Estimation of Atmospheric Fossil Fuel CO₂ Traced by Δ¹⁴C: Current Status and Outlook

Abstract

Fossil fuel carbon dioxide (FFCO₂) is a major source of atmospheric greenhouse gases that result in global climate change. Quantification of the atmospheric concentrations and emissions of FFCO₂ is of vital importance to understand its environmental process and to formulate and evaluate the efficiency of carbon emission reduction strategies. Focusing on this topic, we summarized the state-of-the-art method to trace FFCO₂ using radiocarbon (¹⁴C), and reviewed the ¹⁴CO₂ measurements and the calculated FFCO₂ concentrations conducted in the last two decades. With the mapped-out spatial distribution of ¹⁴CO₂ values, the typical regional distribution patterns and their driving factors are discussed. The global distribution of FFCO₂ concentrations is also presented, and the datasets are far fewer than ¹⁴CO₂ measurements. With the combination of ¹⁴C measurements and atmospheric transport models, the FFCO₂ concentration and its cross-regional transport can be well interpreted. Recent progress in inverse methods can further constrain emission inventories well, providing an independent verification method for emission control strategies. This article reviewed the latest developments in the estimation of FFCO₂ and discussed the urgent requirements for the control of FFCO₂ according to the current situation of climate change.

1. Introduction

Carbon dioxide (CO₂), the most important greenhouse gas, is a significant driver of global warming. In 2019, the annual average concentration of CO₂ reached 410 ppm, which was higher than any time in at least 2 million years [1]. The observed increase in CO₂ concentrations since the beginning of the industrial era is unequivocally caused by human activities, among which the combustion of fossil fuels is responsible for most of the total anthropogenic CO₂ emissions. Global warming has caused increases in the global temperature of the surface and upper ocean, increases in precipitation and sea level, weather, and climate extremes, and decreases in glaciers and sea ice [2,3,4,5]. Besides CO₂, fossil fuel combustion is also a primary contributor to air pollutants [6]. Thus, slowing down the increase in fossil fuel CO₂ (FFCO₂) concentration is of vital importance. According to the Paris Agreement and the sixth assessment report of IPCC (Intergovernmental Panel on Climate Change), CO₂ emissions need to be net negative to hold the global surface temperature lower than 1.5 °C or 2 °C at the end of this century (very low and low greenhouse gas emission scenarios, according to IPCC, 2021). This means that the anthropogenic removal of CO₂ exceed anthropogenic emissions. Under these circumstances, identifying the contribution of FFCO₂ to total atmospheric CO₂, as well as its atmospheric process interpretation and emission estimation, is a fundamental work for studies on its climatic and environmental impacts and on the evaluation of mitigation actions.

Multiple tracers that co-emitted with CO₂ have been used to quantify FFCO₂, including carbon monoxide (CO), sulfur hexafluoride (SF₆), tetrachloroethylene (C₂Cl₄) and even air pollutants, based on the ratio of each tracer to CO₂ [7,8,9,10,11,12,13,14]. However, there are large uncertainties due to the non-fossil emissions of the tracers [15]. Radiocarbon (¹⁴C), a widely used dating method in archaeology, geosciences, etc. [16], is a direct tracer and a promising method to differentiate the emissions of fossil fuel and non-fossil fuel from atmospheric carbon. The abundances of three naturally occurring carbon isotopes ¹²C, ¹³C and ¹⁴C are 98.89%, 1.11%, and ~10⁻¹⁰%, respectively [17]. The radiocarbon content of CO₂ is expressed as Δ¹⁴C or Δ¹⁴CO₂ [18,19]:

$$\mathrm{\Delta }{}_{}{}^{14}\mathrm{C}=\left[\frac{{\left({}_{}{}^{14}\mathrm{C}/{}_{}{}^{12}\mathrm{C}\right)}_{\mathrm{SN}}}{{\left({}_{}{}^{14}\mathrm{C}/{}_{}{}^{12}\mathrm{C}\right)}_{\mathrm{ABS}}}-1\right]\times 1000‰.$$

(1)

(¹⁴C/¹²C)_SN is the ¹⁴C to ¹²C ratio of the sample, and (¹⁴C/¹²C)_ABS is related to the commonly used primary measurement standard Oxalic Acid I. Radiocarbon is cosmogenic, and has a radioactive half-life of 5730 ± 40 years [20]. Thus, there are no ¹⁴C in fossil fuels because they are all depleted during long-term radioactive decay. Since fossil fuel CO₂ contains no ¹⁴C whereas CO₂ from other sources has similar ¹⁴C concentrations with the ambient air, the release of fossil fuel CO₂ will cause a decrease in the ¹⁴C/¹²C ratio in the atmosphere. This was first discovered by Hans Suess [21], and is called the “Suess effect”. With industrial development, atmospheric Δ¹⁴CO₂ decreased by 25‰ between 1890 and 1950 [22]. Then comes the nuclear testing period between the 1950s and the early 1960s, during which large-scale detonations of nuclear bombs produced ¹⁴C atoms in the Northern Hemisphere. Atmospheric Δ¹⁴CO₂ in the Northern Hemisphere increased swiftly and reached a peak value of nearly 1000‰ in 1963, and then decreased after the Limited Nuclear Test Ban Treaty [23,24]. In addition to those mentioned above, other principal influence factors on Δ¹⁴CO₂, include interhemispheric transport, ocean circulation, nuclear power plants and terrestrial biosphere, will be discussed later.

In this review, we focus on the newly added FFCO₂ traced by ¹⁴C, mainly present progress in the 21st century. We first present the commonly used method of Δ¹⁴CO₂ sampling and measuring, as well as the basic theory of FFCO₂ calculation (Section 2). Then, we summarize the atmospheric Δ¹⁴CO₂ trend in several representative background sites, which is essential to the calculation of FFCO₂ (Section 3). In Section 4, we reviewed the measurements of Δ¹⁴CO₂ and the calculated FFCO₂ concentrations globally and present the spatial patterns and temporal variations. The recent progress of the combination of ¹⁴C measurements and atmospheric transport models to interpret FFCO₂ concentration and its cross-regional transport, and to estimate the emissions of FFCO₂, are also reviewed.

2. The Basis of Tracing Fossil Fuel CO₂ Using ¹⁴C

2.1. The Theory of Quantifying Fossil Fuel CO₂ Using ¹⁴C

Observed CO₂ mole fraction (or concentration) is thought to be a mixing of many components, mainly including atmospheric background CO₂, fossil fuel CO₂, biospheric CO₂ and oceanic CO₂. The most commonly used method to constrain recently added FFCO₂ in the atmosphere with ¹⁴C is called the pseudo-Lagrangian method [25,26,27], in which a parcel of air with an initial CO₂ mixing ratio (CO_2bg) and Δ¹⁴CO₂ value (Δ_bg) moves across a polluted region, and then CO₂ mixing ratio and Δ¹⁴CO₂ value are modified to CO_2obs and Δ_obs by the addition of FFCO₂ and other sources or sinks of CO₂. If combining other sources (and sinks) together, the mixing ratio and the Δ¹⁴CO₂ value could be written as CO_2other and Δ_other. Two balance equations for CO₂ mixing ratio and Δ¹⁴C can be formulated as below.

$${\mathrm{CO}}_{2\mathrm{obs}}={\mathrm{CO}}_{2\mathrm{bg}}+{\mathrm{CO}}_{2\mathrm{ff}}+{\mathrm{CO}}_{2\mathrm{other}}$$

(2)

$${\mathrm{\Delta }}_{\mathrm{obs}}{\mathrm{CO}}_{2\mathrm{obs}}={\mathrm{\Delta }}_{\mathrm{bg}}{\mathrm{CO}}_{2\mathrm{bg}}+{\mathrm{\Delta }}_{\mathrm{ff}}{\mathrm{CO}}_{2\mathrm{ff}}+{\mathrm{\Delta }}_{\mathrm{other}}{\mathrm{CO}}_{2\mathrm{other}}$$

(3)

By combining Equations (2) and (3), CO_2ff can be calculated as:

$${\mathrm{CO}}_{2\mathrm{ff}}=\frac{{\mathrm{CO}}_{2\mathrm{obs}}\left({\mathrm{\Delta }}_{\mathrm{obs}}-{\mathrm{\Delta }}_{\mathrm{bg}}\right)}{{\mathrm{\Delta }}_{\mathrm{ff}}-{\mathrm{\Delta }}_{\mathrm{bg}}}-\frac{{\mathrm{CO}}_{2\mathrm{other}}\left({\mathrm{\Delta }}_{\mathrm{other}}-{\mathrm{\Delta }}_{\mathrm{bg}}\right)}{{\mathrm{\Delta }}_{\mathrm{ff}}-{\mathrm{\Delta }}_{\mathrm{bg}}}.$$

(4)

CO_2obs, Δ_obs are measured in collected samples at interested sites. Δ_bg is measured in samples from background sites in general, while free tropospheric measurements can also act as Δ_bg, too [13]. Δ_ff is known to be −1000‰ since CO_2ff is ¹⁴C-free.

The second term of Equation (4) is bias due to the effect of the others:

$$\mathsf{\beta }=\frac{{\mathrm{CO}}_{2\mathrm{other}}\left({\mathrm{\Delta }}_{\mathrm{other}}-{\mathrm{\Delta }}_{\mathrm{bg}}\right)}{{\mathrm{\Delta }}_{\mathrm{ff}}-{\mathrm{\Delta }}_{\mathrm{bg}}}.$$

(5)

some researchers assume β to be zero, which means that all other sources have the same Δ¹⁴C compared to those of the background atmosphere, Δ_other = Δ_bg [26]. The main contributor to uncertainties in β would be heterotrophic respiration, which has large ¹⁴C disequilibrium. The ignorance of β would cause a systematic underestimation of CO_2ff, up to 0.5 ppm in summer and 0.2 ppm in winter [13,27]. There are two other factors that influence atmospheric Δ¹⁴CO₂, air-sea exchange in the oceans, and stratosphere-troposphere transport [28]. However, these exchanges are assumed to affect the background and observed samples equally; thus, normally, they will not be counted in the calculation of FFCO₂.

2.2. Air Sampling and Measurement

Atmospheric Δ¹⁴CO₂ can be measured with direct air sampling. Whole air samples are normally collected using flasks or bags. Short-period and integrated samples can be collected by pump and acid solution, respectively. CO₂ samples can be collected by static absorption using CO₂-free sodium hydroxide (NaOH) or barium hydroxide (BaOH) solutions in flasks [25,29,30]. The primary collection method is the static absorption of CO₂ using CO₂-free sodium hydroxide (NaOH) or barium hydroxide (BaOH) solutions in discrete glass flasks [25,29]. The flasks are exposed to air for collection of integrated samples. Besides ground sites, tall towers, aircrafts, balloons, and even kites are all effective platforms to collect CO₂ samples [13,31,32,33,34].

Air samples reflect near real-time atmospheric Δ¹⁴CO₂, can be used to characterize the FFCO₂ temporal variations with high resolution effectively. However, the representativeness of the air samples is limited to those of the sampling region and period, while little information (spatial and temporal distribution) is known beyond that. In addition, the sample collecting process and/or the site maintenance is labor and cost intensive. Direct sampling of air is not the only way to analyze atmospheric Δ¹⁴CO₂. Plants fix CO₂ from the atmosphere via photosynthesis, offering a unique complementary analysis method.

For plants, their carbon isotopic composition can be used to reflect the mean atmosphere Δ¹⁴CO₂ isotopic composition of their growing period. By collecting plant samples in different regions and analyzing ¹⁴C, FFCO₂ spatial distribution on a large scale can be mapped out. Compared to air samples, collecting plant materials is more convenient and relatively cheap. Tree rings and annual leaves (grasses) are two main types used to reveal the spatiotemporal distribution of FFCO₂ [30,35,36,37,38,39,40]. Each plant species may have its own advantages in addition to those illustrated above. Maize is grown in many countries, so it is convenient to map out the large-scale spatial distribution of fossil fuel influences using corn leaves. Gingko is a perennial and deciduous tree that is widely planted in East Asian countries, urban areas, and rural areas. Thus, it is feasible to separate samples of clean sites from samples of polluted sites. Wine ethanol is a unique plant material that can represent previous sampling years, since the harvest year and region are all written on the label of the wine bottle. Tree rings, a unique plant material, help in the reconstruction of annual atmospheric Δ¹⁴CO₂ for decades or hundreds of years. In practice, however, the sampling of tree rings may be more difficult than that of annual plants since it is difficult to separate one annual ring from the others.

Comparisons of Δ¹⁴CO₂ and/or FFCO₂ between plant materials and air samples show nearly consistent results [30,41,42,43], which verifies the usage of plant materials. Xiong et al. [44] found a significant difference in Δ¹⁴CO₂ between respired CO₂ and bulk organic matter from 21 plant species, suggesting that bias associated with dark respiration should be considered when use ¹⁴C in plants to quantify atmospheric FFCO₂. It should be noted that biomass accumulated by plants only represents daytime Δ¹⁴CO₂ (when photosynthesis occurs), and the sampling should be well planned for different plant species considering their growing period and local climate.

Before the analysis of ¹⁴C, the preparations of air samples included extracting the CO₂ (purification), and the reduction of CO₂ to graphite. The extraction of CO₂ is to remove water cryogenically, freeze CO₂ completely together with N₂O (non-interfering), and without freeze O₂ or CH₄ [13,45]. Graphite is produced by adding hydrogen gas to CO₂ over an iron catalyst [46,47]. The atom counting of each graphite sample is then performed by an accelerator mass spectrometer (AMS). The preparation of annual leaves is a little different from air samples: plant samples need to (1) be cleaned by pure water and then dried, (2) be combusted to CO₂ and then reduced to graphite [35].

Direct atom-counting of ¹⁴C using AMS is a great progress of ¹⁴C analysis methods. Before that, the conventional methods were decay counting, solid carbon using a Geiger–Muller counter, and liquid scintillation counting [48]. The sensitivity was improved around 10⁶ times by AMS over the decay counting methods [49]. With the attempts to reduce sample size and to increase precision, the detection limits have been reduced to ~5 µg of carbon [50,51], and the reported precisions have reached 1‰ [17].

3. Atmospheric Δ¹⁴CO₂ Trend in Background Sites

To characterize the newly added atmospheric FFCO₂, it is necessary to first study the Δ¹⁴CO₂ variations at background sites. Background sites are located in remote areas (high mountain, coastal area, etc.), rarely influenced by local pollution. When analyzing Δ¹⁴CO₂ values from certain sites to deduce the contribution of local or regional fossil fuels, Δ¹⁴CO₂ measured at background sites helps separate it from continental trends. In this study, we summarize the background Δ¹⁴CO₂ measurements in the last two decades from six representative background sites, including Jungfraujoch and Schauinsland (Europe), Niwot Ridge and La Jolla (North America), Waliguan (Asia), and Wellington (Oceania) (Figure 1).

In Europe, Jungfraujoch (JFJ) and Schauinsland (SIL) are the two most representative background sites. Jungfraujoch is located in the Swiss Alps at an elevation of 3450 m a.s.l. and mostly samples air from the free troposphere over [59]. Schauinsland is in Black Forest, Germany, with an elevation of 1205 m a.s.l. Schauinsland normally samples free tropospheric air during the night but is influenced by boundary layer air during the day [60]. The two stations all use 2-week integrated CO₂ samples collected by NaOH solution absorption. Levin et al. [53] found Δ¹⁴CO₂ in both sites showed a steady decreasing trend, about 6‰ per year at the beginning of the 21st century and 3‰ per year on average in 2009–2012. The seasonal features of Δ¹⁴CO₂, they are similar for nearly all the background sites, with maxima recorded during summer/autumn and minima during winter/spring.

Niwot Ridge (NWR), Colorado, USA, has a high elevation (3475 m a.s.l.) continental site, can be used as a proxy for North American free tropospheric air [56]. The measurement of Δ¹⁴CO₂ began in 2003 using whole air samples. According to Turnbull et al. [56], Δ¹⁴CO₂ at NWR decreased by 5.7‰ per year from 2004 to 2006, with a seasonal amplitude of 3–5‰. Lehman et al. [55] extend the dataset to 2011. Measurement in La Jolla, California, is conducted at the Scripps Pier, using whole air samples when meteorological conditions are favorable for collecting clean marine air [54]. The monthly samples show a decreasing trend of 5 ± 0.2‰ per year from 2001 to 2007. The decreasing trends in North American background sites are similar to the two European stations. NWR appears to be a reasonable choice of background air for Northern Hemisphere midlatitude and has been used as background CO₂ and Δ¹⁴CO₂ to quantify FFCO₂ [27,58].

Compared to Europe and North America, the measurements of Δ¹⁴CO₂ in Asian sites are not continuous. Waliguan (WLG) Global Atmosphere Watch (GAW) station, located on top of Mt. Waliguan (3816 m a.s.l.), the northeast part of the Qinghai-Tibetan Plateau, represents the background air for the Eurasian continent. Since Δ¹⁴CO₂ is not measured conventionally on this site, there is only a small amount of data [57,58]. Δ¹⁴CO₂ values at WLG during 2004/2005 are close to those measured at NWR [58]. Even though the values of WLG in 2015 are lower than the other background sites in previous years, they may be similar considering the annual trend at other sites. The observations at some regional background sites in China are also shown in Figure 1, all collected during a short period and mostly lower than the values in the WLG [9].

The world’s longest direct record of atmospheric Δ¹⁴CO₂ was begun at Wellington, New Zealand, in 1954 [52,61]. The sampling sites in Wellington are located in the coastal areas of two islands. Through decades of measurement, the collection method and measurement method have changed several times (details in [52]). In the 21st century, Δ¹⁴CO₂ in Wellington is consistently higher than in Northern Hemispheric sites, as shown in Figure 1. Based on seven global stations, Graven et al. [28] found that the mean Δ¹⁴CO₂ in the Northern Hemisphere was 5‰ lower than that in the Southern Hemisphere over 2005–2007. The interhemispheric exchange time is estimated to be 1.4 years [56,62]. Many researchers have interpreted these contributions to the interhemispheric gradient [24,28,52]. The major cause includes the dilution by ¹⁴C-free fossil fuel emissions in the north, and the weakening of ¹⁴C-depleted ocean upwelling in the south. The oceans are the largest reservoir of carbon, and the principal natural drivers that are responsible for atmospheric Δ¹⁴CO₂. Air-sea ¹⁴C flux is greatly influenced by ocean circulation and atmosphere-ocean CO₂ exchange. The reducing ¹⁴C uptake and the weakening ¹⁴C-depleted upwelling in the Southern Ocean resulted in a decrease in atmospheric Δ¹⁴CO₂ [24].

Among all background sites, the annual decreasing trends of Δ¹⁴CO₂ in the 21st century are similar. According to the observations and modeling conducted by Levin et al. [24], the global long-term trend in Δ¹⁴CO₂ is main influenced by fossil fuel emissions since the 1990s. If fossil fuel emissions continue to increase in a “business-as-usual” scenario in the IPCC Fifth Assessment Report, Δ¹⁴CO₂ will likely drop below the preindustrial level (0‰) in a decade and be reduced to −250‰ by the year 2100. However, if ambitious emission reductions could be conducted, Δ¹⁴CO₂ will be sustained near the preindustrial level through 2100 [63].

In general, it is recommended that the quantification of FFCO₂ need to refer to the corresponding background Δ¹⁴CO₂ values and CO₂ concentrations, due to the spatial gradients in Δ¹⁴CO₂. However, Turnbull et al. [58] estimated FFCO₂ in South Korea with four different background sites (WLG, NWR, Mauna Loa, Hawaii, and Ulaan Uul, Mongolia) separately, and found no substantial change in the results. The enhancements above baseline are typically large compared to the differences caused by the choice of background.

4. Spatial and Temporal Variations of Δ¹⁴CO₂ and FFCO₂

To provide a periodical review of the spatiotemporal characteristics of FFCO₂, we collected Δ¹⁴CO₂ measurements of air and plant samples and/or the calculated FFCO₂ reported in the past two decades (Table 1). Since measurements in Europe and North America have been implemented for decades, we focus more on the recent measurements in Asia (Figure 2, where CO₂ emissions are higher than in other regions [64]). The global FFCO₂ distribution is plotted in Figure 3.

Table 1. Δ¹⁴CO₂ measurements and calculated FFCO₂ concentrations reported in the last two decades.

Location	Sampling Period		14CO2 (‰)	FFCO2 (ppm by Defult)	Site Type/Name	Note (Air Samples with No Notes)	References
Hungary	September 2008–April 2009		−4.5~39.1		city		[65,66]
			23.1~48.1		rural (10 m)
			31.4~47.3		rural (115 m)
Netherlands	2010–2012		35.2, 27.2, 22.6			corn leaves	[42]
Germany	2012		17.2
France	2012		31.7
Poland	July 2011–May 2013		−178.2~4.7	66.6~72.7%			[43]
Romania	August 2012–January 2018		–57~61		industrial area		[67]
Switzerland	June 2013–December 2015			4.3	tall tower		[7]
England	June 2014–August 2015		−35.26~59.61	−1.09~2.27	tall tower		[68]
North America	2004, summer		66.3 ± 1.7		mountain regions, western North America	corn leaves	[35]
			58.5 ± 3.9	2.7 ± 1.5	eastern North America
			55.2 ± 2.3	4.3 ± 1.0	Ohio-Maryland region
California, USA	2004–2005		59.5 ± 2.5	0.3 ± 0.08	North Coast	annual C3 grasses	[37]
			44 ± 10.9	6.1 ± 1.1	San Francisco
			48.7 ± 1.9	4.8 ± 0.9	Central Valley
			27.7 ± 20	13.7 ± 0.4	Los Angeles
Los Angeles, USA	2006–2013		−59.4~29.3		inland Pasadena		[69]
	2009–2013		−18.8~40.4		coastal Palos Verdes
high latitudes,	2008	spring	46.6 ± 4.4			flight	[70]
North America		summer	51.5 ± 5
central California, USA	2009–2012	winter		7.2	Walnut Grove		[71]
		spring		3.1
		summer		3.7
		fall		5.0
southern California, USA	2013–2014	winter		25	California Institute of Technology in Pasadena
		spring		21.6
		summer		25.9
		fall		21.5
		winter		8.2	San Bernardino
		spring		5.1
		summer		11
		fall		10.2
Mexico City	March 2006		20~132				[72]
South Korea	2009		−112.3~−12.4	4.2~13.9	Seoul, metropolitan area	gingko leaves	[73]
			−79.5~43.8	−1.3~10.7	Busan, metropolitan area
			–69.3~28.1	0.2~9.7	Daegu, metropolitan area
			−53.4~−2	3.2~8.2	Daejeon, metropolitan area
			−41.7~19.2	1.1~7	Gwangju, metropolitan area
South Korea	2009		34.8		clean air sites	gingko leaves	[38]
	2010		24.9
	2011		23.1
	2012		14
	2013		8.3
Anmyeondo, South Korea	May 2014–August 2016		−59.5~23.1	9.7 ± 7.8			[9]
Tae-Ahn Peninsula,	2004–2010	all year		4.4, 60%			[58]
South Korea		winter		4.4, 90%
Beijing	March 2009–September 2009		3.4 ± 11.8	16.4 ± 4.9			[74]
			12.8 ± 3.1		suburban sites
			−8.4 ± 18.1		road sites
	2009		−28.2~29.6			corn leaves	[75]
	2014		−53.5 ± 54.8	39.7 ± 36.1, 75.2 ± 14.6%	urban site		[76]
Guangzhou	2010–2011		–16.4 ± 3.0	24 (1–58)			[77]
Xiamen	2014		−8.7 ± 25.3	13.6 ± 12.3, 59.1 ± 26.8%	urban site		[76]
Xi’an	March 2012–March 2013		−41.3 ± 27.4				[30]
	April 2012		−9.7 ± 23.8
	January 2013		−90.4 ± 32.4
	March 2012.03–March 2013			34.2 ± 9.5
	March 2012–March 2013	winter		46.5 ± 8.7
	March 2012–March 2013	summer		26.6 ± 3.4
Xi’an	2013	summer		20.5		annual plants	[78]
	2014	summer		23.5
Xi’an	2014	winter		92.7 ± 9.7			[79]
	2016	winter		61.8 ± 10.6	urban		[80]
	2016	winter		57.4 ± 9.7	suburban
	2016	summer		82.5 ± 23.8	urban
	2016	summer		90 ± 24.8	suburban
Bali, Indonesia	September 2018		2.2 ± 19	6.4 ± 7.5		evergreen leaves	[81]

Table 1. Δ¹⁴CO₂ measurements and calculated FFCO₂ concentrations reported in the last two decades.

Location	Sampling Period		14CO2 (‰)	FFCO2 (ppm by Defult)	Site Type/Name	Note (Air Samples with No Notes)	References
Hungary	September 2008–April 2009		−4.5~39.1		city		[65,66]
			23.1~48.1		rural (10 m)
			31.4~47.3		rural (115 m)
Netherlands	2010–2012		35.2, 27.2, 22.6			corn leaves	[42]
Germany	2012		17.2
France	2012		31.7
Poland	July 2011–May 2013		−178.2~4.7	66.6~72.7%			[43]
Romania	August 2012–January 2018		–57~61		industrial area		[67]
Switzerland	June 2013–December 2015			4.3	tall tower		[7]
England	June 2014–August 2015		−35.26~59.61	−1.09~2.27	tall tower		[68]
North America	2004, summer		66.3 ± 1.7		mountain regions, western North America	corn leaves	[35]
			58.5 ± 3.9	2.7 ± 1.5	eastern North America
			55.2 ± 2.3	4.3 ± 1.0	Ohio-Maryland region
California, USA	2004–2005		59.5 ± 2.5	0.3 ± 0.08	North Coast	annual C3 grasses	[37]
			44 ± 10.9	6.1 ± 1.1	San Francisco
			48.7 ± 1.9	4.8 ± 0.9	Central Valley
			27.7 ± 20	13.7 ± 0.4	Los Angeles
Los Angeles, USA	2006–2013		−59.4~29.3		inland Pasadena		[69]
	2009–2013		−18.8~40.4		coastal Palos Verdes
high latitudes,	2008	spring	46.6 ± 4.4			flight	[70]
North America		summer	51.5 ± 5
central California, USA	2009–2012	winter		7.2	Walnut Grove		[71]
		spring		3.1
		summer		3.7
		fall		5.0
southern California, USA	2013–2014	winter		25	California Institute of Technology in Pasadena
		spring		21.6
		summer		25.9
		fall		21.5
		winter		8.2	San Bernardino
		spring		5.1
		summer		11
		fall		10.2
Mexico City	March 2006		20~132				[72]
South Korea	2009		−112.3~−12.4	4.2~13.9	Seoul, metropolitan area	gingko leaves	[73]
			−79.5~43.8	−1.3~10.7	Busan, metropolitan area
			–69.3~28.1	0.2~9.7	Daegu, metropolitan area
			−53.4~−2	3.2~8.2	Daejeon, metropolitan area
			−41.7~19.2	1.1~7	Gwangju, metropolitan area
South Korea	2009		34.8		clean air sites	gingko leaves	[38]
	2010		24.9
	2011		23.1
	2012		14
	2013		8.3
Anmyeondo, South Korea	May 2014–August 2016		−59.5~23.1	9.7 ± 7.8			[9]
Tae-Ahn Peninsula,	2004–2010	all year		4.4, 60%			[58]
South Korea		winter		4.4, 90%
Beijing	March 2009–September 2009		3.4 ± 11.8	16.4 ± 4.9			[74]
			12.8 ± 3.1		suburban sites
			−8.4 ± 18.1		road sites
	2009		−28.2~29.6			corn leaves	[75]
	2014		−53.5 ± 54.8	39.7 ± 36.1, 75.2 ± 14.6%	urban site		[76]
Guangzhou	2010–2011		–16.4 ± 3.0	24 (1–58)			[77]
Xiamen	2014		−8.7 ± 25.3	13.6 ± 12.3, 59.1 ± 26.8%	urban site		[76]
Xi’an	March 2012–March 2013		−41.3 ± 27.4				[30]
	April 2012		−9.7 ± 23.8
	January 2013		−90.4 ± 32.4
	March 2012.03–March 2013			34.2 ± 9.5
	March 2012–March 2013	winter		46.5 ± 8.7
	March 2012–March 2013	summer		26.6 ± 3.4
Xi’an	2013	summer		20.5		annual plants	[78]
	2014	summer		23.5
Xi’an	2014	winter		92.7 ± 9.7			[79]
	2016	winter		61.8 ± 10.6	urban		[80]
	2016	winter		57.4 ± 9.7	suburban
	2016	summer		82.5 ± 23.8	urban
	2016	summer		90 ± 24.8	suburban
Bali, Indonesia	September 2018		2.2 ± 19	6.4 ± 7.5		evergreen leaves	[81]

Figure 3. The spatial distribution of Δ¹⁴CO₂ traced FFCO₂. The percentage in pie charts represents the fossil fuel component to total CO₂. The grid lines in histograms represent that the FFCO₂ value is 50 ppm. Colors in pie charts and histograms: blue-spring, green-summer, orange-autumn, red-winter, black- yearly values [7,9,35,37,43,58,71,74,76,77,79,80,83].

Figure 3. The spatial distribution of Δ¹⁴CO₂ traced FFCO₂. The percentage in pie charts represents the fossil fuel component to total CO₂. The grid lines in histograms represent that the FFCO₂ value is 50 ppm. Colors in pie charts and histograms: blue-spring, green-summer, orange-autumn, red-winter, black- yearly values [7,9,35,37,43,58,71,74,76,77,79,80,83].

4.1. Spatial Patterns of Δ¹⁴CO₂ and FFCO₂

Δ¹⁴CO₂ measurements in Asia are mostly carried out in China, South Korea, and Japan around the 2010s. There are great differences in Δ¹⁴CO₂ values among cities. Highest Δ¹⁴CO₂ values appear in cities in middle and western China (light orange diamonds in Figure 2), where are sparsely populated. The Δ¹⁴CO₂ values measured in Northeast China (Mohe, Harbin, and Shenyang) and in coastal areas (Baoting, Xiamen, and Guangzhou) are also higher than those in other cities. Lower Δ¹⁴CO₂ values are observed in the winter months in western China (Urumqi, Xining, and Lanzhou) and in big cities in eastern China (Qingdao, Shanghai, and Beijing). For South Korea, the annual averaged Δ¹⁴CO₂ values from the clean sites (Gingko leaves) are consistently above zero, but the values in metropolitan areas are much lower [38,73,82]. Plant materials only represent Δ¹⁴CO₂ in the growing period, which is normally from late spring to early autumn in Asia. Similar spatial patterns of measured Δ¹⁴CO₂ are found in Beijing and Xi’an. In Beijing, Δ¹⁴CO₂ values at urban sites are significantly lower than those observed at suburban sites, and road sites are mostly lower than park sites and campus sites [74,76]. For the observations in Xi’an, Δ¹⁴CO₂ values at suburban sites are significantly and consistently higher than those for urban sites in both winter and summer [80]. On a larger scale, the Δ¹⁴CO₂ values inside the Guanzhong basin, where the capital city Xi’an is located, are lower than the edge and outside the basin [84,85]. The influence of topography also appears in Beijing, where the Δ¹⁴CO₂ values in the northwest area (mountain area) are lower than those in the southeast area due to different dispersion situation [74].

FFCO₂ concentrations calculated with Δ¹⁴CO₂ measurements were carried out in fewer cities. Corresponds to the spatial patterns of Δ¹⁴CO₂, FFCO₂ concentrations are higher in Beijing (39.7 ppm in 2014) and Xi’an (34.2 ppm, 2012–2013), and lower in Xiamen (13.6 ppm, 2014) and Guangzhou (24 ppm, 2010–2011) [30,76,77]. In Bali, Indonesia, FFCO₂ concentrations in densely populated areas reach 25 ppm, while they are lower than 1 ppm in cleaner sites (Δ¹⁴CO₂ varies from −46‰ to 18‰ [81]). For regional background sites, FFCO₂ concentrations are 12.7 ± 9.6 ppm in Lin’an, 11.5 ± 8.2 ppm in Shangdianzi, 4.6 ± 4.3 ppm in Luhuitou (2014–2015 [57]), and 9.7 ± 7.8 ppm in Anmyeondo (2014–2016 [9]). This means that using a regional background site to quantify FFCO₂ would cause a certain underestimation. Most of these studies provided the spatial characteristics of FFCO₂ in these cities for the first time, reflecting current emissions and offering a basis for emission reduction.

In North America, based on samples of corn leaves collected during the summer of 2004, mountain regions of western North America show the smallest influence of FFCO₂ with a mean Δ¹⁴CO₂ of 66.3 ± 1.7‰, while Eastern North America and the Ohio-Maryland region show a larger fossil fuel influence with a mean Δ¹⁴CO₂ of 58.8 ± 3.9‰ and 55.2 ± 2.3‰, respectively [35]. California is another hotspot influenced by fossil fuel, with mean Δ¹⁴CO₂ values of 44.0 ±10.9‰ in San Francisco, and 27.7 ± 20.0‰ in Los Angeles (winter annual grasses [37]). Large regional gradients were captured near urban areas. Take the Los Angeles megacity as an example, Δ¹⁴CO₂ in inland Pasadena (2006–2013) and coastal Palos Verdes peninsula (2009–2013) are about −14.2‰ and 15.0‰, respectively [69]. It seems that Δ¹⁴CO₂ values are higher in North America than in Asia, based on the above-mentioned studies. The reason may be that the measurements in Asian cities were mostly implemented in the 2010s, about 5 to 10 years later than those in North America. Considering that the decreasing trend of Δ¹⁴CO₂ in background sites is about 5‰ per year, there are no significant differences in Δ¹⁴CO₂ values of cities between those two areas. For the newly added FFCO₂ calculated with Δ¹⁴CO₂, the values were over 20 ppm in southern California (2013–2014 [71]), while those in the other parts in North America are consistently lower than 10 ppm, e.g., 2.9–8 ppm in central California, 2.7 ppm and 4.3 ppm in eastern North America and Ohio-Maryland region (2004 summer [35]).

As for Europe, Δ¹⁴CO₂ has been analyzed in countries including Hungary [65,66], Netherlands, Germany, France [42], Switzerland [7], Romania [67], England [68], Poland [43], etc. Plant samples collected from 51 different locations in the Netherlands, Germany, and France, together with model outputs, all capture the regional Δ¹⁴CO₂ gradients. Bozhinova et al. [42] presume that the largest gradients found in the Netherlands and Germany are associated with emissions from energy production and road traffic. In France, the Δ¹⁴CO₂ enrichment from nuclear sources dominates in many samples. Similar regional gradients are also found in Poland between the built-up area of the city and several kilometers from the city center [43]. For FFCO₂, long-term mean (1986–2002) concentration in Heidelberg, Germany is about 10.5 ppm [26]. In Hungary, the winter peaks were about 10–15 ppm, similar to those in Germany, although they were measured during 2008–2010 [65,66]. The concentrations of FFCO₂ calculated using tower-based samples are much lower. In Switzerland, the averaged concentration of FFCO₂ sampled at a 212.5 m tower is 4.3 ppm (2013–2015 [7]). In the UK, the concentration is 1.8 ppm (2014–2015) from a 185 m tower [68]. In the high latitude areas of Eurasia, train-based Δ¹⁴CO₂ observations from Western Russia to Eastern Siberia show an increase in Δ¹⁴CO₂, which shows large FFCO₂ emissions in heavily populated Europe, and gradual dispersion of the fossil fuel plume across Northern Asia [86].

4.2. Temporal Variations of Δ¹⁴CO₂ and FFCO₂

Most cities in the North Hemisphere show significant seasonal differences with Δ¹⁴CO₂ values higher in summer and lower in winter, including Jungfraujoch, Schauinsland [53], Heidelberg [87], Krakow (Poland [43]), Guangzhou [77], Beijing [88], Xi’an [30,79,80,89] and cities in Figure 2 sourced from Zhou et al. [79]. Consequently, FFCO₂ concentrations calculated with Δ¹⁴CO₂ in winter are higher than in summer [30,77,88,90]. For example, the FFCO₂ concentration is 14 ppm in winter and 6.5 ppm in summer Heidelberg [26]. This may be interpreted by the increased fossil fuel consumption and lower boundary layer height in winter, and the intensive biogenic photosynthesis in summer. However, seasonal variations of Δ¹⁴CO₂ (and/or FFCO₂) in some cities are not significant, e.g., in Baoting and Xiamen, China [79,88]. These cities are relatively warm in winter, so there is less fossil fuel consumption for heating. For Gliwice, Poland, Piotrowska et al. [43] attributed this to fluctuations in the measurements resulting from the methodology.

Diurnal variations of FFCO₂ (and/or Δ¹⁴CO₂) are examined with measurements at high temporal resolution. High concentrations of FFCO₂ commonly occur during morning and afternoon rush hours, which obviously result from transportation emissions (Germany [14]; China [76]). Some cities observed nighttime FFCO₂ peaks, which could be related to weak nocturnal atmospheric dispersion, especially the relatively low planetary boundary layer [76,84]. Diurnal FFCO₂ also showed evident variations in the background areas. Niu et al. [88] found that the FFCO₂ concentrations at SDZ decreased rapidly from 31.6 ± 1.3 ppm at 00:00 to 0 ppm at 04:00 during the winter sampling days.

5. Estimation of FFCO₂ and Its Emissions Combining Numerical Models

How to interpret the measurements is also of vital importance, especially with relatively sparse datasets. Here, we present the studies combining Δ¹⁴CO₂ measurements (and/or the calculated FFCO₂) and atmospheric transport models to provide insights into the variation of atmospheric FFCO₂ concentration, to quantify the cross-regional transport, and to estimate the emissions of FFCO₂, etc. Hsueh et al. [35] collected samples from 67 sites across North America and estimated the spatial distribution of carbon sources and sinks with the help of transport models, and further identified fossil fuel emissions as the major driver of regional variability. Riley et al. [37] used a regional transport model to simulate anthropogenic and ecosystem CO₂ fluxes in California. The model well reproduced the regional patterns of FFCO₂, and quantified its fluxes in different directions. Moreover, the model simulations indicated that some areas with high near-surface FFCO₂ mixing ratios may not be expected from local emissions inventories. Wenger et al. [68] developed isotope modeling to simulate ¹²CO₂, ¹³CO₂, and ¹⁴CO₂ directly, and by which they calculated the impact of nuclear and biospheric disequilibrium.

When discussing the observation–model comparisons, possible systematic model biases and short-term observation anomalies need to be noticed. Lafranchi et al. [31] found that their Δ¹⁴CO₂ observations cannot be reproduced by model simulations, with the terrestrial biosphere being responsible for a significant contribution. The interpretations of observation–model comparisons can also be different between air and plant samples, since the latter offers integrated daytime Δ¹⁴CO₂ over months. Influenced by local weather information, plant species, etc., the accumulation of CO₂ may vary during different growing periods. To address this problem, Bozhinova et al. [91] use a crop growth model to reproduce daily fixation of Δ¹⁴CO₂ in maize and wheat plants by making a weighted average of the daily contribution from the atmospheric Δ¹⁴CO₂ mixing ratios. The simulations suggest that the influence of day-to-day plant growth on recorded Δ¹⁴CO₂ signals is not negligible when interpreting plant sampled Δ¹⁴CO₂ values [41,42].

The measurements of Δ¹⁴CO₂ and the derived FFCO₂, combined with transport models, offer an appealing method for evaluating and optimizing the emissions of FFCO₂ (inverse method). Traditionally, FFCO₂ emission inventories are derived from energy and fuel use statistics, combustion efficiencies, and emission factors (“bottom-up” method). These are the basic knowledge for FFCO₂ emissions, but the uncertainties for national annual inventories in developed countries may be 5–10% and even larger in developing countries or on smaller scales with finer resolution [92,93]. For example, the relative differences of FFCO₂ emissions of China based on nine emission inventories are approximately 21%. The provincial-level spatial distribution shows more consistency, while the top 5% of the grid level accounts for 50–90% of total emissions [94]. Inverse modeling is a statistical method used to estimate emissions by narrowing the mismatch between simulations and observations. It has long been used to constrain emissions of CO₂ [95,96], other greenhouse gases, CO, black carbon, [97,98] etc. The big advantage of inverse methods is that the evaluation is more accurate and independent. Turnbull et al. [58] compared modeled and observed FFCO₂ (derived from Δ¹⁴CO₂), and the results are consistent with each other when considering a 63% increase in emissions. Turnbull et al. [99] evaluated FFCO₂ emissions of a point source, the uncertainties of which were better than 10%, representing an improvement by a factor of 2. According to Basu et al. [100], the uncertainties of FFCO₂ emissions for the US national can be constrained within 1% for a whole year and within 5% for most months. Thus, this method may act as an independent way to assess emission reductions and regulations under a global warming background. It should be noted that there are internal errors in the inverse methods, including representation errors, aggregation errors, systematic errors in the transport model, etc. [101]. Thus, the propagation of errors between the Δ¹⁴CO₂ measurements and the inverse models needs to be carefully considered. Moreover, three or more sites are required for the further reduction of uncertainty in the estimates of FFCO₂ emissions [102].

6. Conclusions and Outlook

Radiocarbon (¹⁴C) is a reliable and promising tool for quantifying fossil fuel components in atmospheric CO₂ (FFCO₂). Focusing on the quantification of the atmospheric concentrations and emissions of FFCO₂, we reviewed the ¹⁴CO₂ measurements and the calculated FFCO₂ concentrations conducted mainly in the last two decades. Spatial-temporal characteristics were presented, and the recent progress of the combination of ¹⁴C measurements and atmospheric transport models was also discussed. As the most accurate method to quantify FFCO₂, the radiocarbon technique is promising, although there are several issues that need to be improved currently. Nuclear power plants play a significant role in the quantification of FFCO₂, since the enrichment by Δ¹⁴CO₂ from nuclear sources can partly mask, or even exceed the influence from fossil fuel emissions in some regions [41,68,103]. Thus, Δ¹⁴CO₂ values need to be corrected before quantifying FFCO₂. The combination of atmospheric transport models and reported nuclear industry emissions offers a solution to this issue [104,105]. As for the FFCO₂ emission estimation, it is complex for urban areas, where most FFCO₂ emit from. With the coexistence of biomass burning and/or heterotrophic respiration, the emissions of FFCO₂ may be underestimated. As illustrated in Section 2.1, the “other” term needs to be carefully considered regarding the sources and sinks in the catchment area.

Based on different projections of future CO₂ emissions and atmospheric concentrations, new issues related to ¹⁴C techniques will emerge. The sensitivity of Δ¹⁴CO₂ to newly added FFCO₂ diminishes with an increase in atmospheric FFCO₂. For example, the atmospheric CO₂ concentration and ¹⁴C value were ~380 ppm and 66‰, respectively, in 2003. Thus, 1 ppm of ¹⁴C-free FFCO₂ added to the atmosphere will produce a ¹⁴CO₂ depletion of ~2.8‰ [13]. For the year 2015, atmospheric CO₂ concentration and ¹⁴C value were ~400 ppm and 17‰ (WLG), respectively, resulting in a depleting rate of ~2.5‰ ppm⁻¹-CO₂. This trend is likely to continue in the near future if the emissions of greenhouse gases follow the high, very high, and intermediate scenarios as IPCC assessed. This requires a more precise measurement of ¹⁴C to maintain the current detection capabilities. Meanwhile, the deep ocean upwelling in the Southern Hemisphere may provide ¹⁴C-enriched CO₂ rather than ¹⁴C-depleted CO₂ comparing to atmospheric Δ¹⁴CO₂. On the contrary, if CO₂ removal and emission reduction can be effectively conducted, the ocean and terrestrial ecosystem will shift from carbon sinks to carbon sources as net CO₂ emissions become negative. Under either circumstance, Δ¹⁴CO₂ fluxes and their influences on FFCO₂ quantification need to be reconsidered.

Because the importance of CO₂ emission control has attracted worldwide attention, future fossil fuel fractions in total CO₂ may be greatly influenced by policy factors. According to the Climate Ambition Alliance: Net Zero 2050, more than 100 nations have committed to getting carbon neutral (also called net zero), which means that the CO₂ released into the atmosphere is balanced by its removal from the atmosphere. The CO₂ emissions of these countries account for over 65% of the global total emissions. For example, China announced a carbon peak by 2030 and carbon neutrality by 2060 at the Group of 20 (G20) summit in 2020. According to the guideline to reach carbon peak by 2030 (http://www.gov.cn/zhengce/content/2021-10/26/content_5644984.htm, released in October 2021, latest access on 1 November 2021), the main goals include adjusting the industrial and energy structures, and raising the share of non-fossil fuel energy to around 25% by 2030. How to evaluate the effect of these policies scientifically and accurately is of concern. Though “bottom-up” methods may provide CO₂ emissions for each factory and each county, the radiocarbon technique has its irreplaceable advantages: (a) is an independent verification method disturbed by no political willingness, and (b) may quickly respond to rapid CO₂ emission variations. Thus, a comprehensive carbon emission estimation system is highly recommended in the future for the evaluation of FFCO₂ emissions, containing a well-designed monitoring network of CO₂ and Δ¹⁴CO₂, uniform measurement standard, FFCO₂ quantification method, and the corresponding emission inversion modeling. Until now, most of the Δ¹⁴CO₂ measurements have been conducted in limited cities, and continuous measurements have been conducted in fewer cities. Thus, the measurements need to be further expanded, especially at background sites. Moreover, stable carbon isotopic compositions (¹³C) vary with different types of fossil fuels (coal and liquid fossil fuels) and industrial processes [106], and can also provide more information on the ecosystem carbon cycle. Therefore, the combination of ¹⁴C and ¹³C may further help refine the partitioning of source apportionments for atmospheric CO₂.