = 0.231), reflecting a saturation effect due to congestion and environmental constraints. Mechanism deconstruction confirms that this nonlinear evolution is driven by the synergistic interplay of two core pathways: transportation structure optimization (path coefficient − 0.324) and agglomeration economies (path coefficient 0.452), which operate with varying intensities across different development phases.

Finally, this research offers a scientific basis for differentiated planning strategies tailored to specific stages of urban development. For small and medium-sized cities in the pre-takeoff phase, the priority should be a “Threshold Breakthrough” strategy to overcome low-level equilibrium and rapidly enter the high-yield acceleration window. Conversely, for large and mega-cities at the saturation end of the S-curve, the focus must shift from scale expansion to “Stock Optimization,” utilizing polycentric restructuring and micro-regeneration to mitigate negative externalities. While the IUFI effectively captures macro-level morphological characteristics and universal evolutionary laws across 285 cities, we acknowledge the limitations regarding data granularity. Our current findings provide a strategic systemic roadmap; however, we recognize that the micro-scale mechanisms—such as street-level geometry, 3D built form, and granular building morphology—are essential for fine-tuning localized design interventions. Therefore, bridging the gap between macro-systemic patterns and micro-morphological physics remains a critical priority for our future research, aiming to verify these S-shaped dynamics with higher spatial resolution as data availability improves. Ultimately, by aligning spatial interventions with these critical thresholds and mechanisms, planners can more effectively steer the urban transition towards a low-carbon, resilient, and high-efficiency future.