Toward Sustainable and Equitable Heat Mitigation: Interpretable Machine Learning for Urban Heat Governance in Houston

Abstract

Extreme heat has emerged as a pressing sustainability challenge in rapidly urbanizing metropolitan areas, where built environments intensify thermal exposure and its unequal distribution across socially vulnerable communities. Although previous studies have documented disparities in urban heat exposure, fewer have developed decision-oriented frameworks that can simultaneously quantify heat inequity, identify its dominant drivers, and evaluate mitigation strategies under an explicit equity objective. To address this gap, this study develops an interpretable machine-learning framework to support sustainable and equitable urban heat mitigation in Houston. Using 727 census tracts, we model summer daytime land surface temperature (LST) in 2022 as a function of tract-level natural and built-environment characteristics with XGBoost, interpret model behavior using SHAP, quantify inequity through a Concentration Index relative to social vulnerability, and compare targeted counterfactual intervention scenarios under a dual cooling–equity objective. The results show that heat exposure is disproportionately concentrated in more vulnerable communities, with mean LST increasing from 38.60 °C in low-vulnerability tracts to 39.10 °C in high-vulnerability tracts, alongside a positive and statistically significant Concentration Index. The model demonstrates solid predictive performance (R² = 0.774, RMSE = 0.793 °C), and SHAP results identify coastal distance, NDVI, building height, road density, and building coverage as the principal drivers of tract-level thermal variation. Under equity-targeted intervention scenarios, increasing NDVI and mean building height emerge as the clearest win–win strategies, reducing both average predicted LST and the unequal concentration of heat burden. Overall, this study provides a planning-relevant framework for identifying mitigation priorities that advance urban cooling, equity, and more just forms of climate adaptation.

1. Introduction

Extreme heat is increasingly recognized as one of the most consequential climate-related hazards for cities because it threatens human health [1], stresses energy systems [1], and amplifies existing environmental pressures [2]. These risks are particularly acute in urban areas, where impervious surfaces, dense development, altered urban geometry, and anthropogenic heat emissions intensify the Urban Heat Island (UHI) effect [3,4]. In humid subtropical regions, recent studies have further documented significant seasonal variation in UHI intensity, with the highest magnitudes typically observed during summer months [5,6]. As metropolitan regions continue to expand and redevelop, heat exposure is becoming not only more severe but also more spatially uneven, producing localized thermal hot spots with important implications for urban planning and public health [7,8]. Against this backdrop, urban heat mitigation has become an urgent priority for large metropolitan areas [9,10].

Beyond its environmental and infrastructural impacts, urban heat is increasingly understood as an equity issue [7,11]. Prior studies across U.S. cities consistently show that socially vulnerable populations, including low-income communities and communities of color, are more likely to experience higher heat exposure while also having fewer protective resources, such as tree canopy, cooling amenities, and high-quality housing [12,13,14]. From an environmental justice perspective, such disparities reflect unequal access to urban ecosystem services and cooling resources, which can be understood as part of broader debates on the “right to the city” [15]. This perspective helps frame observed disparities not only as spatial mismatches in mitigation resources but also as potential manifestations of broader environmental injustice.

Recent studies have also advanced the characterization of urban thermal environments by using spatial units that better reflect microclimatic variation. Morphology-based spatial units, such as Local Climate Zones (LCZs) and related climatopic approaches, have been used to delineate areas with more homogeneous microclimatic characteristics than administrative boundaries [16]. Emerging research has also highlighted the importance of nighttime land surface temperature (LST) for capturing thermal inertia and UHI dynamics, as urban materials tend to retain and release heat more strongly under nighttime conditions [17]. Together, these studies have substantially advanced the documentation of unequal heat exposure patterns. However, much of the existing literature remains focused on broad inter-city comparisons, descriptive mapping, or group-based contrasts [18,19]. As a result, while evidence of thermal inequity is now strong, less is known about how cities can translate this evidence into spatially explicit, equity-oriented mitigation priorities [20,21].

This gap is particularly important in Houston. Houston is a humid subtropical metropolitan region with substantial summer heat risk, pronounced heterogeneity in urban form, extensive road infrastructure, varied building morphology, and strong spatial contrasts in socioeconomic vulnerability [22,23]. These characteristics make it a highly relevant case for examining not only where heat burdens are concentrated, but also how alternative planning levers may perform when deployed in the neighborhoods that face the greatest social vulnerability [24,25]. Although previous studies have examined heat vulnerability and thermal environments in Houston [22,26], fewer have provided an integrated framework that links tract-scale heat inequity measurement, interpretable modeling of dominant drivers, and policy-oriented comparison of targeted interventions under a joint cooling-and-equity objective [27,28]. In other words, for a city like Houston, the more practical question is no longer simply whether vulnerable communities are hotter, but which intervention directions are most likely to reduce both heat exposure and inequity when resources are directed to the places that need them most [20,29].

Consequently, to tackle the above gaps, we develop an interpretable machine-learning framework to evaluate equity-oriented urban heat mitigation strategies in the Houston metropolitan area. Using census tracts as the unit of analysis, we model summer daytime land surface temperature as a function of tract-scale natural and built-environment features, quantify heat-exposure inequity relative to social vulnerability using the Concentration Index [30,31], and conduct targeted counterfactual intervention experiments to compare alternative planning levers under a dual cooling–equity objective [32,33]. Specifically, this study targets the above research questions:

• How is summer surface heat exposure distributed along Houston’s social vulnerability gradient, and to what extent is heat disproportionately concentrated in more vulnerable census tracts?
• Can an interpretable machine-learning model reliably capture tract-scale heat exposure using a parsimonious set of natural and built-environment predictors, and what are the dominant drivers of spatial heat variation?
• Under equity-targeted intervention scenarios applied in high-vulnerability neighborhoods, which planning levers generate win–win outcomes by simultaneously reducing mean heat exposure and improving equity, and which levers create trade-offs or lose–lose effects?

Our results reveal a clear and policy-relevant pattern. Across 727 Houston census tracts, summer mean land surface temperature increases from low- to high-vulnerability groups, with the highest temperatures observed in the most vulnerable tracts; the concentration index is positive and statistically significant, indicating that heat exposure is disproportionately concentrated among more vulnerable communities. The XGBoost model captures tract-scale heat variability with solid predictive performance, and SHAP (v0.50.0) interpretation shows that coastal distance is the strongest contextual driver, while building height, road density, building coverage, and NDVI are among the most influential actionable factors [27,34]. Under equity-targeted counterfactual scenarios, increasing NDVI and increasing mean building height emerge as the two clearest win–win strategies, as both reduce average predicted LST and improve equity [29,35]. In contrast, increasing road density and building coverage produces lose–lose outcomes, worsening both heat exposure and its unequal distribution, while river distance and POI density show comparatively weak marginal effects.

This study contributes in several ways. Methodologically, it integrates an interpretable gradient-boosted model, SHAP-based explanation, and the Concentration Index into a unified framework for evaluating urban heat mitigation strategies under an explicit equity objective [27,34]. Empirically, it provides tract-scale evidence on how Houston’s thermal environment is shaped by both contextual natural gradients and modifiable urban-form and greenness characteristics. From an application perspective, it moves beyond simply identifying inequity to comparing targeted intervention pathways in a way that is directly relevant to planning prioritization [20,28]. More broadly, it demonstrates that urban heat strategies should not be judged only by whether they cool the city on average, but also by whether they reduce the unequal concentration of heat burden among socially vulnerable communities [11,32].

2. Datasets and Methodology

This study quantifies inequity in urban heat exposure across socially vulnerable communities in the Houston metropolitan area and evaluates the potential effectiveness of actionable urban-planning levers for simultaneously reducing (i) overall heat exposure and (ii) inequity in its distribution. We use census tracts as the unit of analysis and assemble an integrated tract-level dataset including: (a) remotely sensed land surface temperature (LST) as the heat-exposure outcome; (b) natural and built-environment features hypothesized to shape urban heat; and (c) a tract-level social vulnerability index to define an equity ranking.

Building on this dataset, we (1) model LST using an interpretable gradient-boosted tree approach (XGBoost v3.0.5) to capture nonlinearities and interactions; (2) use SHAP to interpret feature contributions and guide intervention selection; and (3) conduct counterfactual, tract-targeted scaling experiments to compare policy strategies in a consistent “if-then” framework. Finally, we quantify inequity using a Concentration Index (CI) computed relative to social vulnerability ranks, enabling a dual-objective evaluation of “cooling” and “equity” outcomes. The conceptual framework of this study is presented in Figure 1.

2.1. Study Area and Data Collection

This study focuses on the Houston metropolitan area (Texas, USA), a humid subtropical region with substantial summer heat risk and pronounced heterogeneity in urban form (e.g., development intensity, road infrastructure, and building morphology). At the same time, Houston exhibits strong spatial variation in socioeconomic conditions and demographic vulnerability, making it a suitable setting for examining how heat exposure is distributed across vulnerable communities and how targeted interventions may affect both heat and equity outcomes.

This study conducts all analyses at the census-tract scale. Census tracts were selected as the unit of analysis due to their compatibility with publicly available sociodemographic data and their relevance for policy-oriented urban analysis. While alternative spatial frameworks, such as Local Climate Zones (LCZs) and climatopic approaches, have been shown to better capture micro-scale thermal variability associated with urban form [16], the tract-level approach enables the integration of environmental exposure with social vulnerability in a consistent analytical framework. Each tract constitutes one observation with a corresponding LST value, a feature vector describing natural and built environments, and a social vulnerability index. Heat exposure is represented by mean LST in 2022 (LST) [36]. Compared with near-surface air temperature, remotely sensed LST provides finer spatial detail and is more directly responsive to land cover and urban morphology (e.g., vegetation, building coverage/height, roads), which are central to planning interventions. In addition, LST derived from satellite observations enables consistent, high-resolution spatial coverage across the study area, making it particularly suitable for tract-level analysis of intra-urban thermal heterogeneity. While LST does not directly represent human thermal exposure, it serves as a widely used and policy-relevant proxy for surface heat patterns in urban climate studies.

To harmonize raster-based variables (LST and NDVI) with tract boundaries, we apply area-weighted aggregation: for each tract, raster cell values contribute proportionally to their intersection area with the tract polygon. This approach reduces aggregation bias due to pixel–boundary misalignment and improves cross-variable comparability at the tract scale.

2.2. Natural and Built-Environment Feature Construction

Spatial heterogeneity in urban land surface temperature (LST) is typically driven by multiple mechanisms acting in concert. To represent these key processes, this study constructed three groups of features—hydrologic proximity, vegetation conditions, and built-environment morphology—and computed these indicators at the census-tract scale to support subsequent interpretable modeling and scenario-based simulations. The corresponding data sources and variable definitions are summarized in

Table 1. List of features used as model input.

Feature	Source	Mean	Range	Description
LST	MODIS MOD11A2 (Google Earth Engine)	38.640	[0.000, 41.699]	Daytime land surface temperature (LST) in summer 2022 (June–August), aggregated to the census-tract level using area-weighted averaging.
NDVI	Sentinel-2 Level-2A (Google Earth Engine)	0.165	[−0.009, 0.384]	Mean summer NDVI, derived using cloud masking and temporal compositing, then area-weighted aggregated to the tract level.
D2river	Municipal high-resolution hydrology vector datasets	4391.131	[0.000, 27,205.973]	Euclidean distance from the tract centroid to the nearest river.
D2sea	Municipal high-resolution hydrology vector datasets	31,790.585	[0.000, 69,629.555]	Euclidean distance from the tract centroid to the nearest coastline.
Building Coverage	GlobalML Building Footprints	0.148	[0.000, 0.410]	Building footprint area within the tract/tract area (i.e., building coverage ratio).
Building Height	GlobalML Building Footprints	4.936	[1.594, 15.133]	Mean building height, summarized from building height attributes within the tract.
POI Density	OpenStreetMap	68.745	[0.000, 4973.096]	POI density (count/km2), used as a proxy for activity intensity and land-use/functional mix.
Road Density	OpenStreetMap	22.989	[0.000, 180.897]	Road density (km/km2), defined as total road length per unit area, representing transport infrastructure intensity and impervious-surface development.

.

The selected variables were organized into hydrological proximity, vegetation condition, and built-environment morphology/infrastructure dimensions. This design was intended to represent major urban thermal mechanisms while avoiding excessive redundancy among highly overlapping remote-sensing indicators. Potential multicollinearity among the selected predictors was further examined using a correlation matrix and variance inflation factor analysis, as reported in Section 3.2.

Hydrological features: Water bodies can buffer the urban thermal environment by altering the local surface energy balance, facilitating the advection of cooler air, and providing pathways for evaporative latent heat exchange. To quantify hydrologic proximity, we used the project-provided high-resolution hydrological vector datasets (river polyline layer and coastline polygon layer) and computed the Euclidean distance from each census-tract centroid to the nearest river and the nearest coastline. These measures—D2river [37] and D2sea [37], respectively—capture the spatial distance-decay patterns of riverine cooling and coastal thermal modulation.

Vegetation features: Vegetation cover is a key determinant of urban heat exposure, primarily through shading and evapotranspiration that reduce land surface temperature. We used the Normalized Difference Vegetation Index (NDVI) [36] to characterize tract-level vegetation conditions. NDVI was derived from Sentinel-2 Level-2A imagery on the Google Earth Engine platform using cloud masking and temporal compositing, and we calculated the mean NDVI for summer 2022 (June–August) to align with the heat exposure observation window.

Built-environment features: The built environment can substantially shape urban thermal patterns by modifying physical properties such as imperviousness, surface roughness, and thermal capacity. We operationalized built-environment characteristics along three dimensions—building morphology, transport infrastructure, and activity intensity:

• Building coverage and mean building height: Using Microsoft/GlobalML Building Footprints, we delineated building footprints and computed the building coverage ratio (building footprint area/tract area). Building height attributes from the same dataset were summarized to obtain tract-level mean building height (Bldg Coverage, Bldg Height) [38].
• Road density: Based on curated OSM road data (downloaded via OpenStreetMap), we calculated total road length per unit area (km/km²) as a proxy for transport infrastructure density and impervious-surface development intensity (Road Density) [39].
• POI density: Using curated OSM POI data (downloaded via OpenStreetMap), we computed the number of POIs per unit area (count/km²) to represent activity intensity and functional agglomeration (POI Density) [39]. Feature snapshots are shown in Figure 2.

2.3. Social Vulnerability and Inequality Measurement of Urban Heat Exposure

This study focuses on inequities in exposure to urban environmental risks, with particular attention to whether socially vulnerable groups bear a disproportionate heat-exposure burden. To identify communities with higher social vulnerability and to provide a ranking basis for inequality assessment, we constructed a tract-level representation of social vulnerability using sociodemographic and socioeconomic indicators. Specifically, we selected six variables capturing economic deprivation, limited educational attainment, racial/ethnic composition, and age-related sensitivity: poverty status (EP_POV150), unemployment rate (EP_UNEMP), proportion without a high school diploma (EP_NOHSDP), proportion of racial/ethnic minorities (EP_MINRTY), proportion of adults aged 65 and above (EP_AGE65), and proportion of youth aged 17 and below (EP_AGE17) [40].

Following widely used practices in social vulnerability assessment, particularly the Centers for Disease Control and Prevention Social Vulnerability Index (SVI) framework, we adopted an equal-weight (unweighted average) approach to aggregate the standardized indicators [41]. This approach avoids imposing subjective importance differences across dimensions and ensures transparency and comparability across census tracts.

To address differences in scale and improve cross-indicator comparability, these variables were quantile-normalized within the study area and mapped to the [0, 1] interval, where 0 indicates a relatively low level and 1 indicates a relatively high level of the corresponding indicator.

Based on these standardized scores, the social vulnerability index for census tract i, denoted as $V{I}_i$, was defined as the unweighted mean of the six quantile scores:

$$\begin{array}{c}V{I}_i={\displaystyle \frac{1}{6}}{\displaystyle \sum _{k=1}^6}{S}_{ik}\end{array}$$

(1)

where $S_{ik}$ is the quantile score of tract i on the k-th vulnerability indicator. Larger values of $V{I}_i$ indicate higher social vulnerability, implying a greater likelihood of spatial concentration of resource-constrained, health-sensitive, or structurally disadvantaged populations.

To quantify the degree to which urban heat exposure is concentrated along the social vulnerability ranking, we employed the Concentration Index (CI) to measure inequality in “heat exposure relative to vulnerability.” CI evaluates whether heat exposure is disproportionately distributed across groups ordered by vulnerability by comparing the distribution of the outcome variable (e.g., heat exposure) along the vulnerability ranking. It is defined as:

$$CI={\displaystyle \frac{2}{\mu }} \mathrm{Cov}\left(y,r\right)$$

(2)

where $\mu$ is the mean of the heat exposure variable $y$ in the study area (in this study, $y$ can be the observed LST or the model-predicted $\widehat{y}$), and $r$ is the fractional rank of census tracts after sorting by $VI$ from low to high and rescaling to the [0, 1] range, with $r=0$ indicating the least vulnerable and $r=1$ the most vulnerable. A positive CI indicates that higher heat exposure is disproportionately concentrated in more vulnerable communities (“adverse concentration”), whereas a negative CI suggests that heat exposure is more concentrated in less vulnerable communities. Values of CI closer to zero imply a more equitable distribution of heat exposure along the vulnerability gradient.

2.4. Interpretable Machine-Learning Modeling of Urban Heat Exposure

We modeled census-tract–level urban heat exposure as a regression problem, aiming to learn the functional mapping between natural/built-environment features and observed heat exposure. For each census tract i, the feature vector is defined as:

$${\mathbf{X}}_i=\left(x_{i1},x_{i2},\dots ,x_{in}\right)$$

(3)

where n denotes the number of input features (including, in this study, NDVI, hydrologic proximity, POI density, road density, building coverage, and mean building height). The observed heat exposure is denoted by $y_i$ (here LST). The learning objective is to estimate a regression function $f(\cdot )$ such that:

$${\widehat{y}}_i=f\left({\mathbf{X}}_i\right)$$

(4)

where ${\widehat{y}}_i$ is the model-predicted heat exposure for tract i.

To avoid selecting the regression function $f(\cdot )$ a priori, we compared three representative candidate models: multiple linear regression, random forest, and Extreme Gradient Boosting (XGBoost). These models represent different levels of model complexity. Multiple linear regression was included as a transparent baseline model, random forest was included as a commonly used non-parametric ensemble model, and XGBoost was included as a gradient-boosted tree model capable of capturing nonlinear relationships and feature interactions. All candidate models were trained and evaluated using the same input features and validation setting to ensure comparability.

Among the compared models, the tuned XGBoost model achieved the best predictive performance and was therefore selected as the final implementation of $f(\cdot )$ for subsequent SHAP interpretation and counterfactual scenario analysis. XGBoost is a tree-based gradient-boosting ensemble [42,43] that has demonstrated superior performance in capturing nonlinear relationships and higher-order interactions between urban environmental variables and heat exposure [24], while maintaining strong generalization performance under multi-source features [28]. Compared with strong-assumption models such as linear regression, gradient-boosted trees do not rely on distributional assumptions or linear additivity; compared with a single decision tree, they iteratively fit residuals and aggregate multiple weak learners, thereby reducing bias while controlling overfitting. The XGBoost prediction can be expressed as the sum of outputs from M regression trees:

$$\begin{array}{c}{\widehat{y}}_i={\displaystyle \sum _{m=1}^M}{g}_m\left({\mathbf{X}}_i\right) \end{array}$$

(5)

where $g_m(\cdot )$ denotes the m-th regression tree and M is the number of trees.

To ensure reproducibility and mitigate overfitting, we first split the dataset into training and test sets using a fixed random seed. We then applied a two-stage hyperparameter selection strategy. First, we performed cross-validated hyperparameter search on the training set using RandomizedSearchCV (scikit-learn v1.7.2) to identify key structural parameters, including maximum tree depth, row subsampling, column subsampling, and regularization terms. Second, based on the candidate best parameter set, we ran cross-validation using xgboost.cv with early stopping to automatically determine the effective number of boosting iterations (i.e., the optimal number of boosting rounds). The resulting tuned model was subsequently used for scenario simulations and inequality assessment. The same train–test partition and evaluation metrics were used for the comparative models, allowing model selection to be based on empirical predictive performance rather than an a priori assumption about model superiority.

Because spatial data may violate the independence assumption of random cross-validation, we further conducted two spatial diagnostic analyses. First, we mapped model residuals and calculated Moran’s I to test whether prediction errors exhibited spatial autocorrelation. Moran’s I is defined as:

$$I={\displaystyle \frac{N}{W}}{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N} {\displaystyle {\sum }_{j=1}^N} w_{ij}\left(e_i-\overline{e}\right)\left(e_j-\overline{e}\right)}{{\displaystyle {\sum }_{i=1}^N} (e_i-\overline{e}{)}^2}}$$

(6)

where $N$ is the number of census tracts, $e_i$ and $e_j$ are the model residuals for tracts $i$ and $j$, $\overline{e }$ is the mean residual, $w_{ij}$ is the spatial weight between tracts $i$ and $j$, and $W={\sum }_{i=1}^N {\sum }_{j=1}^N{w}_{ij}$. A positive Moran’s I indicates that similar residuals tend to cluster spatially, whereas a value close to zero suggests weak spatial autocorrelation. Second, we implemented spatial block validation as a stricter assessment of spatial generalization. Census tracts were grouped into spatial blocks based on their centroid coordinates in a projected coordinate system, and GroupKFold validation was used to ensure that all tracts within the same spatial block were assigned either to the training set or to the test set, but not both. This design reduces spatial leakage between nearby tracts and provides a more conservative estimate of model performance when entire spatial regions are withheld during validation.

Before interpreting the fitted model using SHAP, we also examined potential multicollinearity among the selected predictors. Pairwise Pearson correlation coefficients were calculated to construct a predictor correlation matrix. In addition, the variance inflation factor (VIF) was computed for each predictor to quantify its linear dependence on the remaining predictors. For predictor $x_j$, the VIF is defined as:

$${VIF}_j={\displaystyle \frac{1}{1-R_j^2}}$$

(7)

where $R_j^{2 }$ is obtained by regressing predictor $x_{j }$ on all other predictors. A larger VIF indicates stronger multicollinearity. In this study, VIF values below 5 were considered to indicate the absence of severe multicollinearity. This diagnostic step was used to assess whether the subsequent SHAP-based interpretation could be substantially affected by redundant predictors.

After this diagnostic check, we employed SHAP (SHapley Additive exPlanations) [34] to attribute XGBoost predictions, enabling mechanism-informed identification of key environmental drivers and intervention levers [27,34,44]. For a given tract i, SHAP decomposes the prediction into a baseline term plus the sum of feature contributions:

$${\widehat{y}}_i={\varphi }_0+{\displaystyle \sum _{j=1}^n}{\varphi }_{ij}$$

(8)

where ${\varphi }_0$ is the global baseline prediction and ${\varphi }_{ij}$ represents the marginal contribution of feature $x_{ij}$ to tract i. Using global importance metrics (e.g., the mean of $\mid {\varphi }_{ij}\mid$) and SHAP dependence plots, we can simultaneously identify (i) which features are most influential and (ii) how the direction and magnitude of each feature’s effect vary across its value range, thereby providing a mechanism-informed basis for subsequent intervention simulations.

2.5. Scaling-Factor Specification for Intervention Scenario Simulations

To evaluate the potential effects of adjustments to different urban planning elements [32,45], we constructed counterfactual intervention scenarios based on the trained regression model, consistent with emerging approaches in urban climate policy assessment [33]. The core idea is to impose a prespecified proportional change on a target feature while holding all other features constant, thereby generating model-based predictions of “how heat exposure would change if this element were increased or reduced.” Without introducing additional assumptions for causal identification, this approach provides a consistent benchmark for comparing policy sensitivity and equity responses across strategies.

Specifically, for any environmental feature $x_j$, we define a scaling factor as:

$$s_j=1+{\mathrm{\Delta }}_j$$

(9)

where ${\mathrm{\Delta }}_j\in [-1.0, 1.0]$ denotes the proportional change relative to the baseline level, corresponding to intervention intensities ranging from a 100% reduction to a 100% increase. For an intervention level $l$(i.e., a given ${\mathrm{\Delta }}_j$), the counterfactual feature vector for census tract $i$ is:

$${\mathbf{X}}_i^{\left(l\right)}=\left(x_{i1},\dots ,s_j\cdot x_{ij},\dots ,x_{in}\right)$$

(10)

that is, only the target feature $x_{ij}$ is scaled, while all other features remain unchanged. Feeding ${\mathbf{X}}_i^{\left(l\right)}$ into the trained model $f(\cdot )$ yields the predicted heat exposure under intervention level $l$:

$${\widehat{y}}_i^{\left(l\right)}=f\left({\mathbf{X}}_i^{\left(l\right)}\right)$$

(11)

We then compute the mean predicted heat exposure ${\mu }^{\left(l\right)}$ under intervention level $l$, as well as the degree of heat-exposure inequality with respect to the social-vulnerability ranking:

$$C{I}^{\left(l\right)}={\displaystyle \frac{2}{{\mu }^{\left(l\right)}}} \mathrm{Cov}\left({\widehat{y}}^{\left(l\right)},r\right)$$

(12)

where $r$ is the fractional rank based on $VI$ (see Equation (2)), and ${\widehat{y}}^{\left(l\right)}$ is the vector of predicted heat exposure across all census tracts under intervention level $l$. By systematically enumerating scenarios across different target features $x_j$ and different ${\mathrm{\Delta }}_j$ values, we derive response curves that characterize each intervention’s (i) cooling effect $\mathrm{\Delta }{\mu }^{\left(l\right)}$ and (ii) equity improvement $\mathrm{\Delta }C{I}^{\left(l\right)}$. These curves enable a comparative assessment of the relative effectiveness of alternative planning strategies in reducing overall heat exposure and mitigating inequities.

3. Results

3.1. Inequality in Urban Heat Exposure

This study uses Houston census tracts as the unit of analysis. After data cleaning and excluding tracts with missing values, 727 tracts were retained (Figure 3). At the aggregate level, summer-mean LST exhibits a clear gradient aligned with social vulnerability (

Table 2. Mean land surface temperature (LST) by vulnerability group.

	Low Vulnerability	Medium Vulnerability	High Vulnerability
Mean LST (Unit: °C)	38.60	38.70	39.10
Kruskal–Wallis, H = 6.48 (p < 0.05).

). Specifically, mean LST is lowest in low-vulnerability tracts (38.60 °C), slightly higher in medium-vulnerability tracts (38.70 °C), and highest in high-vulnerability tracts (39.10 °C). Therefore, more socially vulnerable communities experience systematically higher surface heat exposure. This groupwise pattern is statistically supported by the Kruskal–Wallis test (H = 6.48, p < 0.05), indicating that differences across vulnerability groups are unlikely to be driven by random variation alone.

To quantify whether heat exposure is disproportionately concentrated among vulnerable communities—beyond mean differences across discrete groups—we computed the Concentration Index (CI) relative to the social vulnerability ranking (Section 2.3). The estimated CI is 0.0027 (positive) and is statistically significant (p < 0.05) [30,31], indicating a modest but adverse concentration of heat exposure toward more vulnerable tracts, consistent with environmental justice frameworks [11,29]. Although the CI magnitude is small, its positive sign still implies a consistent directional inequity: vulnerability and higher heat exposure tend to co-occur along the ranking. Consequently, equity-oriented mitigation should prioritize high-vulnerability neighborhoods, not only because they face compounded risks, but also because targeted action in these areas has the greatest potential to improve distributional outcomes.

3.2. Interpreting the Roles of Urban Factors in Heat Exposure

To characterize how built and natural environmental factors shape tract-level heat exposure in Houston, we first compared three regression models using the same input features: multiple linear regression, random forest, and XGBoost. The comparison shows that XGBoost achieved the best overall predictive performance, with the highest R² and the lowest error metrics among the tested models (

Table 3. Comparison of predictive performance across candidate regression models.

Model	R2	MAE (°C)	RMSE (°C)
Multiple Linear Regression	0.341	0.919	1.176
Random Forest	0.594	0.692	0.923
XGBoost	0.626	0.664	0.886

).

Under random cross-validation, the model achieved R² = 0.774, MAE = 0.447 °C, and RMSE = 0.793 °C (Figure 4), indicating good predictive performance when training and testing samples were spatially mixed across the study area [28,31]. To further evaluate spatial dependence in model errors, we calculated Moran’s I for the model residuals. The residual Moran’s I was 0.633 with a simulated p-value of 0.001, indicating statistically significant positive spatial autocorrelation. This result suggests that some spatially structured variation remains in the residuals, which is common in tract-level urban environmental data. In addition to random cross-validation, we further conducted spatial block validation to account for potential spatial dependence among nearby census tracts. Spatial block validation produced lower performance than random cross-validation. This decline is expected under a stricter spatial extrapolation setting and indicates that spatially structured variation remains in the data. Overall, these results suggest that the model captures meaningful tract-level associations while also highlighting the importance of considering spatial dependence in model validation.

To ensure that the SHAP interpretation was not primarily driven by severe predictor redundancy, we examined multicollinearity among the selected input variables using a Pearson correlation matrix and variance inflation factor (VIF) analysis. The correlation matrix showed several physically meaningful associations among urban environmental variables, including a negative correlation between NDVI and road density (r = −0.61) and a positive correlation between road density and building coverage (r = 0.59) (Figure 5). However, no extremely high pairwise correlation was observed among the selected predictors, with all absolute correlation coefficients remaining below 0.7. The VIF results further support this conclusion: all predictors had VIF values below 2.2, well below the commonly used threshold of 5 (

Table 4. Variance inflation factor (VIF) values for selected model predictors.

Predictor	VIF
Road density	2.148
Building coverage	1.821
NDVI	1.796
Building height	1.376
POI density	1.281
Distance to sea	1.152
Distance to river	1.095

). The highest VIF was observed for road density (2.148), followed by building coverage (1.821) and NDVI (1.796), indicating only weak-to-moderate linear dependence among predictors. Together, these results indicate that severe multicollinearity is unlikely to dominate the model interpretation or substantially distort the SHAP-based importance ranking.

After confirming that severe multicollinearity was not present among the selected predictors, to translate predictive performance into planning-relevant insight [21], we used SHAP global importance (Figure 6) to identify dominant drivers of Houston’s spatial heterogeneity in heat exposure [5,6]. Distance to the coastline (D2sea) exhibits the highest contribution, highlighting strong regional background gradients associated with coastal boundary conditions. However, because coastal distance is not directly modifiable through urban planning, it is treated as a contextual driver rather than an actionable intervention lever in the policy simulations (Section 4). Beyond this natural boundary effect, morphology and infrastructure variables show substantial influence [4,35]: mean building height (Bldg Height) and road density (Road Density) rank among the most important predictors [35,44], while building coverage (Bldg Coverage) and vegetation (NDVI) also contribute meaningfully [5,6]—together suggesting that the balance between “hardening intensity” and “green mitigation capacity” is central to tract-level heat patterns. In contrast, distance to rivers (D2river) and POI density (POI Density) exhibit weaker global contributions, implying more limited or context-dependent explanatory power. Taken together, these results motivate the intervention design: by adjusting policy-relevant features related to greening and urban form, it may be possible to influence both heat exposure levels and their inequitable distribution while maintaining practical implementability.

4. Evaluating the Effectiveness of Various Urban Development Strategies

To translate the modeling results into actionable planning insights, this section evaluates the effectiveness of alternative urban development strategies under a dual cooling-equity objective. As outlined in Section 2.5, we designed counterfactual intervention simulations to systematically assess how modifying key environmental features influences both overall heat exposure and its unequal spatial distribution. By establishing a consistent benchmarking framework, these simulations enable us to compare the relative benefits and potential trade-offs of various policy levers when deployed to address urban thermal injustice.

4.1. Annual-Scale Evaluation of Key Factors Shaping Heat-Exposure Inequity

Focusing on the annual-scale response, we operationalize this approach by applying prespecified proportional scaling factors to selected features. Crucially, these adjustments are implemented exclusively within high-vulnerability census tracts (vulnerability index $VI$ above the sample mean), while keeping all other tracts unchanged. This targeted equity-first design explicitly tests whether prioritizing interventions in vulnerable areas can improve distributional equity without sacrificing overall citywide cooling performance.

We quantify inequity using the Concentration Index (CI) computed from predicted summer-mean LST under each scenario and summarize CI responses across scaling levels (Figure 7). Distance to the coastline (D2sea) is excluded because it is not directly modifiable. Overall, the response curves indicate that planning levers differ substantially in both the direction and magnitude of CI change, motivating the comparative strategy ranking in Section 4.3.

Among the tested factors, NDVI shows the most consistent equity benefit [32,35]: increasing vegetation in high-vulnerability areas reduces CI monotonically [32], whereas vegetation loss increases CI, suggesting greening is a robust lever for alleviating the relative heat burden borne by vulnerable communities [11,29,32]. For the built environment, morphology-related levers also matter: increasing mean building height lowers CI, while increasing building coverage raises CI, implying that form optimization may improve equity but further surface hardening/intensification in vulnerable areas may worsen it. In addition, road density exhibits a strongly directional pattern—reducing road density decreases CI markedly, whereas increases tend to leave CI unchanged or shift it upward—highlighting potential equity risks associated with incremental infrastructure expansion. Other features show comparatively weaker or more context-dependent effects and are therefore discussed more briefly in subsequent sections.

Finally, Figure 7 suggests nonlinear and coupled responses across urban features, since vegetation, morphology, and road structure are jointly shaped by land-use intensity and development patterns. These dependencies motivate a tree-based framework (XGBoost) for scenario assessment, which can better capture nonlinearities and interactions and thus provide a more reliable basis for equity-oriented heat-risk mitigation.

4.2. Intervention-Intensity Responses and Asymmetry

The CI response curves in Figure 7 reveal distinct “dose–response” patterns across urban features under targeted interventions in high-vulnerability areas. First, some features exhibit a monotonic improvement pattern [33,45]: as intervention intensity increases, CI decreases consistently, indicating that stronger interventions yield more stable gains in heat-exposure equity [32]. NDVI provides the clearest example, suggesting that sustained increases in vegetation cover and greenness in high-vulnerability neighborhoods deliver robust equity benefits. Mean building height shows a similarly consistent decline in CI, implying that morphology-oriented improvements related to shading and ventilation can generate cumulative equity gains.

Second, certain features display monotonic deterioration: as these characteristics are increased in high-vulnerability tracts, CI rises, indicating amplified inequity. Building coverage shows a clear upward response in Figure 7, suggesting that further intensification of surface hardening and development intensity in disadvantaged communities may have adverse equity consequences.

A third class comprises direction-sensitive/asymmetric features, for which equity responses to “decreases” versus “increases” are not symmetric. Road density exhibits pronounced asymmetry in Figure 7: reducing road density in high-vulnerability tracts leads to a substantial decline in CI, whereas increasing road density tends to keep CI unchanged or shift it upward. This indicates that strategies related to transport infrastructure and impervious-surface expansion are direction-dependent in equity terms—“de-intensification” interventions may generate clearer equity gains, while incremental expansion may entail equity risks.

Finally, some features show weak sensitivity, with relatively flat CI curves over a broad scaling range—such as distance to rivers and POI density—suggesting limited marginal effects on annual-scale heat-exposure inequity or impacts that may manifest indirectly through joint changes with other variables. Overall, the curve shapes in Figure 7 indicate that, under targeted intervention settings, urban features differ not only in the direction of their equity impacts but also in the strength and nonlinearity of their responses to intervention intensity. These patterns provide an empirical basis for designing equity-oriented strategies that are scalable and sustainable.

4.3. Strategy Ranking and Recommendations Under a Dual “Cooling–Equity” Objective

To jointly assess thermal mitigation efficiency and distributive equity [20,32], we compared the targeted intervention scenarios using the changes in citywide mean predicted LST ($\mathrm{\Delta }\mu$) and the Concentration Index ($\mathrm{\Delta }CI$) (

Table 5. Dual-objective outcomes ($\mathrm{\Delta }\mu$ and $\mathrm{\Delta }CI$) for six targeted intervention scenarios in high-vulnerability tracts.

	NDVI	D2river	Building Height	Building Coverage	Road Density	POI Density
Δμ	−0.17783	−0.01827	−0.33581	0.03637	0.06214	−0.00109
ΔCI	−0.00223	−0.00017	−0.00443	0.00069	0.00074	−0.00002

) [30,31], enabling a dual-objective evaluation of alternative planning strategies [20]. Negative $\mathrm{\Delta }\mu$ indicates a net cooling effect, whereas negative $\mathrm{\Delta }CI$ indicates an improvement in equity through a reduced concentration of heat burden in high-vulnerability tracts. Under this dual objective, strategies that reduce both metrics can be regarded as the most desirable intervention options.

As shown in Table 5, increasing mean building height was associated with the largest model-predicted co-benefit [35,46], yielding the largest reduction in mean predicted LST ($\mathrm{\Delta }\mu =-0.33581$) and the greatest improvement in equity ($\mathrm{\Delta }CI=-0.00443$) [32,35]. Increasing NDVI also generated a clear win–win outcome, with substantial reductions in both heat exposure ($\mathrm{\Delta }\mu =-0.17783$) and inequity ($\mathrm{\Delta }CI=-0.00223$). Taken together, these results identify morphology-oriented adjustment and targeted greening as the two most effective intervention directions in high-vulnerability neighborhoods when cooling and equity are considered simultaneously. Because building height may partly reflect broader spatial development patterns, this result should be interpreted as a model-based association rather than a standalone planning prescription.

In contrast, increasing road density and building coverage worsened both outcomes. Road density was associated with increases in both mean LST ($\mathrm{\Delta }\mu =0.06214$) and the Concentration Index ($\mathrm{\Delta }CI=0.00074$), while building coverage showed a similar adverse pattern ($\mathrm{\Delta }\mu =0.03637$, $\mathrm{\Delta }CI=0.00069$). These findings suggest that additional hardening and development intensification in already vulnerable areas may not only elevate thermal exposure, but also reinforce its unequal distribution.

The remaining intervention levers showed comparatively limited marginal effects. Increasing distance to rivers produced only a small cooling and equity benefit ($\mathrm{\Delta }\mu =-0.01827$, $\mathrm{\Delta }CI=-0.00017$), while increasing POI density had effects close to zero overall ($\mathrm{\Delta }\mu =-0.00109$, $\mathrm{\Delta }CI=-0.00002$). Overall, Table 5 indicates a clear strategy ranking: priority should be given to increasing building height and NDVI in high-vulnerability tracts, whereas increasing building coverage and road density should be avoided or treated with caution. It should be noted, however, that reductions in land surface temperature (LST) do not necessarily translate into improvements in human thermal comfort. From an urban physics perspective, factors such as thermal anisotropy and radiative processes at the pedestrian level may lead to different thermal experiences. In particular, increases in surface albedo may reduce surface temperature while increasing reflected shortwave radiation exposure for pedestrians, potentially offsetting cooling benefits. More broadly, these results highlight that intervention effectiveness should be evaluated not only by average cooling gains, but also by the extent to which such gains are distributed more equitably across socially vulnerable communities.

5. Conclusions

Extreme heat has become an increasingly important urban environmental and public-health challenge, and its impacts are often unequally distributed across socially vulnerable communities. While prior studies have documented the existence of urban thermal inequities, fewer have developed an application-oriented framework that can simultaneously quantify heat-exposure inequality, identify its dominant urban drivers, and evaluate potential mitigation strategies under an explicit equity objective. This gap is especially important in Houston, where strong summer heat, pronounced heterogeneity in urban form, and marked spatial variation in social vulnerability make the city a highly relevant case for equity-oriented urban heat research.

To address this gap, this study developed an interpretable machine-learning framework to assess heat-exposure inequity and compare targeted mitigation strategies across Houston census tracts. Using tract-level land surface temperature, natural and built-environment predictors, and a social vulnerability index, we combined XGBoost modeling, SHAP-based interpretation, and Concentration Index analysis with counterfactual intervention experiments. The results show that heat exposure is disproportionately concentrated in more vulnerable tracts, with mean LST increasing along the vulnerability gradient. The model achieved good performance under random cross-validation, while the additional Moran’s I test and spatial block validation indicated that spatial dependence remains relevant in model evaluation. SHAP interpretation identified coastal distance as the strongest contextual factor, while NDVI, building height, road density, and building coverage emerged as influential variables associated with tract-level heat variation. Among the targeted intervention scenarios, increasing NDVI and, to a certain extent, increasing mean building height were associated with win–win outcomes by reducing both average heat exposure and inequity, whereas increasing road density and building coverage generated adverse effects on both objectives. However, the role of building height should be interpreted with caution, as its effects may depend on local urban form and may partly reflect underlying spatial patterns, where taller buildings are more prevalent in lower-vulnerability areas, suggesting that building height may act as a proxy for broader development conditions rather than a directly actionable intervention in isolation.

This study contributes in several respects. Methodologically, it offers a unified and interpretable framework that integrates machine learning, explainable AI, and inequality measurement for urban heat analysis under an explicit equity lens. Empirically, it clarifies how Houston’s thermal landscape is shaped by both structural environmental gradients and modifiable urban-form characteristics. Practically, it moves beyond descriptive identification of inequity toward a decision-oriented evaluation of intervention priorities, showing that urban heat strategies should be assessed not only by their average cooling effects but also by whether they improve the distribution of thermal benefits across vulnerable communities.

Several limitations should also be acknowledged. First, this analysis is based on cross-sectional tract-level conditions in 2022 and therefore does not capture temporal dynamics, seasonal variation, or longer-term changes in urban development and vulnerability. While incorporating multi-year data could provide a more comprehensive understanding, it would also substantially increase data requirements and model complexity. Future research could extend this framework by integrating longitudinal or multi-period data to examine the temporal evolution of heat exposure and its equity implications. Second, the validation results indicate that spatial dependence remains present in the modeling results. Although random cross-validation showed good predictive performance, Moran’s I and spatial block validation suggest that residual spatial structure should be considered when interpreting model outputs. Future work could incorporate additional spatial predictors, such as land-use composition, industrial activities, anthropogenic heat indicators, local climate zones, sky-view factor, or finer-scale urban morphology, to further improve spatial representation. Third, the scenario analysis is counterfactual and stylized, meaning that the simulated intervention effects represent comparative planning directions rather than exact forecasts of real-world implementation outcomes. Additionally, the intervention design assumes that each feature is adjusted independently and that interventions are applied only within high-vulnerability tracts. This simplification does not capture potential synergistic interactions among urban features (e.g., co-evolution of vegetation, morphology, and infrastructure) or the practical feasibility constraints of real-world policy implementation, where planning actions are often interdependent and subject to institutional and spatial limitations. Fourth, the use of tract-level aggregation may mask finer intra-tract variation in exposure and vulnerability. While LST provides a consistent proxy for surface heat patterns, alternative indicators such as near-surface air temperature, land surface thermal indices, or composite human thermal comfort metrics, including UTCI or WBGT, could offer complementary insights into micro-scale thermal exposure and climate vulnerability. Integrating such measures in future work may improve the representation of human-relevant heat risk at finer spatial scales and support more locally targeted mitigation strategies.

Finally, the use of a static social vulnerability index as a proxy for equity may not fully capture differences in adaptive capacity across communities. Lower-vulnerability areas may benefit from greater access to private cooling resources, higher energy affordability, or existing green infrastructure, which can partially offset heat exposure. As a result, the relationship between vulnerability and mitigation needs may be more nuanced than represented in this framework. Future research could incorporate dynamic or multidimensional indicators, such as energy expenditure, cooling access, or green infrastructure availability, to better reflect the complexity of urban heat vulnerability.