Assessing Carbon Emissions’ Impact on Drought in China’s Arid Regions: Cross-Lagged and Spatial Models

Abstract

Global warming is projected to intensify the impact of droughts. Although numerous studies have examined carbon emissions and droughts, few have explored their interactive effects or the spatial spillover effects of carbon emissions on droughts. To address this gap, we use panel data from 2012 to 2021 for China’s arid, semi-arid, and potentially semi-arid regions in the future. First, we estimate city-level carbon emissions data for the study areas based on nighttime light data. We then apply a Random Intercept Cross-Lagged Panel Model to investigate the temporal causal relationship between carbon emissions and droughts. Finally, we employ a dynamic spatial Durbin model with spatial and temporal fixed effects, incorporating one-period-lagged carbon emissions to assess both direct and spatial spillover effects on droughts. The results show that carbon emissions have a statistically significant cross-temporal and spatial impact on droughts, with both current and one-period-lagged carbon emissions exhibiting substantial spatial spillover effects on drought conditions. This research offers valuable insights for cities seeking collaborative approaches to mitigate both carbon emissions and drought risks.

1. Introduction

As global temperatures rise, China is projected to experience increasingly severe drought-induced economic losses. If global warming reaches 2 °C, the economic losses from droughts in China could rise to USD 75 billion [1]. In addition, the annual number of drought days in China has steadily increased [2]. Studies suggest that a 2 °C rise in global temperatures is projected to result in increased drought frequency across Northeast, North, and East China. The Royal Society reports that increased concentrations of carbon dioxide, methane, and nitrous oxide are the primary drivers of global warming, with carbon dioxide having the most significant impact [3]. As of 2024, China was the largest global emitter of carbon dioxide, underscoring the urgent need to analyze the spatial and temporal links between carbon emissions and droughts to address these challenges effectively.

Prior to the introduction of the “carbon peak and carbon neutrality” policy, research on China’s carbon emissions primarily examined the influencing factors [4], temporal–spatial characteristics [5], and regional variations in emissions [6], mainly exploring the carbon emission disparities caused by varying levels of economic development across regions. Recent research has increasingly focused on the impact of policy measures aimed at promoting energy conservation and reducing emissions, together with advancements in carbon emissions forecasting [7,8,9,10], in support of global climate protection efforts. While most studies rely on the Intergovernmental Panel on Climate Change (IPCC) carbon accounting standards to assess emissions across regions, inconsistencies in data collection and reporting at the prefecture level in China often lead to discrepancies between research findings and real emission levels. Based on existing research on energy consumption and lighting [11], some scholars have utilized nighttime lighting data to simulate carbon emissions by fitting them to annual energy consumption data at the national level [12] or regional [13] energy consumption data. This approach is used to study the spatial and temporal distribution of carbon emissions. Similarly, due to the diversity of climate types across China, drought studies have concentrated on the spatial and temporal characteristics of drought [2,14], particularly concerning carbon emissions in arid regions [15]. Additionally, researchers have further explored the relationships among drought, vegetation greenness, and carbon flux [16] to assess the impact of extreme drought events. Since drought is challenging to precisely define in both time and space, researchers have employed multiple indicators [17] to assess its severity. The multi-scale Standardized Precipitation Evapotranspiration Index (SPEI) is commonly used to assess meteorological drought on a large scale [18], as it incorporates both temperature and precipitation data and can capture drought characteristics across various timeframes [18,19]. Positive values of the SPEI indicate wetter conditions, with higher values representing increased wetness. Conversely, negative values signify drought, with lower values indicating more severe aridity.

Despite the growing focus on climate change, limited research has examined the interaction between carbon emissions and drought severity, particularly the spatial spillover effects of carbon emissions on drought conditions. To explore this issue further, this study focuses on arid, semi-arid, and regions that may become semi-arid in the future, selected based on long-term precipitation data. This study treats carbon emissions as the main independent variable using panel data from prefecture-level cities, while drought severity is quantified using the 12-month SPEI as the dependent variable. A Random Intercept Cross-Lagged Panel Model (RI-CLPM) is applied to analyze the reciprocal effects between carbon emissions and drought severity. Additional control variables, accounting for both natural conditions and human activities, are included in a spatial econometric analysis to assess the direct and spillover effects of carbon emissions on drought severity. The goal of this study is to deepen the understanding of the link between carbon emissions and drought severity, offering insights to inform strategies for drought mitigation.

2. Materials and Methods

2.1. Data Source

This study examines 15 Chinese provinces, encompassing 171 prefecture-level administrative units. While the RI-CLPM analysis includes data from all 171 cities, the spatial econometric analysis is based on 164 cities due to data availability issues in some regions. According to the Central People’s Government of the People’s Republic of China [20], regions with annual precipitation below 200 mm are classified as arid, 200–400 mm as semi-arid, 400–800 mm as semi-humid, and above 800 mm as humid. Research suggests that semi-arid regions in China may gradually expand over time [21,22]. To study the impact of carbon emissions on aridity in China’s arid and semi-arid areas, as well as regions that may become semi-arid in the future, and to assess the spatial spillover effects of carbon emissions, we selected the 8th percentile of annual precipitation, 450 mm, as the threshold for semi-humid regions (400–800 mm), minimizing over-selection bias. Based on the average precipitation data from 1982 to 2022 [23], if a province’s annual precipitation fell below 450 mm in a given year, it was recorded once. We then counted the total occurrences of this situation over the period, selecting provinces where it occurred more than 10 times for this study. Due to data limitations, the Xizang Autonomous Region was excluded. Figure 1, displaying selected regions within China’s location, shows the geographical location of the 15 provinces and the frequency of years with average precipitation below 450 mm. Table S1 (the complete table is in the Supplementary File) provides the names and city codes of the selected cities.

To calculate carbon emissions data at the prefecture level, this study utilizes carbon emissions data from 15 provinces between 1997 and 2021, calculated using the IPCC sectoral accounting method, which involves multiple sectors [24,25,26,27,28,29]. Provincial-level carbon emission data can be found in the Carbon Emission Accounts and Datasets (CEADs) database (available at https://www.ceads.net/data/province/ (accessed on 23 June 2024)). Since provincial-level carbon emission data serve as the basis for calculating prefecture-level emissions, regions lacking such data, such as the Xizang Autonomous Region, are excluded from this study. Additionally, nighttime lighting data from 171 cities in these 15 provinces between 1997 and 2021 [30] were also employed. The carbon emissions data for prefecture-level cities were modeled based on an existing study [31], and the results of the fitting were compared with the data from the Emissions Database for Global Atmospheric Research (EDGAR) (available at https://edgar.jrc.ec.europa.eu/gallery?release=v80ghg&substance=CO2&sector=TOTALS (accessed on 23 June 2024)) [32] to ensure the accuracy of the data. The carbon emission data obtained from EDGAR are global in scale and provided in the Network Common Data Form (NetCDF) format. We calculated the sum of all data points within each prefecture-level city in the study area and compared it with the nighttime lighting-based simulated carbon emissions data. To enhance accuracy, we employed the isolation forest method to detect outliers, which were subsequently corrected using smoothing spline interpolation. The data were then logarithmically transformed to minimize regional disparities and are expressed as $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$. Drought severity was assessed using the annual average 12-month SPEI (available at https://www.scidb.cn/en/detail?dataSetId=968592537239420928 (accessed on 21 July 2024)) [33], following standard indicators used in existing research. The obtained SPEI data are provided in monthly Tagged Image File Format (TIFF) with a 12-month time scale (each TIFF file represents the drought conditions for a specific month, calculated based on the water balance for the previous 12 months) [19]. We first calculated the average of all data points within each prefecture-level city to derive the monthly SPEI value for each city based on the corresponding TIFF file. Subsequently, we calculated the average of the data from the 12 months to obtain the annual SPEI value for each prefecture-level city. This repeated averaging method provides a more accurate estimate of the annual SPEI level for a given region, eliminating the influence of extreme cases and reflecting the long-term drought conditions of the area. To account for additional factors affecting drought, we included several control variables. The annual average Fraction of Vegetation Cover (FVC) [34] was used to evaluate the natural environment’s influence on drought severity, based on established studies [35]. Human impact on drought was gauged by the logarithm of population density [$\ln \left(\mathrm{P}\mathrm{o}\mathrm{p}\right)$], calculated using regional demographic data [36]. The proportion of extremely cold and extremely hot days in each city per year was calculated using temperature data from National Centers for Environmental Information [37] with reference to existing studies [38,39,40] to control the impact of extreme weather (Ext_Wea) on the degree of drought. The ratio of tertiary industry GDP to secondary industry GDP was used to measure the degree of urbanization (Ind_Str) in the region and control the impact of urbanization on the degree of drought and GDP data were obtained from the statistical yearbooks of each city. Since nominal GDP data from the statistical yearbook were used, we calculated the real GDP for each prefecture-level city using the GDP deflator based on the year 2000 (with 2000 set to 100). This real GDP is used to construct the spatial weight matrix in the subsequent analysis.

2.2. Theory and Calculation

2.2.1. Carbon Emission

Based on prior research [13,31], this paper develops and fits four models with fixed time effects, excluding an intercept term, to standardize carbon emission estimates. The optimal model is selected based on defined goodness-of-fit criteria, including R-squared and the Akaike Information Criterion (AIC). The four models are as follows:

A linear model

$$PR\_Carbo{n}_{it}=a_1\cdot PR\_Ligh{t}_{it}+{\nu }_t+{\epsilon }_{it},$$

(1)

A logarithmic model

$$PR\_Carbo{n}_{it}=a_2\cdot \ln \left(PR\_Ligh{t}_{it}\right)+{\nu }_t+{\epsilon }_{it},$$

(2)

An exponential model

$$\log \left(PR\_Carbo{n}_{it}\right)=a_3\cdot PR\_Ligh{t}_{it}+{\nu }_t+{\epsilon }_{it},$$

(3)

A power function model

$$\ln \left(PR\_Carbo{n}_{it}\right)=a_4\cdot \ln \left(PR\_Carbo{n}_{it}\right)+{\nu }_t+{\epsilon }_{it},$$

(4)

${PR\_Carbon}_{it}$ represents the carbon emissions of province i in year t, and ${PR\_Light}_{it}$ denotes the total nighttime light values for province i in year t. The term ai represents the regression coefficient in each corresponding fitted equation, ${\nu }_t$ denotes the fixed time effect, and ${\epsilon }_{it}$ is the error term.

The optimal equation is selected based on the fitting results, and the carbon emissions of each city are calculated [31]. The formula is as follows:

$$City\_Carbo{n}_{kt}=PR\_Carbo{n}_{it}\cdot \left({\widehat{C}}_{kt}/{\widehat{P}}_{it}\right),$$

(5)

where ${PR\_Carbon}_{it}$ represents the carbon emissions of province i in year t, ${City\_Carbon}_{kt}$ represents the carbon emissions of the kth city in province i in year t, ${\widehat{C}}_{kt}$ represents the estimated carbon emissions of the kth city in province i in year t calculated using the optimal equation, and ${\widehat{P}}_{it}$ represents the estimated carbon emissions of province i in year t, also calculated using the optimal equation.

To verify the reliability of the simulation, we selected carbon emissions data from the EDGAR and calculated the ${City\_Carbon}_{kt}$ results for fitting. Since the initial provincial data are calculated based on multiple indicators, in order to reduce the interference of abnormal data on the research, we also use the isolated forest method [41,42] to find the ${City\_Carbon}_{kt}$ abnormal values and use the smoothing spline interpolation method to replace the abnormal data to obtain the carbon emissions representing the prefecture-level cities. The data are then taken to the logarithm to reduce the impact of regional differences and is expressed as $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$.

2.2.2. Random Intercept Cross-Lagged Panel Model and Traditional Cross-Lagged Panel Model

The RI-CLPM is an enhancement of the traditional cross-lagged panel model (CLPM) [43], providing a more precise approach for identifying causal relationships between variables over time. This model is extensively applied in psychology and related disciplines [44]. In this study, we use the RI-CLPM to examine the temporal relationship between carbon emissions and drought across 171 cities over a ten-year period (2012–2021). Based on established research [44], this study’s RI-CLPM includes the following variables (for simplicity, c denotes $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$, and s represents SPEI):

Define random intercepts

$$R{I}_c={\displaystyle \frac{1}{10}}{\displaystyle \sum _{t=1}^{10}{c}_t},$$

(6)

$$R{I}_s={\displaystyle \frac{1}{10}}{\displaystyle \sum _{t=1}^{10}{s}_t},$$

(7)

Fluctuation components

$$w_{c_t}=c_t-R{I}_c,$$

(8)

$$w_{s_t}=s_t-R{I}_s,$$

(9)

Cross-lagged effects

$$w_{c_{t+1}}={\alpha }_c{w}_{c_t}+{\beta }_{sc}{w}_{s_t}+{\epsilon }_{c_{t+1}},$$

(10)

$$w_{s_{t+1}}={\alpha }_s{w}_{s_t}+{\beta }_{cs}{w}_{c_t}+{\epsilon }_{s_{t+1}},$$

(11)

Covariance structure

$$Cov\left(R{I}_c,R{I}_s\right)={\sigma }_{R{I}_{cs}},$$

(12)

$$Cov\left(w_{C_t},w_{S_t}\right)={\sigma }_{w_{CS}},$$

(13)

Equations (6)–(13) define the RI-CLPM, where ${\mathrm{c}}_t$ denotes $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ at time t, st denotes the SPEI at time t, and the random intercepts for $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ (${RI}_c$) and the random intercepts for SPEI (${RI}_s$) represent the overall average of the $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and SPEI, respectively. $w_{c_t}$ and $w_{s_t}$ denote the deviations of the observations from the random intercept at each time point t. ${\alpha }_c$ and ${\alpha }_s$ are the autoregressive coefficients, indicating the connection between the $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and SPEI variations at adjacent time points. ${\beta }_{sc}$ and ${\beta }_{cs}$ are the cross-lagged coefficients, representing the lagged effects of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI and the SPEI on $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$, respectively, reflecting their dynamic interaction. ${\epsilon }_{c_{t+1}}$ and ${\epsilon }_{s_{t+1}}$ are the residual terms, indicating the unexplained portions of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and the SPEI at time t + 1. ${\sigma }_{{RI}_{cs}}$ represents the covariance between the random intercepts, reflecting the linear relationship between the overall average levels of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and the SPEI. A positive value indicates that $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and the SPEI are positively correlated at the mean level; ${\sigma }_{w_{cs}}$ represents the covariance between the deviations, reflecting the relationship between $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and the SPEI at a given time point. A positive value at time t signifies that a rise in the deviation of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ is associated with an increase in the deviation of the SPEI. Conversely, a negative value indicates that a higher $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ deviation leads to a reduction in the deviation of the SPEI.

Setting the variance and covariance of all random intercepts in the RI-CLPM to zero [44] results in a model that is statistically equivalent to the traditional CLPM, as follows:

Fluctuation components

$$w_{c_t}=c_t,$$

(14)

$$w_{s_t}=s_t,$$

(15)

Covariance structure

$$Cov\left(w_{c_t},w_{s_t}\right)={\sigma }_{w_{c_t}{w}_{s_t}},$$

(16)

Equations (10) and (11) and (14)–(16) define the traditional CLPM. The difference from the RI-CLPM lies in these equations, where Var(${RI}_c$) = 0, Var(${RI}_s$) = 0, and Cov(${RI}_c$,${RI}_s$) = 0. The volatility components do not subtract the random intercept, making them effectively equivalent to the observed variables. ${\sigma }_{w_{c_t}{w}_{s_t}}$ represents the covariance between the volatility components at time t, which emphasizes the instantaneous correlation over time. The remaining variables are the same as in the RI-CLPM.

To ensure the selected sample size meets the requirements of the RI-CLPM, we conducted a power analysis [45] and performed a chi-square test to compare the RI-CLPM with the simplified traditional CLPM.

2.2.3. Spatial Econometrics

To assess the spatial spillover effects of carbon emissions and drought severity, we apply global Moran’s I and local Moran’s I to measure spatial correlation in exploratory spatial data analysis. The calculations are as follows:

$$I={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}\left(y_i-\overline{y}\right)\left(y_i-\overline{y}\right)}}/S^2{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}}},$$

(17)

$$I_i=\left(y_i-\overline{y}\right){\displaystyle \sum _{j\ne i}{W}_{ij}\left(y_j-\overline{y}\right)}/S^2,$$

(18)

where $\overline{y}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{y}_i}$, $S^2={\displaystyle \frac{1}{n}}{{\displaystyle \sum _{i=1}^n\left(y_i-\overline{y}\right)}}^2$, and n represent the total number of spatial units. $W_{ij}$ is the spatial weight. If $W_{ij}$ ≠ 0, it indicates that region j is a neighbor of region i. Additionally, $y_i$ represents the observed value for region i, while $y_i$ corresponds to the observed value for its neighboring region j.

In spatial econometric analysis, a spatial weight matrix describes the relationships between regions. In order to systematically examine the spatial correlation between regions within the study area, this study first establishes a basic spatial adjacency matrix W1 based on the Queen criterion:

$$W_{ij}=\left\{\begin{array}{c}1,i\ne j\\ 0,i=j\end{array}\right.i,j=1,2,\cdots ,n,$$

(19)

where if i and j are connected by at least one vertex, the weight between them is 1; otherwise, it is 0.

To enhance the robustness of the results, we also examined whether the spatial spillover effect is influenced by the distance between regions: the shorter the distance, the stronger the effect. We constructed an inverse distance squared spatial matrix [46] to test robustness, and W2 is defined as follows:

$$W_{ij}=\left\{\begin{array}{c}1/d_{ij}^2,i\ne j\\ 0,i=j\end{array}\right.\begin{array}{c}\\ \end{array}i,j=1,2,\cdots ,n,$$

(20)

where $d_{ij}^2$ is the square of the distance between cities i and j.

A spatial economic distance weight matrix (W3) [47], considering the economic factors of each region, was constructed as the main spatial weight matrix in this study. W3 is defined as follows:

$$\mathrm{W}3=\mathrm{W}2\cdot diag\left({\overline{R}}_1/\overline{R},{\overline{R}}_2/\overline{R},\dots ,{\overline{R}}_n/\overline{R}\right),$$

(21)

where W2 is the spatial distance matrix, ${\overline{R}}_i={\displaystyle \frac{1}{t_1-t_0+1}}{\displaystyle \sum _{t=t_0}^{t_1}{R}_{it}}$ denotes the average real GDP of city i during the study period, and $\overline{R}={\displaystyle \frac{1}{n\left(t_1-t_0+1\right)}}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{t=t_0}^{t_1}{R}_{it}}}$ indicates the average real GDP across all regions during the same period. Thus, regions with a higher average real GDP exert a more significant influence on the surrounding regions.

To prevent significant spatial or economic differences between cities from affecting the stability and balance of the model through spatial weight matrices, we standardize the weight matrices W2 and W3. After standardization, the sum of each row in the weight matrices equals 1. In other words, for each city, its adjacent weights are adjusted to represent a proportional share.

To further investigate the spatial effect of carbon emissions on drought severity, this study used spatial econometric models to analyze the impact of carbon emissions on drought severity and calculate direct and indirect effects, following the use of the RI-CLPM to explore the causal relationship between carbon emissions and drought over time. A panel model without spatial lag terms was first constructed before developing the spatial econometric model. Additionally, to study the time-lagged impact of carbon emissions on drought severity, the lagged first-period $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and SPEI were incorporated into a dynamic panel.

$$\begin{array}{l}\begin{array}{c}{\mathrm{SPEI}}_{it}={\lambda }_1\ln \left({\mathrm{Carbon}}_{it}\right)+{\lambda }_2{\mathrm{FVC}}_{it}+{\lambda }_3{\mathrm{Ext}\text{\_}\mathrm{Wea}}_{it}+{\lambda }_4\ln \left({\mathrm{Pop}}_{it}\right)+{\lambda }_5{\mathrm{Ind}\text{\_}\mathrm{Str}}_{it}\\ +{\phi }_1\ln \left({\mathrm{Carbon}}_{it-1}\right)+{\phi }_2{\mathrm{SPEI}}_{it-1}+u_{it}\end{array}\\ i=1,\dots N;t=1,\dots ,T\end{array},$$

(22)

where $u_{it}$ = ${\mu }_i$ + ${\gamma }_t$ + ${\epsilon }_{it}$, ${\lambda }_i$ is the coefficient of the impact of the independent variable on the dependent variable, ${\phi }_i$ is the coefficient of the time lag term, ${\mu }_i$ is the spatial fixed effect, ${\gamma }_t$ is the time fixed effect, ${\epsilon }_{it}$ is the random error term, ${\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}}_{it}$ is the standardized precipitation evaporation index of city i in year t, $\ln \left({\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}_{it}\right)$ is the logarithm of carbon emissions of city i in year t, ${\mathrm{F}\mathrm{V}\mathrm{C}}_{it}$ is the vegetation coverage of city i in year t, ${\mathrm{E}\mathrm{x}\mathrm{t}\_\mathrm{W}\mathrm{e}\mathrm{a}}_{it}$ is the proportion of extreme weather in city i in year t, $\ln \left({\mathrm{P}\mathrm{o}\mathrm{p}}_{it}\right)$ is the logarithm of the population density of city i in year t, ${\mathrm{I}\mathrm{n}\mathrm{d}\_\mathrm{S}\mathrm{t}\mathrm{r}}_{it}$ is the industrial structure of city i in year t, $\ln \left({\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}_{it-1}\right)$ is the logarithm of carbon emissions of city i in year t − 1, and ${\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}}_{it-1}$ is the standardized precipitation evaporation index of city i in year t − 1.

Based on previous studies [48,49,50], we conducted a Lagrange multiplier test and its robust statistical variant to determine whether a spatial autoregressive or spatial error model was more appropriate. The results of these tests are presented in

Table A1. The results of the Lagrange multiplier test and the robust Lagrange multiplier test.

Types of Tests	Pooling	Space Fixed	Time Fixed	Space–Time Fixed
LM-lag	23.513 ***	48.807 ***	3.9052 **	16.447 ***
LM-error	26.691 ***	46.958 ***	1.0484	11.449 ***
robust LM-lag	0.0870	1.9785	8.658 ***	11.288 ***
robust LM-error	3.2648 *	0.1297	5.8012 **	6.2894 **

Note: statistical significance is indicated as follows: ***, **, and * represent significance at the 1%, 5%, and 10% levels, respectively.

. Based on the test results, we developed two models: (23) a dynamic spatial Durbin model (SDM) with spatial and temporal fixed effects, and (24) a SDM with spatial and temporal fixed effects but without a time lag term for the dependent variable:

$$\begin{array}{l}{\mathrm{SPEI}}_{it}={\lambda }_1\ln \left({\mathrm{Carbon}}_{it}\right)+{\lambda }_2{\mathrm{FVC}}_{it}+{\lambda }_3{\mathrm{Ext}\text{\_}\mathrm{Wea}}_{it}+{\lambda }_4\ln \left({\mathrm{Pop}}_{it}\right)+{\lambda }_5{\mathrm{Ind}\text{\_}\mathrm{Str}}_{it}\\ +{\phi }_1\ln \left({\mathrm{Carbon}}_{it-1}\right)+{\phi }_2{\mathrm{SPEI}}_{it-1}+\rho {\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{SPEI}}_{it}}+{\vartheta }_1{\displaystyle \sum _{j\ne i}^n{W}_{ij}\ln \left({\mathrm{Carbon}}_{it}\right)}\\ +{\vartheta }_2{\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{FVC}}_{it}}+{\vartheta }_3{\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{Ext}\text{\_}\mathrm{Wea}}_{it}}+{\vartheta }_4{\displaystyle \sum _{j\ne i}^n{W}_{ij}\ln \left({\mathrm{Pop}}_{it}\right)}+{\vartheta }_5{\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{Ind}\text{\_}\mathrm{Str}}_{it}}\\ +{\theta }_1{\displaystyle \sum _{j\ne i}^n{W}_{ij}\ln \left({\mathrm{Carbon}}_{it-1}\right)}+{\theta }_2{\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{SPEI}}_{it-1}}+u_{it}\\ i=1,\dots N;t=1,\dots ,T\end{array},$$

(23)

$$\begin{array}{l}{\mathrm{SPEI}}_{it}={\lambda }_1\ln \left({\mathrm{Carbon}}_{it}\right)+{\lambda }_2{\mathrm{FVC}}_{it}+{\lambda }_3{\mathrm{Ext}\text{\_}\mathrm{Wea}}_{it}+{\lambda }_4\ln \left({\mathrm{Pop}}_{it}\right)+{\lambda }_5{\mathrm{Ind}\text{\_}\mathrm{Str}}_{it}\\ +{\phi }_1\ln \left({\mathrm{Carbon}}_{it-1}\right)+\rho {\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{SPEI}}_{it}}+{\vartheta }_1{\displaystyle \sum _{j\ne i}^n{W}_{ij}\ln \left({\mathrm{Carbon}}_{it}\right)}+{\vartheta }_2{\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{FVC}}_{it}}\\ +{\vartheta }_3{\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{Ext}\text{\_}\mathrm{Wea}}_{it}}+{\vartheta }_4{\displaystyle \sum _{j\ne i}^n{W}_{ij}\ln \left({\mathrm{Pop}}_{it}\right)}+{\vartheta }_5{\displaystyle \sum _{j\ne i}^n{W}_{ij}{\mathrm{Ind}\text{\_}\mathrm{Str}}_{it}}\\ +{\theta }_1{\displaystyle \sum _{j\ne i}^n{W}_{ij}\ln \left({\mathrm{Carbon}}_{it-1}\right)}+u_{it}\\ i=1,\dots N;t=1,\dots ,T\end{array}$$

(24)

where ρ and ${\vartheta }_i$ are the coefficients of the spatial lag term, ${\theta }_i$ represents the coefficient of the combined spatial and temporal lag term, $W_{ij}$ is the spatial weight matrix, and the remaining variables are consistent with Equation (22). Additionally, $\ln \left({\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}_{it-1}\right)$ will be referred to as $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ in the subsequent parts of this study, and ${\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}}_{it-1}$ will be referred to as lag_SPEI in the subsequent parts of this study.

During the process of constructing the dynamic SDM, the Hausman test, Wald test, and likelihood ratio (LR) test were performed. Elhorst pointed out that researchers should exercise caution before abandoning the SDM and should not rely solely on the significance level but also consider the model’s flexibility and adaptability [49]. Based on the test results presented in

Table A2. The results of the Hausman test, Wald test, and likelihood ratio (LR) test.

Types of Tests	Chi-Square Statistic (Degrees of Freedom)	p-Value
Hausman	22.95 (5)	0.0003
Wald_lag	23.80 (7)	0.0012
Wald_error	10.29 (7)	0.1730
LR_lag	23.19 (7)	0.0016
LR_error	10.11 (7)	0.1826

, we selected the dynamic SDM with spatial fixed effects.

3. Results

3.1. Descriptive Statistics of the Variables

Table A3. Results of the four model fits.

Model	R-Squared	Adjusted R-Squared	Akaike Information Criterion
Linear	0.7569634	0.7395539	3426.9352
Logarithmic	0.5518169	0.519712	3656.4314
Exponential	0.5818566	0.5519036	−496.5862
Power	0.8558181	0.8454899	−895.8669

summarizes the results of fitting linear, logarithmic, exponential, and power function models using panel data, all incorporating time fixed effects and omitting the intercept. Among these models, the power function model yielded the highest R-squared (0.8558) and adjusted R-squared (0.8455), along with the lowest AIC value (−895.87). Consequently, the power function model was chosen to estimate carbon emissions. Figure 2 presents the model fit and residual analysis overview. Panel a1 shows the estimation accuracy diagram, a2 shows the residual distribution, and a3 shows the Quantile–Quantile (Q-Q) plot. These three plots illustrate the carbon emissions data for prefecture-level cities simulated using nighttime light data (without outlier replacement or logarithmic transformation) and fitted with EDGAR data. Panel b1 shows the estimation accuracy diagram, b2 shows the residual distribution, and b3 shows the Quantile–Quantile plot. These three plots correspond to the carbon emissions data simulated by nighttime light after outlier replacement and logarithmic transformation ($\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$), fitted with the logarithm of the EDGAR data. Comparing the plots, b1 displays better fitting performance than a1. The R-squared value is higher in b1 (0.65), indicating that b1 explains more of the data variation. The residual distribution in b2 is more uniform and symmetric, while a2 displays a longer tail. The Q-Q plot in b3 displays residuals that are closer to a normal distribution, whereas a3 exhibits more significant deviations. The comparison reveals that the data, after outlier replacement and logarithmic transformation, show a better fit. This further underscores the importance of handling outliers and applying logarithmic transformation to mitigate their impact. Descriptive statistics for all variables, based on data from 164 cities, are provided in

Table 1. Description of the variables.

Variable	Obs	Mean	SD	Min	P25.	Median	P75.	Max
SPEI	1640	0.103601	0.205118	−0.719655	−0.014255	0.115136	0.229059	0.736612
ln(Carbon)	1640	3.219701	1.023457	−0.114833	2.496734	3.369444	4.000356	5.356
FVC	1640	0.484902	0.195377	0.039246	0.385403	0.524377	0.609315	0.841243
Ext_Wea	1640	0.104471	0.034878	0.027322	0.079235	0.101093	0.126027	0.224658
ln(Pop)	1640	4.827631	1.545234	−0.064976	4.12421	5.137982	6.044447	7.133607
Ind_Str	1640	1.244828	0.826715	0.130402	0.712861	1.014653	1.543616	6.068421
lag_ln(Carbon)	1640	3.192188	1.031743	−0.449434	2.476308	3.328708	3.967777	5.356
lag_SPEI	1640	0.102429	0.197656	−0.619156	−0.017313	0.108866	0.225859	0.736612
RGDP	1640	1381.57	2213.507	23.86415	353.4547	788.3353	1461.394	27,564.79

. Figure A1 compares the spatial distribution of the SPEI in 2011 and 2021. Compared to 2011, the spatial distribution of drought severity exhibited noticeable shifts in 2021. In particular, drought conditions intensified in the southwestern and northwestern regions. Although wet conditions in northeast and north China remained relatively stable, the extent of wet areas contracted, with some previously wetter regions transitioning into drought-prone areas.

3.2. Results of the Random Intercept Cross-Lagged Model

Figure 3 presents a schematic of the power analysis results for the RI-CLPM, calculated with the lavaan package [51] in R.

Table A4. Power analysis for random intercept cross-lagged model.

Sample_Size	Time_Points	ICC	Errors	Not_Converged	Inadmissible	Population_Value	Average	Minimum	SD	SEAvg	MSE	Accuracy	Coverage	Power
160	5	0.1	0	0	303	0.2	0.196	−0.122	0.09	0.088	0.008	0.24	0.659	0.43
170	5	0.1	0	0	289	0.2	0.194	−0.081	0.088	0.085	0.008	0.238	0.669	0.457
180	5	0.1	0	0	295	0.2	0.195	−0.086	0.083	0.083	0.007	0.229	0.667	0.457
190	5	0.1	0	0	241	0.2	0.192	−0.118	0.083	0.08	0.007	0.238	0.724	0.497
200	5	0.1	0	0	259	0.2	0.194	−0.048	0.08	0.079	0.006	0.229	0.702	0.509
160	10	0.1	0	0	31	0.2	0.2	−0.097	0.083	0.081	0.007	0.309	0.924	0.658
170	10	0.1	0	0	24	0.2	0.201	−0.084	0.078	0.079	0.006	0.3	0.926	0.719
180	10	0.1	0	0	25	0.2	0.202	−0.019	0.077	0.076	0.006	0.291	0.925	0.74
190	10	0.1	0	0	14	0.2	0.201	−0.005	0.073	0.074	0.005	0.286	0.94	0.764
200	10	0.1	0	0	12	0.2	0.2	−0.008	0.071	0.072	0.005	0.279	0.933	0.796
160	15	0.1	0	0	0	0.2	0.201	−0.025	0.082	0.08	0.007	0.312	0.943	0.702
170	15	0.1	0	0	1	0.2	0.2	−0.069	0.081	0.077	0.007	0.303	0.934	0.717
180	15	0.1	0	0	5	0.2	0.201	−0.019	0.076	0.075	0.006	0.293	0.938	0.747
190	15	0.1	0	0	3	0.2	0.195	−0.031	0.075	0.073	0.006	0.285	0.944	0.758
200	15	0.1	0	0	1	0.2	0.202	−0.065	0.072	0.071	0.005	0.279	0.952	0.803
160	5	0.3	0	0	7	0.2	0.196	−0.146	0.098	0.096	0.01	0.374	0.933	0.526
170	5	0.3	0	0	4	0.2	0.2	−0.144	0.097	0.093	0.009	0.362	0.935	0.603
180	5	0.3	0	0	6	0.2	0.199	−0.107	0.092	0.09	0.009	0.352	0.931	0.6
190	5	0.3	0	0	8	0.2	0.201	−0.149	0.094	0.087	0.009	0.34	0.936	0.629
200	5	0.3	0	0	1	0.2	0.204	−0.051	0.09	0.086	0.008	0.337	0.942	0.66
160	10	0.3	0	0	0	0.2	0.199	−0.089	0.086	0.085	0.007	0.335	0.942	0.665
170	10	0.3	0	0	0	0.2	0.2	−0.103	0.088	0.083	0.008	0.326	0.937	0.656
180	10	0.3	0	0	0	0.2	0.202	−0.093	0.083	0.081	0.007	0.317	0.946	0.707
190	10	0.3	0	0	0	0.2	0.201	−0.016	0.079	0.079	0.006	0.309	0.941	0.718
200	10	0.3	0	0	0	0.2	0.2	−0.073	0.082	0.077	0.007	0.3	0.939	0.739
160	15	0.3	0	0	0	0.2	0.199	−0.053	0.086	0.082	0.007	0.323	0.928	0.672
170	15	0.3	0	0	0	0.2	0.199	−0.033	0.082	0.08	0.007	0.314	0.946	0.697
180	15	0.3	0	0	0	0.2	0.196	−0.087	0.08	0.078	0.006	0.305	0.942	0.709
190	15	0.3	0	0	0	0.2	0.201	−0.034	0.077	0.076	0.006	0.297	0.946	0.763
200	15	0.3	0	0	0	0.2	0.198	−0.054	0.074	0.074	0.005	0.29	0.949	0.752
160	5	0.5	0	0	0	0.2	0.202	−0.208	0.11	0.106	0.012	0.417	0.937	0.492
170	5	0.5	0	0	0	0.2	0.2	−0.176	0.107	0.104	0.011	0.406	0.95	0.51
180	5	0.5	0	0	0	0.2	0.201	−0.137	0.101	0.101	0.01	0.394	0.955	0.534
190	5	0.5	0	0	0	0.2	0.199	−0.141	0.102	0.097	0.01	0.382	0.943	0.545
200	5	0.5	0	0	0	0.2	0.199	−0.118	0.101	0.095	0.01	0.373	0.935	0.545
160	10	0.5	0	0	0	0.2	0.199	−0.168	0.092	0.089	0.008	0.348	0.953	0.599
170	10	0.5	0	0	0	0.2	0.2	−0.085	0.09	0.087	0.008	0.34	0.951	0.637
180	10	0.5	0	0	0	0.2	0.202	−0.116	0.089	0.084	0.008	0.329	0.942	0.665
190	10	0.5	0	0	0	0.2	0.198	−0.058	0.085	0.081	0.007	0.319	0.948	0.671
200	10	0.5	0	0	0	0.2	0.198	−0.073	0.081	0.079	0.007	0.311	0.943	0.704
160	15	0.5	0	0	0	0.2	0.2	−0.125	0.09	0.084	0.008	0.33	0.94	0.657
170	15	0.5	0	0	0	0.2	0.199	−0.089	0.084	0.081	0.007	0.319	0.95	0.674
180	15	0.5	0	0	0	0.2	0.198	−0.106	0.08	0.08	0.006	0.313	0.951	0.695
190	15	0.5	0	0	0	0.2	0.2	−0.03	0.077	0.077	0.006	0.302	0.951	0.739
200	15	0.5	0	0	0	0.2	0.199	−0.034	0.075	0.075	0.006	0.295	0.947	0.742
160	5	0.7	0	0	1	0.2	0.199	−0.245	0.128	0.125	0.016	0.488	0.95	0.41
170	5	0.7	0	0	0	0.2	0.192	−0.336	0.127	0.121	0.016	0.474	0.946	0.372
180	5	0.7	0	0	0	0.2	0.194	−0.269	0.128	0.118	0.016	0.463	0.933	0.416
190	5	0.7	0	0	0	0.2	0.203	−0.297	0.123	0.114	0.015	0.447	0.934	0.471
200	5	0.7	0	0	0	0.2	0.199	−0.2	0.117	0.11	0.014	0.432	0.947	0.472
160	10	0.7	0	0	0	0.2	0.2	−0.117	0.093	0.092	0.009	0.359	0.95	0.602
170	10	0.7	0	0	0	0.2	0.197	−0.182	0.095	0.089	0.009	0.349	0.934	0.595
180	10	0.7	0	0	0	0.2	0.198	−0.094	0.09	0.086	0.008	0.338	0.947	0.626
190	10	0.7	0	0	0	0.2	0.203	−0.139	0.087	0.084	0.008	0.329	0.945	0.673
200	10	0.7	0	0	0	0.2	0.199	−0.043	0.083	0.082	0.007	0.321	0.946	0.679
160	15	0.7	0	0	0	0.2	0.202	−0.053	0.087	0.085	0.008	0.333	0.947	0.679
170	15	0.7	0	0	0	0.2	0.203	−0.084	0.088	0.083	0.008	0.324	0.94	0.695
180	15	0.7	0	0	0	0.2	0.199	−0.107	0.084	0.08	0.007	0.313	0.932	0.695
190	15	0.7	0	0	0	0.2	0.203	−0.019	0.078	0.078	0.006	0.306	0.962	0.735
200	15	0.7	0	0	0	0.2	0.2	−0.062	0.077	0.076	0.006	0.298	0.944	0.75

provides a detailed summary of the Monte Carlo simulation results. The coverage rate in Table A4 remains between 0.93 and 0.95 for all ICC values, demonstrating reliable parameter estimation under these conditions. For a sample size of 170 over 10 years, the power under varying ICC levels is 0.719 (ICC = 0.1), 0.656 (ICC = 0.3), 0.637 (ICC = 0.5), and 0.595 (ICC = 0.7). While increasing the sample size or study duration could enhance power, this research prioritizes arid and semi-arid regions or those transitioning to semi-arid conditions. Increasing the sample size without careful consideration is not recommended, as it may lead to a suboptimal model fit. Consequently, this study explores the use of this model but does not position it as the central focus of the research.

A chi-square test [52,53] comparing the CLPM and RI-CLPM resulted in a DiffChi2 of 146.953, which was significant at the 1% level. This indicates a significant difference between the models, with the RI-CLPM better capturing the data’s features, particularly the random intercept component, which likely accounts for individual heterogeneity. Consequently, this study employs the RI-CLPM to explore the relationship between carbon emissions and drought levels.

Table 2. Combined fit indices and information criteria.

Metric	Value_Standard	Value_Scaled	Type
Chi-square	744.277	519.352	Fit Index
Degree of Freedom	141	141
p-value (Chi-square)	0	0
CFI	0.931	0.939
TLI	0.906	0.918
RMSEA	0.158	0.125
90% CI RMSEA (Lower)	0.147	0.116
90% CI RMSEA (Upper)	0.169	0.135
p-value RMSEA ≤ 0.05	0	0
SRMR	0.112	0.112
AIC	−3434.249		Information Criterion
BIC	−3154.641
SABIC	−3436.453

presents the overall fit indices and information criteria for the RI-CLPM. While the CFI and TLI suggest a good model fit, the RMSEA and SRMR indicate some deficiencies.

Table A5. The regression coefficients in the Random Intercept Cross-Lagged Panel Model.

Regressions	Estimate	Std. Err	z-Value	p-Value
wc2~wc1	0.954	0.016	60.885	0
wc2~ws1	−0.049	0.064	−0.764	0.445
ws2~wc1	0.171	0.022	7.962	0
ws2~ws1	−0.014	0.109	−0.127	0.899
wc3~wc2	0.969	0.037	26.413	0
wc3~ws2	0.1	0.098	1.023	0.306
ws3~wc2	−0.194	0.024	−8.002	0
ws3~ws2	0.578	0.072	8.031	0
wc4~wc3	0.976	0.013	74.951	0
wc4~ws3	−0.079	0.058	−1.358	0.174
ws4~wc3	−0.113	0.023	−4.856	0
ws4~ws3	0.423	0.091	4.64	0
wc5~wc4	1.001	0.02	48.882	0
wc5~ws4	0.098	0.092	1.063	0.288
ws5~wc4	0.235	0.042	5.615	0
ws5~ws4	1.12	0.129	8.689	0
wc6~wc5	0.896	0.024	37.36	0
wc6~ws5	0.239	0.106	2.248	0.025
ws6~wc5	−0.062	0.012	−5.077	0
ws6~ws5	0.48	0.054	8.882	0
wc7~wc6	1.024	0.01	99.976	0
wc7~ws6	0.028	0.05	0.556	0.578
ws7~wc6	−0.163	0.023	−6.987	0
ws7~ws6	0.556	0.078	7.15	0
wc8~wc7	0.972	0.012	82.458	0
wc8~ws7	−0.079	0.046	−1.708	0.088
ws8~wc7	−0.127	0.033	−3.848	0
ws8~ws7	0.526	0.137	3.851	0
wc9~wc8	0.964	0.012	80.4	0
wc9~ws8	−0.059	0.036	−1.628	0.101
ws9~wc8	0.006	0.016	0.384	0.701
ws9~ws8	0.557	0.047	11.938	0
wc10~wc9	0.979	0.008	115.988	0
wc10~ws9	0.041	0.039	1.051	0.293
ws10~wc9	0.13	0.023	5.637	0
ws10~ws9	−0.356	0.121	−2.93	0.003

presents the regression results of the RI-CLPM, where “c” refers to $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and “s” refers to the SPEI. The regression coefficient ${\mathsf{\alpha }}_{\mathrm{c}}$ is significant at the 1% level across all periods, providing evidence of autocorrelation in $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ over time. Similarly, all ${\mathsf{\alpha }}_{\mathrm{s}}$ coefficients except for the period t = 1 are significant at the 1% level, indicating autocorrelation in the SPEI. The coefficient ${\mathsf{\beta }}_{\mathrm{c}\mathrm{s}}$ representing the effect of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI, shows significant negative correlations in periods t = 2, 3, 5, 6, and 7, while periods t = 1, 4, and 9 show significant positive correlations. This suggests a statistically significant cross-time effect of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI. However, the ${\mathsf{\beta }}_{\mathrm{s}\mathrm{c}}$ coefficient, representing the SPEI’s effect on $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$, is only significantly positive in period t = 5 at the 5% level, indicating that the SPEI has minimal cross-time influence on $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$.

The covariance between the ${RI}_c$ and ${RI}_s$ is 0.025 (SE = 0.007, z = 3.535, p < 0.001), suggesting a strong positive correlation between individuals’ long-term average levels of these variables, indicating a shared trend. Variance results are detailed in

Table A6. Results of the Variances section in the Random Intercept Cross-Lagged Panel Model.

Variances	Estimate	Std. Err	z-Value	p-Value
Ric	0.985	0.131	7.534	0.000
Ris	0.003	0.001	3.048	0.002
wc1	0.611	0.110	5.583	0.000
ws1	0.020	0.003	7.453	0.000
wc2	0.018	0.003	6.260	0.000
ws2	0.029	0.005	5.941	0.000
wc3	0.052	0.010	5.299	0.000
ws3	0.010	0.002	5.241	0.000
wc4	0.012	0.002	5.653	0.000
ws4	0.009	0.001	8.145	0.000
wc5	0.013	0.002	5.684	0.000
ws5	0.012	0.003	4.656	0.000
wc6	0.035	0.009	4.068	0.000
ws6	0.014	0.001	9.949	0.000
wc7	0.009	0.001	6.946	0.000
ws7	0.014	0.002	8.190	0.000
wc8	0.007	0.001	5.320	0.000
ws8	0.034	0.005	6.912	0.000
wc9	0.006	0.001	5.472	0.000
ws9	0.007	0.001	9.515	0.000
wc10	0.005	0.001	6.394	0.000
ws10	0.027	0.003	7.621	0.000

. ${\mathrm{R}\mathrm{I}}_{\mathrm{c}}$ is statistically significant, indicating substantial differences in long-term carbon emission levels across individuals. RIs is small but statistically significant, suggesting that while overall variability in drought severity is low, individual differences remain notable. The variance at time point t = 1 ($w_{c_1}$ and $w_{s_1}$) shows a significant value of 0.611 for $w_{c_1}$, indicating substantial variability in $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ at this initial time point. The variance estimate for $w_{s_1}$ at time point 1 is 0.020 and statistically significant, emphasizing that SPEI variability is much smaller compared to $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ at this point. Furthermore, the variances $w_{c_2}$ − $w_{c_{10}}$ and $w_{s_2}-w_{s_{10}}$ are significant across later time periods, revealing consistent variability in both $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and SPEI over the entire time series.

3.3. Spatial Econometric Analysis Results

Table 3. The global Moran’s I for the key independent variable and dependent variable.

Year	ln(Carbon)	SPEI
2012	0.4581 ***	0.7869 ***
2013	0.4296 ***	0.8468 ***
2014	0.4060 ***	0.7528 ***
2015	0.3972 ***	0.8753 ***
2016	0.3940 ***	0.6811 ***
2017	0.4047 ***	0.7957 ***
2018	0.4268 ***	0.8469 ***
2019	0.4370 ***	0.8566 ***
2020	0.4550 ***	0.7502 ***
2021	0.4388 ***	0.6845 ***

Note: statistical significance is indicated as follows: *** represent significance at the 1% level.

presents the results of the global Moran’s I test for $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and the SPEI between 2012 and 2021. All indices are statistically significant at the 1% level. These findings indicate that the distributions of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and the SPEI across the study area are not random; they exhibit clear spatial correlations and clustering patterns throughout the study period. Therefore, spatial correlation should be considered when analyzing the effect of carbon emissions on drought severity to avoid biased results.

Figure A2 presents the Moran scatter plots for $\ln \left({\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}_{2012}\right)$, ${\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}}_{2012}$, $\ln \left({\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}_{2021}\right)$, and ${\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}}_{2021}$. This analysis focuses on comparing the first and final years of the study period. As shown in Figure A2, most cities fall within the first and third quadrants, suggesting a statistically significant positive correlation between carbon emissions and drought severity. Figure 4 displays the significant local spatial autocorrelation for $\ln \left({\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}_{2012}\right)$, ${\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}}_{2012}$, $\ln \left({\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}}_{2021}\right)$, and ${\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}}_{2021}$. It also highlights the spatial autocorrelation between each variable and its neighboring regions, with Z-scores and p-values analyzed (only p-values are indicated in the figure). The figure identifies significant clusters at the 5% significance level of local Moran’s I, classified into four categories: high–high (H-H), where both local and neighboring values exceed the mean; low–low (L-L), where both local and neighboring values are below the mean; high–low (H-L), where local values are above the mean while neighboring values are below; and low–high (L-H), where local values are below the mean while neighboring values are above. In both 2012 and 2021, H-H carbon emission clusters were primarily concentrated in the North China Plain, while L-L clusters were found in the northwest. Compared to the 2012 SPEI (H-H) clusters in the central region, the 2021 SPEI (H-H) regions have significantly decreased, now limited to the northeast and certain coastal cities. Meanwhile, SPEI (L-L) areas have expanded in the west, suggesting that as carbon emissions have risen in some cities, drought severity has also increased.

This study adopts the methodology outlined in previous studies [53,54,55] for spatial econometric analysis.

Table 4. Spatial econometric analysis (spatial weight matrix W3).

Variable	Dynamic	Non-Dynamic
ρ	0.8397 *** (90.311)	0.8468 *** (93.547)
ln(Carbon)	−0.0106 (−0.5387)	−0.0106 (−0.5378)
FVC	0.5732 *** (4.3896)	0.5865 *** (4.4512)
Ext_Wea	−0.3876 *** (−4.2606)	−0.3612 *** (−3.9441)
ln(Pop)	0.1867 (1.4866)	0.1900 (1.5011)
Ind_Str	0.0007 (0.1141)	0.0040 (0.6419)
lag_ln(Carbon)	0.0026 (0.1485)	0.0020 (0.1106)
lag_SPEI	0.0744 *** (5.9497)
W.ln(Carbon)	−0.0628 ** (−2.5133)	−0.0581 ** (−2.3095)
W.FVC	−0.0260 (−1.0645)	−0.0225 (−0.9179)
W.Ext_Wea	0.0743 (1.1998)	0.0783 (1.2552)
W.ln(Pop)	0.0044 (1.3705)	0.0037 (1.1526)
W.Ind_Str	0.0039 (1.1007)	0.0021 (0.6055)
W.lag_ln(Carbon)	0.0567 ** (2.2963)	0.0552 ** (2.2191)
W.lag_SPEI	0.0136 (1.1619)
logLik	1657.625	1638.826
R²	0.8599	0.8577

Note: statistical significance is indicated as follows: *** and ** represent significance at the 1% and 5% levels, respectively; t-test value in parentheses.

presents the estimation results for both the dynamic SDM with spatial and temporal fixed effects and the static version of the model. The results from both models are largely consistent. While the direct effects of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI are insignificant, their spatial lag terms exert significant influences on the SPEI. Specifically, the spatial lag of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ has a significant negative impact on the SPEI at the 5% significance level. This means that higher spatial lag values of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ lead to increased drought severity in the region. Conversely, the spatial lag of $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ has the opposite effect. At the 5% significance level, it shows a positive effect on the SPEI, indicating that an increase in the spatial lag of $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ reduces drought severity in the region. The time lag of the SPEI in the dynamic model has a significant positive effect on the current SPEI, indicating that the dynamic model captures a broader range of temporal dependencies. To analyze specific impacts, we used the decomposition method from an existing study [56].

Table 5. Spatial econometric analysis effect decomposition (spatial weight matrix W3).

Variable	Dynamic			Non-Dynamic
	Direct Effects	Spatial Spillover	Total	Direct Effects	Spatial Spillover	Total
ln(Carbon)	−0.0470	−0.4082 **	−0.4552 **	−0.0460	−0.3996 **	−0.4456 **
lag_ln(Carbon)	0.0326	0.3354 **	0.3680 *	0.0319	0.3385 *	0.3704 *

Note: statistical significance is indicated as follows: ** and * represent significance at the 5% and 10% levels, respectively; the random number seed is set to “12345”. The number of model sampling iterations is 10,000.

provides the effect decomposition for both spatial econometric analyses. In the dynamic model, the direct effects of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ are insignificant. The spatial spillover effect of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ is significantly negative at the 5% level, meaning that higher carbon emissions in neighboring areas worsen local drought conditions. The overall effect of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ is significantly negative at the 5% level, indicating that increased carbon emissions exert negative impacts on both the local area and neighboring regions. The spatial spillover effect of $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ is significantly positive at the 5% level, suggesting that past carbon emissions in neighboring areas positively influence current local conditions. The total effect of $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ is significantly positive at the 10% level, indicating that past carbon emissions have an overall positive impact on both the local region and its neighbors. The static model results are similar to those of the dynamic model, with only minor differences in effect sizes. In the dynamic model, the spatial spillover and total effects of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ are larger than in the static model, while the indirect and total effects of $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ are smaller.

3.4. Robustness Test

3.4.1. Replace the Spatial Weight Matrix

This study employs a spatial weight matrix W2, which accounts solely for geographical proximity, to perform a robustness check of the spatial econometric results. As illustrated in

Table A7. Spatial econometric analysis (spatial weight matrix W2).

Variable	Dynamic	Non-Dynamic
ρ	0.8731 *** (99.944)	0.8788 *** (103.18)
ln(Carbon)	−0.0225 (−1.277)	−0.0228 (−1.2886)
FVC	0.4908 *** (4.1935)	0.5056 *** (4.2941)
Ext_Wea	−0.3706 *** (−4.5325)	−0.3449 *** (−4.1944)
ln(Pop)	0.2030 * (1.8041)	0.2042 * (1.8048)
Ind_Str	0.0031 (0.5611)	0.0055 (0.9969)
lag_ln(Carbon)	0.0002 (0.0102)	0.0002 (0.0116)
lag_SPEI	0.0592 *** (5.2566)
W.ln(Carbon)	−0.0555 *** (−2.6279)	−0.0529 ** (−2.4901)
W.FVC	−0.0204 (−0.9516)	−0.0193 (−0.9037)
W.Ext_Wea	0.0563 (1.0058)	0.0589 (1.0472)
W.ln(Pop)	0.0055 * (1.7819)	0.0051 (1.6365)
W.Ind_Str	0.0017 (0.4585)	0.0003 (−0.0775)
W.lag_ln(Carbon)	0.0474 ** (2.2662)	0.0469 ** (2.2342)
W.lag_SPEI	0.0135 (1.2534)
logLik	1774.578	1759.565
R²	0.8865	0.8853

Note: statistical significance is indicated as follows: ***, **, and * represent significance at the 1%, 5%, and 10% levels, respectively.

, similar to Table 4, the spatial lag terms for $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI remain significant, confirming the substantial influence of carbon emissions on drought severity. However, when only geographical distance is considered, without incorporating economic factors, the impact coefficients decrease, indicating that a more precise estimation of the influence is achieved when both economic and geographical factors are included.

Table 6. Spatial econometric analysis effect decomposition (spatial weight matrix W2).

Variable	Dynamic			Non-Dynamic
	Direct Effects	Spatial Spillover	Total	Direct Effects	Spatial Spillover	Total
ln(Carbon)	−0.0726 **	−0.5317 ***	−0.6044 ***	−0.0730 **	−0.5383 ***	−0.6113 ***
lag_ln(Carbon)	0.0319	0.3365 *	0.3684 *	0.0320	0.3456 *	0.3776 *

Note: statistical significance is indicated as follows: ***, **, and * represent significance at the 1%, 5%, and 10% levels, respectively.

presents the spatial econometric effect decomposition results, using spatial weight matrix W2. In contrast to a spatial weight matrix that incorporates both economic and distance factors, when only distance is considered, the direct effect of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI is significantly negative at the 5% level in both the dynamic and non-dynamic models. This indicates that increasing carbon emissions in a region exacerbate drought conditions.

3.4.2. Divide into Different Time Periods

This study divides the research period into two distinct intervals, 2012–2016 and 2017–2021, and performs spatial econometric analysis for each period to evaluate temporal variations.

Table A8. Spatial econometric analysis by time period (spatial weight matrix W3).

Variable	From 2012 to 2016		From 2017 to 2021
	Dynamic	Non−Dynamic	Dynamic	Non−Dynamic
ρ	0.8385 *** (64.619)	0.8370 *** (64.112)	0.8426 *** (65.469)	0.8506 *** (68.349)
ln(Carbon)	0.0252 (1.1017)	0.0278 (1.2064)	−0.0638 (−1.4172)	−0.070 (−1.5485)
FVC	0.8874 *** (5.7567)	0.9119 *** (5.8784)	0.2686 (0.9854)	0.3068 (1.1244)
Ext_Wea	−0.3797 *** (−3.1842)	−0.3760 *** (−3.1446)	−0.3461 ** (−2.4954)	−0.2304 * (−1.6927)
ln(Pop)	−0.9767 (−1.1427)	−1.0102 (−1.1762)	1.1028 *** (2.9532)	1.0812 *** (2.8866)
Ind_Str	0.0013 (−0.1124)	−0.0003 (−0.0251)	0.0272 *** (2.5863)	0.0300 *** (2.8639)
lag_ln(Carbon)	−0.0262 (−1.2094)	−0.0297 (−1.3683)	−030339 (−0.9786)	−0.0305 (−0.8780)
lag_SPEI	0.0336 ** (2.0210)		0.0655 *** (3.3306)
W.ln(Carbon)	−0.0286 (−1.0450)	−0.0256 (−0.9345)	−0.1213 ** (−2.4903)	−0.1263 *** (−2.5837)
W.FVC	0.0058 (0.2022)	−0.0036 (−0.1250)	−0.0226 (−0.6351)	−0.0443 (−1.2607)
W.Ext_Wea	0.0681 (0.8463)	0.0547 (0.6803)	0.0345 (0.4209)	0.0672 (0.8220)
W.ln(Pop)	0.0022 (0.5506)	0.0015 (0.3667)	0.0073 (1.5142)	0.0073 (1.5070)
W.Ind_Str	−0.0097 * (−1.7664)	−0.0093 * (−1.7244)	−0.0075 (−1.4784)	−0.0055 (−1.0721)
W.lag_ln(Carbon)	0.0244 (0.8989)	0.0234 (0.8573)	0.1011 ** (2.0932)	0.1034 ** (2.1321)
W.lag_SPEI	0.0246 (1.6442)		0.0382 * (1.7188)
logLik	958.8849	955.342	810.228	803.6982
R²	0.8923	0.8912	0.8611	0.8601

Note: statistical significance is indicated as follows: ***, **, and * represent significance at the 1%, 5%, and 10% levels, respectively.

presents the results, in which, compared to those in Table 4, the 2012–2016 period’s spatial econometric analysis shows that the effects of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$, $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$, and their spatial lag terms on the SPEI are not statistically significant at any significance level. However, in the 2017–2021 period, the spatial lag effects of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and $\mathrm{lag}\_\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI become statistically significant. Their impact coefficients are notably larger.

Table 7. Spatial econometric effects decomposition by time periods (spatial weight matrix W3).

Variable		Dynamic			Non-Dynamic
		Direct Effects	Spatial Spillover	Total	Direct Effects	Spatial Spillover	Total
From 2012 to 2016	ln(Carbon)	0.0215	−0.0419	−0.0204	0.0265	−0.0136	0.0129
	lag_ln(Carbon)	−0.0249	0.0141	−0.0107	−0.0304	−0.0080	−0.0384
From 2017 to 2021	ln(Carbon)	−0.1541 **	−1.015 ***	−1.1692 ***	−0.1694 **	−1.1325 ***	−1.3019 ***
	lag_ln(Carbon)	0.0035	0.4208	0.4242	0.0110	0.4727	0.4838

Note: statistical significance is indicated as follows: *** and ** represent significance at the 1% and 5% levels, respectively.

presents the decomposition of spatial econometric effects for both time periods. The effects in the 2012–2016 period are not significant. However, in the 2017–2021 period, the effect of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI is statistically significant at the 5% level, indicating a negative impact. This indicates that the selection of the study’s time span results in different outcomes.

4. Discussion

This study employs the RI-CLPM to examine the relationship between carbon emissions and land drought. The model results indicate that the autoregressive coefficients for $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ and the SPEI are significant at the 1% level, suggesting that past carbon emission levels strongly influence current and future emissions. This highlights the inertia of carbon emissions—once they reach a certain scale in a city or region, significant short-term changes are unlikely. A similar pattern is observed for drought conditions, which are also resistant to sudden short-term shifts. Additionally, a significant positive correlation between the ${\mathrm{R}\mathrm{I}}_{\mathrm{c}}$ and ${\mathrm{R}\mathrm{I}}_{\mathrm{s}}$ suggests that the long-term average levels of carbon emissions and drought exhibit a common trend across regions. The notable variance in the ${\mathrm{R}\mathrm{I}}_{\mathrm{c}}$ indicates considerable differences in long-term levels across regions. Although smaller, the variance in the drought variable is also significant, reflecting measurable variability across regions. This suggests that despite similarities in climate across the study areas, differences in economic development and urbanization contribute to significant regional disparities in carbon emission levels. The cross-lagged effect primarily reveals that carbon emissions have a lagged impact on drought, whereas the reverse effect—drought influencing carbon emissions—is negligible. Consequently, in future spatial econometric studies, both the time-lagged effects of carbon emissions and drought levels will be taken into account.

The results of the global Moran’s I test and the local Moran’s I test show that carbon emissions and drought levels have significant spatial autocorrelation and spatial clustering characteristics, which is largely consistent with previous research results. The areas with high carbon emissions (H-H) are concentrated in the cities of the eastern coastal areas and the North China Plain, and there were no particularly significant changes during the study period. In contrast, the areas with high drought severity (L-L) have gradually expanded from Sichuan Province in 2012 to the northwestern provinces of Gansu and Qinghai, indicating a worsening trend in drought conditions in the northwestern provinces, particularly in Gansu and Qinghai.

The spatial econometric analysis reveals that using the inverse distance squared weighting matrix shows that carbon emissions significantly reduce the direct, indirect, and overall effects on drought. The findings indicate that both in the short and long term, an increase in a city’s carbon emissions will not only exacerbate local drought conditions, but also lead to a deterioration of drought conditions in its neighboring cities. Compared to the current period’s carbon emissions, a lag of one period’s higher carbon emissions has no significant impact on local drought, but will alleviate drought conditions in neighboring cities. Some studies have shown that air pollution can prompt high-emission, high-polluting enterprises to engage in green innovation [57]. We speculate that carbon emissions have a similar effect. A high level of carbon emissions in the past will prompt local and surrounding cities to take corresponding measures to mitigate the impact of carbon emissions on the environment and even improve the aridity of the land. Unlike considering only the distance between cities, when economic factors of different regions are taken into account, that is, when a spatial weight matrix combining economic and distance factors is used for spatial econometric analysis, the direct effect of carbon emissions is no longer significant, which shows that if the economic relationship between cities is not considered when conducting spatial econometric analysis, the impact of carbon emissions on urban drought levels will be overestimated. According to the constructed spatial weight matrix, higher actual GDP levels exert a greater influence on the surrounding regions. In addition, the dynamic model incorporates both the time lag of the dependent variable and the spatial–temporal lag, offering a more comprehensive approach and yielding more precise results. If only a static model is used, there is a risk of underestimating the indirect effect of carbon emissions on surrounding cities. As for why the direct effect of carbon emissions is no longer significant when economic and distance factors are considered, some studies have shown that air pollution is positively correlated with the green innovation of enterprises in the city [58]. Although carbon dioxide is not classified as an air pollutant, it is primarily produced through the combustion of fossil fuels, a process that generates other pollutants. Therefore, it is plausible to suggest that regions with high carbon emissions may also adopt low-carbon innovations, which could offset the local impact of carbon emissions. Surrounding cities with underdeveloped economies are affected by high-carbon-emission cities and cannot respond in time, so droughts are exacerbated. The impact of carbon emissions with a time lag is similar to the results of another spatial weight matrix.

Based on the results of the robustness test of spatial econometric analysis across different time periods, we speculate that the observed differences are related to the variations in total annual carbon emissions.

Table A9. Annual carbon emissions of 15 selected provinces (2011–2021).

Year	Carbon Emissions (Million Metric Tons of CO2)	Growth Rate Compared to 2011 (%)
2011	4724.23
2012	5209.17	10.26
2013	5237.57	10.87
2014	5295.22	12.09
2015	5244.08	11.00
2016	5265.23	11.45
2017	5387.12	14.03
2018	5695.97	20.57
2019	5968.75	26.34
2020	6083.12	28.76
2021	6218.93	31.64

presents the total carbon emissions for the 15 provinces selected in the study from 2011 to 2021, calculated using CEADs data. The total carbon emissions in the 2012–2016 period were below 5300 million metric tons, with an annual growth rate of approximately 12% relative to 2011. However, from 2017 to 2021, total carbon emissions increased annually, with the totals for 2020 and 2021 surpassing 6000 million metric tons, and a growth rate exceeding 30% in 2021 compared to 2011. In the short term, the high level of carbon emissions led to significant direct effects and spatial spillovers of $\ln \left(\mathrm{C}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{n}\right)$ on the SPEI. In the long term, the primary impact stemmed from the spillover effects of cities with higher carbon emissions on neighboring cities. These results suggest that when studying the impact of carbon emissions on drought, attention should be given to the choice of time scale. A shorter time span may lead to biased results, potentially indicating no impact or an exaggerated impact of carbon emissions on drought. We speculate that this is also related to the cumulative effects of carbon emissions, where their significance only emerges once the effects accumulate to a certain level. This further emphasizes the importance of selecting a longer time span for drought studies to obtain more accurate results.

We initially used nighttime light data to estimate carbon emissions for certain cities and employed the RI-CLPM to examine the causal relationship between carbon emissions and drought severity. Subsequently, we incorporated natural and anthropogenic factors as control variables and constructed a dynamic SDM with spatial and temporal fixed effects. The model was applied to explore both the direct effects and spatial spillover effects of carbon emissions on drought. Of course, our study has its limitations. First, the RI-CLPM does not fully accommodate the complexity of our research, leading to some discrepancies between the results and actual conditions. The RI-CLPM is widely used in psychological research, but its application to the study of the relationship between carbon emissions and drought may introduce certain biases. Although this represents a novel approach, we did not conduct a thorough investigation into its suitability for exploring the relationship between carbon emissions and drought. Instead, we focused the research on using the dynamic SDM for analysis. Second, other scholars who have used the dynamic SDM have also conducted endogeneity tests [54,55]. Since our study includes a lag term for carbon emissions, the model differs from those studies, and the RI-CLPM results show no bidirectional influence between carbon emissions and drought. As a result, we did not perform an endogeneity test, which may introduce potential bias in the final outcomes. Additionally, we used FVC to measure vegetation coverage as a control variable; however, we did not provide a detailed distinction between forests, farmland, and urban greenery, nor did we analyze the irrigation characteristics of farmland in different regions. As a result, the actual impact of different plant types on drought severity could not be studied in depth. Finally, due to difficulties in obtaining economic data for certain regions, we were compelled to exclude some regions from the spatial econometric analysis after conducting the RI-CLPM study. This exclusion limits the comprehensive examination of the relationship between carbon emissions and drought across all regions.

5. Conclusions

This study utilized the RI-CLPM and the dynamic SDM with spatial and temporal fixed effects to examine the relationship between carbon emissions and urban drought levels, leading to the following conclusions.

Within the selected study area, carbon emissions have a lagged effect on drought, while drought has almost no lagged effect on carbon emissions.

There is a clear spatial correlation and clustering between carbon emissions and drought. Compared to 2012, regions with high carbon emissions (H-H clusters) are concentrated in the cities of the eastern coastal areas and the North China Plain, while drought-affected areas (based on the SPEI) have expanded from Sichuan Province to the northwestern provinces of Gansu and Qinghai.

When considering only geographic distance between cities, the direct and indirect effects of carbon emissions on cities are significantly negative, with carbon emissions from the previous period showing only a significant indirect effect. When considering both economic factors and geographic distance, carbon emissions have only an indirect effect on drought, and the subsequent effects of carbon emissions are largely similar to those observed under the previous conditions.

Based on the constructed economic distance matrix, carbon emissions exhibit spillover effects on urban drought, with economically developed regions exerting a stronger in-fluence on less developed regions. First, densely populated cities with relatively developed economies and high levels of modernization should avoid merely relocating high-carbon-emission businesses or factories to less densely populated surrounding areas. Given the spatial spillover effects of carbon emissions on drought, cities should share carbon emission data to enable neighboring areas to take timely action on drought-related issues. To effectively address this challenge, governments should promote technical exchanges and cooperation between businesses in the more developed eastern regions, which possess advanced carbon emission management technologies, and high-emission industries in the less developed central and western regions. This will foster cross-regional collaboration, improve carbon emission management technologies across all stages of production, and contribute to the reduction in overall carbon emissions. For businesses that repeatedly fail to comply with policy requirements and consistently generate high carbon emissions, the government should impose punitive measures, including the potential closure of their operations. Additionally, the government should encourage public participation in environmental protection efforts, promote the adoption of clean energy transportation, and raise awareness to involve the public in carbon emission management. Through multi-stakeholder collaborative governance, mutually beneficial outcomes for society, the economy, and the environment can be realized.