This work deals with reconstructing firn layer thicknesses at the deposition time from the firn's observed thickness in ice cores, thus reconstructing the annual accumulation, yielding a timescale and an ice-core chronology. We employed a dynamic time warping algorithm to find an optimal, non-linear alignment between an H

Ice cores provide a continuous record of climatic and environmental data series based on ice’s physical and chemical properties, reflecting past atmospheric composition and climatic variability, (e.g.

Hydrogen peroxide H

The H

The maxima of H

The four Antarctic Stations, Esperanza (ES), Marambio (MA), Faraday–Vernadsky (FV) and Rothera (RO), and the borehole at the DP, on the northern Antarctica Peninsula. The white arrow in the lower right corner inset shows the location of the DP on the peninsula. Both maps were modified from a pan-sharpened scene of the Landsat Image Mosaic of Antarctica (LIMA) by USGS (

The synchronisation of the concentration data to a temperature series is warranted here due to the local accumulation rate, high enough to bring the entire firn horizon deposition period within reach of the four stations' operational span. Both data series independently follow the same seasonal variation and the passing of the years, albeit in their particular manners; the H

We have allowed for the frequency scaling of the peroxide concentration series concerning the uniform frequency temperature content by resorting to dynamic time warping (DTW). DTW is a fast and efficient algorithm for finding an optimal alignment between two sequences through a non-linear warping of one onto the other along the time–depth axis

Notwithstanding DTW being associated with speech recognition

This work shows that DTW is also particularly fit for compensating for the peroxide frequency scaling with depth, realigning it to a temperature data time series and, at the same time, quantifying their dissimilarities. We have used the constant spectral content of the temperature data series as a reference in the pairing transformation through mathematical optimisation, thus yielding an estimate of a relation of depth to time without human intervention. Moreover, the procedure has also confirmed a very high deposition rate for the entire firn horizon at the DP.

We deal with two independent data sets, a H

The temperature time series at the borehole location was estimated through an interpolation procedure on a data set of continuous temperature readings since 1 January 1970, at four Antarctic stations on the Antarctic Peninsula. We will show below that the entire firn layer was accumulated in a shorter period than the

The H

The H

The grey dots are the raw data

Notwithstanding some residual noise left on

The four stations shown in Fig.

We interpolated the daily temperature time series from the four stations shown in Fig.

Only the maximum daily temperature reading at each station was used in the interpolation process. The sea-level-interpolated time series at the DP,

We alleviated aliasing due to the temperature sampling by applying a 2 d low-pass filter to

Figure

The grey dots are the interpolated and decimated temperature time series

Figures

There are two issues to consider here: (i)

The two data series

We warp the series

The process of warping the sample onto the reference series is carried out by seeking the path

The analysis proceeds as follows: begin the process of warping

We observed a decreasing trend in the estimates of

Panel

Once

A simple model of an ice sheet flow considers that as a year's snowfall moves downwards relatively to the surface during its burial process by subsequent deposition undergoing viscoplastic deformation, it becomes progressively thinner, extending laterally due to ice incompressibility. An increase in density ensues with depth as the snow slowly compacts itself into firn and from that into ice. One way to simplify the process is to express all lengths in water-equivalent units (m w.e.), thus allowing one to disregard the compaction of snow

The solid line shows the annual accumulation rate estimates at the DP and the dash-dotted line gives their 11-year moving average. Use the right ordinate for the annual accumulation rate and the left ordinate for borehole depths.

We use the measured

In the simplest model for an ice sheet flow, the total vertical strain of any layer is equal to the total vertical strain of the ice beneath it:

As the older ice is closer to the bedrock, it is more convenient to express the vertical position of an ice particle concerning the rock bed interface using a new vertical axis,

The warping of

We apply an exponential regression to the warped data to produce estimates for the two constants

Nevertheless, as the annual accumulation rate is assumed uniform, we can obtain an estimate for the 27 years before the coring activity of

Location of third-party ice cores sites on the Antarctic Peninsula with their distances to the DP ice core.

Annual snow accumulation in ice cores from the DP (solid line), Bruce Plateau (dashed line), Gomez Plateau (dash-dotted line) and Dyer Plateau (dotted line) for the period 1980–2010.

It is worthwhile ending this section by comparing our estimated annual accumulation variability with data from the three ice cores listed in Table

Stratigraphic dating of ice cores is rooted in the use of reference horizons and annually resolved data to count annual layers to establish a core chronology. The latter uses outward data, e.g. volcanic events, to measure annual layers. This work has resorted to an independent data set, recorded temperature series, as a time reference to reconstruct a given layer thickness

The adopted non-linear numerical algorithm warped the H

The considerable noise content in both series was alleviated through a nonparametric loess filter, which produced clean, smoothed versions of the data series albeit still retaining their complexity, as seen in Figs.

The secular variation in accumulation has revealed a high annual accumulation rate of

The limited time window of the period of our data reveals relatively stable behaviour throughout the 27 years before coring, with an 11-year moving average of the accumulation of

Mathematical procedures for annual layer counting are notoriously more laborious than manual counting; nevertheless, the latter has no other intrinsic quality but its easiness; quality or effectiveness cannot be technically guaranteed. As is the case of the present work, the former approach is indisputably rigorous, able to efficiently estimate the annual layering on the entire data section and disposition-free. The layer counting applied to our data produced annual accumulation figures that differ from those presented here by up to

Comparison of algorithm results with simple layer counting performed on the smoothed versions of our data set suggests inaccuracies are non-uniform and within

We have modified somewhat a COW code from

The interpolated temperature daily series at the sea-level projection of the borehole DP-07-1 we have used is in the file “daily_temperature.asc” published at

JMT worked with the synchronisation of H

The authors declare that they have no conflict of interest.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was fully supported by the Brazilian Antarctic Program (PROANTAR) through the CNPq and CAPES. The present work is part of the ice-core programme Climate of Antarctica and South America (CASA) in association with the Climate Change Institute, University of Maine. The authors also acknowledge the Chilean Antarctic Institute (INACH), the Chilean Air Force (FACh), the Brazilian Air Force and the Brazilian Navy.

This research has been supported by the INCT da Criosfera (CAPES project (grant no. 88887.136384/2017-00)) and the PROANTAR (CNPq project (grant no. 442755/2018-0)).

This paper was edited by Michiel van den Broeke and reviewed by two anonymous referees.