Understanding the Glacial Cycles

J.C. Hargreaves

Paleoclimate Group,Global Warming Division,

Frontier Research System for Global Change.

23 March 2004

Outline of talk.

• An analysis of time-series data of the Glacial Cycles, concen-

tration on the Ice-age terminations.

Hargreaves, JC and Abe-Ouchi, A., Paleoceanography, 18(2): 1035, 2003

• Combining data and models in paleo-climate studies.

Hargreaves, JC and Annan, JD, Climate Dynamics, 19 (5-6): 371-381, 2002

Annan JD, Hargreaves, JC, Edwards, NR, Marsh, R, Ocean Modelling, in press.

• Conclusions and future work.

Data analysis using an antisymmetric wavelet

Development of objective methods for determining the timing of

terminations and analysing the variation of aperiodic and quasi-

periodic oscillation in various paleoclimatic data sets.

The last four ice-ages - [Shackleton 2000 data]

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Air temperature

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Atmospheric CO2

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Data

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Deep ocean temperature

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The ice-age ‘cycles’

• Asymmetrical - slow ice growth, fast terminations.

• Non-identical

Defining a ‘termination’

• “Rapid and abrupt change from extreme glacial to extreme

inter-glacial conditions” [Broecker 1984] – but they look

more complicated than this implies.

• Defining the start of a termination is complicated by small

scale variation in the data. Here we concentrate on finding

the time at which the greatest change occured.

→ Fourier analysis is inappropriate but wavelet analysis

produces a 2-dimensional frequency-location spectrum.

The general forms of the well-known Morlet wavelet and the

less well-known antisymmetric wavelet (Lewalle et al. 1995).

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1Morlet Wavelet

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Estimation of the correspondence between wavelet number and

time scale

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(a) Sine wave, period = 50

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(b) Real part of continuous Morlet wavelet transform

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(c) Continuous antiymmetric wavelet transform

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Analysis of data with Morlet and antisymmetric wavelets

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Summary of qualitative results

• Morlet wavelet – Variations at the higher frequency Milankovitch

time scales are evident. Saw-tooth signal of the ice-ages is

not clearly identified.

• Anti-symmetric wavelet – Terminations are precisely located.

Close-up views of the ice-age terminations in the Shackleton

data.

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Termination 1

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Termination 2

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Termination 3

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Termination 4

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The timings of the ice-age terminations detected in the

Shackleton data by the antisymmetric wavelet analysis.

Lags are calculated relative to the centres of the air temperature ranges. Mb

(Ma) show the average of Terminations T1,T2,T3b (T3a) and T4, assumingthe central values of the T1 and T3 ranges.

Air temp. Deep ocean temp. Carbon dioxide Sea level

time lag time lag time lag time lag timescale scale scale scale

(kyr (kyr) (kyr) (kyr) (kyr) (kyr) (kyr) (kyr) (kyr)BP)

T1 17-18 0 30-55 1.5–5.5 40-60 0.5–1.5 40–60 4.5–6.5 20–35T2 140 0 30 -6 50 0 45 7 20T3a 249-254 0 30-20 0.5 20 1.5 35 7.5 15T3b 0 15.5 55T4 342 0 25 -7 40 -1 35 6 20

Ma 0 30 -2 40 0 35 7 20Mb 0 9 30

Summary of time series analysis 1

The ice-age cycles differ greatly in character from the Milankovitch

driven 23ka and 41ka signals

• They are non-identical and asymmetrical.

• The Morlet wavelet analysis of the carbon dioxide record

showed no clear indication of signal at the 23ka and 41ka

periods, however these frequencies appear in air temp and

ice volume.

• There is a strong signal in all data sets close to 100ka fre-

quency – less significant in the sea-level data.

Summary of time series analysis 2 - results from the antisym-

metric wavelet

• The change in sea-level lags ocean temperature, carbon diox-

ide and air temperature changes by about 7 ka. Within the

accuracy of our results, the other three components are all

approximately co-incident.

• Neither T3 nor T6 fit the description of a termination, since

rather than one large, fast change they consist of a series of

smaller changes over a range of different timescales.

Data Assimilation - combining data with models

Various simple models have been used to study climate change

over the timescales of the Glacial Cycles. These models are run

for 100 ka to 1 Ma, and are typically computationally cheap.

For such models a computationally expensive method such as

the Monte Carlo Markov Chain can be implemented.

In recent years, intermediate complexity GCMs have been being

developed, which aim to run a spatial representation of the full

earth system for of the order of 100 ka. A more efficient data

assimilation technique is required, such as the ensemble Kalman

Filter.

State-of-the art high resolution GCMs are used for snap shot

experiments.

Monte Carlo Markov Chain and a simple Earth System Model

• Model - Three equation model of the sea level, ocean tem-

perature and CO2 concentration of the last 400ka

• Data - Time series data of sea level, deep ocean temperature

and atmospheric CO2 concentration over the last 400ka.

• Parameter estimation - 9 parameters estimated simultane-

ously

• The resulting ensemble spans the range of uncertainty.

• Method produces a prediction of the timing of the next ice

age.

Model Results

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Run with 500 ka of data assimilated. The vertical magenta line shows when assimilation was

halted. The red line at the top is the solar insolation forcing. The green dashed lines are the

results from using the untuned parameters. The black dot-dashed lines are the data. The

dark blue lines show the mean of the ensemble and the light blue lines show the one standard

deviations of the ensemble.

Ensemble Kalman Filter and an Intermediate Complexity Model

• Model - GENIE intermediate complexity AOGCM.

• Data - Spatial climatology of ocean temperature, salinity,

atmospheric temperature, humidity.

• Parameter estimation - 12 parameters estimated simultane-

ously

• The resulting ensemble spans the range of uncertainty of the

climate.

• Can be used to make probabilstic estimates of climate change.

• For this initial experiment, present day climatology was used.

THC Collapse, Recovery, Hysteresis

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Conclusions and Future Work

Analysing data in a complete way is important, particularly on

paleoclimate timescales when relatively few data are available.

From this analysis we have calculated the relative leads and lags

between different components of the earth system at the ice-age

terminations. The different terminations vary somewhat, but the

changes in ice mass consistently lag the other components by

about 7ka.

For climatological estimation using models, lack of knowledge in

the parameters is a much larger cause of uncertainty than the

initial conditions. I have described some assimilation techniques,

based on variation on the parameters, which make optimal use

of the data and produce probabilistic ensembles.

In the future we plan to apply the EnKF to intermediate com-

plexity Earth System Models of paleoclimate states. Use of the

MCMC in other computationally cheap paleoclimate models is

also underway.