Beschreibung: Proxy records represent an invaluable source of information for reconstructing past climatic variations, but they are associated with considerable uncertainties. For a systematic quantification of these reconstruction errors, however, knowledge is required not only of their individual sources but also of their auto-correlation structure, as this determines the timescale dependence of their magnitude, an issue that is often ignored until now. Here a spectral approach to uncertainty analysis is provided for paleoclimate reconstructions obtained from single sediment proxy records. The formulation in the spectral domain, rather than the time domain, allows for an explicit demonstration as well as quantification of the timescale dependence that is inherent in any proxy-based reconstruction uncertainty. This study is published in two parts. In this first part, the theoretical concept is presented and analytic expressions are derived for the power spectral density of the reconstruction error of sediment proxy records. The underlying model takes into account the spectral structure of the climate signal, seasonal and orbital variations, bioturbation, sampling of a finite number of signal carriers, uncorrelated measurement noise, and it includes the effects of spectral aliasing and leakage. The uncertainty estimation method, based upon this model, is illustrated by simple examples. In the second part of this study, published separately, the method is implemented in an application-oriented context, and more detailed examples are presented.

Beschreibung: Compound-specific radiocarbon (14C) dating often requires working with small samples of 〈 100 μg carbon (μgC). This makes the radiocarbon dates of biomarker compounds very sensitive to biases caused by extraneous carbon of unknown composition, a procedural blank, which is introduced to the samples during the steps necessary to prepare a sample for radiocarbon analysis by accelerator mass spectrometry (i.e., isolating single compounds from a heterogeneous mixture, combustion, gas purification and graphitization). Reporting accurate radiocarbon dates thus requires a correction for the procedural blank. We present our approach to assess the fraction modern carbon (F14C) and the mass of the procedural blanks introduced during the preparation procedures of lipid biomarkers (i.e. n-alkanoic acids) and lignin phenols. We isolated differently sized aliquots (6–151 μgC) of n-alkanoic acids and lignin phenols obtained from standard materials with known F14C values. Each compound class was extracted from two standard materials (one fossil, one modern) and purified using the same procedures as for natural samples of unknown F14C. There is an inverse linear relationship between the measured F14C values of the processed aliquots and their mass, which suggests constant contamination during processing of individual samples. We use Bayesian methods to fit linear regression lines between F14C and 1/mass for the fossil and modern standards. The intersection points of these lines are used to infer F14Cblank and mblank and their associated uncertainties. We estimate 4.88 ± 0.69 μgC of procedural blank with F14C of 0.714 ± 0.077 for n-alkanoic acids, and 0.90 ± 0.23 μgC of procedural blank with F14C of 0.813 ± 0.155 for lignin phenols. These F14Cblank and mblank can be used to correct AMS results of lipid and lignin samples by isotopic mass balance. This method may serve as a standardized procedure for blank assessment in small-scale radiocarbon analysis.

Beschreibung: Due to mixing processes, sediment samples taken from a single depth can contain particles (e.g. foraminifera) with a wide range of ages. When radiocarbon measurements are made on samples containing many of these individual particles, the resulting values can hide a lot of internal age variation. Furthermore, if the measured samples contain a material from only a small number of individual particles, the resulting 14C ages will be noisy estimates of the true mean age of material from that depth. Similarly, for proxies such as Mg/Ca, or d18O, the range of ages contained in a single sample results in measurements that represent average values for an extended time period. Again, these values will be noisy if the number of particles per sample is small, but even with large samples, the resulting proxy records are “smoothed out” and the reconstructed amplitude of climate transitions is reduced. The advent of ultra-small-sample 14C dating means that samples consisting of very small numbers of foraminiferal shells now can be dated. This poses both a problem, as individual 14C ages will be less representative of their layer, but also an opportunity as it allows for a direct estimate of the heterogeneity in the age of material at a given depth. We used 14C measurements on samples of 3-30 foraminifera to estimate the underlying standard deviation in the age of individuals picked from the same depth. We repeated this for cores with sedimentation rates ranging from 3-30 cm/kyr and found age-variances consistent with simple sediment mixing models and typical bioturbation depths. These direct estimates of age-variance allow for more realistic estimates of age uncertainty and have already proven useful to use in reconciling apparently inconsistent age-depth profiles from adjacent sediment cores. They also allow for a better-informed interpretation of proxy records, both in terms of the relative timing of events and in terms of the amount of amplitude reduction of the climate signal to be expected at different timescales. Knowing the length of time represented in a single sediment sample also allows us to more clearly interpret changes in the statistics of individual foraminifera variation, whether they can be interpreted as changes to the amplitude of the seasonal cycle, the strength of ENSO variations, or multidecadal climate variation.

Beschreibung: As the availability of high-resolution proxy records increases, the number of large-scale compilations that are built and analyzed continues to grow. Such datasets allow us to disentangle regional and global climate changes from local and proxy specific effects, to better bridge the spatial scales of local proxy recorders vs. global climate models and they support more objective statistical analyses. However, compilations also often combine data for multiple proxy types and which may record different climate variables (e.g. different seasonal or atmospheric vs. water temperatures). Datasets may also vary in quality, and compilations often ignore the expert knowledge of the authors of the original individual paleoclimate datasets as well as site-specific and proxy-specific effects. Here I review current and recent studies that have used global compilations of temperature related proxy data to infer the glacial and Holocene climate evolution and the temporal and spatial structures of climate variability. I demonstrate how the analysis of large-scale compilations can not only improve our knowledge of the evolution of past climate but also provide insight into the potential and limitations of specific paleoclimate proxies and emphasize the importance of realistic uncertainty estimates.

Beschreibung: Here we show how the frequency scaling of a climate reconstruction from sediment proxy records is affected by various sources of uncertainty. Specifically, analytic expressions are derived and illustrated for the power spectral density of a climate reconstruction, based on a simple model that takes into account: the spectral structure of the true climate, uneven recording throughout the year, precession-like orbital modulations of the seasonal cycle, bioturbation, sampling of a finite number of signal carriers from discontinuous slices of sediment material, uncorrelated measurement noise; and that includes the effects of spectral aliasing and leakage. The basic behaviour and the properties of the model are demonstrated, and the implications for the interpretation of climate reconstructions are discussed.

Beschreibung: Proxy climate records are an invaluable source of information about the earth’s climate prior to the instrumental record. The temporal- and spatial-coverage of records continues to increase, however, these records of past climate are associated with significant uncertainties due to non-climate processes that influence the recorded and measured proxy values. Generally, these uncertainties are timescale-dependent and correlated in time. Accounting for structure in the errors is essential to providing realistic error estimates for smoothed or stacked records, detection of anomalies and identifying trend, but this structure is seldom accounted for. In the first of these companion articles we outlined a theoretical framework for handling proxy uncertainties by deriving the power spectrum of proxy error components from which it is possible to obtain timescale-dependent error estimates. Here in part II, we demonstrate the practical application of this theoretical framework using the example of marine sediment cores. We consider how to obtain estimates for the required parameters and give examples of the application of this approach for typical marine sediment proxy records. Our new approach of estimating and providing timescale-dependent proxy errors overcomes the limitations of simplistic single value error estimates. We aim to provide the conceptual basis for a more quantitative use of paleo-records for applications such as model-data comparison, regional and global synthesis of past climate states and data assimilation.

Beschreibung: The statistical properties of climate variability are often reconstructed and interpreted from single proxy records. However, variation in the proxy record is influenced by both climate and non-climate factors, and these must be understood for climate inferences to be reliable.

Beschreibung: Climate reconstructions based on proxy records recovered from marine sediments, such as alkenone records or geochemical parameters measured on foraminifera, play an important role in our understanding of the climate system. They provide information about the state of the ocean ranging back hundreds to millions of years and form the backbone of paleo-oceanography. However, there are many sources of uncertainty associated with the signal recovered from sediment-archived proxies. These include seasonal or depth-habitat biases in the recorded signal; a frequency-dependent reduction in the amplitude of the recorded signal due to bioturbation of the sediment; aliasing of high-frequency climate variation onto a nominally annual, decadal, or centennial resolution signal; and additional sample processing and measurement error introduced when the proxy signal is recovered. Here we present a forward model for sediment-archived proxies that jointly models the above processes so that the magnitude of their separate and combined effects can be investigated. Applications include the interpretation and analysis of uncertainty in existing proxy records, parameter sensitivity analysis to optimize future studies, and the generation of pseudo-proxy records that can be used to test reconstruction methods. We provide examples, such as the simulation of individual foraminifera records, that demonstrate the usefulness of the forward model for paleoclimate studies. The model is implemented as an open-source R package, sedproxy, to which we welcome collaborative contributions. We hope that use of sedproxy will contribute to a better understanding of both the limitations and potential of marine sediment proxies to inform researchers about earth's past climate.

Beschreibung: Understanding the uncertainties associated with proxy-based reconstructions of past climate is critical if they are to be used to validate climate models and contribute to a comprehensive understanding of the climate system. Here we present two related and complementary approaches to quantifying proxy uncertainty. The proxy forward model (PFM) “sedproxy” bitbucket.org/ecus/sedproxy numerically simulates the creation, archiving and observation of marine sediment archived proxies such as Mg/Ca in foraminiferal shells and the alkenone unsaturation index UK’37. It includes the effects of bioturbation, bias due to seasonality in the rate of proxy creation, aliasing of the seasonal temperature cycle into lower frequencies, and error due to cleaning, processing and measurement of samples. Numerical PFMs have the advantage of being very flexible, allowing many processes to be modelled and assessed for their importance. However, as more and more proxy-climate data become available, their use in advanced data products necessitates rapid estimates of uncertainties for both the raw reconstructions, and their smoothed/derived products, where individual measurements have been aggregated to coarser time scales or time-slices. To address this, we derive closed-form expressions for power spectral density of the various error sources. The power spectra describe both the magnitude and autocorrelation structure of the error, allowing timescale dependent proxy uncertainty to be estimated from a small number of parameters describing the nature of the proxy, and some simple assumptions about the variance of the true climate signal. We demonstrate and compare both approaches for time-series of the last millennia, Holocene, and the deglaciation. While the numerical forward model can create pseudoproxy records driven by climate model simulations, the analytical model of proxy error allows for a comprehensive exploration of parameter space and mapping of climate signal re-constructability, conditional on the climate and sampling conditions.