Abstract

There are three major reservoirs for carbon in the Earth at the present time, the core, the mantle, and the continental crust. The carbon in the continental crust is mainly in carbonates (limestones, marbles, etc.). In this paper we consider the origin of the carbonates. In 1952, Harold Urey proposed that calcium silicates produced by erosion reacted with atmospheric CO2 to produce carbonates, this is now known as the Urey reaction. In this paper we first address how the Urey reaction could have scavenged a significant mass of crustal carbon from the early atmosphere. At the present time the Urey reaction controls the CO2 concentration in the atmosphere. The CO2 enters the atmosphere by volcanism and is lost to the continental crust through the Urey reaction. We address this process in some detail. We then consider the decay of the Paleocene-Eocene thermal maximum (PETM). We quantify how the Urey reaction removes an injection of CO2 into the atmosphere. A typical decay time is 100 000 yr but depends on the variable rate of the Urey reaction.

Introduction

The continental crust is a major reservoir for carbon in the Earth. A major question in geology is the origin of the carbon, principally in calcium carbonates. The first successful attempt to explain the origin of calcium carbonates (limestones, marbles) in the continental crust was given by Urey (1952). The basic equation he gave was of the form

CaSiO3+CO2CaCO3+SiO2.
(1)

He proposed that atmospheric CO2 combines with a calcium silicate to generate a calcium carbonate plus silica. A direct quote from his paper states: “As carbon dioxide was formed it reacted with silicates to form limestone. Of course, the silicates may have been a variety of minerals, but the presence of CO2 was always kept at a low level by this reaction or similar reactions just as it is now.”

In the current literature an expanded version of the Urey reaction is given (Blättler and Higgins 2017). To include the role of acid rain the Urey reaction takes the form

CaSiO3+2CO2+H2OCa2++2HCO3¯+SiO2CaCO3+SiO2+CO2+H2O.
(2)

The carbonation takes place when carbon dioxide (carbonic acid) in acid rain dissolves calcium silicate (wollastonite) sediments to give calcium, bicarbonate, and silica. The resulting calcium and bicarbonate ions flow in rivers to the oceans where either organic or inorganic precipitation produces the calcium carbonate.

The three large reservoirs for carbon in the Earth at the present time are the core, mantle, and continental crust. We assume that the core is an isolated reservoir and neglect its role. About 1% of the carbon in the Earth is in the continental crust. Wedepohl (1995) has given a comprehensive study of the composition of the continental crust with an emphasis on carbon. He gives an estimate for the total mass of carbon (c) in the continental crust (cc) at the present time (p) of cMccp = 4.2 × 107 Gt. Hayes and Waldbauer (2006) have reviewed the literature on carbon in the continental crust and suggest that it may be as high as cMccp = 108 Gt. DePaolo (2015) gives a range of 6 to 7 × 107 Gt. In this paper, we take a representative value to be cMccp = 5 × 107 Gt. The mass of carbon in the ocean is about a factor of 103 less than the mass of carbon in the continental crust (Houghton 2007).

Urey (1952, 1956) clearly recognized that the reaction he proposed would efficiently remove CO2 from the Earth's atmosphere, but at that time little was known about the early atmosphere. Although the mass of carbon in the atmosphere today is small (850 Gt), the mass may have been much higher in the past. One of the major differences between Venus and the Earth is atmospheric composition. The atmospheric pressure on Venus is about a factor of 100 greater than the atmospheric pressure on Earth and is 96% carbon dioxide. The mass of carbon in the Venus atmosphere (a) at the present time (p) is cMap = 1.28 × 108 Gt. Scaling the atmospheric carbon masses to the overall masses of Venus and the Earth gives an estimate of the mass of carbon (c) in the early atmosphere (t = 0) of the Earth. The estimated value is cMa0 = 1.57 × 108 Gt (Kasting and Ackerman 1986).

Carbon from the atmosphere to the continental crust

One hypothesis for the origin of the carbon in the continental crust is that it was extracted directly from the atmosphere relatively early in Earth's history. The estimated mass of carbon (c) in the early atmosphere (a) given above, cMa0 = 1.57 × 108 Gt, is substantially larger than the total estimated carbon in the continental crust given above, cMccp = 5 × 107 Gt. The hypothesis of direct extraction from the atmosphere has been discussed in some detail by Kramers (2002) and by Lowe and Tice (2004).

The basic hypothesis is that the mass flux of carbon from the atmosphere to the continental crust, cJa-cc, is controlled by the availability of calcium silicates. In order for the Urey reaction to extract CO2 from the atmosphere the early Earth must have had continental crust to generate surface deposits of calcium silicate. In addition, the Earth must have had oceans in order for the acid rain to catalyze the Urey reaction between atmospheric CO2 and the service deposits of calcium silicates. Little data are available for timing the initiation of the extraction of CO2 from the atmosphere. We will assume that the process begins at a time t0 after the early bombardment and the solidification of the magma ocean at about 4.4 Ga. We further assume that the Urey reaction extracted carbon from the atmosphere at a constant rate cJa-cc until the concentration of CO2 in the atmosphere was reduced to a very low level. During the time, τ0 < t < t0 + τa-cc, the Urey reaction extracts atmospheric carbon to the continental crust. We will specify the mass of carbon extracted from the atmosphere and obtain

Jcacc=Mca0τacc.
(3)

We assume that the mass of carbon in the atmosphere cMa decreases linearly in time from cMa0 to zero during the time period τa-cc and the mass of carbon in the continental crust increases linearly in time.

Assuming all the carbon in the continental crust cMccp was extracted from the atmosphere the dependence on time is given by

Mccc=00tt0Mccc=Mccpc[(tt0)/(τacc)]t0tt0+τaccMccc=Mccpct0+τaccttp
(4)

Taking cMccp = 5 × 107 Gt, t0 = 1 Gyr, and τa-cc = 1 Gyr, the dependence of cMcc on t is given in Figure 1. The required flux of carbon from the atmosphere to the continental crust is cJa-cc = 50 Mtyr-1. It must be emphasized that the value of τa-cc is uncertain and the flux cJa-cc is expected to have considerable variability in time. However it is quite clear that the extraction of carbon from the atmosphere to the continental crust would have been carried out early in Earth's history.

Figure 1.

Dependence of the mass of carbon in the continental crust cMcc on time. Two limiting models are given for adding the present mass cMccp = 5 × 107 Gt. (1) Addition from the atmosphere beginning at t0 = 1 Gyr. All atmospheric carbon is transferred in τa-cc = 1 Gyr at a constant flux cJa-cc = 50 Mtyr-1. (2). Addition from the mantle beginning at t0 = 1 Gyr. Carbon is added at a constant flux cJm-cc = 14.7 Mtyr-1 to the present.

Figure 1.

Dependence of the mass of carbon in the continental crust cMcc on time. Two limiting models are given for adding the present mass cMccp = 5 × 107 Gt. (1) Addition from the atmosphere beginning at t0 = 1 Gyr. All atmospheric carbon is transferred in τa-cc = 1 Gyr at a constant flux cJa-cc = 50 Mtyr-1. (2). Addition from the mantle beginning at t0 = 1 Gyr. Carbon is added at a constant flux cJm-cc = 14.7 Mtyr-1 to the present.

Removal of the volcanic addition of carbon to the atmosphere

When excess carbon in the atmosphere has been depleted by the Urey reaction an approximate steady-state balance is established between the volcanic input of carbon into the atmosphere and the extraction by the Urey reaction. We approximate this balance by the relationship

Jcacc=Mcaτu.
(5)

where cJa-cc is the rate of volcanic input of carbon into the atmosphere. We assume that this extraction rate is constant and is proportional to the mass of carbon in the atmosphere cMa. The characteristic time τu takes account of the rate at which acid rain can interact with calcium silicate sediments, and although we assume that τu is constant it clearly can be a function of time.

A comprehensive model for the variability of atmospheric CO2 over Phanerozoic times has been given by Berner and Kothavala (2001). This model, GEOCARB III, is complex and involves both organic and inorganic processes. Transport of carbon between the atmosphere, oceans, and continental crust is quantified on the million year timescale. The balance is dominated by the exchange of carbon between carbonates in the continental crust and carbon in the surficial reservoirs (oceans and atmosphere) and organic carbon (Berner and Caldeira 1997). When erosion is high, the Urey reaction extracts CO2 from the atmosphere adding carbonates to the continental crust. High erosion rates are associated with low sea level and large continental areas. When erosion is low, the Urey reaction operates in the opposite direction (from right to left in Eq. 1) with carbonates decomposing to give CO2. An example of this metamorphic process is the subduction of carbonate sediments and the generation and return to the atmosphere of CO2 in subduction zone volcanics (Frezzotti et al. 2011).

The present mass of carbon in the atmosphere is 860 Gt (400 ppmv CO2), but this is not a quasi-equilibrium value because of the anthropogenic addition at high fluxes (3.5 Gtyr-1). We will take the 1900 value of 650 Gt (300 ppmv CO2) as the present equilibrium value. This is a typical value for the current glacial epoch (0 to 50 Ma). Values given by the GEOCARB III Model are generally consistent with observations (Royer 2014). Between 50 and 250 Ma, the average values were about 3000 Gt. During the major glacial epoch between 250 and 350 Ma low observed values near 650 Gt are found. Between 350 and 550 Ma, values were considerably higher, typically near 10 000 Gt. This variability reflects variations in both of the variables in Equation 3, the volcanic flux cJa-cc into the atmosphere and the characteristic time τu.

Carbon from the mantle to the continental crust

The second hypothesis for the origin of the carbon in the continental crust is that it comes from the mantle. If the volcanic flux of carbon out of the mantle at ocean ridges and hot spots exceeds the carbon lost to the mantle at subduction zones, the difference will be added to the continental crust. Some of the volcanic carbon input will enter the atmosphere and will be transferred to the continental crust through the Urey reaction. However, some will enter the oceans and will be converted directly to carbonates without entering the atmosphere.

Rates of carbon loss from the mantle by volcanism and lost by subduction will certainly vary over geologic time, but the variations are uncertain. Again, we assume that the plate tectonic processes required for carbon transfer began at a time t0 after the solidification of the magma ocean at about 4.5 Ga. We further assume that the transfer of carbon out of the mantle has been at a constant rate cJm-cc until the present time tp. Assuming all the carbon in the continental crust has been extracted from the mantle, the dependence on time is given by

Mccc=00tt0Mccc=Mccpc[(tt0)/(tpt0)]t0ttp+τacc.
(6)

The mass of carbon in the continental crust increases linearly in time over the period t0 to tp. The required flux of carbon from the mantle to the continental crust is given y

Jcmcc=Mcccptpt0.
(7)

Taking cMccp = 5 × 107 Gt, t0 = 1 Gyr, and tp = 4.4 Gyr the dependence of cMcc on t is given in Figure 1. The required flux of carbon from the mantle to the continental crust is cJm-cc = 14.7 Mtyr-1.

We next consider the estimate for the present loss of carbon from the mantle to the atmosphere. Dasgupta and Hirschmann (2010) have summarized the available data on the loss of carbon from the mantle to the surface reservoirs and give values in the range cJm-s = 36 ± 24 Mtyr-1. Just as carbon is lost from the mantle by volcanism, carbon is returned to the mantle by subduction. A detailed study of carbon fluxes at subduction zones has been given by Kelemen and Manning (2015). These authors suggest that the downward flux of carbon at global subduction zones is 53 ± 13 Mtyr-1. However a substantial fraction of this carbon never makes it to the mantle due to subduction zone volcanism. They suggested that 24 ± 24 Mtyr-1 reach the mantle. Clearly it is quite possible that all the carbon in the continental crust could have come from the mantle. This conclusion was also given by Hayes and Waldbauer (2006).

In Figure 1 we give examples of the two limiting cases, the carbon in continental crust comes entirely from the atmosphere and the carbon comes entirely from the mantle. In the first case the addition is early in time and in the second case it is more uniform in time. Observations of the mass of carbonates in the continental crust as a function of age could distinguish between the two cases, but the data are sparse. Observations of the mass of carbon in the atmosphere as a function of time could also be a constraint. An example given by Rye et al. (1995) utilizing studies of paleosols concluded that the mass of carbon in the atmosphere at 2.2 to 2.75 Ga was less than 105 Gt. The conclusion is that the extraction of a significant mass of carbon from the atmosphere to the continental crust was completed by t = 2 Gyr. However, how large this mass was is uncertain.

Paleocene-Eocene thermal maximum

The decay of the Paleocene-Eocene thermal maximum (PETM) can be used to quantitatively constrain the role of the Urey reaction. The PETM was a period of elevated global temperatures (4 to 5 °C) and high atmospheric CO2 beginning at 56.3 Ma, the onset lasted less than 10 Kyr and the subsequent decay lasted about 100 Kyr (Mclnerney and Wing 2011). Storey et al. (2007) have made a strong case for associating the PETM with flood volcanism resulting from the opening of the north Atlantic.

Isotope studies have quantitatively documented the PETM. These studies have been reviewed by Gutjahr et al. (2017). These authors also provided estimates for the carbon content of the atmosphere during the PETM. They suggest that the background carbon mass in the atmosphere before and after the PETM was cMab = 1400 Gt and the peak mass of carbon was cMa0 = 3050 Gt.

We now carry out an analysis of the decay of the PETM due to the loss of CO2 from the atmosphere by the Urey reaction. We extend the balance given in Equation 5 to include the transient removal of carbon from the atmosphere and write

dMacdt=J(acc)bcMacτu.
(8)

From Equation 5 the background mass of carbon in the atmosphere is given by

Mabc=τuJ(acc)bc.
(9)

We prescribe an initial mass of carbon in the atmosphere at t = 0, cMa0 and solve Equation 7 taking τu to be constant with the result

Mac=(Ma0cMabc)et/τu+Mabc.
(10)

The excess mass of carbon in the atmosphere cMa0cMab decays exponentially as the Urey reaction extracts carbon from the atmosphere.

We next obtain the dependence of atmosphere carbon mass on time during PETM based on the model dependence given in Equation 10. Taking the values cMab = 1400 Gt and cMa0 = 3050 Gt with τu = 100 kyr the model results are given in Figure 2.

Figure 2.

Dependence of the atmosphere carbon mass values cMa for the PETM anomaly on time tPETM relative to the onset of the anomaly. The values are from our relaxation model given in Equation 11 with cMab = 1400 Gt and cMa0 = 3050 Gt and τu = 100 kyr.

Figure 2.

Dependence of the atmosphere carbon mass values cMa for the PETM anomaly on time tPETM relative to the onset of the anomaly. The values are from our relaxation model given in Equation 11 with cMab = 1400 Gt and cMa0 = 3050 Gt and τu = 100 kyr.

We now return to Equation 9. This result relates the background atmospheric carbon mass cMab to the background rate of volcanic input of CO2 carbon into the atmosphere cJ(a-cc)b and the Urey reaction rate τu. During the PETM we have taken the background carbon mass cMab = 1400 Gt. Taking τu = 100 kyr we find from Equation 9 that cJ(a-cc)b = 14 Mtyr-1. This is an independent determination of the volcanic flux of carbon into the atmosphere at that time. As discussed above, we take the present equilibrium mass of carbon in the atmosphere to be cMab = 6500 Gt. Assuming that cJ(a-cc)b = 14 Mtyr-1 we require from Equation 9 that τu = 50 kyr. This is our estimated relaxation time for a carbon excursion today.

Discussion

Urey (1952) proposed the Urey reaction, Equation 1, to explain the origin of carbonates in the continental crust. He argued that the reaction would essentially remove all CO2 from the atmosphere. It is now accepted that in analogy to Venus, there may have been a large mass of carbon in the Earth's early atmosphere, as much as 108 Gt. However, only a fraction of this may have survived the moon forming impact. We give a very simplified model for the extraction of carbon from the atmosphere to the continental curst, taking the extraction rate cJa-cc to be constant. There are basically no constraints on the variation of this rate with time. If a significant fraction of the carbon in the continental crust was extracted from the atmosphere, it is likely that it occurred early in Earth's history as illustrated in Figure 1.

The Urey reaction also controls the equilibrium mass of carbon in the atmosphere after the removal of any large initial concentration. The input of carbon to the atmosphere is from volcanism and we show that the equilibrium mass of carbon in the atmosphere cMab is proportional to the rate of volcanic injection cJa-cc divided by a characteristic Urey time τu. We quantify the value of τu by studying the observed relaxation of the Paleocene-Eocene thermal maximum, which occurred at 56 Ma, and the relaxation time is about τu = 105 yrs.

We also give a simplified model for the extraction of carbon from the atmosphere to the continental crust. If the volcanic loss of carbon from the mantle by volcanism exceeds the return of carbon by subduction, the difference is added to the continental crust. If the volcanic carbon enters the oceans organic precipitation creates carbonates. If the volcanic carbon enters the atmosphere it enters the continental crust by the Urey reaction. Current estimates of carbon fluxes from and to the mantle are sufficient to have produced all the carbon in the continental crust. At the present time, it is not possible to quantify the relative importance of carbon addition to the continental crust from the early atmosphere and the mantle.

Implications

We have addressed two major questions concerning carbon in the atmosphere in this paper. The first is the origin of the carbon in the continental crust. We conclude that it is possible the carbon could have been extracted either from the early atmosphere or from the mantle over a longer period of time. Studies of the concentration of carbon in the atmosphere and continental crust over geologic time are required and should receive a high priority.

The second question we have addressed is the relaxation of injections of carbon into the atmosphere back to equilibrium values. We quantify this by studying the Paleocene-Eocene thermal maximum (PETM). This has obvious implications for the recovery from the process of anthropogenic injection of carbon into the atmosphere. We find the relaxation time to be about 50 000 years.

Acknowledgment

It is with great sadness that we note the death of Louise Kellogg on April 14, 2019.

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