The micro-prediction method is based on micro-data and plays a leading role in prediction. Micro-data are measured on a monthly basis, which is timelier in reflecting the changes in industrial energy consumption and predicting industrial carbon emission trends compared to macro-data, which is measured on an annual basis. On the other hand, the calculation method of micro-carbon emissions can reflect the changes in key carbon-emitting industries within the industry, facilitate the government to formulate reasonable carbon reduction policies, and urge key carbon-emitting enterprises in various industries to rectify their emission levels.

Macro-prediction methods are based on macro-data and have a stronger robustness in prediction. Macro-data, measured on an annual basis, can reflect the changes in energy consumption across various industries over the years and have a lower probability of missing data, making it more reliable than micro-data and their predictions. On the other hand, macro-carbon emission prediction can reflect the total carbon emissions of various industries, and compared to micro-carbon emission prediction methods, it can, to some extent, reflect the carbon emission impact of non-key industries.

Because the combined prediction method of fixed weights cannot reflect the advantage at every time point in the prediction timescale, the ability to learn a model is only limited to the model itself; so, we introduce the GIOWA combination prediction method (Cao et al., 2022). According to the fitting accuracy learning error characteristics of the results of each individual term prediction method, we obtain deeper and more detailed learning from the model. The prediction results of each single-term prediction method at each moment are optimized with the optimization criteria of the minimum sum of errors, the minimum sum of the absolute value of error, and the minimum error minimum, which allow us to obtain combined predicted carbon emissions closer to the real carbon emissions.

For carbon emission prediction, m single-term prediction methods are used. It should be noted that x _t is the measured carbon emission at time t; x _it is the predicted carbon emission at time t in the timescale; g _it is the λ power error at time t in the timescale; g _t = x _t ^λ− x _it ^λ; and λ = l in this paper. Let W = (w ₁, w ₂, …, w _m) and T be the weight of the m single-term prediction method in the combined prediction method: a i t = 1 − x t − x i t x t x t − x i t x t < 1 0 x t − x i t x t ≥ 1 .   i = 1 , 2 , ⋯ , m , t = 1 , 2 , ⋯ N . (13)

Here, ɑ _it is the prediction accuracy of time point t within the timescale of the i-monomial prediction method. If ɑ _it ∈ [0,1], then ɑ _it is the induced value of predicted carbon emission x _it. An m-monomial prediction method constitutes m two-dimensional arrays ((ɑ _1t, ɑ _1t), (ɑ _2t, ɑ _2t), …, (ɑ _mt, ɑ _mt)), and ɑ _1t, ɑ _2t, …, ɑ _mt are the combined prediction models obtained by the optimization criteria of different error types.

At λ = 1, the GIOWA combined prediction model is the induced ordered weighted arithmetic mean (IOWA) combined prediction model. x ^ t = ∑ i = 1 m w i x i t , t = 1 , 2 , ⋯ , N . (14)

The a-index (it) of the conventional weighted arithmetic average at time t is the subscript of the prediction accuracy, expressed as follows: f w a 1 t , x 1 t , a 2 t , x 2 t , ⋯ , a m t , x m t = ∑ i = 1 m w i x α − i n d e x i t . (15)

Then, Eq. 15 is the predicted carbon emission based on the combination of IOWA operators generated at time t by a _1t, a _2t, …, a _mt. By combining the microscopic and macroscopic prediction results and using the GIOWA combination calculation method, the combined prediction results can minimize the sum of error squares, realize the fit with the actual value, and then realize the prediction.

Combination prediction not only inherits the timeliness characteristics of micro-prediction but also inherits the strong robustness of macro-prediction. The learning of the error characteristics based on the fitting accuracy of various single-item prediction methods at different time points in the timescale has a deeper and more detailed understanding of the model. The optimization criteria for the prediction results of each single-item prediction method at each time point are present to minimize the sum of squared errors, absolute sum of errors, absolute value of errors, and extreme difference of errors, to obtain a combination prediction of carbon emissions that is closer to the actual carbon emissions. Compared to traditional carbon emission prediction methods, heterogeneous data sources are more extensive and reflect the energy consumption situation of industries more comprehensively, which inevitably makes the results of combined prediction models more accurate.

This paper takes the state-level new district of an eastern city as the empirical object (hereinafter referred to as region J) to obtain the energy consumption data on the energy-using enterprises in the region from 2020 to 2021, and the region J energy data are obtained from the enterprise survey. Through the proposed carbon emission calculation model, the carbon emissions of energy enterprises in region J are calculated, and the total carbon emission of the region is characterized.

Seven energy sources in region J were selected to calculate their carbon emissions: raw coal, natural gas, gasoline, diesel, liquefied petroleum gas, petroleum coke, and electricity. The total carbon emission from 2017 to 2021 and the carbon emissions of energy-using enterprises are shown in Figure 3. Through Eqs 1-3 and using these seven energy sources and carbon emissions data as training samples for the LSTM, the parameters in the equations are calculated to realize the LSTM in the next prediction.

As shown in Figure 3, the carbon emissions of region J from 2017 to 2021 have increased slowly at first, from 2019 to the maximum point, and then decreased sharply in 2020. As region J is one of the largest modern industrial clusters, with developed manufacturing, steel and petrochemical industries, and large energy consumption, the carbon emissions of energy enterprises account for approximately 58% of their total carbon emissions. The carbon emissions of housing and transportation account for approximately 20% and 17% of the total carbon emissions in the region, respectively. With the outbreak of COVID-19 in 2020, the production capacity of region J energy enterprises decreased, and the energy consumption decreased, resulting in a temporary decline in region J carbon emissions.

The total carbon dioxide emissions of the construction industry are equal to the sum of all the fuel combustion carbon emissions within the industry boundary and the corresponding emissions generated by the electricity and heat purchased by the enterprise, excluding the corresponding emissions used for transport vehicles. The total carbon dioxide emission of the cement production enterprise is equal to the sum of all fuel combustion emissions, process emissions, electricity and heat purchased by the enterprise, and the corresponding emissions of the electricity and heat output of the enterprise. The carbon emission of the transportation industry is mainly divided into two parts: road transportation and urban transportation. Residential carbon emissions are composed of the daily carbon emissions of residents using natural gas in their daily lives and the houses themselves. It should be noted that, except for the transportation industry, the carbon emissions of automobiles used for transportation purposes in other industries belong to the carbon emissions of the transportation industry, rather than being included from the carbon emissions of the industry.

The proportion of the carbon emissions of region J energy-using enterprises in the total carbon emissions of the region is significant. In order to analyze the impact of region J industries on the regional carbon emissions, the energy-using enterprises are divided into different industries, according to the national standard GB/T 4754-2021, Industry Classification of National Economy, and the carbon emissions of various industries are counted, as shown in Table 1.

Table 1 lists the key enterprises in the industries with high-electricity carbon emissions from 2020 to 2021. Among them, manufacturing and wholesale and retail occupied 14% and 22% of the carbon emissions of energy enterprises, respectively, while power, heat supply, real estate, and other industries accounted for a relatively low proportion.

The results of screening strongly correlated industries using DTW correlation analysis and employing the upper quartile box plot method are shown in Table 2. According to Table 2, the correlation of region J carbon emissions for industries and regions, manufacturing, wholesale and retail, construction, housing, and transportation are the strong correlation indicators of region J carbon emissions. Therefore, the carbon emission data on each indicator and region in the first 21 months of 2020–2021 in region J were selected as the training set, and the data on the last 3 months from 2020 to 2021 were selected as the test set and by Eqs 7, 8 modeling under LSTM as a prediction algorithm.

To demonstrate the feasibility of using the LSTM algorithm at the micro-level, we introduce the comparative experiment of the particle swarm algorithm, using the average error value to evaluate the superiority of the LSTM algorithm at the micro-level.

Through Table 3, we found that the fitting effect of the LSTM algorithm is better than that of the particle swarm algorithm. In order to ensure the superiority of the algorithm, we set the iterations of the same as 200 iterations.

Through the LSTM model, the mapping network of the data on strongly related industries, residential, and traffic carbon emissions to the region was obtained, and the carbon emissions of region J in 2022 was predicted. The predicted results are shown in Figure 4.

Compared with the true carbon emission value obtained through the carbon emission calculation method given in the IPCC guideline, the average error of the trained prediction model in this paper is 0.53% and the prediction error is 0.35%, which verifies the effectiveness and feasibility of the proposed carbon emission prediction method in urban areas.

The macro-data in this article are sourced from statistical yearbooks of various regions; therefore, the macro-data are divided on an annual scale. The STIRPAT algorithm, as an extensible random environmental impact assessment model, has excellent prediction results in terms of the elastic impact of human factors on the environment. In this paper, using the STIRPAT algorithm, the fitting and prediction of regional carbon emissions are realized based on the variables of the per capita GDP data, population data, and the calculated energy consumption structure and energy intensity of strongly related industries.

We obtain the region J per capita GDP data and population data from 2017 to 2022 and calculate the energy consumption structure, energy intensity, and other variables of strongly related industries. All variables were diagnosed by least-common squares collinearity, and all the variance inflation factors (VIFs) did not exceed the tolerance value of 10, indicating that there was no problem of collinearity among the variables.

According to Eqs 11, 12. Ridge regression was fitted based on the extended STIRPAT model. The results of the ridge regression analysis are shown in Figure 5. In the ridge plot, the value range of the ridge parameter k is set as (0,10), and the interval is 1. When k = 2 , the regression coefficient of each variable is locally stable, and the estimated ridge regression coefficient of k = 2 is selected as the correlation coefficient of the variable.

According to Eqs 9, 10. The STIRPAT model between the available carbon emissions and the variables is given as follows: ln ⁡ I = 0.0185 ⁡ ln ⁡ P + 0.0781 ⁡ ln ⁡ B − 1.1353 ⁡ ln ⁡ G + 0.0111 ⁡ ln ⁡ E + 0.6552 .

Applying a significance test to each variable, all variables passed with a level of 5% and showed a good fit. From the coefficient analysis, for every 1% increase in the energy consumption structure of region J strongly related industries in the region, the carbon emissions of the region will increase by 0.0459%, with the most significant impact on the carbon emissions. For every 1% increase in the population, per capita GDP, and the energy intensity of strongly related industries in region J, carbon emissions will increase by 0.0185%, 0.0781%, and 1.1353%, respectively. Therefore, based on the ridge regression analysis, the carbon emission of region J from 2017 to 2021 is predicted by the STIRPAT algorithm, and the prediction results are shown in Figure 6.

Compared with the true carbon emissions value obtained through the carbon emission calculation method in the IPCC guideline, the prediction error of the proposed prediction model in this paper is 1.05%, which verifies the effectiveness and feasibility of the proposed carbon emission prediction method in urban areas.

The GIOWA combination method has high flexibility and adaptability. The partial weights can be adjusted and reconfigured according to the requirements. The weight is adjusted according to the prediction results and the degree of error to maintain the effectiveness and adaptability of the predicted carbon emission portfolio. The micro-forecast is based on energy consumption data, such as enterprise-level electricity consumption, while the macro-forecast is based on the regional economy and population. There are differences between the two benchmarks and nonlinear links. The GIOWA combination prediction method is used to achieve a more accurate prediction of regional carbon emissions.

The initial weight of the micro-forecast data and macro-prediction is set according to the degree of error between micro- and macro-data. Therefore, the initial weight for the micro-forecast ratio is 0.75, and the macro-layer ratio is 0.25. Based on Eqs 13–15, the GIOWA combination prediction is shown in Figure 7 shows the result of calculating the GIOWA combination and comparing the microscopic and macroscopic prediction curves.

The prediction effect of the combined prediction value is much better than that of the micro-prediction effect and the macro-prediction. The errors for each prediction are shown in Table 4.

Compared with the macro-prediction error, the combined prediction is reduced by 0.88%, improving the accuracy of 83.81%, reducing the micro-prediction error by 0.185%, and improving the accuracy of 52.11%. The feasibility and validity of the combined prediction are verified.

The initial weight of the combined prediction will be updated in real time, based on the historical data. The micro-prediction and macro-prediction error will not always be constant. With 5 years as a sample set, each year should update the micro- and macro-prediction method and calculate the corresponding error value. Selecting the smallest error value prediction method and obtaining the prediction value, through the error value comparison combination prediction initial weight, enables the reduction of the prediction error.