StalAge – An algorithm designed for construction of speleothem age models

Here we present a new algorithm (StalAge), which is designed to construct speleothem age models. The algorithm uses U-series ages and their corresponding age uncertainty for modelling and also includes stratigraphic information in order to further constrain and improve the age model. StalAge is applicable to problematic datasets that include outliers, age inversions, hiatuses and large changes in growth rate. Manual selection of potentially inaccurate ages prior to application is not required. StalAge can be applied by the general, non-expert user and has no adjustable free parameters. This offers the highest degree of reproducibility and comparability of speleothem records from different studies. StalAge consists of three major steps. Firstly, major outliers are identified. Secondly, age data are screened for minor outliers and age inversions, and the uncertainty of potential outliers is increased using an iterative procedure. Finally, the age model and corresponding 95%-confidence limits are calculated by a Monte-Carlo simulation fitting ensembles of straight lines to sub-sets of the age data.We apply StalAge to a synthetic stalagmite ’sample’ including several problematic features in order to test its performance and robustness. The true age is mostly within the 95%-confidence age limits of StalAge showing that the calculated age models are accurate even for very difficult samples. We also apply StalAge to three published speleothem datasets. One of those is annually laminated, and the lamina counting chronology agrees with the age model calculated by StalAge. For the other two speleothems the resulting age models are similar to the published age models, which are both based on smoothing splines. Calculated uncertainties are in the range of those calculated by combined application of Bayesian chronological ordering and a spline, showing that StalAge is efficient in using stratigraphic information in order to reduce age model uncertainty.The algorithm is written in the open source statistical software R and available from the authors or as an electronic supplement of this paper.     

Precise microsampling of poorly laminated speleothems for U-series dating

One of the principal reasons why speleothems are recognised as important palaeoclimate archives is their suitability for accurate and precise uranium-series (U-series) age determination. Sampling speleothem sections for U-series dating is straightforward in most cases because visible growth layers are preserved. However, this is not always the case, and here we describe a sampling strategy whereby growth layers are resolved from trace-element images produced by laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). We apply this method to a section of an Italian subaqueous speleothem (CD3) that lacks persistent visible growth layering.Trace-element imaging revealed growth layers that are strongly non-planar in their geometry owing to the speleothem's pronounced euhedral crystal terminations. The most prominent trace-element layers were first digitized as x, y vector contours. We then interpolated these in the growth-axis direction to generate a series of contour lines at ∼250-μm increments. The coordinates of these contours were used to guide the sampling via a computerised micromilling lathe. This produced a total of 22 samples for U-series dating by multi-collector ICP-MS. The dating results returned ages in correct stratigraphic order within error. Close inspection of the U-series data and the derived depth–age model suggests that the main source of model-age uncertainty is unrelated to the contour sampling but instead more associated with how closely spaced the model ages are in time, i.e. the model age density. Comparisons between stable oxygen and carbon isotope profiles derived from aliquots of the dating samples and two other stable isotope profiles from CD3 spanning the same time period compare very favourably. Taken together, this suggests that our trace-element contouring method provides a reliable means for extracting samples for dating (and other geochemical analyses), and can be applied to similar speleothems lacking visible growth layering.     

Modelling of solute transport in rivers under different flow rates: A case study without transient storage

A methodology to derive solute transport models at any flow rate is presented. The novelty of the proposed approach lies in the assessment of uncertainty of predictions that incorporate parameterisation based on flow rate. A simple treatment of uncertainty takes into account heteroscedastic modelling errors related to tracer experiments performed over a range of flow rates, as well as the uncertainty of the observed flow rates themselves. The proposed approach is illustrated using two models for the transport of a conservative solute: a physically based, deterministic, advection-dispersion model (ADE), and a stochastic, transfer function based, active mixing volume model (AMV). For both models the uncertainty of any parameter increases with increasing flow rate (reflecting the heteroscedastic treatment of modelling errors at different observed flow rates), but in contrast the uncertainty of travel time, computed from the predicted model parameters, was found to decrease with increasing flow rate.     

A method to anchor floating chronologies in annually laminated speleothems with U–Th dates

Stalagmites occasionally present laminae which, when demonstrated to be annual, may be used to construct an annually resolved chronology. Such annually laminated records provide an opportunity to improve the precision of age models based on other dating techniques. Since annually laminated stalagmites sometimes present a complex stratigraphy with lateral variations in lamina thickness associated with changing macroscopic growth shapes, a procedure for lamina counting is developed here, which complements other methods of speleothem lamina counting. Regardless of the complexity of laminae, when the exact date of a laminated section is unknown, lamina counting provides a floating chronology. This paper describes a method to anchor floating chronologies in speleothems using the least-squares fit of the lamina counting to the radiometric dates (typically U–Th). The estimation of uncertainties in the age model is also considered, which accounts for uncertainties in the lamina counting as well as the fit of the lamina count to the radiometric dates. The uncertainty of this fit does not depend on the analytical uncertainty of the radiometric dates or the precision in the lamina counting, and simply considers all the available dates and their distance to the proposed age model. As an example, the method was applied to a stalagmite from Northern Spain and its accuracy was compared with the annually resolved and cross-dated Greenland chronology during the 8.2 ka event. Although this method has been described for stalagmites, it could be applied to other records in which cross-dating techniques would not be suitable.     

High-resolution U–Pb dating of an Early Pleistocene stalagmite from Corchia Cave (central Italy)

Recent developments in the uranium–lead (U–Pb) dating of speleothems have opened up new opportunities in palaeoclimate research. An important goal in this new frontier is to produce palaeoclimate records underpinned by precise and accurate age models, which together will increase the range of palaeoclimate questions that can be addressed by the speleothem research community. In this paper, we investigate the level of age-model precision that is achievable by applying high-resolution U–Pb dating of a stalagmite (CC8) from Corchia Cave (Italy) whose period of growth spans part of the Middle Pleistocene Transition (∼970–810 ka). Focussing largely on the periods encompassing three glacial terminations, we carried out age sampling of CC8 at a density similar to that performed in many studies of younger (i.e. U–Th-dated) speleothems. Using a combination of Tera–Wasserburg isochron and model age approaches, coupled with age-depth modelling, our results show that age-model uncertainties of ∼4 kyr are possible, equivalent to a precision of about 0.4%. At this level of precision palaeoclimate time series derived from speleothems of this age can be used to test hypotheses of orbital forcing.     

A framework for dealing with uncertainty due to model structure error

Although uncertainty about structures of environmental models (conceptual uncertainty) is often acknowledged to be the main source of uncertainty in model predictions, it is rarely considered in environmental modelling. Rather, formal uncertainty analyses have traditionally focused on model parameters and input data as the principal source of uncertainty in model predictions. The traditional approach to model uncertainty analysis, which considers only a single conceptual model, may fail to adequately sample the relevant space of plausible conceptual models. As such, it is prone to modelling bias and underestimation of predictive uncertainty.     

The integrated effects of climate and hydrologic uncertainty on future flood risk assessments

This work examines future flood risk within the context of integrated climate and hydrologic modelling uncertainty. The research questions investigated are (1) whether hydrologic uncertainties are a significant source of uncertainty relative to other sources such as climate variability and change and (2) whether a statistical characterization of uncertainty from a lumped, conceptual hydrologic model is sufficient to account for hydrologic uncertainties in the modelling process. To investigate these questions, an ensemble of climate simulations are propagated through hydrologic models and then through a reservoir simulation model to delimit the range of flood protection under a wide array of climate conditions. Uncertainty in mean climate changes and internal climate variability are framed using a risk‐based methodology and are explored using a stochastic weather generator. To account for hydrologic uncertainty, two hydrologic models are considered, a conceptual, lumped parameter model and a distributed, physically based model. In the conceptual model, parameter and residual error uncertainties are quantified and propagated through the analysis using a Bayesian modelling framework. The approach is demonstrated in a case study for the Coralville Dam on the Iowa River, where recent, intense flooding has raised questions about potential impacts of climate change on flood protection adequacy. Results indicate that the uncertainty surrounding future flood risk from hydrologic modelling and internal climate variability can be of the same order of magnitude as climate change. Furthermore, statistical uncertainty in the conceptual hydrological model can capture the primary structural differences that emerge in flood damage estimates between the two hydrologic models. Copyright © 2014 John Wiley & Sons, Ltd.     

Structural uncertainty assessment in a discharge simulation model

Abstract

A major goal in hydrological modelling is to identify and quantify different sources of uncertainty in the modelling process. This paper analyses the structural uncertainty in a streamflow modelling system by investigating a set of models with increasing model structure complexity. The models are applied to two basins: Kielstau in Germany and XitaoXi in China. The results show that the model structure is an important factor affecting model performance. For the Kielstau basin, influences from drainage and wetland are critical for the local runoff generation, while for the XitaoXi basin accurate distributions of precipitation and evapotranspiration are two of the determining factors for the success of the river flow simulations. The derived model uncertainty bounds exhibit appropriate coverage of observations. Both case studies indicate that simulation uncertainty for the low-flow period contributes more to the overall uncertainty than that for the peak-flow period, although the main hydrological features in these two basins differ greatly.

Citation Zhang, X. Y., Hörmann, G., Gao, J. F. & Fohrer, N. (2011) Structural uncertainty assessment in a discharge simulation model. Hydrol. Sci. J. 56(5), 854–869.     

Implications of model uncertainty for the mapping of hillslope‐scale soil erosion predictions

An integrated modelling approach (MIRSED) which utilizes the process‐based soil erosion model WEPP (Water Erosion Prediction Project) is presented for the assessment of hillslope‐scale soil erosion at five sites throughout England and Wales. The methodology draws upon previous uncertainty analysis of the WEPP hillslope soil erosion model by the authors to qualify model results within an uncertainty framework. A method for incorporating model uncertainty from a range of sources is discussed as a first step towards using and learning from results produced through the GLUE (Generalized Likelihood Uncertainty Estimation) technique. Results are presented and compared to available observed data, which illustrate that levels of uncertainty are significant and must be taken into account if a meaningful understanding of output from models such as WEPP is to be achieved. Furthermore, the collection of quality, observed data is underlined for two reasons: as an essential tool in the development of soil erosion modelling and also to allow further constraint of model uncertainty. Copyright © 2001 John Wiley & Sons, Ltd.     

Methods and code for ‘classical’ age-modelling of radiocarbon sequences

Age–depth models form the backbone of most palaeoenvironmental studies. However, procedures for constructing chronologies vary between studies, they are usually not explained sufficiently, and some are inadequate for handling calibrated radiocarbon dates. An alternative method based on importance sampling through calibrated dates is proposed. Dedicated R code is presented which works with calibrated radiocarbon as well as other dates, and provides a simple, systematic, transparent, documented and customizable alternative. The code automatically produces age–depth models, enabling exploration of the impacts of different assumptions (e.g., model type, hiatuses, age offsets, outliers, and extrapolation).     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

A new probabilistic technique to build an age model for complex stratigraphic sequences

The age models of fluvio-lacustrine sedimentary sequences are often subject of discussions in paleoclimate research. The techniques employed to build an age model are very diverse, ranging from visual or intuitive estimation of the age-depth relationship over linear or spline interpolations between age control points to sophisticated Bayesian techniques also taking into account the most likely deposition times of the type of sediment within the sequence. All these methods, however, fail in detecting abrupt variations in sedimentation rates, including the possibility of episodes of no deposition (hiatus), which is the strength of the method presented in this work. The new technique simply compares the deposition time of equally thick sediment slices from the differences of subsequent radiometric age dates and the unit deposition times of the various sediment types. The percentage overlap of the distributions of these two sources of information, together with the evidence from the sedimentary record, helps to build an age model of complex sequences including abrupt variations in the rate of deposition including one or many hiatuses.     

Os isotope dating and growth hiatuses of Co-rich crust from central Pacific

Up to now, accurate determination of the growth age and hiatuses of the Co-rich crust is still a difficult work, which constrains the researches on the genesis, growth process, controlling factors, regional tectonics, paleo-oceanographic background, etc. of the Co-rich crust. This paper describes our work in determining the initial growth age of the Co-rich crust to be of the late Cretaceous Campanian Stage (about 75-80 Ma), by selecting the Co-rich crust with clear multi-layer structures in a central Pacific seamount for layer-by-layer sample analysis and using a number of chronological methods, such as Co flux dating, dating by correlation with 187Os/188Os evolution curves of seawater, and stratigraphic divi- sion by calcareous nannofossils. We have also discovered growth hiatuses with different time intervals in the early Paleocene, middle Eocene, late Eocene and early-middle Miocene, respectively. These re- sults have provided an important age background for further researches on the Co-rich crust growth process and the paleo-oceanographic environment evolution thereby revealed in the said region.     

HYBRID SEISMIC MODELLING: A TECHNIQUE TO COMBINE PHYSICAL AND COMPUTER METHODS FOR VERTICAL WAVE INCIDENCE*

A hybrid seismic modelling technique has been developed to investigate complex geological phenomena. Those parts of a geological structure which are too complicated to be treated theoretically are studied by two-dimensional physical models; other sections of the structure which can be treated theoretically, i.e., inhomogeneities in the vertical direction, are modelled by computer methods. A feedback process is used to combine the results of both physical and computer modelling. Horizontally layered coal-seam models are presented to test the hybrid modelling technique for normal incidence. A comparison of the hybrid seismograms with pure synthetic seismograms shows an acceptable conformity for normal incidence. A hybrid zero-offset section is shown to investigate a complex geological structure in the Ruhr coalfield in Germany.     

Bayesian age-depth modelling of Late Quaternary deposits from Wet and Blanche Caves,Naracoorte, South Australia: A framework for comparative faunal analyses

Bayesian age-depth models were constructed for two Late Quaternary aged fossil-bearing sedimentary sequences from caves in south eastern South Australia. The deposits in Wet and Blanche Caves contain dense assemblages of vertebrate fossils, largely the result of owl pellet accumulation. While individually calibrated radiocarbon determinations from the fossil sequences have provided a chronology for their accumulation, there was limited capacity available with such data to (a) temporally constrain assemblages associated with different depositional units and layers within the two sites, (b) interpret the chronological relationships among successive units and layers and (c) correlate sedimentary units and layers of similar age between the two deposits. Here, Bayesian age-depth models were constructed in OxCal for the Wet and Blanche Cave sequences, incorporating the available radiocarbon data and stratigraphic information collected during their excavation. Despite the low precision of the age-depth models for Wet and Blanche Caves which results in part from there being only single radiocarbon determinations available for a number of units and layers, the models enabled the relationships within and between the two sites to be established. Of particular utility for future faunal analyses is quantification of the temporal relationship between strata from the two sites, where groups of individual layers from Blanche Cave were found to be temporally equivalent with the longer-duration units in Wet Cave. We suggest that the use of Phase modelling, as performed here, is useful for cave deposits that have complex depositional histories and even in such instances where, as is common for palaeontological sites, few radiocarbon data are collected relative to the time-spans of tens of millennia that are often represented by them.     

Sensitivity analysis of prior model probabilities and the value of prior knowledge in the assessment of conceptual model uncertainty in groundwater modelling

A key point in the application of multi‐model Bayesian averaging techniques to assess the predictive uncertainty in groundwater modelling applications is the definition of prior model probabilities, which reflect the prior perception about the plausibility of alternative models. In this work the influence of prior knowledge and prior model probabilities on posterior model probabilities, multi‐model predictions, and conceptual model uncertainty estimations is analysed. The sensitivity to prior model probabilities is assessed using an extensive numerical analysis in which the prior probability space of a set of plausible conceptualizations is discretized to obtain a large ensemble of possible combinations of prior model probabilities. Additionally, the value of prior knowledge about alternative models in reducing conceptual model uncertainty is assessed by considering three example knowledge states, expressed as quantitative relations among the alternative models. A constrained maximum entropy approach is used to find the set of prior model probabilities that correspond to the different prior knowledge states. For illustrative purposes, a three‐dimensional hypothetical setup approximated by seven alternative conceptual models is employed. Results show that posterior model probabilities, leading moments of the predictive distributions and estimations of conceptual model uncertainty are very sensitive to prior model probabilities, indicating the relevance of selecting proper prior probabilities. Additionally, including proper prior knowledge improves the predictive performance of the multi‐model approach, expressed by reductions of the multi‐model prediction variances by up to 60% compared with a non‐informative case. However, the ratio between‐model to total variance does not substantially decrease. This suggests that the contribution of conceptual model uncertainty to the total variance cannot be further reduced based only on prior knowledge about the plausibility of alternative models. These results advocate including proper prior knowledge about alternative conceptualizations in combination with extra conditioning data to further reduce conceptual model uncertainty in groundwater modelling predictions. Copyright © 2009 John Wiley & Sons, Ltd.     

A multimethod approach to inform epikarst drip discharge modelling: Implications for palaeo‐climate reconstruction

Resolving the hydrological processes that form speleothems and the palaeo‐climate archives that they contain is difficult. Typical approaches to hydrological investigation are not suited to karst landscapes, geophysics are seldom applied, drip monitoring and modelling have limitations, and ignoring potential hydrological impacts can result in a proxy record that does not reflect the external environment. We aim to understand the processes and controls that have created a palaeo‐climate proxy record preserved in a speleothem (JC001) in the “Grotto of Oddities,” part of the Jersey Cave at the Yarrangobilly Caves, Australia, to infer the likely nature and resolution of this record. Electrical resistivity tomography (ERT), traditional surveying, and drip discharge monitoring (April 2013 to February 2015) were used to investigate the structure and hydrology of the epikarst overlying the Grotto of Oddities. Data collected through these methods were then used to construct a physically informed and parsimonious drip hydrology model. Geophysics showed that changes in hillslope above the Grotto of Oddities are collocated with a region of low resistivity, which forms an epikarstic reservoir acting to supply enhanced discharge to the speleothem. Drip monitoring showed hysteretic behaviour with a distinct threshold response, and a simple drip classification indicated that the speleothem associated with the drip has the potential to record palaeo‐seasonality or an annual–decadal signal. Discharge modelling indicated discharge was comprised of quick and slow flow, and that discharge is probably perennial. These multimethod results together indicate that the speleothem likely represents a palaeo‐climate record of a length and resolution unprecedented for nonglacial areas of the Southern Hemisphere and for Australia in particular and will significantly enhance current knowledge of the climate of southeast Australia. Although ERT methods have previously been applied in the karst landscape, to our knowledge, this represents the first application of these multiple methods in combination as an approach to assess the fidelity of a speleothem, based on an understanding of the hydrological processes for palaeo‐climate reconstruction.     

On building finite element models of structures from modal response

We develop two algorithms for estimating member stiffnesses and masses of a structure from measured modal response in conjunction with a finite element model of the structure. The mathematical model has known geometry and topology and parameterized constitutive properties. A few of the natural frequencies are measured and the corresponding modes are sampled at certain locations in space. The proposed algorithms are based on the concept of minimizing the sum of the squares of errors, specified as an index of discrepancy between the model and the structure, over all of the measured modes. The recursive quadratic programming method is used to solve the non-linear constrained estimation problem. Both proposed estimators can handle incompletely measured models, have robust convergence, and are amenable to modelling of complex structures. We demonstrate the use of our parameter estimation algorithm by applying it to identify the properties of a building from measured data.     

自适应非结构有限元MT二维起伏地形正反演研究

在山区进行MT勘探时,用规则网格有限元方法模拟起伏地形会受到限制.本文采用非结构三角网格可以有效地模拟任意二维地质结构,如起伏地形、倾斜岩层和多尺度构造等.正演引入自适应有限元方法,其在网格剖分过程中能根据单元误差自动细化网格,保证了正演结果的精度.将自适应有限元与Occam算法结合,且引用并行处理技术提高正反演计算速度.通过对比两个理论模型,讨论了地形对MT正演响应的影响;其次进行了不同地电模型带地形反演展示了本文算法的正确性和适用性;最后将该方法应用于实测MT数据处理,证明了自适应非结构有限元方法是复杂地形下处理MT数据的有力工具.     

Quasi-2D hybrid joint inversion of seismic and geoelectric data

Many joint inversion schemes use 1D forward modelling in the integrated interpretation of various geophysical data. In extending the joint inversion approach to the investigation of 2D structures, the discretization of the model parameters and the appropriate choice of the forward‐modelling procedure play a very important role. In this paper, a hybrid seismic–geoelectric joint inversion method is proposed for the investigation of 2D near‐surface geological structures. The electric and seismic models are coupled together through the use of common boundaries between the adjacent layers. Assuming a 2D model composed of homogeneous layers with curved boundaries, a fast ray‐tracing algorithm is used for the calculation of refraction seismic traveltime data. In the geoelectric forward modelling, a locally 1D approximation is used. The boundary surfaces are written in the form of series expansion; the inversion algorithms are formulated for the expansion coefficients and the petrophysical parameters as unknowns. Two versions of the inversion method are proposed: in versions A and B, interval‐wise constant functions and Chebyshev polynomials are, respectively, used as basis functions of the series expansion. The versions are tested by means of synthetic and in situ measured data. The tests show that both methods are stable and accurate.