Electricity generation emission factors (EGEF) quantify the relationship between amount of pollutant emitted and amount of electricity generated. Quantifying variability among calculated EGEFs is important when EGEFs are used for decision-making. Variabilities in EGEF on an annual basis due to variability in the amount of coal, natural gas, and petroleum emissions within the fuel mix are quanti ed for California, Texas, and New York in 2017. The results show a higher coecient of variation for SO2andNOxcompared to CO2EGEF. Changes in the EGEF over time are studied using decomposition analysis for California, Texas, and New York from 1990 to 2017. The results show that the main factor in reducing EGEF in California is the improving generation eciency of power plants; in Texas, it is the increasing the ratio of renewable to non-renewable electricity generation; and in New York, it is the changing mix of fossil fuels that are consumed for electricity generation. The e ect of variability of EGEF on environmental impact categories is analyzed. Eutrophication of air, eutrophication of water, and smog formation are subject to high uncertainty because SO2andNOxEGEFs are used to quantify these impacts, whereas global warming potential has less uncertainty because it only uses CO2EGEF. Keywords: electricity generation emission factor, fossil fuel emission factor, decomposition analysis, Monte Carlo simulation, environmental impact assessment Nomenclature 1 AP Acidi cation Potential 2 C Emissions from electricity generation (kg) 3 Cfuel Emission by each fossil fuel type (coal, natural gas, or petroleum) (kg) 4 EF Emission factor 5 EGEF Electricity generation emission factor 6 E Eciency 7 EIA U.S. Energy Information Administration 8 EPA U.S. Environmental Protection Agency 9 EA Eutrophication of air 10 EW Eutrophication of water 11 efuel Emission factor for each fossil fuel (kg-emissions/MMBtu) 12 Ffuel Energy input by each fossil fuel type (coal, natural gas, or petroleum) (MMBtu) 13 FF Fossil fuel 14 G Total electricity generation by state (MWh) 15 Email address: amanda.d.smith@utah.edu (Amanda D. Smith) Preprint submitted to Elsevier January 17, 2022 GWP Global Warming Potential 16 HH Human health 17 IDA Index decomposition analysis 18 LMDI Logarithmic mean divisia index analysis 19 mfuel The electricity generation from each fossil fuel divided by the total electricity generation 20 from all fossil fuels (coal, natural gas, and petroleum) 21 NG Natural gas 22 Pet Petroleum 23 PV Photovoltaics 24 SA Smog Air 25 U.S. United States 26 ufuel The energy input divided by the electricity generation for each fossil fuel (MMBtu/MWh) 27 Q Electricity generation by all fossil fuels (coal, natural gas, and petroleum) (MWh) 28 Qfuel Electricity generation by each fossil fuel type (coal, natural gas, or petroleum) (MWh) 29 1. Introduction 30 Climate change has rami cations on ecosystems, human health, and the energy sector (National Oceanic 31 and Atmospheric Administration, 2019). Human activities and energy consumption, on both global and 32 regional scales, are driving climate change (Stocker et al., 2013). The electricity sector alone contributed to 33 27.5% of 2017 greenhouse gas emissions in the United States (U.S.), making the sector the country's second- 34 largest source of greenhouse gas emissions (U.S. Environmental Protection Agency (EPA)) and an essential 35 factor in reducing or mitigating climate change. Electricity generation in uences ecosystems, human health, 36 and the climate by releasing CO2,SO2, and NOxemissions through fossil fuel{ red generation. Monitoring 37 and measuring the greenhouse gas emissions resulting from electricity generation empowers a country or region 38 to move toward a low-carbon future (Khan, 2019a). However, the quanti cation of greenhouse gas emissions 39 resulting from electricity generation has been associated with a variety of uncertainties and variabilities that 40 may a ect such decision-making and carbon management (Li and Huang, 2012). Therefore, de ning and 41 quantifying these variabilities and changes in electricity generation{related emissions is also essential. This 42 study aims to de ne and quantify these factors accordingly. 43 In this work, we investigate variations between calculated electricity generation emission factor (EGEF) 44 values across U.S. states. Moreover, we quantify the key factors underlying changes in these EGEFs from 45 1990 to 2017. This work was conducted at the state level, and we have focused on three U.S. states to 46 illustrate a variety of cases. We chose California, Texas, and New York for this analysis because they are 47 three of the country's most populous states. Also, they encompass a wide range of climate conditions and 48 sociopolitical systems, and more electricity sector{related data is publicly available for these three states 49 than for many other U.S. states. Moreover, each of these three states is located in one of the country's 50 three major electrical grid interconnections. California lies within the Western Interconnection; the vast 51 majority of Texas lies within the Electric Reliability Council of Texas (ERCOT); and New York lies within 52 the Eastern Interconnection (U.S. Department of Energy Oce of Electricity (2019)). These three states 53 have implemented progressive strategies to increase their renewable electricity generation and reduce their 54 electricity generation carbon footprints (Barbose, 2017). 55 This work addresses the following key research questions: 56 1. How do EGEFs (that is, the range of expected values for CO2,SO2, and NOxemissions per unit of 57 electricity) vary across in three U.S. states of California, Texas, and New York? 58 2. How did these EGEFs change from 1990 to 2017, and what underlying factors drove these changes in 59 each of the studied states? 60 2 3. Can we reasonably quantify electricity generation's environmental impacts at the state level, given the 61 uncertainty surrounding the data used to calculate these states' emission factors? 62 In the following subsections, we discuss the research background related to each of these key questions. 63 1.1. How do EGEFs (that is, the range of expected values for CO2,SO2, and NOxemissions per unit of 64 electricity) vary across in three U.S. states of California, Texas, and New York? 65 We de ne the term \emission factor" (EF) according to its use by the U.S. EPA: \An EF is a representative 66 value that attempts to relate the quantity of a pollutant released to the atmosphere with an activity associated 67 with the release of that pollutant" (U.S. EPA). A fossil fuel EF is the quantity of emissions per unit of energy 68 content in a fuel (kg emissions/MMBtu), and this quantity is often provided as a single value; for example, 69 the \EFs for greenhouse gas inventories" document by the EPA provides nationwide averages for coal, natural 70 gas, and petroleum, which are responsible for 66%, 32%, and 1% of total U.S. CO2emissions for electricity 71 generation (U.S. Energy Information Administration (EIA), 2019). In reality, a fossil fuel EF's value varies 72 year-to-year across di erent regions and types of combustion devices (Roy et al., 2009) due to the di erent 73 eciencies associated with power plants, various origins and sub-types of each fossil fuel used, and di erences 74 in the accuracy of emission measurements in each power plant. 75 EF value di erences can signi cantly a ect quanti cations of CO2emissions (Liu et al., 2015). An 76 electricity generation EF (EGEF) calculates the emissions released per unit of electricity generation (kg 77 emissions/MWh generated). The greenhouse gas emissions associated with renewable and nuclear energy used 78 to generate electricity are signi cantly lower and less variable than the emissions associated with electricity 79 generation using fossil fuels: life-cycle greenhouse gas emissions have been reported at 45 (g CO2/kWh) for 80 Photovoltaics (PV), 11 (g CO2/kWh) for wind, 12 (g CO2/kWh) for nuclear energy, and 1,000 (g CO2/kWh) 81 for coal (National Renewable Energy Laboratory, 2013). Thus, PV, wind, and nuclear emissions' impact on 82 EGEF were neglected in the present study, and the EGEF can be quanti ed using a weighted sum of the 83 EFs for the individual energy sources in a state's fuel mix, multiplied by their consumption rates. 84 Several studies in the literature have investigated the e ects of variabilities in the energy sources emissions 85 on emissions accounting of the electricity generation. 86 Some studies analyzed variabilities in EGEF due to considering the marginal EGEF. Marginal EGEF 87 is a metric to account for the changes in the electricity generation emissions as a result of an additional 88 unit of electricity (Hawkes (2010) and Khan (2019a)). Studies that consider the marginal EGEF have shown 89 variabilities in EGEF when the marginal EGEF is used compared to the average EGEF. For example, 90 Siler-Evans et al. (2012) quanti ed the variabilities of marginal EGEF compared to the average EGEF for 91 eight regional electricity generations. Their results showed that the marginal EGEFs were di erent from 92 the average EGEFs up to 36% for the CO2EGEF, 280% for the SO2EGEF, and 161% for NOxEGEF. 93 Zheng et al. (2015) quanti ed the marginal EGEF and compared the marginal EGEF with the average EGEF 94 for two case studies. Their results showed that the marginal EGEF was up to 50% higher than the average 95 EGEF. 96 Some studies focused on the variabilities in the generation mix with seasons, days, and time of the 97 day, and its e ect on the EGEF (Khan, 2019b). Especially, the penetration of renewable sources and their 98 intermittent electricity generation results in changes in the generation mix and variability of EGEF. For 99 example, Khan et al. quanti ed the temporal variability of EGEF in Bangladesh (Khan, 2018) and New 100 Zealand (Khan et al., 2018). They studied the variabilities in EGEF because of the changes in the electricity 101 demand, the penetration of renewable sources, and the di erence in the eciency of power plants to generate 102 electricity. Their results showed up to 40% variabilities in the EGEF. St-Jacques et al. (2020) studied the 103 temporal EGEF of eight regions in the electrical zone of Ontario. They showed high variabilities in EGEF 104 for di erent electrical zones compared to the average EGEF. 105 The mentioned studies perform an essential analysis in quanti cation and variability analysis of EGEF 106 due to an additional unit of electricity demand and the changes in the time of electricity use. However, the 107 EF of fossil fuels used to generate electricity can vary year-to-year due to the di erent eciencies associated 108 with power plants, various origins and sub-types of each fossil fuel used, and di erences in the accuracy of 109 emission measurements in each power plant. Hence, the annual variability of each fossil fuel EF changes the 110 annual EGEF. 111 To the best of our knowledge, two studies performed variability analysis of fossil fuel EF to generate 112 electricity. 113 3 Wang et al. (2019) used bootstrap and Monte Carlo simulations to determine methane EF variability 114 for coal, using data from 11,000 power plants in China. They found high variability for methane EFs, 115 which varied widely compared to the average EF values used in the 2006 Intergovernmental Panel on Climate 116 Change (IPCC) \Guidelines for National Greenhouse Gas Inventories." Roy et al. (2009) created equations 117 for estimating coal EFs in India, nding this approach e ective in reducing the uncertainty surrounding 118 EFs for this fuel type. This approach yielded estimated EFs that were proposed to be more realistic than 119 national-average EFs in representing coal EFs throughout India. 120 These studies have analyzed coal EF variability in emissions accounting in India and China. The literature 121 has neglected, however, to analyze EGEFs' variability, based on variabilities in each fossil fuel EFs at the 122 U.S. state level, while considering the data's limitations. Therefore, the current study's rst objective is to 123 analyze EGEF' variability with the available energy-source EFs at the state level, using our three selected 124 states. 125 1.2. How did these emission factors change from 1990 to 2017, and what underlying factors drove these 126 changes in each of the studied states? 127 EGEFs change over the years because of changes in the power generation process. In this work, we 128 consider four major factors involved in those changes (Ang and Su (2016), Goh et al. (2018a), and Goh 129 et al. (2018b)): (1) the fossil fuel share e ect (i.e., fossil fuels' share of electricity generation to non{fossil 130 fuels'|hydro-power, biomass, renewables, and nuclear|share of electricity generation), (2) the fossil fuel 131 mix e ect (i.e., the mix of fossil fuels consumed for electricity generation), (3) the generation eciency e ect 132 (i.e., power plants' generation eciency), and (4) the EF e ect (i.e., fossil fuel EFs). Understanding how 133 EGEF can be broken down into these four factors can reveal the most e ective factors in reducing EGEFs. 134 Decomposition analysis is a method of breaking the EGEF down into several prede ned factors (Ang, 135 2004). Index decomposition analysis (IDA) is a useful method for performing decomposition analysis and 136 evaluating the main forces driving changes in CO2emissions over the years (Xu and Ang (2013) and Zhang 137 et al. (2013)). 138 Decomposition analysis of EGEFs has enabled a new understanding of the essential factors driving changes 139 in EGEFs over the years. Ang and Su (2016) broke down the CO2EGEF in 10 Southeast Asian countries 140 from 1990 to 2013. The results of this decomposition index identi ed the factor responsible for the largest 141 reductions in several countries' EGEFs: in Myanmar, this factor was an improvement in the country's fossil 142 fuel share e ect; in Singapore and Thailand, this factor was changes in the countries' fossil fuel mix e ects; 143 and in Vietnam, Brunei, and Malaysia, this factor was an improvement in power plants' generation eciency 144 e ect. Liu et al. (2017) used the IDA method to analyze the forces driving EGEFs at the provincial level in 145 China. They concluded that an improvement to the generation eciency e ect was the most essential factor 146 in reducing China's EGEFs from 2000 to 2014. 147 Decomposition analysis of CO2emissions has also been conducted using electricity generation in the U.S. 148 Jiang and Li (2017) used the LMDI (log mean Divisia index analysis) method to break down CO2emissions 149 in the U.S. from 1990 to 2014, concluding that the country's fossil fuel mix e ect played the most signi cant 150 role in reducing electricity CO2emissions from 1990 to 2005 (and in the CO2emissions predicted between 151 2005 and 2030). Mohlin et al. (2019) studied changes in CO2emissions at the U.S. state level from 1990 152 to 2015, showing that states' fossil fuel share e ect and fossil fuel mix e ect were the main factors driving 153 changes in CO2emissions. 154 The studies above demonstrated that the fossil fuel share e ect, the fossil fuel mix e ect, and the gener- 155 ation eciency e ect tend to account for the largest share of changes in EGEFs (Ang and Su (2016), Malla 156 (2009), and Jiang and Li (2017)), and the most important factors di er between the national and provincial 157 levels (Liu et al. (2017) and Mohlin et al. (2019)). Decomposition analysis of U.S. EGEFs is vital because 158 magnitudes of greenhouse gas emissions resulting from electricity generation vary by location (de Chalendar 159 et al., 2019) since U.S. states may belong to di erent electrical grid balancing authority areas, may have 160 implemented di erent renewable energy policies (DSIRE), or may target di erent energy source mixes over 161 the years while facing di erent public pressures to act upon these targets. 162 The current study builds on the work of Mohlin et al. (2019) by examining variability and di erent 163 possible values for EGEFs, including changes in SO2andNOxEGEF, extending the studied period to 2017, 164 and focusing on three selected states that provide di erent case studies illustrating this variability. Thus, 165 4 this study's second objective is to study EGEF changes over the years in California, Texas, and New York 166 at the individual-state level. 167 1.3. Can we reasonably quantify electricity generation's environmental impacts at the state level, given the 168 uncertainty surrounding the data used to calculate these states' emission factors? 169 If EGEFs are part of a decision-making process, then any metrics calculated using variations that a ect 170 EGEF values will also involve variability that is associated with the calculated metrics. The term \environ- 171 mental impact," as it is used here, describes the consequence of a plan, policy, or process. It is an example of 172 a method used for decision- and policy-making. Environmental impact quanti cation is a method of evalu- 173 ating a system or process's environmental e ects through four damage categories: human health, ecosystem 174 quality, climate change, and resources (Jolliet et al., 2003). To quantify electricity generation's environmental 175 impacts, a computational tool can be used rst to create a deterministic estimate. The variability associated 176 with EGEF can be used with the analytical tool to quantify a resulting variability in environmental impacts. 177 Traci, an open-source environmental impact assessment tool developed by the U.S. EPA (2012), was used in 178 this study to quantify environmental impacts. 179 Many studies have quanti ed electricity generation's environmental impact, but few analyses have incor- 180 porated uncertainty and variability into their results. Chen and Corson (2014) used a Monte Carlo simulation 181 to determine the e ects of EFs' uncertainty in three environmental impact categories. They concluded that 182 EFs' variability and uncertainty could shift decision outcomes, based on environmental impact assessments. 183 Sonnemann et al. (2003) estimated the e ect of site-speci c uncertainties and variability in measuring EGEF 184 resulting from a waste incinerator, showing that signi cant uncertainties are associated with EGEFs because 185 of inventory data uncertainties. 186 Tools that help decision-making can be improved if their results' uncertainties and variabilities are more 187 transparent (Tenney et al., 2006). We were unable to locate a study investigating the variability of a decision- 188 making tool's results, based on U.S. EGEFs' variability. The lack of such a study may be due to a lack of 189 reliable data on emissions', EFs', and EGEFs' uncertainty and variability. Therefore, the current study's 190 third objective was to quantify how EGEFs' variability a ects the environmental impacts, using the limited 191 data available from reliable sources. 192 Our analysis in this paper presents the following novel contributions: 193 1. The range and variability of EGEFs for CO2,SO2, and NOxassociated with fossil fuel electricity 194 generation in the U.S. are quanti ed deterministically for all U.S. states. These EGEFs are quanti ed 195 stochastically, using a Monte Carlo simulation for the three selected states. 196 2. The CO2EGEF is broken down for the three selected states, showing how those EGEFs have changed 197 over time by revealing the main factors that have in uenced changes to EGEFs between 1990 and 2017. 198 3. We quantify the variability of electricity generation's environmental impacts due to variability in 199 EGEFs. However, we caution against relying on any quanti cation of electricity generation's envi- 200 ronmental impacts at the U.S. state level. 201 2. Methodology 202 The following three subsections discuss the methods we used to address each of this study's three objec- 203 tives, respectively. 204 2.1. Emission factors' distribution for electricity generation 205 This subsection explains our methodology in determining fossil fuel EFs' variability in the U.S. in 2017 206 and then using that variability to identify the probability distribution of EGEFs at the state level in 2017. 207 This subsection comprises three parts. First, the data sources and assumptions used to determine the EGEFs 208 are described. Second, the formulations used to calculate EGEFs are presented. Third, the Monte Carlo 209 simulation statistical tool is used to identify the results' variability and probability distribution. 210 5 2.1.1. Data sources and assumptions 211 Three data sources from the \Electricity Detailed State Data from 1990 to 2017" webpage by the U.S. 212 EIA were used to calculate energy-source EGEFs at the state level: 213 1. Annual data (from 1990 to 2018) for net generation by type of producer (e.g., the total electric power 214 industry, electric generators, electric utilities, combined heat and power, and commercial power) and 215 fuel type (e.g., coal, natural gas, petroleum, hydroelectric conventional, and wind) for 50 U.S. states. 216 2. Annual data (from 1990 to 2018) for fossil fuel consumption used for electricity generation by producer 217 type (e.g., total electric power industry, electric generators, electric utilities, combined heat and power, 218 and commercial power) and fuel type (e.g., coal, natural gas, petroleum, and other gases) for 50 U.S. 219 states. 220 3. Annual data (from 1990 to 2017) for the electric power industry's estimated emissions ( CO2,SO2, and 221 NOx) for 50 U.S. states. 222 We made four assumptions in considering the fuels used for electricity generation at the state level: 223 1. Only emissions associated with fossil fuels' combustion were considered, and emissions from the pro- 224 duction, processing, transmission, and storage of energy sources were omitted from our calculations. 225 We made this assumption because of the available electricity generation and emissions data from the 226 EIA \Electricity Detailed State Data from 1990 to 2017" documents' exclusion of other parts of the 227 energy sources life cycle and focus on the production side of energy sources for electricity generation . 228 2. Emissions associated with renewables (hydro, wind, solar, biomass, and geothermal) and nuclear energy 229 were also excluded from our calculations. Amponsah et al. (2014) reviewed greenhouse gas emissions 230 at di erent stages of renewable technologies. In most cases (except for two instances using biomass 231 technology), greenhouse gas emissions from power plant operations were less than 20 kg CO2eq/MWh, 232 which is less than greenhouse gas emissions associated with the use of fossil fuels to generate electricity 233 (National Renewable Energy Laboratory, 2013). 234 3. \Other biomass" and \wood and wood derived fuels" energy sources from the \Electricity Detailed 235 State Data from 1990 to 2017" documents were also excluded from our EGEF calculation. The three 236 selected fossil fuels (i.e., coal, natural gas, and petroleum) are the top-three CO2emitters, accounting 237 for 99% of CO2, 82% of SO2emissions, and 82% of NOxemissions in U.S. electricity generation during 238 2017. The main energy source excluded from our analysis is \wood and wood derived fuels," which 239 account for 16% of SO2emissions; moreover, \other biomass" and \wood and wood derived fuels" 240 respectively account for 8% and 5% of NOxemissions. \Other biomass" and \wood and wood derived 241 fuels" were omitted from this study because their consumption data is not available in the \Electricity 242 Detailed State Data from 1990 to 2017" EIA documents. 243 4. The \other" fuel type was omitted because its heating value is unavailable, and it accounted for only 244 0.3% of total U.S. electricity generation in 2017, which is a marginal amount (\Electricity Detailed 245 State Data from 1990 to 2017" EIA documents). 246 2.1.2. Electricity generation emission factor calculation 247 EF of fossil fuels can be calculated by dividing emissions at the state level for each fuel type by the 248 amount of the consumption of that fuel to generate electricity (kg emissions/MMBtu), using Equation 1 249 (Intergovernmental Panel on Climate Change, 2006). EGEFs at the state level can be calculated using 250 Equation 2, based on fuel consumption rates and fuel EFs, divided by electricity generation at the state level. 251 Emission Factor fuel= Emissions =Fuel Consumption (1) EGEF =Pn fuel=1Fuel ConsumptionfuelEmission Factor fuel Electricity Generation(2) 6 2.1.3. Statistical analysis 252 Probabilistic techniques, such as Monte Carlo simulation, can serve as a practical statistical tool in 253 analyzing variability (Environmental Protection Agency, 1997). This study used the ve-step Monte Carlo 254 simulation procedure described by Hiraishi et al. (2001) to quantify EGEFs' variability at the state level. 255 1. Specify source-category uncertainties; fossil fuel EFs (kg CO2/MMBtu, kg SO2/MMBtu, and kg 256 NOx/MMBtu) for coal, natural gas, and petroleum are variable in the U.S. 257 2. Set up the necessary information: the quantities of CO2,SO2, and NOxemissions, fossil fuel consump- 258 tion rates, and electricity generation are available in the \Electricity Detailed State Data from 1990 to 259 2017" document by the EIA for all 50 U.S. states in 2017. Fossil fuel EFs' probability density functions 260 were computed using the available continuous distributions in the SciPy Python library (SciPy library, 261 2019). 262 3. Select random variables: random CO2,SO2, and NOxEF variables (kg CO2/MMBtu, SO2/MMBtu, 263 orNOx/MMBtu) were generated for coal, natural gas, and petroleum. 264 4. Estimate EGEFs: EGEFs were calculated for Texas, California, and New York using fossil fuel consump- 265 tion rates (MMBtu) multiplied by fossil fuel EFs' random variable (kg CO2/MMBtu, SO2/MMBtu, or 266 NOx/MMBtu), using Equation 2. 267 5. Iterate and monitor the results: the EGEF value from Step 4 was stored, and then the process was 268 repeated from Step 3. 269 These ve steps were simulated using continuous distributions in the SciPy library in Python, and 10,000 270 samples from fossil fuel EFs were generated to show EGEFs' variability for the study's three emission types 271 at the state level. 272 2.2. The most in uential elements of electricity generation emission factors 273 This subsection describes the study's methodology to break EGEFs down into in uential factors at the 274 state level from 1990 to 2017. 275 Two main methods were used for this decomposition analysis: structural decomposition analysis (SDA), 276 which uses input-output models, and IDA, which implements index number theory (Goh et al., 2018b). 277 IDA has been successfully applied in the literature to evaluate di erent factors' impacts on energy and 278 changes in emissions over the years (Zhang et al., 2013). In 2004, after 25 years of research on decomposition 279 analysis, researchers had not reached an agreement on the best decomposition method (Ang, 2004). Popular 280 decomposition methods belong to two main groups: (1) methods linked to the Laspeyres index (i.e., the 281 impact of a factor is calculated while all the other factors are constant at their base year) and (2) methods 282 linked to the Divisia index (i.e., a weighted sum of logarithmic growth rates is used) (Ang et al., 1998). 283 The advantage of the Divisia index approach (i.e., the concept of logarithmic change) over the Laspeyres 284 index approach (i.e., the familiar concept of percentage changes) is the Divisia index symmetric and addi- 285 tive features of relative changes (Ang, 2004). The symmetric feature of the Divisia index means that, in 286 quantifying relative changes between two numbers, the order of the numbers does not a ect relative change 287 values. For example, an absolute value of log(1 =5) equals log(5 =1), but a percentage change between these 288 two numbers gives values of 5 and 0.20 (1/5). The additive feature of the Divisia index means that two 289 relative changes can be summed or subtracted. For example, log(5 =1) equals log(5 =3) added to log(3 =1). 290 But, using the concept of percentage changes, 5 does not equal 1.67 (5/3) added to 3, which gives 4.67. 291 For cross-country or regional analysis, conventional decomposition methods leave signi cant residuals, 292 and perfect decomposition methods (e.g., LMDI)|which leave no residuals|have been suggested instead 293 (Zhang and Ang, 2001). Ang (2004) concluded that LMDI is the most \elegant" decomposition method, 294 from a theoretical perspective, for use in regional studies. Therefore, considering its additive and symmetric 295 features and its leaving no residuals, we selected the LMDI method for the current study. 296 To apply the LMDI method to changes in EGEFs from this study's base year (1990) to its nal year 297 (2017) at the state level, Equation 3 was used as the governing equation to be broken down into four factors 298 7 (Ang and Su, 2016). 299 EGEF =C G=3X fuel=1Q GQfuel QFfuel QfuelCfuel Ffuel(3) C Emissions from electricity generation (kg) 300 G Total electricity generation by state (MWh) 301 Q Electricity generation by all fossil fuels (coal, natural gas, and petroleum) (MWh) 302 Qfuel Electricity generation by each fossil fuel type (coal, natural gas, or petroleum) (MWh) 303 Ffuel Energy input by each fossil fuel type (coal, natural gas, or petroleum) (MMBtu) 304 Cfuel Emission by each fossil fuel type (coal, natural gas, or petroleum) (kg) 305 Equation 3 can be rewritten as Equation 4 (Ang and Su, 2016). 306 EGEF =3X fuel=1pmfuelufuelefuel (4) p The proportion of electricity produced from fossil fuels in the total electricity generation (MWh/MWh) 307 mfuelThe electricity generation from each fossil fuel divided by the total electricity generation from 308 all fossil fuels (coal, natural gas, and petroleum) (MWh/MWh) 309 ufuel The energy input divided by the electricity generation for each fossil fuel generation (MMBtu/MWh) 310 efuel The EGEF of each fossil fuel (kg-emissions/MMBtu) 311 Next, the total change in EGEFs at the state level from 1990 (the base year) to 2017 was shown as  Vtotal312 (kg emissions/MWh) and broken down into  Vp(fossil fuel share e ect),  Vm(fossil fuel mix e ect),  Vu313 (generation eciency e ect), and  Ve(EF e ect) (kg emissions/MWh) factors in Equation 5. 314 Vtotal=VTV0= Vp+ Vm+ Vu+ Ve (5) Further equations for the LMDI method are available in Appendix (also, see Ang et al. (1998), Ang 315 (2005), Ang et al. (2011), and Ang and Su (2016) for detailed methodology). 316 2.3. The e ects of electricity generation emission factors' present variability on environmental impact quan- 317 ti cation 318 This subsection describes the methodology we used to quantify the e ects of EGEFs' variabilities on 319 environmental impact categories during 2017 in California, Texas, and New York, using the ve-step Monte 320 Carlo procedure presented earlier under Subsection 2.1. 321 Environmental impact quanti cation anticipates a system or process's environmental e ects through four 322 damage categories: human health, ecosystem quality, climate change, and resources (Jolliet et al., 2003). 323 Midpoint categories can be used to connect emission inventory data to damage categories. Six midpoint 324 categories were used in the current study: global warming potential (GWP), acidi cation potential (AP), 325 human health (HH), eutrophication air (EA), eutrophication water (EW), and smog air (SA). These midpoint 326 categories were chosen because they connect CO2,SO2, and NOX|the available emissions data in this 327 study|to the damage categories. GWP a ects climate change. AP, EA, EW, and SA a ect ecosystem 328 quality. Finally, HH and SA a ect human health (Jolliet et al., 2003). 329 Traci, an open-source environmental impact assessment tool developed by the EPA, was used in this 330 study to determine the environmental impacts of electricity generation at the state level by providing the 331 characteristic factors shown in Table 1. Traci was selected for this study as a free, U.S.{based tool developed 332 by the EPA, a reliable source for environmental studies. 333 To quantify the impact categories, rst, the characteristic factors (Table 1) are collected for CO2,SO2, 334 andNOXfrom the Traci tool; second, these three characteristic factors are multiplied by the three EGEF 335 ofCO2,SO2, and NOX; and third, the sum of the three multiplied values results in the equivalent emission 336 8 Characteristic factor CO2SO2NOx GWP (kg CO2-eq/kg substance) 1 0 0 AP (kg SO2-eq/kg substance) 0 1 0.7 HH (kg PM 2:5-eq/kg substance) 0 0.061 0.007 EA (kg N-eq/kg substance) 0 0 0.044 EW (kg N-eq/kg substance) 0 0 0.291 SA (kg O3-eq/kg substance) 0 0 24.79 Table 1: Characteristic factors of CO2,SO2, and NOxfor six impact categories (GWP, AP, HH, EA, EW, and SA) from the U.S. EPA (2012). of each impact category. For example, to quantify the AP ( SO2-eq) using the Traci tool, the second row of 337 Table 1 is used. This row shows that the characteristic factor of CO2is zero (kg SO2-eq/kg substance), SO2 338 is 1 (kg SO2-eq/kg substance), and NOxis 0.7 (kg SO2-eq/kg substance) for AP. Hence, the CO2EGEF (lb 339 CO2/MWh) is multiplied by zero, SO2EGEF (lb SO2/MWh) is multiplied by 1 (kg SO2-eq/kg substance), 340 andNOxEGEF (lb NOx/MWh) is multiplied by 0.7 (kg SO2-eq/kg substance). Their sum results in each 341 state's AP of EGEF (lb SO2-eq/MWh). 342 A Monte Carlo simulation was used to calculate the variability of electricity generation's environmental 343 impacts, following the ve-step procedure described in Subsection 2.1. 344 1. Specify source category uncertainties: EGEFs are variable (kg CO2/MWh, kg SO2/MWh, and kg 345 NOx/MWh) in California, Texas, and New York, based on the results of the rst objective identi ed 346 in Subsection 3.1. 347 2. Set up the necessary information: characteristic factors of CO2,SO2, and NOxfor six impact categories 348 (GWP, AP, HH, EA, EW, and SA) were obtained from the Traci, which are shown in Table 1. EGEFs' 349 probability density functions can be calculated using the Subsection 2.1 method and are shown in Table 350 5 in Appendix. 351 3. Select random variables: random variables for CO2,SO2, and NOxEGEF (kg CO2/MWh, SO2/MWh, 352 orNOx/MWh) were determined for California, Texas, and New York. 353 4. Estimate the environmental impact: GWP, AP, HH, EA, EW, and SA were calculated for California, 354 Texas, and New York using the Traci characteristic factors in Table 1, multiplied by CO2,SO2, and 355 NOxEGEF random variables from Step 3. 356 5. Iterate and monitor the results: The environmental impact categories' values from Step 4 were stored, 357 and then the process was repeated from Step 3 to show the variability of EGEFs' environmental impacts 358 in California, Texas, and New York during 2017. 359 3. Results and Discussion 360 The results obtained by addressing each of this study's three objectives are discussed in the three subsec- 361 tions below. 362 3.1. Emission factors' distribution for electricity generation 363 This subsection rst reveals the CO2,SO2, and NOxEF distributions of coal, natural gas, and petroleum 364 in the U.S. during 2017. Next, the variability of CO2,SO2, and NOxEGEFs are presented for California, 365 Texas, and New York in 2017. 366 The EF units for fossil fuels are compatible with the units in the \EFs for greenhouse gas inventories" 367 document by the EPA, kg of emissions per MMBtu of fossil fuel consumption. 368 The probability distribution of CO2EFs for coal, natural gas, and petroleum are shown in Figures 1, 2, 369 and 3, and their statistics are given in Table 2. The median of CO2EF using coal was 95.38 kg- CO2/MMBtu 370 (0.32 kg- CO2/kWh), while the corresponding median for natural gas was 56.38 kg- CO2/MMBtu (0.19 kg- 371 CO2/kWh), and the corresponding median for petroleum was 73.92 kg- CO2/MMBtu (0.25 kg- CO2/kWh). 372 The average results for coal, natural gas, and petroleum EF were 95.52, 53.06, and 73 kg- CO2/MMBtu 373 (0.33, 0.18, and 0.25 kg- CO2/kWh), respectively, in the \EFs for greenhouse gas inventories" document by 374 9 Type of EF Distribution Std dev Mean Median Coecient of (kg/mmBTU) (kg/mmBTU) (kg/mmBTU) variation % CO2of Coal Levy Stable 10.22 98.01 95.38 10.43 CO2of Natural gas Power Log-Normal 2.63 56.71 56.38 4.65 CO2of Petroleum Johnson SU 8.53 77.13 73.92 11.06 SO2of Coal Folded Cauchy 0.06 0.09 0.08 61.56 SO2of Natural gas Cauchy 0.00 0.00 0.00 36.25 SO2of Petroleum Pearson Type III 0.17 0.16 0.11 109.08 NOxof Coal Folded Cauchy 0.03 0.07 0.07 38.12 NOxof Natural gas Folded Cauchy 0.10 0.07 0.03 155.71 NOxof Petroleum Johnson SB 0.07 0.11 0.10 66.42 Table 2: Statistics of CO2,SO2, and NOxEFs of coal, natural gas, and petroleum in the U.S. during 2017 the EPA. A coecient of variation (i.e., the data's standard deviation, divided by the data's mean) can be 375 used to compare uncertainty across data sets when means di er. The coecients of variation for CO2EF 376 using coal, natural gas, and petroleum were 10.43%, 4.65%, and 11.06%, respectively. 377 Figure 1: Probability distribution of CO2EFs for coal in the 50 U.S. states during 2017. Figure 2: Probability distribution of CO2EFs for natural gas in the 50 U.S. states during 2017. Figure 3: Probability distribution of CO2EFs for petroleum in the 50 U.S. states during 2017. The probability distribution of SO2EFs for coal, natural gas, and petroleum are shown in Figures A.1, 378 A.2, and A.3 in Appendix, and their statistics are given in Table 2. The median of SO2EF using coal 379 was 0.08 kg- SO2/MMBtu (0.27 g- SO2/kWh), while the corresponding median for natural gas was 0.0 kg- 380 SO2/MMBtu (0.0 g- SO2/kWh), and the corresponding median for petroleum was 0.11 kg- SO2/MMBtu (0.37 381 g-SO2/kWh). The coecient of variation for SO2EFs using coal, natural gas, and petroleum were 61.56%, 382 36.25%, and 109.08%, respectively. 383 The probability distribution of NOxEFs for coal, natural gas, and petroleum are shown in Figures A.4, 384 A.5, and A.6 in Appendix, and their statistics are given in Table 2. The median of NOxEFs using coal 385 was 0.07 kg- NOx/MMBtu (0.24 g- NOx/kWh), while the corresponding median for natural gas was 0.03 kg- 386 NOx/MMBtu (0.10 g- NOx/kWh), and the corresponding median for petroleum was 0.10 kg- NOx/MMBtu 387 (0.34 g- NOx/kWh). The coecient of variation for NOxEFs using coal, natural gas, and petroleum were 388 38.12%, 155.71%, and 66.42%, respectively. 389 The probability density functions of these nine EF types are depicted in Figures 1{3 and A.1{A.6, and 390 10 Figure 4: CO2EGEF distribution in Texas during 2017, using sources' (i.e., coal, natural gas, and petroleum) EF distributions Type of EGEF Distribution Std dev Mean Median Coecient of (lb/kWh) (lb/kWh) (lb/kWh) variation % CO2in California Generalized Extreme 19.07 403.58 400.6 4.73 CO2in Texas Tukey Lambda 97.03 1291.67 1291.25 7.51 CO2in New York Generalized Extreme 17.77 391.96 389.22 4.53 SO2in California Logarithm of the Gamma 0.05 0.01 0.0 767.39 SO2in Texas Hyperbolic Secant 28.12 2.57 0.8 1093.1 SO2in New York Pearson Type III 0.33 0.05 0.03 697.78 NOxin California Generalized Half-Logistic 6.81 0.65 0.25 1043.14 NOxin Texas Logarithm of the Gamma 16.25 2.13 0.91 764.04 NOxin New York Generalized Half-Logistic 6.33 0.63 0.25 1000.39 Table 3: Statistics of CO2,SO2, and NOxEGEFs of California, Texas, and New York during 2017 their statistics are shown in Table 2. In Step 3 of this study's Monte Carlo method, random variables 391 from probability density functions were generated and combined, based on each state's share of coal, natural 392 gas, and petroleum (i.e., energy mix). In Step 4 of this study's Monte Carlo method, 10,000 samples were 393 generated to calculate the CO2,SO2, and NOxEGEFs. The probability distribution of EGEFs using CO2, 394 SO2, and NOxof the study's 10,000 samples are shown in Figures 4, A.7, and A.8 for Texas. 395 TheCO2,SO2, and NOxEGEFs in Texas were, respectively, 1,166 lb CO2/MWh, 1.3 lb SO2/MWh, 396 and 0.8 lb NOx/MWh in 2017, as per the \State Electricity Pro les in 2017" EIA document. The median 397 values|using Figures 4, A.7, and A.8|were, respectively, 1,293.25 lb CO2/MWh, 0.83 lb SO2/MWh, and 398 0.9 lb NOx/MWh, shown in Table 3, re ecting 10.9%, 36%, and 12.5% respective di erences between the 399 median values in this study and the data in the \Electricity Detailed State Data from 1990 to 2017" EIA 400 document. The coecient of variation (i.e., the data's standard deviation, divided by the data's mean) is 401 shown in Table 3 for CO2,SO2, and NOxEGEFs in Texas, which are 7%, 697%, and 1061%, respectively. 402 Figures A.9, A.10, and A.11 in Appendix show the distributions of CO2,SO2, and NOxEGEFs in 403 California. 404 TheCO2,SO2, and NOxEGEFs in California were, respectively, 474 lb CO2/MWh, 0.0 lb SO2/MWh, 405 and 0.7 lb NOx/MWh in 2017, as per the \State Electricity Pro les in 2017" EIA document. The median 406 values|using Figures A.9, A.10, and A.11|were, respectively, 400.76 lb CO2/MWh, 0.0 lb SO2/MWh, and 407 0.24 lb NOx/MWh, shown in Table 3, re ecting 15.4%, 0%, and 95% respective di erences between the 408 median values in this study and the data in the \Electricity Detailed State Data from 1990 to 2017" EIA 409 document. The coecient of variation is shown in Table 3 for CO2,SO2, and NOxEGEFs in California, 410 which are 4.8%, 505%, and 1444%, respectively. 411 Figures A.12, A.13, and A.14 in Appendix show the distribution of CO2,SO2, and NOxEGEFs in 412 11 New York. The CO2,SO2, and NOxEGEFs in New York were, respectively, 439 lb CO2/MWh, 0.3 lb 413 SO2/MWh, and 0.5 lb NOx/MWh in 2017, as per the \State Electricity Pro les in 2017" EIA document. 414 The median values|using Figures A.12, A.13, and A.14|were, respectively, 389.22 lb CO2/MWh, 0.03 lb 415 SO2/MWh, and 0.25 lb NOx/MWh, shown in Table 3, re ecting 11.3%, 90%, and 50% di erences between 416 the median values in this study and the data in the \Electricity Detailed State Data from 1990 to 2017" EIA 417 document. The coecient of variation is shown in Table 3 for CO2,SO2, and NOxEGEFs in New York, 418 which are 4.6%, 699%, and 1,000%, respectively. 419 The variabilities in the EGEFs of this study are due to the variabilities in the EF of each energy source to 420 generate electricity. Therefore, the main factor that causes the variabilities in EGEF of this study is di erent 421 from the main factor that causes the variabilities in studies that quanti ed marginal EGEF or temporal EGEF 422 in the literature. However, comparing the EGEF variabilities of studies in the literature with variabilities in 423 this study can show the range and magnitude of variabilities of EGEF in the literature. Hawkes (2010) stated 424 the marginal EGEF in the Great Britain of 1521 lb- CO2/MWh for 2002{2009, with error bars at 10%. Also, 425 IPCC's report on EGEF of power plants to generate electricity is associated with 1% to 10% uncertainty in 426 CO2EGEFs. Therefore, the coecient of variations of this study (4.73% for California, 7.51% for Texas, 427 and 4.53% for New York) for CO2EGEF is in a similar range of uncertainties of variabilities in EGEFs in 428 the literature. 429 Two conclusions can be drawn from a comparison of this study's results for the three states examined: 430 1. For the three states, SO2andNOxEGEFs showed signi cant variability compared to CO2EGEFs. 431 2. EGEFs for states with higher shares of coal, natural gas, and petroleum were estimated to di er less 432 from the EIA document values. The shares of emissions in Texas, California, and New York were as 433 follows: 434 (a) In Texas, 99% of CO2, 94% of SO2, and 94% of NOxemissions for electricity generation resulted 435 from coal, natural gas, and petroleum consumption, respectively, which resulted in the lowest 436 di erence between this study's calculated values and the EIA document values. 437 (b) In California, coal, natural gas, and petroleum accounted for 95% of CO2emissions, 45% of SO2 438 emissions, and 73% of NOxemissions, respectively, for electricity generation. Including other 439 energy sources (i.e., \wood and wood derived fuels," \other biomass," and \other") would improve 440 estimations of SO2andNOxEGEFs in California. 441 (c) In New York, coal, natural gas, and petroleum were responsible for 97% of CO2emissions, 71% 442 ofSO2, and 63% of NOxemissions for electricity generation, respectively. Including other en- 443 ergy sources (i.e., \wood and wood derived fuels," \other biomass," and \other") would improve 444 estimations of SO2andNOxEGEFs in New York. 445 3.2. The most in uential elements of electricity generation emission factors 446 This subsection breaks down four in uential elements (the fossil fuel share e ect, the fossil fuel mix e ect, 447 the generation eciency e ect, and the EF e ect) of EGEFs to show how these four elements changed EGEFs 448 at the state level from 1990 to 2017. 449 The LMDI method was performed for the study's three examined states: Texas, California, and New 450 York. The results of this process for the fossil fuel share e ect, the fossil fuel mix e ect, the generation 451 eciency e ect, the EF e ect, and the sum of all four e ects (i.e., the total) are shown in Figure 5. 452 Figure 5 shows that total EGEFs have decreased in all three examined states from 1990 to 2017. The 453 highest reduction occurred in New York, and the lowest reduction occurred in California. 454 The fossil fuel share e ect was responsible for 42%, 36%, and 37% of the EGEF changes from 1990 to 455 2017 in Texas, California, and New York, respectively. This nding shows that fossil fuels' share of electricity 456 generation in the three states has decreased, substituted by renewables, nuclear energy, and biomass. From 457 1990 to 2017, coal, natural gas, and petroleum's shares of electricity generation changed from 92% to 75% in 458 Texas, from 50% to 43% in California, and from 61% to 38% in New York. 459 The fossil fuel mix e ect was responsible for 15%, 36%, and 63% of the EGEF changes in Texas, California, 460 and New York, respectively, from 1990 to 2017. This change in electricity EGEFs reveals that the three states' 461 fuel mixes changed to environmentally friendly fossil fuels by decreasing the shares of coal and petroleum and 462 increasing the shares of natural gas from 1990 to 2017. Coal and petroleum's shares of electricity generation 463 12 Figure 5: A comparison of Texas, California, and New York's respective changes in CO2EGEFs from 1990 to 2017 (lb CO2)/MWh reduced by 13% and 1%, respectively, in Texas, 2% and 3% in California, and 18% and 25% in New York. 464 Natural gas shares increased by 2% in California and 20% in New York. 465 The generation eciency e ect was responsible for 45%, 60%, and 19% of the EGEF changes in Texas, 466 California, and New York, respectively, from 1990 to 2017. This change means that more electricity was 467 generated from one unit of fossil fuel over the years because of improved eciency for power plants or 468 generators. The de nition of \generation eciency" is compatible with the heat rate of fossil fuels (i.e., 469 the energy input to a system, divided by electricity generation).The heat rate values of coal, natural gas, 470 and petroleum have improved over the years in the U.S. (U.S. Energy Information Administration, 2019b). 471 Changes to the generation eciency e ect with heat rate values are shown in Figures 1, 2, and 3 in the 472 supplementary materials for California, Texas, and New York. 473 The EF e ect increased in the three studied states, which shows that more emissions were produced from 474 one unit of fossil fuel over the years. This increase in the EF e ect might have resulted from these states' 475 using more exact metrics. 476 The \Annual energy outlook 2019: with projections to 2040" EIA document described several elements 477 that have in uenced EGEFs. Three of these elements that can be quanti ed over the years were selected 478 for observation in this study: natural gas prices, levelized costs of solar and wind energy, and old power 479 plants' retirement capacity. Other elements can also change EGEFs but were not considered in this study. 480 The selected three factors are part of a system, interconnecting with one another. The following connections 481 show, to some extent, how these three elements might a ect EGEFs over the years, though they share no 482 simple cause-and-e ect relationship. 483 Natural gas prices alter the fossil fuel mix e ect by decreasing coal- red power generation's competitiveness 484 (the \Annual energy outlook 2019: with projections to 2040" EIA document). Therefore, it is expected to see 485 lower EGEFs of fossil fuel mix e ect with lower natural gas prices. Figures 4, 5, and 6 in the supplementary 486 materials show the CO2EGEFs of the fossil fuel mix e ect and natural gas prices in California, Texas, and 487 New York from 1990 to 2017. 488 Levelized costs of electricity of solar and wind power decreased, based on a Lazard report, from 2009 to 489 2017. Such policies and renewables' LCOE helped EGEFs for the fossil fuel share e ect decrease over the 490 years at the state level. Figures 7, 8, and 9 in the supplementary materials show the renewable LCOE and 491 fossil fuel share e ects in California, Texas, and New York from 1990 to 2017. 492 The retirement of older and less-ecient power plants e ectively reduced EGEFs at the state level over 493 the years (U.S. EIA, 2019). Figures 10, 11, and 12 in the supplementary materials show the capacity for 494 coal-, natural gas{, and petroleum-based power plants' retirement during each studied year in California, 495 Texas, and New York, respectively. 496 13 Type Unit Std dev Mean Median Coecient of variation % GWP of California lb CO2-eq/MWh 19.07 403.58 400.6 4.73 GWP of Texas lb CO2-eq/MWh 97.03 1291.67 1291.25 7.51 GWP of New York lb CO2-eq/MWh 17.77 391.96 389.22 4.53 AP of California lb SO2-eq/MWh 4.77 0.46 0.18 1028.66 AP of Texas lb SO2-eq/MWh 30.31 4.06 1.58 746.23 AP of New York lb SO2-eq/MWh 4.44 0.49 0.21 905.02 HH of California lb PM 2:5-eq/MWh 0.05 0.01 0.0 961.4 HH of Texas lb PM 2:5-eq/MWh 1.72 0.17 0.06 997.87 HH of New York lb PM 2:5-eq/MWh 0.05 0.01 0.0 665.49 EA of California lb N-eq/MWh 6.81 0.65 0.25 1043.14 EA of Texas lb N-eq/MWh 16.25 2.13 0.91 764.04 EA of New York lb N-eq/MWh 6.33 0.63 0.25 1000.39 EW of California lb N-eq/MWh 1.98 0.19 0.07 1043.14 EW of Texas lb N-eq/MWh 4.73 0.62 0.26 764.04 EW of New York lb N-eq/MWh 1.84 0.18 0.07 1000.39 SA of California lb O3-eq/MWh 168.77 16.18 6.12 1043.14 SA of Texas lb O3-eq/MWh 402.88 52.73 22.55 764.04 SA of New York lb O3-eq/MWh 156.83 15.68 6.19 1000.39 Table 4: Statistics of GWP, AP, HH, EA, EW, and SA of California, Texas, and New York during 2017 3.3. The e ects of electricity generation emission factors' present variability on environmental impact quan- 497 ti cation 498 This subsection discusses the variabilities of six environmental impact categories|global warming poten- 499 tial (GWP), acidi cation potential (AP), human health (HH), eutrophication air (EA), eutrophication water 500 (EW), and smog air (SA)|based on variability in EGEFs in California, Texas, and New York in 2017. 501 The results' SO2andNOxcharacteristics for GWP, which are shown in Table 1, stood at zero. Thus, 502 CO2EGEFs drove GWP in this study. The median value of Texas's GWP (1292 [lb CO2-eq/MWh]) exceeded 503 California's GWP (401 [lb CO2-eq/MWh]) and New York's GWP (389 [lb CO2-eq/MWh]), which are shown 504 in Table 4. This nding is compatible with the higher CO2EGEFs of Texas compared to California and 505 New York, which are shown in Table 3. As we have shown, a coecient of variation (i.e., the data's standard 506 deviation divided by the data's mean) can be used to compare data sets' uncertainty when means di er. This 507 study's coecients of variation for GWP were 4.8%, 7.4%, and 4.5 % for California, Texas, and New York, 508 respectively. These values equal the coecient of variation for CO2EGEFs in Table 3 since they represent 509 the same data's coecient of variation. 510 Acidi cation potential was calculated based on SO2emissions (with a characteristic factor of 1 [kg SO2- 511 eq/kg substance]) and NOxemissions (with a characteristic factor of 0.7 [kg SO2-eq/kg substance]). The 512 median value of Texas's AP (1.58 [lb SO2-eq/MWh]) exceeded California's AP (0.18 [lb SO2-eq/MWh]) and 513 New York's AP (0.21 [lb SO2-eq/MWh]), which are shown in Table 4. This nding is compatible with 514 the higher SO2andNOxEGEFs of Texas compared to California and New York shown in Table 3. The 515 coecient of variation for AP were 1029%, 746%, and 905% for California, Texas, and New York, respectively. 516 Human health's impact was calculated based on SO2emissions (with a characteristic factor of 0.061 517 [PM 2:5-eq/kg substance]) and NOxemissions (with a characteristic factor of 0.007 [ PM 2:5-eq/kg substance]). 518 The median value of Texas's HH (0.06 [lb SO2-eq/MWh]) exceeded California's HH (0.0 [lb [ PM 2:5-eq/MWh]) 519 and New York's AP (0.0 [lb [ PM 2:5-eq/MWh]), which are shown in Table 4. This nding is compatible with 520 the higher SO2andNOxEGEFs of Texas compared to California and New York shown in Table 3. The 521 coecient of variation for HH were 767%, 1093%, and 697% for California, Texas, and New York, respectively. 522 The eutrophication of air, water, and smog formation were calculated based on NOxEGEFs, with char- 523 acteristic factors of 0.044 kg N-eq/kg substance for the eutrophication of air, 0.291 kg N-eq/kg substance 524 for the eutrophication of water, and 24.793 kg O3-eq/kg substance for the smog formation. The coecients 525 of variabilities for each state were constant across the three categories because of the constant variability 526 ofNOxEGEF for each state, which equaled 1043%, 764%, and 1000% (shown in Table 4) for California, 527 Texas, and New York, respectively. These values equal the coecient of variation for NOxEGEFs in Table 528 3 since they represent the same data's coecient of variation. 529 GWP, which represents CO2EGEFs' variability, had the lowest coecient variability among the assessed 530 environmental categories. The coecients of variability for EA, EW, and SA were constant, as NOxEGEFs' 531 variability remained the same for each state. Also, EA, EW, and SA had the highest coecient variability 532 14 among the environmental categories examined. These results show that higher variabilities are associated 533 with environmental impacts that use SO2andNOxEGEFs. 534 Figures A.17{ A.22 shows the statistical visualization of showing the changes in the minimum, maximum, 535 median, and range of the six environmental impact categories (i.e., GWP, AP, HH, EA, EW, and SA) in 536 California, Texas, and New York from 1990 to 2017. 537 4. Limitations and future work 538 This work involved the following limitations: 539 We assumed the three fossil fuel types|coal, natural gas, and petroleum|were used identically in 540 di erent states. This assumption was incorrect; di erent sub-types of coal, natural gas, and petroleum 541 are used for electricity generation. Also, fossil fuels' characteristics di er, depending on the fuels' region 542 of extraction, as data for the 50 U.S. states, categorized into these three main fossil fuel types, in the 543 EIA's \Electricity Detailed State Data from 1990 to 2017" document reveal. 544 Moreover, we neglected \wood and wood derived fuels," \other biomass," and \other" in quantifying 545 EGEFs in this study since their consumption rate data were unavailable in the \Electricity Detailed 546 State Data from 1990 to 2017" EIA document. However, \Electricity Detailed State Data from 1990 547 to 2017" EIA document on electricity emissions stated \wood and wood derived fuels" is responsible 548 for 16% of SO2emissions and 5% NOxemissions from electricity generation in the U.S. Also, \other 549 biomass" is responsible for 8% of NOxemissions from electricity generation in the country. 550 The characteristic factors of quantifying environmental impacts, shown in Table 1, are also site-speci c, 551 depending on a region of study. In this study, an average number for the three U.S. states that we 552 considered was obtained since data on site-speci c characteristics were unavailable in the U.S., to the 553 best of our knowledge. 554 CO2emission, electricity generation, and energy source consumption data were available for approxi- 555 mately 6,000 power plants throughout the U.S., which enabled a calculation of CO2EGEFs. EGEFs 556 are more concentrated and show less variability when the data derives from power plants, instead of 557 states. However, a limitation of using data from power plants is that SOxandNOxemissions are 558 unavailable in the data sets within the \Electricity emissions by plant and by region" EIA document, 559 and only CO2EGEFs could be calculated. This problem limited our estimation of SOxandNOx 560 EGEFs, as well as our calculations of the variability in environmental impacts from di erent categories 561 involving SOxandNOxEGEFs. 562 The potential topics for future work following up on the current study are as follows. 563 A consumption based method of accounting electricity generation emissions should be considered in 564 future work since the current study focused on the production side. A consumption based accounting 565 system considers the emissions from outside the system boundary (Ghaemi and Smith, 2020) and 566 considers how changes in demand a ect EGEFs. It also includes upstream (i.e., fossil fuel extraction, 567 re nery, material manufacturing, and construction) and downstream (i.e., marketing, transmission, and 568 distribution) emissions from electricity generation . 569 In the current study, variability in environmental impacts and electricity generation were limited to 570 variability in EGEFs from fossil fuels. Measurement uncertainties regarding fossil fuel consumption, 571 emissions, and electricity generation reveal more information on variability in environmental impacts 572 and electricity generation. 573 Four factors were broken down from the current study's governing equation of electricity generation, 574 using the LMDI method. Other factors could be broken down from the governing equation using 575 the LMDI method, such as sector-speci c factors, to reveal more information about how EGEFs have 576 changed in California, Texas, and New York. 577 15 5. Conclusions 578 As we have shown, the year-to-year variability in fossil fuel emission factors (EF) in the 50 U.S. states has 579 caused variations in the annual quantities of electricity generation emission factors (EGEF) at the state level. 580 Knowing the range of expected values for EGEFs enables an understanding of the decision risks associated 581 with fossil fuel EFs. The relative ranges (i.e., the ratios of the ranges and the means of the data set) for 582 CO2EGEFs were 43%, 59%, and 42% in California, Texas, and New York, respectively, during 2017. The 583 coecients of variation or relative standard deviations (i.e., the ratio of standard deviation and the mean of 584 the data set) were 4.7%, 7.4%, and 4.5% for CO2EGEFs in California, Texas, and New York, respectively, 585 in 2017. These variabilities in EGEFs have shown that using site-speci c fossil fuel EFs is necessary when 586 making important decisions using EGEFs. 587 Moreover, this study by using the background data from Energy Information Administration (EIA) has 588 shown that EGEFs changed from 1990 to 2017 in the U.S. Four elements that a ect these EGEF changes can 589 be broken down from the governing equation (Equation 3) for electricity generation: (1) the fossil fuel share 590 e ect (i.e., the share of fossil fuel to non{fossil fuel [hydro-power, biomass, renewables, and nuclear energy] 591 in electricity generation), (2) the fossil fuel mix e ect (i.e., the mix of fossil fuels consumed for electricity 592 generation), (3) the generation eciency e ect (i.e., power plants' generation eciency), and (4) the EF 593 e ect (i.e., the EFs of energy sources). California, Texas, and New York reduced their EGEFs from 1990 to 594 2017 by 100, 227, and 316 lb CO2/MWh, respectively. The most e ective element of this reduction in New 595 York was the fossil fuel mix e ect, which reduced the state's EGEFs by 198 lb CO2/MWh. In California, 596 the generation eciency e ect decreased the state's EGEFs by 60 lb CO2/MWh. In Texas, the EGEF has 597 been mitigated by 130 lb CO2/MWh because of changes in the fossil fuel share e ect. These results indicate 598 that state-speci c laws and regulations should be enacted to e ectively mitigate EGEFs since each state's 599 potential to reduce electricity generations emissions di ers. 600 Variability and uncertainty in EGEFs a ect the decision-making tools' results. One such decision-making 601 tool used in the emissions reduction eld is environmental impact assessments. EGEFs are used to calculate 602 electricity generation's environmental impact, which shows the variability in environmental impact results. In 603 this study, global warming potential showed the lowest variability among such results, with relative standard 604 deviations of 4.8%, 7.4%, and 4.5% in California, Texas, and New York, respectively, in 2017. Eutrophication 605 of air, water, and smog formation (based on NOxemissions) showed the highest variability because of EGEFs' 606 variability. herefore, calculated environmental impacts will vary signi cantly when considering SO2orNOx607 EGEFs compared with considering CO2EGEFs. As a result, decision-makings that use eutrophication of 608 air, water, and smog formation categories are unreasonable due to dealing with relatively high uncertainty 609 compared to decision-makings that use global warming potential. 610 Funding 611 This research did not receive any speci c grant from funding agencies in the public, commercial, or 612 not-for-pro t sectors. 613 CRediT authorship contribution statement 614 Zahra Ghaemi : Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Soft- 615 ware, Visualization, Writing - original draft, and Writing - review & editing. Amanda D. Smith : Concep- 616 tualization, Methodology, Project administration, Supervision, and Writing - review & editing. 617 Acknowledgements 618 We appreciate the assistance and support provided by the University of Utah Department of Facilities 619 Management. 620 16 Data Availability 621 Three data sources from the \Electricity Detailed State Data from 1990 to 2017" webpage by the U.S. 622 Energy Information Administration were used to calculate electricity generation emission factors at the U.S. 623 state level from 1990 to 2017 in this paper: 624 1. The annual data for net electricity generation (Net Generation by State by Type of Producer by Energy 625 Source (EIA-906, EIA-920, and EIA-923) excel le) 626 2. The annual data for fossil fuel consumption used for electricity generation (Fossil Fuel Consumption for 627 Electricity Generation by Year, Industry Type and State (EIA-906, EIA-920, and EIA-923) excel le) 628 3. The annual data for the electric power industry's estimated emissions ( CO2,SO2, and NOx) (U.S. 629 Electric Power Industry Estimated Emissions by State (EIA-767, EIA-906, EIA-920, and EIA-923) 630 excel le) 631