On the similarity and apparent cycles of isotopic variations in East Antarctic snow and ice cores

On the similarity and apparent cycles of isotopic variations in

East Antarctic snow and ice cores

Thomas Münch ^1,2 , Thomas Laepple ¹ , Mathieu Casado ^3,1 , Maria Hoerhold ¹ , Amaelle Landais ³ and Sepp Kipfstuhl ¹

1 Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Germany

2 Institute of Physics and Astronomy, University of Potsdam, Germany

3 Laboratoire des Science du Climat et de l’Environment – IPSL, France

Cycles in climatic parameters (?)

Cycles in climatic parameters (?)

Periodic seasonal cycle (temperature).

0 1 2 3 4 5

-1.0 -0.5 0.0 0.5 1.0

Year

Idealized seasonal cycle

Cycles in climatic parameters (?)

Periodic seasonal cycle (temperature). Quasi-periodic oscillations (e.g. ENSO).

1880 1900 1920 1940 1960 1980 2000 2020 -40

-20 0 20 40

Year (CE)

Southern Oscillation Index

data: http://www.bom.gov.au/climate/current/soihtm1.shtml

0 1 2 3 4 5

-1.0 -0.5 0.0 0.5 1.0

Year

Idealized seasonal cycle

Cycles in climatic parameters (?)

Periodic seasonal cycle (temperature). Quasi-periodic oscillations (e.g. ENSO).

1880 1900 1920 1940 1960 1980 2000 2020 -40

-20 0 20 40

Year (CE)

Southern Oscillation Index

data: http://www.bom.gov.au/climate/current/soihtm1.shtml

0 1 2 3 4 5

-1.0 -0.5 0.0 0.5 1.0

Year

Idealized seasonal cycle

-50 -45 -40 -35

δ18 O (‰)

•  Stable isotopes from Antarctic snow are interpreted as proxy for temperature.

•  What is the origin of the apparent cycles in the isotopic time series?

warm Isotopes @ EDML

Similar “cycles” in East Antarctic isotope profiles

EDML

MP DK DF

South Pole

Vostok

S2 EDC

Similar “cycles” in East Antarctic isotope profiles

EDML

~ 18 cm annual accumulation of snow

Δ

~ 19 cm average distance between maxima

Similar “cycles” in East Antarctic isotope profiles

South Pole

accum. ~ 20 cm Δ

~ 20 cm

Casado et al. (2017), Cryosphere Disc.

Depth (m)

EDML

~ 18 cm annual accumulation of snow

Δ

~ 19 cm average distance between maxima

Similar “cycles” in East Antarctic isotope profiles

Dome C

accum. ~ 8 cm Δ

~ 18 cm

South Pole

accum. ~ 20 cm Δ

~ 20 cm

EDML

~ 18 cm annual accumulation of snow

Δ

~ 19 cm average distance between maxima

Similar “cycles” in East Antarctic isotope profiles

Vostok

accum. ~ 7 cm Δ

~ 22 cm

EDML

~ 18 cm accum.

Δ

~ 19 cm

Casado et al. (2017), Cryosphere Disc.

Depth (m)

Dome C

accum. ~ 8 cm Δ

~ 18 cm

South Pole

accum. ~ 20 cm

Δ

~ 20 cm

Similar “cycles” in East Antarctic isotope profiles

Accumulation rates differ by a factor of four between

sites, but distances between maxima are rather constant

(~18–24 cm within the first metres of snow).

Understanding observed cycles

1.  Mathematics for crossing statistics of random noise: Rice’s formula

2.  Model for signal formation of

isotope profiles

Rice’s formula

How often does a random time series cross the zero line / have maxima?

0 20 40 60 80 100 -4

-2 0 2 4

Time

Value

-4 -2 0 2 4

Value

Rice’s formula

How often does a random time series cross the zero line / have maxima?

White noise of variance 1

Power-law noise (slope 1.5) of variance 1

Rice’s formula

How often does a random time series cross the zero line / have maxima?

White noise of variance 1

Power-law noise (slope 1.5) of variance 1

Ø  Formula by S. O. Rice (Rice, 1944, 1945):

Expected distance between upward crossings:

Expected distance between maxima:

-2 0 2 4

Value

-4 -2 0 2 4

Value <latexit sha1_base64="DYayolEQbWSZBwg5AmBAgGBhSJA=">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</latexit>

Isotope profiles qualitatively

-55 -50 -45 -40 -35

50 m 3 m

0 m

δ18O (‰)

0 m Horizontal position Depth

On local scale: large spatial variability created in depositional process.

Snow

Ice 0 m

~ 100 m

Modified from: Münch et al. (2018), Cryosphere

Adapted from:

Centre for Ice and Climate, University of Copenhagen

With depth: smoothing due to diffusional mixing of vapour

within the snow and firn column.

Isotope profiles qualitatively

-55 -50 -45 -40 -35

50 m 3 m

0 m

δ18O (‰)

0 m Horizontal position Depth

On local scale: large spatial variability created in depositional process.

Ø  Null hypothesis:

Rice’s formula for diffused white noise:

Snow 0 m

~ 100 m

Diffusion length

<latexit sha1_base64="i7E8TC3SF460sZN2QkGEPe62bXA=">AAACGXicbVA9SwNBEN3z2/gVtbQ5DIJVuIuCNoKghaWCUSEXwtxmLi7u3p27c2JY7m/Y+FdsLBSx1Mp/4yam8OvBwOO9GWbmxbkUhoLgwxsbn5icmp6ZrczNLywuVZdXzkxWaI5NnslMX8RgUIoUmyRI4kWuEVQs8Ty+Ohj45zeojcjSU+rn2FbQS0UiOJCTOtUgOkRJ0LER4S1ZBbdludeIchGZa002SjRw2yjtVllGRvQUdKq1oB4M4f8l4YjU2AjHnepb1M14oTAlLsGYVhjk1LagSXCJZSUqDObAr6CHLUdTUGjadvhZ6W84pesnmXaVkj9Uv09YUMb0Vew6FdCl+e0NxP+8VkHJbtuKNC8IU/61KCmkT5k/iMnvCo2cZN8R4Fq4W31+CS4McmFWXAjh75f/krNGPQzq4cl2bb8ximOGrbF1tslCtsP22RE7Zk3G2R17YE/s2bv3Hr0X7/WrdcwbzayyH/DePwHBlqHz</latexit>

Modified from: Münch et al. (2018), Cryosphere

With depth: smoothing due to diffusional mixing of vapour

within the snow and firn column.

(More realistic) Forward model for isotope profiles

1.  Isotopic seasonal cycle driven by local temperatures.

2.  Part of variance (fraction ξ) transferred to noise in depositional process.

3.  Diffusion and densification of signal.

Structure of isotopic signal & cycle length

-10-50510-10-505100.20.40.6

cycle length (m) δ18O anom. ( ‰) δ18O anom. ( ‰)

ξ = 1, white noise

ξ = 0, periodic input signal ξ = 0.5, mixed input signal

densi

ca tion only densi

ca tion & di

usion

Structure of isotopic signal & cycle length

-10-50510-10-505100.00.20.40.6

cycle length (m)

0 2 4 6 8 10

snow depth (m)

0 2 4 6 8 10

snow depth (m)

0 2 4 6 8 10

snow depth (m) δ18O anom. ( ‰) δ18O anom. ( ‰)

ξ = 1, white noise

ξ = 0, periodic input signal ξ = 0.5, mixed input signal

densi

ca tion only densi

ca tion & di

usion

Laepple et al. (2018), Cryosphere

Structure of isotopic signal & cycle length

-10-50510-10-505100.20.40.6

cycle length (m) δ18O anom. ( ‰) δ18O anom. ( ‰)

ξ = 1, white noise

ξ = 0, periodic input signal ξ = 0.5, mixed input signal

densi

ca tion only densi

ca tion & di

usion

Depth dependency of

“cycle length” informs

about nature of signal.

Observed vs. theoretical “cycle lengths”

Laepple et al. (2018), Cryosphere

Observed vs. theoretical “cycle lengths”

Laepple et al. (2018), Cryosphere

Cycle lengths increase with depth nearly everywhere,

suggesting noise-dominated isotope signal.

Summary

•  Similar “cycle lengths” across East Antarctic are no direct climatic features but effect of diffusional

smoothing.

•  This suggests a mostly noise-dominated isotope signal.

•  Similar smoothing effects could be important for other proxies, e.g. bioturbation in marine sediments.

•  for more details:

Laepple, Münch, et al. (2018), The Cryosphere, 12(1), 169–187.

Depth

Similar power spectra across Antarctic sites

No significant spectral power around the wavelengths corresponding to either the annual accumulation rate or the average “cycle” length.

Laepple et al. (2018), Cryosphere