A model for soil 14CO2 and its implications for using 14C to date pedogenic carbonate

Abstract A diffusion-reaction model for soil 14 CO 2 is described that analyzes the 14 CO 2 distribution in soils. It shows that the 14 C content of soil CO 2 is not the same as that of atmospheric CO 2 and varies with depth depending on various factors. The most important factors affecting the 14 C content of soil CO 2 include the 14 C content of soil organic matter, the relative contribution of root respired CO 2 to total CO 2 production, soil respiration rate, atmospheric CO 2 concentration and 14 CO 2 content, and soil properties such as temperature and moisture content etc. The 14 C content of soil CO 2 not only can be a sensitive indicator of the residence time of decomposing organic matter in the soil, but also determines the 14 C content of pedogenic carbonate. Our model suggests that soil CO 2 could be enriched or depleted in 14 C relative to atmospheric CO 2 , depending on the relative contribution of root respiration to total soil respiration and on the turnover rate of the soil organic matter contributing to the soil CO 2 . Therefore, the initial 14 C dates of soil carbonate could differ from the true ages of pedogenesis. The processes and factors considered by the model are a first step in determining whether the 14 C content of soil carbonate could lead to reliable dates of pedogenesis.

ganic matter, which is a mixture of compounds with different turnover rates (TRUMBORE et al., 1990;TRUMBORE, 1993). Moreover, the 614C value of organic matter changes with depth and time ( GOH et al., 1976;O'BRIEN and STOUT, 1978;TRUMBORE, 1993)) suggesting that the COZ produced at different depths should have different 14C contents depending on the 14C content of soil organic matter at that depth and also on the relative contribution of root respiration to the total CO1 production. HAAS et al. ( 1983) and THORSTENSON et al. (1983) observed lower 14C contents in respired CO2 during winter time due to oxidation of older soil organic matter in the absence of significant root respiration. However, their model failed to describe the "C02depth profile observed in their study. DORR and MUNNICH ( 1986) also observed an annual 14C variation of soil-respired COZ, which they suggested is controlled by the seasonally varying contribution of root respiration and CO2 produced by microbial decomposition of organic matter.
Presently, there is no adequate model describing the 14C02 distribution in soils. Previous studies on soil CO*, and 6 13C values of soil CO*, and pedogenic carbonates indicate that the CO1 and carbonate in a soil system are in isotopic equilibrium. This implies that any detrital carbonate dissolved in the soil is overwhelmed by soil CO2 and the isotopic composition of pedogenic carbonate is determined by the isotopic composition of soil CO2 ( CERLING, 1984, 199 1;CERLING et al., 1989;QUADE et al., 1989;AMUNDSON et al., 1989;CER-LING and QUADE, 1992). If this is the case, the 14C content of pedogenic carbonate should also be determined by 14C content of soil CO2 and inherited dead carbon should not affect the age of soil pedogenic carbonate. Therefore, a better understanding of 14C02 distribution in soils would have very important implications not only in the study of organic carbon cycling in soils, but also in the application of 14C to date soil carbonate. Furthermore, the 14C content of soil CO2 is an important parameter in modeling variations of atmo-spheric j4C content as well as for determining the initial value for "'C groundwater dating, because groundwater recharges through soils.
In this study, we incorporate the "C02 isotopic species into a diffusion-reaction model which is expanded on the 6 13C (CO,) model of CERLING ( 1984 1. The purpose of our modeling is ( 1) to help us better understand the 14C02 distribution in soils; (2) to evaluate the different factors affecting soil 14C02 such as the relative contribution of root respired CO* to total CO2 production, soil respiration rate, 14C content of soil organic matter, atmospheric CO* concentration and 14C02 content, soil properties, and temperature etc.; and (3) to explore the potential appli~tion of using soil pedogenic carbonate to 14C date soils or landforms.
A DIFFUSION-REACIION MODEL FOR j4C0, Carbon dioxide is produced in soils by biological processes and is transported to the atmosphere by diffusion ( KIRKHAM and POWERS, 1972;JURY et al., 199 1) . The diffusion mechanism applies to its isotopic species '%JOz, 13C0,, and "COr as well THORSTENSON et al., 1983;CER-LING, 1984, 1991CERLING~~ al., 1989;QUADE et al., 1989). Different isotopic species of CO2 react and diffuse independently of each other according to their own concentration gradient and their own sources and sinks THORSTENSON et al., 1983). Since the concentration of 14C02 in a soil profile is controlled by the production and decay of "C02, and by diffusion through the soil to the atmosphere, the concentration of 14COz can be described by a diffusion- where Cl' represents the 14C02 concentration in the soil air ( moles/cm3), 0:' is the diffusion coefficient of 14COz in the soil (cm2/sec), @a:" is the production of "COz in the soil by organic matter decom~~tion and root respiration (moles/ cm'/sec), and X the decay constant of 14C (3.84 X 10-'2/ set). Since the term XCi4 is much smaller compared to the other terms on the right side of the equation, the above equation can be reduced to (2) To model "C02, information is needed regarding the production of 14C02 (+i4) in a soil. With the simplified assumption that soil COz is primarily produced (a) by root respiration with practically no difference in 14C from atmospheric COz, and (b) by decomposition of soil organic matter with the same 14C content as decomposing organic matter, the relative contribution of these two reservoirs to the soil 14C02 production can be calculated with a two-component mixing model following the equation: ( 14C/ "C), = F*( 14C/ '%),.,.+(I -F)*(i4C/'2C)stm.,where(i4C/'2C)zisthe'4C content of biolo~~ly produced CO2 in the soil at depth z; F is the relative contribution of CO2 from organic matter decomposition, the fraction of CO2 derived from root respiration is 1 -F, and ( 14C/ '2C)o.m. and ( 14C/ "C),,, are 14C content of decomposing organic matter and the atmosphere, respectively. The production of "C02 can then be described by: @i"(z) = @I2 14C02 ( 1 where a* and @" are the total CO2 and *'CO, production rates, respectively; 6 13CQ is the 6 13C value for respired CO2 , and RP~B is the ratio ( '%/ "C) in the isotopic standard PDB.
Using the notation, where S j4C is the permil value for 14C content ( STUIVER and POLACHE, 1977), and & is the absolute 14C/12C ratio in the isotopic standard ( NBS oxalic acid). The 6 14C notation here is the same as that used in oceanography and is not corrected for d 13C. Substituting the notation into Eqn. 4,

914(z) = "'*[F($$+ l)(R,,)
Assuming that the soil can be approximated as a one-dimensional box with a non-flux boundary at depth L, the following boundary conditions exist: For the condition that the '"C content of decomposing organic matter diminishes with depth in a linear fashion, i.e., s'4Co.m. = A + Bz, which is the case in most soils (O'BRIEN and STOUT, 1977;TRUMBORE et al., 1990, SCHARPENSEEL et al., 1989, and that +* and F is constant with depth, the steady-state solution to Eqn. (8) where C$ and Cl' are CO* and 13CCi2 concentrations in the atmosphere; C: and C:' are corresponding concentrations in the soil air; and 0: and 0:' are diffusion coefficients for COz and "COz, respectively. The diffusion coefficient for CO* in soil is related to that in air (Da+) by where c is the free air porosity in the soil, and p is a tortuosity factor (KIRKHAM and POWERS, 1972;JURY et al., 1991). where D%l is the diffusion coefficient for COz in air under standard conditions (To = 25°C and P" = 1 bar pressure) and is taken to be 0.144 cm2/s.  The diffusion coefhcients of 14C02 and '*CO2 are related Using Eqns. 6, 7, and 8 and using various values of soil respiration, an atmospheric CO2 concentration of 300 ppm, and atmospheric 6 "C and 6 14C values of -6% (pre-industrial value) and 0% (pre-bomb value), respectively, it is possible to calculate "C0, ( 6 14C) profiles in soils for various conditions. Figure 1 shows how the 6 14C value of soil COz varies with depth in a model soil where the 14C02 concentration is diffusion-controlled. The parameters for the model soil are listed in Table 1. This diagram displays several important features: The 6 14C value of soil CO1 is not necessarily the same as that of atmosphe~c C02, ~~0~~ it has been assumed so in previous studies using 14C to date soil carbonate. However, the present-day analytical precision at best is rt3k, and for most accelerator labs the analytical precision is +8%0. Therefore, when F is small, for example F = 0.1, the 6 14C value of soil CO2 can be considered the same as that of atmospheric CO=. The S14C values of soil CO2 are not constant with depth. The 6 14C values of soil CO2 depend on the S14C values of soil organic matter, soil respiration, and the relative contribution of CO2 derived from organic matter decomposition to total COz production (F) . When the fraction of CO, derived from organic matter d~om~sition (F) # 0, the 6 14C values of soil CO, vary continuously from the atmospheric value at the soil-atmosphere interface to more negative values at depth. Increasing the value of F, the 6 14C values of soil CO, at any depth become more negative. When F = 0, the S 14C values of soil CO2 vary continuously from the atmospheric value at the soil-atmosphe~ interface to more positive values at depth. This increase in 6 14C values is a result of diffusion effects on the different isotopic species ( CERLING et al., 199 1). If the 14C data are corrected for isotope fractionation using 13C data (i.e., A14C in STUIVER and POLACH, 1977), this diffusion com~nent will not be seen. Figure 2 shows how the 6 14C values of soil COz vary with soil respiration rates. It is evident that at a given value of F, the higher the soil respiration, the more the S14C values of soil COz deviate from that of atmospheric COz. When all soil CO2 is derived from root respiration and/ or decomposition of short-lived organic matter which has the same 14C content as the atmospheric CO2, the 6 14C values of soil CO2 are relatively enriched (up to 8.5% at 15°C) compared to 6 r4C values of atmospheric CO2 (Fig. 3 ) due to diffusion effects. The lower the respiration rate or the higher the value of the diffusion coefficient, the less enriched the 6 14C values of soil COz are relative to the 614C values of atmospheric COz . When soil respiration = 0, the 6 14C values of soil CO2 are the same as the 6 14C values of atmospheric CO2 . Again, considering the present-day analytical precision of +8k for 14C analysis, this diffusion effect on r4C content of soil CO2 would be beyond detection.
These figures show soil "C02 relationships for pre-industrial atmospheric conditions. To use this model to evaluate present-day soil conditions, one must change the atmospheric boundary conditions for COz , '*C02, and 14C02. In our test of the model against empirical data given below, various "'C,, values are used, based on the reported data.

OBSERVATIONS IN SOILS
It is important to establish if the above "C02 model is valid in soils. Presently, there are few 14C02 depth profiles available. In Fig. 4, the 14C data (reported as A 14C, percent modem carbon (pmc) = (6'4C/1000 + 1)(1 -2*(25 + 6 13C)/ lOOO)* 100) for soil CO2 and CO2 concentrations (data obtained in May) from site #6 in HAAS et al. ( 1983) and THORSTENSON et al. ( 1983) are plotted (different symbols represent different sampling dates) and compared to our model calculation (solid line). Since there were no "Co.m. data and no COz production information reported in their study, we assumed that the r4C02 production is an exponenac:" tial function of depth as (Pi4(z) = @:4(0)e-b' withaz =Oatz=L(L=380cmwasusedinthemodelcalculation), where @i"(O) is the production of 14C02 at surface and b is a constant (we use b = 0.003 in the model calculation). We also assume that production of CO2 is an exponential function of depth in their soil as a:(z) = @~ (0) depth for soils where all CO2 is derived from root respiration and/or decomposition of short-lived organic matter. It can be seen that the S14C values of soil CO2 are relatively enriched compared to 8 "'C values of atmospheric CO* due to diffusion effects. Figure 3 (a) shows that the lower the respiration rate, the less enriched the 6 "C values of soil CO* are relative to the 6 14C values of atmospheric CO*. Figure 3 (b) shows the effect of varying diffusion coefficient on the 14C content of soil air.
where C:" and C,+ are "C02 and CO2 concen~ations in the soil; Ci' and C,* are corresponding concentrations in the atmosphere; and L and L' are the depth of the non-flux boundaries for 14C02 and CO*, respectively (the non-flux boundary is a boundary where COz or 14C02 concentration gradient equals to zero). Other assumed parameters used in our model calculation are listed in Table 2. In their study, THORSTENSON et al. ( 1983) concluded that the measured 14C0, profiles cannot be readily explained with a diffusion model due to some as yet unexplained mechanisms. However, Fig. 4 suggests that our curve fits their data reasonably well, except for one datum point at the 15.9 meter depth. This point represents a groundwater CO* sample and, therefore, may be contaminated by carbon from other sources. The goodness ofthe fit is adequate to strongly suggest that vertical diffusion is indeed the dominant mass-transport mechanism affecting 14COz and CO2 distribution in this soil. It should be noted that S"'C value of atmospheric COz (the upper boundary condition) is greater than 0% (the boundary condition used in Figs. l-3 ) . This is because present atmospheric The goodness of the fits suggests that diffusion is indeed the dominant mechanism affecting the CO* and "COz distribution in the soil. The datum point at 15.9 meter depth represents a groundwater sample and, therefore, may be contaminated by carbon from other sources.
14C content is elevated above natural levels by nuclear weapons testing and use. Figure 5 compares the 14C02 and CO2 data from two Oxisol profiles (a forest soil and a 17-year-old pasture soil which is a degraded forest soil) from Paragominas in Brazil ( NEP~TAD et al., unpubi. data)  The solid dots represent a forest soil and the open circles a pasture soil (a degraded forest soil). For each soil, the "'CO, and CO* data are fitted using the same set of parameters (i.e., same respiration rate, diffusion coefficient, porosity, temperature, and pressure). Diffusion appears to be the dominant mechanism controlling the '"CO, and CO,, distributions in these two soils. and Nepstad. The measured CO1 respiration rates for May are 25 mmoles/m*/h for the forest soil and 10 mmoles/m2/h for the pasture soil. For each soil, the 14C02 and CO2 data are fitted using the same set of parameters (i.e., respiration rate, diffusion coefficient, porosity, temperature, and pressure) ( Table 2). The measured CO2 respiration rate for the forest soil seems too high because it requires an unreasonably high diffusion coefficient and/or porosity to produce the observed soil 14C02 and CO2 profiles. The high respiration rate reflects the decomposition of abundant litter on the forest floor which could have contributed significant amounts of CO2 to the total CO2 flux measured at the soil surface and higher production of CO2 in the upper 2 meters of the soil. In our model calculation we used a value of 13 mmoles/m'/ h for respiration rate for the forest soil which gives a reasonable fit to both the 14C02 and CO2 data. Again, vertical diffusion appears to be the dominant mass-transport mechanism affecting 14C02 and CO2 distribution in these soils. However, unlike the data of HAAS et al. ( 1983)) the 14C content of soil CO2 is greater than present atmospheric values. Since soil CO2 is produced by root respiration and decomposition of soil organic matter which is a heterogeneous mixture of compounds turning over at different rates, the observed 14C profiles hem suggest that the fractions of soil organic matter whose turnover contribute the most to the soil CO2 contains a considerable quantity of bomb-produced 14C.

IMPLICATIONS FOR '% DATING OF SOIL CARBONATE
Dates from soil carbonates have been considered unreliable estimates of the age of pedogensis because of unknown initial 14C/ "C ratios in the carbonate and the possibility of subsequent contamination with environmental 14C (CALLEN et al., 1983). Comparison of carbonate 14C ages with 14C ages of coexisting organic matter suggests that radiocarbon dates calculated from pedogenic carbonate in arid areas were about 500 to 7000 radiocarbon years too old (WILLIAMS and Po-LACH, I969 ). On the other hand, radiocarbon dates of pedogenie carbonate from the sub-humid part of southeastern Australia were much younger than either the known age of deposition in which the carbonate is segregated, or the likely age of pedogenesis (BOWLER and POLACH, 197 1). These discrepancies have been attributed to an initial low 14C content of soil carbonate due to the limestone dilution effect and/or secondary contamination by environmental 14C. The limestone dilution effect (BARTLETT, 195 1;BROECKER and WALTON, 1959) states that soil carbonate derives half of its C from dead calcium carbonate and another half from atmospheric CO?, suggesting that radiocarbon age of such carbonate would be about one half-life of 14C (about 5570 years) older than the true age. However, studies on soil CO2 and 6 13C of soil CO2 and pedogenic carbonates indicate that the CO2 and its isotopic species in a soil system are in isotopic equilibrium. This implies that C derived from dissolving detrital carbonate is ultimately lost through isotopic exchange with soil CO1 and isotopic composition of pedogenic carbonate is determined by the isotopic composition of soil CO:! (CERLING, 1984(CERLING, , 1991CERLING et al., 1989;QUADE et al., 1989;CERLING and QUADE, 1992). We have shown that 14C content of soil CO2 can be depleted or enriched relative to that of atmospheric CO2 depending on various factors. Soil carbonate formed during the early development of a soil, when 14C content of soil organic matter is about the same as that of the atmospheric C02, could have 14C ages younger than the true age of the pedogensis. On the other hand, carbonate formed later on in a soil, could have 14C ages older than the true age of the carbonate precipitation. Elsewhere, we ( AMUNDSON et al., 1993) explore in detail the effects of our diffusion/reaction model on carbonate 14C ages.

CONCLUSIONS
The distribution of 14C02 in soils can be described by a diffusion-reaction model. The 14C content of soil CO2 varies with depth depending on many factors: the 14C content of soil organic matter, the relative contribution of root respiration to total CO2 production, soil respiration rate, atmospheric CO2 concentration and 14C content, soil properties, temperature, etc. Our model suggests that 14C ages of pedogenie carbonate could be older or younger than the true age of pedogensis. While there are other factors that can also affect the 14C age of a carbonate sample (such as sample thickness, i.e., the total time required to form the sample being measured), our basic understanding of the initial 14C contents of pedogenic carbonates is the first step to critically evaluating their potential as indicators of landform age.