4.1. Assessing the Magnitude of Chronological Improvement
[15] Ideally, a sediment core would possess either easily datable foram tests or enough fresh organic material to separate specific compounds at an adequate yield for radiocarbon dating. Near KC49, at the lowlatitude reaches of the Antarctic Peninsula, the latter seemed a viable option in terms of the amount of organic material. Dates from specific compounds as well as compound classes proved to be highly ambiguous indicating significant reworking of the sediment and mixing of organic material of different ages [Ohkouchi et al., 2000]. In the subice shelf sediments of KC5, fresh sterols were not extractable from any horizon below the surface sediments due to both low productivity below the ice shelf and dilution of organic material by diagenetically altered material [Roe et al., 2006]. In both cases, reworked organic material has likely attained a higher degree of diagenetic stability, yielding leverage by which fresh organic material could be isolated and dated.
[16] The aim of this experiment was to release fresher material first. Neither combustion nor pyrolysis is perfect in this regard. Pyrolysis was chosen as preferable because it is less purely a chemical distinction. Fresh organic debris was expected to yield more volatile products than diagenetically altered organic material. The results in Figures 4–6 illustrate success in separating, to a first order, components of different ages.
[17] The results in Figures 4–6 also indicate the significant improvement in chronology achieved by this method. Despite the improvement, the results show that the actual ages of these sediment horizons, while better constrained, remain unknown (KC49) or unresolved (KC5). Pyrolysis of NaHCO_{3} illustrates an ideal situation where the pyrolysis products of carbon sources (one source from dehydration of NaHCO_{3} at ∼180°C, and another from decomposition of Na_{2}CO_{3} at ∼850°C) with different thermal stabilities are well separated and easily differentiable (Figure 3). It is unrealistic to expect such an ideal resolution of carbon components when dealing with multiple sources of organic material. Instead, an optimistic expectation for our approach would be the resolution of a lowtemperature age plateau. The significant differences between lowtemperature ages in KC49 244–245 (i.e., the lack of a lowtemperature age plateau) indicate that even the lowesttemperature fraction contains at least some older, allochthonous material, and the proportion of this material increases from a value greater than zero in the lowesttemperature fraction. Greater mixing of preaged carbon into the first temperature interval would be expected of less finely resolved KC5. Thus the youngest age from this approach represents a maximum age constraint for the autochthonous material in this particular core horizon, and it is likely that the actual age of autochthonous material may be younger. In order to apply this method to compare sedimentary records to highresolution paleoclimate archives, a means to estimate the maximum likelihood ages of the autochthonous carbon fraction must be established.
[18] A twopoint mixing model with both an autochthonous and an allochthonous endmember would be desirable; however, neither core lends enough clues for success with such a simplified approach. Figures 4b and 5 illustrate that the method confidently determines the isotope ratios of the allochthonous endmember in KC49 244–245 cm (i.e., there is a hightemperature age plateau), with a δ^{13}C ratio of −26.8 ± 0.6‰ and a f_{M} of 0.079 ± 0.012 calculated from the averages and standard deviations of the final four temperature intervals. In the absence of either a complementary lowtemperature plateau or knowledge of the mixture proportions, however, a mixing model cannot be constructed. If ages were known with better confidence either upcore or down core as in KC5, an extrapolation could be made to 244–245 cm and used to estimate the absolute age of the young AIOM and, subsequently, the proportion of older material present. Although sediment deposited in diatomaceous horizons above 244–245 cm in the core may yield higher proportions of autochthonous organic material, the sediment core KC49 contains no horizons with datable material other than AIOM, rendering this approach to establishing a mixing model unwieldy. The situation in KC5 is not much improved despite knowledge of foraminifer ages. Here, the subsampling of pyrolysis products was not of high enough resolution to estimate either a preaged or autochthonous endmember. Furthermore, in presence of differential deposition [Mollenhauer et al., 2005] and bioturbation relative to particle size [Bard, 2001], the question of the true age of AIOM would remain in spite of a foramifer age.
4.2. An Objective Estimate of the Autochthonous Component
[19] Without the necessary information for construction of a simple mixing model, an independent method by which ages, isotope ratios, and relative contributions of AIOM components can be conceived using only the structure of the thermograph in Figure 5. Even in the absence of discrete peaks such as those provided by NaHCO_{3} (Figure 3), the KC49 thermograph demonstrates the presence of multiple components simply in terms of variations in the radiocarbon and stable isotopic compositions of individual temperature fractions. In absence of the lowtemperature plateau, two inflection points on the rising limb of the thermograph can be conceived to signify changes in proportions of young, intermediate, and old sources of carbon. An estimation of the amounts of these components can be used to approach the maximum likelihood age and the relative proportion of the young AIOM component with an assumption about the pyrolysis kinetics of the individual AIOM components.
[20] In similar stable isotopic measurements of pyrolysis products, a Gaussian distribution of pyrolysis activation energies constituted a workable firstorder approximation where the pyrolysis kinetics of the chemical classes present within the substrate were not precisely known [Cramer, 2004]. The thermograph of KC49 244–245 (Figure 5) can be decomposed into three Gaussian curves using a nonlinear regression procedure (Figure 7). An attempt to decompose the thermograph into four Gaussian curves resulted in an increase in iterations of the model from 18 to 111, which supports the significance of the inflection points suggested by the structure of the thermograph and illustrates the futility of trying to discern minor components (components that are small enough to not cause thermograph inflection points) despite the likelihood of their presence. Although several local minimizations exist, the two most plausible solution sets are shown in Table 2.
Table 2. Gaussian Parameters of Plausible Solution Sets to the Nonlinear Regression of the Thermograph Data^{a}  Solution 

1  2 


Component 1   
Height, μmol/mol  606  308 
Center, °C  324  286 
Width, °C  82  57 
Component 2   
Height, μmol/mol  569  2296 
Center, °C  409  473 
Width, °C  47  120 
Component 3   
Height, μmol/mol  2814  805 
Center, °C  505  532 
Width, °C  95  64 
RMSR  14.32  21.73 
[21] With three significant components of unknown age and δ^{13}C, the nine measurements of these quantities can be used to describe an overdetermined system of linear equations:
where superscripts M and C refer to measurements and significant components, respectively. In this case, i is the number of measurements and j is the number of components. Vectors [A] can be either fractions modern of radiocarbon (uncorrected for δ^{13}C) or stable isotope compositions, with the component fraction matrix [f] determined by the nonlinear regression of Gaussian solutions to the thermograph with the minimum residual summed between temperature divisions used during the experiment. To account for all CO_{2} evolved during each ith temperature interval of each pyrolysis, we use the equality,
whereby each ith row of the component fraction matrix [f] must sum to 1.
[22] Radiocarbon solutions of equation (1) for the proportions in Table 3 must be constrained to prevent negative fractions modern. Further, fractions modern uncorrected for stable isotope composition are used in vector [A^{M}], but fractions modern are recorrected to specific component δ^{13}C values from vector [A^{C}] after equation (1) has been solved for both isotopes measured. No constraints were applied to the stable isotope solutions to the system. For both the radiocarbon and δ^{13}C systems, a constrained nonlinear routine was employed, with initial guesses similar to the simple algebraic solutions. Equation (1) was solved for [f] constructed from two plausible Gaussian regression solution sets (Table 2) despite one set producing a significantly lower residual. The solution of equation (1) using Gaussian regression 2 (Table 2) includes a component with f_{M} < 0, rendering it unstable and confirming the lesser root mean square of the residuals of solution 1 as an indicator of the most realistic solution.
Table 3. Component Proportions of Gaussian Decomposition, Solution 1^{a}Interval  Component 

1  2  3 


1  0.96  0.00  0.03 
2  0.62  0.15  0.23 
3  0.20  0.33  0.47 
4  0.06  0.21  0.73 
5  0.01  0.05  0.94 
6  0.00  0.01  0.99 
7  0.00  0.00  1.00 
8  0.00  0.00  1.00 
9  0.00  0.00  1.00 
Total  0.16  0.08  0.76 
[23] At an age of 10,520 years, the youngest component in the solution to equation (1) is indistinguishable from the maximum age constraint provided by direct measurement of the lowtemperature pyrolysis age. All of the stable isotope values in the δ^{13}C solution set are within published measurements on compound class carbon isotopic values from nearby Antarctic seas [Ohkouchi and Eglinton, 2006]. The model is consistent, but how accurate is this objective estimate of the actual age and proportion of autochthonous material at this core depth in KC49? The answer lies in the assumptions about reaction kinetics for the pyrolysis of sedimentary organic material from the east coast of the Antarctica Peninsula. It is prudent, therefore, to constrain the autochthonous age with an independent approach for comparison in absence of knowledge of the exact reaction kinetics.
[24] Comparing endmember characteristics with inverse cumulative yield normally results in a linear relationship if the model is of simple mixing. Assuming the amount of autochthonous carbon is negligible in the temperature intervals after the first, this relationship (Figure 8) can provide further constraint on the age of the autochthonous component. The slope of this linear relationship (b) is related to the autochthonous age (expressed here as Δ^{14}C) by
where subscripts s and t refer to autochthonous and allochthonous components, respectively, and N is the number of micromoles of carbon in the lowesttemperature interval, assuming that only negligible amounts of the autochthonous component were present in temperature intervals 2–9 and that the final four intervals are representative of the preaged endmember. In other words, the age difference between the autochthonous component and the oldest allochthonous carbon is related to the slope of the linear relationship in Figure 8, in proportion to the amount of autochthonous material in the lowesttemperature interval. Given information about the age of the allochthonous component and the proportion of autochthonous component in the lowesttemperature interval, an additional age constraint on the autochthonous component can be derived. Again, Figure 5 illustrates that a fair estimate of the allochthonous fraction is provided by the final four temperature intervals (f_{M} = 0.079 ± 0.012). Further, the Gaussian decomposition approach allows a viable estimate of the fraction of autochthonous material in the first temperature fraction (0.96, Table 3); however, it does not provide a straightforward uncertainty (the largest uncertainty is likely the model selection, in any case). If the first temperature interval was entirely autochthonous carbon, these values would yield an age of 9650 ± 330 ^{14}C years. This age decreases to 9020 ± 300 ^{14}C years if it is assumed that the lowesttemperature interval consisted of only 90% autochthonous carbon. Such a range in compositions is not entirely out of the question, especially in the case where our assumption of Gaussian reaction kinetics is not accurate. The range in ages of these scenarios varies from the maximum likelihood Gaussian component age of 10,520 ^{14}C years by significantly more than the analytical uncertainties of radiocarbon dates in this age range. Still, the difference between these maximum likelihood ages is much less than the difference between bulk dates and the maximum age constraint directly measured from the lowtemperature fraction.
[25] The KC5 subice shelf core provides an additional test of the pyrolysis method against known ages from foraminifer tests in each horizon. Figure 9 shows a Gaussian decomposition for both horizons using the same initial guess. The resulting four Gaussian distributions of major components does well to fit the thermograph of this core which is significantly more descriptive in both horizons than the analyzed horizon of KC49. Gaussian components from each horizon in KC5 are centered on the same temperatures indicating a geochemical significance of the components. Unfortunately, only 2–3 actual measurements were made on these horizons rendering the system of equations (equation (1)) underdetermined (i < j). This has two consequences. First, equation (1) cannot be explicitly solved for either isotope measurement. Second the inverse yield mixing model discussed above would be in violation of its assumptions of no mixing in the first temperature interval due to the higher temperature defining that interval. This is not to say that every one radiocarbon date must become nine to employ this method; rather enough measurements need to be made to equal or be greater than the amount of major components and at least one sample must come from at or near the cutoff temperature where preaged carbon begins to volatilize to alleviate the two consequences, respectively.
4.3. Improving the Method
[26] Evaluation of these two mathematical approaches relative to each other aids in determining which one is more accurate; however, the question is immaterial in comparison to the difference between these age estimations and the bulk AIOM age. The Gaussian approach relays a maximum likelihood age estimation, which is as likely as the assumption of Gaussian pyrolysis activation energies. The linear model approach yields another maximum age constraint which is lower than this maximum likelihood age. The linear mixing model approach makes the assumption of two components in the mixture with negligible amounts of the lowtemperature component in subsequent intervals. Conceptually this is favorable, and the Gaussian approach supports the second assumption with only 4% of the autochthonous component being distributed over the remaining 8 temperature intervals. However, the Gaussian approach strongly suggests a third major component which depicts reality more complex than the two component linear model. The difference between these two estimates, however insignificant relative to our assumptions and the bulk age, illustrates that more must be understood about the pyrolysis reactions, but it is not large enough to discredit the significant improvement in chronology offered by this analytical method. Furthermore, improvement of the method is tangible.
[27] Analytically, sampling resolution is ultimately limited by sample size. Our effort to choose a target sample size of 12 μmol C in the proof of concept experiment (KC49) minimized counting error on AMS analysis of small samples while maximizing the amount of temperature bins analyzed. Sampling at shorter temperature intervals than this is certainly possible but involves a proportional decrease in precision. Short of establishing a maximum likelihood age from the nine radiocarbon measurements, the Gaussian decomposition of the thermograph provides a firstorder estimate of the lowtemperature cutoff point at which allochthonous C becomes mixed with the youngest major component (Figures 4 and 9). The amount of CO_{2} evolved from KC49 before this temperature (250°C) is approximately 5 μmol (a small but measurable amount), whereas the next 60°C resulted in an additional 7 μmol C.
[28] Sampling at a higher resolution in the temperature domain without sacrificing AMS measurement precision of robust small samples (>10 μmol C) would be ideal. Simply increasing the amount of sediment loaded into the reactor does not seem a viable option. Larger sediment weights either carry enough thermal inertia even during exceedingly slow temperature ramps and/or are volumetrically large enough to be differentially heated by thermal heterogeneities within the furnace to blur the resolution between components. This was observed by the lack of return to baseline levels of CO_{2} evolution measured photometrically, even at temperatures as high as 1000°C for several tens of minutes, during pyrolysis of larger samples (∼0.5 g). Without increasing sample size, the mathematical approach laid out above illustrates that it is likely that we can analyze a nearly pristine sample of autochthonous C, with some sacrifice in precision on a 5 μmol sample. Attempts to observe any lowtemperature plateau in multiple aliquots of the first 5 μmol for an unequivocal estimate of this age is unlikely due to the higher statistical counting error associated with sample sizes less than 5 μmol. Of course, our estimation of 275°C as the temperature at which mixing of predated C begins to happen during pyrolysis would benefit greatly from a critical assessment of the assumption of Gaussian pyrolysis activation energies of the components.
4.4. Differential Deposition and Bioturbation
[29] Our data corroborate a number of recent reports [Mollenhauer and Eglinton, 2007; Mollenhauer et al., 2005, 2006; Villinski et al., 2008] demonstrating that sediment being immobilized at the bottom of the infaunal mixing zone at a given time can have disparate age distributions. Several studies have focused both on the roles of differential bioturbation [Bard, 2001] and differential deposition [Mollenhauer et al., 2003, 2005] in producing varying age distributions of different particle classes (e.g., forams versus alkenones) in the same sediment core horizon. In these reports, age differences within a sediment horizon vary up to 4500 years [Mollenhauer et al., 2005]. In addition, Mollenhauer and Eglinton [2007] have presented a conceptual model with differential degradation of organic components as cause for large differences in Δ^{14}C. Our resolution of different AIOM components for radiocarbon dating demonstrates age differences between components (∼10,000 years) that significantly exceed typical infaunal mixing increments. This poses the question of how the age distributions of differently aged, contemporaneously immobilized sediment components change under the actions of bioturbating infauna. Since the first published work concerning bioturbation [Darwin, 1881], the reigning assumption has been of uniform sediment age distributions at the time of deposition into the infaunal mixing horizon. Questions of individual sediment components with different ages have not normally been considered.
[30] Figure 10 shows a series of scenarios involving sediment deposited with different components having age distributions and component proportions similar to those in core KC49, 244–245 cm (Figure 7 and Table 3). The homogenized increment of sediment represents an amount of time,
where m is the depth of the homogeneous, or bioturbated, layer and r_{d} is the increment of sediment deposited in a unit time (r_{d} = dL/dT based on the formulation of Berger and Heath [1968], where dL is the thickness of sediment deposited per unit time, dT). Varying this ratio varies the magnitude of the bioturbation footprint on the original sediment age distributions (Figure 10, right side). At the large homogenized increment T_{m} = 2400 years (Figure 10), the age distribution of the bulk sediment begins to resemble a nonnormal unimodal distribution, but is far from the original component age distributions because considerable blending has occurred.
[31] The age distribution centroids of the falling sediments as well as their relative proportions in Figure 10 were identical to those in calculated from Gaussian decomposition of KC47 244–245 cm (Figure 10 and Table 3). The widths of the component distributions were chosen on the basis of the assumption that allochthonous organic material (Figure 10, blue and green distributions) is associated with fine particles which have a relatively large lateral component to their settling velocities and are more likely to have been entrained and resettled numerous times. The sharp distribution employed on the youngest sediment component (Figure 10, red distributions) corresponds to a narrower distribution of ages that would best describe a coarse sediment component (such as a foraminiferal test relative to a clay particle) having a similar settling history to organic material which could be considered autochthonous. The model shown Figure 10 does not incorporate differential sedimentation rates, differential bioturbation, nor environmental signals as in the work by Bard [2001], but the establishment of firstorder effects of bioturbation on different age distributions of sediments within a single historical layer provides a foundation on which to incorporate differential bioturbation approaches with the abundant evidence of differential deposition. With evidence of differentially aged sedimentary components increasing as dating techniques are refined, it is important to provide improved models dealing with signal deconvolution as paleoceanographers and paleoclimatogists aim to compare sedimentary records from different regions during important, dynamic epochs of Earth history.