Data Set ID: 

Bubble Number-density Data and Modeled Paleoclimates, Version 1

This data set includes bubble number-density measured at depths from 120 meters to 560 meters at 20-meter intervals in both horizontal and vertical samples. The data set also includes modeled temperature reconstructions based on the model developed by Spencer and others (2006).

NSIDC does not archive these data.

  • Ice Core Records > Ice Core Air Bubbles > ICE CORE AIR BUBBLES
  • Snow/Ice > Snow/Ice Temperature > ICE TEMPERATURE
Data Format(s):
  • Excel
Spatial Coverage:
N: -79.433333, 
S: -79.433333, 
E: -112.3, 
W: -112.3
Spatial Resolution:Not SpecifiedSensor(s):DSLR
Temporal Coverage:
  • 10 January 2008 to 18 June 2008
Temporal ResolutionNot specifiedMetadata XML:View Metadata Record
Data Contributor(s):Richard Alley, John Fegyveresi

Geographic Coverage

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Detailed Data Description

Spencer et al. (2006) showed that bubble number-density in polar ice can be quantitatively modeled as a function of temperature and accumulation rate. Here their model was applied to new bubble number-density data obtained from an ice core at the West Antarctic Ice Sheet (WAIS) Divide site to produce a new paleoclimate reconstruction for the two millennia prior to 1700 CE (Fegyveresi 2011).

The WAIS Divide drilling site is located at 79°28.0580 S, 112°05.1890 W, ~160 km from the previous Byrd ice-core drilling site and 24 km from the current West Antarctic ice-flow divide on the Ross Sea side. Refer to Figure 1. This drilling location was chosen because it provides an excellent high- time-resolution analogue to the central Greenland ice cores in terms of ice accumulation rate (~22cm a-1), thickness (~3465 m), average annual surface temperature (-31.1°C), and gas-age-ice-age difference (~225 years) (Conway et al. unpublished). (Fegyveresi 2011)

Map of the WAIS Divide Drilling Site
Figure 1. Map of the WAIS Divide Drilling Site

The technique of Spencer et al. (2006) allows reconstruction of either paleotemperatures or paleo-accumulation rates by fitting a semi-empirical steady-state model to measured number-densities of bubbles in (ice-core) glacier ice (Lipenkov et al. 1998Alley and Fitzpatrick 1999). Temperature and accumulation rate are the primary drivers of polar firn densification, and the integrated effects of these two drivers on density and grain growth are recorded in the number-density of bubbles formed during the sintering process as the firn is transformed into ice at the pore close-off depth (Spencer 1999Spencer et al. 2006). That number-density is then conserved in the bubbly ice following pore close-off. This allows use of a combined firn-densification/grain-growth model to invert for either the firnification paleotemperature or paleo-accumulation rate, provided the other parameter is known, as described by Spencer et al. (2006). Here we define pore close-off depth as the depth at which firn has reached a total density of 90 percent of the average ice density(Herron and Langway 1980) (Fegyveresi 2011).

Accumulation rate can be determined independently for the WAIS Divide site, as described below, so we use bubble data to solve for temperature history here. The transformation of snow to firn, and ultimately to ice, is principally governed by the temperature and by the weight of overlying accumulated snow (Gow 1968b). In higher-accumulation environments, this process is achieved more rapidly due to greater overburden pressures. The crystal size at the depth of bubble trapping is controlled by the time to transformation, and by the crystal growth rate, which is primarily controlled by temperature. For these reasons, faster transformation is favored by higher temperature and/or higher accumulation rate. Faster transformation in turn gives a smaller gas-age-ice-age difference, and climate records from bubble number-density with higher time resolution(Fegyveresi 2011).

Because of this dependence on accumulation rate and temperature, there are large geographic variations in pore close-off depths and firnification times. At higher-accumulation sites such as WAIS Divide, Antarctica, or Summit, Greenland, pore close-off takes only a few hundred years, and may even be achieved in decades at sites of exceptionally high accumulation such as parts of Law Dome, Antarctica. In contrast, at a low-accumulation site such as Vostok, Antarctica, the process can take a few thousand years and is significantly more sensitive to slow temporal accumulation-rate changes, that is rate changes through interglacial/glacial transitions (Sowers et al. 1992). The captured bubbles in glacier ice thus preserve a record of environmental conditions during the time that the enclosing ice was still firn, with time resolution that depends on accumulation rate and temperature. However, the pore close-off process is not instantaneous, introducing slight additional smoothing. For WAIS Divide, pore close-off depth is identified at 823kgm-3 ice density, 90 percent of average ice density for the study sample set (Fegyveresi 2011).


Data are provided in Microsoft Excel format (.xls)

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File and Directory Structure

Data are available on the FTP site in the directory. Within this directory, there is one Microsoft Excel file, BND_data_2011.xls. The spreadsheet contains 12 columns. See Table 1 for a description of the columns.

Table 1: Content in Microsoft Excel Spreadsheet
Column Description
A Depth of sample in meters
B Horizontal sample ID
C Calculated bubble number-density for horizontal samples
D Error bar on the horizontal calculations. (Standard deviation of measurements)
E Calculated horizontal temperaturse in kelvin
F Error bar on horizontal temperatures converted from the error in Column D
G Vertical sample ID
H Calculated bubble number-density for vertical samples
I Error bar on the vertical calculations. (Standard deviation of measurements)
J Calculated vertica; temperaturse in kelvin
K Error bar on vertical temperatures converted from the error in Column I
L Horizontal error bar representing the plus and minus firnifcation times of the samples
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File Size

30 KB

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Spatial Coverage

WAIS Divide, Antarctica

Southernmost Latitude: 79.433333° S
Northernmost Latitude: 79.433333° S
Westernmost Longitude: 112.3° W
Easternmost Longitude: 112.3° W

Spatial Resolution

Depths from 120 meters to 562 meters (covering 440 total meters) at 20-meter intervals in both horizontal and vertical samples

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Temporal Coverage

Data Set Temporal Coverage
Data were collected from 10 January 2008 through 18 June 2008.

Paleo Temporal Coverage
300 BCE to 1700 CE

Temporal Resolution

Each sample at these shallow depths represents 1 to 4 years of time in the core.

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Parameter or Variable

Bubble Number-Density (bubbles cm-3)
Temperature (K)

Sample Data Record

Figure 2 is sample data from the BND_data_2011.xls data file.

sample data record
Figure 2. Sample Data Record

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Software and Tools

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Data Acquisition and Processing

Data Acquisition Methods

In order to employ the bubble number-density model and create the temperature reconstructions in this study, both bubble number-density data and accumulation rates were necessary. Bubble number-density data were acquired by preparing digital imaging and analyzing bubble thin sections obtained from ice at 23 depths from the WDC06A WAIS Divide ice core. Accumulation rates necessary for the model were estimated from ice-layer thickness after correcting for ice-flow strain and densification. For dating purposes, a depth-age scale for the WDC06A based on annual layers resolved in chemistry data was used (Fegyveresi 2011).

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Data Processing Steps

Ice-core bubble thin sections for measurement of bubble number-densities were prepared either in the field or at the US National Ice Core Laboratory's (NICL) -26°C sample-preparation room. First, single-piece 10 cm long samples were cut from the appropriate WDC06A ice-core sections; typically, both vertical and horizontal sections were prepared. The vertical sections cannot be oriented unambiguously relative to the ice-flow direction, but the near isotropy of bubbles observed in horizontal sections means that no bias is introduced by this difficulty when we use a typical bubble size to correct for cut-bubble effects in section analysis, as described below. Samples were collected at 20 m depth intervals. In total, the 23 samples from the WDC06A ice core (cut on-site during the 2007/08 WAIS Divide field season) were taken at depths ranging from 120 to 562 m. Before cutting and preparing the bubble thin sections, these 10 cm samples were first used for total ice-density measurements (Fegyveresi 2011).

Following density measurement, a vertically oriented slab of ice ~1.5 cm thick was cut from the side of the sample using a bandsaw, followed by a ~1.5 cm thick horizontally oriented piece from the top of the sample. Each of these smaller samples were then cleaned using a microtome, sandwiched between glass plates, and bonded using a bead of water on the perimeter of the sample. The use of glue on potential bubble sections was avoided because of the possibility of introducing bubbles in the glue (Fegyveresi 2011).

After setting, each sample was cut in half using a bandsaw to create two separate thin ~5 mm samples bound on one side by glass, with one sample destined for thin-section analysis and the other for bubble analysis. The bubble sections were microtomed to a thickness of ~1.25 mm to ensure that they were thin enough that interpretation would not be complicated by numerous bubbles overlapping one another. Samples thinner than ~1.25 mm are prone to breakage during microtoming. Finally, sample ice thicknesses were determined by taking measurements of overall sample thickness and glass-plate thickness alone using a precision digital vernier caliper. Each sample was photographed, with scale, using a Nikon D80 D-SLR camera with an 18-135 mm Zoom- Nikkor AF 105 mm Micro lens, and Nikkon's Camera Control Pro Software at the NICL on a side-lit stage in a dark room (Fegyveresi 2011).

Raw images were processed to obtain bubble number-density data. Refer to Fig. 3. An area of ~150mm2 was selected on each sample that was most free of smudges, cracks, or other marks and thus provided the cleanest and most consistent area of the bubble section. This size was chosen in order to provide enough bubbles to prevent statistical fluctuations in the results, but without generating too much work for the analysts. Assisted by an edge-detection algorithm, rare remaining non-bubbles such as smudges, glass marks, cracks, etc. were shaded out and removed, while partial bubbles (those for which the illumination had not produced a completely closed convex figure in the image) were manually edited to elucidate more clearly ambiguous edges, or removed if located on one of the image edges. Refer to Equation 1. Next, each edited image was converted into an eight-bit binary image, using the same threshold in all cases, in order to highlight the bubbles and improve identification of bad pixels and overlooked spots. Finally, colored versions of the binary images were overlain on their originally edited counterparts to check for any outstanding errors. Extensive checking shows that our thresholds are set such that we do not introduce spurious bubbles so there is no need to conduct a second check by overlaying the original image on the binary image (Fegyveresi 2011).

In Figure 3, the following ledgend applies:

a raw data
b non-partial and non-edge bubbles blacked out
c after binary conversion, with bubbles highlighted for clarity and bad pixels edited out
d final step of overlaying the binary on (b) to check for errors
Figure 3. Four-step Clean-up Process Used on 150mm2 Bubble Sections

This complete process was applied to two non-over lapping areas of each raw bubble-section image, and the average was used in our calculations. In addition, the entire image-processing procedure was repeated independently by a different analyst for each of these areas on each image to establish reproducibility. After all final image reads and edits were completed, software scripts were used to automatically measure all of the bubble features and pertinent data. In addition to bubble number-density, various other bubble statistics were measured for potential future use such as average inscribed bubble radius, bubble elongation, bubble perimeter, etc. (Fegyveresi 2011).

The bubble number-density is the count of bubbles with centers that fall within a specified volume. However, because bubbles are not geometrical points, some bubbles with centers outside a sample volume will be cut by the sides or the upper or lower faces of the sample, and thus will appear within the sample. Corrections must be made like that identified in Underwood (1970). The corrections are simplified by the fairly narrow size distribution exhibited by the bubbles, allowing us to use the mean bubble size taken as the average inscribed radius, R, returned by the software. This introduces a very minor error because the bubbles centered outside the sample influence the average value, but based on our experience, use of a full Saltykov-type correction would introduce much greater error (Underwood 1970Alley 1987). We eliminated all bubbles touching the sides of our L x L square sampling regions where L is the edge length, which is equivalent to counting only those bubbles with centers at least a distance R inside the squares. We cannot similarly tell which bubbles have centers above the upper face or below the lower face of a sample, so we count all bubbles with centers in a volume extending a distance R above the upper face and R below the lower face. Using measured ice thicknesses and including these corrections, the final calculated bubble number-density can be represented by

equation 1

One additional minor correction was needed. Bubbles form at approximately atmospheric pressure, and are then compressed fairly rapidly until the internal bubble pressure nearly equals the ice overburden pressure. Further compression is then very slow to maintain the internal pressure at the ice overburden pressure, until clathrate formation removes the bubbles (Gow, 1968a). The finite thickness of a sample, together with the progressive vertical compaction of the ice column from this bubble compression, causes the number of bubbles with centers within a given thickness to increase slightly with depth. This is not a climatic effect and must be corrected. Here a correction is made to the ice density of 915kgm-3 using

equation 2

Where BO is the observed bubble number-density (bubbles cm-3), PM is the measured ice density for the given sample (kgm-3), PA is the calculated average ice density (kgm-3) and BC is the corrected bubble number-density (bubbles cm-3). In all cases, this correction is quite small. Note also that the incompressible strain of ice from ice-sheet flow increases the horizontal distance between bubble centers while decreasing the vertical distance. Thus the net effect on bubble number-density is zero so no correction is needed (Fegyveresi 2011).

For each horizontal and vertical sample, four separate readings (two readings each for two independent analysts) were averaged together to arrive at a single corrected bubble number-density value; the mean and standard deviation are plotted against depth. Refer to Figure 4. The 1σ error in bubble number-density (bubbles cm-3) is ±16.78 horizontally and ±13.74 vertically (Fegyveresi 2011).

In Figure 4, the error bars are 1σ uncertainty of reproducibility across samples.

Figure 4. Final Horizontal and Vertical Bubble Number-densities Plotted against Depth.

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References and Related Publications

Contacts and Acknowledgments

Richard Alley
Pennsylvania State University
Department of Geosciences
426 Deike Building
University Park, PA 16802

John Fegyveresi
Pennsylvania State University
Department of Geosciences
426 Deike Building
University Park, PA 16802


This research was supported by NSF OPP Grant Numbers 0539578.

Document Information

Document Creation Date

August 14, 2014

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