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Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method
Quaternary Geochronology xxx (2014) 1e8
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Research paper
Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method Helena Hercman, Micha1 Ga˛ siorowski, Jacek Pawlak* Institute of Geological Sciences, Polish Academy of Sciences, Research Center in Warsaw, Twarda 51/55, PL-00818 Warszawa, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 October 2012 Received in revised form 12 December 2013 Accepted 8 January 2014 Available online xxx
In this study, we tested the MOD-AGE procedure for non-parametric ageedepth model computations for several lake sediment sequences dated by the 210Pb method. MOD-AGE uses the randomization method (a type of Monte Carlo simulation) for ageedepth model construction and confidence band estimation and the LOESS (locally weighted scatterplot smoothing) method for fitting of the ageedepth function. To validate the constructed ageedepth models, we used (1) sediments of known age and (2) an independent radiometric dating method (radiocarbon dating). All tests confirmed that the MOD-AGE algorithm is a suitable tool for the calculation of ageedepth models for lake sediment sequences. We also tested the MOD-AGE procedure for calculations based on the results of two different dating methods. The tests indicated that an ageedepth model based on both data sets, i.e., probability distributions of 210Pb dates and radiocarbon dates, is more consistent than the ageedepth models based only on one of the two data sets. The important advantage of MOD-AGE compared to other algorithms is that it models both age and depth value as well as their confidence bands while considering the uncertainties of these values. Ó 2014 Elsevier B.V. All rights reserved.
Keywords: Ageedepth model Randomization LOESS method 210 Pb dating
1. Introduction Paleoenvironmental studies apply many biological, chemical, and physical proxies, usually with high resolutions down to tenths of a millimeter (e.g., XRF scanning). However, it is impossible to date every horizon of collected sediment sequences, and the ability to date a material, the time range of the dating method, and the cost of analysis are the primary restrictive factors. In addition, we also typically require the ages of undated horizons and every point of a sequence (interpolation possibility). Therefore, we must know the continuous relation between age and depth. An accurate chronology is crucial for many paleoclimatological studies. This is accomplished using models of ageedepth relationships. An ageedepth model is a specific case of a general problem where two values describing the locations of points in a graph are reported with some uncertainty. In our case, these values are the depths and ages of specific points. Two major problems are associated with the construction of an ageedepth model: (1) modeling the age and depth of dated points while reflecting the uncertainty of both modeled values, and (2) choosing a fitting method.
* Corresponding author. E-mail addresses: [email protected] (H. Hercman), mgasior@twarda. pan.pl (M. Ga˛ siorowski), [email protected] (J. Pawlak).
The most important features characterizing a reliable agee depth model are the following: (1) modeled values should be reported with their uncertainties; (2) the ageedepth function and its confidence bands should be modeled; (3) it should be possible to model the ages of sediments older than the oldest-dated samples, and the uncertainties of this propagation (extrapolation) should be known; (4) the model should not be over-complicated and should represent the reality and remain in agreement with analytical data; and finally, (5) the model should be monotonic. It is known that the age of sediments from a specific depth depends on the deposition rate and post-deposition processes (e.g., resuspension, focusing, sedimentation gaps (hiatuses), dehydration, and mineralization of organic matter). Very often, an agee depth model is simply regarded as a plot of age measurements versus sediment depth (Lotter and Hofmann, 2003; Ga˛ siorowski and Hercman, 2005) with incorrect assumptions of the linearity of the ageedepth function and no concern for the processes mentioned above. The sedimentation rate is calculated by dividing the sediment thickness by the time of sedimentation. Functions matching the deptheage line (e.g., partial least square) provide a much better approximation of the “true” ratio of sediment thickness to time (Fedotov et al., 2004). However, calculations using these methods are not exact. Typically, these models do not take into account the uncertainty of depth and age measurements (e.g., the uncertainty of the activity of measuring a specific isotope).
1871-1014/$ e see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.quageo.2014.01.001
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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Additionally, most of the existing ageedepth models use parametric methods and require a number of assumptions. It is difficult to verify whether these assumptions are fulfilled by our data set. Increasing the computing power allows us to introduce nonparametric methods for ageedepth modeling. In this paper, we test a MOD-AGE procedure of non-parametric ageedepth model computation using the “randomization” method (a type of Monte Carlo simulation) proposed by Hercman and Pawlak (2012). The MOD-AGE model takes into consideration not only the uncertainty of activity measurements but also the uncertainty of depth determinations and complete information about the distributions of both values. MOD-AGE works with any numerical dating methods if we know (or assume) the probability distributions describing the age and depth values. 1.1. Ageedepth model construction Several methods for constructing ageedepth models have been proposed. Typically, these methods involve specific dating procedures, mostly with radiocarbon. OxCal, a popular radiocarbon calibration software, implements chronology construction procedures using a Bayesian approach (Bronk Ramsey, 2008). Oxcal software can also estimate an ageedepth model by using age information from different sources, such as from different dating methods or chronological information that provides the known age of an archeological culture. Blaauw and Christen (2005) published Bayesian procedures for “wiggle-matching” radiocarbon chronologies using piece-wise linear accumulation (Bpeat). Heegaart et al. (2005) proposed mixed-effects modeling for radiocarbon chronologies that assume symmetrical distributions as an estimation of calibrated dates. The “clam” procedure (classical ageedepth model) is based on a Monte Carlo simulation that uses radiocarboncalibrated age distributions as the modeled data (Blaauw, 2010). Blaauw and Christen (2011) published the “bacon” approach for chronology construction based on radiocarbon dates and using a priori knowledge about the deposition rate using gamma autoregressive semiparametric models. Only a few methods for constructing ageedepth models using other dating techniques have been published. Hercman (2009) proposed the idea of using a Monte Carlo simulation as a tool for constructing an ageedepth model based on 230Th/U, radiocarbon, and 210Pb-dating results. Scholz and Hoffmann (2011) published the R-code of StalAge, a procedure for constructing an ageedepth model specifically from U-seriesedated speleothems, which takes into account the uncertainties of age estimations assuming a Gaussian distribution. StalAge incorporates the stratigraphic information from sample locations in the profile and testing procedures for outliers. Final StalAge model is constructed using a Monte Carlo simulation to linearly fit the data based on subsets of age dates. Hercman and Pawlak (2012) proposed more general software (MOD-AGE) that functions for any relationship estimation of two values that are known with their uncertainties. It takes into account the uncertainties of depth estimations and stratigraphical information. The final model is constructed using the LOESS method and a Monte Carlo simulation for its confidence bands. 2. Methods We use MOD-AGE software to construct an ageedepth model (Hercman and Pawlak, 2012). The MOD-AGE algorithm uses a Monte Carlo (MC) simulation for the construction of an ageedepth model and the estimation of its confidence band. Knowing the actual distributions of depth and age, we can simulate possible ageedepth relations. Using the results of a large number of simulations, we can determine the most probable ageedepth relation
and its confidence interval. The input data for the MOD-AGE algorithm are probability distributions describing the ages and depths of a set of samples in a profile. A normal distribution has been assumed for the depth measurements (distance from the sediment surface) based on repetitions of measurements for the same point. The age distribution is estimated using basic measurements that depend on the dating method (Fig. 1). For the radiocarbon method, the probability distributions of calibrated radiocarbon ages (CRA) are used directly for model construction (Fig. 1A). For the 210Pb method, we use the results of 210Pb activity measurements and assume normal distributions for activity (Fig. 1B). Fig. 1 is a flow chart describing the “randomization” procedure for determining the ageedepth model, with confidence intervals for the radiocarbon (A) and 210Pb (B) methods. The procedures are described below. First, we have to acquire a series of M samples from the studied profile (Hi is depth of the ith point, estimated with accuracy dHi) for an age determination. The radiocarbon method (Fig. 1A) is based on 14 C activity measurements, and the conventional radiocarbon ages are calibrated. For each analyzed sample, we obtain a probability distribution of the calibrated radiocarbon age (CRA). The first step of the procedure is to randomly select a sub-data set (j-th) from the basic data. For depth selection, we use a random number generator of normal distribution with an expected value equal to the depth estimation and a dispersion value equal to the error of the depth estimation. For CRA, we use the “roulette method” in which every CRA is represented by a roulette wheel that has an area equal to 1. Age values are represented on the roulette wheel as sections of the area based on their probabilities. The random selection of each agevalue probability is proportional to the area of its respective section of the roulette wheel. The second step of the procedure is the construction of an ageedepth model for the sub-data set. Finally, a time scale (ageedepth model) with a confidence interval is calculated based on the j realizations of the ageedepth model. Using the 210Pb dating method (Fig. 1B), we measure the 210Pb activities, and each activity (Ai) is accompanied by its uncertainty (dAi). Using a computer algorithm, sub-samples (sub-data sets) originating from the original data set are then produced (j subsamples). Each sub-data set is produced using a random-number generator with a normal distribution, an expected value equal to the activity measured and a dispersion value equal to the measured error of the activity. The second step of the procedure is the calculation of ages using an adequate model (e.g., for 210Pb dating, it could be the constant rate of supply (CRS) model or the constant initial concentration model (CIC); Appleby, 2001). This calculation is followed by the construction of an ageedepth model and the calculation of a time scale with a confidence interval based on the j realizations of the ageedepth model. The ageedepth model is estimated on the basis of several dated samples from a selected profile. A sample’s position in the profile relative to those of other samples provides a priori information about the sample’s age (superposition rule). This information should be taken into account when modeling the ageedepth relation. The stratigraphic correction procedure applied in the MODAGE algorithm uses probability calculus, which assumes that the ages of all the samples are correctly estimated. Information about the probability distribution of the samples’ ages is used to estimate the most probable sequence consistent with the superposition rule (Hercman and Pawlak, 2012). Samples in which the ages are inconsistent with the superposition rule are treated as outliers and are not represented by the ageedepth model. The ageedepth model is a continuous relation between age and depth, and it is possible to use any fitting method for the construction of a model (linear fitting, LOESS, SPLINES, GAM, etc.). We use the LOESS (locally weighted scatterplot smoothing) method.
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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B
A H1 H2 . . . Hi
M data points dH1 CRA1 dH2 CRA2 . . . . . . dHi CRAi
j-th randomistaion of M data
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H1 H2 . . . Hi
j times (j > 1000)
M data points dH1 A1 dA1 dH2 A2 dA2 . . . . . . . . . dHi Ai dAi
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age~depth model for j-th data
age calculation for j-th data
Time scale and confidence interval estimation
age~depth model for j-th data
j times (j > 1000)
Time scale and confidence interval estimation Fig. 1. Flow-chart of ageedepth model construction for radiocarbon (A) and
With LOESS, the fitting confers greater weight to data points located closer to the points of estimation than to those located farther away. The LOESS model should be useful for accommodating natural changes in the deposition rate, and it depends on an assumed value for the SPAN factor, which is defined as the percentage of data points that are used for the model estimation (Cleveland and Devlin, 1988). A higher SPAN value results in a smoother curve; MOD-AGE uses the highest SPAN value that is consistent with the data in the error range, which provides the smoothest model consistent with the data. 2.1. Testing the model We applied the MOD-AGE model to four sediment sequences dated by using the 210Pb method (Fig. 2). These measurements of 210 Pb were performed in the Isotope Dating and Paleoenvironmental Research Laboratory of the Institute of Geological
Fig. 2. Location of lake sediment sequences dated by the 210Pb method: 1,2 e Mylof skie Górne lake; 4 e Morskie Oko lake; 5 e Przedni Staw Polski lake. lake; 3 e Kazun
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Pb (B) dating methods.
Sciences PAS in Warsaw. The activity of 210Pb was determined indirectly using measurements of the activity of 210Po according to the procedure described by Appleby (2001). The uncertainty of the activity measurements is described by a normal distribution and depends on many factors, including the concentration of Po in the sample, the mass of the sample, the duration of the measurement, and the precision of the spike calibration. The ages of the subsamples with 210Pb-activity measurements were calculated with the CRS model (Appleby, 2001). Radiocarbon measurements were performed by the Poznan Radiocarbon Laboratory using the AMS technique. The measured radiocarbon ages were calibrated with OxCal software ver. 4.10 (Bronk Ramsey, 2009) using the IntCal09 calibration curve (Reimer et al., 2009). The depth measurement, similar to any measurement of a physical value, has an uncertainty, and to obtain a reliable agee depth model, this uncertainty must be determined for every dated sample. The uncertainty of a depth measurement depends on several factors, such as the type of material (semi-liquid, solid, dry, fine or coarse), the type of core sampler, and the technique used for core splitting. We assumed that the depth value is described by a normal distribution. For example, the mean uncertainty of the depth determination for a 1-m-long detrital gyttja sequence cored with a Kajak-type gravity corer and sampled in the field could be 0.002 m. This estimation is based on 100 measurements of the same point in the specific profile. The reliability of the computed model can be realized in a number of ways. In the first case, we used a sediment sequence of known age. This sequence was cored in the Mylof dam lake (Fig. 2), one of the oldest dam lakes in northern Poland. The dam was built in 1848, and the transition from river into reservoir facies, i.e., from fluvial sands into gyttja, was very clear (Fig. 3, MY3 core). The 210Pbdating method was used to obtain the dates, and the sediment sequence was old enough to reach the lead limit (w150 years); thus, the age of the river-dam lake transition was modeled. Fig. 4 presents the ageedepth model estimated for lake sediments cored from the Mylof dam lake (MY3). The presented agee
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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1 2 3 Fig. 3. Lithological diagrams of MY3 and MY2 profiles from the Mylof dam lake: 1 e fluvial sands, 2 e silty gyttja, 3 e detritous gyttja; solid line e bulk sediment density, dashed line e water content.
depth model was estimated based on 19 dates obtained using the 210 Pb method. The profile of dam lake sediments was 45 cm long, and we can expect that the age of sediments from the beginning of the lake-sediment profile (a 43-cm depth) should be slightly younger than 1848 AD. The age of sediments from the 43-cm depth, based on the estimated ageedepth model, is in the range of 1841 AD to 1870 AD, with the most probable age being 1856 AD (Fig. 4). Therefore, the age of the oldest dam lake sediments from the Mylof dam lake obtained using the ageedepth model is consistent with the historical age of the Mylof dam.
A lake sediment sequence obtained from another core taken from the Mylof dam lake (My2, 45-cm long) did not reach the floor of the lake sediments. The estimated ageedepth model based on sixteen 210Pb dates is shown in Fig. 5, and this model could be used for estimating the depth of the floor of lake sediments. The Mylof dam was built in 1848, and the ageedepth model shows that sediments of that age should be in a range of depth from 48 cm to 60 cm, with the most probable depth being 50 cm. This result is consistent with the lithology of the deposits: all 45-cm cored sediments are gyttja (reservoir facies).
Fig. 4. Ageedepth model estimated for the Mylof dam lake sediments, MY3 core: solid line e ageedepth model, dotted lines e 2-sigma confidence band, dots e randomized data points.
Fig. 5. Ageedepth models estimated for the Mylof dam lake sediments, MY2 core: solid line e ageedepth model, dotted lines e 2-sigma confidence band, dots e randomized data points.
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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Another possible way to test the reliability of a model is to use other dating methods. We studied a sediment sequence from the Morskie Oko lake (Tatra Mountains, South Poland). The top of the sequence was dated using the 210Pb-dating method (Sienkiewicz and Ga˛ siorowski, submitted for publication), and twelve dates obtained by the 210Pb method were used for the ageedepth model estimation (Fig. 6). We also dated the remains of spruce leaves using the radiocarbon method and used this date to validate the 210 Pb-based model. Organic macro remains from a 13-cm horizon were dated by the radiocarbon method, and the 95% confidence band for the obtained radiocarbon age was 1740 AD-1840 AD and 1870 AD-present. The age of the same sediments obtained by the ageedepth model is in the range of 1810 AD to 1840 AD. The estimated age depth-model based on 210Pb dates is consistent with the radiocarbon age and demonstrates that an age range of radiocarbon dates from 1740 AD to 1840 AD is more probable than a younger age range. 2.2. Merging the models Fig. 6. Ageedepth model estimated for the Morskie Oko lake sediments: solid line e ageedepth model, dotted lines e 2-sigma confidence band, dark gray dots e randomized data points for 210Pb method, light gray dots e randomized data points for 14C method.
In many studies, the chronology of sediment sequences is built using two or more dating methods (e.g., 210Pb, radiocarbon, or 137 Cs). A single profile dated by two different dating methods can
Fig. 7. Ageedepth models for profiles dated by two dating techniques. A e ageedepth models for the Przedni Staw Polski lake estimated independently for 210Pb and radiocarbon skie Górne lake estimated independently for 210Pb and radiocarbon methods; C e combined ageedepth model for the Przedni Staw methods; B e ageedepth models for the Kazun skie Górne lake sediments. Solid lines e ageedepth models, dotted lines e 2-sigma confidence bands, dots e Polski lake sediments; D e combined ageedepth model for the Kazun randomized data points.
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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give two inconsistent ageedepth models. If both models are presented together, this inconsistency is usually visible as a sharp change of slope in the ageedepth function at the depth where the dating method changes (e.g., in Ga˛ siorowski and Sienkiewicz, 2010). We tested MOD-AGE on a sediment sequence from the Kazunskie Gorne lake (KAG), an oxbow lake located in the Vistula river valley near Warsaw, and Przedni Staw Polski (PSP), an alpine lake located in the Tatra Mountains (southern Poland) (Fig. 2). The top of the sequences were dated with the 210Pb method, and older sediments were dated with the radiocarbon method (Ga˛ siorowski and Hercman, 2005; Sienkiewicz and Ga˛ siorowski, submitted for publication). For the two sets of measurements, independent ageedepth models based on 210Pb and 14C dates from the PSP and KAG lakes were estimated (Fig. 7A, B). The 210Pb ageedepth model estimates for the sediment profiles are inconsistent with the agee depth model estimates based on radiocarbon dates (Fig. 7A,B). The sharp border (changes in the modeled deposition rate) at the point of method change is absent (Fig. 7B) for the KAG profile. Independent ageedepth model estimates for the profile cored from the PSP lake reconstructed different sedimentation rates (Fig. 7A). However, the oldest part of the range of the youngest 14C date is consistent with the 210Pb ageedepth model, and specific 210Pb
dates are in the confidence band of the 14C ageedepth model (Fig. 7A). Combined ageedepth models based on dates obtained from different geochronological methods estimated using MODAGE software are presented in Fig. 7C and D. In the case of the KAG lake sediment sequence, the uniform ageedepth model does not show a sharp border that would indicate a change in the reconstructed deposition rate. The uniform ageedepth model estimated for the sediment section cored from the PSP lake shows one uniform deposition rate for the entire profile; the difference for the segment between 5 and 8 cm is likely related to the sediment compaction process. In contrast to the two independent ageedepth models, the uniform ageedepth model is more consistent at the border between the dates obtained by the 14C and 210Pb methods. Several methods of ageedepth model construction have been proposed for the profiles dated by the radiocarbon method, and most of them allow the use of results from other methods to create a combined model. All of the proposed approaches utilized a real distribution of calibrated radiocarbon ages; however, the results of other dating methods assume normal distribution as an age description. The StalAge method (Scholz and Hoffmann, 2011), which was developed as a tool for chronology construction based on U-series dating, uses normal distributions for the age
Fig. 8. Ageedepth models estimated by two different modeling programs. A e ageedepth model for the Przedni Staw Polski lake estimated by MOD-AGE; B e ageedepth model for skie Górne lake estimated by MOD-AGE; C e ageedepth model for the Przedni Staw Polski lake estimated by OxCal; D e ageedepth model for the Kazun skie Górne lake the Kazun estimated by OxCal. Solid lines e ageedepth models, dotted lines e 2-sigma confidence bands, dots e randomized data points for MOD-AGE software (A and B), black distributions e calibrated radiocarbon ages distributions (C and D).
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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description. Conversely, MOD-AGE permits the use of real age distributions for any method, and it also allows the assumption of a normal distribution if required, real age distribution is especially important for samples with ages close to the dating method limit and when the skewness in the real distributions of the described age are significant. Fig. 8 presents a comparison of ageedepth models of the PSP and KAG sediment sections obtained using MOD-AGE (Fig. 8A and B) and OxCal (Fig. 8C and D). OxCal is the most popular tool for radiocarbon data calibration and analysis, including chronology construction. We used a P-sequence for the OxCal model construction (Bronk Ramsey, 2009) that assumes monotonic growth and is based on a random Poisson process. For the P-sequence, the parameters are defined by the user and indicate a possible range of change in the rate of deposition. We chose the highest value for this parameter for which the highest agreement of model and data was found (Scholz et al., 2012). Both MOD-AGE and OxCal produce a smooth chronology at the point of change from 210Pb to 14C data, and both models agree in their confidence intervals. Differences in the obtained chronologies are more visible when comparing models for data close to the dating method limit. Fig. 9 presents the MOD-AGE (thicker line) and OxCal (thinner line) models for a portion of the KAG profile dated by the 210Pb method. Black points show randomized values of dating results that consider 210Pb measurement results and depth uncertainties. Visible skewness for older samples causes the confidence range for MOD-AGE to be asymmetrical, which could have an impact on the extrapolation of the chronology beyond the dated portion of the profile. Next significant difference between MODAGE and other approaches is taking account depth estimations uncertainties. 2.3. MOD-AGE advantages and disadvantages The basic advantage of the MC approach used by MOD-AGE is its non-parametric quality. The model does not rely on any assumptions about the age distribution and data scattering along a fitted line. Additionally, it is a general method that may be used for any age model (e.g., CIC, CRS etc.) and assumed method for ageedepth model building (linear fitting, LOESS, SPLINES, GAM etc.). The problem of the depth-age relation applies to all chronologies
skie Górne lake using the 210Pb Fig. 9. Ageedepth models estimated for the Kazun method and estimated by MOD-AGE (thicker lines) and OxCal (thinner lines). Solid lines e ageedepth models, dotted lines e 2-sigma confidence bands.
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regardless of the dating method used (e.g., U-series, radiocarbon, Pb, thermoluminescence). The use of a general tool makes it possible to build a model for a sediment sequence that was dated by different methods, taking into account the real distributions of age and uncertainty of the depth. A major disadvantage of the MOD-AGE model is its susceptibility to hiatuses or episodes of very fast sedimentation, which are recorded in sediment sequences between dated horizons. These events may be lost by the MOD-AGE model, which will generate a false function of age and depth dependence. Consequently, false dates can be obtained, especially for samples older than the range of the dating method. This problem is a result of the general “philosophy” of utilizing MOD-AGE. The ageedepth model is a continuous relation between age and depth and should be constructed only for continuously deposited profiles or parts of these profiles. We decided to use the simplest possible model that was consistent with the analytical data. As a result, we obtained monotonic models with the minimum possible curvature. Ageedepth modeling should incorporate knowledge of the dating methods used for the studied profile. Additionally, any model construction should involve several main stages: (1) data analysis for the elimination of coarse errors, (2) analysis of the profile for hiatus traces and dated sample quality, (3) ageedepth model construction for continuously growing parts of the profile, and (4) a final model verification to ensure the concordance of the dating results with the model. All of these stages require specific knowledge and experience, and a lack of proper assessment and analysis at any stage can lead to an incorrect result.
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3. Conclusions All of the tests confirmed that the MOD-AGE algorithm is a suitable tool for calculating ageedepth models for lake-sediment sequences. There are several existing methods to calculate agee depth functions, but they are typically associated with a specific dating technique. MOD-AGE has a universal quality and can be applied to any dating technique. Moreover, it can be applied to calculate any function between two data sets for which the probability distribution is known or assumed. Therefore, it can construct one consistent ageedepth model based on two or more dating techniques. Other algorithms, such as OxCal, can also estimate one consistent ageedepth model based on more than one dating technique; however, these models require assumptions about the age distributions and usually assume that distributions of nonradiocarbon dated data are normal. These assumptions could be problematic for ages that are close to the limit of the dating method. MOD-AGE is an algorithm based on non-parametric methods and therefore does not depend on assumptions, which are sometimes difficult to verify. An important advantage of MOD-AGE is that it can consider the uncertainty of depth measurements. The precision of the depth determination can have a similar influence on the deptheage curve shape as age uncertainty. Several fitting methods can be used to fit the function; we applied the LOESS method, which, in our opinion, produces the ageedepth function closest to the “natural” relation observed in sediment sequences. With this method, the points located closer to the fitted fragments of the curve have the greatest influence on it shape. The idea behind this assumption is that closely located sections of a sediment sequence should be the most similar. The most important disadvantage of the MOD-AGE is its susceptibility to hiatuses in sediment sequences; MOD-AGE recognizes these as episodes of lower sedimentation rate. This is a consequence of the MOD-AGE philosophy of ageedepth model construction. In fact, the construction of an ageedepth model for a
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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sequence in which the hiatuses are known makes no sense. In such a case, separate ageedepth models should be calculated for each part of the sediment sequence that is located between hiatuses. Additionally, in the case of significant changes in the sedimentation rate, MOD-AGE recognizes the changes but presents a smoothed ageedepth curve because it estimates the simplest realization for known analytical points. Acknowledgments Two anonymous reviewers are acknowledged for their helpful comments, which substantially improved the manuscript. This study was partially funded by the National Science Centre and Higher Education grant no. NN306 077436. New version of MODAGE is available please contact authors via [email protected]. Editorial handling by: T. Higham References Appleby, P.G., 2001. Chronostratigraphic techniques in recent sediments. In: Last, W.M., Smol, J.P. (Eds.), Tracking Environmental Changes Using Lake Sediments, Basin Analysis, Coring, and Chronological Techniques, vol. 1. Kluwer Academic Publishers, Dordrecht, pp. 171e203. Blaauw, M., 2010. Methods and code for “classical” age-modelling of radiocarbon sequences. Quat. Geochronol. 5, 512e518. Blaauw, M., Christen, J.A., 2005. Radiocarbon peat chronologies and environmental change. Appl. Stat. 54, 805e816. Blaauw, M., Christen, J.A., 2011. Flexible palaeoclimate age-depth models using an autoregressive gamma process. Bayesian Anal. 6, 457e474. Bronk Ramsey, C., 2008. Deposition models for chronological records. Quat. Sci. Rev. 27, 42e60. Bronk Ramsey, C., 2009. Bayesian analysis of radiocarbon dates. Radiocarbon 51, 337e360.
Cleveland, W.S., Devlin, S.J., 1988. Locally-weighted regression: an approach to regression analysis by local fitting. J. Am. Stat. Assoc. 83, 596e610. Fedotov, A., Kazansky, A.Y., Tomurhuu, D., Matasova, G., Ziborova, G., Zheleznyakova, T., Vorobyova, S., Phedorin, M., Goldberg, E., Oyunchimeg, T., Narantsetseg, T., Vologina, E., Yuldashev, A., Kalugin, I., Tomurtogoo, O., Grachev, M., 2004. A 1-Myr record of paleoclimates from Lake Khubsugul, Mongolia. Eos 85, 387e390. Ga˛ siorowski, M., Hercman, H., 2005. Recent changes of sedimentation rate in three Vistula oxbow lakes determined by 210Pb dating. Geochronometria 24, 33e40. Ga˛ siorowski, M., Sienkiewicz, E., 2010. 20th century warming and acidification as recorded in two alpine lakes in the Tatra Mountains (South Poland, Europe). Sci. Total Environ. 408, 1091e1101. Heegaart, E., Birks, H.J.B., Telford, R.J., 2005. Relationships between calibrated ages and depth in stratigraphical sequences: an estimation procedure by mixedeffect regression. Holocene 15, 1e7. Hercman, H., 2009. Agewdepth model construction using full information from samples age and depth distribution basing on 230Th/U, radiocarbon and 210Pb dating results. In: 15th International Congress of Speleology Proceedinga, vol. 2, p. 1024. Hercman, H., Pawlak, J., 2012. MOD-AGE: an agewdepth model construction algorithm. Quat. Geochronol. 12, 1e10. Lotter, A.F., Hofmann, G., 2003. Development of the late-glacial and Holocene diatom flora in the lake Sedmo Rilsko (Rila Mountains, Bulgaria). In: Tonkov, S. (Ed.), Aspects of Palynology and Paleoecology, pp. 171e183. Reimer, P.J., Baillie, M.G.L., Bard, E., Bayliss, A., Beck, J.W., Blackwell, P.G., Bronk Ramsey, C., Buck, C.E., Burr, G.S., Edwards, R.L., Friedrich, M., Grootes, P.M., Guilderson, T.P., Hajdas, I., Heaton, T.J., Hogg, A.G., Hughen, K.A., Kaiser, K.F., Kromer, B., McCormac, F.G., Manning, S.W., Reimer, R.W., Richards, D.A., Southon, J.R., Talamo, S., Turney, C.S.M., van der Plicht, J., Weyhenmeyer, C.E., 2009. IntCal09 and Marine09 radiocarbon age calibration curves, 0e50,000 years cal BP. Radiocarbon 51, 1111e1150. Scholz, D., Hoffmann, D., 2011. StalAge e an algorithm designed for construction of speleothem age models. Quat. Geochronol. 6, 369e382. Scholz, D., Hoffmann, D.L., Hellstrom, J., Bronk Ramsey, C., 2012. A comparison of different methods for speleothem age modelling. Quat. Geochronol. 14, 94e104. Sienkiewicz, E., Ga˛ siorowski, M., 2014. Changes in trophic state in three mountain lakes in southern Poland according to palaeobiological record. Polish J. Environ. Stud. (submitted for publication).
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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Research paper
Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method Helena Hercman, Micha1 Ga˛ siorowski, Jacek Pawlak* Institute of Geological Sciences, Polish Academy of Sciences, Research Center in Warsaw, Twarda 51/55, PL-00818 Warszawa, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 October 2012 Received in revised form 12 December 2013 Accepted 8 January 2014 Available online xxx
In this study, we tested the MOD-AGE procedure for non-parametric ageedepth model computations for several lake sediment sequences dated by the 210Pb method. MOD-AGE uses the randomization method (a type of Monte Carlo simulation) for ageedepth model construction and confidence band estimation and the LOESS (locally weighted scatterplot smoothing) method for fitting of the ageedepth function. To validate the constructed ageedepth models, we used (1) sediments of known age and (2) an independent radiometric dating method (radiocarbon dating). All tests confirmed that the MOD-AGE algorithm is a suitable tool for the calculation of ageedepth models for lake sediment sequences. We also tested the MOD-AGE procedure for calculations based on the results of two different dating methods. The tests indicated that an ageedepth model based on both data sets, i.e., probability distributions of 210Pb dates and radiocarbon dates, is more consistent than the ageedepth models based only on one of the two data sets. The important advantage of MOD-AGE compared to other algorithms is that it models both age and depth value as well as their confidence bands while considering the uncertainties of these values. Ó 2014 Elsevier B.V. All rights reserved.
Keywords: Ageedepth model Randomization LOESS method 210 Pb dating
1. Introduction Paleoenvironmental studies apply many biological, chemical, and physical proxies, usually with high resolutions down to tenths of a millimeter (e.g., XRF scanning). However, it is impossible to date every horizon of collected sediment sequences, and the ability to date a material, the time range of the dating method, and the cost of analysis are the primary restrictive factors. In addition, we also typically require the ages of undated horizons and every point of a sequence (interpolation possibility). Therefore, we must know the continuous relation between age and depth. An accurate chronology is crucial for many paleoclimatological studies. This is accomplished using models of ageedepth relationships. An ageedepth model is a specific case of a general problem where two values describing the locations of points in a graph are reported with some uncertainty. In our case, these values are the depths and ages of specific points. Two major problems are associated with the construction of an ageedepth model: (1) modeling the age and depth of dated points while reflecting the uncertainty of both modeled values, and (2) choosing a fitting method.
* Corresponding author. E-mail addresses: [email protected] (H. Hercman), mgasior@twarda. pan.pl (M. Ga˛ siorowski), [email protected] (J. Pawlak).
The most important features characterizing a reliable agee depth model are the following: (1) modeled values should be reported with their uncertainties; (2) the ageedepth function and its confidence bands should be modeled; (3) it should be possible to model the ages of sediments older than the oldest-dated samples, and the uncertainties of this propagation (extrapolation) should be known; (4) the model should not be over-complicated and should represent the reality and remain in agreement with analytical data; and finally, (5) the model should be monotonic. It is known that the age of sediments from a specific depth depends on the deposition rate and post-deposition processes (e.g., resuspension, focusing, sedimentation gaps (hiatuses), dehydration, and mineralization of organic matter). Very often, an agee depth model is simply regarded as a plot of age measurements versus sediment depth (Lotter and Hofmann, 2003; Ga˛ siorowski and Hercman, 2005) with incorrect assumptions of the linearity of the ageedepth function and no concern for the processes mentioned above. The sedimentation rate is calculated by dividing the sediment thickness by the time of sedimentation. Functions matching the deptheage line (e.g., partial least square) provide a much better approximation of the “true” ratio of sediment thickness to time (Fedotov et al., 2004). However, calculations using these methods are not exact. Typically, these models do not take into account the uncertainty of depth and age measurements (e.g., the uncertainty of the activity of measuring a specific isotope).
1871-1014/$ e see front matter Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.quageo.2014.01.001
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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Additionally, most of the existing ageedepth models use parametric methods and require a number of assumptions. It is difficult to verify whether these assumptions are fulfilled by our data set. Increasing the computing power allows us to introduce nonparametric methods for ageedepth modeling. In this paper, we test a MOD-AGE procedure of non-parametric ageedepth model computation using the “randomization” method (a type of Monte Carlo simulation) proposed by Hercman and Pawlak (2012). The MOD-AGE model takes into consideration not only the uncertainty of activity measurements but also the uncertainty of depth determinations and complete information about the distributions of both values. MOD-AGE works with any numerical dating methods if we know (or assume) the probability distributions describing the age and depth values. 1.1. Ageedepth model construction Several methods for constructing ageedepth models have been proposed. Typically, these methods involve specific dating procedures, mostly with radiocarbon. OxCal, a popular radiocarbon calibration software, implements chronology construction procedures using a Bayesian approach (Bronk Ramsey, 2008). Oxcal software can also estimate an ageedepth model by using age information from different sources, such as from different dating methods or chronological information that provides the known age of an archeological culture. Blaauw and Christen (2005) published Bayesian procedures for “wiggle-matching” radiocarbon chronologies using piece-wise linear accumulation (Bpeat). Heegaart et al. (2005) proposed mixed-effects modeling for radiocarbon chronologies that assume symmetrical distributions as an estimation of calibrated dates. The “clam” procedure (classical ageedepth model) is based on a Monte Carlo simulation that uses radiocarboncalibrated age distributions as the modeled data (Blaauw, 2010). Blaauw and Christen (2011) published the “bacon” approach for chronology construction based on radiocarbon dates and using a priori knowledge about the deposition rate using gamma autoregressive semiparametric models. Only a few methods for constructing ageedepth models using other dating techniques have been published. Hercman (2009) proposed the idea of using a Monte Carlo simulation as a tool for constructing an ageedepth model based on 230Th/U, radiocarbon, and 210Pb-dating results. Scholz and Hoffmann (2011) published the R-code of StalAge, a procedure for constructing an ageedepth model specifically from U-seriesedated speleothems, which takes into account the uncertainties of age estimations assuming a Gaussian distribution. StalAge incorporates the stratigraphic information from sample locations in the profile and testing procedures for outliers. Final StalAge model is constructed using a Monte Carlo simulation to linearly fit the data based on subsets of age dates. Hercman and Pawlak (2012) proposed more general software (MOD-AGE) that functions for any relationship estimation of two values that are known with their uncertainties. It takes into account the uncertainties of depth estimations and stratigraphical information. The final model is constructed using the LOESS method and a Monte Carlo simulation for its confidence bands. 2. Methods We use MOD-AGE software to construct an ageedepth model (Hercman and Pawlak, 2012). The MOD-AGE algorithm uses a Monte Carlo (MC) simulation for the construction of an ageedepth model and the estimation of its confidence band. Knowing the actual distributions of depth and age, we can simulate possible ageedepth relations. Using the results of a large number of simulations, we can determine the most probable ageedepth relation
and its confidence interval. The input data for the MOD-AGE algorithm are probability distributions describing the ages and depths of a set of samples in a profile. A normal distribution has been assumed for the depth measurements (distance from the sediment surface) based on repetitions of measurements for the same point. The age distribution is estimated using basic measurements that depend on the dating method (Fig. 1). For the radiocarbon method, the probability distributions of calibrated radiocarbon ages (CRA) are used directly for model construction (Fig. 1A). For the 210Pb method, we use the results of 210Pb activity measurements and assume normal distributions for activity (Fig. 1B). Fig. 1 is a flow chart describing the “randomization” procedure for determining the ageedepth model, with confidence intervals for the radiocarbon (A) and 210Pb (B) methods. The procedures are described below. First, we have to acquire a series of M samples from the studied profile (Hi is depth of the ith point, estimated with accuracy dHi) for an age determination. The radiocarbon method (Fig. 1A) is based on 14 C activity measurements, and the conventional radiocarbon ages are calibrated. For each analyzed sample, we obtain a probability distribution of the calibrated radiocarbon age (CRA). The first step of the procedure is to randomly select a sub-data set (j-th) from the basic data. For depth selection, we use a random number generator of normal distribution with an expected value equal to the depth estimation and a dispersion value equal to the error of the depth estimation. For CRA, we use the “roulette method” in which every CRA is represented by a roulette wheel that has an area equal to 1. Age values are represented on the roulette wheel as sections of the area based on their probabilities. The random selection of each agevalue probability is proportional to the area of its respective section of the roulette wheel. The second step of the procedure is the construction of an ageedepth model for the sub-data set. Finally, a time scale (ageedepth model) with a confidence interval is calculated based on the j realizations of the ageedepth model. Using the 210Pb dating method (Fig. 1B), we measure the 210Pb activities, and each activity (Ai) is accompanied by its uncertainty (dAi). Using a computer algorithm, sub-samples (sub-data sets) originating from the original data set are then produced (j subsamples). Each sub-data set is produced using a random-number generator with a normal distribution, an expected value equal to the activity measured and a dispersion value equal to the measured error of the activity. The second step of the procedure is the calculation of ages using an adequate model (e.g., for 210Pb dating, it could be the constant rate of supply (CRS) model or the constant initial concentration model (CIC); Appleby, 2001). This calculation is followed by the construction of an ageedepth model and the calculation of a time scale with a confidence interval based on the j realizations of the ageedepth model. The ageedepth model is estimated on the basis of several dated samples from a selected profile. A sample’s position in the profile relative to those of other samples provides a priori information about the sample’s age (superposition rule). This information should be taken into account when modeling the ageedepth relation. The stratigraphic correction procedure applied in the MODAGE algorithm uses probability calculus, which assumes that the ages of all the samples are correctly estimated. Information about the probability distribution of the samples’ ages is used to estimate the most probable sequence consistent with the superposition rule (Hercman and Pawlak, 2012). Samples in which the ages are inconsistent with the superposition rule are treated as outliers and are not represented by the ageedepth model. The ageedepth model is a continuous relation between age and depth, and it is possible to use any fitting method for the construction of a model (linear fitting, LOESS, SPLINES, GAM, etc.). We use the LOESS (locally weighted scatterplot smoothing) method.
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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B
A H1 H2 . . . Hi
M data points dH1 CRA1 dH2 CRA2 . . . . . . dHi CRAi
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age~depth model for j-th data
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Time scale and confidence interval estimation Fig. 1. Flow-chart of ageedepth model construction for radiocarbon (A) and
With LOESS, the fitting confers greater weight to data points located closer to the points of estimation than to those located farther away. The LOESS model should be useful for accommodating natural changes in the deposition rate, and it depends on an assumed value for the SPAN factor, which is defined as the percentage of data points that are used for the model estimation (Cleveland and Devlin, 1988). A higher SPAN value results in a smoother curve; MOD-AGE uses the highest SPAN value that is consistent with the data in the error range, which provides the smoothest model consistent with the data. 2.1. Testing the model We applied the MOD-AGE model to four sediment sequences dated by using the 210Pb method (Fig. 2). These measurements of 210 Pb were performed in the Isotope Dating and Paleoenvironmental Research Laboratory of the Institute of Geological
Fig. 2. Location of lake sediment sequences dated by the 210Pb method: 1,2 e Mylof skie Górne lake; 4 e Morskie Oko lake; 5 e Przedni Staw Polski lake. lake; 3 e Kazun
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Pb (B) dating methods.
Sciences PAS in Warsaw. The activity of 210Pb was determined indirectly using measurements of the activity of 210Po according to the procedure described by Appleby (2001). The uncertainty of the activity measurements is described by a normal distribution and depends on many factors, including the concentration of Po in the sample, the mass of the sample, the duration of the measurement, and the precision of the spike calibration. The ages of the subsamples with 210Pb-activity measurements were calculated with the CRS model (Appleby, 2001). Radiocarbon measurements were performed by the Poznan Radiocarbon Laboratory using the AMS technique. The measured radiocarbon ages were calibrated with OxCal software ver. 4.10 (Bronk Ramsey, 2009) using the IntCal09 calibration curve (Reimer et al., 2009). The depth measurement, similar to any measurement of a physical value, has an uncertainty, and to obtain a reliable agee depth model, this uncertainty must be determined for every dated sample. The uncertainty of a depth measurement depends on several factors, such as the type of material (semi-liquid, solid, dry, fine or coarse), the type of core sampler, and the technique used for core splitting. We assumed that the depth value is described by a normal distribution. For example, the mean uncertainty of the depth determination for a 1-m-long detrital gyttja sequence cored with a Kajak-type gravity corer and sampled in the field could be 0.002 m. This estimation is based on 100 measurements of the same point in the specific profile. The reliability of the computed model can be realized in a number of ways. In the first case, we used a sediment sequence of known age. This sequence was cored in the Mylof dam lake (Fig. 2), one of the oldest dam lakes in northern Poland. The dam was built in 1848, and the transition from river into reservoir facies, i.e., from fluvial sands into gyttja, was very clear (Fig. 3, MY3 core). The 210Pbdating method was used to obtain the dates, and the sediment sequence was old enough to reach the lead limit (w150 years); thus, the age of the river-dam lake transition was modeled. Fig. 4 presents the ageedepth model estimated for lake sediments cored from the Mylof dam lake (MY3). The presented agee
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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depth model was estimated based on 19 dates obtained using the 210 Pb method. The profile of dam lake sediments was 45 cm long, and we can expect that the age of sediments from the beginning of the lake-sediment profile (a 43-cm depth) should be slightly younger than 1848 AD. The age of sediments from the 43-cm depth, based on the estimated ageedepth model, is in the range of 1841 AD to 1870 AD, with the most probable age being 1856 AD (Fig. 4). Therefore, the age of the oldest dam lake sediments from the Mylof dam lake obtained using the ageedepth model is consistent with the historical age of the Mylof dam.
A lake sediment sequence obtained from another core taken from the Mylof dam lake (My2, 45-cm long) did not reach the floor of the lake sediments. The estimated ageedepth model based on sixteen 210Pb dates is shown in Fig. 5, and this model could be used for estimating the depth of the floor of lake sediments. The Mylof dam was built in 1848, and the ageedepth model shows that sediments of that age should be in a range of depth from 48 cm to 60 cm, with the most probable depth being 50 cm. This result is consistent with the lithology of the deposits: all 45-cm cored sediments are gyttja (reservoir facies).
Fig. 4. Ageedepth model estimated for the Mylof dam lake sediments, MY3 core: solid line e ageedepth model, dotted lines e 2-sigma confidence band, dots e randomized data points.
Fig. 5. Ageedepth models estimated for the Mylof dam lake sediments, MY2 core: solid line e ageedepth model, dotted lines e 2-sigma confidence band, dots e randomized data points.
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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Another possible way to test the reliability of a model is to use other dating methods. We studied a sediment sequence from the Morskie Oko lake (Tatra Mountains, South Poland). The top of the sequence was dated using the 210Pb-dating method (Sienkiewicz and Ga˛ siorowski, submitted for publication), and twelve dates obtained by the 210Pb method were used for the ageedepth model estimation (Fig. 6). We also dated the remains of spruce leaves using the radiocarbon method and used this date to validate the 210 Pb-based model. Organic macro remains from a 13-cm horizon were dated by the radiocarbon method, and the 95% confidence band for the obtained radiocarbon age was 1740 AD-1840 AD and 1870 AD-present. The age of the same sediments obtained by the ageedepth model is in the range of 1810 AD to 1840 AD. The estimated age depth-model based on 210Pb dates is consistent with the radiocarbon age and demonstrates that an age range of radiocarbon dates from 1740 AD to 1840 AD is more probable than a younger age range. 2.2. Merging the models Fig. 6. Ageedepth model estimated for the Morskie Oko lake sediments: solid line e ageedepth model, dotted lines e 2-sigma confidence band, dark gray dots e randomized data points for 210Pb method, light gray dots e randomized data points for 14C method.
In many studies, the chronology of sediment sequences is built using two or more dating methods (e.g., 210Pb, radiocarbon, or 137 Cs). A single profile dated by two different dating methods can
Fig. 7. Ageedepth models for profiles dated by two dating techniques. A e ageedepth models for the Przedni Staw Polski lake estimated independently for 210Pb and radiocarbon skie Górne lake estimated independently for 210Pb and radiocarbon methods; C e combined ageedepth model for the Przedni Staw methods; B e ageedepth models for the Kazun skie Górne lake sediments. Solid lines e ageedepth models, dotted lines e 2-sigma confidence bands, dots e Polski lake sediments; D e combined ageedepth model for the Kazun randomized data points.
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give two inconsistent ageedepth models. If both models are presented together, this inconsistency is usually visible as a sharp change of slope in the ageedepth function at the depth where the dating method changes (e.g., in Ga˛ siorowski and Sienkiewicz, 2010). We tested MOD-AGE on a sediment sequence from the Kazunskie Gorne lake (KAG), an oxbow lake located in the Vistula river valley near Warsaw, and Przedni Staw Polski (PSP), an alpine lake located in the Tatra Mountains (southern Poland) (Fig. 2). The top of the sequences were dated with the 210Pb method, and older sediments were dated with the radiocarbon method (Ga˛ siorowski and Hercman, 2005; Sienkiewicz and Ga˛ siorowski, submitted for publication). For the two sets of measurements, independent ageedepth models based on 210Pb and 14C dates from the PSP and KAG lakes were estimated (Fig. 7A, B). The 210Pb ageedepth model estimates for the sediment profiles are inconsistent with the agee depth model estimates based on radiocarbon dates (Fig. 7A,B). The sharp border (changes in the modeled deposition rate) at the point of method change is absent (Fig. 7B) for the KAG profile. Independent ageedepth model estimates for the profile cored from the PSP lake reconstructed different sedimentation rates (Fig. 7A). However, the oldest part of the range of the youngest 14C date is consistent with the 210Pb ageedepth model, and specific 210Pb
dates are in the confidence band of the 14C ageedepth model (Fig. 7A). Combined ageedepth models based on dates obtained from different geochronological methods estimated using MODAGE software are presented in Fig. 7C and D. In the case of the KAG lake sediment sequence, the uniform ageedepth model does not show a sharp border that would indicate a change in the reconstructed deposition rate. The uniform ageedepth model estimated for the sediment section cored from the PSP lake shows one uniform deposition rate for the entire profile; the difference for the segment between 5 and 8 cm is likely related to the sediment compaction process. In contrast to the two independent ageedepth models, the uniform ageedepth model is more consistent at the border between the dates obtained by the 14C and 210Pb methods. Several methods of ageedepth model construction have been proposed for the profiles dated by the radiocarbon method, and most of them allow the use of results from other methods to create a combined model. All of the proposed approaches utilized a real distribution of calibrated radiocarbon ages; however, the results of other dating methods assume normal distribution as an age description. The StalAge method (Scholz and Hoffmann, 2011), which was developed as a tool for chronology construction based on U-series dating, uses normal distributions for the age
Fig. 8. Ageedepth models estimated by two different modeling programs. A e ageedepth model for the Przedni Staw Polski lake estimated by MOD-AGE; B e ageedepth model for skie Górne lake estimated by MOD-AGE; C e ageedepth model for the Przedni Staw Polski lake estimated by OxCal; D e ageedepth model for the Kazun skie Górne lake the Kazun estimated by OxCal. Solid lines e ageedepth models, dotted lines e 2-sigma confidence bands, dots e randomized data points for MOD-AGE software (A and B), black distributions e calibrated radiocarbon ages distributions (C and D).
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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description. Conversely, MOD-AGE permits the use of real age distributions for any method, and it also allows the assumption of a normal distribution if required, real age distribution is especially important for samples with ages close to the dating method limit and when the skewness in the real distributions of the described age are significant. Fig. 8 presents a comparison of ageedepth models of the PSP and KAG sediment sections obtained using MOD-AGE (Fig. 8A and B) and OxCal (Fig. 8C and D). OxCal is the most popular tool for radiocarbon data calibration and analysis, including chronology construction. We used a P-sequence for the OxCal model construction (Bronk Ramsey, 2009) that assumes monotonic growth and is based on a random Poisson process. For the P-sequence, the parameters are defined by the user and indicate a possible range of change in the rate of deposition. We chose the highest value for this parameter for which the highest agreement of model and data was found (Scholz et al., 2012). Both MOD-AGE and OxCal produce a smooth chronology at the point of change from 210Pb to 14C data, and both models agree in their confidence intervals. Differences in the obtained chronologies are more visible when comparing models for data close to the dating method limit. Fig. 9 presents the MOD-AGE (thicker line) and OxCal (thinner line) models for a portion of the KAG profile dated by the 210Pb method. Black points show randomized values of dating results that consider 210Pb measurement results and depth uncertainties. Visible skewness for older samples causes the confidence range for MOD-AGE to be asymmetrical, which could have an impact on the extrapolation of the chronology beyond the dated portion of the profile. Next significant difference between MODAGE and other approaches is taking account depth estimations uncertainties. 2.3. MOD-AGE advantages and disadvantages The basic advantage of the MC approach used by MOD-AGE is its non-parametric quality. The model does not rely on any assumptions about the age distribution and data scattering along a fitted line. Additionally, it is a general method that may be used for any age model (e.g., CIC, CRS etc.) and assumed method for ageedepth model building (linear fitting, LOESS, SPLINES, GAM etc.). The problem of the depth-age relation applies to all chronologies
skie Górne lake using the 210Pb Fig. 9. Ageedepth models estimated for the Kazun method and estimated by MOD-AGE (thicker lines) and OxCal (thinner lines). Solid lines e ageedepth models, dotted lines e 2-sigma confidence bands.
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regardless of the dating method used (e.g., U-series, radiocarbon, Pb, thermoluminescence). The use of a general tool makes it possible to build a model for a sediment sequence that was dated by different methods, taking into account the real distributions of age and uncertainty of the depth. A major disadvantage of the MOD-AGE model is its susceptibility to hiatuses or episodes of very fast sedimentation, which are recorded in sediment sequences between dated horizons. These events may be lost by the MOD-AGE model, which will generate a false function of age and depth dependence. Consequently, false dates can be obtained, especially for samples older than the range of the dating method. This problem is a result of the general “philosophy” of utilizing MOD-AGE. The ageedepth model is a continuous relation between age and depth and should be constructed only for continuously deposited profiles or parts of these profiles. We decided to use the simplest possible model that was consistent with the analytical data. As a result, we obtained monotonic models with the minimum possible curvature. Ageedepth modeling should incorporate knowledge of the dating methods used for the studied profile. Additionally, any model construction should involve several main stages: (1) data analysis for the elimination of coarse errors, (2) analysis of the profile for hiatus traces and dated sample quality, (3) ageedepth model construction for continuously growing parts of the profile, and (4) a final model verification to ensure the concordance of the dating results with the model. All of these stages require specific knowledge and experience, and a lack of proper assessment and analysis at any stage can lead to an incorrect result.
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3. Conclusions All of the tests confirmed that the MOD-AGE algorithm is a suitable tool for calculating ageedepth models for lake-sediment sequences. There are several existing methods to calculate agee depth functions, but they are typically associated with a specific dating technique. MOD-AGE has a universal quality and can be applied to any dating technique. Moreover, it can be applied to calculate any function between two data sets for which the probability distribution is known or assumed. Therefore, it can construct one consistent ageedepth model based on two or more dating techniques. Other algorithms, such as OxCal, can also estimate one consistent ageedepth model based on more than one dating technique; however, these models require assumptions about the age distributions and usually assume that distributions of nonradiocarbon dated data are normal. These assumptions could be problematic for ages that are close to the limit of the dating method. MOD-AGE is an algorithm based on non-parametric methods and therefore does not depend on assumptions, which are sometimes difficult to verify. An important advantage of MOD-AGE is that it can consider the uncertainty of depth measurements. The precision of the depth determination can have a similar influence on the deptheage curve shape as age uncertainty. Several fitting methods can be used to fit the function; we applied the LOESS method, which, in our opinion, produces the ageedepth function closest to the “natural” relation observed in sediment sequences. With this method, the points located closer to the fitted fragments of the curve have the greatest influence on it shape. The idea behind this assumption is that closely located sections of a sediment sequence should be the most similar. The most important disadvantage of the MOD-AGE is its susceptibility to hiatuses in sediment sequences; MOD-AGE recognizes these as episodes of lower sedimentation rate. This is a consequence of the MOD-AGE philosophy of ageedepth model construction. In fact, the construction of an ageedepth model for a
Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001
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sequence in which the hiatuses are known makes no sense. In such a case, separate ageedepth models should be calculated for each part of the sediment sequence that is located between hiatuses. Additionally, in the case of significant changes in the sedimentation rate, MOD-AGE recognizes the changes but presents a smoothed ageedepth curve because it estimates the simplest realization for known analytical points. Acknowledgments Two anonymous reviewers are acknowledged for their helpful comments, which substantially improved the manuscript. This study was partially funded by the National Science Centre and Higher Education grant no. NN306 077436. New version of MODAGE is available please contact authors via [email protected]. Editorial handling by: T. Higham References Appleby, P.G., 2001. Chronostratigraphic techniques in recent sediments. In: Last, W.M., Smol, J.P. (Eds.), Tracking Environmental Changes Using Lake Sediments, Basin Analysis, Coring, and Chronological Techniques, vol. 1. Kluwer Academic Publishers, Dordrecht, pp. 171e203. Blaauw, M., 2010. Methods and code for “classical” age-modelling of radiocarbon sequences. Quat. Geochronol. 5, 512e518. Blaauw, M., Christen, J.A., 2005. Radiocarbon peat chronologies and environmental change. Appl. Stat. 54, 805e816. Blaauw, M., Christen, J.A., 2011. Flexible palaeoclimate age-depth models using an autoregressive gamma process. Bayesian Anal. 6, 457e474. Bronk Ramsey, C., 2008. Deposition models for chronological records. Quat. Sci. Rev. 27, 42e60. Bronk Ramsey, C., 2009. Bayesian analysis of radiocarbon dates. Radiocarbon 51, 337e360.
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Please cite this article in press as: Hercman, H., et al., Testing the MOD-AGE chronologies of lake sediment sequences dated by the 210Pb method, Quaternary Geochronology (2014), http://dx.doi.org/10.1016/j.quageo.2014.01.001