Effects of dating errors on nonparametric trend analyses of speleothem time series

A fundamental problem in paleoclimatology is to take fully into account the various error sources when examining proxy records with quantitative methods of statistical time series analysis. Records from dated climate archives such as speleothems add extra uncertainty from the age determination to the other sources that consist in measurement and proxy errors. This paper examines three stalagmite time series of oxygen isotopic composition (δ<sup>18</sup>O) from two caves in western Germany, the series AH-1 from the Atta Cave and the series Bu1 and Bu4 from the Bunker Cave. These records carry regional information about past changes in winter precipitation and temperature. U/Th and radiocarbon dating reveals that they cover the later part of the Holocene, the past 8.6 thousand years (ka). We analyse centennial- to millennial-scale climate trends by means of nonparametric Gasser–Müller kernel regression. Error bands around fitted trend curves are determined by combining (1) block bootstrap resampling to preserve noise properties (shape, autocorrelation) of the δ<sup>18</sup>O residuals and (2) timescale simulations (models StalAge and iscam). The timescale error influences on centennial- to millennial-scale trend estimation are not excessively large. We find a "mid-Holocene climate double-swing", from warm to cold to warm winter conditions (6.5 ka to 6.0 ka to 5.1 ka), with warm–cold amplitudes of around 0.5‰ δ<sup>18</sup>O; this finding is documented by all three records with high confidence. We also quantify the Medieval Warm Period (MWP), the Little Ice Age (LIA) and the current warmth. Our analyses cannot unequivocally support the conclusion that current regional winter climate is warmer than that during the MWP

Optimal heavy tail estimation―Part I: Order selection

The tail probability, P, of the distribution of a variable is important for risk analysis of extremes. Many variables in complex geophysical systems show heavy tails, where P decreases with the value, x, of a variable as a power law with a characteristic exponent, α. Accurate estimation of α on the basis of data is currently hindered by the problem of the selection of the order, that is, the number of largest x values to utilize for the estimation. This paper presents a new, widely applicable, data-adaptive order selector, which is based on computer simulations and brute force search. It is the first in a set of papers on optimal heavy tail estimation. The new selector outperforms competitors in a Monte Carlo experiment, where simulated data are generated from stable distributions and AR(1) serial dependence. We calculate error bars for the estimated α by means of simulations. We illustrate the method on an artificial time series. We apply it to an observed, hydrological time series from the River Elbe and find an estimated characteristic exponent of 1.48±0.13. This result indicates finite mean but infinite variance of the statistical distribution of river runoff

BINCOR: An r package for estimating the correlation between two unevenly spaced time series

This paper presents a computational program named BINCOR (BINned CORrelation) for estimating the correlation between two unevenly spaced time series. This program is also applicable to the situation of two evenly spaced time series not on the same time grid. BINCOR is based on a novel estimation approach proposed by Mudelsee (2010) for estimating the correlation between two climate time series with different timescales. The idea is that autocorrelation (e.g. an AR1 process) means that memory enables values obtained on different time points to be correlated. Binned correlation is performed by resampling the time series under study into time bins on a regular grid, assigning the mean values of the variable under scrutiny within those bins. We present two examples of our BINCOR package with real data: instrumental and paleoclimatic time series. In both applications BINCOR works properly in detecting well-established relationships between the climate records compared. © Technische Universitaet Wien

Recurrence-based time series analysis by means of complex network methods

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos (2011

Tropical Atlantic Cooling and Freshening in the Middle of the Last Interglacial From Coral Proxy Records

The last interglacial (LIG; Marine Isotope Substage 5e, ~127–117 ka) experienced globally warmer than modern temperatures; however, profound differences in regional climate occurred that are relevant to the assessment of future climate change scenarios. Tropical Atlantic sea surface temperature (SST) and hydrology are intrinsic to the spatiotemporal evolution of past and future climate. We present eight monthly resolved coral Sr/Ca and δ18O records (130–118 ka) to reconstruct mean western tropical Atlantic SST and seawater δ18O changes during the LIG. Cooler and fresher than modern surface waters are indicated for the middle of the LIG at ~126 ka. This was followed by a rapid transition to modern‐like SSTs and salinities that characterized the remaining part of the LIG. Our results, which account for differences found among corals, proxies, and SST calibration uncertainties, agree with western tropical Atlantic sediment records. Together, they suggest that an oceanic regime existed that differed from today

Recent contrasting winter temperature changes over North America linked to enhanced positive Pacific‐North American pattern

Recently enhanced contrasts in winter (December‐January‐February) mean temperatures and extremes (cold southeast and warm northwest) across North America have triggered intensive discussion both within and outside of the scientific community, but the mechanisms responsible for these contrasts remain unresolved. Here we use a combination of observations and reanalysis data sets to show that the strengthened contrasts in winter mean temperatures and extremes across North America are closely related to an enhancement of the positive Pacific‐North American (PNA) pattern during the second half of the 20th century. Recent intensification of positive PNA events is associated with amplified planetary waves over North America, driving cold‐air outbreaks into the southeast and warm tropical/subtropical air into the northwest. This not only results in a strengthened winter mean temperature contrast but increases the occurrence of the opposite‐signed extremes in these two regions.Key PointsThe enhanced contrasts in winter mean temperatures and extremes in North America are observedRecent enhancement of positive PNA is a main cause of the contrasting winter temperature changesThe study provides a framework for detection and attribution of climate change in North AmericaPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115952/1/grl53404_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/115952/2/grl53404.pd

Forecasting the underlying potential governing the time series of a dynamical system

Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for ‘potential analysis’ of tipping points which altogether serves anticipating, detecting and forecasting nonlinear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin.NERCAXA Research FundEuropean Commissio

USDA Forecasts Of Crop Ending Stocks: How Well Have They Performed?

This study analyzes forecasts of U.S. ending stocks for corn, soybeans, and wheat issued by the USDA. The proposed efficiency tests focus on forecast revisions. Forecast errors are decomposed into monthly unforecastable shocks and idiosyncratic residuals. The error covariance matrix allows for heteroscedasticity and auto-correlations. Results suggest that the USDA forecasts are inefficient, providing strong evidence that the USDA is conservative in forecasting the ending stocks. Unforecastable shocks are heteroscedastic, and idiosyncratic residuals are small. Results are consistent across the three decades analyzed, but soybean forecasts are found to be considerably worse from 2005 to 2015

Sea ice dynamics across the Mid-Pleistocene transition in the Bering Sea.

Sea ice and associated feedback mechanisms play an important role for both long- and short-term climate change. Our ability to predict future sea ice extent, however, hinges on a greater understanding of past sea ice dynamics. Here we investigate sea ice changes in the eastern Bering Sea prior to, across, and after the Mid-Pleistocene transition (MPT). The sea ice record, based on the Arctic sea ice biomarker IP25 and related open water proxies from the International Ocean Discovery Program Site U1343, shows a substantial increase in sea ice extent across the MPT. The occurrence of late-glacial/deglacial sea ice maxima are consistent with sea ice/land ice hysteresis and land-glacier retreat via the temperature-precipitation feedback. We also identify interactions of sea ice with phytoplankton growth and ocean circulation patterns, which have important implications for glacial North Pacific Intermediate Water formation and potentially North Pacific abyssal carbon storage