Urban Climate Dynamics: Analyzing the Impact of Green Cover and Air Pollution on Land Surface Temperature—A Comparative Study Across Chicago, San Francisco, and Phoenix, USA

Abstract

Rapid urbanization worldwide has significantly altered urban climates, creating a need to balance urban growth with thermal environmental quality for sustainable development. This study examines the relationship between land surface temperature (LST) and urban characteristics, particularly focusing on how green cover can mitigate urban heat and how air pollution can increase temperatures. Recognizing the predictive value of LST for urban heat island (UHI) intensity, we analyzed three distinct U.S. cities—Chicago, San Francisco, and Phoenix—each characterized by unique climate and urban planning features. This study investigates the relationship between atmospheric pollutants (SO₂, NO₂, CO, O₃) and the Normalized Difference Vegetation Index (NDVI) with land surface temperature (LST) using regression and correlation analyses. The analysis aims to elucidate how changes in atmospheric pollutants and NDVI affect variations in land surface temperature. Regression analysis is employed to estimate the coefficients of independent variables and quantify their impact on LST. Correlation analysis assesses the linear relationships between variables, providing insights into their pairwise associations. The study also examines multicollinearity between independent variables to identify potential confounding factors. The results reveal significant associations between atmospheric pollutants, NDVI, and land surface temperature, contributing to our understanding of the environmental factors influencing LST dynamics and informing climate change mitigation strategies. The observed inconsistencies in correlations across cities highlight the importance of the local context in environmental studies. Understanding these variations can aid in developing tailored urban planning policies that consider unique city characteristics for more effective climate resilience. Furthermore, a positive association was consistently obtained between pollutants and LST, indicating that increased pollution levels contribute to higher surface temperatures across different urban settings.

1. Introduction

Urbanization, characterized by the expansion of cities and the transformation of natural landscapes into built environments, has profound effects on local climates. One of the most significant consequences of rapid urbanization is the urban heat island (UHI) effect, where urban areas experience higher temperatures than their rural counterparts. This phenomenon is primarily driven by the replacement of vegetation with impervious surfaces such as concrete and asphalt, which absorb and retain heat [1]. These temperature variations within cities are influenced by the level and type of urbanization. UHIs exacerbate existing urban heat, posing health risks to residents, particularly during the hot summer months, impacting both children and adults and diminishing urban quality of life [2]. Understanding and mitigating the UHI effect is crucial for enhancing thermal comfort, reducing energy consumption, and improving public health in urban areas [3].

The interplay between land surface temperature (LST) and urban characteristics, including green cover and air pollution, is a critical area of study for urban climatology. Vegetation plays a key role in mitigating the UHI effect by providing shade, releasing moisture through transpiration, and reflecting a portion of solar radiation [4]. The Normalized Difference Vegetation Index (NDVI) is a widely used indicator of green cover, allowing researchers to quantify the extent and health of vegetation in urban areas [5]. Higher NDVI values generally correspond to cooler surface temperatures, highlighting the importance of urban greening initiatives in UHI mitigation [6]. Several research studies have investigated the impact of NDVI and UHI in major cities worldwide. Rani et al. (2018) demonstrated a correlation between temporal NDVI and surface temperature [7]. Venkatraman et al. (2024) analyzed the city of Sao Paulo, Brazil, over four decades (1992–2022) using remote sensing and indices like NDVI and LST to assess the intensity of UHI throughout this period [8]. Sharmin et al. (2024) studied the coastal city of Cardiff, exploring the spatiotemporal variations in LST, NDVI, and other indices [9]. These studies emphasize the need for enhanced research, policies, and preparedness to effectively respond to and mitigate the effects of urban heat, particularly through the integration of greenery and green spaces in urban planning efforts.

On the other hand, atmospheric pollutants such as sulfur dioxide (SO₂), nitrogen dioxide (NO₂), carbon monoxide (CO), and ozone (O₃) can exacerbate urban heat by contributing to the greenhouse effect and altering atmospheric chemistry [10]. These pollutants absorb and re-radiate infrared radiation, increasing surface temperatures and impacting air quality [11]. The relationship between air pollution and LST is complex and multifaceted, necessitating comprehensive studies to disentangle the various contributing factors and their interactions. Cichowicz and Bochenek (2024) underscored the impact of UHI and urban pollution islands (UPI) on human quality of life [12]. Han et al. (2024) investigated the role of green spaces in mitigating air pollution and the UHI effect, emphasizing the crucial role of urban greening in understanding these dynamics across seasons [13]. Iungman et al. (2024) analyzed 946 European cities to assess how different urban configurations influence air pollution and the UHI effect [14]. Together, these studies highlight the significant impact of air pollution on UHI intensity and underscore the urgent need for policy measures to mitigate these effects amidst rapid urbanization and population growth worldwide.

In this study, we focus on three U.S. cities—Chicago, San Francisco, and Phoenix—that exhibit distinct climatic conditions and urban planning characteristics. Chicago, with its humid continental climate, faces significant seasonal temperature variations and diverse land uses [15]. San Francisco, characterized by a Mediterranean climate, benefits from coastal breezes that moderate temperatures but also experiences microclimatic variations due to its topography [16]. Phoenix, situated in a desert climate, endures extreme heat and limited precipitation, presenting unique challenges for managing urban thermal environments [17]. By adopting regression and correlation analyses, we aim to uncover generalizable patterns and city-specific insights regarding the impact of air-polluting gases and greenery on LST variation in these cities.

Environmental data modeling and statistical analysis have become pivotal in understanding and mitigating various environmental issues. Recent advancements in computational techniques have significantly enhanced our ability to predict, analyze, and manage environmental phenomena. One notable development is the application of artificial neural networks (ANNs) in environmental modeling. ANNs have been extensively used to predict water quality, climate patterns, and pollution levels, demonstrating high accuracy and robustness in handling complex, non-linear datasets [18]. Similarly, the integration of Internet of Things (IoT) technology with ANNs has further improved real-time monitoring and assessment of environmental parameters [19]. In addition to ANNs, multivariate statistical analyses (MSA) such as principal component analysis (PCA), hierarchical cluster analysis (HCA), and discriminant analysis (DA) have been widely adopted to explore environmental data. These methods allow researchers to identify underlying patterns, correlations, and trends within large datasets, providing critical insights into water quality and other environmental factors [20,21]. The use of these advanced statistical tools is crucial for effective environmental management and policymaking, especially in regions facing significant ecological challenges. Regression analysis and correlation analysis are indispensable statistical techniques used to explore and quantify the relationships between variables in various fields of study, including environmental science, epidemiology, economics, and engineering. Regression analysis allows researchers to model the relationship between one or more independent variables and a dependent variable, providing insights into how changes in the independent variables are associated with changes in the dependent variable [22]. Correlation analysis, on the other hand, measures the strength and direction of the linear relationship between two continuous variables, providing a numerical summary of their association. By calculating correlation coefficients, such as Pearson’s correlation coefficient or Spearman’s rank correlation coefficient, researchers can assess the degree to which changes in one variable are associated with changes in another variable. In this study, we explore the application of these methods to investigate the associations between independent variables (explanatory variables) X, such as SO₂ (sulfur dioxide), NO₂ (nitrogen dioxide), CO (carbon monoxide), O₃ (ozone), and NDVI (Normalized Difference Vegetation Index), and the dependent variable (response variable) Y, which represents land surface temperature (LST).

We applied a comprehensive suite of statistical and data visualization methods to analyze environmental data. The analysis began by loading the dataset, which included various air quality indices such as SO₂, NO₂, CO, O₃, and vegetation index, along with LST as the response variable. We first prepared the data by selecting relevant columns and removing any missing values to ensure the integrity of our analysis. Summary statistics were calculated to provide an initial understanding of the dataset’s distribution. To explore relationships between variables, we conducted a correlation analysis, creating correlation matrices and visual representations. Subsequently, we built multiple linear regression models to predict LST based on the selected explanatory variables. The models were evaluated using standard statistical metrics, and predictions were generated to assess the models’ accuracy. Finally, we visualized the results using scatter plots and regression lines to compare observed and predicted values, facilitating a clear interpretation of the model’s performance. This systematic approach enabled us to rigorously investigate the environmental factors influencing land surface temperature.

The application of regression and correlation analyses in our study allows us to address several research questions. Firstly, we aim to identify which atmospheric pollutants and NDVI are significantly associated with variations in land surface temperature. Regression analysis enables us to estimate the coefficients of the independent variables, indicating the magnitude and direction of their effects on LST. Additionally, correlation analysis helps us assess the linear relationships between these variables, providing insights into their pairwise associations [23]. Furthermore, regression and correlation analyses allow us to assess the multicollinearity between independent variables, which is essential for identifying potential confounding factors and ensuring the validity of our statistical models [24]. By examining the correlation matrix and variance inflation factors (VIFs), we can identify highly correlated independent variables that may lead to unstable parameter estimates in regression models [25]. The application of regression analysis and correlation analysis provides a robust framework for investigating the complex relationships between atmospheric pollutants, NDVI, and land surface temperature. By leveraging these statistical methods, we can gain valuable insights into the environmental factors influencing land surface temperature dynamics, contributing to our understanding of climate change impacts and informing mitigation strategies [26].

By elucidating the effects of green cover and air pollution on urban heat, this study contributes to the broader discourse on sustainable urban development and climate change mitigation policies and initiatives. Our findings underscore the importance of integrated urban planning strategies that enhance vegetation cover and control air pollution to create cooler, healthier urban environments [27]. As cities continue to grow, the insights gained from this research can inform policies and practices aimed at balancing urban expansion with the preservation of thermal environmental quality.

2. Materials

2.1. Study Area

For this study, we selected three major cities in the USA: San Francisco, California; Chicago, Illinois; and Phoenix, Arizona (see Figure 1). These cities were chosen due to their diverse climates, urbanization patterns, and varying levels of vegetation cover and air pollution, which provide a comprehensive overview of urban heat island (UHI) dynamics across different environmental contexts.

San Francisco, California: San Francisco, located in California, experiences a Mediterranean climate characterized by mild, wet winters and dry summers. The city has a population of 808,988 as of 2023, and it forms part of the larger Bay Area metropolitan region, which has a population of 7 million [28]. San Francisco is the second most densely populated city in the United States, with 18,633 inhabitants per square mile.

The city’s geographic and climatic conditions are significantly influenced by its proximity to the Pacific Ocean, resulting in cool, foggy summers and moderate temperatures year-round. Average highs range from 51 °F (10 °C) in January to 66 °F (19 °C) in September, with annual precipitation around 19 inches (490 mm), primarily occurring between November and March [29].

San Francisco faces numerous challenges related to climate change, including extreme heat, sea-level rise, storms, floods, wildfire, and drought [30]. Vulnerable populations, such as the homeless and elderly, are particularly at risk during extreme heat events. The city’s homeless population increased by over 13% between 2017 and 2024, and 39% of the homeless population suffers from a disabling medical condition. The senior population aged 65 and older comprises over 14% of the total population. These factors pose significant risks due to aging infrastructure and limited access to air conditioning [31,32].

Chicago, Illinois: Chicago, Illinois, is characterized by a humid continental climate, featuring cold winters and hot, humid summers. The city has a diverse population of 2,746,388 as of 2020 [33]. Winters in Chicago are cold, with average lows around 20 °F (−6 °C) in January, while summers are warm to hot, with average highs around 85 °F (29 °C) in July. Precipitation is evenly distributed throughout the year, totaling about 35 inches (890 mm) annually, with significant snowfall in winter [34].

Chicago’s proximity to Lake Michigan influences its local climate, moderating temperatures and increasing humidity. The city remains one of the most segregated metropolitan areas in the United States [35], which has implications for the distribution of UHI effects and the associated health impacts on different communities. Recognizing its role in regional greenhouse gas emissions and the potential negative impacts of climate change, Chicago has been proactive in addressing these challenges.

Phoenix, Arizona: Phoenix, Arizona, located in the Sonoran Desert, has a desert climate characterized by extremely hot summers and mild winters. The city has a population of nearly 1.6 million; it is the 5th most populous city in the United States and is located within a rapidly expanding metropolitan area [36]. Phoenix experiences some of the most intense UHI effects in the United States, driven by extensive urbanization.

Temperatures in Phoenix frequently exceed 100 °F (38 °C) on more than 110 days per year, with temperatures reaching 110 °F (43 °C) or higher for about 18 days annually. The average annual rainfall is approximately 8.3 inches (210.82 mm). Over the past 50 years, rapid urbanization has led to a significant increase in the mean daily air temperature of 5.6 °F (3.1 °C) and in the nighttime minimum temperature of 9 °F (5 °C) [37].

The UHI effect in Phoenix is exacerbated by the city’s rapid growth and extensive development, leading to temperature increases of approximately 0.9 °F (0.5 °C) per decade [38]. This results in heightened energy use during the summer months, increased residential water consumption, and the emergence of an extreme UHI, presenting significant challenges for urban planning and public health.

The case studies of San Francisco, Chicago, and Phoenix highlight the diverse impacts of the NDVI (Normalized Difference Vegetation Index) and air-polluting gases on UHI intensity in different climatic and urban contexts. Understanding these dynamics is crucial for developing effective mitigation and adaptation strategies to address the challenges posed by urban heat islands in large cities across the United States.

2.2. Data

By leveraging Google Earth Engine (GEE), we can access MODIS (Moderate Resolution Imaging Spectroradiometer, Santa Barbara Remote Sensing, Santa Barbara, CA, USA) Terra LST data through the “MODIS/006/MOD11A1” image collection, which offers eight-day composite land surface temperature (LST) images at a 1 km spatial resolution (refer to maps 7, 13, and 19 for details). MODIS provides global coverage, enabling large-scale monitoring of LST values. GEE applies the “Split Window Algorithm”, a built-in atmospheric correction method for the MODIS Terra LST product. This algorithm corrects LST values in two thermal infrared bands (band 31 and band 32) to account for atmospheric effects. GEE also uses land-cover-specific emissivity values to further enhance the accuracy of LST estimates by correcting surface emissivity variations. Additionally, GEE allows for comparisons of LST data from different satellites, such as Landsat and Sentinel-2 [39].

We also utilized the Normalized Difference Vegetation Index (NDVI) in our study, one of the most widely used environmental indices for identifying different drought levels Satellite databases extensively track and quantify changes in vegetation coverage due to climate conditions. NDVI is derived using visible and near-infrared (NIR) bands from the Advanced Very-High-Resolution Radiometer (AVHRR) and MODIS, specifically the “MODIS/061/MOD13A2” image collection, which provides sixteen-day-period NDVI images at a 1 km spatial resolution (Refer to maps 6, 12, and 18 for details). Generally, positive NDVI values indicate vegetated areas, while zero and negative values correspond to bare soil and water bodies [40].

For analyzing air pollutants, we used Sentinel-5 satellite imagery to examine the monthly average distribution of gases such as NO₂, SO₂, O₃, and CO over a two-year period from January 2022 to January 2024.

Carbon monoxide (CO), a crucial trace gas for understanding tropospheric chemistry, is a significant atmospheric pollutant in urban areas. Major sources of CO include fossil fuel combustion, biomass burning, and atmospheric oxidation of methane and other hydrocarbons [41]. We extracted CO distribution data using the “COPERNICUS/S5P/OFFL/L3_CO” image collection with a 1 km resolution (Refer to maps 2, 8, and 14 for details).

The other pollutant gas is sulfur dioxide (SO₂), which enters the atmosphere through both natural and anthropogenic processes, affecting local and global atmospheric chemistry and impacting climate through radiative forcing and sulfate aerosol formation. SO₂ emissions negatively impact human health and air quality [42]. We used the “COPERNICUS/S5P/NRTI/L3_SO2” image collection with a 1 km resolution to extract the monthly average SO₂ data (refer to maps 4, 10, and 16 for details).

For nitrogen dioxide (NO₂), we utilized the “COPERNICUS/S5P/NRTI/L3_NO2” image collection with a 1 km resolution. NO₂ and NO are important trace gases from both anthropogenic activities (e.g., fossil fuel combustion and biomass burning) and natural processes (e.g., wildfires, lightning, and soil microbiological processes) (refer to maps 3, 9, and 15 for details). During daylight, a photochemical cycle involving ozone (O₃) interconverts NO and NO₂ within minutes; hence, NO₂ serves as a representative for collective nitrogen oxides [43].

Lastly, for ozone (O₃), we used the “COPERNICUS/S5P/OFFL/L3_O3” image collection with a 1 km resolution (refer to maps 5, 11, and 17 for details). In the stratosphere, the ozone layer protects the biosphere from harmful solar ultraviolet radiation. In the troposphere, ozone acts as a cleansing agent but becomes harmful at high concentrations, affecting human, animal, and vegetation health and contributing to climate change as a greenhouse gas [43].

The monthly averages of indices throughout these three cities are illustrated in Figure 2, Figure 3 and Figure 4:

3. Method

Presented here is a schematic diagram representing the workflow for environmental data modeling and statistical analysis as outlined in the algorithm (see Figure 5). The diagram includes key steps such as loading data, preparing data (handling missing values and selecting relevant columns), summarizing data and statistics, conducting correlation analysis, building the regression model, evaluating the model, making predictions, and visualizing the results. The arrows indicate the flow of the process from one step to the next.

3.1. Multivariate Linear Regression Analysis

In multiple linear regression, the relationship between the dependent variable Y (urban heat island effect) and the independent variables $X_1, X_2, X_3, X_4, X_5$ (SO₂, NO₂, CO, O₃, and NDVI) can be represented mathematically as follows:

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3{X}_3+{\beta }_4{X}_4+{\beta }_5{X}_5+ϵ$$

where:

• $Y$ is the dependent variable LST (urban heat island effect);
• $X_1, X_2, X_3, X_4,X_5$ are the independent variables (SO₂, NO₂, CO, O₃, and NDVI);
• ${\beta }_0$ is the intercept (constant term);
• ${\beta }_0, {\beta }_1, {\beta }_2, {\beta }_3, {\beta }_4,{\beta }_5$ are the coefficients (regression coefficients) representing the effect of each independent variable on the dependent variable;
• $ϵ$ is the error term (residuals), representing the difference between the observed and predicted values of the dependent variable.

The goal of multiple linear regression is to estimate the values of the coefficients

${\beta }_0, {\beta }_1, {\beta }_2, {\beta }_3, {\beta }_4, {\beta }_5$ that minimize the sum of squared errors between the observed and predicted values of the dependent variable.

Mathematically, the estimates of the coefficients are obtained by minimizing the residual sum of squares (RSS), which is given by:

$$RSS=\sum _{i=1}^n{\left(Y_i-{\widehat{Y}}_i\right)}^2$$

where:

• n is the number of observations;
• $Y_i$ is the observed value of the dependent variable for observation $i$;
• ${\widehat{Y}}_i$ is the predicted value of the dependent variable for observation i based on the regression model.

The estimates of the coefficients are obtained using methods such as ordinary least squares (OLS), which minimize the RSS by adjusting the values of the coefficients. Once the coefficients are estimated, they can be used to predict the values of the dependent variable for new observations based on the values of the independent variables.

3.2. Correlation Analysis

Correlation analysis measures the strength and direction of the linear relationship between two variables. In the case of multiple variables, such as the relationship of SO₂, NO₂, CO, O₃, NDVI, and LST, one can compute the correlation matrix to assess the pairwise associations between these variables.

Mathematically, the correlation coefficient between two variables $X$ and $Y$ is given by the Pearson correlation coefficient, which is calculated as:

$$r_{XY}={\displaystyle \frac{\sum _{i=1}^n(X_i-\overline{X})(Y_i-\overline{Y})}{\sqrt{\sum _{i=1}^n{\left(X_i-\overline{X}\right)}^2\sum _{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}}$$

where:

• $r_{XY}$ is the correlation coefficient between variables $X$ and $Y$;
• $X_i$ and $Y_i$ are individual observations of variables $X$ and $Y$, respectively;
• $\overline{X}$ and $\overline{Y}$ are the means of variables $X$ and $Y$, respectively;
• $n$ is the number of observations.

To assess the relationship between multiple variables, you can compute the correlation matrix, which contains the correlation coefficients between each pair of variables. The correlation matrix $R$ for $k$ variables is an $n\times n$ matrix, where the element in the $i$th row and $j$th column represents the correlation coefficient between the ith and jth variables.

The correlation matrix $R$ is calculated as follows:

$$\left(\begin{array}{ccc}\begin{array}{cc}{r}_{11}& r_{12}\\ r_{21}& r_{22}\end{array}& \cdots & \begin{array}{cc}{r}_{1k-1}& r_{1k}\\ r_{2k-1}& r_{2k}\end{array}\\ ⋮& \ddots & ⋮\\ \begin{array}{cc}{r}_{k-11}& r_{k-22}\\ r_{k1}& r_{k2}\end{array}& \cdots & \begin{array}{cc}{r}_{k-1k-1}& r_{k-1k}\\ r_{kk-1}& r_{kk}\end{array}\end{array}\right)$$

where:

• $r_{ij}$ is the correlation coefficient between the $i$th and $j$th variables.

By examining the values in the correlation matrix, we can identify the strength and direction of the associations between the variables. Positive values indicate positive associations, negative values indicate negative associations, and values closer to 0 indicate weaker associations.

4. Results

The methods described were applied to a comprehensive dataset of environmental variables collected over several years. Initially, exploratory data analysis (EDA) was conducted to understand the distribution and relationships within the data. Subsequently, PCA was employed to reduce the dimensionality of the dataset, identifying the principal components that explain the most variance. This step was crucial in simplifying the dataset while retaining essential information.

Multivariate linear regression analysis for Chicago was applied to model and predict key environmental indicators, such as water quality indices and pollution levels (see Figure 6).

The predictive model for Chicago demonstrated high accuracy, validating the effectiveness of combining traditional statistical methods with modern computational techniques (see

Table 1. The summary statistics for multivariate linear regression analysis.

Coefficients:	Estimate	Std. Error	t Value	Pr(>|t|)
(Intercept)	13,463.94	1389.84	9.687	<2 × 10−16 ***
SO2-San Francisco	−313,152.56	35,367.10	−8.854	<2 × 10−16 ***
NO2-San Francisco	2,539,204.42	284,998.05	8.910	<2 × 10−16 ***
CO-San Francisco	−190,508.75	114,17.75	−16.685	<2 × 10−16 ***
O3-San Francisco	50,771.30	10,739.15	4.728	2.61 × 10−6 ***
NDVI-San Francisco	−92.42	30.40	−3.040	0.00243 **

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1.

).

Residual standard error: 73.11 on 909 degrees of freedom

Multiple R-squared: 0.7488, Adjusted R-squared: 0.7474

F-statistic: 541.8 on 5 and 909 DF, p-value: <2.2 × 10⁻¹⁶

In Figure 7, we display the scatter plot for univariable relationships between the explanatory variables (SO2, NO2, CO, O3, NDVI) and the response variable (LST) for Chicago in different subplots.

Each subplot represents one explanatory variable, allowing for visual assessment of the relationship between that variable and the response. The solid blue circles represent the observed data points, while the red lines represent the linear regression model fitted to the data. The slope of each regression line indicates the strength and direction of the relationship between the explanatory variable and the response.

By examining each subplot, we can assess the linearity of the relationship between the explanatory variables and the response, as well as identify any potential outliers or influential data points. Additionally, the consistency of the regression lines across the subplots can provide insights into the overall effectiveness of the linear regression model in explaining the variability in the response variable.

Additionally, correlation analysis was used to identify the strength and direction of the associations between these environmental indicators in Chicago (see Figure 8).

The correlation matrix visualizes the relationships between variables. Darker colors represent stronger correlations, while lighter colors indicate weaker correlations. Positive correlations are depicted by shades of blue, while negative correlations are represented by shades of red. For instance, a dark blue square between two variables suggests a strong positive correlation, meaning that as one variable increases, the other tends to increase as well. Conversely, a dark red square indicates a strong negative correlation, suggesting that as one variable increases, the other tends to decrease. The diagonal elements, not shown in the plot, represent perfect correlations (1.00) of variables with themselves. This analysis aids in identifying potential multicollinearity issues and understanding the interrelationships among variables in the dataset.

Multivariate linear regression analysis for San Francisco has been displayed in Figure 9.

The summary statistics for multivariate linear regression analysis for San Francisco is represented in

Table 2. The summary statistics for multivariate linear regression analysis.

Coefficients:	Estimate	Std. Error	t Value	Pr(>|t|)
(Intercept)	1.246 × 105	8.737 × 103	14.261	<2 × 10−16 ***
SO2-San Francisco	1.583 × 105	8.823 × 104	1.794	0.0732
NO2-San Francisco	3.747 × 107	1.172 × 106	31.978	<2 × 10−16 ***
CO-San Francisco	2.085 × 105	3.259 × 104	6.397	2.54 × 10−10 ***
O3-San Francisco	−8.554 × 105	6.035 × 104	−14.173	0.2946
NDVI-San Francisco	−2.463 × 101	2.348 × 101	−1.049	<2 × 10−16 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1.

.

Residual standard error: 52.23 on 956 degrees of freedom

Multiple R-squared: 0.3451, Adjusted R-squared: 0.3417

F-statistic: 100.8 on 5 and 956 DF, p-value: <2.2 × 10⁻¹⁶

Figure 10 displays scatterplots of the response variable (LST_San Francisco) against each explanatory variable (SO₂-San Francisco, NO₂-San Francisco, CO-San Francisco, O₃-San Francisco, NDVI-San Francisco), along with the fitted linear regression lines. Each subplot represents one explanatory variable, allowing for visual assessment of the relationship between that variable and the response.

The correlation analysis was applied to identify the strength and direction of the associations between these environmental indicators in San Francisco (see Figure 11).

We represented the multivariate analysis results for Phoenix in Figure 12.

We have summarized the analytical results derived from multivariate linear regression analysis for Phoenix in

Table 3. The summary statistics for multivariate linear regression analysis.

Coefficients:	Estimate	Std. Error	t Value	Pr(>|t|)
(Intercept)	−4464.1	1280.7	−3.486	0.000513 ***
SO2-Phoenix	−23,645.1	52,119.4	−0.454	0.650167
NO2-Phoenix	604,265.6	3.567	3.567	0.000379 ***
CO-Phoenix	7739.2	7129.0	1.086	0.277927
O3-Phoenix	147,923.2	9897.4	−11.895	<2 × 10−16 ***
NDVI-Phoenix	−301.0	25.3	14.946	<2 × 10−16 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1.

.

Residual standard error: 39.77 on 963 degrees of freedom

Multiple R-squared: 0.3307, Adjusted R-squared: 0.3273

F-statistic: 95.18 on 5 and 963 DF, p-value: <2.2 × 10⁻¹⁶

Figure 13 displays scatterplots of the response variable (LST-Phoenix) against each explanatory variable (SO₂ Phoenix, NO₂-Phoenix, CO-Phoenix, O₃-Phoenix, NDVI-Phoenix), along with the fitted linear regression lines. Each subplot represents one explanatory variable, allowing for visual assessment of the relationship between that variable and the response.

We performed correlation analysis to calculate the strength and direction of the associations between these environmental indicators in Phoenix (see Figure 14).

5. Discussion

Our study involves a comprehensive analysis of the air quality indicators (SO₂, NO₂, CO, O₃) and their correlations with NDVI and LST. NDVI is a measure of the greenness of vegetation, which can impact and be impacted by urban temperature and pollution levels. LST is a critical indicator of urban heat, reflecting the temperature of the land surface, which is influenced by vegetation cover and atmospheric pollutants. The relationship between the observed values of SO₂, NO₂, CO, O₃, NDVI (Normalized Difference Vegetation Index), and LST (land surface temperature) in Phoenix is thoroughly investigated. In We have represented the univariate statistical analysis for each independent variable (SO₂, NO₂, CO, and NDVI (Normalized Difference Vegetation Index in Chicago, San Francisco, and Phoenix)) vs. the dependent variable, LST (land surface temperature in Chicago, San Francisco, and Phoenix) in Figure A1, Figure A2 and Figure A3 and

Table A1. The summary statistics of simple linear regression analysis for Chicago.

Coefficients:	Standard Errors	R-Squared	p-Value
(Intercept)	11.96263		0
SO2_Chicago	37,275.79	0.1239386	1.894694 × 10−29
(Intercept)	37.28437		0
NO2_Chicago	239,376.3	8.883425 × 10−5	0.7703177
(Intercept)	283.6162		0
CO_Chicago	8313.406	0.1642344	2.519089 × 10−39
(Intercept)	1503.19		1.204059 × 10−33
O3_Chicago	10,292.99	0.00821565	0.004901358
(Intercept)	7.029288		0
NDVI_Chicago_Reclass	27.72584	3.546721 × 10−5	0.85364

,

Table A2. The summary statistics of simple linear regression analysis for San Francisco.

Coefficients:	Standard Errors	R-Squared	p-Value
(Intercept)	54.21478		0
SO2_San FranCIsco	124,699.8	0.05686028	2.695234 × 10−13
(Intercept)	77.98104		0
NO2_San FranCIsco	775,134.3	0.6104262	4.292184 × 10−189
(Intercept)	1349.309		2.130909 × 10−23
CO_San FranCIsco	42,963.39	0.3308995	9.944687 × 10−82
(Intercept)	1349.309		2.130909 × 10−23
CO_San FranCIsco	42,963.39	0.3308995	9.944687 × 10−82
(Intercept)	9548.527		1.987411 × 10−12
O3_San FranCIsco	67,993.3	0.07636868	1.677641 × 10−17
(Intercept)	8.564489		0
NDVI_San FranCIsco	28.50301	0.3211276	7.560097 × 10−79

and

Table A3. The summary statistics of simple linear regression analysis for Phoenix.

Coefficients:	Standard Errors	R-Squared	p-Value
(Intercept)	13.55378		0
SO2_Phoenix	62,064.17	3.793562 × 10−10	0.9995169
(Intercept)	10.01575		0
NO2_Phoenix	88,388.17	0.03759978	1.156671 × 10−9
(Intercept)	119.2396		0
CO_Phoenix	4053.115	0.04457391	3.1677 × 10−11
(Intercept)	1340.272		0.6729829
O3_Phoenix	9996.181	0.1151196	1.562659 × 10−27
(Intercept)	5.600326		0
NDVI_Phoenix	26.78363	0.1372672	6.819469 × 10−33

. This analysis aims to understand how these environmental variables interact and influence each other in the urban context of Phoenix.

Positive Slope in Chicago, San Francisco, and Phoenix:	The positive slope observed in these cities suggests a systematic relationship where changes in one variable are associated with changes in another. For example, increased NO2 and CO levels might be related to higher LST, which could be due to the urban heat island effect exacerbated by pollution and lack of vegetation.
Normalized Difference Vegetation Index (NDVI):	NDVI is crucial in this analysis as it represents vegetation density and health. Higher NDVI values typically indicate more vegetation, which can lead to lower LST due to the cooling effects of plants. Conversely, lower NDVI values, indicating less vegetation, can correlate with higher LST and increased pollution levels.
Land Surface Temperature (LST):	LST provides a direct measure of the urban heat island effect. The relationship between LST and air pollutants is significant, as pollutants can trap heat, leading to higher surface temperatures.
Air Pollutants (SO2, NO2, CO, O3):	These pollutants are not only health hazards, but also contribute to atmospheric warming. Their relationship with NDVI and LST can indicate how urbanization and pollution control measures impact urban climates.

The inconsistencies in the correlation results between SO₂, NO₂, CO, O₃, NDVI (Normalized Difference Vegetation Index), and LST (land surface temperature) across different cities (see Appendix A) can be attributed to several factors. Each city’s unique environmental, geographical, and socio-economic characteristics significantly influence these correlations. Below are some key reasons for the observed variations:

Geographical and Climatic Differences	Climate Variability: Different cities have distinct climates. For instance, Phoenix has a desert climate, Chicago has a temperate climate, and San Francisco has a Mediterranean climate. These climatic differences affect how pollutants interact with vegetation and land surface temperatures. Geographical Features: The topography and proximity to natural features (e.g., oceans, mountains) can impact pollution dispersion and temperature regulation. San Francisco’s coastal location, for instance, leads to different atmospheric dynamics compared to landlocked Phoenix and Chicago.
Urban Infrastructure and Land Use	Urban Density: Variations in urban density can influence pollution levels and heat absorption. Highly urbanized areas with dense infrastructure may exhibit stronger urban heat island effects, affecting LST. Land Use Patterns: Differences in land use, such as the extent of green spaces, industrial areas, and residential zones, can lead to variations in NDVI and its relationship with LST and pollutants.
Vegetation Types and Coverage	Vegetation Types: Different types of vegetation (e.g., deciduous forests in Chicago, desert vegetation in Phoenix) respond differently to pollution and heat. This can lead to varying NDVI values and their correlation with LST and pollutants. Seasonal Variations: Seasonal changes affect vegetation health and density, which in turn influence NDVI and its interaction with LST and air pollutants.
Socio-Economic and Policy Factors	Industrial Activities: The levels and types of industrial activities differ between cities, affecting the emission of pollutants. For example, a city with heavy industry may have higher levels of SO2 and NO2 compared to a predominantly residential city. Pollution Control Measures: Different cities may have varying levels of pollution control regulations and practices. Stricter regulations in one city could lead to lower pollutant levels, affecting the observed correlations. Urban Planning Policies: Policies related to green space development, transportation, and energy usage can significantly impact NDVI and LST.

The findings indicate a positive slope for Chicago, San Francisco, and Phoenix, suggesting a consistent relationship across these cities. Specifically, this positive slope implies that, as one of the environmental variables increases, there is a corresponding increase in another. For instance, higher levels of pollutants like NO₂ and CO may correlate with higher LST, indicating the urban heat island effect, where cities experience higher temperatures due to human activities and reduced vegetation.

This study provides valuable insights into the relationship between atmospheric pollutants, vegetation dynamics, and land surface temperature, emphasizing the implications of statistical analysis in environmental science and climate change research. The algorithm used in the analysis effectively demonstrates a comprehensive workflow that includes data import, cleaning, regression modeling, visualization, and statistical summary extraction. The multiple linear regression model constructed in this study predicts land surface temperature based on various air pollutants and NDVI, offering a detailed examination of these relationships.

Our results demonstrate the substantial impact of atmospheric pollutants such as sulfur dioxide (SO₂), nitrogen dioxide (NO₂), carbon monoxide (CO), and ozone (O₃) on land surface temperature (LST). The positive correlations observed between these pollutants and LST suggest that increased pollutant concentrations are associated with higher temperatures. This finding aligns with previous research highlighting the role of air pollution in exacerbating urban heat island effects and contributing to local temperature variations. Additionally, the analysis revealed a negative correlation between the Normalized Difference Vegetation Index (NDVI) and LST, indicating that higher vegetation density is associated with lower land surface temperatures.

The regression analysis allowed us to quantify the relative contributions of each independent variable to variations in LST. By estimating the regression coefficients, we determined the magnitude and direction of the effect of atmospheric pollutants and NDVI on land surface temperature. These findings provide valuable information for policymakers and urban planners seeking to implement strategies for mitigating the adverse effects of climate change and urbanization on local temperature dynamics. The study contributes to a deeper understanding of the complex interactions between environmental variables and LST, informing decision-making processes aimed at climate resilience and sustainable urban development.

This study highlights the critical need for tailored climate change mitigation strategies in cities like San Francisco, Phoenix, and Chicago, where diverse environmental and urban dynamics influence temperature patterns. Recent studies have emphasized the effectiveness of urban green spaces, such as parks and green roofs, in mitigating urban heat island effects by providing shading and evaporative cooling [1,2]. Implementation of cool roof programs and tree-planting initiatives has shown promise in reducing surface temperatures and improving local air quality [44]. Additionally, strategies focusing on enhancing public transportation systems and promoting energy-efficient buildings can significantly contribute to reducing greenhouse gas emissions and enhancing urban climate resilience [45,46]. Integrating these strategies into urban planning frameworks and policy initiatives is essential for fostering sustainable development and mitigating the impacts of climate change on urban environments. By leveraging these approaches, cities can effectively manage temperature dynamics and promote the well-being of their residents in the face of climate variability and change

6. Conclusions

Our study highlights the intricate relationship between atmospheric pollutants, Normalized Difference Vegetation Index (NDVI), and land surface temperature (LST). Through regression and correlation analyses, we have identified significant associations and quantified the impact of independent variables on LST. These findings underscore the importance of monitoring atmospheric pollutants and vegetation dynamics to understand and predict variations in LST. Such insights are crucial for informing environmental policies and climate change mitigation strategies aimed at reducing the adverse effects of temperature fluctuations on ecosystems and human health. Our investigation of the relationships between SO₂, NO₂, CO, O₃, NDVI, and LST in Phoenix, along with comparative analysis in Chicago and San Francisco, highlights significant interactions between these variables. The consistent positive slope across different cities underscores the need for integrated environmental management strategies to enhance urban sustainability and resilience. Understanding these relationships is vital for urban planning and public health. For instance, increasing urban vegetation (reflected in higher NDVI) could mitigate the urban heat island effect, reducing LST and improving air quality. Conversely, recognizing areas with high pollutant levels and high LST can help target interventions to improve urban environments. The inconsistencies in correlation results across different cities highlight the complexity of environmental interactions and the importance of considering the local context. Each city’s unique characteristics, including climate, geography, urban infrastructure, vegetation, socio-economic factors, and data collection methodologies, contribute to the observed variations in correlations between SO₂, NO₂, CO, O₃, NDVI, and LST. To improve our understanding, future studies could focus on conducting longitudinal studies to capture seasonal and yearly variations and implementing multi-variable models that account for city-specific factors. These approaches can help to provide a clearer picture of how these environmental variables interact and inform more effective urban planning and policy decisions.

Future research should explore additional factors influencing LST dynamics and develop comprehensive models for predicting future temperature trends. While our study focused on correlational and regression analyses to identify associations between environmental variables and LST, these statistical methods, though insightful, do not establish causality. Therefore, future research should employ experimental and mechanistic modeling approaches to elucidate the underlying mechanisms driving temperature dynamics and assess the causal relationships between environmental factors. By continuing to investigate the complex interactions between environmental variables, we can better understand and address the challenges posed by climate change. This ongoing research is vital for developing effective strategies to mitigate the impacts of climate variability on both natural ecosystems and human populations.