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  <front>
    <journal-meta><journal-id journal-id-type="publisher">CP</journal-id><journal-title-group>
    <journal-title>Climate of the Past</journal-title>
    <abbrev-journal-title abbrev-type="publisher">CP</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Clim. Past</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1814-9332</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/cp-15-811-2019</article-id><title-group><article-title>Decadal-scale progression of the onset of<?xmltex \hack{\break}?> Dansgaard–Oeschger warming events</article-title><alt-title>Progression of the onset of DO warming events</alt-title>
      </title-group><?xmltex \runningtitle{Progression of the onset of DO warming events}?><?xmltex \runningauthor{T. Erhardt et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Erhardt</surname><given-names>Tobias</given-names></name>
          <email>erhardt@climate.unibe.ch</email>
        <ext-link>https://orcid.org/0000-0002-6683-6746</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff3">
          <name><surname>Capron</surname><given-names>Emilie</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Rasmussen</surname><given-names>Sune Olander</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4177-3611</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Schüpbach</surname><given-names>Simon</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Bigler</surname><given-names>Matthias</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0184-4013</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff4">
          <name><surname>Adolphi</surname><given-names>Florian</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0014-8753</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Fischer</surname><given-names>Hubertus</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2787-4221</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Climate and Environmental Physics, Physics Institute &amp; Oeschger Center for Climate Change Research,<?xmltex \hack{\break}?> University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Tagensvej
16,<?xmltex \hack{\break}?> 2200 Copenhagen, Denmark</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET, UK</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Quaternary Sciences, Department of Geology, Lund University, Sölvegatan 12, 22362 Lund, Sweden</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Tobias Erhardt (erhardt@climate.unibe.ch)</corresp></author-notes><pub-date><day>25</day><month>April</month><year>2019</year></pub-date>
      
      <volume>15</volume>
      <issue>2</issue>
      <fpage>811</fpage><lpage>825</lpage>
      <history>
        <date date-type="received"><day>13</day><month>December</month><year>2018</year></date>
           <date date-type="rev-request"><day>17</day><month>December</month><year>2018</year></date>
           <date date-type="accepted"><day>13</day><month>April</month><year>2019</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2019 Tobias Erhardt et al.</copyright-statement>
        <copyright-year>2019</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019.html">This article is available from https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019.html</self-uri><self-uri xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019.pdf">The full text article is available as a PDF file from https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e158">During the last glacial period, proxy records throughout the Northern
Hemisphere document a succession of rapid millennial-scale warming events,
called Dansgaard–Oeschger (DO) events. A range of different mechanisms has
been proposed that can produce similar warming in model experiments; however,
the progression and ultimate trigger of the events are still unknown. Because
of their fast nature, the progression is challenging to reconstruct from
paleoclimate data due to the limited temporal resolution achievable in many
archives and cross-dating uncertainties between records. Here, we use new
high-resolution multi-proxy records of sea-salt (derived from sea spray and
sea ice over the North Atlantic) and terrestrial (derived from the central
Asian deserts) aerosol concentrations over the period 10–60 ka from the
North Greenland Ice Core Project (NGRIP) and North Greenland Eemian Ice
Drilling (NEEM) ice cores in conjunction with local precipitation
and temperature proxies from the NGRIP ice core to investigate the
progression of environmental changes at the onset of the warming events at
annual to multi-annual resolution. Our results show on average a small lead
of the changes in both local precipitation and terrestrial dust aerosol
concentrations over the change in sea-salt aerosol concentrations and local
temperature of approximately one decade. This suggests that, connected to the
reinvigoration of the Atlantic meridional overturning circulation and the
warming in the North Atlantic, both synoptic and hemispheric atmospheric
circulation changes at the onset of the DO warming, affecting both the
moisture transport to Greenland and the Asian monsoon systems. Taken at face
value, this suggests that a collapse of the sea-ice cover may not have been
the initial trigger for the DO warming.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e170">Ice-core records from Greenland reveal millennial-scale warming episodes in
the course of the last glacial period, called Dansgaard–Oeschger (DO) events
<xref ref-type="bibr" rid="bib1.bibx10 bib1.bibx43" id="paren.1"/>. During their onset, temperatures in
Greenland increased rapidly by 10–15 <inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C from  cold stadial (GS,
Greenland Stadial) to  warmer interstadial (GI, Greenland Interstadial)
conditions within a few decades <xref ref-type="bibr" rid="bib1.bibx29 bib1.bibx23 bib1.bibx60" id="paren.2"/>, coinciding with an almost doubling of the local snow
accumulation <xref ref-type="bibr" rid="bib1.bibx2" id="paren.3"/>. Moreover, aerosol records from Greenland
ice cores show coinciding rapid changes in aerosol concentrations during the
onset of the events. These changes are partly caused by reduced atmospheric
lifetime of the aerosols due to increased precipitation scavenging en route
and partly by changes in aerosol sources <xref ref-type="bibr" rid="bib1.bibx16 bib1.bibx59" id="paren.4"/>.</p>
      <?pagebreak page812?><p id="d1e194">Other proxy records throughout the Northern Hemisphere also document the
widespread environmental imprint of these rapid warming events. Marine
sediment cores <?xmltex \hack{\mbox\bgroup}?><xref ref-type="bibr" rid="bib1.bibx13" id="paren.5"/><?xmltex \hack{\egroup}?> and aerosol records from Greenland
<?xmltex \hack{\mbox\bgroup}?><xref ref-type="bibr" rid="bib1.bibx62" id="paren.6"/><?xmltex \hack{\egroup}?> show a reduction in perennial sea-ice cover in the
Nordic Sea and Arctic Basin, and ocean circulation proxies indicate an
increase in the Atlantic meridional overturning circulation (AMOC)
<xref ref-type="bibr" rid="bib1.bibx36" id="paren.7"/>. Records from North America indicate a change in
the moisture advection from the Pacific with drier conditions during the warm
interstadial periods likely related to changes in atmospheric circulation
<xref ref-type="bibr" rid="bib1.bibx72 bib1.bibx3" id="paren.8"/>. These circulation changes coincide with
increased wildfire activity in North America as clearly imprinted in the
Greenland ice-core record <xref ref-type="bibr" rid="bib1.bibx16" id="paren.9"/>. Furthermore, records from
Eurasia indicate rapid changes in the local ecosystems <xref ref-type="bibr" rid="bib1.bibx56" id="paren.10"/>.
In the lower latitudes, speleothem and sediment records from both South
America <xref ref-type="bibr" rid="bib1.bibx74 bib1.bibx12" id="paren.11"/> and eastern Asia <xref ref-type="bibr" rid="bib1.bibx75" id="paren.12"/>
indicate a northward displacement of the Intertropical Convergence Zone
(ITCZ) at the time of DO warming <xref ref-type="bibr" rid="bib1.bibx8" id="paren.13"/> resulting in rapid changes
in tropical hydroclimate and methane emissions from the tropical wetlands
<xref ref-type="bibr" rid="bib1.bibx4" id="paren.14"/>. A recent synchronization of cosmogenic radionuclide
records from ice cores and low-latitude speleothems back to 45 kyr ago shows
that atmospheric circulation changes in the tropics occurred synchronously
with the Greenland warming within the cross-dating uncertainties of around
180 years <xref ref-type="bibr" rid="bib1.bibx1" id="paren.15"/>. The atmospheric circulation changes associated
with the Asian monsoon systems documented in the Asian speleothems also
reduced the mobilization and export of mineral dust aerosol from the central
Asian deserts during the warm stadial periods as documented by downstream
sediment records <xref ref-type="bibr" rid="bib1.bibx48 bib1.bibx25" id="paren.16"/>.</p>
      <p id="d1e239">A range of different, non-exclusive mechanisms that produce interstadial-like
warming events during pre-industrial and glacial climate conditions have been
proposed and tested in model experiments. These include the direct modulation
of the AMOC by freshwater addition to the North Atlantic
<xref ref-type="bibr" rid="bib1.bibx31" id="paren.17"><named-content content-type="pre">e.g.</named-content></xref>, where ceasing artificial freshwater forcing in
the North Atlantic results in an increasing strength of the AMOC and
subsequently increasing Greenland temperatures. Many of the proposed
mechanisms involve the reduction of North Atlantic sea-ice cover either as
a driving or amplifying process for the warming. In both coupled and
uncoupled model experiments, the removal of winter sea-ice cover in the North
Atlantic and Nordic Seas alone generates an increase in Greenland
temperatures and snow accumulation rates similar to observations by exposing
the relatively warm underlying ocean <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx34" id="paren.18"/>. Experiments with
coupled atmosphere and ocean show that this reduction in sea-ice cover can be
induced by changes in the wind stress over the sea ice either arising
spontaneously <xref ref-type="bibr" rid="bib1.bibx30" id="paren.19"/> or controlled by elevation changes of the
Laurentide Ice Sheet <xref ref-type="bibr" rid="bib1.bibx82" id="paren.20"/>. Furthermore, heat accumulation under
the sea ice during stadials can destabilize the otherwise strongly stratified
water column, eventually leading to breakdown of the stratification and
melting of the sea ice from below <xref ref-type="bibr" rid="bib1.bibx13 bib1.bibx26" id="paren.21"/>.
Alternatively, <xref ref-type="bibr" rid="bib1.bibx47" id="text.22"/> and <xref ref-type="bibr" rid="bib1.bibx69" id="text.23"/> describe the
occurrence of spontaneous DO-like oscillations in their fully coupled model
caused by the buildup and breakdown of a meridional salinity gradient
between the open and the sea-ice-covered North Atlantic. The collapse of the
salinity gradient then leads to a rapid disintegration of the sea-ice cover
and an invigoration of the AMOC. In summary, it is clear that sea ice is a
crucial factor in generating the full climatic change seen at the DO warming
<xref ref-type="bibr" rid="bib1.bibx33" id="paren.24"/>. However, the sequence of events, and whether the sea-ice loss
is triggered by atmospheric or oceanic changes, differs between the proposed
mechanisms.</p>
      <p id="d1e269">In any case, the progression and possible interaction between the distinct
processes that can partake in the DO warming are difficult to constrain from
paleo-observations, and their validity therefore difficult to test, especially
as some of the proposed mechanisms lead to virtually indistinguishable model
results <xref ref-type="bibr" rid="bib1.bibx6" id="paren.25"/>. The relative timing between the start of DO events
in proxy records of different parts of the Earth system can yield critical
insight into their spatiotemporal progression and possible causal relations.
However, due to the fast onset of the DO events, relative time differences
are expected to be on the order of years to decades, requiring very high
temporal resolution of paleo-records and often unattainable small relative
dating uncertainties between records from different archives.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Data and methods</title>
      <p id="d1e283">Multi-proxy records from ice cores are ideally suited for this type of
investigation, as they contain information about different parts of the Earth
system in the same archive and thus with negligible relative dating
uncertainty when measured on samples from the same depths. Two studies have
previously tapped into this potential and used high-resolution proxy data
from the North Greenland Ice Core Project (NGRIP) ice core to investigate the
onset of the Holocene, GI-1 and GI-8c using two different approaches to infer
the timing of changes in the different proxies <xref ref-type="bibr" rid="bib1.bibx63 bib1.bibx68" id="paren.26"/>. In the study presented here, we greatly expand on these two
studies by using new high-resolution records of mineral dust and sea-salt
aerosol as indicated by calcium (<inline-formula><mml:math id="M2" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and sodium (<inline-formula><mml:math id="M3" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>)
concentrations from both the NGRIP <xref ref-type="bibr" rid="bib1.bibx43" id="paren.27"/> and North Greenland
Eemian Ice Drilling (NEEM) <xref ref-type="bibr" rid="bib1.bibx42 bib1.bibx59" id="paren.28"/> Greenland deep ice
cores. The datasets span the complete time interval from 10 to 60 ka and
include all interstadial onsets from GI-17.2 to the onset of the Holocene.
The aerosol records were measured using continuous flow
analysis (CFA), allowing for exact
co-registration of the aerosol concentration records at<?pagebreak page813?> the millimetre scale
and resulting in sub- to multi-annual resolution, depending on the thinning
of the ice (<xref ref-type="bibr" rid="bib1.bibx55" id="altparen.29"/>; <?xmltex \hack{\mbox\bgroup}?><xref ref-type="bibr" rid="bib1.bibx28" id="altparen.30"/><?xmltex \hack{\egroup}?>).
Sodium concentrations were determined using an absorption photometric method
and calcium concentrations using a fluorimetric detection <xref ref-type="bibr" rid="bib1.bibx61 bib1.bibx55 bib1.bibx28" id="paren.31"/>. We further use the NGRIP GICC05 annual
layer thickness record, based on the identification of seasonal variations in
the aforementioned aerosol and visual stratigraphy records, as a measure of
relative local accumulation rate changes <xref ref-type="bibr" rid="bib1.bibx66 bib1.bibx67" id="paren.32"/>
as well as 4- to 7-year (5 cm) resolution <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> measurements
on the ice from NGRIP as a proxy for local temperature changes
<xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx19" id="paren.33"/>. All data are shown in Fig. <xref ref-type="fig" rid="Ch1.F1"/>
in decadal resolution on their respective timescales. Between the individual
datasets, the co-registration uncertainty is limited by the absolute depth
assignment of the datasets. This uncertainty is typically on the order of a
few millimetres for CFA data and around a
centimetre between <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> and CFA data, which translates to a
co-registration uncertainty in the sub-annual range.</p>
      <p id="d1e367">For both ice cores, the current versions of the GICC05 age scale were used,
which in the case of NEEM has been transferred from NGRIP using volcanic
match points <xref ref-type="bibr" rid="bib1.bibx49 bib1.bibx2 bib1.bibx66 bib1.bibx50" id="paren.34"/>. All ages are given relative to 1950. Even though at the
volcanic match points the dating uncertainty is relatively small, the
uncertainty introduced by the interpolation between the match points
generally precludes direct comparison of absolute timing between the two
cores with the precision required for this study.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e375">Investigated records from the NEEM <bold>(a, b)</bold> and NGRIP ice
cores <bold>(c–f)</bold>. Panels <bold>(a)</bold>, <bold>(d)</bold> show the new aerosol
records of <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <bold>(a, c)</bold> and <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> <bold>(b, d)</bold>
alongside the NGRIP layer thickness (<inline-formula><mml:math id="M8" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>) <bold>(e)</bold> and ice
<inline-formula><mml:math id="M9" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> records <bold>(f)</bold>. All records are shown as decadal
averages on their respective version of the GICC05 age scale relative to 1950
<xref ref-type="bibr" rid="bib1.bibx67 bib1.bibx50" id="paren.35"/>. The vertical lines mark the investigated
interstadial onsets as given by <xref ref-type="bibr" rid="bib1.bibx51" id="text.36"/>. Note that the vertical
scales for the aerosols and annual layer thickness are logarithmic.</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019-f01.png"/>

      </fig>

      <p id="d1e462">Mineralogy and isotopic composition of mineral dust aerosol from central
Greenland indicate that its dominant glacial sources are the central Asian
Taklamakan and Gobi deserts <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx65" id="paren.37"/>. Large dust
storms occurring during spring can lift dust up into the westerly jet stream
where it is transported over long ranges and at high altitudes
<xref ref-type="bibr" rid="bib1.bibx64 bib1.bibx54" id="paren.38"/>. The dust emission and subsequent entrainment into
the jet are strongly dependent on the specific synoptic circulation in the
area which itself is governed by the latitudinal position of the westerly jet
<xref ref-type="bibr" rid="bib1.bibx41 bib1.bibx54" id="paren.39"/>. Under current conditions, the position of the
westerly jet over central Asia varies seasonally, changing from south to
north of the Tibetan plateau during late spring, in unison with the northward
movement of the East Asian Summer Monsoon rain belt <xref ref-type="bibr" rid="bib1.bibx58 bib1.bibx81" id="paren.40"/>. During the last glacial, the jet was located further south, and,
especially during cold periods, was enabling more frequent or even permanent
conditions for the deflation and entrainment of the central Asian dust
<xref ref-type="bibr" rid="bib1.bibx9 bib1.bibx41" id="paren.41"/>. Once in the jet stream, the mineral dust
aerosol is transported above the cloud level and is largely protected from
scavenging by precipitation and transported efficiently to Greenland
<xref ref-type="bibr" rid="bib1.bibx59" id="paren.42"/>. This allows us to interpret changes in calcium
concentration records in terms of changes in the conditions needed for dust
entrainment, i.e. the latitudinal position of the westerly jet and the Asian
hydroclimate.</p>
      <p id="d1e484">Sodium-containing sea-salt aerosols are produced either by bubble bursting at
the surface of the open ocean or blowing saline snow on the surface of
sea ice <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx80" id="paren.43"/>. Sea-salt aerosol is transported
together with moist air masses from the North Atlantic onto the Greenland ice
sheet <xref ref-type="bibr" rid="bib1.bibx24" id="paren.44"/>. Under current conditions, aerosol transport
models point at the emission from blowing snow from winter sea ice as the
dominant source of sea-salt aerosol for Greenland in winter and suggest that
this source is responsible for a large fraction of the seasonal variability
seen in ice-core records <xref ref-type="bibr" rid="bib1.bibx22 bib1.bibx52" id="paren.45"/>. However, on
interannual timescales, the influence of the atmospheric transport and
deposition dominates the variability at the central Greenland sites for
recent times, due to the overall low contribution of sea-ice-derived aerosol
to the total sea-salt aerosol budget <xref ref-type="bibr" rid="bib1.bibx53" id="paren.46"/>. Under glacial
conditions, the extended multi-year sea-ice cover moves both sources of
open-ocean and sea-ice-derived sea-salt aerosols further away from the
ice-core sites. Intuitively, this would lead to a reduction in sodium
deposition on the ice sheet due to the longer transport. However, the
opposite is observed in the Greenland ice-core records of the last glacial
with much higher concentrations during cold climate periods than during
warmer periods <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx15" id="paren.47"/>. Isolating the effect of
the more distal sources, <xref ref-type="bibr" rid="bib1.bibx32" id="text.48"/> have shown that the more
extensive sea ice around Antarctica under glacial conditions would lead to
reduced sea-salt aerosol transport to the ice sheet. This effect, however, is
overcompensated by changes in the atmospheric circulation that enhance
production and transport during the glacial in comparison to present-day
conditions, leading to an observed increase in sea-salt aerosol concentrations
in Antarctic ice cores <xref ref-type="bibr" rid="bib1.bibx77" id="paren.49"/>. This suggests that changes in the
transport and deposition regimes must be responsible for a large fraction of
the glacial–interglacial and stadial–interstadial variability observed in the
Greenland ice-core records <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx15" id="paren.50"/>. One plausible
explanation for the apparently more efficient transport of sea-salt aerosol
to Greenland during the cold periods is the drier conditions over the cold,
sea-ice-covered North Atlantic compared to open-ocean conditions. This
implies that changes in the sea-ice cover do affect the sea-salt aerosol
concentrations in the Greenland ice cores not only because of an influence on
the source of the sea-salt aerosol but also on the efficiency of its
transport, i.e. its deposition en route. Reduced sea-ice cover increases
evaporation from the open ocean, resulting in increased scavenging en route
and subsequently reduced transport efficiency of sea-salt aerosol to the
Greenland ice sheet, especially because of its co-transport with moist air
masses from the North Atlantic <xref ref-type="bibr" rid="bib1.bibx24" id="paren.51"/>. In turn, this<?pagebreak page814?> allows us
to interpret the stadial–interstadial changes in sodium concentrations in the
ice cores as qualitative indicators of the extent of the sea-ice cover in the
North Atlantic.</p>
      <p id="d1e515">In combination, the records of water isotopic composition, annual layer
thickness and <inline-formula><mml:math id="M10" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M11" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> concentrations in the ice allow
us to study the phasing between changes in local temperature and
precipitation on the Greenland ice sheet, North Atlantic sea-ice cover and
dust deflation from the central Asian deserts, respectively. To quantify this
phase relationship, we employ a probabilistic model of the transitions to
determine their individual start and endpoints as well as the uncertainties
of these points. The model describes the stadial-to-interstadial transition
as a linear (in the case of the <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> record) or exponential
transition (i.e. a linear transition fitted to the log-transformed data for
all other records) between two constant levels, accounting for the intrinsic
multi-annual, auto-correlated variability of the proxy records using an AR(1)
noise process. This description of the transition is similar to the one used
by <xref ref-type="bibr" rid="bib1.bibx63" id="text.52"/>, who used a bootstrapping parameter grid-search
algorithm to determine the ramp parameters and their uncertainties
<?xmltex \hack{\mbox\bgroup}?><xref ref-type="bibr" rid="bib1.bibx40" id="paren.53"/><?xmltex \hack{\egroup}?>. However, here we use probabilistic inference to
determine the parameters of the ramp as well as those describing the
multi-annual variability of the records and their
uncertainties, conditioning on the data.
Inference is performed on the model using an ensemble Markov chain Monte
Carlo sampler <xref ref-type="bibr" rid="bib1.bibx20 bib1.bibx17" id="paren.54"/> to obtain posterior
samples for all parameters of interest as well as the parameters of the AR(1)
noise model. In this way, any correlations between parameter estimates and
their uncertainties are transparently accounted for. More details on the
inference and the mathematical description of the probabilistic model can be
found in Appendix A. In addition to the start and endpoints, we estimate the
temporal midpoints of the transitions, as they are less influenced by the
multi-annual variability that dominates the uncertainties of the timing
estimates. However, here we focus on the interpretation of the phase
relationship of the parameters at the onset of the stadial-to-interstadial
transitions to constrain the causal relationships of the trigger of the DO
events.</p>
      <p id="d1e568">The transition model is individually applied to approximately 500-year
sections of the data at the highest constantly available temporal resolution
(i.e. number of years per<?pagebreak page815?> observation) around the stadial to interstadial
transitions in each of the records on their respective timescales
<xref ref-type="bibr" rid="bib1.bibx66 bib1.bibx67 bib1.bibx51" id="paren.55"/>. The exact width of the
window was adjusted to account for gaps in the data and the onset of other
transitions within the 500-year window. Because of the thinning of layers due
to ice flow, the time resolution decreases from 2 years for the onset of the
Holocene to 3 years at the onset of GI-17.2 for the NGRIP CFA data, from 2 to
4 years for the NEEM CFA data and from 4 years at the onset of the Holocene
to 7 years for the NGRIP isotope data. The annual layer thickness data were
down-sampled to match the NGRIP CFA data resolution. Note that using the
overall lowest available temporal resolution (7 years) for the analysis leads
to practically the same results, albeit with slightly larger uncertainties.
It is also worth noting that the largest source for uncertainties in our
estimates stems from the multi-annual variability of the proxy records that
cannot be alleviated by higher-resolution records.</p>
      <p id="d1e574">An example of one of the fitted transitions, the onset of GI-8c in
<inline-formula><mml:math id="M13" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, is shown in Fig. <xref ref-type="fig" rid="Ch1.F2"/> alongside marginal
posterior distributions for the onset, midpoint and end of the transition.
The absolute timing estimates for each proxy are used to infer the leads and
lags between the different records, propagating all uncertainties. In the
following, all estimates from the probabilistic inference are given as
marginal posterior medians and their uncertainties as marginal 90 %
credible intervals.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e596">Example of a fitted ramp for the <inline-formula><mml:math id="M14" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> data from the onset
of GI-8c. Panel <bold>(a)</bold> shows the data together with the marginal posterior
median of the fitted ramp (thick black line). Shaded areas indicate the
marginal posterior 5th and 95th percentiles. Panel <bold>(b)</bold> shows the
marginal posterior densities for the onset, midpoint and endpoint of the
transition (from right to left). </p></caption>
        <?xmltex \igopts{width=184.942913pt}?><graphic xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019-f02.png"/>

      </fig>

      <p id="d1e625">As pointed out above, the cross-dating uncertainty between the two ice cores
does not allow for sufficiently precise inter-core comparison of the absolute
timing of the transitions; however, the comparison of the lags between aerosol
records of one ice core to those of another is not affected by these
uncertainties. Under the assumption that the DO events show the same imprint
in both ice-core records, this enables crosschecking of the results between
the two records.</p>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
      <p id="d1e636">Time differences of the onset, midpoints and endpoints of the
stadial-to-interstadial transitions in <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>
and annual layer thickness relative to the transition in <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> are
shown in Fig. <xref ref-type="fig" rid="Ch1.F3"/>. All inferred change points and timing
differences can be found in the Supplement. The timing differences for the
<inline-formula><mml:math id="M18" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and layer thickness records relative to <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> for
individual events are subtle and their uncertainties are large, but overall
they indicate a consistent picture of the phase relationship between the
different events, which is the same for the two ice cores. For most events,
the decrease in <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> concentrations leads to the decrease in
<inline-formula><mml:math id="M21" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> at the beginning, midpoint and end of the transition. Similarly,
the beginning of the increase in annual layer thickness slightly leads the
start of the decrease in sea-salt aerosol concentrations, though the detected
lead is more variable between individual DO events. Nevertheless, the data
are overall consistent with a lead of the increase in annual layer thickness at
the midpoint of the transitions. In the case of the <inline-formula><mml:math id="M22" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>
record, timing differences are much more variable between the individual
events with no clear tendency for neither leads nor lags relative to
<inline-formula><mml:math id="M23" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>. For all of the transitions, the inferred timing differences
relative to the onset of the transition in <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> are smaller than the
duration of the transition itself in each of the proxy records. That means
that none of the proxies exhibit a complete stadial–interstadial transition
before the onset of the transition in the sea-salt aerosol concentration.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e767">Timing differences for the individual interstadial onsets:
<bold>(a)</bold> the NGRIP <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> record, <bold>(b–d)</bold> timing
difference of NGRIP <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, layer thickness (<inline-formula><mml:math id="M27" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>) and
<inline-formula><mml:math id="M28" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> records, as well as the NEEM <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> record
relative to the transition in the respective <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> records at the
onset <bold>(b)</bold>, midpoint <bold>(c)</bold> and end <bold>(d)</bold> of the
transition. No timing results are given for transitions where there are data
gaps in one of the necessary datasets. Error bars show the marginal posterior
5th and 95th percentiles and the symbol the marginal posterior median. Note
the different axis scaling for the start, midpoints and endpoints. All
inferred absolute timings, the transition durations and the lags relative to
<inline-formula><mml:math id="M31" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> can be found in the Supplement.</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019-f03.png"/>

      </fig>

      <?pagebreak page816?><p id="d1e876">For each individual transition, the uncertainties are large compared to the
leads and lags, and only a few events show leads that are bigger than zero
with a probability larger than 95 %. However, based on the overall
tendency of a lead for both <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and layer thickness relative to
<inline-formula><mml:math id="M33" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> between the GI onsets, we combine the individual estimates of the
leads and lags for each core to determine an average timing difference for
the investigated proxies. To combine the estimated timing difference of the
individual DO onsets, Gaussian kernel density estimates of the posterior
samples were multiplied together. Note that this implicitly assumes that the
timing differences for all interstadial onsets in the parameters investigated
here are the result of the same underlying process or, in other words, are
similar between the interstadial onsets. This assumption differs from the
assumption used in other studies of relative phasing of Southern and Northern
Hemisphere climate and changes in precipitation source regions during the
last glacial <xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx37 bib1.bibx7" id="paren.56"/>. In these studies, the
stacking of the climate events assumes that the complete progression of the
climate event is a realization of the same underlying process, which is a
wider and more restrictive assumption, as it encompasses the whole transition
and not only its onset. The combined estimates are calculated for the data
from the two cores separately so that the consistency of the timing between
<inline-formula><mml:math id="M34" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M35" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> between records can be tested. Probability
density estimates for the lead of the other parameters relative to
<inline-formula><mml:math id="M36" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> at the transition onset, midpoint and endpoint are shown in
Fig. <xref ref-type="fig" rid="Ch1.F4"/>. They clearly show that, on average, both the
reduction in terrestrial aerosol concentration and the increase in
annual layer thickness precede the reduction in sea-salt aerosol for all
stages of the transition, whereas no significant lead or lag is identified
between <inline-formula><mml:math id="M37" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M38" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e973">Combined probability density estimates of the lag of the
<inline-formula><mml:math id="M39" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, layer thickness and <inline-formula><mml:math id="M40" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> transitions relative
to the respective point in the <inline-formula><mml:math id="M41" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> records for the
onset <bold>(a)</bold>, midpoint <bold>(b)</bold> and end <bold>(c)</bold> of all
transitions from stadial to interstadial for the two
cores.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019-f04.png"/>

      </fig>

      <p id="d1e1030">In the combined estimate, <inline-formula><mml:math id="M42" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> concentrations start to decrease
<inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">7</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years before <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> in the NGRIP record and
<inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">8</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years in the NEEM record, where the error margins refer to the
5th and 95th marginal posterior percentiles. They reach the midpoint of the
transition <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">9</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">8</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years before <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and the
endpoint <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">6</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years, respectively.</p>
      <p id="d1e1184">Furthermore, local accumulation rates at NGRIP start to increase
<inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">7</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years earlier than <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> starts to decrease, reaching the
midpoint <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">15</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years and its interstadial level
<inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">12</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years earlier.</p>
      <p id="d1e1255">Note, that the density functions shown in Fig. <xref ref-type="fig" rid="Ch1.F4"/> cannot be
used to infer timing differences between the other parameters. This is a
direct result of the estimates being conditional on the timing of the
transition in sodium, leading to large correlations between the lag estimates
for the other parameters. That means that even though, e.g. two<?pagebreak page817?> probability
density functions of the differences relative to the transition in sodium
largely overlap, it does not necessarily mean that their relative timing
difference is equal to zero. In the case of the timing difference between the
transition onsets of the increase in annual layer thickness and the decrease
in <inline-formula><mml:math id="M55" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> concentrations, the combined lead of the change in annual
layer thickness relative to <inline-formula><mml:math id="M56" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is not larger than zero at the
0.95 probability level with <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msubsup><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> years. To establish the most
probable sequence of events at the transition offset, we calculate the
average order of the onset times, shown for NGRIP in Fig. <xref ref-type="fig" rid="Ch1.F5"/>.
The average positions show that the change in accumulation and <inline-formula><mml:math id="M58" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>
concentrations about equally likely occur first, whereas the transitions in
<inline-formula><mml:math id="M59" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M60" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> about equally likely occur last. The same
analysis for the NEEM results confirms this sequence.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e1350">Combined order statistics for the onset of the transition. The
colours indicate the probability of observing the onset of the transition in
the parameter on the <inline-formula><mml:math id="M61" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis at the position on the <inline-formula><mml:math id="M62" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis. This
illustrates that during the onset of the DO warming, the changes in
accumulation and <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> concentrations about equally likely occur
first, whereas the transitions in <inline-formula><mml:math id="M64" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M65" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> about
equally likely occur last.</p></caption>
        <?xmltex \igopts{width=227.622047pt}?><graphic xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019-f05.png"/>

      </fig>

</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
      <p id="d1e1419">Using much lower resolution mineral dust and ice <inline-formula><mml:math id="M66" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> data
from NGRIP, <xref ref-type="bibr" rid="bib1.bibx57" id="text.57"/> reported coinciding onsets within 5 to 10 years
and a combined lag of <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula> years for GI-1 through GI-24 demonstrating the
close connection between the Asian and North Atlantic climate during all of
the DO events. In light of the low temporal resolution of the data used
(0.55 m corresponding to 7–98 or 38 years on average) and the small timing
differences that emerge in the combination of the individual interstadial
onsets presented here, the results of <xref ref-type="bibr" rid="bib1.bibx57" id="text.58"/> are compatible with
the outcomes presented here. Our results are also in good agreement with the
more detailed studies of the onset of the Holocene and GI-1
<xref ref-type="bibr" rid="bib1.bibx63" id="paren.59"/> and GI-8c <xref ref-type="bibr" rid="bib1.bibx68" id="paren.60"/>. Similar to the presented
study, <xref ref-type="bibr" rid="bib1.bibx63" id="text.61"/> and <xref ref-type="bibr" rid="bib1.bibx68" id="text.62"/> (using high-resolution
data from the NGRIP ice core) also infer slight leads of changes in
terrestrial aerosol concentrations and accumulation rate and moisture sources
ahead of the changes in marine aerosols and local temperature in good
agreement with our results from the respective DO onsets. These results are
also overall in good agreement with the other transitions investigated here.
As the study presented here now covers 19 warming events starting from
60 kyr ago and independently investigates the phasing in two ice cores, this adds
significant evidence to the initially inferred phasing.</p>
      <?pagebreak page818?><p id="d1e1466">Two studies into Greenland <xref ref-type="bibr" rid="bib1.bibx59" id="paren.63"/> and Antarctic
<xref ref-type="bibr" rid="bib1.bibx38" id="paren.64"/> aerosol records have recently shown that a large part of
the variability on centennial and millennial timescales in these records can
be explained by the tight coupling between the hydrological cycle and the
aerosol transport to the ice sheets. This coupling is a direct result of the
efficient removal of aerosols during transport by precipitation scavenging
leading to a negative correlation between en-route precipitation and aerosol
concentration in the ice. On the short timescales investigated here, this
tight coupling breaks down. This has previously been indicated for Antarctica
by the lack of coherence at shorter periods <xref ref-type="bibr" rid="bib1.bibx38" id="paren.65"/> and here by
the lack of synchronous changes between snowfall, water isotopic composition
and/or aerosol concentrations during the onset of the warming events. This
can be explained by the observation that, under glacial conditions, models
show that the interannual variability of the accumulation is governed by
changes in the frequency of the advection of marine air masses to the
Greenland ice sheet (<?xmltex \hack{\mbox\bgroup}?><xref ref-type="bibr" rid="bib1.bibx44" id="altparen.66"/><?xmltex \hack{\egroup}?>; <xref ref-type="bibr" rid="bib1.bibx39" id="altparen.67"/>).
Furthermore, the overall reduced amount of snowfall during the glacial is a
result of generally decreased moisture advection <xref ref-type="bibr" rid="bib1.bibx39" id="paren.68"/>. For the
stadial–interstadial transitions, these model results and the lack of
synchronous changes in the data presented here suggest a large influence of
atmospheric dynamics on the change in snow accumulation as well. This is
further supported by other proxy evidence from central Greenland
<xref ref-type="bibr" rid="bib1.bibx27" id="paren.69"/> and is similarly observed in West Antarctica
<xref ref-type="bibr" rid="bib1.bibx18" id="paren.70"/>. An increase of the advection of air masses from lower
latitudes would result in an increase of the snow accumulation as more
moisture is transported to the ice sheet but in unchanged sea-salt
concentrations in the precipitation and subsequently the ice core, as these
air masses still carry the same amount of sea-salt aerosol. This leads to a
decoupling of changes in the sea-salt aerosol deposition flux vs. the
concentrations in the ice; i.e. the deposition flux per event stays constant
but the number of precipitation events increases. In turn, this means that
the covariance of snowfall on the sea-salt deposition that is apparent on
centennial and millennial timescales <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx38" id="paren.71"/> is
less important at the interannual scale, where atmospheric dynamics dominate
over thermodynamic changes. This view of changed precipitation frequency at
the very beginning of the DO onset is supported by the apparent asynchrony of
snowfall and <inline-formula><mml:math id="M68" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>. Similar to <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>
remains unchanged if only the frequency of precipitation events is increased
with otherwise unaltered seasonality (and thus isotopic signature). Only
later in the transition do thermodynamically driven changes in precipitation
amount and seasonality affect <inline-formula><mml:math id="M71" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx76" id="paren.72"/>.</p>
      <p id="d1e1553">The reduction of perennial sea-ice cover during DO events that is documented
in proxy records <xref ref-type="bibr" rid="bib1.bibx62 bib1.bibx13" id="paren.73"/> has a large influence on
Greenland temperature and accumulation due to the exposure of the warm ocean
in the North Atlantic as shown by model experiments <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx34" id="paren.74"/>.
The increased moisture availability over the open ocean which leads to the
snowfall in Greenland likely also decreases the transport efficiency of
marine aerosol to the Greenland ice sheet due to the increased precipitation
and washout en route. In turn, this leads to the observed synchronous start
in the transitions in ice <inline-formula><mml:math id="M72" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M73" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> concentrations.
This is in good agreement with transient simulations of DO events
<xref ref-type="bibr" rid="bib1.bibx69 bib1.bibx70" id="paren.75"/> showing that as soon as the North
Atlantic sea-ice cover is reduced, both evaporation and precipitation over
the ocean as well as temperatures in Greenland rapidly increase. The decrease
of the sea-ice cover is also expected to cause a coinciding increase in
snowfall. However, the increase in snow accumulation as observed in the
annual layer thickness occurs slightly earlier than the changes in sea-salt
aerosol and <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>, indicative of an initial increase of the
advection of marine air masses to the ice sheet at the onset of the DO events
unrelated to changes of the sea-ice cover. A plausible cause for this change
in advection would be a shift in the jet-stream location and thus in the
track of the low-pressure systems over the North Atlantic
<xref ref-type="bibr" rid="bib1.bibx78" id="paren.76"><named-content content-type="pre">e.g.</named-content></xref>.</p>
      <p id="d1e1608">Mineral dust, like sea-salt aerosol, is deposited very efficiently during
snowfall events because small amounts of precipitation remove most of the
aerosol load from the air column <xref ref-type="bibr" rid="bib1.bibx11 bib1.bibx82" id="paren.77"/>. That means
that an increase in snowfall frequency would not affect the observed dust
concentration in the ice, despite the changing snow accumulation. As pointed
out by <xref ref-type="bibr" rid="bib1.bibx59" id="text.78"/>, on centennial to millennial timescales,
changes in the central Asian dust source strengths by a factor of
approximately 4 are needed to explain the complete amplitude between stadials
and interstadials observed in the ice cores, as further supported by downwind
sediment records <xref ref-type="bibr" rid="bib1.bibx48 bib1.bibx25" id="paren.79"/>. The deflation of the dust
from the central Asian source regions is strongly dependent on location of
the westerly jet <xref ref-type="bibr" rid="bib1.bibx41 bib1.bibx54" id="paren.80"/> that under current conditions
covaries with the East Asian Summer Monsoon on seasonal timescales
<xref ref-type="bibr" rid="bib1.bibx58" id="paren.81"/>. During the glacial conditions, the westerly jet was
located further south than today, leading to more frequent or even permanent
conditions for dust emission <xref ref-type="bibr" rid="bib1.bibx9 bib1.bibx41" id="paren.82"/>. As
low-latitude proxy records indicate northward movements of the ITCZ during
the DO events <xref ref-type="bibr" rid="bib1.bibx74 bib1.bibx12 bib1.bibx75 bib1.bibx79" id="paren.83"/>,
synchronous within approximately 180 years <xref ref-type="bibr" rid="bib1.bibx1" id="paren.84"/>, we
hypothesize that the accompanying change in atmospheric circulation causes a
reduction of the dust deflation during interstadials. Because the reduction
in mineral dust aerosol concentrations in the ice core occurs before the
reduction in sea-salt aerosol, the data imply that this change in
atmospheric circulation happens before the reduction in the sea-ice cover in
the North Atlantic. This is further supported by the fact that changes in
deuterium excess at the onset of GI-1 and GI-8c, indicating changes in
moisture transport from the North Atlantic to Greenland, occur after the
onset of the transition in mineral dust aerosol <xref ref-type="bibr" rid="bib1.bibx63 bib1.bibx68" id="paren.85"/>. Antarctic records of deuterium excess that indicate changes of
moisture sources also show a rapid shift at the onset of the Greenland
interstadials, interpreted as a change in the Southern Hemisphere westerlies
explaining part of the signal observed in multiple Antarctic
<inline-formula><mml:math id="M75" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> records <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx7" id="paren.86"/>. This further
supports the hypothesis of rapidly changing atmospheric circulation during
the DO events not only in the Northern Hemisphere but globally.
Nevertheless, the fact that for all transitions the inferred timing
difference relative to the transition in <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> is smaller than the
duration of the transition<?pagebreak page819?> in that parameter indicates that the respective
parts of the climate system co-evolved over the transition. That means that
the changes in atmospheric circulation at the DO onset were not completely
decoupled from the change in sea-ice cover and Greenland temperature.</p>
      <p id="d1e1668">Due to the small timing differences between the records, it is worth noting
that water isotope records from polar ice cores are subject to smoothing by
diffusion. For the NGRIP isotope record, the diffusion length at the end of
the last glacial is on the order of 5–10 cm
<xref ref-type="bibr" rid="bib1.bibx19" id="paren.87"/>, influencing the high-frequency variability. For the
analysis here, the diffusion means that the rapid increase of the
<inline-formula><mml:math id="M77" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> signal at the DO onsets would be slightly shifted towards
earlier times, leading to lower apparent lags between the aerosol records and
the water isotope record. Thus, the inferred lead of <inline-formula><mml:math id="M78" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> over
<inline-formula><mml:math id="M79" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> can be regarded as a conservative estimate.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e1723">The multi-proxy records of the timing differences from two ice cores at the
onset of the DO events allow us to investigate the temporal progression of
Northern Hemisphere environmental change at the onset of the events in high
temporal resolution. Even though the inferred timing differences carry large
uncertainties for single events, they are overall consistent between the two
investigated ice-core records and over all DO events indicating their
robustness. The qualitative agreement between the DO events allows for the
combination of the timing differences from the individual DO events to
estimate a better constrained succession of the environmental changes during
the onset of the DO events. Both the initial increase in snow accumulation
and the reduction of <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> occur about a decade before the
reduction in <inline-formula><mml:math id="M81" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and the increase in local temperature. Taken at face
value, this sequence of events suggests that the collapse of the North
Atlantic sea-ice cover may not be the initial trigger for the DO events and
indicates that synoptic and hemispheric atmospheric circulation changes
started before the reduction of the high-latitude sea-ice cover that
ultimately coincided with the Greenland warming. The progression of
environmental changes revealed in the Greenland aerosol records provides a
good target for climate models explicitly modelling both water isotope and
aerosol transport that aim at transiently simulated DO events.</p>
      <p id="d1e1751"><?xmltex \hack{\newpage}?>Using our ice-core data, we can only derive the relative timing of changes in
the atmospheric circulation and the North Atlantic surface conditions related
to the DO warming. Our results cannot provide a direct constraint on the
increase in AMOC which may potentially precede changes in sea-surface
conditions and atmospheric circulation. Recent studies using marine sediment
records <xref ref-type="bibr" rid="bib1.bibx21" id="paren.88"><named-content content-type="pre">e.g.</named-content></xref> suggest a centuries-long lead of AMOC
changes; however, the response time of the proxies, their limited resolution
and dating precision may not allow an unambiguous answer yet. This question
requires further studies, especially in light of model studies both with
<xref ref-type="bibr" rid="bib1.bibx45 bib1.bibx46" id="paren.89"/> and without freshwater hosing
<xref ref-type="bibr" rid="bib1.bibx82 bib1.bibx30 bib1.bibx47" id="paren.90"><named-content content-type="pre">i.e.</named-content></xref> in the North Atlantic
that show that the temperature and precipitation response in Greenland is
synchronous to AMOC changes.</p>
</sec>

      
      </body>
    <back><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d1e1772">All data needed to reproduce the figures and results of
the study are archived on PANGAEA (<ext-link xlink:href="https://doi.org/10.1594/PANGAEA.896743" ext-link-type="DOI">10.1594/PANGAEA.896743</ext-link>;
<xref ref-type="bibr" rid="bib1.bibx14" id="altparen.91"/>).</p>

      <p id="d1e1781">The transition points and timing differences including their uncertainties
for all investigated GS/GI transitions are supplied in the Supplement.</p>

      <p id="d1e1784">NGRIP <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">18</mml:mn></mml:msup><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula> data and the GICC05 age scale for the NGRIP and
NEEM ice cores are available at
<uri>http://www.iceandclimate.nbi.ku.dk/data/</uri> (last access: 18 April 2019).</p>

      <p id="d1e1803">The code to reproduce the analysis and all figures is available at
<uri>https://github.com/terhardt/DO-progression</uri> (last access: 18 April 2019)
or upon request to the corresponding author.</p>
  </notes><?xmltex \hack{\clearpage}?><app-group>

<?pagebreak page820?><app id="App1.Ch1.S1">
  <label>Appendix A</label><title>Transition model</title>
      <p id="d1e1820">The transition between cold and warm states is described by a linear ramp of
amplitude <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></inline-formula>, starting at <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> lasting for a time of <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math></inline-formula>:

              <disp-formula id="App1.Ch1.S1.Ex1"><mml:math id="M86" display="block"><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false" mathvariant="normal">^</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mfenced open="{" close=""><mml:mtable columnspacing="1em" rowspacing="0.2ex" class="cases" columnalign="left left" framespacing="0em"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>≥</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

        <inline-formula><mml:math id="M87" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> in this case is the log-transformed concentrations and layer thicknesses
and non-transformed relative isotope ratios.</p>
      <p id="d1e2024">Each observation <inline-formula><mml:math id="M88" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> of the transitions is made with additive error
<inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from an irregularly sampled AR(1) noise model to account for the
multi-annual variability of the proxy records as given by

              <disp-formula id="App1.Ch1.S1.Ex2"><mml:math id="M90" display="block"><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false" mathvariant="normal">^</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        for <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mi>i</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, with

              <disp-formula id="App1.Ch1.S1.Ex4"><mml:math id="M92" display="block"><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="italic">τ</mml:mi></mml:mfrac></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        where

              <disp-formula id="App1.Ch1.S1.Ex5"><mml:math id="M93" display="block"><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msubsup><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mfrac><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="italic">τ</mml:mi></mml:mfrac></mml:mrow></mml:msup></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        and for the first observation with

              <disp-formula id="App1.Ch1.S1.Ex6"><mml:math id="M94" display="block"><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        where <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>∣</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> denotes the conditional probability of <inline-formula><mml:math id="M96" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> given <inline-formula><mml:math id="M97" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula>. The
use of an irregularly sampled AR(1) process enables the transparent handling
of missing data or sampling with less than annual resolution. The two
parameters of the noise process are the marginal standard deviation <inline-formula><mml:math id="M98" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>
and the auto-correlation time <inline-formula><mml:math id="M99" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> given in the same units as the data and
sampling time, respectively. Both standard deviation and auto-correlation
time of the noise process are determined from the data alongside the timing
parameters of the transition and are treated as nuisance parameters. For the
probabilistic inference, the following priors were used:

              <disp-formula specific-use="align"><mml:math id="M100" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0.0</mml:mn><mml:mo>,</mml:mo><mml:msup><mml:mn mathvariant="normal">50.0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Gamma</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">2.0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0.0</mml:mn><mml:mo>,</mml:mo><mml:msup><mml:mn mathvariant="normal">10.0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Gamma</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">2.5</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">0.15</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mo>∝</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">10</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

          with the following distribution functions:

              <disp-formula specific-use="align"><mml:math id="M101" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>N</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>|</mml:mo><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow></mml:msqrt><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mi>exp⁡</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="italic">μ</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi mathvariant="normal">Gamma</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>|</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Γ</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

          where <inline-formula><mml:math id="M102" display="inline"><mml:mi mathvariant="normal">Γ</mml:mi></mml:math></inline-formula> is the gamma function.</p>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S1.F6"><?xmltex \currentcnt{A1}?><label>Figure A1</label><caption><p id="d1e2726">Timing uncertainty as a function of SNR for the NGRIP datasets. The
uncertainty in the onset of the transition increases with lower SNR, as
defined by the amplitude of the transition over the amplitude of the noise.
Note that the linear fits are only for illustration.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019-f06.png"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="App1.Ch1.S1.F7"><?xmltex \currentcnt{A2}?><label>Figure A2</label><caption><p id="d1e2738">Lag relative to the transition onset in <inline-formula><mml:math id="M103" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> vs. SNR in the
respective parameters for the NGRIP data. None of the parameters show a
systematic connection of the inferred leads and lags with their SNR.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://cp.copernicus.org/articles/15/811/2019/cp-15-811-2019-f07.png"/>

      </fig>

      <p id="d1e2758">Inference was performed using an ensemble Markov chain Monte Carlo (MCMC)
sampler <xref ref-type="bibr" rid="bib1.bibx20" id="paren.92"/> implemented in the Python programming language
<xref ref-type="bibr" rid="bib1.bibx17" id="paren.93"/>. Samplers were run for 60 000 iterations using 60
ensemble members, using every 600th sample, resulting in 6000 posterior
samples of the six parameters determining the transition and noise model. The
noise model parameters were not interpreted and treated as nuisance
parameters.</p>
      <p id="d1e2767">Because the model explicitly accounts for variability around the transition
model in the data, it is possible to assess the impact of the magnitude of
this variability on the<?pagebreak page821?> precision of the inferred timings. Intuitively, the
larger the multi-annual variability in the dataset compared to the amplitude
of the transition, the more uncertain the inferred timing estimates should
be. To test this, Fig. <xref ref-type="fig" rid="App1.Ch1.S1.F6"/> shows the marginal posterior
standard deviation of the inferred onset of the transition as the
signal-to-noise ratio (SNR), as defined by the ratio of the amplitude of the
transition over the standard deviation of the noise term. It shows that the
higher the SNR, the lower the posterior standard deviation of <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Or, in
different terms, the clearer the transition is visible, the more precise the
timing inference. Because the uncertainties are propagated to the lead/lag
calculations and the combined estimate we take this into
account.
This becomes clear when plotting the leads/lags relative to <inline-formula><mml:math id="M105" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> as a
function of the SNR in the respective parameters as shown in
Fig. <xref ref-type="fig" rid="App1.Ch1.S1.F7"/>. The figure shows no systematic connection between
SNR and inferred lags.</p><?xmltex \hack{\clearpage}?><supplementary-material position="anchor"><p id="d1e2796">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/cp-15-811-2019-supplement" xlink:title="zip">https://doi.org/10.5194/cp-15-811-2019-supplement</inline-supplementary-material>.</p></supplementary-material>
</app>
  </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2807">MB, SS and HF performed CFA measurements in the field at
NGRIP and/or NEEM. MB and SS carried out raw data analysis. TE and HF
designed the study. TE carried out the data analysis which was developed by
TE in exchange with SOR. All authors discussed the results and contributed to
the interpretation and to the manuscript, which was written by TE.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2813">The authors declare that they have no conflict of
interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2819">The Division for Climate and Environmental Physics, Physics Institute,
University of Bern acknowledges the long-term financial support of ice-core
research by the Swiss National Science Foundation (SNSF) under project
nos. 200020_172506, 20FI20_137635, 10FI21_119612, 200020_159563 and
20-063333.00, as well as by the Oeschger Center for Climate Change Research.
Emilie Capron was funded by the European Union's Seventh Framework Programme
for research and innovation under the Marie Skłodowska-Curie Actions (grant
agreement no. 600207). Sune Olander Rasmussen and Emilie Capron gratefully
acknowledge the Carlsberg Foundation for support to the project
ChronoClimate. Florian Adolphi is supported through a grant by the Swedish
Research Council (Vetenskapsrådet no. 2016-00218). NGRIP is directed and
organized by the Department of Geophysics at the Niels Bohr Institute for
Astronomy, Physics and Geophysics, University of Copenhagen. It is supported
by funding agencies in Denmark (SNF), Belgium (FNRS-CFB), France (IPEV and
INSU/CNRS), Germany (AWI), Iceland (RannIs), Japan (MEXT), Sweden (SPRS),
Switzerland (SNF) and the US (US NSF, Office of Polar Programs). NEEM is
directed and organized by the Centre of Ice and Climate at the Niels Bohr
Institute and US NSF, Office of Polar Programs. It is supported by funding
agencies and institutions in Belgium (FNRS-CFB and FWO), Canada (NRCan/GSC),
China (CAS), Denmark (FIST), France (IPEV, CNRS/INSU, CEA and ANR), Germany
(AWI), Iceland (RannIs), Japan (NIPR), South Korea (KOPRI), the Netherlands
(NWO/ALW), Sweden (VR), Switzerland (SNF), the United Kingdom (NERC) and the
US (US NSF, Office of Polar Programs) and the EU Seventh Framework
Programmes Past4Future and WaterundertheIce. The authors also gratefully
acknowledge the contributions of the countless people that facilitated and
took part in both the ice-core drilling and processing as well as the CFA
melting campaigns. The authors would further like to thank the reviewers for
their useful comments that helped to improve the manuscript.</p></ack><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2824">This paper was edited by Elizabeth Thomas and reviewed by Bradley Markle and one anonymous referee.</p>
  </notes><ref-list>
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<abstract-html><p>During the last glacial period, proxy records throughout the Northern
Hemisphere document a succession of rapid millennial-scale warming events,
called Dansgaard–Oeschger (DO) events. A range of different mechanisms has
been proposed that can produce similar warming in model experiments; however,
the progression and ultimate trigger of the events are still unknown. Because
of their fast nature, the progression is challenging to reconstruct from
paleoclimate data due to the limited temporal resolution achievable in many
archives and cross-dating uncertainties between records. Here, we use new
high-resolution multi-proxy records of sea-salt (derived from sea spray and
sea ice over the North Atlantic) and terrestrial (derived from the central
Asian deserts) aerosol concentrations over the period 10–60&thinsp;ka from the
North Greenland Ice Core Project (NGRIP) and North Greenland Eemian Ice
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and temperature proxies from the NGRIP ice core to investigate the
progression of environmental changes at the onset of the warming events at
annual to multi-annual resolution. Our results show on average a small lead
of the changes in both local precipitation and terrestrial dust aerosol
concentrations over the change in sea-salt aerosol concentrations and local
temperature of approximately one decade. This suggests that, connected to the
reinvigoration of the Atlantic meridional overturning circulation and the
warming in the North Atlantic, both synoptic and hemispheric atmospheric
circulation changes at the onset of the DO warming, affecting both the
moisture transport to Greenland and the Asian monsoon systems. Taken at face
value, this suggests that a collapse of the sea-ice cover may not have been
the initial trigger for the DO warming.</p></abstract-html>
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