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ARTICLE IN PRESS 14 N.D. Sheldon, N.J. Tabor / Earth-Science Reviews xxx (2009) xxx–xxx Fig. 9. Mass-balance of major and trace elements. Ca and Na are lost throughout the profiles, whereas both K and Rb were added. pedogenesis. The equation for delineating pedogenesis from addition is: Δ P = τ K − τ Rb ð13Þ where Δ P is the change in K due to pedogenesis. Fig. 10 shows Δ P values as a function of depth in the same paleosol in Fig. 9B. The adjusted K loss is now similar to that of Na, another alkali element, which is similar to the pattern observed in modern basalt-parented soils (Chadwick et al., 1999). Thus, mass balance may be used to differentiate between different pedogenic processes and sources of elemental additions and losses. The obvious limitation to applying any type of mass balance calculation is being able to demonstrate that one or more elements was immobile or nearly immobile during weathering. Because true immobility is unlikely, the relative degree of immobility is important. ε i,w values of ±0.4 indicate limited mobility, but ideally, unless there is a strong basis for inferring addition or removal by physical weathering processes, values closer to 0 are preferable. For example, when volcanic rocks weather, many of the mafic minerals (e.g., olivine, pyroxene, plagioclase feldspar) chemically weather readily under most pH conditions, whereas rutile (TiO 2 ) will only be removed by physical weathering except at very acidic pH conditions. Thus, addition of Ti 4+ is unsurprising in that case and the relative degree of enrichment will in fact be tracking pedogenesis, and at least indirectly, giving weathering intensity. If on the other hand ε Ti,w is less than 0 in the same setting, that suggests that some erosion of the paleosol has taken place or that there has been downprofile translocation of the Ti-bearing minerals. Distinguishing between those processes is key to understanding how that paleosol developed. Therefore, care is needed in selecting and testing “immobile” elements to ensure that they truly represent pedogenic immobility. The other factor that is important in considering mass balance results is the role that formation time plays. Short duration, intense weathering may result in similar elemental gains and losses as long duration, low intensity weathering. Tightly constraining formation times for paleosols, in particular for pre-Quaternary paleosols, is very difficult, though a few methods have been proposed that are independent of chemical composition (cf. Sections 5.2.3–5.2.4; Birkeland, 1999; Retallack, 2001a,b; Sheldon, 2003; Retallack, 2005b). For example, Sheldon (2003) used data from Markewich et al. (1990) to propose the following relationship relating formation time (T f in years) to Bt horizon thickness (T Bt ): where R 2 =0.87, no error function was calculated because the relation falls apart for very long-formation times. Retallack (2005b) did something similar for Bk horizons where he found a relationship between soil age (A in Ka) and nodule size (S in cm): A = 3:92S 0:34 ð15Þ where R 2 =0.57 and the standard error is 1.8 Ka. While these chronofunctions hold some promise for paleosols with either Bt or Bk horizons, they are both based on relatively few data (n=10 for Sheldon, 2003; n=9 for Retallack, 2005b) and many soil/paleosols types lack those particular horizons. Semi-quantitative relationships discussed in Birkeland (1999) also offer some promise for at least making appropriate order-of-magnitude age estimates, but significantly more work is needed in this area. 5.3.2. Precambrian atmospheric CO 2 from mass balance Because Precambrian paleosols formed at the Earth's surface, in direct contact with the atmosphere at the time of their formation, they are considered to be one the best lines of evidence for determining the composition of the Precambrian atmosphere (e.g., Zbinden et al., 1988; Holland and Zbinden, 1988; Rye et al., 1995; Rye and Holland, 1998; Retallack, 2001b; Sheldon, 2006b). The three gases of primary interest are CO 2 and CH 4 (Pavlov et al., 2000, 2003) as greenhouse gases that allowed the Earth to overcome the “faint young Sun” paradox (Kasting, 1993) early in its history, and O 2 , because there is T f = 17:07 ðT Bt Þ 2 + 645:8 ðT Bt Þ ð14Þ Fig. 10. True K mass balance. Please cite this article as: Sheldon, N.D., Tabor, N.J., Quantitative paleoenvironmental and paleoclimatic reconstruction using paleosols, Earth- Science Reviews (2009), doi:10.1016/j.earscirev.2009.03.004
ARTICLE IN PRESS N.D. Sheldon, N.J. Tabor / Earth-Science Reviews xxx (2009) xxx–xxx 15 extensive evidence to suggest that O 2 levels increased substantially at ~2.3 Ga ago (various; Bekker et al., 2004 and references therein). Understanding the “faint young Sun” paradox is one of the fundamental questions in Earth Sciences, because with significantly reduced solar insolation, the Earth should have been completely glaciated if there was not significantly higher levels of greenhouse forcing than at present (Kasting, 1993). As will be discussed further below in Section 6.2, one of the difficulties of reconstructing CO 2 and CH 4 levels is to divorce the method from assumptions about precisely what level of oxygen was present. For example, Holland and Zbinden (1988) discuss a method that looks at the balance between O 2 and CO 2 as indicated by weathering processes in a ~1.1 Ga old paleosol in the form of a ratio between CO 2 and O 2 consumption. Of potentially wider applicability is a method for calculating CO 2 levels that is independent of any assumptions about the atmospheric O 2 level. Sheldon (2006b) presented such a model based on mass-balance calculations (see Section 5.3.1) of silicate weathering that related elemental weathering to atmospheric CO 2 levels. During silicate weathering, total CO 2 consumption can be approximated by the following reactions: MgO þ 2CO 2 þ H 2 O→Mg 2þ þ 2HCO − 3 CaO þ 2CO 2 þ H 2 O→Ca 2þ þ 2HCO − 3 Na 2 O þ 2CO 2 þ H 2 O→2Na þ þ 2HCO − 3 K 2 O þ 2CO 2 þ H 2 O→2K þ þ 2HCO − 3 ð16Þ ð17Þ ð18Þ ð19Þ where, for example, each mole of base cation (e.g., MgO) liberated requires two moles of CO 2 (e.g., Holland and Zbinden, 1988). Although other elements are weathered, with few exceptions (e.g., a quartz arenite) the parent rock concentration of the bases in reactions (17– 20) are at least 1–2 orders of magnitude larger than any other mobile element. Because K may be remobilized metasomatically and accumulated in paleosols after burial (e.g., Maynard, 1992), it has to be dealt with differently than Ca, Mg, and Na, typically by assuming that K mass transfer values should be equal to Na mass transfer values or potentially, by using Eq. (14). Mass transfer values (Eq. (12)) for each of those individual cations can be transformed into mass fluxes as follows: m j;flux gcm − 2 = ρ p C j;p 100 Z = D Z j;w Z =0 τ j;w ðÞ z dZ ð20Þ where Z is the depth in the soil profile and D j,w is the total depth of the profile (e.g., Chadwick et al., 1990). Given that many Precambrian paleosols have been deeply buried and show evidence of significant compaction (e.g., Retallack, 1986 showed ptygmatically folded quartz dikes), it is necessary to decompact the paleosols to their original thickness D j,w using Eq. (4). After the compaction-corrected mass fluxes are calculated for each individual base cation and coverted to moles, because 2 mol of CO 2 are required to liberate each mole of base cation (Eqs. 17–20) the total flux of CO 2 required for the observed weathering (M) is given by: M mols CO 2 cm − 2 =2 X m j; flux ð21Þ Soils do not form instantaneously, so to calculate a true flux value, M must be divided by time (T). With limited biological productivity as in the Precambrian, the time-averaged flux (M/T) is a product of two distinct sources of CO 2 ,CO 2 in the atmosphere being added by rainfall to the soils (X rain ), and CO 2 added by direct diffusion into the soils (X diff ). Holland and Zbinden (1988) quantified X rain and X diff as follows: M T mol cm − 2 yr − 1 K CO2 r = X rain + X diff ≈pCO 2 + κ D CO 2 α 10 3 L ð22Þ where pCO 2 is the partial pressure of atmospheric CO 2 (atm), K CO2 is the Henry's Law constant for CO 2 , r is rainfall rate (cm yr − 1 ), D CO2 is the diffusion constant for CO 2 in air (0.162 cm 2 s − 1 ; CRC Handbook), α is the ratio of diffusion constant for CO 2 in soil divided by the diffusion constant for CO 2 in air (discussed below), L is the depth to the water table, and κ is a constant which is the ratio of seconds in a year divided by the number of cm 3 per mol of gas at standard temperature and pressure (1.43×10 3 (s cm 3 )/(mol year)). There is no explicit term including any CO 2 processes involving a terrestrial biosphere (i.e., it is assumed to play a negligible role), a point that was further discussed by Sheldon (2006b), but which is a reasonable simplifying assumption (however, see Yapp and Poths, 1993). Eq. (23) also assumes that the CO 2 diffusion constant and gradient are constant with depth, and that the partial pressure of atmospheric CO 2 is much larger than the partial pressure of CO 2 at the water table (depth=L). Eq. (23) can be rearranged to solve for atmospheric pCO 2 as follows: M pCO 2 = h i T K CO r 2 + κ D ð23Þ CO α 2 10 3 L Thus, by quantifying M using direct measurements of paleosol mass balance and estimating T and L, it is possible to calculate the partial pressure of atmospheric CO 2 at the time the paleosols formed. Sheldon (2006b and supplemental materials) discusses the uncertainties in the model assumptions, but in general, only T is poorly constrained and makes a significant (N10%) difference to the calculated pCO 2 value. Among the results of applying this mass-balance paleobarometer were that the pCO 2 value ~2.2 Ga ago was 23 ×3 3 times present atmospheric levels (PAL), an amount insufficient to overcome the “faint young Sun” paradox at that time, that similar pCO 2 values persisted until at least 1.8 Ga ago, and that much lower pCO 2 values were present by 1.1 Ga ago (Sheldon, 2006b). Each of those conclusions was based on analysis of multiple contemporaneous or near-contemporaneous paleosols. The finding that pCO 2 levels at ~2.2 Ga ago were insufficient to overcome the “faint young Sun” paradox is further supported by atmospheric modeling results (Pavlov et al., 2000, 2003), which also suggest the need for an additional greenhouse gas such as CH 4 . The third conclusion, of relatively low pCO 2 levels (b10 PAL) ~1.1 Ga ago is also supported by recent results from a completely independent proxy, a paleobarometer derived from calcified cyanobacteria (Kah and Riding, 2007). Thus, if a reasonable estimate for T may be made, then this method appears to be very useful for estimating Precambrian pCO 2 . 5.4. Paleotemperature In addition to isotopic paleothermometers (see Section 7 below), there have been recent attempts to develop paleothermometry based on empirical relationships relating mean annual temperature (MAT) to the geochemical composition of modern soils. Using data from Marbut (1935) and modern measurements of MAT, Sheldon et al. (2002) proposed the following relationship between MAT and salinization of a Bw or Bt horizon (Table 3): Tð ○ CÞ = − 18:5S +17:3 ð24Þ Please cite this article as: Sheldon, N.D., Tabor, N.J., Quantitative paleoenvironmental and paleoclimatic reconstruction using paleosols, Earth- Science Reviews (2009), doi:10.1016/j.earscirev.2009.03.004
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