4 research outputs found
Anomaly Detection in Paleoclimate Records using Permutation Entropy
Permutation entropy techniques can be useful in identifying anomalies in
paleoclimate data records, including noise, outliers, and post-processing
issues. We demonstrate this using weighted and unweighted permutation entropy
of water-isotope records in a deep polar ice core. In one region of these
isotope records, our previous calculations revealed an abrupt change in the
complexity of the traces: specifically, in the amount of new information that
appeared at every time step. We conjectured that this effect was due to noise
introduced by an older laboratory instrument. In this paper, we validate that
conjecture by re-analyzing a section of the ice core using a more-advanced
version of the laboratory instrument. The anomalous noise levels are absent
from the permutation entropy traces of the new data. In other sections of the
core, we show that permutation entropy techniques can be used to identify
anomalies in the raw data that are not associated with climatic or
glaciological processes, but rather effects occurring during field work,
laboratory analysis, or data post-processing. These examples make it clear that
permutation entropy is a useful forensic tool for identifying sections of data
that require targeted re-analysis---and can even be useful in guiding that
analysis.Comment: 15 pages, 7 figure
Seasonal temperatures in West Antarctica during the Holocene
The recovery of long-term climate proxy records with seasonal resolution is rare because of natural smoothing processes, discontinuities and limitations in measurement resolution. Yet insolation forcing, a primary driver of multimillennial-scale climate change, acts through seasonal variations with direct impacts on seasonal climate1. Whether the sensitivity of seasonal climate to insolation matches theoretical predictions has not been assessed over long timescales. Here, we analyse a continuous record of water-isotope ratios from the West Antarctic Ice Sheet Divide ice core to reveal summer and winter temperature changes through the last 11,000 years. Summer temperatures in West Antarctica increased through the early-to-mid-Holocene, reached a peak 4,100 years ago and then decreased to the present. Climate model simulations show that these variations primarily reflect changes in maximum summer insolation, confirming the general connection between seasonal insolation and warming and demonstrating the importance of insolation intensity rather than seasonally integrated insolation or season duration2,3. Winter temperatures varied less overall, consistent with predictions from insolation forcing, but also fluctuated in the early Holocene, probably owing to changes in meridional heat transport. The magnitudes of summer and winter temperature changes constrain the lowering of the West Antarctic Ice Sheet surface since the early Holocene to less than 162 m and probably less than 58 m, consistent with geological constraints elsewhere in West Antarctica4-7
A universal rank-order transform to extract signals from noisy data
We introduce an ordinate method for noisy data analysis, based solely on rank
information and thus insensitive to outliers. The method is nonparametric,
objective, and the required data processing is parsimonious. Main ingredients
are a rank-order data matrix and its transform to a stable form, which provide
linear trends in excellent agreement with least squares regression, despite the
loss of magnitude information. A group symmetry orthogonal decomposition of the
2D rank-order transform for iid (white) noise is further ordered by principal
component analysis. This two-step procedure provides a noise "etalon" used to
characterize arbitrary stationary stochastic processes. The method readily
distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the
logistic map from white noise. Ranking within randomness differs fundamentally
from that in deterministic chaos and signals, thus forming the basis for signal
detection. To further illustrate the breadth of applications, we apply this
ordinate method to the canonical nonlinear parameter estimation problem of
two-species radioactive decay, outperforming special-purpose least square
software. It is demonstrated that the method excels when extracting trends in
heavy-tailed noise and, unlike the Thiele-Sen estimator, is not limited to
linear regression. Lastly, a simple expression is given that yields a close
approximation for signal extraction of an underlying generally nonlinear
signal.Comment: 26 pages, 18 figure