Quantifying factory-scale CO₂/CH₄ emission based on mobile measurements and EMISSION-PARTITION model: cases in China

The vehicle-based GHG emission monitoring system (VGMS) contains four parts: an electric bus, in situ sensor (PICARRO G2201-i), meteorological instrument, and global positioning system (GPS) (see figure 1(a)). PICARRO G2201-i could sample CO₂ and CH₄ simultaneously. For CO₂, the accuracy of samples is ±0.2 parts per million (ppm). For CH₄, the accuracy of samples is ±5.0 parts per billion. The meteorological instrument collects ambient temperature, ambient pressure, ambient relative humidity, wind speed, and wind direction. A GPS records the location of sample points during the measured track.

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VGMS has collected the GHG distribution in three field campaigns, including the cities in Inner Mongolia (A), Hebei (B), and Liaoning (C) in China, see figure 2. These three cities have different industries and factories. The amount of coal mined in A could reach 6.5 billion tons per year, and crude steel production in B was more than 1.30 billion tons in 2021. The main purpose of the field experiments is quantifying CO₂ emissions from industrial parks and methane leakage from some energy conversion units. Therefore, sample tracks of VGMS contain the GCD industry peak and LG factories, ZN steel factory, ZN Chemical Plant, and XC waste incineration plant.

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From August 2021 to December 2021, four monitoring experiments were conducted by our group, as shown in table 2. It worth noting that the Picarro analyzer was calibrated by the standard concentration of GHGs in each track, see S3. In addition, the anomalous values caused by vehicle emissions around the sampling vehicle were removed during the measurements.

The diffusion of gases emitted from strong emission sources could be modeled by a multi-sources Gaussian dispersion model (formula (1)):

$$\begin{align}C & = \sum\limits_{i = 1}^n \frac{{{{\text{Q}}_i}}}{{2\pi u{\sigma _{i,y}}{\sigma _{i,z}}}}\,\exp\, \left(\frac{{ - {{({y_i})}^2}}}{{\sigma _{i,y}^2}}\right) \left\{ \,\exp\, \left(\frac{{ - {{(z - {H_i})}^2}}}{{\sigma _{i,z}^2}}\right)\right. \nonumber\\ &\quad \left. + \,\exp\, \left(\frac{{ - {{(z + {H_i})}^2}}}{{\sigma _{i,z}^2}}\right)\right\} + B \end{align} \tag{ 1 }$$

$$\begin{align}{\sigma _{i,y}} = a \cdot {({x_i})^b}\end{align} \tag{ 2 }$$

$$\begin{align}{\sigma _{i,z}} = c \cdot {({x_i})^d}.\end{align} \tag{ 3 }$$

The coordinate system of the field campaign is set according to the location of emission source and wind direction (figure 1(b)). The location of each emission source is set as the coordinate origin (O) in its corresponding coordinate system, wind direction is set as the X axis, Y is perpendicular to the X axis, and Z is perpendicular to XOY. C(m) is GHG concentration of the m_th samples, Q_i is GHG emission intensity of the i_th point source, for i = 1,2,3 ...n, n is total number of strong point sources; u is the wind speed, H_i is the effective GHG emission height of the i_th point source, ${\sigma _{i,y}}$ and ${\sigma _{i,z}}$ are the horizontal and vertical diffusion parameters that refer to the i_th point source, respectively, B is the background concentration of GHG in the measured area, a, b is the horizontal diffusion coefficient, and c, d is the vertical diffusion coefficient.

To solve for the unknown parameters in formulas (1)–(3), including Q_i, H_i, a, b, c, d, and B, EMISSION-PARTITION, see figure 3, whose kernel is particle swarm optimization (PSO) coupled with interior point penalty function (IPPF). First, the potential range of unknown parameters are defined according to PSO model, and the fitness value of PSO was set as formula (4), see S1 in supplementary:

$$\begin{equation}F = {\left( {\frac{{\sum\limits_{k = 1}^m \left(C_{}^{^{\prime}}(k) - {C_{}}(k)\right)}}{{{C_{}}(k)}}} \right)^2}.\end{equation} \tag{ 4 }$$

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C(k) is the actual measured samples, C'(k) is the simulated concentration, m is the total number of the selected concentration samples used to retrieve emission rate. This step is repeated 100 000 times to acquire the Parameters domain of each unknown parameter. Then, the solution of unknown parameters is further determined by IPPF function, and the penalty function of IPPF in this step also refers to formula (4). Results of unknown parameters could be retrieved when F achieved the minimum value.

2.3.1. Uncertainty analysis

Formula (5) was used to determine the uncertainty of quantified emission rate through relevant variables in actual experiments:

$$\begin{equation}{\varepsilon _t} = \sqrt {\varepsilon _n^2{\text{ + }}\varepsilon _m^2{\text{ + }}\varepsilon _w^2 + \varepsilon _d^2}\, .\end{equation} \tag{ 5 }$$

_t is defined uncertainty of retrieved emission rate, and _n, _m, _w , and _d represent the uncertainty caused by number of samples, accuracy of samples, wind speed, and wind direction, respectively. It is noted that the uncertainty of each item was referring to the corresponding value in sensitivity analysis, see section 3.2. Uncertainties of wind speed and direction are defined by standard deviation of 2 min collections of wind speed and direction around the emission source. Uncertainty of sample accuracy is referenced by the calibrated experiment of PICARRO by standard gases, which is about 0.1%. We presented the detailed processes in calculating _t in S2.

In this section, we take CO₂ emission source quantification as an example. First, we set up different numbers of emission sources, including 1, 2, and 3. Then, we generated simulated values of CO₂ concentration downwind according to formula (1) based on the parameters (true values) shown in table 1; the spatial resolution was 2 m. Then, 150 simulated points were randomly selected, and a relative error of 1.5% was added for the hypothetical measurement points. In order to make OSSE close to the real measurement scene, we set the uncertainty of wind speed as ±0.5 m s⁻¹ and the uncertainty of wind direction as ±50°. It is worth noting that the uncertainty was far larger than that of actual meteorological instruments. The lower and upper boundary of each parameter was set as shown in table 1. Then, the unknown parameters were calculated by EMISSION-PARTITION and repeated 10 000 times. Finally, the mean value of the retrieved Q was treated as the final retrieved value (see table 2).

The conventional diffusion parameters (a, b, c, and d) are empirically determined based on atmospheric stability. There is a large uncertainty due to the topographic characteristics of the studied area, solar radiation energy, different types of emission sources, etc.

As shown in table 1, the values of a, b, c, and d are nearly the same as the settings, and the maximum of standard deviation is only 0.01, indicating that EMISSION-PARTITION can calculate diffusion parameters without prior information. In addition, the retrieved H was also accurate, with only a 0.7 m bias to 15.0 m, which helps to reconstruct CO₂ diffusion from emission sources. It is worth noting that the accuracy of the solution of the emission sources will decrease with the increase in number of emission sources, because more emission sources will bring additional parameters in the solutions by EMISSION-PARTITION. As shown in table 1, even in the case of three emission sources, the accuracy of retrieved emission rates was still better than 2.7%, with a standard deviation of less than 4%. In summary, the EMISSION-PARTITION has a self-adjusting function to reach the optimal solutions in unknown parameters and reduce the uncertainties in final retrievals.

In the actual field campaign, the concentrations of samples of gases and meteorological factors would be influenced by the performance of the equipped instruments in the vehicle-based monitoring system. In this section, we evaluate the stability of the EMISSION-FUN model with different measured parameters, and we analyzed the uncertainties of different wind speeds, wind directions, and sampling accuracy, and the influence of different sampling quantities on the final emission assessment. Here, we take a single point source as an example and use the control variables method for sensitivity analysis of the analyzed parameters. The average of 10 000 repetitions was used as the inverse result, and the standard deviation was calculated based on the results of 10 000 repetitions.

As shown in figure 4(a), we analyzed the effect of different errors in wind speed on final retrieved emission rate, and the uncertainty of the retrieved Q increases with the wind speed error. However, it is worth noting that even when uncertainty in wind speed is 1.6 m s⁻¹, with a 53% bias to 3.0 m s⁻¹, the retrieved Q has 2.5 kg s⁻¹ bias to the actual value, and the standard deviation is only 3.1 kg s⁻¹. EMISSION-PARTITION is not sensitive to the additional errors in wind directions (figure 4(b)); the retrieved emission rates are in the range of 59.8–60.74 kg s⁻¹, and the standard deviations of emission rates are less than 0.34 kg s⁻¹. The number of samples and the sampling accuracy determine limiting equations and accuracy of the basis of judgment in the EMISSION-PARTITION solution process. As shown in figure 3(c), the standard deviation of Q increases with the additional errors in samples, but even with a sampling error of 6%, the standard deviation of Q is only 2.1 kg s⁻¹. The number of samples has the largest impact on the final emission inversion (figure 4(d)). For example, the standard deviation can reach 15.2 kg s⁻¹ when the number of samples is 20, but it would be less than 0.7 kg s⁻¹ if the number of samples was more than 120. In general, EMISSION-PARTITION can improve the accuracy of the emission intensity by adjusting the input parameters dynamically according to the PSO algorithm and achieving the global optimal solution according to the IPPF.

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As shown in figure 5, the CO₂ concentrations collected by our monitoring system have a large variation range in all field campaigns, for example, 425–520 ppm in B. CO₂ concentration are higher in urban areas (figures 5(b)–(d)) because of multiple irregularities in urban emission sources in cities and sampling time is winter. Both B and C countries have large amounts of heating equipment, and the enhanced CO₂ values from these emission sources have been acquired by the monitoring system. Samples on roads show the lowest values, which are smaller than those in the industrial park, due to strong emission sources in the industrial park. Overall, the vehicle-based monitor can obtain CO₂ distribution characteristics under different land use types.

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3.3.1. CH₄ distribution

Because CH₄ was not sampled in the B field campaign, only A and two tracks in C were analyzed in this section. In figure 6, similar to CO₂, CH₄ concentration is also higher in urban areas, for example, it could be up to 2.61 ppm in the main city of C. This is due to methane production from gas leaks or garbage fermentation in residential areas. It is noteworthy that samples around factories in C do not show strong CH₄ enhancement values, which may be caused by their energy consumption; most factories use solid fossil fuels to serve as energy for production. The vehicle-based monitoring system only detected enhanced CH₄ concentration in the industrial park of A, ZN Chemical Plan.

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Based on the field campaign presented in figures 4 and 5, the quantitative assessment in different numbers of emission sources was performed based on EMISSION-PARTITION, which contains chemical plants, waste incineration plants, and coal washing plants.

3.4.1. Single CO₂ emission source

In section 3.2 it is shown that more samples will lead to higher accuracy and stability in quantifying emission rate, and this has also been validated in actual cases. Two hundred and five samples were collected for the ZN Chemical Plant, while only 25 samples were measured around the XF waste incineration plant. In figures 7(c) and (f), we can also see that the CO₂ point source diffusion reconstruction for the ZN Chemical Plant is much better than that for the XF Waste Incineration Plant. The R2 in figure 7(c) is higher than the R2 in figure 7(f), and the RMSE is only 0.03 mg m⁻³ in figure 7(c) and 11.7 mg m⁻³ in figure 7(f). This indicates that a high sampling rate will help to reduce the uncertainty of emission assessment.

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3.4.2. Multi-point CO₂ emission sources

The two CO₂ emission sources in the MX coal washing plant are mainly the two coal crusher machines. In this case, the amount of samples is 125 for quantifying CO₂ emission rate. The R² is 0.92 and RMSE is 10.4 mg m⁻³, which show less consistency than that shown in figure 7(c). The additional emission source and fewer samples would reduce useful residual observation restrictions.

Figure 8(d) represents triple CO₂ emission sources in the ZN Chemical plant, and the number of selected samples for quantification is 300. As shown in figure 8(e), the values of samples are much larger than those in previous cases. The distance between the emission source and vehicle monitoring system is extremely small, and the minimum value is only 26 m. In figure 8(f), although R² is 0.89, RMSE is 46.3 mg m⁻³. Firstly, the number of unknown parameters in this case is the greatest; a smaller distance between samples and emission sources would lead to unstable diffusion of CO₂. This case indicates that a closer proximity of samples around the emission source is not always beneficial for emission quantification.

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3.4.3. Single CH₄ emission source

Two CH₄ enhancements due to strong emission sources were observed during the A cruise, both of them in the ZN chemical plant. The main operation of this plant is gas coal liquefaction, which may cause leakage during the liquefying process. As is shown in figure 9, the vehicle-based monitoring system has the ability to capture the enhanced methane concentration adequately, with more than 200 samples of enhancement for each source. The R² between results calculated by EMISSION-PARTITION and the actual samples is greater than 0.96, and RMSEs are not larger than 0.04 mg m⁻³. This demonstrates that for a single methane source, a good inverse response can be obtained with sufficient sampling. It is proven that for a single methane source, the EMISSION-PARTITION can rebuild the dispersion of methane with reliable performance.

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3.4.4. Summary of the emission rate

We quantified the emission rate from single point sources with similar methods, including the other test method (OTM) 33 A model proposed by the US EPA and IPPF model developed by Shi et al 2022, Brantley et al 2014b, Shi et al 2021).

4.1.1. OTM33A

The main principle of OTM33A is getting the peak GHG concentration among the samples based on the Gaussian fitting, and then the emission rate is calculated by an integral with two dimensions (formula (6)). The diffusion parameters σ_y and σ_z are regarded as certain values by the distance from the source and different atmospheric stabilities, which are determined by CH₄ control-release experiments by the EPA:

$$\begin{align}G(y,z) & = a1 \times {\mathop \iint \nolimits }\exp - \left( {\frac{{{{(y)}^2}}}{{2{\sigma _y}^2}} + \frac{{{{(z)}^2}}}{{2{\sigma _z}^2}}} \right)\nonumber\\& = 2\pi \times a1 \times {\sigma _y} \times {\sigma _z}\end{align} \tag{ 6 }$$

y is crosswind distance (m), z is vertical distance (m), a1 is peak average methane concentration (g m⁻³) as determined by Gaussian fit, σ_y is standard deviation of the crosswind plume concentration (m), and σ_z is standard deviation of the vertical plume concentration (m).

4.1.2. IPPF

Based on the network of gas sensors and Gaussian dispersion model, the IPPF model could also be used to obtain the emission rate and diffusion parameters using a single strong point source (see formula (5)). However, the values of a, b, c, and d are restricted according to the Pasquill method and GB3840-83 (China) (Hanna et al 1982, Shi et al 2020).

As is shown in figure 10(a), emission rates of ZN are 4.3 ± 0.4, 3.2 ± 1.2, and 7.1 ± 2.4 kg s⁻¹ calculated by EMISSION-PARTITION, IPPF, and OTM33A, respectively. The emission rate of XC calculated by EMISSION-PARTITION, 22.3 ± 6.4 kg s⁻¹, is lower than that calculated by the other two methods. It is worth nothing that OTM33A would always overestimate the emission rate in two cases, because the values of σ_y and σ_z in OTM33A are defined by EPA experiments of CH₄ diffusion and are larger than those of CO₂. Comparing the quantified emission rates of CH₄, the mean difference of the two cases is about 0.5 g s⁻¹. Notably, EMISSION-PARTITION has the significant benefit of the lowest uncertainty among the three methods.

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The increasing greenhouse effect will cause various ecological problems and threaten human environments (Liu et al 2022). Energy saving and emission reduction are important measures to mitigate this hazard. As a first step, we need to precisely assess current GHG emissions from different sectors, which are not reliable and quantifiable because of the imperfect construction of various GHG emission inventories in developing countries (Su et al 2017). This is detrimental to the formulation of environmental policies and improvement in global climate change (Luo et al 2022). This study presented a movable vehicle-based monitoring system and EMISSION-PARTITION model, which can quickly assess the emission intensity of strong sources based on the concentration data collected in real time. This program has high flexibility to realize the monitoring function, provide data support for governments, promote the improvement of timeliness and accuracy of self-announced emissions in developing and developed countries, establish penalty mechanisms, and finally, urge enterprises and factories to complete the conversion from reliance on oil and fossil fuels to clean energy (Xiao et al 2021). In the future, our developed vehicle-based monitoring system could include in situ sensors for pollutant gases, such as NO₂, CO, and SO₂, to simultaneously evaluate the emission rate of pollutant gas and GHG and assess energy use efficiency.