Nitrogen Oxide Emissions as a Proxy for Simplifying Large-Scale Emission Inventories and Tracking Decarbonization

Abstract

Decarbonizing energy production is critical to slowing the effects of climate change and furthering global sustainability. Progress is often gauged via carbon dioxide (CO₂) emissions; however, sources of CO₂ vary beyond combustion, presenting a significant challenge to accurate tracking due to these various sources and sinks and the ubiquitous nature of CO₂ in the atmosphere. Nitrogen oxide (NO_X) emissions have previously been proposed as a surrogate for tracking sustainability, as they are primarily released from combustion processes. Facility-level data from Canada’s National Pollutant Release Inventory and Greenhouse Gas Reporting Program over a six-year period is used to assess the correlation between NO_X and CO₂ emissions from integrated facilities across Canada. Combustion-related CO₂ emissions accounting for approximately 94% of Canadian industrial emissions are examined, targeting eleven industries which together encompass over 90% of combustion emissions. Multiple linear regressions (MLRs) on each industry correlating NO_X, CO₂, and the inventory methods used (i.e., emission factors (EFs), source monitoring, mass balance, engineering estimates, and speciation) show R² values ranging from 0.81 to 0.96 for all but one industry. Several industries indicate that the methods used to calculate emissions influence the correlation of CO₂ to NO_X, highlighting issues in the current inventory techniques. The NO_X-to-CO₂ ratios calculated for the integrated facilities are similar to the ratios of the published main process-level EFs for NO_X to CO₂ (where available). These MLR models on NO_X could be used to predict CO₂ emissions with relative ease and accuracy in other jurisdictions, thereby simplifying large-scale emission inventory compilation while tracking sustainability.

1. Introduction

Carbon dioxide (CO₂) is the predominant greenhouse gas causing climate change. While there are a wide variety of anthropogenic CO₂ emission sources, combustion of fossil fuels dominates the issue [1]. CO₂ is also subject to atmospheric flux, due to various carbon sinks, such as plant respiration, oceans, and wetlands [2]. Such variability makes tracking CO₂ to gauge the effectiveness of sustainability efforts a complex issue. Several United Nations Sustainable Development Goals (UN SDGs) relate to sustainability with regard to CO₂ emissions [3], with many complex indicators used to track humanity’s progress represented in terms of three pillars: environmental, social, and economic. The combustion of fossil fuels has been linked not only to the environmental pillar of sustainability but to the social and economic pillars as well [4]. While the primary global concern regarding fossil fuel combustion is its production of greenhouse gases (GHGs) causing climate change, it is important to note that many pollutants which are harmful to human health and the environment are produced via combustion, with countries and individuals of lower economic status often being exposed to higher levels of these pollutants [4].

1.1. NO_X as a Proposed Indicator for Sustainability

Nitrogen oxides (NO_X) are a biproduct of combustion, formed primarily in three ways: thermal NO_X, prompt NO_X, and fuel NO_X [5]. Thermal NO_X is produced when high temperatures force the combination of oxygen and nitrogen in air [5]. Prompt NO_X is produced when nitrogen in the air combines with fuel, where fuel NO_X is produced by fuels which contain nitrogen [5]. Unlike CO₂, NO_X is not subject to atmospheric flux and is produced almost exclusively via combustion [4,6]. As such, it has previously been proposed to track sustainability from the perspective of burning fossil fuels [4] for its potential to predict CO₂ emissions [7]. While NO_X is a pollutant of concern by itself, as it is a precursor to ground-level ozone and hence smog, its presence as a product of combustion can be used to more easily track fossil fuel-related CO₂ production.

Decarbonization refers to eliminating carbon emissions to the amount which can be stored by nature [8]. This will primarily involve the cessation of fossil fuel combustion as a source of energy [8]. There are many ways to track CO₂ emissions, but they are often skewed by biogenic CO₂ sources [4]. Previously, NO_X has been used as a sustainability indicator from the human health, decarbonization, and air pollution standpoints, as it connects to all three United Nations pillars of sustainability [4]. The authors found that NO_X is produced consistently alongside global GHGs and acts as a reliable tracking method [4]. They also found that the manner in which CO₂ data is collected can heavily influence the data itself [4], rendering the reliability of CO₂ tracking to date questionable.

Only one other prior study could be found which uses NO_X directly as a surrogate for CO₂ measurement [7]. Yang et al. used a top-down approach to predict CO₂ emissions, generating relationships between NO_X and CO₂ to predict urban CO₂ emissions [7]. This study tested three different cities in hot climates around the world using satellite observations, finding that the use of NO_X as a predictor reduced grid-cell-level uncertainties [7]. They make the argument for using empirical relationships between CO₂ and NO_X to calculate CO₂ rather than prior established ratios [7]. It should be noted that they found unreliable relationships during stagnation events [7], pointing to a common issue with top-down emission inventorying. Their work points to the possibility of using reliable ratios of NO_X to CO₂ to calculate CO₂ emissions, as they were able to accurately predict CO₂ emissions from one hour in the future using their developed ratios [7]. The question remains as to whether the strategy is also usable to replace bottom-up methods, which are commonly used for facility-scale inventories. Other issues arise from the use of proxy variables to disaggregate top-down inventories, and the accuracy is thus directly dependent on the availability of data such as population density and land use [9]. Top-down inventory methods can also lead to emission leakage, as the measurement accuracy is subject to atmospheric variables such as wind.

1.2. Use of National Pollutant Release Inventory Data in Sustainability

National Pollutant Release Inventory (NPRI) data has previously been proposed as an under-utilized resource for tracking sustainability, specifically for United Nations Sustainable Development Goal (UN SDG) 12: Responsible Consumption and Production [10]. This particular UN SDG is heavily linked to the combustion of fossil fuels, as their consumption and eventual combustion is not only unsustainable from a resource standpoint but also regarding the emissions they produce. NPRI data offers the opportunity to track facility-level reported emissions of pollutants rather than rates, commitments, and intensities of participating UN countries [10]. The NPRI is Canada’s constituent in a global network of pollutant release registries, with over 50 participating countries [10]. In Canada, NPRI data is under-utilized in research, with approximately 10 research articles published annually using the data, despite being openly available and containing a wide range of variables [11]. The availability of similar data in other countries makes NPRI data an appealing option for tracking sustainability measures, since any validated methods could be adopted in other jurisdictions, assuming similarity in industrial sources.

1.3. Difficulties in Emission Inventories

On a national level, CO₂ and NO_X are inventoried by different offices in Canada: the NPRI and the GHGRP. In Canada, 55.8% of GHG emissions are attributed to sectors which report to these programs: heavy industries, oil and gas, waste, and electricity [12]. Data from these programs shows that a single facility may use different techniques for each pollutant [13,14], which unnecessarily convolutes the process for facilities, when in fact the emissions of most air pollutants (particularly those emanating from combustion) are correlated and thus could be inventoried together using the same method. NO_X inventory methods are more established, with data available online dating back to 1993 [15], whereas the GHGRP only dates back to 2004 [16]. The number of reporting facilities with respect to each pollutant are also very different, as shown in Table 1. Canadian GHG emissions were reduced by 8.5% from 2005 to 2023 [12]. This result is promising, although longer-term trends show an increase of 14.4% from 1990 to 2023 [12]. While this in and of itself is a major issue reflecting the intensity of lifestyle-related emissions from countries with developed economies [4], another issue that these figures highlight is the time it took to produce them. Many published GHG values from the Government of Canada are from several years prior. The availability of timely published data is a major issue highlighting the need for fast, reliable GHG assessments.

Many emission inventory techniques exist, and the choice of which to use is often dominated by data availability, funds, and time. Monitoring and direct measurement is largely considered the most reliable for facility-level inventories, with uncertainties in larger-scale inventories often being dominated by point sources [17]. The United States Environmental Protection Agency (US EPA)’s AP-42 compilation of EFs does not have very many EFs for CO₂, adding another level of difficulty to a bottom-up inventory approach. The most cost-effective method is often the use of activity-level data and EF correlations, a technique with higher uncertainty compared to techniques such as continuous emission monitoring [17]. A strategy which combines the cost-effectiveness and convenience of EFs with the accuracy of continuous emission monitoring could not only fast-track emission publications but also improve accuracy.

1.4. Emission Reporting Variation from Inventory Method

Compiling emission inventories is time-consuming and expensive, resulting in cities and organizations across the world constantly proposing new methods in an attempt to simplify the process [18]. Many city-scale inventories propose new methods rather than follow existing ones, as the lack of consistent data across all regions and industries makes it difficult for every organization to follow the same framework [18]. That being said, a dataset can be heavily influenced by the method used to collect the data [4], indicating an accuracy issue when different methods are used for inventorying emissions.

Traditionally, top-down inventory methods are considered less accurate than bottom-up inventory methods, due to the increased reliance on surrogates and assumptions necessary to complete the inventory that lack site-specific process information [19]. The type of calculations used in the emission inventory preparation affects the accuracy of the inventory, as the calculations are contingent on the implied assumptions as well as the type and quality of data available [19]. Different published emission inventories can provide underestimated and overestimated emissions depending simply on the inventory methods used [20]. Despite the fact that urban spaces account for 70% of emissions [21], urban GHG emissions are often underestimated due to lack of accounting for all sources [22], as well as at a larger scale due to differences in estimation methods [23]. This issue is consistent across sectors and emission sources, as emissions from wildfires, airplanes, and all urban sources vary by dataset and the inventory method used [19,22,23,24].

Table 1. Main data sources. Raw data available in Supplementary Materials.

Data	Details	Reporting Threshold	Year Implemented	Reporting Facilities (Pollutant-Specific)
GHGRP [16,25]	Tonnage of CO2, inventory method used, combustion sources for each facility	10,000 tonnes carbon dioxide equivalent (CO2e) [14]	2017 [14]	1862
NPRI [15,26]	Tonnage of NOX, inventory method for NOX	20 tonnes NOX 10 tonnes NOX Stack release [13]	2022 [13]	22,733

Table 1. Main data sources. Raw data available in Supplementary Materials.

Data	Details	Reporting Threshold	Year Implemented	Reporting Facilities (Pollutant-Specific)
GHGRP [16,25]	Tonnage of CO2, inventory method used, combustion sources for each facility	10,000 tonnes carbon dioxide equivalent (CO2e) [14]	2017 [14]	1862
NPRI [15,26]	Tonnage of NOX, inventory method for NOX	20 tonnes NOX 10 tonnes NOX Stack release [13]	2022 [13]	22,733

1.5. United Nations Sustainable Development Goals and Global Trends

The UN SDGs provide an all-encompassing view of global sustainability [3]. While the UN SDGs are useful in uniting the globe towards common objectives with concrete milestones, they have been criticized for their sheer complexity, with all 17 goals having numerous indicators to assess progress [4]. NPRI data has previously been used to track these indicators [11], and any opportunity to reduce the complexity of tracking sustainability with respect to these widely accepted UN SDGs should be explored. This coupled with the uncertainty often present in large-scale GHG inventories attributed to point sources presents a clear opportunity.

1.6. Purpose

The purpose of this study is to facilitate country-wide CO₂ predictions and reduce the time, energy, and money put into tracking industrial sustainability. The goal is to develop and prove a high-level proxy for CO₂ production from industrial sources. NO_X is assessed as a surrogate for tracking sustainability specifically with respect to calculating nation-wide industrial emissions disaggregating solely by sector. This study develops high-level relationships with as few variables as possible while maintaining a high R² value in the correlations. The intent is to find a way to determine, based on NO_X emissions, whether Canada is moving towards carbon neutrality. With the scale of required reductions being so large, rapid tracking with a general estimate can be beneficial from a monetary and time perspective.

2. Materials and Methods

Industrial emissions in Canada are inventoried using a combination of EFs, mass balance, engineering estimates, monitoring, and speciation. CO₂ and NO_X emissions are reported to two separate programs: the GHGRP and the NPRI, respectively. The data sources and reporting thresholds for NO_X and CO₂ emissions are provided in Table 1. Both datasets specify quantity of emissions, inventory methods used, and industrial sector. NPRI data specifies one inventory method (from EFs, mass balance, engineering estimates, monitoring, and speciation), while GHGRP data often specifies multiple inventory methods, excluding speciation. Records from the GHGRP were matched to NPRI data by NPRI identification number and year in Microsoft Excel, creating a dataset including the quantity of emissions from each facility in each year, inventory methods, and sector. Next, all combustion-related industrial sectors were disaggregated into separate datasets.

Figure 1 shows which combinations of methods were the most common for all facilities analyzed in this study. The most common combination is a hybrid method for CO₂, where some combination of the other methods was employed, and EFs for NO_X. Approximately 20% of facilities used exclusively EFs for both pollutants, leaving the vast majority with a variety of methods whose pollutants’ correlations cannot be explained solely by the common use of EFs. A hybrid approach indicates using any combination of monitoring and direct measurement, mass balance, engineering estimates, and emission factors to calculate CO₂. There is a lack of CO₂ EFs from the US EPA’s AP-42, while Canada’s CO₂ EFs are fuel-based, essentially enabling a mass-balance approach based on complete combustion. The correlation being investigated is thus not based on the use of EFs for both pollutants, as EFs are only available for NO_X for most pollutants.

For this study, data was analyzed from 2018 to 2023 from both programs, and the locations of the facilities are shown in Figure 2 [27]. This figure shows an intensity of facilities in Alberta, which are dominated by the oil and gas industry.

From 2022 onward, the GHGRP has provided emissions for each facility broken down by source, including flaring, venting, stationary fuel combustion, industrial activities, on-site transportation, and waste disposal [25]. The fraction of CO₂ emissions accounting for the sum of flaring, stationary fuel combustion, and industrial activities was calculated for each facility (these activities were assumed to be combustion). These fractions were then used to estimate combustion CO₂ emissions for each facility from previous years. These values were used going forward as combustion-related total CO₂ emissions for correlation to NO_X.

The total combustion CO₂ emissions for each industrial sector were calculated, and the sectors were ranked. Sectors accounting for a total of 90% of CO₂ combustion emissions were analyzed, with these facilities shown in Figure 2. The selected industries and their respective combustion emission totals are shown in

Table 2. Industries comprising 90% of combustion-related CO₂ emissions and their respective tonnages of CO₂ alongside the data quantities for each sector. Each report from every facility in each year was treated as an independent observation, with the number of data points representing the total reports for the sector over the entire study period.

Industry	Sum of CO2 from Combustion (tonnes)	Number of Facilities	Number of Data Points
Fossil fuel electric power generation	352,990,000	107	488
In situ oil sand extraction	197,010,000	28	145
Oil and gas extraction (except oil sands)	128,210,000	713	2364
Mined oil sand extraction	94,940,000	5	30
Iron and steel mills and ferro-alloy manufacturing	89,180,000	22	90
Cement manufacturing	56,750,000	14	74
Petroleum refineries	39,770,000	12	59
Petrochemical manufacturing	35,060,000	11	46
Chemical fertilizer (except potash) manufacturing	34,740,000	9	54
Primary production of alumina and aluminum	34,670,000	12	64
Chemical pulp mills	15,520,000	36	142

, summarizing all available reports for all facilities from 2018 to 2023.

NO_X and CO₂ for each of the selected sectors are plotted in Figure 3 and Figure 4, along with a simple linear regression with a forced intercept through the origin (i.e., if there is no combustion, then neither CO₂ or NO_x are produced). In most cases, a reasonable R² value is obtained. These R² values generated automatically for the trendlines in Excel are used strictly for initial diagnostic purposes to assess the relative usefulness of linearly correlating NO_X and CO₂. The hypothesis of this initial comparison is that for all industries, as NO_X increases, so too does CO₂.

Each industrial sector was then subject to a multiple linear regression (MLR) to find a linear relationship between CO₂ and NO_X, treating CO₂ as the dependent variable and NO_X, the CO₂ inventory method, and the NO_X inventory method as independent variables. All data for each sector from all facilities and years were correlated. Microsoft Excel’s Data Analysis Tools’ Regression was used, with the regression constant (intercept) set to zero. Since NPRI data specifies only one inventory method, n − 1 binary dummy variables were created for the NO_X inventory method, with n denoting the number of different inventory methods for the sector being analyzed. For CO₂, each of the four inventory methods was given its own binary variable, since often multiple inventory methods were used. Binary variables were created by adding a data column that was equal to 1 if a certain condition was met: the inventory method column was equal to the method specified for that binary variable. Four regressions were run for each sector: one simple regression with CO₂ as the dependent variable and NO_X as the independent variable, one including each of the inventory methods as independent variables (with the appropriate number of binary variables depending on the industry), and one including both inventory methods as independent variables. The data points were treated independently and not categorized by year, assuming the processes did not change aside from the activity level year to year. Prior to running the models, any data points without a specified inventory method for either pollutant were removed. Outputs from the regressions included Analysis of Variance (ANOVA) tables and regression statistics, including R² values and p-values, which can be used to determine which independent variables are considered significant.

3. Results

While many of the linear regressions in Figure 3 and Figure 4 show promising R² values, multiple linear regressions increase the accuracy of the models in all the selected industries. For most industries, the method has about 10% contribution to the variance if using NO_X to produce CO₂. In some industries, such as the primary production of alumina and aluminum, the prediction is hugely dependent on the inventory method, perhaps pointing to an issue with the methods used to predict emissions with respect to one or both pollutants. Even including the inventory method, approximately 10% of the variance remains unaccounted for by the regression. The best models were for petrochemical manufacturing, mined oil sand extraction, petroleum refineries, and chemical fertilizer, all achieving R² values higher than 0.9. In each of these sectors, the best model was achieved using both pollutants’ inventory methods in the regression, highlighting the influence of the inventory technique statistically. In practice however, the coefficients for the inventory methods only accounted for up to 4% of overall emissions, so while they may have been statistically significant, they were not critical to an accurate estimate. The R² values for all regressions run for each industry are shown in

Table 3. R² values for all regressions run to predict CO₂ emissions using NO_X emissions and CO₂ and NO_X inventory methods. Inventory methods for both pollutants include mass balance, emission factors, monitoring and direct measurement, and engineering estimates.

Industry	Explanatory Variables	R2
Fossil fuel electric power generation	NOX emissions	0.85
	NOX emissions and NOX inventory method	0.86
	NOX emissions, NOX inventory method, and CO2 inventory method	0.87
	NOX emissions and CO2 inventory method	0.86
In situ oil sand extraction	NOX emissions	0.79
	NOX emissions and NOX inventory method	0.84
	NOX emissions, NOX inventory method, and CO2 inventory method	0.88
	NOX emissions and CO2 inventory method	0.88
Oil and gas extraction (except oil sands)	NOX emissions	0.30
	NOX emissions and NOX inventory method	0.39
	NOX emissions, NOX inventory method, and CO2 inventory method	0.40
	NOX emissions and CO2 inventory method	0.38
Mined oil sand extraction	NOX emissions	0.83
	NOX emissions and NOX inventory method	0.91
	NOX emissions, NOX inventory method, and CO2 inventory method	0.96
	NOX emissions and CO2 inventory method	0.96
Iron and steel mills and ferro-alloy manufacturing	NOX emissions	0.79
	NOX emissions and NOX inventory method	0.84
	NOX emissions, NOX inventory method, and CO2 inventory method	0.87
	NOX emissions and CO2 inventory method	0.84
Cement manufacturing	NOX emissions	0.81
	NOX emissions and NOX inventory method	0.82
	NOX emissions, NOX inventory method, and CO2 inventory method	0.84
	NOX emissions and CO2 inventory method	0.84
Petroleum refineries	NOX emissions	0.84
	NOX emissions and NOX inventory method	0.89
	NOX emissions, NOX inventory method, and CO2 inventory method	0.92
	NOX emissions and CO2 inventory method	0.89
Petrochemical manufacturing	NOX emissions	0.91
	NOX emissions and NOX inventory method	0.94
	NOX emissions, NOX inventory method, and CO2 inventory method	0.97
	NOX emissions and CO2 inventory method	0.94
Chemical fertilizer (except potash) manufacturing	NOX emissions	0.87
	NOX emissions and NOX inventory method	0.91
	NOX emissions, NOX inventory method, and CO2 inventory method	0.93
	NOX emissions and CO2 inventory method	0.92
Primary production of alumina and aluminum	NOX emissions	0.45
	NOX emissions and NOX inventory method	0.80
	NOX emissions, NOX inventory method, and CO2 inventory method	0.82
	NOX emissions and CO2 inventory method	0.76
Chemical pulp mills	NOX emissions	0.80
	NOX emissions and NOX inventory method	0.82
	NOX emissions, NOX inventory method, and CO2 inventory method	0.83
	NOX emissions and CO2 inventory method	0.82

.

The models for each industry using only NO_X as an explanatory variable are shown in

Table 4. Model equations for each industry using only NO_X alongside R² values and percentage changes of model-calculated CO₂ from reported CO₂.

Sector	NOX (tonnes)	Equation	R2	Calculated CO2	% Difference from Reported CO2
Fossil fuel electric power generation	504,560	CO2 = 488 NOX	0.85	246,330,000	22
In situ oil sand extraction	122,860	CO2 = 1134 NOX	0.79	139,300,000	28
Oil and gas extraction (except oil sands)	490,180	CO2 = 149 NOX	0.30	72,820,000	43
Mined oil sand extraction	97,960	CO2 = 692 NOX	0.83	67,820,000	29
Iron and steel mills and ferro-alloy manufacturing	60,260	CO2 = 1574 NOX	0.79	94,840,000	−6.3
Cement manufacturing	128,320	CO2 = 392 NOX	0.81	50,280,000	8.5
Petroleum refineries	57,260	CO2 = 536 NOX	0.84	30,680,000	23
Petrochemical manufacturing	35,600	CO2 = 1051 NOX	0.91	37,420,000	−6.7
Chemical fertilizer (except potash) manufacturing	46,840	CO2 = 610 NOX	0.87	28,600,000	18
Primary production of alumina and aluminum	6320	CO2 = 2857 NOX	0.45	18,060,000	48
Chemical pulp mills	107,100	CO2 = 133 NOX	0.80	14,220,000	8.4

. Many models with good R² values show reasonable similarity to the reported CO₂ values. Given the prevalence of data similar to that of the NPRI globally [11], these regression models have potential for transferability to other jurisdictions. The percentage differences from the reported CO₂ values shown in Table 4 are mostly positive, indicating an underestimation by the regression models. The percentage differences were calculated from the totals after removing those data points which did not specify the inventory method, since those values were not included in the regression, not from the original sectoral totals.

Case Study: Portland Cement Comparison to US EPA EFs

Comparing the regression coefficients in this study to the ratios of CO₂ to NO_X published EFs from the United States Environmental Protection Agency (US EPA) facilitates validation of the methods presented. The issue, however, is that for most industries evaluated, there are a plethora of US EPA EFs encompassing the variety of processes ongoing in each industry. Without data on which processes are actually used at each facility, the comparison is near impossible, highlighting the complexity of preparing emission inventories. The only industry with enough EFs to compare is that of cement manufacturing, as Portland Cement is a well-established industrial process. The ratio of US EPA CO₂ to NO_X EFs for Portland Cement is 339:1, which is similar to the regression coefficients found for cement manufacturing shown in Table 4. The combined US EPA EFs would actually underestimate the ratio of CO₂ to NO_X compared to this study, which is consistent with other studies’ claims of EFs leading to underestimation of emissions [28]. Figure 5 shows the comparison of US EPA EFs for Portland Cement processes, four out of five of which have smaller ratios than the regression. All of the NO_X EFs have a quality rating of D (below average). For CO₂, two are rated D, while one is rated C (average) and one is rated E (poor). The EF with the worst rating is the only EF whose ratio gives a higher slope than the regression. Thus, these EF representations of the industry may not be the most reliable.

4. Discussion

Of the eleven industrial sectors analyzed, all of them had improved R² values when one or both inventory methods were included as explanatory variables. The improvement was not significant for all sectors, while for some, the methods explained an additional 35% of the variance. For the primary production of alumina and aluminum, the use of EFs for NO_X accounting was the only significant variable according to the p-values of the regression, making it the only sector where tonnes of NO_X were not statistically significant to the model. It would be expected for correlations to exist were the same inventory methods consistently used for both CO₂ and NO_X, as would be the case if EFs were used for both. Most of the time however, EFs are not exclusively used for both pollutants, as shown in Figure 1.

Several sectors had comparable R² values (rounding to two significant digits) for two of the regressions run. In all sectors with two regressions tied for the highest R² value, those regressions used both the CO₂ and NO_X inventory methods and just the CO₂ inventory method. Four sectors show models where the CO₂ inventory method is more significant than the NO_X inventory method, while two show the NO_X inventory method as more significant, and the other five have them tied, with both methods together creating the best model. The significance of the inventory method used, for NO_X and CO₂, thus varies by industrial sector.

All industrial sectors except for the primary production of alumina and aluminum show at least one CO₂ inventory method as a statistically significant (p-value < 0.05) explanatory variable in the best model for that industry. The primary production of alumina and aluminum is the only model where the R² value went from insignificant (under 0.7) to over 0.8 with the addition of inventory methods, and the only statistically significant variable was the use of NO_X as an inventory method. Treating this industry as an outlier, all other industries attribute significant variance to the CO₂ inventory method used. Furthermore, no industrial sector shows using exclusively the NO_X and NO_X inventory method as producing the best model. This provides an argument in favor of using NO_X as a surrogate to track and calculate CO₂. This also indicates that using exclusively NO_X values to calculate CO₂ may indeed be more accurate than calculating CO₂ independently, as it varies with the inventory method much less than it is impacted by the NO_X inventory method.

For all industrial sectors, the inventory method accounted for a variation in CO₂ emission values of less than 2% of the total emissions for that sector. While this variation is significant in some cases in terms of tonnage of emissions, in terms of variance from the total, it is minimal. NO_X could thus be used alone to calculate CO₂ emissions (as shown in Table 4), as the coefficients for inventory methods are essentially added on if that method is used, since they are binary variables.

There is a lack of CO₂ EFs available from the US EPA’s AP-42 compilation of EFs [29]. This increases the challenge of inventorying CO₂ for facilities and highlights that those facilities which use EFs likely use site-specific EFs, which are independent of NO_X. Since bottom-up inventory methods are process-specific while the emissions reported are facility-wide, the use of EFs for both NO_X and CO₂ does not actually increase the chance of correlation. Notably, AP-42 has published EFs for CO₂ for aluminum production but not for NO_X, highlighting the uniqueness of this process, which could explain the lack of a reliable model produced for this sector. The Government of Canada has some published EFs, which are almost exclusive to fuel combustion [30], varying the type of fuel but not the process of combustion. If these EFs are those used by the industries examined in this study, these would further introduce CO₂ uncertainty and remove correlation to NO_X EFs, promoting the need for a reliable CO₂ estimation strategy and the independence of EFs. Furthermore, of all the methods, monitoring and direct measurement was the second least prevalent after mass balance, despite the fact that it is widely considered the most reliable method. Worth noting is that even when using monitoring and direct measurement for CO₂, unlike NO_X, there are background concentrations which often go unaccounted for. The argument of using NO_X as a surrogate for CO₂ tracking is furthered by better reporting for NO_X—in 2023, 22,733 Canadian facilities reported their NO_X emissions, while only 1862 facilities reported their CO₂ emissions [16,26]. Given the US EPA AP-42’s lack of EFs for CO₂, this study offers a reliable alternative for those facilities which do not have access to other inventory methods.

The use of NO_X abatement technologies will affect the R² value of the correlation, as they introduce more variability into the data. Correlating NO_X and CO₂ inclusive of any abatement technologies examines the full Canadian context, which is the goal of this study, rather than facilitating facility-level prediction. Making the prediction as high-level as possible means finding a general average which may be used for rapid large-scale calculations. Most industries do not use NO_X abatement technologies, outside of coal-fired power plants implementing low-NO_X burners. Since all but two of the correlations show reasonable R² values, the effects of abatement technologies on most industries are not significant to a large-scale calculation model.

The poor correlation for the oil and gas sector could be due to variation in the level of sweetening (removal of hydrogen sulfide and carbon dioxide) as well as other process variations. The use of flaring can vary from location to location and would substantially affect the ratio of CO₂ to NO_X. The poor correlation in the aluminum sector likely arises from process differences between bauxite processing and recycled aluminum processing. The data showed high variation among the facilities’ ratios of CO₂ to NO_X, as the two processes for aluminum production vary greatly. These correlations should not be used for predictive modelling, as more specificity may be required for these sectors to differentiate between each unique process, which defeats the purpose of using the simplified proxy.

5. Conclusions

Inventorying GHG emissions is time-consuming and costly. Each year, facilities report to the GHGRP and NPRI separately, preparing independent documents to submit to each program. The time and money taken to prepare these reports could be better invested were the process to be streamlined. The issue is highlighted by the sheer number of published EFs in the US EPA and the simultaneous lack of EFs for CO₂, which only increases uncertainty when specific data is unavailable to make use of these EFs. The MLR models in this study provide an alternative for predicting emissions, and a methodology for other industries and facilities to develop their own. The model variability based on the inventory method used highlights the need for a standard method procedure, while this is limited by facility resources. The results and literature suggest that using direct monitoring for NO_X emissions and using models with a simple ratio, such as those suggested here, to calculate CO₂ emissions would provide a comparable level of accuracy to the current GHG inventorying while saving time and money. With Canada needing to reduce emissions at a very large scale, rapidly tracking Canada’s move towards carbon neutrality is critical.