Download Supporting Material Age description The chronology is from a visual

Supporting Material
Age description
The chronology is from a visual stratigraphy of the ice with ± 1 % age uncertainty
[Kobashi et al., 2008; Alley et al., 1997]. A recent study indicated that the GISP2
chronology could be too old by ~30 years for the earlier part of the past 4000 years, as a
tightly constrained GICCO05 chronology using three ice cores (GRIP, NGRIP, and
DYE-3) [Vinther et al., 2006] indicated that a reference volcanic horizon of the Minoan
Thera eruption had an age of 1642 ± 5 B.C.E compared to 1673 ± 37 B.C.E in the
GISP2 chronology. The error should have accumulated before the age of a later
reference horizon (the Mount Vesuvius eruption) at 79 ± 1 C.E., as it is the oldest
historically dated horizon [Vinther et al., 2006]. The gas ages are calculated with a firn
densification/heat diffusion model by Goujon et al. [2003] with inputs of surface
temperature from the calibrated 18Oice [Cuffey and Clow, 1997; Stuiver et al., 1995] and
accumulation rate data [Alley et al., 1997]. The gas age uncertainty is estimated to be
~20 years [Kobashi et al., 2008]. The data resolution and sampling density are 1 sample
per ~20 years from 2000 B.C. E. to 953 C.E. and ~3 samples per ~10 years from 953
C.E. to 1950 C.E. [Kobashi et al., 2008].
Supplemental methods
The isotope ratios of nitrogen and argon are constant in the atmosphere on time
scales of 105 years [Mariotti, 1983; Allegre et al., 1987]. Therefore, isotopic deviations
in the ice core from the atmospheric ratios can be attributed to processes in the firn layer
(an unconsolidated snow layer on the top of ice sheets) [Severinghaus et al., 1998] and
to a lesser extent to gas leaks from the ice after coring [Kobashi et al., 2008;
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Severinghaus et al., 2003]. A dominant mechanism for gas movement in the firn layer is
molecular diffusion, where two isotopic fractionation processes occur, “gravitational
settling” and “thermal diffusion” [Severinghaus et al., 1998]. Gravitational settling is
driven by gravity and is a function of firn thickness [Craig et al., 1988; Schwander,
1989]. Thermal fractionation is induced by the temperature gradient between the top
and bottom of the firn layer [Severinghaus et al., 1998]. The magnitude of thermal
fractionation under a given temperature gradient is specific to the gas species, and its
coefficients can be measured by laboratory experiments [Grachev and Severinghaus,
2003a,b]. Therefore, the measurement of two isotopic ratios (15N and 40Ar as
deviations from atmospheric values) in air bubbles in ice cores allows us to separate the
two effects and thus to reconstruct the past depth and temperature gradient (T) of the
firn layer. The estimated T s and published accumulation rates [Alley et al., 1997] are
used as inputs for a firn densification / heat diffusion model [Goujon et al., 2003] to
calculate surface temperatures over the past 4000 years. At each 1-year step, the model
calculates the density and temperature profile in the firn and ice sheet according to the
inputs [Kobashi et al., 2008; Kobashi et al., 2010]. Then, the surface temperature of the
next model year is calculated by adding the T to the modelled temperature at the
bottom of the firn [Kobashi et al., 2008; Kobashi et al., 2010].
The calculation of the temperature for the past 4000 years mostly follows the
methodology developed by Kobashi et al. [2008]. Differences and important points are
described here. The observed argon isotope data (40Arobserved) are corrected
(40Arcorrected) for gas-loss fractionation in the following manner: 40Arcorrected =
40Arobserved + 0.0073  Ar/N2corrected, where Ar/N2corrected represents Ar/N2 values
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corrected for gravitational settling [Severinghaus et al., 2003; Kobashi et al., 2010]. The
coefficient +0.0073 ‰ per ‰ is an empirical correction coefficient for argon leakage
found by calculating the surface temperature and finding the best fit between the
calculated borehole temperatures and the observations. This value is slightly smaller
than the +0.0075 ‰ per ‰ used for the past 1000-year calculation [Kobashi et al.,
2010], but it is closer to the value of +0.007 ‰ per ‰ derived in Severinghaus et al.
[2003]. Figure S2 shows the reconstructed borehole temperatures and surface
temperature histories using a coefficient of 0.007, 0.0073, or 0.0075 ‰ per ‰, and it
shows that the general trend of the Greenland temperature for the past 4000 years is not
affected by the choice of the coefficient. The long-term cooling trend is modestly
affected by the choice of coefficients, as the calculations with the coefficients of 0.007,
0.0073, and 0.0075 ‰ per ‰ generate long-term cooling of -1.6, -1.1, and -0.8 C per
4000 years, respectively (Fig. S2).
The model calculates the surface temperature using the calibrated 18Oice [Cuffey
and Clow, 1997; Stuiver et al., 1995] from 24,300 Before Present (B.P.; Present is 1950
C.E.) to 11,650 B.P. Then, from 11,650 B.P. to 2207 B.C.E., we used a Holocene
temperature trend by Vinther et al. (Agassiz/Rendland Holocene temperature
reconstruction; deviation from the present temperature) [Vinther et al., 2009] adding 32.6 C, which produced the borehole temperature history that best matched the
observations [Alley et al., 1990; Clow et al., 1996] (Fig. 2). From 2207 B.C.E. onward,
the calculation switches to the T method. A Monte Carlo simulation is conducted to
estimate the error of the temperature history [Kobashi et al., 2010]. Ten thousand
synthetic T time series are produced by adding normally distributed random signals
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with standard deviations of ±1 ºC, ±0.7 ºC, and ±0.6 ºC for the depths with 1, 2, and 3
samples analyzed, respectively. These are slightly larger than the analytical errors of 0.9
ºC, 0.6 ºC, and 0.5 ºC [Kobashi et al., 2008] to include unquantifiable errors in the
model. For each calculation, the calculated borehole temperatures are compared with
the observed data. Only 80 temperature histories, whose average root mean square
difference from the observations taken from the upper 1500 m of the ice sheet is smaller
than 0.05 ºC, are used to calculate the mean surface temperature history and error bands
(Fig. 2). Therefore, the resultant temperature history is more consistent with the
observed borehole temperature [Kobashi et al., 2010]. The value of 0.05 ºC is close to
the uncertainty of the borehole temperature observations [Vinther et al., 2009]. The
general trend of the temperature history is not affected by this selection process, but it
causes a slight increase in the long-term cooling trend from -1.1 C to -1.5 C per 4000
years (Fig. S3).
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