Organic carbon (OC) stored in Arctic permafrost
represents one of Earth's largest and most vulnerable terrestrial carbon
pools. Amplified climate warming across the Arctic results in widespread
permafrost thaw. Permafrost deposits exposed at river cliffs and coasts are
particularly susceptible to thawing processes. Accelerating erosion of
terrestrial permafrost along shorelines leads to increased transfer of
organic matter (OM) to nearshore waters. However, the amount of terrestrial
permafrost carbon and nitrogen as well as the OM quality in these deposits
is still poorly quantified. We define the OM quality as the intrinsic
potential for further transformation, decomposition and mineralisation. Here,
we characterise the sources and the quality of OM supplied to the Lena River
at a rapidly eroding permafrost river shoreline cliff in the eastern part of
the delta (Sobo-Sise Island). Our multi-proxy approach captures bulk
elemental, molecular geochemical and carbon isotopic analyses of Late
Pleistocene Yedoma permafrost and Holocene cover deposits, discontinuously
spanning the last ∼52 kyr. We showed that the ancient
permafrost exposed in the Sobo-Sise cliff has a high organic carbon content
(mean of about 5 wt %). The oldest sediments stem from Marine Isotope
Stage (MIS) 3 interstadial deposits (dated to 52 to 28 cal ka BP) and are
overlaid by last glacial MIS 2 (dated to 28 to 15 cal ka BP) and Holocene
MIS 1 (dated to 7–0 cal ka BP) deposits. The relatively high average chain
length (ACL) index of n-alkanes along the cliff profile indicates a
predominant contribution of vascular plants to the OM composition. The
elevated ratio of iso- and anteiso-branched fatty acids (FAs) relative to mid- and long-chain (C ≥ 20) n-FAs in the interstadial MIS 3 and the interglacial MIS 1 deposits
suggests stronger microbial activity and consequently higher input of
bacterial biomass during these climatically warmer periods. The overall high
carbon preference index (CPI) and higher plant fatty acid (HPFA) values as
well as high C/N ratios point to a good quality of the preserved OM and thus
to a high potential of the OM for decomposition upon thaw. A decrease in
HPFA values downwards along the profile probably indicates stronger OM decomposition in the oldest (MIS 3) deposits of the cliff. The
characterisation of OM from eroding permafrost leads to a better assessment
of the greenhouse gas potential of the OC released into river and nearshore
waters in the future.
Introduction
Climate warming puts permafrost, especially ice-rich permafrost, in the
terrestrial Arctic at risk of thawing (e.g. Strauss et al., 2021b). Permafrost,
by definition, is ground that stays below 0 ∘C for 2 or more
consecutive years. Terrestrial permafrost ecosystems are affected by ongoing
climate warming with consequences for geomorphological, hydrological and
biogeochemical processes from a local to regional scale (IPCC, 2019). Almost
twice as much carbon is stored in the permafrost region than what is
currently contained in the atmosphere (Hugelius et al., 2014; Mishra et al.,
2021), making permafrost carbon dynamics a globally relevant issue (Grosse
et al., 2011; Schuur et al., 2008; Strauss et al., 2021a; Turetsky et al.,
2020). Total estimated soil organic carbon (SOC) storage for the permafrost
region is ∼1100–1600 Gt, of which 181 ± 54 Gt is attributed to
deep permafrost (below 3 m depth) of the Yedoma region (Hugelius et al.,
2014; Strauss et al., 2021b, 2013).
Warming throughout the Arctic prolongs the season for permafrost thaw and
open ice-free water bodies, resulting in increasing erosion of ice- and
carbon-rich permafrost sediments exposed at coasts (Günther et al.,
2013; Jones et al., 2020). Very ice-rich permafrost deposits (i.e. 50–90 vol % ice) such as the Late Pleistocene Yedoma Ice Complex (Schirrmeister
et al., 2013; Strauss et al., 2017) are particularly vulnerable to rapid
thermo-denudation and thermo-erosion processes along river shores (Costard
et al., 2014; Kanevskiy et al., 2016; Stettner et al., 2018; Fuchs et al.,
2020). Vonk et al. (2013b) showed that Yedoma ice-wedge meltwater can
increase the decomposition of organic matter (OM) due to co-metabolising effects. Another
potential impact of the decomposition of terrestrial OM and discharge with
Arctic river water is the change in biochemical properties that may increase
ocean acidification and anthropogenic carbon dioxide uptake from the
atmosphere (Semiletov et al., 2016). Furthermore, Semiletov et al. (2016)
estimated that 57 % of the terrestrial organic carbon in the East
Siberian Shelf originates from ancient Pleistocene-age permafrost C, such as
Yedoma deposits adjacent to river or coastal zones. Extensive river networks
like the Lena River, especially in their delta zones, carry large nutrient
OM loads to the nearshore zone and onto the Arctic
Shelf (Mann et al., 2022; Sanders et al., 2022). The Arctic river discharge
has increased significantly in recent decades, transporting organic-rich waters
to the nearshore area (Holmes et al., 2012, 2021). Increased
riverbank erosion of Arctic rivers following warming during the last few
decades constitutes an important mechanism of carbon export from land to water
(Zhang et al., 2017, 2021; Fuchs et al., 2020). The studies cited here stress the
need to better understand the interactions between thawing permafrost and
river and nearshore waters.
The study of fossil biomolecules and other OM characteristics provides
insights into the composition and level of OM decomposition and hence can
greatly improve estimates of the greenhouse gas potential of thaw-mobilised
OM from permafrost deposits (Andersson and Meyers, 2012;
Sánchez-García et al., 2014). A few studies have previously focused
on molecular biomarkers in north-eastern Siberian permafrost deposits (e.g.
Zech et al., 2010; Höfle et al., 2013; Strauss et al., 2015; Stapel et
al., 2016; Jongejans et al., 2020). In general, the abundance and distribution of
n-alkanes, which are long-chained, single-bond hydrocarbons, are used for
OM characterisation where the chain length of n-alkanes indicates OM sources.
In our study, we measure molecular biomarkers (n-alkanes, n-fatty acids) and use
established biomarker proxies and indices such as the average chain length (ACL)
of n-alkanes, the carbon preference index (CPI) and the higher plant
fatty acid (HPFA) index to test whether they mirror the OM degree of
decomposition and reflect the OM quality in ancient permafrost deposits.
Additionally, analyses of the total organic carbon content (TOC), the stable
carbon isotope ratios (δ13C of TOC), the total nitrogen (TN) content and TOC/TN (here referred to as the C/N ratio) are applied to our sample
set. Hierarchical clustering is used to identify the stratigraphical units
along the sample profile based on the major changes in OM composition.
Thus, the OM characteristics of permafrost deposits, rapidly eroding at a
cliff site in the eastern Lena Delta, are analysed for the first time for
biomarkers. The set of frozen samples was obtained along a 25 m vertical
cliff profile with a relatively high sampling density of about 1 m covering
all exposed cryostratigraphic units. In this study, we aim (1) to
characterise the OM composition of ancient permafrost that accumulated under
different climate conditions; (2) to assess the degree of decomposition that
the OM already experienced; and (3) to hypothesise, based on the
decomposition legacy, the potential of future decomposability and microbial
decomposition of the permafrost OM.
Overview of the Sobo-Sise Yedoma cliff. (a) Location of the
Sobo-Sise Yedoma cliff in the Lena Delta in north-eastern Siberia (Landsat 5
mosaic (band combination 5, 4, 3) including scenes from 2009 and 2010;
Landsat 5 image courtesy of the US Geological Survey); (b) picture of the
Sobo-Sise Yedoma cliff from the east to west; (c) cross-section of the
cliff profile (adapted from Wetterich et al., 2020a) indicating the three
vertically sampled sections: SOB18-01, SOB18-03 and SOB18-06.
Study area
The Lena River forms the largest delta in the Arctic, covering an area of
29×103 km2 (Schneider et al., 2009), and discharges the second-highest freshwater load into the Laptev Sea, with a mean annual discharge of
525 km3 yr-1 (Holmes et al., 2021). It also transports
summer “heat” from the south to the north (Yang et al., 2005). The study
area on Sobo-Sise Island (Fig. 1a–b) is located in the continuous
permafrost zone. The island stretches between the Sardakhskaya and
Bykovskaya main channels in the eastern part of the delta. In addition to
the modern floodplain, there are three geomorphic units in the delta
(Grigoriev, 1993; Schwamborn et al., 2002). While the first unit consists of
Holocene floodplains and could occur in the whole delta area, the second
unit consists of Late Pleistocene and Holocene fluvial deposits that are
mostly located in the north-western part of the delta and are cut off from
the current delta dynamics (Schirrmeister et al., 2011b). The third
geomorphological unit consists of erosional remnants of a Late Pleistocene
accumulation plain with ice-rich Yedoma Ice Complex deposits and is present
mainly in the west, south and east of the delta (Schwamborn et al., 2002;
Wetterich et al., 2008; Morgenstern et al., 2011). According to a landform
classification for Sobo-Sise Island, 43 % of the land surface is occupied
by Yedoma uplands and Yedoma slopes and 43 % is thermokarst basins with the
remaining 14 % being thermokarst lakes (Fuchs et al., 2018). The terrain
is affected by thermokarst processes (Nitze and Grosse, 2016) and surface
thaw subsidence (Chen et al., 2018).
The distinct surface morphology of Sobo-Sise Island includes Yedoma uplands
intersected by thermo-erosional valleys and thermokarst basins. Syngenetic
permafrost formation in polygonal tundra landscapes over long periods in the
Late Pleistocene formed thick deposits with large ice wedges that are
exposed at the cliff (Schirrmeister et al., 2011b, 2020; Strauss et al.,
2015; Jongejans et al., 2018). Schirrmeister et al. (2011b) attributed parts
of the third geomorphological unit in the Lena Delta in the western and
southern parts of the delta to remnants of a Yedoma accumulation plain. This
formed during the Late Pleistocene when the Lena River had its delta farther
north. Radiocarbon ages corroborated that Yedoma deposits on Sobo-Sise
Island accumulated during the Late Pleistocene between about 52 and 15 cal ka BP. Substantial hiatuses were found at about 36–29 cal ka BP and at 20
to 17 cal ka BP, which may be related to fluvial erosion and/or changed
discharge patterns of the Lena River (Wetterich et al., 2020a). Middle to
Late Holocene ages from 6.36 to 2.5 cal kyr BP were found in the uppermost
cover deposits of the cliff, which is also in agreement with other cover
deposits found on top of Yedoma such as on the nearby Bykovsky Peninsula
(Schirrmeister et al., 2002; Grosse et al., 2007).
The Sobo-Sise Yedoma cliff has an average height of 22 m with a maximum
height of 27.7 m above the river water level (m a.r.l.) (Fuchs et al., 2020)
and is affected by fluvio-thermal erosion. The current average shoreline
retreat rate, which was calculated using satellite data, is 15.7 m yr-1
(2015–2018), which is remarkably high (Fuchs et al., 2020). In comparison,
retreat rates were lower for other Yedoma cliffs such as on Kurungnakh
Island in the central Lena Delta (4.1–6.9 m yr-1; Stettner et al.,
2018) and at the Itkillik exposure in Alaska (11 m yr-1; Kanevskiy et al.,
2016) but even higher for Muostahk Island (29.4 m yr-1; Günther
et al., 2013) and Cape Mamontov Klyk (21 m yr-1; Günther et al.,
2015). The Sobo-Sise Yedoma cliff (72∘32′ N, 128∘17′ E;
Fig. 1c) extends over 1660 m in length and faces north towards the
Sardakhskaya Channel. Here, the water discharge amounts to about 8000 m3 s-1 during the summer-low period (Fedorova et al.,
2015) and the Lena River is ice-covered for about 8 months per year between
October and May. The river ice thickness reaches up to 2 m. Water depth at
the beginning of the Sardakhskaya Channel (close to Stolp and Sardakh
islands) can reach up to 22 m (Fedorova et al., 2015) and is approximately
11 m in front of the Sobo-Sise Yedoma cliff, allowing for water flow
underneath the river ice cover during the winter months (Fuchs et al.,
2020).
MethodsSample collection
The Sobo-Sise Yedoma cliff was sampled in three overlapping vertical
sediment profiles (Fig. 1b) covering the entire exposed permafrost section
(profile SOB18-01, 24.1 to 15.7 m a.r.l.; profile SOB18-03, 18.2 to 10.2 m a.r.l.; profile SOB18-06, 13.4 to 0.9 m a.r.l.). Each profile was
cryolithologically described (see Wetterich et al., 2018, 2020a), and samples
were collected at 0.5 m intervals by rappelling down on a rope from the top
of the cliff. We used an axe and hammer to extract defined cubes of frozen
ground (∼20×10×10 cm) from the cliff wall. Samples were
collected after cleaning and scraping off the outermost unfrozen and frozen
parts of the cliff wall in order to collect frozen, uncontaminated samples.
Then, the samples were lifted upwards, cleaned and subsampled for biomarker
analysis. In total, we collected 61 sediment samples, of which 28 were
selected for biomarker analysis at about 1 m intervals covering the entire
exposed section. The samples were stored frozen in pre-combusted glass jars,
apart from 9 samples (SOB18-06-09 to SOB18-06-34) which were initially
stored in plastic whirl packs before being transferred in a frozen state to
glass containers after transport to the laboratories.
Sedimentological organic matter parameters
Prior to bulk geochemical analyses, all samples were freeze-dried
(Sublimator, ZIRBUS technology), ground and homogenised (Fritsch
PULVERISETTE 5 planetary mill; 8 min at 360 rotations per minute). Total
elemental carbon (TC) and total nitrogen (TN) content of sediment samples in
weight percentage (wt %) were measured with a carbon–nitrogen–sulfur
analyser (vario EL III, Elementar) with a detection limit of 0.1 wt % for
carbon and nitrogen. Samples below this detection limit were set to 0.05 wt % so that the statistics could be calculated. Total organic carbon
(TOC) content in weight percentage (wt %) was measured with a TOC analyser
(vario MAX C, Elementar; analytical accuracy of 0.1 wt %). The TOC to TN
(C/N) ratio has been used as a rough first indicator of the degree of OM
decomposition with decreasing values indicating proceeding decomposition
(Palmtag et al., 2015). The stable carbon isotope ratio (δ13C)
of TOC reflects both the initial contribution from different plant species
and plant components and OM decomposition processes (Gundelwein et al.,
2007). Samples for δ13C analyses were treated with hydrochloric
acid (20 mL, 1.3 M) to remove carbonates, heated on a hotplate (97.7 ∘C for 3 h) and subsequently washed with distilled water. The
samples were filtered (Whatman Grade GF/B, nominal particle retention of 1.0 µm), after which the residue was dried and ground. All δ13C
samples were measured using a DELTA V Advantage isotope ratio mass spectrometer (MS) equipped
with a Flash 2000 analyser (Thermo Fisher Scientific; analytical accuracy of
0.15 ‰), using helium as a carrier gas. The δ13C (13C/12C) value is reported in per mille
(‰) compared to the standard ratio Vienna Pee Dee
Belemnite (VPDB).
Lipid biomarker analyses
Lipid biomarkers provide information on a molecular level about the source
of OM, the environmental conditions during deposition and the degree of
decomposition. In this study, we focused on n-alkanes in the aliphatic OM
fraction and n-fatty acids in the polar hetero-compound fraction. Changes in
their relative abundance can provide an indication of the degree of
decomposition (Kim et al., 2005) as outlined below. We analysed the
n-alkane distributions of all 28 samples and selected 13 samples for the
analysis of n-fatty acids. The selection of the n-fatty acids was made to
cover the entire profile continuously (approximately every 2 m).
Extraction and fraction separation
Following freeze-drying and grinding, biomarker subsamples were transferred
into glass jars. Extraction and separation were conducted according to
Schulte et al. (2000) and Strauss et al. (2015). Samples were processed in
two batches, each containing 14 samples. We weighed between 8 and 11 g in
extraction cell bodies fit for the accelerated solvent extractor (ASE 200
Dionex). Dichloromethane / methanol (volume ratio of 99:1) was used as a
solvent mixture for OM extraction. Each sample was held in a static phase
(5 min heating phase, 20 min at 75 ∘C and 5 MPa). Dissolved
compounds were then further concentrated at ∼42∘C
using a closed-cell concentrator (TurboVap 500 Zymark), and the remaining
solvent was evaporated under N2. Afterwards, internal standards were
added: 5α-androstane for the aliphatic fraction, ethylpyrene for the
aromatic fraction, 5α-androstan-17-one for the NSO (nitrogen,
sulfur and/or oxygen) neutral polar fraction and erucic acid for the NSO
fatty-acid fraction (80 µL each from respective 100 µg mL-1
standard solutions). Subsequently, an asphaltene precipitation was performed
to remove compounds with higher molecular complexity (asphaltenes) by
dissolving the extracts in a small amount of dichloromethane and adding a
40-fold excess of n-hexane. Precipitated asphaltenes were removed by
filtration through a sodium-sulfate-filled funnel. Subsequently, the
n-hexane-soluble portion was separated by medium-pressure liquid
chromatography (MPLC) (Radke et al., 1980) into three fractions of different
polarities: aliphatic hydrocarbons, aromatic hydrocarbons and polar hetero-compounds (NSO compounds). Finally, the NSO fractions of 13 samples were
split into an acid and neutral polar (alcohol) fraction using a KOH-impregnated column. While the n-fatty-acid potassium salts were attached to
the silica gel, the neutral polar compounds were eluted with
dichloromethane. After remobilising the n-fatty acids by protonation of their
salts with formic acid, the n-fatty-acid fraction was obtained with
dichloromethane.
GC-MS measurements and compound quantification
n-Alkanes and n-fatty acids were analysed using gas chromatography coupled
with a mass spectrometer (GC-MS; GC – Trace GC Ultra and MS – DSQ, both
Thermo Fisher Scientific). Prior to the analyses, n-fatty acids were
methylated with diazomethane. The GC was equipped with a cold injection
system operating in the splitless mode. The injector temperature was
programmed from 50 to 300 ∘C at a rate of 10 ∘C s-1. Helium was used as carrier gas with a constant flow of 1 mL min-1. After injection, the compounds of interest were separated on an
SGE BPX5 fused-silica capillary column (50 m length, 0.22 mm i.d., 0.25 µm film thickness) using the following temperature conditions: initial
temperature of 50 ∘C (1 min isothermal), heating rate of 3 ∘C min-1 to 310 ∘C, held isothermally for 30 min.
The MS operated in the electron impact mode at 70 eV. Full-scan mass spectra
were recorded from m/z 50–600 at a scan rate of 2.5 scans s-1. Using
the software Xcalibur (Thermo Fisher Scientific), peaks in the GC-MS run were
quantified using the internal standards for n-alkanes and n-fatty acids. All
biomarker concentrations are expressed in micrograms per gram of dry sediment
(µg g-1 sed.) and per gram of TOC (µg g-1 TOC).
Lipid biomarker indicesAverage chain length
The n-alkane average chain length (ACL) is the weighted average number of
carbon atoms used for determining OM sources. Long-chain odd-numbered
n-alkanes (C ≥ 21) are essential constituents that serve as biomarkers for
higher terrestrial plants (Eglinton and Hamilton, 1967; Eglinton and
Eglinton, 2008; Schäfer et al., 2016), whereas shorter chain lengths
indicate bryophyte, bacterial or algal origin (Cranwell, 1984; Rieley et
al., 1991; Kuhn et al., 2010). A change in the ACL can suggest a change in
the terrestrial source biota. We used the equation (Eq. 1) first described
by Poynter (1989) but with a chain interval from C23 to C33
following Strauss et al. (2015) and Jongejans et al. (2018):
ACL=∑i⋅Ci∑Ci,
where C denotes concentration and i the carbon number.
Biogeochemical parameters of the Sobo-Sise Yedoma cliff: total
organic carbon (TOC) content, total nitrogen (TN) content, carbon-to-nitrogen (C/N) ratio, bulk stable carbon isotope ratios (δ13C),
radiocarbon ages and modelled age in calibrated kiloyears before present (cal kyr BP). Data points are displayed over cliff height from the cliff top at 25 m above river level (a.r.l.) to cliff bottom at 0 m a.r.l. The three sections of
SOB18 are plotted separately for each parameter (black, dark grey and light
grey circles). Units I, II (grey rectangle) and III correspond to Marine
Isotope Stage (MIS) 1 to 3, respectively. The radiocarbon ages were
published in Wetterich et al. (2020a).
Carbon preference index
The CPI (carbon preference index) was originally introduced by Bray and
Evans (1961) as the ratio of odd- to even-numbered n-alkanes and indicates
the level of OM transformation, which decreases with progressing maturation.
OM decomposition leading to lower CPI values is a measure of thermal
alteration referring to rocks or oils on a geological timescale. However,
this ratio, as well as the very similar odd-over-even predominance (OEP)
ratio, was previously used in Quaternary permafrost deposits as an indicator
for OM decomposition (Zech et al., 2009; Strauss et al., 2015; Struck et
al., 2020; Jongejans et al., 2020). Based on these studies, we refer to
values over 5 as less degraded OM of high quality. Equation (2) describes the CPI
and was modified after Marzi et al. (1993) using C23-33 as a chain
length interval.
CPI23-33=∑oddC23-31+∑oddC25-332∑evenC22-32
Higher plant fatty acids
For each sample, the absolute n-fatty-acid (FA) concentration was measured
and the most abundant homologue's chain length was identified. In addition,
we looked at the share of iso- and anteiso-branched FAs, which are indicators for
microbial biomass (Rilfors et al., 1978; Stapel et al., 2016). Furthermore,
we calculated the higher plant fatty acid (HPFA) index, which is the
relative amount of the long-chain n-fatty acids to long-chain n-alkanes in the
sediments. The HPFA index was introduced by Strauss et al. (2015) following the
principles of the HPA index of Poynter (1989), only with using fatty acids
instead of wax alcohols (Eq. 3). The HPFA index reflects the degree of
preservation of OM due to the higher lability of n-fatty acids in relation to
n-alkanes (Canuel and Martens, 1996). The preferential decomposition of fatty
acids is due to their functional group leading to a chemical polarisation
within the molecule forming an attack point for geochemical or
microbiological decomposition and/or decarboxylation (Killops and Killops,
2013). Therefore, a decrease in the HPFA index indicates increased OM
decomposition. We use this index for internal comparison where higher values
(above the mean) indicate a comparatively higher-quality OM.
HPFA=∑n-fattyacidsC24C26C28∑n-fattyacidsC24C26C28+∑n-alkanesC27C29C31
Data analysis
In order to identify the stratification along the cliff based on the OM
characteristics of the permafrost sediments, the data set was clustered
using a constrained agglomerative hierarchical clustering of a distance
matrix (chclust of the rioja package, in R version 4.0.4) (Juggins, 2019).
We applied the non-parametric Kruskal–Wallis (> two groups) test
for statistical analyses of the data to compare all major parameters (TOC,
C/N, n-alkanes, ACL, CPI, short and long n-fatty acids, HPFA index, and
(iso- + anteiso-branched) / (mid- and long-chain n-fatty acids)) between the identified clusters. In
the Results section, we report the p values; the correlation coefficients are
reported in the Supplement (Table S1).
Results
The uppermost sediments of the cliff consisted of Holocene-age sediments
(from 24.1 to 22.5 m a.r.l.; upper part of SOB18-01) on top of Late Pleistocene
Yedoma sediments from 22.2 m a.r.l. down to the cliff base at the river water
level. A detailed cryostratigraphic description is given in Wetterich et al. (2020a).
Sedimentological organic matter parameters
TOC content was highest in the topmost sample and ranged from <0.1 wt % (below the detection limit, sample SOB18-01-18 at 15.7 m a.r.l.) to 25.5 wt % (SOB18-01-01 at 24.1 m a.r.l.). Both the minimum and the maximum TOC values
were found within profile SOB18-01 (Fig. 2). The average TOC content was
4.9 wt % (standard deviation (SD) 4.7, n=28) and values decreased from
the cliff top downwards with two values higher than 10 wt % at 24.1 m a.r.l.
(SOB18-01-01; 25.5 wt %) and at 16.2 m a.r.l. (SOB18-03-05; 11.3 wt %). TN
content had an average of 0.3 wt % (SD 0.2), and the highest value was
also found at 24.1 m a.r.l. (SOB18-01-01; 0.8 wt %) and the lowest at 15.7 m a.r.l. (SOB18-01-18; <0.1 wt %). C/N ratios ranged from 7.2 to 30.5
(Fig. 2) and displayed, except for the uppermost sample, only little
variability over the cliff profile with a mean of 13.2 (SD 4.2). The
δ13C values ranged from -25.2 ‰ (SOB18-01-12 at 18.7 m a.r.l.) to -29.4 ‰ (SOB18-03-05 at
16.2 m a.r.l.) and had an average of -27.2 ‰ (SD 1.1).
There was a significant negative correlation between δ13C and
C/N values (r-0.59 (Pearson correlation), p<0.01). Radiocarbon
ages of selected plant remains were determined on a MICADAS system. These
data and a Bayesian age–depth model were published by Wetterich et al. (2020a). The laboratory methods were described in detail by Mollenhauer et al. (2021). The radiocarbon ages ranged from 2.50 (at 23.7 m a.r.l.) to 51.88 cal kyr BP (at 0.9 m a.r.l.).
Biomarker parameters of the Sobo-Sise Yedoma cliff. The first four
columns show n-alkane parameters: short-chain (C14–C20), and long-chain (C21–C33) n-alkane concentrations (both in µg g-1 TOC), the n-alkane average chain length (ACL23-33), and
n-alkane carbon preference index (CPI23-33). The last five columns
show n-fatty-acid parameters: short-chain (C8–C20), mid-chain
(C21–C23) and long-chain (C24–C32) n-fatty-acid
concentrations (in µg g-1 TOC); the ratio of iso- and
anteiso-branched saturated fatty acids (C11, C13, C15 and C17)
to mid- and long-chain (C ≥ 21) n-fatty acids; and the higher plant fatty
acid (HPFA) index. Data points are displayed over cliff height from the cliff
top at 25 m above river level (a.r.l.) to cliff bottom at 0 m a.r.l. The three
sections of SOB18 are plotted separately for each parameter (black, dark
grey and light grey circles). Units I, II (grey rectangle) and III
correspond to Marine Isotope Stage (MIS) 1 to 3.
Biomarkersn-Alkanes
n-Alkanes were detected in the range between n-C14 and n-C35 and
showed a strong odd-over-even carbon number predominance. The relative
n-alkane concentration increased in the lower part of the cliff, closer to
the river level. Relative n-alkane concentrations ranged from 1 to 172 µg g-1 TOC (mean 30, SD 42) for the short-chain (C14 to C20)n-alkanes and from 119 to 3214 µg g-1 TOC (mean 1068, SD 886)
for the long-chain (C21 to C33) n-alkanes (Fig. 3). The absolute
concentrations were also higher in the lower part of the cliff for the short-chain
(mean 1 µg g-1 sed., SD 1) and long-chain n-alkanes (mean 41 µg g-1 sed., SD 31). The main dominating n-alkane chain length
was n-C27 in the lower part of the cliff and alternated between
n-C27 and n-C29 in the upper part (Fig. S1). Four samples were
dominated by the n-C31n-alkane.
The n-alkane-based ACL showed variations between 27.1 (SOB18-06-19 at 4.5 m a.r.l.) and 29.0 (SOB18-01-06 at 21.7 m a.r.l.) with a mean of 28.0 across the
cliff (SD 0.50; Fig. 3). The CPI of n-alkanes (n-C23 to n-C33)
ranged from 5.76 (SOB18-06-15; 6.5 m a.r.l.) to 16.29 (SOB18-06-05; 11.5 m a.r.l.)
with a mean value of 9.89 (SD 2.79). Below 7 m a.r.l., the CPI significantly
decreased.
n-Fatty acids
We found n-FAs with carbon numbers between C8 and C32. The n-FAs
showed a strong even-over-odd carbon number predominance. Furthermore,
hydroxy FAs (C6 to C8), iso-branched FAs (C10 to C19),
anteiso-branched FAs (C11, C12, C13, C15 and C17),
monounsaturated FAs (C16 to C20 and C24), unsaturated iso- and
anteiso-branched FAs (C17), cyclopropyl FAs (C17 and C19), di- and
triunsaturated FAs (C18), and phytanic acid were detected (Fig. S2,
Table S2). Concentration of long-chain n-FAs (C24 to C32) ranged
from 290 µg g-1 TOC at 24.1 m a.r.l. to 2346 µg g-1 TOC
at 1.4 m a.r.l. (mean 1041 µg g-1 TOC, SD 655). The most abundant
long-chain n-FA was n-C24 for all samples, except at 16.7 m a.r.l.
(n-C26) (Figs. 2 and S2). The mid-chain n-FA (C21 to
C23) concentration ranged from 121 to 1250 µg g-1 TOC
(mean 463 µg g-1 TOC, SD 314) and was highest at 22.7 m a.r.l.
The short-chain n-FA concentration (C8 to C20) ranged from 120 to
968 µg g-1 TOC (mean 560 µg g-1 TOC, SD 212) and
was highest in the bottom sample at 1.4 m a.r.l. Among the short-chain FAs,
the n-C16 dominated all samples (Fig. S2). The iso- and
anteiso-branched FAs were more abundant in the bottom section of the cliff and
lowest in the middle section, and the ratio of iso- and anteiso-branched saturated
fatty acids (C11, C13, C15 and C17) to mid- and long-chain (C ≥ 21) n-FAs ranged from 0.03 to 0.32 (mean 0.13, SD 0.09; Figs. 3 and S2). The HPFA index had a mean value of 0.63 (SD 0.11,
n=13), a minimum of 0.45 (SOB18-06-17 at 5.5 m a.r.l.) and a maximum of 0.86
(SOB18-01-04 at 22.7 m a.r.l.) close to the cliff top. Overall, HPFA values
below 16 m a.r.l. were slightly lower than in the upper section.
Statistical separation of the Sobo-Sise Yedoma cliff profile and
selected carbon parameters of the separated cliff units. (a) Clustering of
samples with y axis representing cliff height from the cliff top at 25 m above
river level (a.r.l.) to cliff bottom at 0 m a.r.l. Unit I corresponds to Marine
Isotope Stage (MIS) 1, unit II to MIS 2 and unit III to MIS 3. Resulting box
plots allow better visualisation of the OM distribution along the Sobo-Sise
Yedoma cliff profile: (b) total organic carbon (TOC) content (in wt %),
(c) short-chain n-alkane concentration (in µg g-1 TOC), (d) higher
plant fatty acid (HPFA) index, and (e) ratio of iso- and anteiso-branched saturated fatty
acids (C11, C13, C15 and C17) to mid- and long-chain
(C ≥ 21) n-fatty acids.
Clustering
We identified three main sub-groups using agglomerative hierarchical
clustering (Fig. 4a): unit I from 24.1 to 22.7 m a.r.l. (n=3), unit II from
21.7 to 16.7 m a.r.l. (n=7) and unit III from 16.2 to 1.4 m a.r.l. (n=18). Our
clustering matched the three cryostratigraphic units as defined by Wetterich
et al. (2020a), which further corresponded to MIS 1, MIS 2 and MIS 3 from the
top to the bottom. The TOC content (Fig. 4b) and C/N ratio were
significantly the highest in unit I and lowest in unit II (p<0.01 and
p<0.05, respectively; Fig. 2 and Table S1). The short-chain (C14 to
C20) and long-chain (C21 to C33) n-alkane concentration,
expressed in µg g-1 TOC, was higher in unit III, but the
differences were only significant for the short-chain n-alkanes (p<0.01) (Fig. 4c). The short-chain (C8 to C20), mid-chain (C21 to
C23) and long-chain (C24 to C32) n-fatty-acid concentrations
expressed in µg g-1 TOC did not differ significantly between the
units. The ACL and CPI values were similar for each unit (Fig. 3). The
HPFA index was significantly different between the units (p<0.05)
with the highest values in unit I and lowest values in unit III (Fig. 4d). The
share of iso- and anteiso-branched FAs compared to mid- and long-chain n-FAs was highest
in unit III and lowest in unit II (Fig. 4e), but the differences were not
significant.
DiscussionTerrestrial organic matter at the interface between permafrost and riverOrganic matter source
We found that the n-alkane distributions were dominated by the long-chain
n-alkanes (C ≥ 21) and that short-chain n-alkanes only played a marginal
role (Fig. S1). The most abundant n-alkane homologues in the entire data set
were n-C27, n-C29 and n-C31, which indicates that the OM stemmed
from higher land plants (Eglinton and Hamilton, 1967). This is confirmed by
the dominance of long-chain n-FAs (C24–C32) with a strong even-over-odd carbon number predominance (Fig. S2). The relatively high ACL across
the cliff (Fig. 3) indicates a predominant contribution of vascular
plants, which corroborates the pollen record presented by Wetterich et al. (2021). Their results indicated the presence of tundra–steppe vegetation
during MIS 3–2, while MIS 1 pollen spectra of the uppermost three samples
indicated a shift from tundra–steppe to shrub–tundra vegetation. Occasional
warmer-than-today summers were recorded during the early MIS 3 as well as the
presence of low-centre polygons with favourable (stable) aquatic conditions
during MIS 3. Cooler and drier summer conditions as well as unstable
(draining and rewetting phases) aquatic conditions were reconstructed for MIS 2 (Wetterich et al., 2021). In our study, the elevated ratio of
iso- and anteiso-branched FAs relative to mid- and long-chain (C ≥ 21) n-FAs in unit I
(MIS 1) and III (MIS 3) compared to unit II (MIS 2; Figs. 4e and S2)
suggests stronger microbial activity during the warmer MIS 3 and MIS 1
periods (Rilfors et al., 1978; Stapel et al., 2016) and points to a higher
input of bacterial biomass during that time. Additionally, we found a
significant abundance of short-chain FAs, especially n-C16 in all samples
(Fig. S2). However, these FAs are common not only in bacterial but also in
eukaryotic microorganisms (Gunstone et al., 2007) and thus represent a
mixing signal. Therefore, we focused here on iso- and anteiso-branched FAs as they are
more specific biomarkers for bacterial biomass (Kaneda, 1991).
The source and nature of the OM preserved in permafrost influence both its
quantity and its quality (Jongejans et al., 2018). TOC, TN, C/N and δ13C variations result from changes in biomass productivity and/or
decomposition, from different OM sources, from changes in depositional
conditions influencing OM preservation, and from different characteristics of
Cryosol formation. Generally, enriched δ13C and low TOC and C/N
values, as we found in unit II and III (Fig. 2), are typical of Yedoma
deposits that formed during cold stages (Schirrmeister, 2012). However,
climate variations during the last ice age were differentiated into warmer
interstadials (e.g. MIS 3) and colder stadial periods (e.g. MIS 2) which
climatically triggered changes in vegetation and Cryosol formation. At the
Sobo-Sise Yedoma cliff, the TOC values were higher during MIS 1 and 3
compared to the last glacial (MIS 2) deposits, suggesting higher OM
accumulation, which was presumably triggered by higher biomass production.
The TOC values from the MIS 3 and MIS 2 sediments of the Sobo-Sise Yedoma
cliff (<0.1 wt %–11.3 wt %, mean 4.0 wt %) were significantly
higher (p<0.01) than those of other Siberian Yedoma sites (<0.1 wt %–27 wt %, mean 3.0 wt %; 17 study sites, 719 samples) but very
similar to data from Kurungnakh Island (mean 3.8 wt %) which is located
about 70 km west-south-west of Sobo-Sise Island in the central Lena
Delta (Strauss et al., 2012, 2020). Likely, the high TOC values in the
Sobo-Sise record are a result of past wetter conditions leading to the
formation of peat layers. Comparably to the Kurungnakh Island Yedoma record,
the Sobo-Sise Yedoma cliff is characterised by silty sediments with multiple
layers enriched in peat pointing to palaeosol formation during permafrost
aggradation. The MIS 3 deposits contained rather less decomposed twigs and
grass remains as well as single peaty lenses (15–20 cm in diameter) and peat
layers (10–20 up to 130 cm thick). A similar occurrence of single-twig
remains (2–4 mm in diameter), dark brown spots, finely dispersed organic
remains and peaty lenses (5–25 cm in diameter) was found in MIS 2
deposits, while MIS 1 deposits contained many more peaty components, i.e.
numerous peaty lenses (2–25 cm in diameter), which was reflected in higher
TOC values compared to MIS 3 and MIS 2 deposits (Wetterich et al., 2020a).
At 16.2 m a.r.l., we found a peak in TOC (11.3 wt %, SOB18-03-05) and a
simultaneously depleted δ13C value (-29.4 ‰). High TOC and low δ13C values have been found to be
indicative for peat accumulation and low decomposition under wetter
conditions in a more anaerobic regime (Wetterich et al., 2009; Schirrmeister
et al., 2011a; Strauss et al., 2012). These peat layers can form by moss
accumulation which is hardly decomposed and/or incorporated soon upon
accumulation. From a biomarker perspective, this sample was not much
different regarding the biomolecular composition, indicating a similar
organic biomass (Fig. S2). The higher relative abundance of iso- and
anteiso-FAs relative to mid- and long-chain FAs in this sample may point to
increased microbial activity and thus microbial decomposition during the time of
deposition in this OM-rich sample. Considering palaeoenvironmental studies
from Kurungnakh Island in the central Lena Delta, palaeosol formation was
intensified by relatively warm and wet summers during the climate optimum of
the interstadial MIS 3 between 40 and 32 ka BP (Wetterich et al., 2008, 2014). Therefore, it is very likely that this layer is a
buried palaeosol layer containing peaty material.
Organic matter quality
OM from different vegetation types was incorporated from the active layer
into the permafrost during and after different phases of decomposition. The
biogeochemical and biomarker proxies outlined in the previous section mainly
describe the sources and composition of permafrost OM. In addition,
biomarker ratios provide information on the decomposition level of the OM
and, with that, the potential “decomposability” (quality) of the respective
permafrost OM upon thaw. The OM assessment of this study via agglomerative
clustering found an overall high OM quality of the Sobo-Sise Yedoma deposits
with high CPI values (mean 9.89) and higher C/N ratios (mean 13.24)
compared to the other Yedoma deposits such as those on the Buor Khaya
Peninsula (central Laptev Sea) with mean C/N values of about 10 (Strauss et
al., 2015). The elevated C/N value in the top sample of the Sobo-Sise record
likely results from the influence of modern plants rooted in the active
layer. For the rest of the profile, the C/N ratios were rather uniform. The
high CPI in our study is comparable to other Yedoma sites as reported by
Strauss et al. (2015) for the Buor Khaya Peninsula (mean 11.6) and Jongejans
et al. (2018) for the Baldwin Peninsula (western Alaska; 12.2). At the
Sobo-Sise Yedoma cliff, the CPI values scattered around a mean of 9.89 and
decreased in the lowermost 7 m of the cliff profile. This could probably
indicate a higher level of OM decomposition for the lower cliff part but
can also be influenced by the vegetation type and species prevailing during
the early MIS 3 with stagnant water and partly warmer-than-today summer climate
conditions (Wetterich et al., 2021). The HPFA values (0.45–0.86, median
0.61) are a bit higher compared to Yedoma deposits investigated by Strauss
et al. (2015) on the Buor Khaya Peninsula (0.15–0.69, median 0.54). Overall,
the HPFA significantly decreased downwards (Fig. 4d; p<0.05),
especially below unit II, which suggests that the OM is further decomposed
downwards. This fits the assumption that there was more time for OM
decomposition for the older lower cliff parts of the palaeo-active layer. A
higher decomposition for the lower cliff part is also supported by the
highest ratio of the iso- and anteiso-branched FAs vs. mid- and long-chain FAs in the MIS 3 deposits (Fig. 4e), indicating a higher relative amount of microbial
biomass and suggesting higher microbial activity during this warmer
interval.
Previous studies showed that mineral-associated OM can make up a substantial
fraction of the OM in permafrost soils, which protects the OM from
decomposition (Dutta et al., 2006; Mueller et al., 2015). We
found that the biomarker concentrations are negatively correlated with the
mean grain size published by Wetterich et al. (2020b) (Fig. S3).
Especially the negative correlation between the grain size and the short-
(p<0.01), mid- and long-chain n-FA concentrations (p<0.05) are
significant. This suggests that, even though the n-FAs are generally
vulnerable with respect to decomposition, the n-FAs might to some extent be
protected from OM decomposition upon mobilisation and transport. On top of
the preferred decomposition of short-chain n-alkanes over their long
counterpart (Elias et al., 2007), the stronger negative correlation (even
though not significant) between the grain size and the long-chain
n-alkanes compared to their short-chain counterpart could suggest that the
latter might be more vulnerable to decomposition or might reflect the
different sources of these biomolecules. While long-chain n-alkanes are derived
from higher land plants and enter the soil by deposition, short-chain
n-alkanes might contain a significant portion of microbial biomass, whose
abundance depends on the availability of appropriate substrates.
As outlined above, three stages of permafrost aggradation on Sobo-Sise
Island linked to climatic variability were identified according to Wetterich
et al. (2020a). OM preservation during these stages is strongly impacted by
the duration of freezing and thawing periods, the associated presence and
absence of oxygen in the soil, the related level of microbial activity,
and/or physical protection of the OM by the inorganic matrices (e.g. Fe
complexation) (Freeman et al., 2001; Hedges and Keil, 1995; Lützow et
al., 2006). As these factors are all closely interlinked, it is almost
impossible to decipher the control of these processes on the finally
preserved OM biomarker signatures.
Implications
Nitzbon et al. (2020) found that terrestrial permafrost-locked OC will be
significantly thaw-affected by 2100, and it could even be up to 3-fold
(12-fold) more under warming scenario RCP4.5 (RCP8.5) compared to
previous estimates if including thermokarst-inducing processes. Deep OM as
characterised in our study can be released by deep disturbance processes
such as thermokarst development, thermal erosion or riverbank erosion. Our findings show
that freshly thawed and high-quality OM was frozen in the cliff sediments
and is now being mobilised rapidly as is shown by the high annual erosion rates
of 15.7 m yr-1 as reported by Fuchs et al. (2020) (2015–2018, in the
long term 9 m yr-1). Furthermore, we suggest that the very ice-rich
cliff wall sections are not exposed to aerobic conditions for very long time
periods before being eroded into the Lena River. Thus, aerobic microbial
decomposition of the OM at the cliff front is presumably playing only a
minor role. Additionally, cliff erosion is mainly driven by thermo-erosion
and niche formation at the base of the ice-rich Yedoma cliff, resulting in
block failure instead of slow gradual cliff retreat (Fuchs et al., 2020).
Accordingly, some of the OM in the cliff may not even become exposed to the
air and thaw at all before being eroded into the river. Fuchs et al. (2020)
showed an average loss of 5.2×106 kg OC yr-1 and 0.4×106 kg N yr-1 (2015–2018). For the OC flux sourced from permafrost and peat
deposits (and in particular from erosive locations like our study site on
Sobo-Sise Island), Wild et al. (2019) estimated 0.9×108 kg C yr-1.
By using a biomarker approach (e.g. n-alcohols, n-fatty acids, n-alkanes) on
sub-aquatic sediments, van Dongen et al. (2008) found a lower degree of
decomposition of the old terrestrial OM released by the great eastern Arctic
rivers, including the Lena River, compared to the western Eurasian Arctic.
Thus, they predicted greater remineralisation rates and release of carbon
dioxide and methane. Our biomarker findings of terrestrial permafrost fit
well into this scenario. Winterfeld et al. (2015) studied the lignin phenol
composition of the Lena River, Lena Delta and Laptev Sea nearshore zones
and proposed that OM decomposition is considerable after permafrost thawing
on land and during transport and sedimentation in the water. The present
study on the OM origin and the annual OC erosion rates at the Sobo-Sise
Yedoma cliff complements ongoing research on mobilisation of
permafrost-locked carbon from Late Pleistocene Yedoma deposits, while
thermal erosion is a widespread and climate-sensitive phenomenon in the
Yedoma domain, covering nearly 5×105 km2 in Siberia and Alaska
(Strauss et al., 2021b). This indicates the high potential of thermal
erosion for mobilisation and release upon thaw of not only large amounts of
carbon but also well-preserved OM into the aquatic system of the Lena Delta
and nearshore Laptev Sea and Arctic Ocean areas, which will affect local but
likely also regional biogeochemical cycles in the marine realm (Grotheer et
al., 2020; Tanski et al., 2021; Mann et al., 2022) and the shelf seas. Once
mobilised and transported into inland waters, permafrost-derived OC can be
rapidly used by aquatic microorganisms, increasing OM decomposition in
riverine and coastal Arctic waters (Vonk et al., 2012, 2013a, 2015; Drake et
al., 2015; Mann et al., 2015). Vonk et al. (2012) studied the organic matter
exported from the fast-eroding Yedoma cliff of Muostakh Island, which is
located about 120 km south-east of the Sobo-Sise Yedoma cliff. They found
that decomposition of Yedoma OM prior to delivery to the ocean was
substantial. In their study of OM mobilisation by retrogressive thaw slumps
in Canada, Bröder et al. (2021) found that the majority of the exported
OC was derived from permafrost deposits. However, they also found that
Pleistocene permafrost deposits mostly contained less labile, slowly cycling
permafrost OC. Similarly, Bröder et al. (2019) showed that more than
half of the carbon transported and deposited on the shelf sea floor likely
resists decomposition on a centennial scale while the rest decays
relatively slowly. Furthermore, OM mobilised from Pleistocene or Holocene
permafrost by rapid thermokarst and mass-wasting processes contribute
different shares of particulate and dissolved organic matter (Kokelj et al.,
2021; Shakil et al., 2020), which has implications for decomposition and
transport. In addition, Karlsson et al. (2011) hypothesised that Yedoma OC,
associated with mineral-rich matter from coastal erosion, is ballasted and
thus quickly settles to the bottom. Increasing thermokarst and mass-wasting
processes, as well as river and coastal erosion, will continue to mobilise
both labile and recalcitrant OM from Pleistocene permafrost deposits, and it
is still largely unknown what short- and long-term effects this will have on
the release of greenhouse gases and alteration of biochemical processes in
nearshore waters.
Conclusions
Sedimentological and biogeochemical analyses showed that the sediments
exposed at the Sobo-Sise Yedoma cliff contain a high TOC content (mean 5 wt %) and well-preserved OM (C/N mean 13.2, mean CPI 9.89) in comparison
to other Yedoma permafrost sites. Our study corroborated the
palaeoenvironmental data from the Sobo-Sise Yedoma cliff from previous
research which suggested that Yedoma formation during the interstadial MIS 3
and the accumulation of the topmost Holocene deposits (MIS 1) were
associated with more microbial activity than during the stadial MIS 2. In
addition, our findings suggest that mainly high-quality OM has been
freeze-locked perennially into permafrost during the Late Pleistocene to
Holocene. Although the OM quality seems to be overall fairly high (TOC, C/N
and CPI), biomarker parameters indicate a higher level of OM decomposition
for the bottom 7 m (CPI) or even for the bottom 15 m (HPFA) of the cliff
profile of MIS 3 age, and less OM accumulation during MIS 2 in contrast to
the warmer MIS 3 and 1 sequences is assumed. At the Sobo-Sise Yedoma cliff,
representing an example of rapidly eroding permafrost shorelines in the Lena
Delta, OM with a high decomposition potential is being mobilised from almost
all sections of the cliff profile. This material is suggested to rapidly
enter the fluvial and probably also the offshore aquatic ecosystem. Thus, OM
mobilisation at the Sobo-Sise Yedoma cliff and similarly eroding permafrost
sites bear the potential to impact the carbon dynamics, the biogeochemistry,
and the riverine and nearshore marine ecosystems.
Data availability
The data presented in this study are freely available in the PANGAEA data
repository (10.1594/PANGAEA.935672, Haugk et al., 2022). Cryolithological and geochronological data
from the Sobo-Sise Yedoma cliff are available in PANGAEA (10.1594/PANGAEA.919470, Wetterich et al.,
2020b).
The supplement related to this article is available online at: https://doi.org/10.5194/bg-19-2079-2022-supplement.
Author contributions
CH and JS designed this study and drafted a first version of the
manuscript. CH carried out the lipid biomarker analyses and interpretation,
with help from LLJ, CK and KM. SW, LS and AK conducted the sampling and field
studies. CH, JS and LLJ led the manuscript writing. All co-authors
contributed to the manuscript writing process.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
This study was carried out within the CACOON project and the joint
Russian–German expeditions Lena 2018 and Sobo-Sise 2018 supported by the
Samoylov Research Station. We thank Michael Fritz (AWI Potsdam) and Aleksey
Aksenov (Arctic and Antarctic Research Institute, St Petersburg) for
supporting the permafrost sampling on Sobo-Sise in August 2018. We thank
Justin Lindemann (AWI Potsdam) and Anke Sobotta (German Research Centre for
Geoscience) as well as Hanno Meyer and Mikaela Weiner (AWI ISOLAB Facility)
for support with laboratory analysis.
Financial support
This research has been supported by the Bundesministerium für Bildung und Forschung (grant no. 03F0806A), UK Research and Innovation (grant no. NE/R012806/1) and the Deutsche Forschungsgemeinschaft (grant no. WE4390/7-1).The article processing charges for this open-access publication were covered by the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI).
Review statement
This paper was edited by Sebastian Naeher and reviewed by two anonymous referees.
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