The formulation of carbon reduction policy is one of the important measures to reduce greenhouse gases. The STIRPAT model has been one of the main methods used to analyse the impact factors of carbon emissions in recent years. The variable parameters in this model include the impacts of the environment, population, GDP per capita, energy intensity, and urbanisation rate on carbon emissions from energy consumption [20]. In this study, the indicators in the model were replaced with anthropogenic source carbon emission variables, resident population, and carbon intensity to obtain the mathematical expression of the extended STIRPAT model.

where

Y

is the total amount of carbon emissions,

X
1

,

X
2

,

X
3

,

X
4

,

and
 

X
5

are the drivers of carbon emissions, representing the transport mode, carbon intensity, urbanisation level, energy mix, and industrial mix respectively, and

?
1

,

?
2

,

?
3

,

?
4

,

and
 

?
5

are the elasticity factors of the indicator, and

t

is the year of time. The proportion of factors influencing the level of carbon emissions varies from city to city, which in turn requires that the carbon emission analysis is tailored to the local and temporal context. The interactions among different driving factors can effectively reveal the dynamic pattern change of urban agglomeration carbon emission efficiency [21]. In this study, spatial correlation coefficients were introduced for the analysis of carbon emission efficiency, with Moran scatter plots representing the spatial correlation of the data, where the correlation and aggregation dynamics of the variable data are represented by the spatial distributivity and correlation analysis. The mathematical expression is shown in Equation (2).

where

I

 
and
 

I
i

are the spatial autocorrelation and local autocorrelation, respectively,

n

is the number of spatial cells,

x
i

 

and
 

x
y

are the carbon emissions of the city unit

i
,
 
j

and

x
¯

are the mean values of the variables,

W

i
j

is the contiguous space weight matrix, and

Z

is the normalised form of the sample space. When two urban units are adjacent, the spatial weight matrix has a value of 1 and vice versa, and when the local autocorrelation is significantly positive, it indicates that the spatial difference between the urban unit and its neighbouring city is small and vice versa. When its value is zero, it indicates that the spatial distribution of the sample spatial units shows randomness. The coefficient of variation is also used to express the relative differences among urban transport carbon emissions, and its value is positively correlated with carbon emissions. Its formula is Equation (3).

where

m

is the number of cities, and

Y
¯

is the average carbon emissions. Distinct propel factors have different carbon reduction effects, and strengthening carbon emission forecasting can be an effective way to analyse carbon budgets and their reduction potential factors [22]. This study made use of the grey GM(1,1) model for carbon emission forecasting analysis, i.e., the original data columns were cumulated and new series were generated and differentiated to obtain the model GM(1,1), as in Equation (4).

where

X

1

 

and
 

X

10

are the original and cumulative data columns, respectively,

n

is the number of data points,

n

 
and
 

a

are the development factor and grey dosage, respectively, and

k

is the number of samples in the series. The changes in the dynamic characteristics of the different driver variables can be expressed by means of an impulse response function, which effectively responds to the standard deviation shocks caused by the perturbation of the variables over a certain period of time, and whose mathematical expression is shown in Equation (5).

where

?

is the random perturbation value, and

n

is the number of periods.