Uncertainty In Reconstruction Research Articles

The Long‐Term Cooling Trend in East Antarctic Plateau Over the Past 2000 Years Is Only Robust Between 550 and 1550 CE

AbstractThe uncertainties in Antarctic climate reconstructions due to scarcity of proxy records have restricted the understanding of mechanisms of climate change, and further hindered the improvement of climate models. Here, we provide a new climate record derived from water stable isotopes in a Dome A, East Antarctica ice core. Together with six other ice core records, the Dome A record is used to investigate temperature changes in East Antarctic Plateau (EAP) during period 1–1900 CE. Our results show that, a previously reported long‐term cooling trend in EAP during the recent (pre‐1900 CE) 1900 years is only robust between 550 and 1550 CE. A combination of solar and volcanic forcing may have induced the EAP centennial‐scale cold events, and further caused the long‐term cooling trend from 550 to 1550 CE with a small contribution from orbital forcing.

Monte Carlo-based patient internal dosimetry in fluoroscopy-guided interventional procedures: A review.

This systematic review aims to understand the dose estimation approaches and their major challenges. Specifically, we focused on state-of-the-art Monte Carlo (MC) methods in fluoroscopy-guided interventional procedures. All relevant studies were identified through keyword searches in electronic databases from inception until September 2020. The searched publications were reviewed, categorised and analysed based on their respective methodology. Hundred and one publications were identified which utilised existing MC-based applications/programs or customised MC simulations. Two outstanding challenges were identified that contribute to uncertainties in the virtual simulation reconstruction. The first challenge involves the use of anatomical models to represent individuals. Currently, phantom libraries best balance the needs of clinical practicality with those of specificity. However, mismatches of anatomical variations including body size and organ shape can create significant discrepancies in dose estimations. The second challenge is that the exact positioning of the patient relative to the beam is generally unknown. Most dose prediction models assume the patient is located centrally on the examination couch, which can lead to significant errors. The continuing rise of computing power suggests a near future where MC methods become practical for routine clinical dosimetry. Dynamic, deformable phantoms help to improve patient specificity, but at present are only limited to adjustment of gross body volume. Dynamic internal organ displacement or reshaping is likely the next logical frontier. Image-based alignment is probably the most promising solution to enable this, but it must be automated to be clinically practical.

Pressure‐Driven Poiseuille Flow Inherited From Mesozoic Mantle Circulation Led to the Eocene Separation of Australia and Antarctica

AbstractThe separation between Australia and Antarctica occurred during the final stages of the break‐up of Pangea. Reconstructions of the rifting of the Australian plate away from Antarctica show fast spreading rates since Mid‐Eocene (45 Ma). These reconstructions can be used to understand and quantify the forces driving the Australia/Antarctica separation, and to test hypotheses on mechanisms that may be of shallow (i.e., lithosphere) or deep (i.e., mantle) origin. Analytical calculations indicate that plate‐boundary forces are highly unlikely to be a plausible candidate to explain such a separation. Thus, we use a recently developed global coupled models of mantle and lithosphere dynamics, here we show that this event, whose kinematics are reproduced in our models within the bounds of the reconstruction uncertainties, owes to a significant degree to the pressure‐driven asthenospheric Poiseuille flow associated with the mantle buoyancy field inherited from viscous circulation history throughout the Mesozoic. On the contrary, in simulations when such a buoyancy field is replaced by another one resulting from a random distribution of mantle temperature–thus not representative of Earth’s mantle circulation history–the rapid northward motion of Australia does not occur. Similarly, suppressing contemporaneous plate‐boundary processes (i.e., subduction of the Pacific ridge at the Aleutians and healing of the India‐Australia ridge) from our models does not have a noticeable effect on the Australia‐Antarctica kinematics. Thus, a pressure‐driven Poiseuille mantle flow must be considered, at least in this example and possible elsewhere, as a main driver of plate tectonics.

Interpreting the lake-status record of the East Asian monsoon using a hydrological model – Addendum

The East Asian monsoon (EAM) has experienced significant changes over the past 10,000 years that influenced East Asian agricultural development. However, the magnitude and extent of the EAM precipitation fluctuations at 6 ka remain unresolved, owing to uncertainty in individual lake records and substantial variations in the expansion limits in simulations of the mid-Holocene EAM precipitation. Here we present an approach based on multiple lake-level records using the “1D lake level—2D lake area—3D catchment hydrology” model to reconstruct the precipitation patterns in northern China, and to further quantify the extent of the EAM precipitation expansion in the mid-Holocene relative to today. The precipitation reconstructions suggest an ~550–1100 km northward expansion and an ~530–840 km westward migration of the EAM at 6 ka. At that time, the EAM precipitation domain covered over 6 million square kilometers. Thus, this approach mitigates the uncertainty and arbitrariness of reconstructions of the limit of the EAM precipitation fields and provides a benchmark for future climate modeling studies.

On the model uncertainties in Bayesian source reconstruction using an ensemble of weather predictions, the emission inverse modelling system FREAR v1.0, and the Lagrangian transport and dispersion model Flexpart v9.0.2

Abstract. Bayesian source reconstruction is a powerful tool for determining atmospheric releases. It can be used, amongst other applications, to identify a point source releasing radioactive particles into the atmosphere. This is relevant for applications such as emergency response in case of a nuclear accident or Comprehensive Nuclear-Test-Ban treaty verification. The method involves solving an inverse problem using environmental radioactivity observations and atmospheric transport models. The Bayesian approach has the advantage of providing an uncertainty quantification on the inferred source parameters. However, it requires the specification of the inference input errors, such as the observation error and model error. The latter is particularly hard to provide as there is no straightforward way to determine the atmospheric transport and dispersion model error. Here, the importance of model error is illustrated for Bayesian source reconstruction using a recent and unique case where radionuclides were detected on several continents. A numerical weather prediction ensemble is used to create an ensemble of atmospheric transport and dispersion simulations, and a method is proposed to determine the model error.

Robust optimization for HDR prostate brachytherapy applied to organ reconstruction uncertainty

Purpose. Recently, we introduced a bi-objective optimization approach based on dose-volume indices to automatically create clinically good HDR prostate brachytherapy plans. To calculate dose-volume indices, a reconstruction algorithm is used to determine the 3D organ shape from 2D contours, inevitably containing settings that influence the result. We augment the optimization approach to quickly find plans that are robust to differences in 3D reconstruction. Methods. Studied reconstruction settings were: interpolation between delineated organ contours, overlap between contours, and organ shape at the top and bottom contour. Two options for each setting yields 8 possible 3D organ reconstructions per patient, over which the robust model defines minimax optimization. For the original model, settings were based on our treatment planning system. Both models were tested on data of 26 patients and compared by re-evaluating selected optimized plans both in the original model (1 organ reconstruction, the difference determines the cost), and in the robust model (8 organ reconstructions, the difference determines the benefit). Results. Robust optimization increased the run time from 3 to 6 min. The median cost for robust optimization as observed in the original model was −0.25% in the dose-volume indices with a range of [−0.01%, −1.03%]. The median benefit of robust optimization as observed in the robust model was 0.93% with a range of [0.19%, 4.16%]. For 4 patients, selected plans that appeared good when optimized in the original model, violated the clinical protocol with more than 1% when considering different settings. This was not the case for robustly optimized plans. Conclusions. Plans of high quality, irrespective of 3D organ reconstruction settings, can be obtained using our robust optimization approach. With its limited effect on total runtime, our approach therefore offers a way to account for dosimetry uncertainties that result from choices in organ reconstruction settings that is viable in clinical practice.

Unsupervised Anomaly Segmentation Via Multilevel Image Reconstruction and Adaptive Attention-Level Transition

In product inspection scenarios, the objects have different characteristics of textures and different potential anomalies. Still, traditional methods cannot precisely segment structural anomalies and achieve optimal performance on all object categories. This article introduces a flexible multilevel image reconstruction (MLIR) framework for the unsupervised anomaly segmentation task. The MLIR integrates multiple generators with different downsampling ratios to serve as multiple reconstruction levels and leverage an adjustable perceptual similarity measurement to obtain the featurewise reconstruction errors, overcoming the challenge of detecting multiscale anomalies. Leveraging embeddings with different receptive fields for reconstruction, generators perform differently on the same target. Therefore, we depend on the reconstruction uncertainty to propose an adaptive attention-level transition (ALT) strategy that optimizes the detection performance automatically according to the target’s category. ALT adjusts the weights of both reconstruction levels and feature measurement scales simultaneously to utilize features at a consistent level for reconstruction and anomaly detection (AD). This strategy remarkably improves the system’s adaptivity for different applications. Moreover, we propose reducing the signal-to-noise ratio (SNR) of the images by adding pepper noise so that the reconstruction process is framed as an image denoising task, which improves feature extraction and image restoration robustness. We conduct extensive experiments on the MVTec AD dataset and demonstrate that the proposed method performs satisfactorily to different categories and achieves the state-of-the-art (SOTA) performance.

Robust reconstruction of scattering surfaces using a linear microphone array

The analysis of sound scattered by a rough surface and measured by multiple microphones positioned in the far field yields an estimate of the unknown scattering surface profile. Expanding from previous work, the approach used in this paper is based on an expansion and linearization of the Kirchhoff integral equation, and applies to a low density of receivers. Here, the original algorithm is modified in order to reduce the measurement bias, and extended to broadband signals to over-constrain the problem and improve its robustness. The improved method is rigorously assessed alongside the original algorithm and its small perturbation version, for a two-dimensional geometry and for scattering surfaces with a spatial power-function spectrum. The impact of the measurement setup and surface characteristics on the reconstruction uncertainty are evaluated by means of numerical simulations. Additional experimental data obtained for three known surface profiles reveal the impact of noise and measurement uncertainties. The optimal measurement configuration requires a trade-off between resolution (higher at high frequencies), and robustness (higher at low frequencies). This limit is overcome at least partially by the proposed multiple-frequency extension. The resulting measured uncertainties were close to the theoretical expectation of approximately 2% of the acoustic wavelength.

Accelerating Uncertainty Quantification for Nonlinear Inverse Scattering Problems With High Contrast Media by Direct Envelope Methods and Krylov Subspace Iterative Integral Equation Solvers

Uncertainty quantification related to nonlinear inverse scattering problems often involves the posterior covariance matrix that cannot be effectively estimated but still need to be considered as an important part of the nonlinear inverse scattering problem. The objective of this work is to show how to take advantage of a Bayesian framework to estimate the uncertainty of velocity reconstruction in the nonlinear inverse scattering imaging. The key ingredients are twofold. On the one hand, we rely on a Kalman Filter method, equipped with an optimization scheme, to solve the inverse problem. We use the distorted Born iterative method to formulate the sensitivity kernel. It directly uses an explicit representation of the data sensitivity function in terms of Green functions, rather than the indirect optimization approach based on the adjoint state method, in which the Green’s functions are based on integral equations. On the other hand, we use the direct envelope methods to provide the initial guess (large-scale smooth model) to overcome the nonlinearity in the inverse scattering problems. We first investigate the uncertainty of velocity imaging in high contrast media. Then we show by means of Lippmann-Schwinger-type equations that the uncertainty of multiparameter inverse scattering problems can be addressed. Numerical results dealing with the uncertainty of nonlinear inverse scattering problems in the case of both isotropic and anisotropic media highlight the important role played by uncertainty quantification.

Gluon polarization measurements from longitudinally polarized proton-proton collisions at STAR

The gluon polarization contribution to the proton spin is an integral part to solve the longstanding proton spin puzzle. At the Relativistic Heavy Ion Collider (RHIC), the STAR experiment has measured jets produced in mid-pseudo-rapidity, |η| < 1.0, and full azimuth, ϕ, from longitudinally polarized pp collisions to study the gluon polarization in the proton. At center of mass energies = 200 and 510 GeV, jet production is dominated by hard QCD scattering processes such as gluon-gluon (gg) and quark-gluon (qg), thus making the longitudinal double-spin asymmetry (ALL ) sensitive to the gluon polarization. Early STAR inclusive jet ALL results at = 200 GeV provided the first evidence of the non-zero gluon polarization at momentum fraction x > 0.05. The higher center of mass energy = 510 GeV allows to explore the gluon polarization as low as x ∼ 0.015. In this talk we will present the recent STAR inclusive jet and dijet ALL results at = 510 GeV, and discuss the relevant new analysis techniques for the estimation of trigger bias and reconstruction uncertainty, the underlying event correction on the jet energy and its effect on jet ALL . Dijet results are shown for different topologies in regions of pseudo-rapidity, effectively scanning the x-dependence of the gluon polarization.

Automated reconstruction of cast-off blood spatter patterns based on Euclidean geometry and statistical likelihood

Cast-off spatter patterns exhibit linear trails of elliptical stains. These characteristic patterns occur by centrifugal forces that detach drops from a swinging object covered with blood or other liquid. This manuscript describes a method to reconstruct the motion, or swing, of the object. The method is based on stain inspection and Euclidean geometry. The reconstructed swing is represented as a three-dimensional region of statistical likelihood. The reconstruction uncertainty corresponds to the volume of the reconstructed region, which is specific to the uncertainties of the case at hand. Simple numerical examples show that the reconstruction method is able to reconstruct multiple swings that are either intersecting or adjacent to each other. The robustness, spatial convergence, computing time of the reconstruction method is characterized. For the purpose of this study, about 20 cast-off experiments are produced, with motion of the swinging object documented using video and/or accelerometers. The swings follow circular or arbitrary paths, and are either human- or machine-made. The reconstruction results are compared with the experimentally documented swings. Agreement between measured and reconstructed swings is very good, typically within less than 10 cm. The method used in this study is implemented as a numerical code written in an open source language, provided in an open access repository, for purposes of transparency and access.

Quantifying Structural Uncertainty in Paleoclimate Data Assimilation With an Application to the Last Millennium

AbstractPaleoclimate reconstruction relies on estimates of spatiotemporal relationships among climate quantities to interpolate between proxy data. This work quantifies how structural uncertainties in those relationships translate to uncertainties in reconstructions of past climate. We develop and apply a data assimilation uncertainty quantification approach to paleoclimate networks and observational uncertainties representative of data for the last millennium. We find that structural uncertainties arising from uncertain spatial covariance relationships typically contribute 10% of the total uncertainty in reconstructed temperature variability at small (∼200 km), continental, and hemispheric length scales, with larger errors (50% or larger) in regions where long‐range climate covariances are least certain. These structural uncertainties contribute far more to errors in uncertainty quantification, sometimes by a factor of 5 or higher. Accounting for and reducing uncertainties in climate model dynamics and resulting covariance relationships will improve paleoclimate reconstruction accuracy.

A Comparison of the CMIP6midHoloceneandlig127kSimulations in CESM2

AbstractResults are presented and compared for the Community Earth System Model version 2 (CESM2) simulations of the middle Holocene (MH, 6 ka) and Last Interglacial (LIG, 127 ka). These simulations are designated as Tier 1 experiments (midHoloceneandlig127k) for the Coupled Model Intercomparison Project phase 6 (CMIP6) and the Paleoclimate Modeling Intercomparison Project phase 4 (PMIP4). They use the low‐top, standard 1° version of CESM2 contributing to CMIP6 DECK, historical, and future projection simulations, and to other modeling intercomparison projects. ThemidHoloceneandlig127kprovide the opportunity to examine the responses in CESM2 to the orbitally induced changes in the seasonal and latitudinal distribution of insolation. The insolation anomalies result in summer warming over the Northern Hemisphere continents, reduced Arctic summer minimum sea ice, and increased areal extent of the North African monsoon. The Arctic remains warm throughout the year. These changes are greater in thelig127kthanmidHolocenesimulation. Other notable changes are reduction of the Niño3.4 variability and Drake Passage transport and a small increase in the Atlantic Meridional Overturning Circulation from thepiControltomidHolocenetolig127ksimulation. Comparisons to paleo‐data and to simulations from previous model versions are discussed. Possible reasons for mismatches with the paleo‐observations are proposed, including missing processes in CESM2, simplifications in the CMIP6 protocols for these experiments, and dating and calibration uncertainties in the data reconstructions.

Phylogenetic diversity metrics from molecular phylogenies: modelling expected degree of error under realistic rate variation

AbstractAimPhylogenetic diversity or phylo‐diversity measures use information about evolutionary history and relationships to inform conservation priorities. These metrics are usually derived from the branches of molecular phylogenies. But inferring phylogenetic timescale from molecular data relies on many assumptions about the evolutionary process, most of which are based on statistical convenience rather than biological information. Here we ask whether known patterns of variation in rate of molecular evolution can lead to errors in phylo‐diversity measures.LocationGlobal.MethodsWe generated sequences with biologically realistic rate variation, parameterized by empirically well‐supported relationships between species traits, macroevolutionary patterns and rate of molecular evolution. We then tested how well commonly used phylo‐diversity measures from these phylogenies reflected the true evolutionary history.ResultsWe show that reconstructed Faith’s phylogenetic diversity (FPD) measures differ from true values by an average of about 10% and up to 38%. Species rankings based on evolutionary distinctness (ED) are also affected by rate variation, with the ranks of taxa changing by up to 10‐11 positions after estimation.Main conclusionsWe have shown that realistic levels of rate variation can generate error in FPD and ED measures that could potentially influence prioritization ranking. Studies using metrics based on molecular phylogenetic branch lengths should consider the likely effect of uncertainty in phylogenetic reconstruction on their conclusions.

Deep ensemble analysis for Imaging X-ray Polarimetry

We present a method for enhancing the sensitivity of X-ray telescopic observations with imaging polarimeters, with a focus on the gas pixel detectors (GPDs) to be flown on the Imaging X-ray Polarimetry Explorer (IXPE). Our analysis determines photoelectron directions, X-ray absorption points and X-ray energies for 1-9keV event tracks, with estimates for both the statistical and model (reconstruction) uncertainties. We use a weighted maximum likelihood combination of predictions from a deep ensemble of ResNet convolutional neural networks, trained on Monte Carlo event simulations. We define a figure of merit to compare the polarization bias–variance trade-off in track reconstruction algorithms. For power-law source spectra, our method improves on the current planned IXPE analysis (and previous deep learning approaches), providing ∼45% increase in effective exposure times. For individual energies, our method produces 20%–30% absolute improvements in modulation factor for simulated 100% polarized events, while keeping residual systematic modulation within 1σ of the finite sample minimum. Absorption point location and photon energy estimates are also significantly improved. We have validated our method with sample data from real GPD detectors.

Formation and migration of magnetic particles associated with iron oxide transformation at a hillslope scale

Iron oxides are widespread on the surface of the Earth as a weathering product of iron-bearing primary minerals, which often accompany the enrichment of magnetic particles under aerobic conditions. The magnetic properties determined by the content and ratio of magnetic particles have been widely employed in paleoclimate reconstructions and erosion simulations. However, water redistribution at a slope scale could cause a phase transformation of iron oxides and a corresponding change in magnetic properties. In this study, we investigated a catena with a distinct soil colour change from red to yellow, which commonly occurs in tropical and subtropical hilly and mountainous regions. From upslope to downslope, the free iron oxide content decreases while the amorphous iron oxide content increases. The hematite diminishes significantly while the goethite shows little variation. The ferrimagnetic particles decrease in phase with hematite except for the finest superparamagnetic particles. However, the concentration of finer ferrimagnetic particles relative to coarser particles and the concentration of ferrimagnetic particles relative to antiferromagnetic particles both increase downslope. This increase validates the formation path of ferrimagnetic particles as an intermediate product of hematite but reveals more significant particle growth and transformation into hematite with decreasing water activity in granitic soils with low iron content. In addition, these processes could be enhanced by the preferential migration of the finest ferrimagnetic particles or their transformation from amorphous iron oxides enriched downslope. The slope-scale redistribution of iron oxides and related magnetic particles increases their uncertainty in paleoclimate reconstruction and erosion simulation but brings promising prospects to trace geomorphic evolution and hydrologic change over the long term.

Validation and calibration of soil δ2H and brGDGTs along (E-W) and strike (N-S) of the Himalayan climatic gradient

Reconstructing the timing of mountain range uplift and the evolution of high-altitude plateaus is important when attempting to understand potential feedbacks between tectonics and climate at geological timescales. This requires proxies that are able to accurately reconstruct elevation during different time periods in the past. Often, the sensitivity of climatic parameters to elevation gradients, recorded in geological archives such as soils, is used to estimate paleoelevations. However, most proxies reflect an indirect response to elevation change, adding uncertainties to reconstructions. In this study, we aim to identify those sources of uncertainty with respect to elevation reconstructions and test if the combined application of two such proxies, i.e., stable isotopes (δ2H) of plant waxes in modern soils and surface waters and bacterial membrane lipids (brGDGTs) in soils, which can potentially reduce uncertainties in the estimation of (paleo-) elevation. We performed this study in four Himalayan catchments (from west to east: Sutlej, Alaknanda, Khudi, and Arun), of which each individual catchment is subject to a unique precipitation regime, relative influences of moisture sources, and vegetation cover. In total, we analyzed 275 surface water samples, 9 precipitation samples, 131 xylem water samples, and 60 soil samples, which were collected between 2009 and 2014.The following key observations were made: Soil nC31-alkane δ2H values (δ2Hwax) in the Sutlej, Alaknanda, Khudi, and Arun generally record surface water δ2H values, confirming that the first-order control on the plant wax isotopic signature is precipitation δ2H and, therefore, the elevation in orogenic settings. We identified aridity as the factor that introduces scatter to this relationship. BrGDGT-derived Mean Annual Temperature (MAT) correlates in a statistically significant manner with sample site elevation and a 14-year annual average of remotely sensed land-surface temperature, showing that the main process influencing the brGDGT distribution is the adiabatic cooling of air.In an effort to combine these proxies to improve uncertainties in elevation reconstruction, elevations were inferred from both the δ2Hwax and brGDGT distributions. Arid, high elevation sites appear to underestimate actual sample site elevations using δ2H values while sites subject to high (>23–25 °C) annual temperatures overestimate the actual sample site elevation using brGDGT distributions. Elevations inferred from both proxies under such paleoclimatic conditions should be interpreted with caution. Elevations derived from the brGDGT distribution appear to most accurately reconstruct elevation. However, we show that the difference in elevation between the two proxies, described by the proposed ΔElevation parameter, can provide information on the hydrological conditions of the soil’s depositional environment. In conclusion, we emphasize that knowledge of the sample site’s climatic conditions are essential to reconstruct elevation from paleoarchives. In particular, knowledge of moisture availability and annual air temperatures are important, as these have been found to cause the largest scatter in the observed data.

Dose-response relationships for radiation-related heart disease: Impact of uncertainties in cardiac dose reconstruction

Background and purposeRadiation-related heart disease (RRHD) can occur many decades after thoracic radiotherapy for Hodgkin lymphoma (HL) or childhood cancer (CC). To quantify the likely risk of RRHD for patients treated today, dose–response relationships derived from patients treated in previous decades are used. Publications presenting these dose–response relationships usually include estimates of uncertainties in the risks but ignore the effect of uncertainties in the reconstructed cardiac doses. Materials/methodsWe assessed the systematic and random uncertainties in the reconstructed doses for published dose–response relationships for RRHD risk in survivors of HL or CC. Using the same reconstruction methods as were used in the original publications, we reconstructed mean heart doses and, wherever possible, mean left-ventricular doses for an independent case-series of test patients. These patients had known, CT-based, cardiac doses which were compared with the reconstructed doses to estimate the magnitude of the uncertainties and their effect on the dose–response relationships. ResultsFor all five reconstruction methods the relationship between reconstructed and CT-based doses was linear. For all but the simplest reconstruction method, the dose uncertainties were moderate, the effect of the systematic uncertainty on the dose–response relationships was less than 10%, and the effects of random uncertainty were small except at the highest doses. ConclusionsThese results increase confidence in the published dose–response relationships for the risk of RRHD in HL and CC survivors. This may encourage doctors to use these dose–response relationships when estimating individualised risks for patients—an important aspect of personalising radiotherapy treatments today.

Interpreting the lake-status record of the East Asian monsoon using a hydrological model

AbstractThe East Asian monsoon (EAM) has experienced significant changes over the past 10,000 years that influenced East Asian agricultural development. However, the magnitude and extent of the EAM precipitation fluctuations at 6 ka remain unresolved, owing to uncertainty in individual lake records and substantial variations in the expansion limits in simulations of the mid-Holocene EAM precipitation. Here we present an approach based on multiple lake-level records using the “1D lake level—2D lake area—3D catchment hydrology” model to reconstruct the precipitation patterns in northern China, and to further quantify the extent of the EAM precipitation expansion in the mid-Holocene relative to today. The precipitation reconstructions suggest an ~550–1100 km northward expansion and an ~530–840 km westward migration of the EAM at 6 ka. At that time, the EAM precipitation domain covered over 6 million square kilometers. Thus, this approach mitigates the uncertainty and arbitrariness of reconstructions of the limit of the EAM precipitation fields and provides a benchmark for future climate modeling studies.

A spectral approach to estimating the timescale-dependent uncertainty of paleoclimate records – Part 1: Theoretical concept

Abstract. 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 has been 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 and 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, and 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.