In this paper, the main work about the modeling is designing an air pollution module and realizing the hard-link with the original DICE model (as shown in
Figure 1). In the DICAE model, the economy module and the climate module are same as that in the DICE model [
23], so we do not introduce them in this paper. Besides, the explanations of the objective function, as well as how to construct the air pollution module and how it connects with other modules are given in the next sections.
2.1.2. The Air Pollution Module
The air pollution module includes the quantitative description of air pollutant emissions co-emitted with CO2 emissions, their damages to the socioeconomic system and the costs of abatement. It should be noted that we only analyze one type of air pollutant, NOX, in this study because of data limitation, and we hope to incorporate more air pollutants, expanding the scope of model applications in future work.
● NOX emissions
Nitrogen oxides co-emitted with carbon dioxides mainly come from the combustion of coal, oil and natural gas [
25], and carbon emissions from energy consumption are also mainly derived from these three major fossil fuels. In this context, we can build the relationship between CO
2 and NO
X based on the homology of emissions.
Assuming that the total energy consumption of the economy is
, and the proportions of coal, oil and natural gas are
,
,
; The proportion of CO
2 emissions produced by energy consumption is
; CO
2 emission factors (emissions from per unit of fuel) of coal, oil and natural gas are
,
,
, and NO
X emission factors are
,
,
; CO
2 emissions and NO
X emissions are
and
, respectively. Thus, we can use two equations below to represent the emissions.
Please note that the NO
X emissions calculated in Equation (2) are only the emissions from fossil fuel combustion, under the assumption that all the NO
X co-emitted with CO
2 comes from the combustion of coal, oil and natural gas. According to Equations (2) and (3), we can get another equation to express NO
X emissions:
Then we use
to indicate the amount of NO
X emissions co-emitted by a unit of CO
2 emission, calling it co-emit coefficient.
Based on the above equations, it is possible to calculate the NO
X emissions based on the CO
2 emissions and the energy consumption structure. In addition, if there are actions to reduce CO
2 and NO
X, Equation (6) needs to be modified. Here we use
and
to indicate the emission reduction rates of CO
2 and NO
X, respectively, so now their relation satisfies the following equation.
The emission factors in this paper are collected from IPCC EFDB (Emission Factor Database) [
26], and their values are shown in
Table 1.
According to the IPCC AR4 report, CO2 emissions produced by fossil fuels account for more than 80% of the total anthropogenic CO2 emissions. Therefore, we set the parameter as 0.8.
This study assumes that the changes of the energy consumption structure are exogenous. Considering the time span and fitting effect of the energy structure data, we choose the data from the baseline scenario of the Emissions Prediction and Policy Analysis (EPPA) model developed by Massachusetts Institute of Technology (MIT) [
27], and get the proportion trends of fossil fuels in the energy consumption structure through the Curve Fitting Toolbox in MATLAB [
28] (the coefficient of determination R-square is over 95%). The precise expressions are shown below:
The coefficients in the above equations are obtained from data fitting, and their values are shown in
Table 2.
● NOX damages
Inspired by the DICE model, which divides the impacts of carbon dioxide on the socio-economic system into two parts—environmental damages caused by emissions and control costs of mitigation measures, we divide the impacts of NO
X into damages and costs in the DICAE model. As for damages of air pollutants, many studies have approximated them as human health losses. For example, Yang et al. represented the environmental damages of SO
2, NO
X and PM
10 by the value of premature deaths [
29]. Thus, in this paper, we also indirectly quantify the environmental damages of NO
X emissions through health impairment. Meanwhile, in terms of abatement costs, this paper fits a cost curve of NO
X abatement, which will be described in detail in the next sub-section.
To evaluate the health impacts caused by NO
X, the inhalation factor method inferred by Li was adopted [
30]. Inhalation factor refers to the proportion of total pollutants absorbed by the human body, so it is a dimensionless parameter and can also be called exposure efficiency [
31]. This method calculates the inhaled dose in human body firstly, then calculates the health impacts through a dose-response coefficient, and it can be used to evaluate the economic losses further.
The formula for calculating the health damages of NO
X is as follows:
where
is the health losses (incidence and mortality);
is the coefficient of dose-response, which represents the health impacts caused by per unit of inhaled NO
X; The inhalation factor is
, and the value is 2.47 × 10
−6 [
32];
indicates the NO
X emissions which we have discussed in the previous section.
● NOX reduction costs
In this paper, the reduction costs are calculated based on the NO
X emission data in the RAINS model developed by IIASA [
33].
Figure 2 shows the NO
X reduction cost curve, and the corresponding function of the curve is:
where
,
,
;
refers to the reduction rate of NO
X, and
refers to the reduction costs.
2.1.3. Linking with the DICE Model
After creating the air pollution module, we can extend the DICE model into the DICAE model. As shown in
Figure 1, carbon emissions in the climate module connect with NO
X emissions in the air pollution module, which has already been realized through Equation (7). And environmental damages and reduction costs of air pollutants would influence the final output in the economic module through the following Equations (13)–(18).
In the original economic module, the production function is based on a Cobb-Douglas function which is fixed-scale returns, and then we introduce a climate-feedback coefficient to form an expression of the aggregate output:
where
is the total economic output at time
;
,
and
represent the total factor productivity, capital stock and labors (population) at time
;
represents the capital elasticity;
is the climate-feedback coefficient which is calculated by environmental damages
and mitigation costs
of CO
2, and its specific expression is:
After introducing the air pollution module, we update the above equations:
By adding NOX reduction costs , Equation (16) adjusts the climate-feedback coefficient into a climate & environment-feedback coefficient . Then this paper reflects the health damages of NOX on the population and productivity. Concretely, the mortality rate would affect the effective labors , while the incidence rate could reduce the actual productivity .
Consequently, the two-way feedback between the air pollution module and the original DICE model is realized in the DICAE model. The DICAE model totally includes 45 parameters and 29 variables, since the number of equations is greater than the number of variables, the optimal solution for each variable can be obtained. We solve this NLP problem using the GAMS software [
34].