Breaking Ice Hockey Sticks:

Can Ice be Trusted?

Jonathan J. Drake

8/6/2013

It has been claimed by those supporting the hypothesis of anthropogenic global warming (AGW) that

ice core measurements prove that levels of carbon dioxide in contemporary air are much greater

than prior to the industrial revolution as a result of burning earth-sourced hydrocarbons, more

generally known as ‘fossil fuels’. Data from South Pole snow, firn and shallow ice cores demonstrate

this premise is unsubstantiated and in fact incorrect. All gas species and isotopes fractionate as they

become trapped in the ice sheet and therefore cannot represent absolute concentrations of

constituents in historic air.

Breaking Ice Hockey Sticks: Can Ice be Trusted?

Abstract

It has been claimed by those supporting the hypothesis of anthropogenic global warming (AGW) that

ice core measurements prove that levels of carbon dioxide in contemporary air are much greater

than prior to the industrial revolution as a result of burning earth-sourced hydrocarbons, more

generally known as fossil fuels. The data analysed in this document is from the South Pole and has

been reassessed in various ways. Also, the findings of the authors of the paper that published the

data are highlighted.

The conclusions drawn are that all gaseous species or isotopes undergo fractionation during capture

into the ice sheet. This means that absolute concentrations of trapped air components are not

representative of the atmosphere at the time or close to the time of their capture.

It is also shown that there is divergence between the purported carbon dioxide record and the

modelled oxygen record – based upon fossil fuel usage data – that occurs as the capture process

completes.

Introduction

One of the cornerstones of the Anthropogenic Global Warming hypothesis is the claim that there

was a level of carbon dioxide that was lower and more stable in the so-called pre-industrial times

compared to the contemporary period. The evidence for this is predominantly based upon

concentration measurements of carbon dioxide (CO2), other gas species and isotopes from ice cores,

in particular those from Antarctica. These have become increasingly important as they are claimed

to be almost perfect archives of past atmospheres.

The theory goes that air is trapped in snow as it accumulates on the ground and as the snow

gradually compresses into ice some of the air is integrated into the resultant ice sheet as bubbles.

The bubbles then contain a record of past atmospheric gas concentrations. When the ice is drilled,

cores are collected and the recovered gases are analysed and claimed to accurately represent past

atmospheres.

Those supporting the AGW hypothesis maintain that this entrapment process has no effect on the

carbon dioxide record. To a certain extent, they accept that other gases and isotopes fractionate

during and after capture. Carbon dioxide is claimed to be a special case and as such does not

undergo most of these processes; in particular it does not fractionate relative to the main

atmospheric components during capture.

Is this correct? This document assesses some of the data obtained from shallow depths, at the top

of the ice sheet where snow compresses into ice.

Inspection of the data

The concentrations of a variety of gases have been measured from snow, firn and ice, including

carbon dioxide, at the South Pole, and these will form the principal focus of this assessment. To that

end, reference is made to the paper and data presented by Jeffrey P. Severinghaus & Mark O. Battle,

EPSL 2006: South Pole 2001 and Siple Dome 1996 firn air experiments. This paper will be referred to

as SB2006. Their results for the South Pole ice core are shown as recorded in Figure 1, where the

data is given in relative terms, apart from CO2 which is in absolute concentration.

The lock-in depth or bubble/pore close-off depth is 116m. This is the depth at which the majority of

pores have closed to become bubbles within the ice. It should be clear from this that all the gas

species are displaying relative fractionation, to some extent, both in the snow/firn (above about

116m) and in the ice (below about 116m). The rate of fractionation with depth increases around the

lock-in depth and in some cases reverses.

Why have the SB2006 researchers decided to retain carbon dioxide in absolute concentration (ppm)

whilst all the other gases have been given in per mil relative to a reference (zero depth)? Figure 2

shows the CO2 data normalised in the same way as the other curves but the axis inverted so that it

can be compared to the O2/N2 profile. The reason for comparing CO2 to O2/N2 is simply that they

would be expected to show complimentary trends since O2 is used to create CO2 when hydrocarbons

are burnt in air. Clearly, with this scaling they show a similarity and this will be considered in more

detail later.

All the gases fractionate differently but the two noble gases, Xe and Kr follow similar trends. Ne and

O2 as a pair fractionate in a similar manner, but differently to Xe and Kr. CO2 appears unique within

the set in that it continuously falls with depth whereas all the others tend to increase, but that could

be due to the known contemporary atmospheric increase.

However, the gas species relative concentration fractionation is only part of the story. The South

Pole dataset also contains some isotopic records which are presented in Figure 3. Again, all the

isotopes are displaying fractionation with similar general trends to the gas concentrations and again

there is a distinct change in the relationship with depth at around the bubble close-off.

The change in trends in the region of bubble close-off may suggest that there is more than one

fractionation mechanism is present. This will be discussed later.

Figure 1: Fractionation of various gases with depth as presented in SB2006.

Figure 2: Fractionation of various gases with depth relative to zero depth.

Figure 3: Isotopic fractionation with depth.

At this point, we will move on to looking at the carbon dioxide record in more detail. Of particular

interest is the change in concentration of carbon dioxide with depth and how it is linked to the

assigned chronology. Model data from appendix figures A4 & A6 of SB2006 were used to create a

relationship between sample depth and date. Figure 5 shows the CO2 record using the assigned

dates of the captured gas. The corresponding depths are plotted on the right axis, and the bubble

close-off depth is marked. It is difficult to see any strong semblance between these so a slightly

different approach was taken since there is the possibility of different mechanisms taking place

above and below the bubble close-off depth.

Graphs in Figure 6 & Figure 7 use the same CO2 time series with corresponding depths. They use the

same chronology but focus on different date intervals. As stated earlier, there appears to be

different trends above and below the bubble close-off depth. This depth was used as a break point

estimate for separating the distinct relationships either side. Figure 6 & Figure 7 show there is a

strong similarity between the CO2 concentration and depth profiles on either side of bubble close-

off. This is not immediately obvious if they are considered by looking at the full range of CO2 and

depth as shown in Figure 5. Also, it appears that the relationship alters at a point near to, but not

precisely, the bubble close-off depth and will be referred to as the knee depth.

Note: There is an apparent discontinuity in the data at 1976-1977, the reason for which is not

known and has not been chased down.

For the purposes of the rest of this investigation, a knee depth will be defined as the depth at which

linear function fits to data, above and below the sudden change in fractionation with depth,

intercept. By splitting the data into two, based around the approximate knee depth of 113.2m for

CO2, two linear trends can be fitted. The absolute knee depth designation, as described above, can

have significant uncertainty but it has little effect on the linear fits applied either side of this point.

The linear trend equations were calculated from Figure 8 and yielded these equations:

Y1 = 775.1 - 3.921*X (113m to 125.2m), R2 = 0.9740

Y2 = 369.3 - 0.3004*X (0m to 113m), R2 = 0.9952

It could be argued that a fit other than linear would be more appropriate, which may be true;

however it is irrelevant for the purposes of this study.

From these linear trends, four important points are highlighted. Firstly, the trend of concentration

as a function of depth in the ice, or at least the region examined, limited by the available data, is

about 13 times greater below the knee depth, i.e. in the ice. Secondly, in both regions there is a

reduction in CO2 as the depth increases. Thirdly, the trends either side of knee point are quite linear

with depth, apart from the region of transition. Fourthly, changes in the trends exist for the other

gas species and isotopes presented in SB2006.

Next, if we zoom in on the depth region around bubble close-off, Figure 9, there is a noticeable

difference in the depth at which the trends change; the knee depth in the curves has a spread either

side of the bubble close-off depth. By eye, linear trends were fitted to both sides of the knee for

each gas and the intersection depth determined as the knee depth. A more thorough analysis might

yield slightly different values, but for illustrative purposes the method is adequate.

Table 1 provides the knee depth and a number of physical parameters including kinetic diameter. It

is curious to note that there might be a relationship between the knee depth and kinetic diameter as

shown in Figure 10. However there seems to be stronger relationship between knee depth and

molecular weight as shown in Figure 11. In both these graphs two trends are plotted; one for all the

data (blue) and the other omitting isotopes (cyan).

So what could the reason of the variation in the knee depth? A possible explanation is the reduction

of pore size with increasing depth as can be seen from diffusivity and density plots, Figure 12 &

Figure 13. The mechanisms by which the snow compresses into ice are complex but the resultant

process is well known. Snow falling on the surface builds up and traps a certain amount of air within

its relatively open structure. As more gathers, the lower levels effectively compress and as the

depth increases the more compression takes place. During this process, the voids at low levels are

reduced in size and the air that was originally trapped in them is squeezed and migrates upwards.

As this happens the voids become pores and capillaries develop. Many of these pores and capillaries

are connected with the capillaries providing channels for the pore air to reach the less dense

material above. This the pore and capillary diameters reduce with depth. Due to the need for the

lower air to move out of the lower levels, the bulk of the capillaries provide a pathway upwards to

the surface. Eventually, the pore spaces, and in particular, the capillaries become similar in

diameter to the molecules of air restricting the effective movement. However, due to the varying

sizes, shapes and masses of the gases constituting the air, some will become more constrained than

others at any given depth. As the ice compresses further, there will be a small but significant

upward air motion against which downward diffusion takes place.

At some point, the capillaries become so narrow that the pores effectively close. With further

compression the pressure inside the pore grows and a different diffusion scenario is created. There

is then a pressure imbalance across either a microscopic pore opening or membrane and this can

induce fractionation analogous with membrane separation that is widely used throughout industry.

Molecules escaping from the pressurised pores and bubbles are then exposed to the capillary and

tend to be forced along it, although some upward diffusion will also be present. Any diffusion

downwards is acting against a small but significant largely pressure-induced upward flow.

The result of the compaction process is in effect two fold. Firstly, there is a continuously gradated

molecular sieve above bubble close-off and secondly, at the transition, there is a molecular

membrane sieve that has a differential pressure across it. Thus, it would be expected that as gases

and their isotopes become captured into the ice sheet that significant relative fractionation would

take place. This explains the observed trends with depth and also means that the atmospheric

composition of free air above the ice sheet cannot be preserved within the ice.

However, it should be remembered that the above description has not touched on situations when

the snow melts and refreezes rapidly, in effect instantly creating a thick seal. Generally, that is a rare

occurrence at the South Pole and when it is observed, the data is usually rejected on the basis that

they do not conform to the expected trends.

Above all, it is important to realise that all the processes taking place are driven by climatic

conditions and thus there will be a modulation of the fractionation in response to them.

Furthermore, all the climatic conditions are determined by temperature and so a fairly high level of

coherence between temperature and fractionation of the trapped air is to be expected. Inherently

there will also be a similar degree of correspondence between all the gaseous components.

Indeed it is conceivable that when an atmosphere of constant, uniform composition is subjected to

varying temperature and trapped in ice by this mechanism, under a uniform accumulation rate, the

recovered gas will show little resemblance to the original. The composition will however reflect the

temperature to some degree.

At this juncture, it seems appropriate to mention that glaciologists, or at least some, use the collision

diameter for CO2 of 3.9Å which is rather naïve value to use in such systems. It is essentially an

average size attributed to a linear molecule. The dimension that should be used in this type of

situation is the smallest dimension – critical or kinetic diameter – which for CO2 is around 3.3Å. By

using the collision diameter and comparing it to O2 and N2 it is purported that CO2 does not

fractionate by molecular sieving when air is included in ice sheets because 3.9Å is greater than the

ice lattice gaps estimated to be ~3.6 Å. However, most studies of gas permeability and diffusion

through membranes and porous media, outside of this climate science discipline, use the critical or

kinetic diameter. Figure 4 illustrates some molecular dimensions, but be aware these are not the

same as kinetic diameters, as implied by the name.

Figure 4: Illustration of molecular shapes and dimensions from using molecular simulations for screening of zeolites for separation of CO2/CH4 mixtures. Chemical Engineering Journal, Volume 133, Issues 1–3, 15 September 2007, Pages 121–131.

Figure 5: Carbon dioxide concentration and sample depth as a function of assigned date when plotted in entirety on a single graph.

Figure 6: Carbon dioxide concentration and sample depth as a function of assigned date. Depth scale has been shifted to create an overlay of the curves below bubble close-off.

Figure 7: Carbon dioxide concentration and sample depth as a function of assigned date. Depth scale has been shifted to create an overlay of the curves above bubble close-off.

Figure 8: Carbon dioxide concentration as a function of sample depth but split around the knee depth.

Figure 9: Zooming in on the region of bubble close-off.

Table 1: Trapped air composition measures and associated parameters. * = values that are unknown and substituted with those for the dominant natural isotope.

Measure Knee Depth

(m)

Uncertainty

(m)

Solubility in water at

0°C (ml/100g water)

Molecular

Weight

Kinetic

Diameter (Å)

CO2 113.23 0.2 171.3 44 3.3

dO2/N2 115.75 0.2 5.89 32 3.46

dNe/N2 115.68 0.2 1.23 20 2.75

dKr/N2 124.27 0.2 11 84 3.6

dXe/N2 122.82 0.2 24.1 131 3.96

d15N 116.05 0.2 2.35* 15 3.64*

d40Ar/Ar38 116.92 0.2 5.2* 40 (38) 3.4*

d40Ar/Ar36 117.79 0.2 5.2* 40 (36) 3.4*

Figure 10: Kinetic diameter as a function of knee depth for the gases and isotopes at South Pole.

Figure 11: Molecular weight as a function of knee depth for the gases and isotopes at South Pole.

Figure 12: Bulk density as a function of depth.

Figure 13: Deduced effective diffusivity of carbon dioxide.

It is important to remember that the matrix through which filtering and fractionation takes place is

not a constant size and is dynamic. As such it will be difficult, maybe impossible, to model and

correct the data to recover the original atmospheric compositions. At present, the prevailing data

and theoretical mechanism uncertainties will likely mean that potential de-convolution attempts

yield poor results. However, it may be possible to obtain reasonable estimates via empirical

methods, but that will not be considered any further in this document.

Various methods have been used by the glaciologists to match the relatively linear instrumental

record for carbon dioxide with the depth profile in order to create a chronology; mostly correlation.

Not surprisingly, the fairly linear concentration gradient with depth can be readily made to

correspond with the instrumentation record. However, this leads to issues that are glossed over in

most papers but that will be explained here.

Assuming the assigned gas age is correct for CO2 then it should also be largely correct for other

gases. If that is not the case then the composition of the enclosed air cannot be representative of

the original atmosphere. So why are the measured gas concentrations in SB2006 only shown as

depth profiles and not as chronologies? It is easy to find out by creating a depth to time scale using

the data for CO2 and applying it to the other gases. Figure 14 through Figure 17 show the results and

it should be obvious from these that there is a problem with the gas ages being defined by the

carbon dioxide chronology, unless something dramatic happened to the atmosphere around 1980,

which of course is ridiculous.

For the larger noble gas molecules, the reason for the sudden change in concentration around 1980

is clear when considered alongside the deduced effective diffusivity of CO2 and ice density, as shown

in Figure 18 & Figure 19. Simply, they are being fractionated by the ice structure in which they are

restrained.

Another Problem

There are numerous problems in SB2006 when examined in detail; some have been touched on in

this document. However, they are insignificant in comparison to one that is brought to attention

within the paper itself, in the appendix. Here the authors demonstrate that they cannot reconcile

the O2/N2 with the assumed correct CO2 record from ice cores. They find that the O2/N2 data shows

fractionation that is about a factor of 4 greater than ‘expected’. Whilst they show this in a graph – a

copy of which can be seen in Figure 21 – they do not use scales that allow a visual comparison. Since

the data has been made available it is simple to plot it on more suitable scales, Figure 20 which also

provides the depth scale and indications of the close-off and knee depths. As can be seen, the

divergence of the O2/N2 data from the CO2 derived models begins around the depth where the ice

seals the bubbles, about 1980 on the timescale. This is confirmed by image overlay in Figure 22 and

a detail plot of the close-off region is given in Figure 23.

So the O2/N2 and CO2 data are only consistent over a relatively short, approximately linear period

which is coincident with the region above bubble close-off. As has been shown, there is a change in

fractionation at this point due to a transformation in the dynamic physical processes taking place.

The correlation of the matched region should therefore also be considered suspect and more than

likely spurious.

Conclusion

This analysis has shown that fractionation takes place both in the snow/firn and below bubble close-

off in the transition zone/ice for all the observed gases and isotopes. The data provided in SB2006

does not support the assertion that ice is able to trap and retain the composition of ancient or even

contemporary air. This is not particular to the South Pole; it is observed in all locations around the

globe, although the amount and nature of fractionation varies considerably and is dependent upon

local climatic conditions.

Ice core data cannot and should not be considered as a valid archive of past atmospheres, at least

not without correcting for the fractionation that takes place. The United Nations Intergovernmental

Panel on Climate Change relies heavy upon the assertion that the ice core record is infallible,

particularly with regard to a pre-industrial level of carbon dioxide, this document undermines that

cornerstone. Low levels of carbon dioxide in the ice core records are mostly due to fractionation.

Figure 14: d40Ar and d38Ar on carbon dioxide chronology.

Figure 15: dKr/N2 and dXe/N2 on carbon dioxide chronology.

Figure 16: d15N on carbon dioxide chronology.

Figure 17: Ne and O2 on carbon dioxide chronology.

Figure 18: Deduced effective diffusivity and ice density as function of carbon dioxide date.

Figure 19: Deduced effective diffusivity and ice density as function of carbon dioxide date with scales adjusted for comparison.

Figure 20: Comparison of dO2/N2 models, data and orthodox CO2 time series.

Figure 21: Graph from SB2006 showing model and CO2 time series.

Figure 22: Scaled original graph of O2/N2 models from CO2 in SB2006 with firn/ice data overlay.

Figure 23: Close-up of firn transition showing model and data divergence.

Figure 24: Various gas and isotopes on CO2 chronology.

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