Quantification of fossil fuel CO₂ from combined CO, δ¹³CO₂ and Δ¹⁴CO₂ observations

We present a new method for partitioning observed CO₂ enhancements (CO₂xs) into fossil and biospheric fractions (C_ff and C_bio) based on measurements of CO and δ¹³CO₂, complemented by flask-based Δ¹⁴CO₂ measurements. This method additionally partitions the fossil fraction into natural gas and petroleum fractions (when coal combustion is insignificant). Although here we apply the method only to discrete flask air measurements, the advantage of this method (CO- and δ¹³CO₂-based method) is that CO₂xs partitioning can be applied at high frequency when continuous measurements of CO and δ¹³CO₂ are available. High-frequency partitioning of CO₂xs into C_ff and C_bio has already been demonstrated using continuous measurements of CO (CO-based method) and Δ¹⁴CO₂ measurements from flask air samples. We find that the uncertainty in C_ff estimated from the CO- and δ¹³CO₂-based method averages 3.2 ppm (23 % of the mean C_ff of 14.2 ppm estimated directly from Δ¹⁴CO₂), which is significantly less than the CO-based method which has an average uncertainty of 4.8 ppm (34 % of the mean C_ff). Using measurements of CO, δ¹³CO₂ and Δ¹⁴CO₂ from flask air samples at three sites in the greater Los Angeles (LA) region, we find large contributions of biogenic sources that vary by season. On a monthly average, the biogenic signal accounts for −14 to +25 % of CO₂xs with larger and positive contributions in winter and smaller and negative contributions in summer due to net respiration and net photosynthesis, respectively. Partitioning C_ff into petroleum and natural gas combustion fractions reveals that the largest contribution of natural gas combustion generally occurs in summer, which is likely related to increased electricity generation in LA power plants for air-conditioning.

1 Introduction

The world's cities account for up to 70 % of global greenhouse gas (GHG) emissions, while covering less than 2 % of the Earth's surface (IPCC, 2014). Cities around the world have started implementing mitigation strategies to reduce carbon dioxide (CO₂) emissions and collaborate with each other in organizations such as the C40 Cities Climate Leadership Group (https://www.c40.org/, last access: 25 October 2023) and the Global Covenant of Mayors for Climate & Energy (https://www.globalcovenantofmayors.org/, last access: 25 October 2023). To support urban efforts, monitoring systems are necessary to evaluate and verify reductions attributable to specific mitigation strategies (Turnbull et al., 2022).

Current understanding of anthropogenic CO₂ emissions mainly derives from methods that estimate aggregate emissions in a domain using economic statistics such as total fuel sales or activity data such as total distance traveled for on-road vehicle emissions. These “bottom-up” methods provide specific location and process information that relies on mapping the source-specific emission factors and measurements of activities (e.g., McDonald et al., 2014; Gurney et al., 2019; Gately and Hutyra, 2017; Super et al., 2020). In contrast, more recently “top-down” methods that quantify emissions from measurements of atmospheric CO₂ have been used to estimate emissions. These top-down approaches typically use either a mass balance technique where an initial estimate is not required (e.g., Mays et al., 2009; Cambaliza et al., 2014; Heimburger et al., 2017; Ahn et al., 2020) or an inverse/data assimilation approach where observations and a prior map of emissions are combined to generate a best estimate (e.g., Bréon et al., 2015; Staufer et al., 2016; Sargents et al., 2018; Turner et al., 2020; Lauvaux et al., 2016, 2020).

To estimate anthropogenic CO₂ emissions using top-down methods, it is crucial to separate the fossil fuel signals from the biogenic signals, which can vary from negative (uptake) to positive (emission) across the annual cycle. Recent analyses of urban CO₂ suggest that biogenic emissions and uptake have significant magnitudes relative to fossil fuel fluxes, especially during the growing season (Sargent et al., 2018; Vogel et al., 2019; Miller et al., 2020). Previous top-down studies have used biosphere models to estimate biogenic fluxes and have then focused on determining the balance of emissions attributable to fossil fuel combustion assuming that the biogenic emissions are known (Sargent et al., 2018; Turner et al., 2020; Lauvaux et al., 2020). However, even with recent improvements in biosphere models (Wu et al., 2021; Gourdji et al., 2022) the actual magnitude and variability of these fluxes are still not well constrained (Hardiman et al., 2017; Winbourne et al., 2022), potentially leading to unknown observational bias in the associated estimates of fossil-fuel-derived emissions.

Radiocarbon (¹⁴CO₂) provides the ability to separate biogenic and anthropogenic CO₂ fluxes and mole fractions from an observational point of view (e.g., Levin et al., 2003; Turnbull et al., 2006). Observational methods rely on the fact that fossil fuels and the resultant CO₂ produced during combustion are completely devoid of ¹⁴C (i.e., Δ¹⁴C${}_{\mathrm{ff}}=-\mathrm{1000}$ ‰ on the widely used delta scale; Stuiver and Polach, 1977). Measurements of Δ¹⁴CO₂, acquired at timescales of weeks to months allow quantification of seasonal variations in biogenic and fossil contributions to the atmospheric CO₂ mole fraction (e.g., Djuricin et al., 2010; Miller et al., 2012; Turnbull et al., 2015). ¹⁴C methods typically require air sample collection, preparation and analysis via accelerator mass spectrometry, which limits the number of measurements, although a number of promising optical methods for in situ ¹⁴CO₂ measurement at natural abundance are currently being developed (Fleisher et al., 2017; Genoud et al., 2019; McCartt and Jiang, 2022).

On the other hand, carbon monoxide (CO) is a widely used tracer that can be measured continuously in situ using high-precision optical analyzers (e.g., Vogel et al., 2010; Newman et al., 2013; Turnbull et al., 2015; Lauvaux et al., 2020). CO is often co-emitted with fossil fuel CO₂ (CO₂ff) during incomplete combustion. If the COxs:CO₂ff ratio (R_ff, where COxs is the CO enhancement above the background) is well constrained, continuous CO measurements combined with R_ff can provide an estimate of continuous CO₂ff. A few studies have applied this method to estimate fossil fuel emissions for a moment in time during an airborne measurement campaign (Graven et al., 2009; Turnbull et al., 2011). However, with this approach it is challenging to identify interannual trends because R_ff at a site may vary significantly on timescales ranging from hours to years (Levin and Karstens, 2007; Vogel et al., 2010). The CO:CO₂ emission ratio can vary by sources depending on the carbon content of the fuel and combustion conditions. Due to the impacts of atmospheric transport at a given observation site and the variability in the source combination in time and space, R_ff also varies in time and space. Additionally, CO produced from oxidation of volatile organic compounds (VOCs) can have an effect (Vimont et al., 2019).

Vardag et al. (2015) proposed dividing fossil fuel emissions further into two groups that may display less variability in the CO:CO₂ emission ratio. If one group is well constrained by CO and the other by ¹³CO₂, each group can be identified by combining CO and ¹³CO₂ observations. Vardag et al. (2015) focused on separating traffic from non-traffic emissions or biofuel emissions from the other fossil fuel emissions. However, no significant benefit of combining CO and ¹³CO₂ was found because traffic and biofuel CO₂ do not produce a distinct CO:CO₂ emission ratio or ¹³CO₂ isotopic signatures compared to the other CO₂ff source terms.

Here, we differentiate CO₂ signals from biogenic, petroleum and natural gas sources by combining CO, δ¹³CO₂ and Δ¹⁴CO₂ measurements. The combination of Δ¹⁴CO₂ and δ¹³CO₂ has been used previously to distinguish biogenic, petroleum and natural gas signals for air sampling events (Lopez et al., 2013; Djuricin et al., 2010) and at a seasonal scale (Newman et al., 2016). In contrast, the combination of CO and δ¹³CO₂, which can both be measured at high frequency, enables source partitioning at higher temporal resolution. We demonstrate the agreement between the existing Δ¹⁴CO₂ and δ¹³CO₂ and newly proposed CO and δ¹³CO₂ methods. This establishes the utility of the CO and δ¹³CO₂ method in partitioning CO₂xs into fossil fuel and biogenic components, with further partitioning of fossil fuel sources into petroleum and natural gas sources, in the megacity of Los Angeles (LA).

2 Methods

Here, we describe two methods for separating fossil fuel and biogenic components from atmospheric CO₂ measurements in the complex urban environment of the megacity of Los Angeles (LA). Section 2.2 describes our application of the method already described by Newman et al. (2016) using Δ¹⁴CO₂ and δ¹³CO₂ observations. The details of the new method utilizing CO and δ¹³CO₂ measurements are described in Sect. 2.3. Briefly, we take advantage of the fact that the combination of the CO:CO₂ emission ratio and the ¹³CO₂ isotopic signature reveals a very distinct pattern for biogenic, petroleum and natural gas sources. However, this approach requires knowledge of the CO:CO₂ emission ratio and the isotopic signature of each source. We apply isotopic signatures reported by previous studies, and CO:CO₂ emission ratios are determined for LA using measurements of CO, δ¹³CO₂ and Δ¹⁴CO₂ from flask samples. Flask measurements are described in Sect. 2.1, and the source apportionment from Δ¹⁴CO₂ and δ¹³CO₂ observations, which is used to derive CO:CO₂ emission ratios for each source, is described in Sect. 2.2.

2.1 Measurements

We use measurements from air samples collected at 14:00 local standard time at three existing Los Angeles Megacity Carbon Project sites: the University of Southern California (USC); California State University, Fullerton (FUL); and Granada Hills (GRA) (Miller et al., 2020). Air samples were collected from November 2014 to March 2016 using the National Oceanic and Atmospheric Administration (NOAA) programmable flask packages (PFPs) and programmable compressor packages (Sweeney et al., 2015). The samples were sent back to the NOAA Global Monitoring Laboratory where greenhouse gases including CO₂ as well as CO mole fractions were measured using NOAA's high-precision/high-accuracy greenhouse gas measurement system (Sweeney et al., 2015). After the measurement, residual air is extracted from PFP flasks, and CO₂ is isolated for ¹⁴C measurement using established cryogenic and mass spectrometric techniques (Lehman et al., 2013). Samples are purified, graphitized and packed into individual targets at the University of Colorado, Boulder, Institute of Arctic and Alpine Research (INSTAAR), and then sent to the University of California, Irvine, Keck Carbon Cycle Accelerator Mass Spectrometer Facility, for high-precision Δ¹⁴C measurement. 1σ measurement uncertainty is ∼1.8 ‰, equivalent to ∼ 1.2 parts per million (ppm) of recently added fossil fuel CO₂. δ¹³CO₂ in PFP samples is measured by dual-inlet isotope ratio mass spectrometry with a precision of approximately 0.02 ‰ at the INSTAAR Stable Isotope Laboratory (Vaughn et al., 2004; Sweeney et al., 2015).

Enhancement of each species is defined relative to a time-dependent background level, which is based on nighttime (02:00 local standard time) measurements made at Mount Wilson Observatory (MWO; Fig. 1) located at 1670 m above sea level. Nighttime air at MWO generally represents the relatively clean, well-mixed free troposphere since polluted LA Basin boundary layer air has typically descended back into the basin by this time. After an additional step of filtering obvious outliers corresponding to pollution events indicated by anomalously elevated concentrations, values were interpolated to the time of observations within the LA Basin by fitting curves to the screened MWO data (Fig. 2). A further analysis of associated CO measurements indicates that background reconstructed using nighttime air samples from MWO is representative of clean background air coming from either onshore or offshore (Miller et al., 2020).

Figure 1 Map of the greater Los Angeles region. The three Los Angeles Megacity Carbon Project sites are marked in cyan, and the Mount Wilson Observatory used to define background values is marked in yellow. Map data © Google Maps 2022.

Figure 2 Time series of CO₂, CO, δ¹³C and Δ¹⁴C. The black line represents background values. The dates are labeled as month/year.

2.2 Partitioning CO₂ signals using flask-based Δ¹⁴CO₂ and δ¹³CO₂ measurements

Our general approach to distinguishing CO₂ signals from biogenic, petroleum and natural gas sources using Δ¹⁴CO₂ and δ¹³CO₂ follows the procedure described by Newman et al. (2016). Following previous derivations (e.g., Turnbull et al., 2006; Miller et al., 2020), we start with the definition for CO₂ff, which is based on mass balances for the atmospherically conserved quantities Δ¹⁴C × CO₂ and CO₂:

$$\begin{array}{}\text{(1)}& C_{\mathrm{ff}}={\displaystyle \frac{C_{\mathrm{obs}}({\mathrm{\Delta }}_{\mathrm{obs}}-{\mathrm{\Delta }}_{\mathrm{bkg}})}{({\mathrm{\Delta }}_{\mathrm{ff}}-{\mathrm{\Delta }}_{\mathrm{bkg}})}}-{\displaystyle \frac{C_{\mathrm{r}}({\mathrm{\Delta }}_{\mathrm{r}}-{\mathrm{\Delta }}_{\mathrm{bkg}})}{({\mathrm{\Delta }}_{\mathrm{ff}}-{\mathrm{\Delta }}_{\mathrm{bkg}})}}.\end{array}$$

Measured CO₂ mole fractions and Δ¹⁴C values are abbreviated as C and Δ. The subscripts obs, bkg, ff and r represent observations, background, fossil fuel and respiration, respectively. Δ_ff is equal to −1000 ‰. As in the Miller et al. (2020) study focusing on LA, we estimate the value of the small respiratory term, $C_{\mathrm{r}}({\mathrm{\Delta }}_{\mathrm{r}}-{\mathrm{\Delta }}_{\mathrm{bkg}})/({\mathrm{\Delta }}_{\mathrm{ff}}-{\mathrm{\Delta }}_{\mathrm{bkg}})$, as 0.25 ppm. The overall uncertainty in C_ff for LA measurements during 2015 is approximately 1.2 ppm, which includes 100 % uncertainty assigned to the respiratory term. C_ff and C_bio (C_bio=C_xs–C_ff) are calculated for all available flask air samples during the 2014–2016 sampling period, at a frequency of approximately 3 times per week at each of the three sites.

C_ff is then separated into signals from petroleum and natural gas combustion using ¹³C:¹²C ratios (δ¹³C as defined by standard isotopic definition; Craig, 1957) measured on the same air samples. First, the flux weighted-mean δ¹³C signature of all sources located in the observation footprints (δ_src) is determined on a sample-by-sample basis using the combined mass balances for δ¹³C × CO₂ and CO₂:

$$\begin{array}{}\text{(2)}& {\mathit{\delta }}_{\mathrm{src}}={\displaystyle \frac{{\mathit{\delta }}_{\mathrm{obs}}\times C_{\mathrm{obs}}-{\mathit{\delta }}_{\mathrm{bkg}}\times C_{\mathrm{bkg}}}{C_{\mathrm{obs}}-C_{\mathrm{bkg}}}},\end{array}$$

where δ is shorthand for δ¹³CO₂. The uncertainties in C_obs, C_bkg, δ_obs and δ_bkg are 0.1 ppm, 1.5 ppm, 0.02 ‰ and 0.08 ‰, respectively. The obs uncertainties are measurement uncertainties, while the bkg uncertainties are determined as the standard deviation of the difference between the observations and their smoothed-curve representation at MWO. The median uncertainty in δ_src is 3.0 ‰ and is calculated by propagating the uncertainties listed above, including covariance between δ¹³C and δ¹³C × CO₂.

Figure 3 Monthly mean fractional contributions (f) of biosphere (green), petroleum (red) and natural gas (yellow) to CO₂xs at each site, as determined from Δ¹⁴C and δ¹³C observations (Sect. 2.2). The sum of the fractions is 1 in each month. The dates are labeled as month/year.

Figure 4 Monthly mean CO₂xs partitioned into biosphere (green), petroleum (red) and natural gas (yellow) signals, as determined from Δ¹⁴C and δ¹³C observations, at each site. The black marker indicates CO₂xs. The dates are labeled as month/year.

We combine C_ff (Eq. 1) and δ_src (Eq. 2) to determine the δ¹³C signature of fossil fuel emissions, δ_ff:

$$\begin{array}{}\text{(3)}& {\mathit{\delta }}_{\mathrm{src}}={\mathit{\delta }}_{\mathrm{ff}}\times f_{\mathrm{ff}}+{\mathit{\delta }}_{\mathrm{bio}}\times \left(\mathrm{1}-f_{\mathrm{ff}}\right).\end{array}$$

Rearranging yields

$$\begin{array}{}\text{(4)}& {\mathit{\delta }}_{\mathrm{ff}}={\displaystyle \frac{{\mathit{\delta }}_{\mathrm{src}}-{\mathit{\delta }}_{\mathrm{bio}}\times (\mathrm{1}-f_{\mathrm{ff}})}{f_{\mathrm{ff}}}},\end{array}$$

where f is the fraction. Following Newman et al. (2016), we take the isotopic signature of biospheric CO₂ fluxes (δ_bio) to be $-\mathrm{26.6}\pm \mathrm{0.5}$ ‰ based on the analysis of Northern Hemisphere mid-latitude CO₂ and δ¹³C observations (Bakwin et al., 1998b), which reflects the predominance of C₃ photosynthesis. However, because LA turfgrasses, which could account for a significant fraction of urban CO₂ fluxes (Miller, 2020), are often C₄ species (e.g., Bermuda and Buffalo grasses), we also conduct tests using ${\mathit{\delta }}_{\mathrm{bio}}=-\mathrm{20}$ ‰, representing a C3–C4 mix (Fig. S1). When we change δ_bio from −26.6 ‰ to −20 ‰, f_pet decreases by 0.04, and f_ng increases by 0.05, which is smaller than the median uncertainty in f_pet and f_ng, which is 0.17 and 0.16, respectively. f_ff is the fraction of C_ff in C_xs, i.e., $C_{\mathrm{ff}}/C_{\mathrm{xs}}$, and $\mathrm{1}-f_{\mathrm{ff}}=f_{\mathrm{bio}}$. Lastly, the proportions of C_ff emitted by petroleum (pet) and natural gas (ng) combustion, f_pet and f_ng, are calculated from the values of δ_ff:

$$\begin{array}{}\text{(5)}& {\displaystyle }{\mathit{\delta }}_{\mathrm{ff}}={\mathit{\delta }}_{\mathrm{pet}}\times f_{\mathrm{pet}/\mathrm{ff}}+{\mathit{\delta }}_{\mathrm{ng}}\times \left(\mathrm{1}-f_{\mathrm{pet}/\mathrm{ff}}\right),\text{(6)}& {\displaystyle }{f}_{\mathrm{pet}/\mathrm{ff}}={\displaystyle \frac{{\mathit{\delta }}_{\mathrm{ff}}-{\mathit{\delta }}_{\mathrm{ng}}}{{\mathit{\delta }}_{\mathrm{pet}}-{\mathit{\delta }}_{\mathrm{ng}}}}.\end{array}$$

We use values of $-\mathrm{25.5}\pm \mathrm{0.5}$ ‰ for δ_pet (Newman et al., 2016; measurements in 2014) and $-\mathrm{40.2}\pm \mathrm{0.5}$ ‰ for δ_ng (Newman et al., 2008); $f_{\mathrm{pet}}=f_{\mathrm{ff}}\times f_{\mathrm{pet}/\mathrm{ff}}$, and $f_{\mathrm{ng}}=f_{\mathrm{ff}}\times f_{\mathrm{ng}/\mathrm{ff}}$, where $f_{\mathrm{ng}/\mathrm{ff}}=\mathrm{1}-f_{\mathrm{pet}/\mathrm{ff}}$. We use temporally constant δ¹³C signatures for petroleum, natural gas and biogenic sources (and sinks), although with additional processed-based information, this assumption could be relaxed in the future. Note that although pet, ng and bio signatures are fixed, both δ_src and δ_ff vary with time, meaning that f_bio, f_pet and f_ng all vary at the frequency of the air sampling. Samples with calculated $f_{\mathrm{pet}/\mathrm{ff}}$ values outside the range of 0 and 1, corresponding to small CO₂xs and large uncertainty in δ_src, are excluded from the analysis.

Figure 5 Monthly variations in $\mathrm{COxs}/{\mathrm{CO}}_{\mathrm{2}}\mathrm{xs}$ (R_src) and $\mathrm{COxs}/{\mathrm{CO}}_{\mathrm{2}}\mathrm{ff}$ (R_ff) at each site. $\mathrm{COxs}/{\mathrm{CO}}_{\mathrm{2}}\mathrm{ff}$ is calculated using ¹⁴C observations. The dates are labeled as month/year.

2.3 Partitioning CO₂ signals using CO and δ¹³CO₂ measurements

Although we can determine f_bio, f_pet and f_ng at the frequency of discrete flask sampling events using the method described in Sect. 2.2, here we describe how comparable CO₂xs fractions can in theory be determined at high frequency using continuous measurements of CO and δ¹³CO₂. To evaluate the method, we compute the relative contributions of biogenic, petroleum and natural gas sources to CO₂xs using flask air CO and δ¹³CO₂ measurements and compare these to values obtained using the Δ¹⁴CO₂-guided approach for the same samples by applying the following system of equations:

$$\begin{array}{}\text{(7)}& {\displaystyle }{R}_{\mathrm{src}}=R_{\mathrm{bio}}\times f_{\mathrm{bio}}+R_{\mathrm{pet}}\times f_{\mathrm{pet}}+R_{\mathrm{ng}}\times f_{\mathrm{ng}},\text{(8)}& {\displaystyle }{\mathit{\delta }}_{\mathrm{src}}={\mathit{\delta }}_{\mathrm{bio}}\times f_{\mathrm{bio}}+{\mathit{\delta }}_{\mathrm{pet}}\times f_{\mathrm{pet}}+{\mathit{\delta }}_{\mathrm{ng}}\times f_{\mathrm{ng}},\text{(9)}& {\displaystyle }\mathrm{1}=f_{\mathrm{bio}}+f_{\mathrm{pet}}+f_{\mathrm{ng}}.\end{array}$$

R_src represents the $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio of the total source, which is the observed $\mathrm{COxs}/{\mathrm{CO}}_{\mathrm{2}}\mathrm{xs}$ ratio, and we use R to refer to the $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ emission ratios of individual CO₂xs components (bio, pet and ng). For now, we assume that R of each source is constant over a year-long period and over the greater LA region (discussed in Sect. 3.2); especially with high-frequency CO and δ¹³CO₂ measurements, this assumption could easily be relaxed (discussed in Sect. 3.3).

R values and δ¹³C signatures for bio, pet and ng are needed to solve Eqs. (7)–(9). δ¹³C signatures are specified in Sect. 2.2; R values are obtained via multiple linear regression of Eq. (7) using observed R_src and f values determined using Δ¹⁴C and δ¹³C of CO₂ measurements as described in Sect. 2.2. Then we solve Eqs. (7)–(9) for new f values, f^′. This new CO₂xs partitioning (i.e., $f_{\mathrm{bio}}^{\prime }$, $f_{\mathrm{pet}}^{\prime }$, $f_{\mathrm{ng}}^{\prime })$ based on CO and δ¹³CO₂ observations is used to calculate new values of C_ff and C_bio (i.e., $C_{\mathrm{ff}}^{\prime }$ and $C_{\mathrm{bio}}^{\prime })$.

3 Results and discussion

3.1 Contribution of biogenic, petroleum and natural gas sources to CO₂ excess

We calculated the fractional contribution of petroleum, natural gas and biospheric fluxes to total CO₂xs each month from April 2015 to March 2016 using Δ¹⁴CO₂ and δ¹³CO₂ observations recorded at FUL, USC and GRA. The results are given in Table S1 and presented in Fig. 3. Figure 4 presents the results in terms of the relative CO₂xs contribution from each source at each site. We observe seasonal variation in CO₂xs from each source. Fossil fuel is the dominant CO₂ emissions source at each site, which agrees with the findings of Newman et al. (2016) and Miller et al. (2020). Annually averaged across all three sites, biogenic emissions account for 6 % of CO₂xs. Biogenic emissions are larger and positive in winter and smaller and negative in summer, indicating winter respiration and uptake in summertime, generally consistent with the results of Miller et al. (2020). Note that in this study, we do not partition C_bio into an urban biosphere component and other components. Other components include the oxidation of biogenic carbon including ethanol added to gasoline, and human and other animal food and waste (which can only be positive and are unlikely to vary much seasonally). If, as in Miller et al. (2020), we accounted for the always positive ethanol, food and waste signals, we would likely observe similarly large seasonal drawdown associated with urban vegetation.

Table 1 Bottom-up CO₂ emission, CO emission and R ($\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio) estimates for each source sector and fuel type for the LA Basin based on the Vulcan 3.0 and the US Environmental Protection Agency (EPA) National Emission Inventory for the 2011 (NEI 2011) product. NEI 2011 is scaled by the emissions with a fuel consumption dataset from the US Energy Information Administration (EIA) State Energy Data System (SEDS) to estimate 2015 CO emissions.

Table 2 $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratios (R) and δ¹³C signatures used to determine the relative contribution of biogenic, petroleum and natural gas sources.

^a R calculated from Table 1. These values are not used for CO₂xs partitioning and are for reference only.
^b R calculated from CO, δ¹³CO₂ and Δ¹⁴CO₂ flask observations. These values are used in this study.
^c δ¹³C from previous studies (Bakwin et al., 1998a; Newman et al., 2008).

We also observe spatial differences: the USC site exhibits a smaller contribution of the biosphere (3 % of annual average CO₂ excess) compared to FUL and GRA (9 % and 5 % of total CO₂ excess, respectively). However, these modest annual average biospheric contributions mask significant seasonal activity. On a monthly basis, maximum positive biogenic contribution is observed in November at 25 %, 26 % and 22 % at USC, FUL and GRA (percentage of total CO₂ excess, respectively). And the maximum negative contribution, driven by net photosynthesis, is observed in July with values of −22 %, −13 % and −12 % at USC, FUL and GRA (percentage of total CO₂ excess, respectively).

The network average C_ff is 11.0 ± 14.5 ppm in winter (November–February; median and standard deviation) and 12.2 ± 6.6 ppm in summer (May–August). No significant difference is observed in winter and summer C_ff. This corresponds to the seasonality in Hestia-LA emissions, which indicates C_ff inputs are only 3 % higher in winter. High variability observed in wintertime C_ff agrees with Miller et al. (2020), which is likely caused by increased temperature inversion trapping as the cold ground surface in winter cools the air layer right above the ground. While Hestia-LA estimated the relative contribution of petroleum and natural gas to fossil fuel emissions as 75 % and 25 %, we observe a lower contribution of petroleum, 67 %, and a larger contribution of natural gas, 33 %. Furthermore, the top-down seasonality of petroleum and natural gas (Fig. 4), which as fractions of C_ff should be largely independent of mixing, is clearly evident. The proportions of natural gas in fossil fuel signals are 40 % and 36 % in summer and 34 % and 30% in winter at FUL and USC (Fig. 3). The increase in the natural gas contribution observed in summer can be explained by the increase in natural-gas-generated electricity in LA power plants to provide for air-conditioning in summer (Newman et al., 2016; He et al., 2019) as well as the air dominantly blowing from the southwest during summer. GRA, located northwest of USC by ∼ 35 km without an electricity generation facility nearby, shows the opposite pattern (24 % in summer and 40 % in winter). This suggests the local influence of increased natural gas usage for heating in the winter.

Figure 6 Comparison of f_ff and $f_{\mathrm{ff}}^{\prime }$ (a) and C_ff and $C_{\mathrm{ff}}^{\prime }$ (b). The black lines represent 1:1 relationships, and different colors indicate different sites.

Figure 7 Uncertainty in $C_{\mathrm{ff}}^{\prime }$ for varying temporal resolution of R (N weeks). R is determined for each data point solving Eq. (7) using CO, ¹³CO₂ and ¹⁴CO₂ observations within a moving window of 2N weeks. For the CO-based method, R_ff is smoothed using a 2N-week moving window.

3.2 CO:CO₂ emission ratio (R) values of biogenic, petroleum and natural gas sources

Monthly, site-based R_src varies between 5.5–11.4 ppb ppm⁻¹ (Fig. 5), with a mean and standard deviation of 8.2 ± 1.6 ppb ppm⁻¹ (relative SD = 19 %). Greater variability is seen in R_ff (lower panel), with a mean and SD of 9.6 ± 2.1 ppm (relative SD = 22 %). To understand and predict the variation in R_ff, we further divide the fossil fuel emissions into petroleum and natural gas emissions. Applying the calculated f values from Δ¹⁴CO₂ and δ¹³CO₂ observations (Sect. 2.2., Fig. 3), we solve Eq. (7) for each source's $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ emission ratio, R (Table 2). Note that we exclude negative flask-based values of COxs (and corresponding R_src values) and CO₂ff (and corresponding f_ff values) as non-physical. Likewise, positive δ_src values and $f_{\mathrm{pet}/\mathrm{ff}}$ values (and corresponding f_pet and f_ng values) outside the range of 0–1 are also excluded. A bootstrapping method is used to calculate the mean and uncertainty of possible $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratios. The $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratios of petroleum (R_pet) and natural gas (R_ng) combustion emissions are 12.2 ± 0.6 ppb ppm⁻¹ and 2.3 ± 1.2 ppb ppm⁻¹, respectively. As discussed above, the proportion of natural gas in fossil fuel emissions is bigger in summer, resulting in smaller R_ff in summer at FUL and USC. We find the value of 1.8 ± 0.8 ppb ppm⁻¹ for R_bio, which is non-zero because biofuel (mainly corn-based ethanol) in the gasoline in California with a large $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio signal is included in the biogenic sources, while respiratory $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratios approach 0. A larger contribution of the biosphere with a low $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio in winter offsets the large R_ff, lowering the variability in R_src at each site.

We compare our model-determined $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratios of each source (Table 2) to bottom-up inventory-based estimates (Table 1). $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratios of each source constrained from our model and the observational data approach agree well with the bottom-up inventory-based estimates. Sources contributing a high percentage of CO₂ emissions strongly influence the total $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio. The $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio of petroleum combustion is greatly affected by on-road emissions and industrial emissions (contributing 60 % and 28 % of total petroleum CO₂ emissions). Natural gas is mostly dominated by non-mobile emissions (electricity production, residential, commercial and industrial, sequentially), resulting in a low $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio.

3.3 Estimation of CO₂ff based on CO and δ¹³CO₂ observations

Table 2 shows the $\mathrm{CO}/{\mathrm{CO}}_{\mathrm{2}}$ ratio and δ¹³C signature of each source. The combination of the R and δ signals reveals a distinct pattern for each source: the biosphere has low near-zero R, petroleum has high R and natural gas has low R. Petroleum and biosphere CO₂ have similar δ values, whereas natural gas has a very low δ. By substituting these values into Eqs. (7)–(9), f^′ values are calculated, and then we calculate $C_{\mathrm{ff}}^{\prime }$ by multiplying the sum of $f_{\mathrm{pet}}^{\prime }$ and $f_{\mathrm{ng}}^{\prime }$ by CO₂xs measured every few days. We compare $f_{\mathrm{ff}}^{\prime }$ and $C_{\mathrm{ff}}^{\prime }$ to f_ff and C_ff (determined using ¹⁴C observations) in Fig. 6. The assessment for each source is shown in Figs. S2 and S3. The R² values are 0.63 and 0.90 for $f_{\mathrm{ff}}^{\prime }$ and $C_{\mathrm{ff}}^{\prime }$, respectively.

If R values are allowed to vary in time, it is likely to improve the precision of the method. We calculate the uncertainty in $C_{\mathrm{ff}}^{\prime }$ for varying temporal resolutions of R (solid black line in Fig. 7). We find that the uncertainty increases when the size of the window increases from 1 week to 10 weeks; in other words, allowing temporal variation in R improves the precision of the method. However, the uncertainty decreases slightly beyond the 10-week window. This is likely caused by the reduction in the error of R values (not shown) as the number of observations used to find R (by solving Eq. 7) increases. In summary, the ideal flask sampling frequency for this method would be higher than every 2 weeks. In cases where this is impossible, it is better to assume constant R values.

The uncertainty in $C_{\mathrm{ff}}^{\prime }$ estimated using the CO-based method is also shown in Fig. 7 (dashed black line). The CO-based method also provides improved precision of the method when flask sampling is available at higher frequency. However, the CO- and δ¹³CO₂-based method shows greater confidence than the CO-based method for the whole range of adjusted temporal resolution in R. When using constant R values (temporal resolution of 50 weeks), the uncertainty is 3.2 ppm (the 1σ standard deviation of differences between C_ff and $C_{\mathrm{ff}}^{\prime })$ for the CO- and δ¹³CO₂-based method, while it is 4.8 ppm for the CO-based method. This improvement is likely associated with the additional information provided by δ¹³CO₂ that constrains the effective R_ff and further separates fossil fuel sources into sub-categories (petroleum and natural gas sources).

4 Conclusions

We present a CO- and δ¹³CO₂-based method to estimate CO₂ff that is based on flask-based Δ¹⁴CO₂ measurements. We applied the method to measurements from flask samples collected in the LA Basin every few days in the afternoon for more than 1 year (2015–2016). The proposed method was assessed by comparing it to a more traditional Δ¹⁴CO₂-based method. The CO and δ¹³CO₂ approach can be applied to continuous measurements of CO₂, CO and δ¹³CO₂, which can provide CO₂ff estimates at higher temporal resolution and with greater accuracy than previously applied CO-based methods.

We analyzed three locations in the megacity of Los Angeles, partitioning observed CO₂ enhancements (CO₂xs) into biogenic, petroleum and natural gas sources. We observed a substantial biogenic signal that varies from −14 % to +25 % of CO₂xs over the course of the year, with positive contributions in winter and negative contributions in summer due to net respiration and net photosynthesis, respectively. Furthermore, partitioning CO₂ff into petroleum and natural gas combustion fractions revealed that natural gas combustion has the largest contribution in summer, potentially due to an increase in electricity generation at LA power plants for air-conditioning.