Constructing Proxy Records from Age Models (COPRA)
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Clim. Past, 8, 1765–1779, 2012 www.clim-past.net/8/1765/2012/ Climate doi:10.5194/cp-8-1765-2012 of the Past © Author(s) 2012. CC Attribution 3.0 License. COnstructing Proxy Records from Age models (COPRA) S. F. M. Breitenbach1, K. Rehfeld2,3, B. Goswami2,4, J. U. L. Baldini5, H. E. Ridley5, D. J. Kennett6, K. M. Prufer7, V. V. Aquino7, Y. Asmerom8, V. J. Polyak8, H. Cheng9,10, J. Kurths2, and N. Marwan2 1Geological Institute, Department of Earth Sciences, ETH Zurich, 8092 Zurich, Switzerland 2Potsdam Institute for Climate Impact Research (PIK), 14412 Potsdam, Germany 3Department of Physics, Humboldt Universitat¨ zu Berlin, Newtonstr. 15, 12489 Berlin, Germany 4Department of Physics, University of Potsdam, Karl-Liebknecht Str. 24–25, 14476 Potsdam, Germany 5Department of Earth Sciences, Durham University, Durham DH1 3LE, UK 6Department of Anthropology, The Pennsylvania State University, University Park, PA 16803, USA 7Department of Anthropology, University of New Mexico, Albuquerque, NM 87131, USA 8Department of Earth and Planetary Sciences, University of New Mexico, Albuquerque, NM 87131, USA 9Institute of Global Environmental Change, Xi’an Jiaotong University, Xi’an, China 10Department of Earth Sciences, University of Minnesota, Minneapolis, MN 55455, USA Correspondence to: S. F. M. Breitenbach ([email protected]) Received: 5 June 2012 – Published in Clim. Past Discuss.: 19 June 2012 Revised: 26 September 2012 – Accepted: 6 October 2012 – Published: 31 October 2012 Abstract. Reliable age models are fundamental for any archives store information about climate parameters in strati- palaeoclimate reconstruction. Available interpolation proce- graphic, and, hence, chronological order. dures between age control points are often inadequately re- The proxy-record in question is generally given against ported, and very few translate age uncertainties to proxy un- depth and must be related to a time scale before any attempt certainties. Most available modeling algorithms do not allow of interpretation can be made. This is done by dating individ- incorporation of layer counted intervals to improve the con- ual points within the sediment column using layer counting, fidence limits of the age model in question. radiometric dating (e.g. 14C-, or U-series), or marker hori- We present a framework that allows detection and interac- zons (e.g. tephrochronology). The (growth-) depth-age rela- tive handling of age reversals and hiatuses, depth-age mod- tionship can be determined for each proxy data point (the eling, and proxy-record reconstruction. Monte Carlo simula- actual age modeling). Limitations on sample material, ana- tion and a translation procedure are used to assign a precise lytical costs, and time considerations allow for dating of only time scale to climate proxies and to translate dating uncer- a few points within a proxy record, and various methods are tainties to uncertainties in the proxy values. The presented employed for the age modeling process. Naturally, the qual- framework allows integration of incremental relative dating ity of any age model depends on the number of dates and the information to improve the final age model. The free soft- associated uncertainties (Telford et al., 2004). ware package COPRA1.0 facilitates easy interactive usage. Inevitably, each dating method comes with inherent un- certainties, and herein lies one basic caveat for any climate reconstruction: the time frame is not as absolute (i.e., pin- pointed in time) as one wishes and the uncertainties must 1 Introduction be accounted for when interpreting these proxies. Dating un- certainties are often only discussed for discrete dated points, Palaeoclimate reconstructions are a way to relate recent vari- rather than the entire age model. Blaauw et al. (2007) and ability in climatic patterns to past changes and to discuss Blaauw (2010) present possible ways of resolving this issue. the significance of such changes. They are based on proxy Scholz and Hoffmann (2011) point out that the interpolation records, retrieved from a large variety of natural archives procedures and techniques used are often not described in such as trees, glaciers, speleothems, or sediments. Such Published by Copernicus Publications on behalf of the European Geosciences Union. 1766 S. F. M. Breitenbach et al.: COnstructing Proxy Records from Age models (COPRA) adequate detail and lack of consistency and objectivity can interpolation choices, deals with potential outliers and esti- cause difficulties when different records are to be compared mates the uncertainties of the constructed age model at de- or reanalyzed, or wherever leads and lags between different sired depths. StalAge was especially designed for speleothem reconstructions are studied. The problem is becoming more U-series age modeling and allows for detection and handling acute because the spatio-temporal coverage of proxy records of outlier and hiatuses. None of five recently compared mod- now allows for spatio-temporal analysis using complex net- eling procedures translates the dating uncertainties to proxy works (Rehfeld et al., 2011, 2012) and more quantitative re- uncertainties Scholz et al. (2012). Blaauw et al. (2007) and constructions (Hu et al., 2008; Medina-Elizalde and Rohling, Blaauw (2012) discuss this problem and show a Bayesian- 2012). In order to obtain meaningful results from such stud- based solution for 14C-based chronologies. ies, we must be able to consider the uncertainties of the com- In this study however, COPRA takes this idea a step fur- pared records. ther to actually quantify the proxy errors for given ages. Establishing a methodology for comparing different proxy Here, the age uncertainties have been transferred to the proxy records is challenging because of the apparent uncertainties domain using conditional probability (Prob(A|B), where A in the ages at which the proxy values are known. Such a and B are probabilistic events), which is a crucial difference method would require something equivalent to the “inertial to the study by Blaauw et al. (2007). This method results frame of reference” in physics – a reference system that pos- in an uncertainty-free time axis. Time domain-fixed proxy sesses certain universally valid properties without exception. records can subsequently be used for direct statistical com- In the particular case of proxy record construction, such an parison with other, equally treated, time series. Age model invariant “referential” quantity is the physical time. Physi- constructions can be further improved with the incorpora- cal time is the same for any proxy source, and the differences tion of additional information into the numerical procedure, arise only in the deposition, growth, measurement and finally, such as counted intervals between at least two “absolute”- the estimation of the proxy in question. In this study we es- dated points (Dom´ınguez-Villar et al., 2012). We also intro- tablish a method for constructing such a precise time scale duce a novel approach to proxy modeling that attempts to in- for proxy records with Gaussian uncertainty distribution. The tegrate the pragmatic and theoretical aspects of reconstruct- primary goal of age modeling is to construct meaningful time ing a proxy record from the measurement data in a holistic series that relate uncertainties in climate proxies with depth- framework. Moreover, this approach allows the assignment age relationships and associated errors. We propose to im- of the proxy values to an precise (i.e. error-free) time scale prove the age modeling by including pointwise depth infor- by translating the dating uncertainties to uncertainties in the mation, i.e., layer counting data (if available). Previous ap- proxy values. proaches, both Bayesian and Monte Carlo-based, do not usu- A precise time scale1 is a sequence of error-free calen- ally include both relative (i.e., layer counting) and pointwise dar dates that represent the true chronological dates at which depth information together in order to improve the overall time the proxy signals were recorded in the core. Usually, the chronology. Only recently, a methodology has been proposed most likely age is somehow assigned to a measured proxy to combine layer counted floating chronologies with U-series value. But now we pose the converse question: which proxy dates (Dom´ınguez-Villar et al., 2012). These authors anchor value is most likely for a given year? Instead of considering the layer counted chronology to the radiometrically dated ages with uncertainties, we now have the uncertainty entirely chronology using a least squares fit of a linear relation be- in the proxy value. The precise time has the benefit that we tween the two and also estimate the corresponding age model can statistically compare different proxy records directly, be- uncertainties because of the layer count data inclusion. In- cause their time axes are identical, fixed, and without any stead, we use the least squares fit to estimate the minimum error. These time axes are not necessarily equidistant. “distance” between the radiometric age model and the layer With COPRA (COnstruction of Proxy Record from Age counted age model – a significant difference of our approach models) we propose a new, heuristic, framework that bridges from that of their’s. the gap between the uncertainties in “age” and the uncertain- Ignoring the uncertainties between dated points in a se- ties in the “proxy record”. The introduced software imple- quence interrupts the error propagation and the true uncer- mentation allows one to interactively detect and handle typ- tainty behind the time series remains hidden. Most avail- ical complications such as reversals and hiatuses, and nar- able approaches use the mean or median of the age model row the age uncertainty by supplying additional information, to construct the final proxy record, leaving a disjoint be- tween the errors of the constructed age model and the final 1Here we differentiate between the commonly used term “abso- proxy uncertainties. Several techniques have been developed lute” dating, which means that a numerical age was computed, and to construct consistent age models and uncertainty estimates the term precise (true) time axis.