TCThe CryosphereTCThe Cryosphere1994-0424Copernicus GmbHGöttingen, Germany10.5194/tc-9-1089-2015Constraints on the δ2H diffusion rate in firn from field measurements at Summit, Greenlandvan der WelL. G.BeenH. A.van de WalR. S. W.SmeetsC. J. P. P.MeijerH. A. J.h.a.j.meijer@rug.nlCentre for Isotope Research (CIO), Energy and Sustainability Research Institute Groningen (ESRIG), University of Groningen, 9747AG Groningen, the NetherlandsInstitute for Marine and Atmospheric Research Utrecht (IMAU), University of Utrecht, 3584 CC Utrecht, the Netherlandspresent address: Institute of Climate and Environmental Physics, University of Bern, 3012 Bern, SwitzerlandH. A. J. Meijer (h.a.j.meijer@rug.nl)22May2015931089110324November201411February201523April201524April2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/9/1089/2015/tc-9-1089-2015.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/9/1089/2015/tc-9-1089-2015.pdf
We performed detailed 2H isotope diffusion measurements in the upper
3 m of firn at Summit, Greenland. Using a small snow gun, a thin snow
layer was formed from 2H-enriched water over a 6 × 6 m2 area. We
followed the diffusion process, quantified as the increase of the δ2H
diffusion length, over a 4-year period, by retrieving the layer
once per year by drilling a firn core and slicing it into 1 cm layers and
measuring the δ2H signal of these layers.
We compared our experimental findings to calculations based on the model by
Johnsen et al. (2000) and found substantial differences. The
diffusion length in our experiments increased much less over the years than
in the model. We discuss the possible causes for this discrepancy and
conclude that several aspects of the diffusion process in firn are still
poorly constrained, in particular the tortuosity.
Introduction
The relative abundance of the stable isotopes 2H and 18O in ice
cores is one of the most powerful proxies of the palaeotemperature over the
last 800 kyr (Jouzel and EPICA community, 2007). The
global meteoric water cycle acts as a global-scale isotope distillation
system, through a continuous process of evaporation and condensation. It
leads to a depletion of the abundance of heavier isotopes in the water
molecules, which depletion increases with higher latitudes or rather, in
fact, with lower temperature. In the polar regions, especially on Antarctica
and Greenland, the precipitation containing this temperature-dependent
isotope content is conserved, and by drilling deep ice cores on strategic
places on these ice caps the precipitation of over 100 000 years
(Dahl-Jensen et al., 2013; Johnsen et al., 2001) or even close to a million years
(Oerter et al., 2004; Stenni et al., 2010) can be recovered.
Accurate, high-spatial-resolution isotope abundance measurements on this ice
core material then reveal the “proxy” temperature signal.
As said, the signals are proxies, implying that their relation with past
temperature is solid, but not necessarily linear, and not even of a constant
character through time or in space. Most of this proxy character is due to
the complex and time-dependent relation between temperature and circulation
patterns in the atmosphere, influencing the behaviour of the isotope
distillation system. Some of it, however, is due to processes that influence
the isotopic abundance pattern after deposition. Apart from processes acting
only on very fresh snow still at or close to the surface (firn ventilation
and sublimation; Neumann and Waddington, 2004; Sokratov and Golubev, 2009), the main process is
diffusion. This smears out, and can eventually wash away, spatial gradients
in the isotope abundances. Diffusion takes place in the solid-ice phase, but
especially, at a rate some 5 orders of magnitudes higher, in the firn phase.
In the latter case, the diffusion process is governed by the continuous
evaporation and condensation of ice particles into and from the air
channels. While in the vapour phase, the water molecules travel a certain
distance before freezing back to the solid phase. The process is relatively
fast, especially in the first years after deposition, when the firn density
is still low, and summer temperatures still affect the firn temperature. On
the central Greenland ice sheet, the isotope diffusion process decreases the
seasonal cycle amplitude by typically a factor of 5 and effectively
influences all timescales of decadal variability and shorter
(Andersen et al., 2006a; Vinther et al., 2006).
Isotope diffusion in firn was discovered by Langway (1967) and is
well understood in the qualitative sense. Quantification, however, is more
difficult, as the rate depends critically on the density of the firn and,
moreover, on the tortuosity of the firn, i.e. the shape and size of the air
channels between the ice crystals. Furthermore even grain size might play a
role. Several laboratory experiments have been performed on the isotope
diffusion rate (Jean-Baptiste et al., 1998; Pohjola et al., 2007; van der Wel et al., 2011a), and expressions
for the rates that include a parameterization for the tortuosity dependence
have been formulated (Cuffey and Steig, 1998; Johnsen et al., 2000; Whillans and Grootes, 1985) and tested
(Pohjola et al., 2007; van der Wel et al., 2011a).
Corrections for isotope diffusion (usually to reconstruct the original
precipitation signal: “back diffusion”) are currently performed routinely.
The last publication that we are aware of that shows the “raw”, uncorrected
isotope signals together with the corrected ones is by Johnsen (1977). So,
in spite of the fact that the process is difficult to quantify,
back diffusion is applied routinely for the interpretation of ice cores,
even for short(er) timescales (Bolzan and Pohjola, 2000; Vinther et al., 2006).
As the process is difficult to quantify, we found the isotope diffusion rate
worth further investigation, especially since (1) isotope diffusion has
gained renewed attention, after the discovery (by Johnsen et al.,
2000) that the difference of the diffusion rate for 2H and 18O
(“differential diffusion”) is dependent only on the temperature of the firn.
Differential diffusion has thus the potential of becoming a powerful new
palaeotemperature proxy by itself (Simonsen et al.,
2011; van der Wel, 2012). (2) All laboratory experiments on diffusion rates
have been performed on artificially produced “firn”: shaved ice flakes
(Jean-Baptiste et al., 1998; Pohjola et al., 2007) or, at best, snow produced by a snow gun
(van der Wel et al., 2011a). However, it was realized that
the tortuosity, the 3-D shape of the air channels between the crystals, is
important for the diffusion rate, and it is well conceivable that this
differs considerably between artificial “snow” and real snow. (3) Most
laboratory experiments have concentrated on the high-density regime, where
tortuosity effects are most pronounced but where the diffusion process is
slow. Here, we concentrate on the initial phase of firnification where
diffusion is fastest.
For these three reasons we decided to design and perform a field experiment
in which we could measure the 2H isotope diffusion rate for real snow.
Using a snow gun, we produced a thin layer of artificially made snow,
enriched in 2H (enriched 18O water is too expensive and rare for
such a field experiment), on a field site at Summit station, Greenland, a
site with temperatures below 0 ∘C all year (at least prior to
2012). In the 4 years that followed, 2008–2011, we went back to the place
four times and drilled shallow cores (from 1 to close to 4 m over the
years) in which we recovered our original layer, now diffused well into the
original firn surrounding it. Isotope analysis in the laboratory yielded the
width of the diffused profile over the years. Together with the temperature
of the layer, which was logged, and the measured density, this enabled us to
compare the actually measured diffusion rate with the value from the
generally used expression and parameterization by Johnsen et al. (2000).
In the following chapters, we start with the theoretical description of
isotope diffusion, including our approach to numerically simulate our
experiments. Next, we describe the field experiment. After that, we present
the results of our measurements and discuss those extensively. We end with
some conclusions and a design for a follow-up experiment.
Isotope diffusion in firn
In general, diffusion is the macroscopic description of microscopic random
movements that, in combination with a gradient in the concentration of a
certain constituent, cause a decrease of this gradient. The most commonly
used macroscopic description originates from Fick, a 19th-century German
physiologist. According to his second law, and considering only one
spatial dimension, the effects of diffusion on the isotope concentration C
are described as
∂C∂t=Ω∂2C∂z2,
where Ω is the diffusion coefficient, also called diffusivity, and t
and z are the temporal and spatial coordinates, respectively. In our
specific case, C would be the concentration of water molecules containing a
2H isotope. In practice, however, the 2H concentration is
expressed as the deviation of this concentration from that of a reference
material. This deviation is denoted by δ2H and is defined as
δ2H=RsampleRreference-1,
where R is the abundance ratio of the rare isotope with respect to the
abundant isotope: 2H / 1H. δ2H is usually expressed in
per mill (‰). As the difference between concentration and ratio is
very small for 2H, to a good approximation the diffusion equation is
also valid using δ2H. Therefore, we may change Eq. (1) into
∂δ2H∂t=Ωf2∂2δ2H∂z2,
where Ωf2 is the firn diffusivity for δ2H, for
which an expression was derived by Johnsen et al. (2000):
Ωf2=mpsatΩa2RTτα21ρf-1ρice.
Here m is the molar mass of water (in kg), R the gas constant (J K-1) and
T the temperature in Kelvin. ρf and ρice are the firn
and ice density (kg m-3), respectively (ρice= 917 kg m-3).
For the water vapour saturation pressure psat we use the
parameterization given by Murphy and Koop (2005):
psat=e9.550426-5723.265T+3.53068ln(T)-0.00728332T,
with psat in Pa and T in Kelvin. As psat is exponentially
dependent on temperature, this parameter is the main cause for temperature
dependence of the diffusion process. The other terms in Eq. (4), except the
tortuosity τ (and m and R), are temperature-dependent as well: apart
from the temperature itself, these are the ice–vapour fractionation factor
α2 and the diffusivity of deuterated water vapour in air
Ωa2. For the most abundant water molecule 1H216O
the diffusivity in air is given in square metres per second (m2 s-1) by Hall and Pruppacher (1976):
Ωa=0.211×10-4TT01.94p0p,
where T is the temperature, T0 is 273.15 K, p is the pressure at Summit
(680 hPa during summer, the time when the diffusion process is the most
active) and p0 is equal to 1013 hPa (1 atmosphere).
For water molecules containing a 2H atom, the diffusivity is slightly
lower (Merlivat, 1978):
Ωa2=Ωa1.0251.
The ice–vapour fractionation factors – that is, the difference in ratio of
rare and abundant isotopes in ice and vapour under equilibrium conditions –
are functions of temperature and were measured by Merlivat and Nief (1967)
for Deuterium:
α2=0.9098e16 288T2.
Finally, the tortuosity τ depends on the structure of the open
channels in the firn. We adopt – initially – the parameterization as a
function of the density of the firn that was given by Johnsen et al. (2000):
1τ=1-1.30ρfρice2forρf≤804.3kgm-3.
This parameterization leads to increasingly high values for τ as the
density ρf approaches the density of pore close-off. For lower
densities, however, the effects due to tortuosity are assumed to be minor:
according to this parameterization the value of τ varies between 1.15
and 1.25 in the density range of our experiment (300–350 kg m-3). Of
course, this paramterization is a gross oversimplification of the real
process, as it neglects the influence of varying grain sizes and shapes.
Nevertheless, it seems to have served its goal reasonably well under widely
varying circumstances.
Diffusion decreases gradients and thus leads to an overall smoothing of the
original signal. The general solution to the differential Eq. (3) given
an initial profile δH0(z) is a convolution of this initial
profile with a Gaussian distribution:
δ2H(z,t)=1σ2(t)2π∫-∞∞δ2H0(z′)exp(z-z′)22σ22(t)dz′.
The amount of smoothing – that is, how the values of the original profile
δ2H0 at positions z′ influence the value
δ2H(z, t) – is determined by the width of the Gaussian curve
σ2. The physical meaning of this width is the diffusion length, which
is the average displacement of the deuterated water molecules. If the
original distribution δ2H0(z, t= 0)
is a Dirac distribution (infinite at z= 0, and zero everywhere else, such
that its total integrated area is M), Eq. (10) leads to
δ2H(z,t)=Mσ2(t)2πexp-z22σ22(t).
The squared value of σ is directly related to the isotopic
diffusivity in firn and the elapsed time:
σ22(t)=∫0t2Ωf2(t′)dt′.
In such an idealized case, the profile that would be recovered would show a
pure Gaussian profile, and its width would be directly related to the diffusivity.
The calculation of the width of such a profile would simply require the
numerical integration of Eq. (12). For each time step, Ωf2
needs to be calculated with the appropriate values for the variables
(temperature and/or density) for that time step.
In reality, the original distribution δ2H0(z, t= 0)
is of course never a Dirac function. In our experiment, however, the initial
signal does resemble a Dirac function, but with a finite value for the peak
value and a finite width of this peak. Furthermore, we deposit our layer of
2H-enriched snow on a background that is not constant but that shows the
natural seasonal cycle (subject to diffusion during previous years).
Finally, in our experiment we sample the firn layer with a limited spatial
resolution (of 1 cm). Hence we use a numerical model for the simulation of
our findings, taking these complications into account (see Sect. 4.3).
Comparison of the numerically calculated σ's with those from the
field experiment enable us to test the validity of Eq. (4) and the
terms it contains (most notably the parameterization for the tortuosity,
Eq. 9). The isotope effects (Eqs. 7 and 8) and obviously
the saturation pressure of water vapour (Eq. 5) are generally
considered to be well known and are treated here as constants without
uncertainty. Recently, Ellehoj et al. (2013) reinvestigated the ice–vapour fractionation factor α2
(Eq. 8) and found it to be larger, from ≈ 1 % at -15 ∘C to
over 3 % at -40 ∘C. Although such changes are highly significant
when studying, for example, the hydrological cycle, for our study such
changes are of minor importance.
The field experiment
For the production of 2H-enriched snow under polar field conditions, we
built a snow gun installation. The snow gun itself was a small instrument
designed for home garden use (CHS Snowmakers, type “Cornice”). The gun
produces a very fine spray of droplets which precipitate as dry, fluffy
snow, provided the ambient temperature is low enough (at most -5 ∘C,
preferably several degrees lower). We built the necessary air compressor
and water pump system on a compact, gasoline-motor-driven cart. The
installation was capable of producing ≈ 300 kg of snow per hour. We
produced snow on an area of typically 6 m × 6 m, such that we would have
ample space for drilling two–three hand cores per year for 4 years without
interference. We aimed for a snow layer of 2–3 cm and allowed for loss of
snow spraying outside the field, so we used about 1000 litres of water. We
contained this amount of water in an inflatable children's paddling pool,
which is easily transportable and also forms a good thermal isolation (we
added a foam mat underneath).
The water was enriched to a level of typically δ2H = 1000 ‰ by
adding 250 g of pure D2O (Sigma-Aldrich) (depending on the natural δ2H level of the water used).
In August 2007, we produced an area of 2H-enriched snow in the field on
pristine snow, about 2 km away from camp Summit (central Greenland,
72∘35′ N 38∘25′ W, elevation of 3216 m). The station is
operated by the American-based CH2M HILL Polar Services (formerly Veco Polar
Resources). In the summer months, there is frequent access for both people
and equipment with Hercules C130 aircraft. Temperatures are always below
0 ∘C (at least during the years of our fieldwork).
The production of the 2H-labelled layer of snow at Summit,
8 August 2007. From left to right the air compressor/water pump rack, the
inflatable water container and the snow gun.
On 8 August 2007, we produced our enriched layer in about 5 h, using
≈ 1000 L of local surface meltwater, enriched to
δ2H = 1294 ± 3 ‰. We also dyed the water
with a red food colorant, to make our produced snow layer visible. Figure 1
shows the site while producing snow. The wind speed was low that day, so
most of the produced snow landed on our area (marked with poles). It was a
sunny day, with temperatures reaching -5 ∘C, which impeded dry
snow production. Therefore we produced snow at a reduced production rate.
Still, the produced layer on parts of our area was ice rather than snow,
especially close to the snow gun. After finishing the snow production, we
carefully inspected the area, such that we could try to avoid the places
with ice formation when sampling in later years.
A thermistor was placed at the surface, co-located with our layer and
connected to a data logger close to one of the poles. Temperatures were
logged every 3 h. In this way a high-resolution continuous temperature
record for our layer would be available.
Prior to our snow making, we took samples from the pristine snow layer for
isotope analysis, to a depth of about 50 cm. We also performed snow density
measurements, to the same depth, with 10 cm resolution.
The night after the snow was produced, the layer got covered under a few
centimetres of fresh snow.
Afterwards, the depth of the snow layer was monitored by the Summit crew
members every month by measuring the height of each of the five poles that
marked the field; this went on until the final sampling day in 2011. At that
time our snow layer was close to 3 m below the surface.
These careful snow height measurements provided us with the information
needed to recover our layer in the consecutive years. In the years 2008,
2009, 2010 and 2011 (that is, 352, 643, 1102 and 1460 days after the
production of the layer) we returned to Summit to drill shallow firn cores
with a hand corer (Kovacs Mark II). We drilled two–three cores every year
(labelled A, B, C) and made sure that we recovered the expected depth of
our layer ± some 50 cm (as the depth registered at the five poles
around our field scattered by 20–30 cm over the years). Figure 2 shows the
depth of our layer as a function of time based on those pole height
measurements, together with the points indicating the actual depth of the
enriched layer (or rather the depth of the maximum δ2H value)
as revealed by the isotope measurements later in the lab.
The depth of the enriched snow layer as a function of time, based
on measuring the height of each of the five poles that mark the field (lines),
together with the points indicating the actual depth of the enriched layer
as revealed by the isotope measurements later in the lab (two to three
points per year).
Still in the field, we cut the cores into 1 cm slices with a custom-built
device and stored the slices in individual air-tight plastic bags (Toppits
Zipper). Soon after, we let the slices melt and pored them over into
lockable plastic sample transport tubes (Elkay products) that had been
tested for their long-term isotope integrity.
In the field, we also secured the logged temperatures of the past year, and
in 2010 and 2011 we performed again 10 cm resolution density measurements,
now also using our hand corer.
Back in our laboratory in Groningen, we performed δ2H and
δ18O isotope ratio measurements on all samples using our
routine equipment (van der Wel, 2012). The combined uncertainties were
±0.06 ‰ for δ18O and 0.6 to 2 ‰ for δ2H (depending on the level of
enrichment). In all of the total of 10 cores drilled over the years, we found
our enriched layer, close to the depth expected based on the pole height measurements (Fig. 2).
Density measurements, with depth resolution of 10 cm, performed at
our site in the years 2007, 2010 and 2011. The depths have been shifted such
that our enriched layer (with an estimated thickness of typically 2 cm) is at
relative depth zero. Our enriched layer, deposited at the end of the summer
of 2007, is on top of a summer layer with lower density than the preceding
and following winter layers.
The temperature registration of the thermocouple, at the same depth
as the layer. The dashed lines are interpolations for the times we did not
have temperature measurements available. The insert shows the first month of
data in detail.
ResultsDensity and temperature
For the simulation of the diffusion of our enriched layer, reliable values
for both the temperature and the density are the most important input
values. Figure 3 shows the density measurements that we performed over the
years, all measured close to the area of the enriched layer, grouped in a
single plot. The depths have been shifted (using the information shown in
Fig. 2) such that our enriched layer is at depth zero. The data show that
our enriched layer, deposited at the end of summer, is on top of a layer with
lower density than the preceding and following winters. This summer–winter
effect is beautifully demonstrated by Albert and
Shultz (2002) from Summit in 2000, and our data are in agreement with their
findings (shown in their Fig. 2). Based on their and our data we use an
initial density of 300 kg m-3 for our diffusion calculations, with a
gradual increase of 10 (kg m-3) yr-1.
The temperature registration of the thermocouple, at the same depth as the
layer, is shown in Fig. 4. Unfortunately, in spite of our efforts, two
larger parts of the total temperature profile were lost. Figure 4 shows the
interpolations that we made. We estimate the extra uncertainty in the
diffusion calculations due to this omission to be minor. Fortunately, the
first full year of data has been recovered. This is the part when the layer
is still so shallow that the diurnal temperature cycle (which we capture by
our 3-hourly temperature sampling) is still noticeable (see insert in the
figure for the first month). As the diffusion rate is exponentially
dependent on temperature, capturing this first period in detail is crucial
for the results of the numerical simulations.
The results for the diffusion length σ and for the
net peak height for all profiles. The increase of σ as a function of
time is clearly visible. The uncertainties in the second column are those
from the fitting procedure. The final combined uncertainties in the results
are presented in the third column. Except for 2008, all measured values per
year agree within their uncertainties. The net peak height is also dependent
on the initial thickness of the enriched layer. Therefore the found peak
height is variable within and between years.
For each sampling year, two–three records for both δ2H and
δ18O were measured (labelled A, B, C). δ2H
contains the crucial diffusion information: the broadened (and weakened)
profile around our original layer of enriched δ2H. The quality
of our collected profiles was variable. Some of the profiles showed one or
two samples (= cm) that had δ2H values almost as high as the
original enriched water, whereas all other samples were close to the natural
values. We attribute this to ice formation during the snow production,
reducing diffusion rates dramatically. Fortunately, for every year we also
had profiles without such irregularities, which showed a clear,
Gaussian-shaped profile above background.
Figure 5 shows two of the δ2H profiles, 2008B, and 2011A,
respectively. The effect of diffusion is directly visible, both in the width
of the peak, and in its height. For the quantitative determination of both,
however, we need to correct for the natural δ2H seasonal cycle
that interferes with the diffused pattern of our original enriched layer. We
used the δ18O profile to reconstruct the natural
δ2H seasonal cycle. δ2H and δ18O in
precipitation show both a very similar seasonal cycle, with the amplitude of
the δ2H cycle being around 8 times as large as that of
δ18O. Contrary to that of δ2H, the δ18O
seasonal cycle is not influenced by our layer: the water used was in fact
recent snow at Summit, with δ18O ≈-30 ‰ very
close to the value of the top layer of our field.
In Fig. 5, δ18O is shown as well, with scale ratio 1 : 8 with
respect to the δ2H scale. For the reconstruction of the natural
δ2H signal the δ2H -δ18O ratio for all
our 10 profiles was fitted individually, by using the flanks of the
profiles. Subsequently, we corrected our measurements for this
reconstruction of the natural δ2H signal, thereby obtaining the
net diffusion profile.
For each of the 4 years, we had two profiles available (and even 3 for
2008 and 2010). Only one of these 10 profiles (2008A) was not useful: the
deposited layer consisted only of ice and diffusion had hardly taken place.
Figure 6 shows all other net δ2H profiles, together with the
Gaussian fits, after subtracting the background signal. The width of the
fit, which is the diffusion length σ (see Eqs. 10 and 11), is also indicated.
Not all profiles are of equal quality: half of them showed the presence of
ice inside our deposited layer, visible through one isolated high
δ2H value in the profile (on most occasions the ice layers had already
been noticed in the field); as those points are not representative for the
diffusion process, we discarded them. This happened for profiles 2008B,
2009B, 2010B, 2010C and 2011A. Furthermore, some points had to be discarded
that resulted from contamination of samples with snow/firn from other depths
that happened during the coring process (such contamination was also visible
in the δ18O signal). Discarded points are shown in the plots in
brown. Table 1 shows the results for the diffusion length σ and the
net peak height for all profiles. The increase of σ as a function of
time is clearly visible. Contrary to σ, the net peak height is not
only dependent on the diffusion time, but also on the initial thickness of
the enriched layer. Therefore the found peak height is expected to be
variable within and between years.
Two examples of δ2H profiles obtained in this work,
from 2008 (core B) and from 2011 (core A). The effect of
diffusion is directly visible, both in the width of the peak and in its
height. The δ18O signal is shown in blue, with scale ratio 1 : 8
with respect to the δ2H scale.
The nine net δ2H profiles for the four consecutive
years, together with the Gaussian fits. The width of the fit, which is the
diffusion length σ, is listed in the plots. The brown circles are
measurements discarded from the fit for various reasons (see text). The increase
of σ over the years is clearly visible.
The results for the diffusion length σ. The points are the
experimental results. The set of four higher-lying curves (one black, three
in shades of blue) is the result of the numerical simulation using the
Johnsen et al. (2000) model. The black one is the direct calculation of
σ; the three blue ones result from the full numerical procedure
starting with an enriched layer with 6, 18 and 30 mm initial thickness.
Clearly, there is a systematic mismatch between the
experimental results and the numerical simulations, increasing with time.
The fit curve through the measurements is constructed by lowering the
diffusivity by 25 % in the first year, up to 40 % in the last. Finally,
the black dotted line shows the numerical result using a fixed, higher value
for τ (1.6).
The uncertainties given in the second column in Table 1 are those from the
fitting procedure. While they give a good indication for the fit quality,
the final combined uncertainty in the results is, of course, considerably
higher. The main experimental uncertainty lies in the representation of the
“z axis”, the depth. We estimate this error to be ±3 % of the
value, leading to an error in σ of about 0.10. The icy character of
our deposited layer in some profiles form another principal source of error:
although on both sides of such an ice layer the firn diffusion process takes
place, and we can thus use those profiles for a σ measurement, the
width of the fitted Gaussian curve will still be influenced by the presence of
the icy character of the original layer itself. Therefore, we have increased
the uncertainties for such profiles to ±0.25 cm. The uncertainty
caused by the δ18O-based background correction is negligible.
The final attributed errors are given in the “uncertainty” column. Except
for 2008, all measured values per year agree within these uncertainties. As
each year had at least one core with, and at least one core without, ice in
our deposited layer, the fact that their diffusion lengths agree with each
other shows that these ice layers did not influence the diffusion length
significantly in this experiment.
Comparison with the numerical simulation
The simplest way of simulating our experiment is to numerically integrate
Eq. (12) using the known temperature and density as a function of time
(Eq. 4). However, the real experimental situation is more complicated. To
accurately simulate the experimental situation, we first calculated the
diffused δ2H pattern as a function of time from the original
δ2H0(z, t= 0) pattern around our enriched layer with an added “pulse” of enriched
δ2H. We know the value of this enriched δ2H
(1294 ‰), but the thickness of the layer is unknown and
variable. Therefore we calculated the profiles for three initial layer
thicknesses: 6, 18 and 30 mm. As the next step, we corrected the diffused
pattern for the slight compaction that occurred (inversely proportional to
the small increase in density), and we sampled the diffused patterns with the
spatial resolution of the experiment (1 cm). Then, we simulated the
correction for the natural δ2H seasonal cycle using the also
diffused and sampled δ18O profile, in the same way as we did
with the experimental profiles. Finally, we fitted the net δ2H
profile with a Gaussian function.
The actual peak height fits of the profiles (red circles). They are
compared to the numerical simulations with initial layer thicknesses of 6,
18 and 30 mm, for which the diffusion length is fitted to the experimental
points in Fig. 7. All experimental points are in the range spanned by the
numerical calculations. The values for the ice layers that we removed from
our profiles are also indicated (half-filled squares): all but one lie
outside the possible range for diffused firn profiles, identifying them once
more as ice layers.
Figure 7 shows the results for σ achieved this way, as well as the
σ from the direct integration of Eq. (12). The differences
between the numerical calculations at variable initial thickness are quite
small, especially for the values of σ for later years, indicating
that the effects of sampling and the background correction are minimal.
Figure 7 also contains the experimental diffusion lengths and thus
embodies the main results of this work. Clearly, there is a systematic
mismatch between the experimental results and the numerical simulations,
increasing with time. To fit the data, the simulated curves need to be
≈ 25 % lower in the first year, up to ≈ 40 % in the
final year. This implies a lowering of Ωf2 up to a factor
of 2.5 (as σ is proportional to the square root of Ωf2).
This lowered fit curve is also shown in Fig. 7. (The black dotted
line in between will be described in the discussion section.) All in all,
Fig. 7 suggests that either there is an experimental flaw or else one or more
parameters included in Eq. (4), or Eq. (4) as a whole, are not
adequate. Below we discuss various possibilities influencing the average
value of σ and its dependence on time.
The full numerical procedure also results in a peak height, which at any
point of time is proportional to the width of the initial enriched
δ2H pulse. Indicated in Fig. 8 (red dots) are the actual peak height
fits of the profiles (see Table 1). They are compared to the numerical
simulations for layers with initial thicknesses 6, 18 and 30 mm, for which
the diffusion length is fitted to the experimental points in Fig. 7 (the
red dotted line). All experimental points are in the range spanned by the
numerical calculations. The values for the ice layers that we removed from
our profiles are also indicated: the position of four out of five of them in
this plot clearly corroborates them as ice layers, as an initial layer
thickness of 30 mm is about the maximum realistic value for our snow layer.
Discussion
The considerable discrepancy between our experimental results and the
numerical calculations based on Johnsen et al. (2000) came as a surprise.
The theoretical description of the firn diffusion process by Johnsen et al. (2000),
a further development of work by Johnsen (1977) and Whillans and Grootes (1985), has
been used for the description (and back correction) of diffusion in many ice
core projects.
The large majority of the papers describes, or “back-corrects”, the
influence of firn diffusion as it is recorded in the ice below pore
close-off. There, the ice carries the result of firn diffusion integrated
over the entire firn phase. Examples of such work, restricted to Greenland,
are Vinther et al. (2006, 2010), Masson-Delmotte et al. (2005), Andersen
et al. (2006b), Jouzel et al. (1997), White et al. (1997)
and Simonsen et al. (2011). The last publication concentrates on
the so-called differential diffusion, the difference in diffusion between
δ18O and δ2H, which is only dependent on the
temperature of the firn while diffusion takes place. This idea was in fact
the main subject of Johnsen et al. (2000).
Below we will dicuss three possible causes for the discrepancy. They are
(1) our experimental conditions, especially the formed ice in the deposited
layer; (2) a considerable influence of tortuosity already in the uppermost
metres of the firn, contrary to the assumptions in Johnsen et al. (2000);
and (3) invalidity of the assumption that no gradient in isotopic
composition builds up within the firn grains.
Experimental conditions
The occurrence of an ice layer can practically block the diffusion process.
We do, however, firmly believe that our results have not been seriously
influenced by ice formation. Each year contained both a profile with and
one without the indication of ice formation inside our deposited layer. Yet,
for each of the 4 years that we sampled, the results for the diffusion
length agree very well. As the occurrence of an ice layer almost stops the
diffusion process (see e.g. van der Wel et al., 2011b), one would expect large scattering within and between
years if ice formation inside our deposited layer indeed played an
important role. The fact that they do not can be explained by the fact that
the water vapour from such an ice layer will immediately encounter natural
snow layers in which the diffusion process occurs naturally. Only the ice
layer itself will continue to contain a high level of enrichment and in the
end produces a δ2H value that needs to be excluded from the fit
to the data, as we did.
Even in the absence of ice, the density of our artificial snow layer is
probably higher than that of fresh Summit snow. When trying to fit the
results of Fig. 7 using higher densities we find that we would need a more
or less plausible density of around 380 kg m-3 for the first year, but
increasingly higher values for the subsequent years, up to 520 kg m-3
for the 2011 results. Such compaction of a layer, initially already denser
than its surroundings, in just 4 years is unrealistic. Furthermore, again
the diffusion process will immediately encounter natural snow as soon as the
process starts. So, in the course of the years, with diffusion lengths
getting larger and the signal profile getting dominated by the region
outside the original layer, one can expect any initial effect of higher
density to weaken. However, we observe the opposite: the deviation between
our experimental results and the simulations based on Johnsen et al. (2000)
increases in the course of the years.
Tortuosity
The diffusion length σ is inversely proportional to the square root
of the tortuosity τ. If the discrepancy between our results and the
numerical simulation were entirely due to higher tortuosity in our
experiment than the range of 1.15–1.3 given by Eq. (9), we would need
the tortuosity to be between 2.5 and 3. To see to what extent this would be
plausible, we have gathered relevant information from the literature
describing both firn isotope diffusion and gas diffusion. To facilitate a proper
comparison, we first have to define the tortuosity in an unambiguous manner:
Ωf=Ωaϕτwiththeporosityϕ=1-ρfρice.
Here Ωa is the diffusivity of the compound (water vapour in our
case or, more precisely, deuterated water vapour) through a certain area of
free air, and Ωf the effective diffusivity through that same
area, but now filled with firn. The porosity φ accounts for the
effective open area available for the diffusion process, whereas the
tortuosity accounts for the shape of the air channels. In the case of
perfectly straight air channels, τ would be 1.
The Whillans and Grootes model (Whillans and
Grootes, 1985) was the first to describe firn diffusion in a detailed
manner, but they did not include the influence of tortuosity. Instead of the
porosity, they included the density at pore close-off ρc:
ϕ*=1-ρfρc.
Using this φ* is equivalent to using Eq. (13), with
τ=ϕϕ*=1-ρf/ρice1-ρf/ρc.
As the difference between ρice and ρc is rather small
(Whillans and Grootes (1985) used 830 kg m-3 for ρc),
effective tortuosity values remain close to 1 except for densities
approaching ρc.
Cuffey and Steig (1998) performed a detailed – that is, time-resolved – study of
firn diffusion showing the dampening of the seasonal cycle in
δ18O in the shallow GISP-B core (based on the data published by
Stuiver and Grootes (2000) and Stuiver et al. (1995)) and compared that to the
Whillans and Grootes (1985) model (taking the low atmospheric pressure at
Summit into account). They concluded that the model agreed well for the
upper metres (starting, however, from a depth of 1.5 m) but that the
diffusion effects produced by the model were too large for larger depths.
The diffusivity of the model needed to be decreased by a factor of about 1.7
to match the data. They built this into the model by decreasing the maximum
density at which firn diffusion still occurs, from 830 down to (a fitted
best value of) 730 kg m-3. Using Eq. (15) their results can again be
expressed as using a tortuosity factor that is now considerably higher than
in the original Whillans and Grootes (1985) model. However, even in this
study the depth resolution is limited to the length of one seasonal cycle
(typically 50 cm); they ignored the top 1.5 m, and their numerical
procedure concentrated on the amplitude of the seasonal cycle only, not
taking into account for example the diffusion differences between original
summer and winter snow. The temperature driving the diffusion process is parameterized.
Johnsen et al. (2000) modified the Whillans and Grootes (1985) model, the
main difference being the explicit introduction of the tortuosity factor.
Other differences, with relatively small (< 5 %) influence, are a
different parameterization of the water vapour diffusivity through free air,
and the more complete treatment of the isotope effects. The tortuosity that
Johnsen et al. (2000) used (Eq. 9) is based on a fit to gas diffusion
measurements by Schwander et al. (1988),
performed on firn samples from Siple station, Antarctica. The density range
of these measurements was between 500 and 750 kg m3. Schwander et al. (1988)
present the tortuosity as it is defined in Eq. (13) in their
Fig. 5. Tortuosity values they found increased with the density from 2 to 7.
They also provided a table (their Table 1) that may give rise to some
confusion. The effective diffusivity that is given there is in fact
Ωf/ϕ (“the flux per unit cross section in the open pores”) (J. Schwander,
personal communication, 2014). So, dividing the diffusivity given in that table by the open
air diffusivity Ωa directly yields 1/τ.
Their results for tortuosity were generally, although coarsely, confirmed by
Jean-Baptiste et al. (1998), who did the
first diffusion measurements on deuterium isotopes in firn: they measured
the isotope diffusion around the connection of firns with distinctly
different isotopic composition. The firn was, in fact, crushed ice. They
used densities between 580 and 760 kg m-3. Both the Schwander et
al. (1988) results and those by Jean-Baptiste et al. (1998)
have thus been performed for higher densities only. Using the
Schwander et al. (1988) parameterization by
Johnsen et al. (2000) for our experiment, with densities varying from 300 to
350 kg m3, means a substantial extrapolation.
More recent measurements of firn diffusivity are presented in studies by
Pohjola et al. (2007) and by van der Wel et
al. (2011a). Both studies have improved on the work by
Jean-Baptiste et al. (1998), since they
have identified the interface between the two stacks with different isotopic
composition as the weak spot of such experiments. By connecting several
layers of different thickness, they could identify possible problems with
these interfaces, for example when such an interface was much more porous
than the bulk material. Due to these effects, the results by
Pohjola et al. (2007), at a density range of 480–500 kg m-3,
did not produce consistent results for the tortuosity.
Van der Wel et al. (2011a), however, managed
to make an ideal multi-layer snow stack (produced with the same snow gun
that we used in the present study). At a density of 415 kg m-3, they
were able to fit their diffused isotope profiles using the expression by
Johnsen et al. (2000), thereby finding a tortuosity of 1.18 ± 0.08
(compared to the value 1.36 that follows from Eq. 9).
Whereas this latter piece of information indicates tortuosity values hardly above 1
for low densities, various gas diffusion measurements show considerably
higher values. Fabre et al. (2000) performed gas
diffusivity measurements on site in Vostok, Antarctica, and at an alpine
site (Col du Dome). They express their results in the same fashion as
Schwander et al. (1988) (they also show their results for comparison) and
also give various model results for the tortuosity.
Albert and Shultz (2002) performed detailed gas
diffusivity and permeability measurements on the top 10 m of snow and
firn at Summit station. They mention the tortuosity, defined in their paper
as the reciprocal from our Eq. (13) as a side result, and quote the
value of ∼ 0.5 for the top layer of the snow. When looking at their
data, however, it seems that they used a different definition for the
tortuosity and actually determined the ratio Ωf/Ωa
to be 0.5. In more recent work by the same group, they avoid the
term tortuosity altogether and instead report on the Ωf/Ωa ratio.
Adolph and Albert (2013) describe an improved way to measure gas diffusivity
through firn, and they report a series of diffusion measurements performed
on firn from Summit. From the results in their Table 1 (in which they also
quote their previous result from 2002) we can deduce the tortuosity as
defined in Eq. (13). A subsequent paper by the same authors
(Adolph and Albert, 2014) reports on even more diffusivity measurements
(and includes the ones reported in 2013).
Recently several large firn gas transport studies were published, one of
them (Buizert et al., 2012) concentrating on the
NEEM site in northern Greenland. These authors tuned six firn air transport
models to firn concentration measurements of a set of 10 reference trace
gases. Whereas the fit quality of the tracer concentrations is high, for the
upper 4.5 m the fit is underdetermined, and the spread of the molecular
diffusivity profiles for CO2 is large. Furthermore, convective mixing
plays a role in modelling these upper 4.5 m, a process that influences
gas transport far more than the firn itself (see below). In direct firn gas
diffusion experiments convective mixing is avoided, making such results more
useful for describing firn diffusivity.
We give an overview of the tortuosity from all these results, according to
our Eq. (13), in Fig. 9. This figure includes the tortuosity by
Cuffey and Steig (1998), which follows from Eq. (15),
and the parameterization for the Schwander et al. (1988) data used by
Johnsen et al. (2000) (and thus also by us in the previous chapters).
Furthermore, as a lower limit, we have included the theoretical result by
Weissberg (1963), which he derived for spheres that can
partly overlap or even fuse:
ΩfΩa=ϕ1-12ln(ϕ).
Using Eq. (13) this is equivalent to
τ=1-12ln(ϕ).
Looking at Fig. 9, we observe large scatter indeed. In the higher-density
region the tendency towards higher values for τ is clear, but there is
a considerable discrepancy between the Schwander et al. (1988) values (based
on CO2 and O2 diffusion through firn from Siple Dome, Antarctica)
and the Fabre et al. (2000) ones (Vostok, Antarctica, and the Col du Dome
alpine site based on SF6 and CO2 diffusion) on the one hand and
the results by Adolph and Albert (2014) (using SF6
diffusion through firn from Summit station) on the other. Although the
Adolph and Albert (2014) results show some
higher values, in general their results for τ are much lower
Figure 6
in Adolph and Albert (2013) suggests the opposite. This is, however, because the authors interpreted the
results in Table 1 of Schwander et al. (1988) as Ωf, whereas
they are in fact Ωf/φ (A. C. Adolph, and J. Schwander,
personal communication, 2014).
, and thus the diffusion process would occur more rapidly. The
real firn vapour diffusivity experiments by Jean-Baptiste et al. (1998), especially the
highest density measurement, seem to corroborate the Schwander et al. (1988)
and Fabre et al. (2000) results. Furthermore, as is clear from
the work of Cuffey and Steig (1998), the total firn
diffusion process on Summit can be described using their parameterization,
which is not very different from the Schwander et al. (1988) measurements,
and the Johnsen et al. (2000) parameterization.
Results of various tortuosity measurements from the literature, with
τ defined according to our Eq. (13). The symbols are the results
of the various measurements: the red squares are laboratory firn diffusion
measurements (by Jean-Baptiste et al., 1998, and van der Wel et al., 2011a); the blue circles CO2 and
O2 gas diffusion measurements through firn from Siple dome, Antarctica
(Schwander et al., 1988); and the green triangles SF6 gas diffusion
measurements through firn from Summit (Adolph and
Albert, 2013, 2014). Finally pale brown triangles are the results by
Fabre et al. (2000) for SF6 gas diffusion in Vostok and Col du
Dome. The black dash-dotted line is the parameterization for the Schwander
et al. (1988) data in the Johnsen et al. (2000) model. The grey dashed curve
is the tortuosity that is equivalent to the fit that Cuffey and Steig (1998) made to isotope seasonal
cycles in the Summit firn layer. Furthermore, as a lower limit, we have
included the theoretical result, interpreted as τ, by
Weissberg (1963), which he derived for spheres that can
partly overlap or even fuse. For discussion of the results, see text.
However, the Adolph and Albert (2014) results
also suggest higher values for τ at lower densities. This is in
contrast with the only firn vapour measurement at low densities by
van der Wel et al. (2011a) that gives a value that is
lower than the Weissberg (1963) theoretical model. In
contrast to that, the Adolph and Albert (2014)
results suggest that a higher tortuosity in the low-density region of
≈ 1.5 is probably a better choice than the low values given by the
extrapolation of the Johnsen et al. (2000) parametrization. The value range
of 2.5–3, however, that we need to fit our data, is not supported by any
data in the low-density range. In Fig. 7, we show the numerical results
for σ using a fixed tortuosity of 1.6. Whereas for the first year
agreement is reasonable, in the following years the deviation increases: in
the experiments, diffusion is slowing down, and this is unlikely to be
caused by tortuosity (or density) increases.
The clearest conclusion of all, however, is that the parameterization of
τ as a function of density (or porosity) is an oversimplification.
Albert and Shultz (2002) show the structural
changes of the fresh snow in its first years: whereas the density hardly
changes, grain size rapidly grows, and the permeability (and likely also the
diffusivity) increases. In that paper, they report a single diffusivity
result (included in Fig. 9) on the top 20 cm of the firn, yielding τ= 1.36
for ρ= 326 kg m-3. This suggests that, for the youngest
firn, time since deposit is a more important parameter than density.
Furthermore, τ will have a different course in time for winter than
for summer snow.
All in all, we conclude that for the simulation of our experiment, choosing
a τ of ≈ 1.6 would be a fair choice given the data available,
but a value range of τ= 2.5–3, needed to fit our data using the
Johnsen et al. (2000) simulation, is not plausible.
Isotope homogeneity within the firn grains
In the model by Johnsen et al. (2000), several assumptions have been made:
the effects of firn ventilation are negligible,
there is continuous isotopic equilibrium between the ice grain surfaces and the
vapour,
the ice grains themselves remain isotopically homogeneous.
One or more of these issues have been addressed by several authors, among whom Whillans and
Grootes (1985), Jean-Baptiste et al. (1998),
Johnsen et al. (2000) themselves and Neumann and
Waddington (2004). The latter paper describes a very detailed numerical
model in which in the first place the influence of firn ventilation is
quantified. They conclude that isotope exchange in the upper few metres is
more rapid than follows from models such as that of Whillans and Grootes (1985)
and Johnsen et al. (2000). However, they also state that the
ventilation process is especially important in low-accumulation zones, such
as the Antarctic Plateau. For the Summit site, its influence will probably
only be marginal. Moreover, whereas firn ventilation might lead to changes
in the overall isotopic composition, its character will not be the same as
diffusion; especially it will not influence the diffusion pattern, and thus
the diffusion length fit, of our enriched layer.
The model by Neumann and Waddington (2004) also
allows for a disequilibrium between the ice grain surface and the vapour.
Although the isotope exchange rate is not well known, they conclude that the
ice phase is not in isotopic equilibrium with the vapour at any depth in the
firn. This effect would slow down the influence of diffusion. Somewhat
surprisingly, however, these authors assume the grains themselves to be and
remain isotopically homogenous. This is in fact the point that the other
authors touch upon. Isotope diffusion in ice, and thus inside the grains, is
10 orders of magnitude smaller than vapour diffusion through air. At
-20 ∘C, for example, the solid-ice diffusivity is about
1 × 10-15 m2 s-1 (Whillans and Grootes, 1985), whereas vapour diffusion
through air, according to Eq. (6) (Hall and Pruppacher,
1976), yields 2.7 × 10-5 m2 s-1 at Summit. In contrast, the water
molecules spend 5 to 6 orders of magnitude more time in the solid than in
the vapour phase (depending both on temperature and density of the firn).
Both Whillans and Grootes (1985) and Johnsen et al. (2000) have incorporated
this into their model by dividing the free vapour diffusion rate by this
residence time ratio. Nevertheless, the solid-ice diffusivity remains some 5
orders of magnitude slower than the effective vapour diffusion. Whillans and
Grootes (1985) have investigated this and concluded that, given the average
size of the firn grains, the isotopic homogeneity assumption is valid.
Jean-Baptiste et al. (1998), however, show in a
numerical model that their model description of their firn diffusion
experiment would indeed be influenced for grain sizes of 1mm and larger.
Johnsen et al. (2000) conclude that grain homogeneity will not occur based
on ice diffusion alone “for the coarse grained (2 mm) summer layers”. As
they on the other hand conclude from observations that the isotopic seasonal
cycle can disappear completely due to diffusion, they propose grain boundary
migration as a different mechanism for more rapid grain isotope homogenization.
The ratio between the effective firn vapour diffusion and solid-ice
diffusion is the largest for low densities, as then the solid-to-vapour
residence time ratio is the lowest. These are the circumstances of our
experiment. Furthermore, the detailed microstructure experiments by
Albert and Shultz (2002) show substantial growth
of grain size in the first years after deposition. Together, these
circumstances will probably cause a substantial inhomogeneity in the ice
grains, thereby slowing down diffusion to below the rate described by Eq. (4).
Conclusions and outlook
With this experiment, we have observed isotope diffusion in the natural
setting of Summit in the first 4 years after deposit down to about 3 m
depth. The idea of determining the diffusion length as the Gaussian
width of an initial thin layer substantially enriched in deuterated water
worked very well indeed. The results, however, indicate a substantially
lower diffusivity than expected based on the well-established model by
Johnsen et al. (2000). Our attempt to explain this difference brought us to
the following conclusions:
Although we can not be fully sure whether the characteristics of the enriched
layer itself, with some local ice formation, has slowed down the diffusivity,
it is very likely that the diffusion lengths we have obtained resemble the
true diffusivity of deuterated water in the upper layers of Summit firn,
because the diffusion takes place in the original snow layers after some time.
Tortuosity is in general poorly characterized. Several of the firn and gas
diffusion experiments over the years lead to a very scattered total picture.
The parametrization used by Johnsen et al. (2000) is probably not correct for
Summit; based on recent gas diffusion experiments by Adolph and Albert (2014),
tortuosity is probably considerably larger in the uppermost layers,
but in contrast not as large in the deeper firn. Density is a poor measure
for tortuosity, certainly in the upper metres of firn, and considerable
differences between summer and winter layers are likely to exist.
Nevertheless, the discrepancy between our results and the Johnsen et al. (2000)
model cannot be explained by higher tortuosity alone, as the value
that would be needed to fit our data is definitely outside the plausible range.
It is likely that isotopic inhomogeneity exists within the ice grains in the
firn, as the vapour diffusion process is orders of magnitude faster than
solid-ice diffusion. This effect is only partly compensated by the much
longer residence time of the molecules in the solid phase. This
inhomogeneity, and its slowing effect on diffusion, depends critically on
grain size. In the first years after snow deposition, grains tend to grow
(Albert and Shultz, 2002), thereby effectively slowing down diffusion. Of the
three possible causes for the discrepancy between our data and the
simulations, isotopic inhomogeneity is thus the most plausible: it would
explain why gas diffusion measurements (and thus also the parameterization
used by Johnsen et al., 2000) are not entirely valid for firn vapour
diffusion. In the first stage of the diffusion process, the part that our
experiment monitors, ice grain inhomogeneity would slow down the diffusion
process, but in a later stage the inhomogeneity would diminish or even
disappear again. Combined with lower values for the tortuosity at greater
density (such as for instance those by Adolph and Albert, 2014) the total
integrated diffusivity would still fit to the well-known isotope signals in
the ice. To prove (or disprove) this hypothesis, a new model framework needs
to be developed to incorporate grain inhomogeneity into the model.
Jean-Baptiste et al. (1998) and especially Neumann and Waddington (2004) have
shown pathways towards such models.
Although the model by Johnsen et al. (2000) has been used extensively and
successfully, this has to our knowledge never been done in the amount of
detail we present. Rather, it has been used to describe the integrated
diffusion over the entire firn phase, expressed as the total diffusion length
caused by it. This integrated diffusion length is a rather forgiving
parameter: it does not matter whether the diffusion length grows rapidly
initially and then slows down, or if it increases more steadily over the
years. Moreover, due to compaction the diffusion length even decreases again,
although the diffusion effects (such as the decrease of the amplitude of the
seasonal cycle) of course are not lessened. According to the model, the major
part of the diffusion length is built up in just the upper 10 m (see
also Simonsen et al., 2011), and the maximum values are achieved around 30 m
depth; from then onwards, the compaction leads to a gradual decrease
in diffusion length. These features of the model have, to the best of our
knowledge, never been checked experimentally.
An experiment to perform such a decisive test would consist of two parts:
first is the high-resolution (typically 2 cm) isotope measurement of the
upper ≈ 30 m of a firn core. With a modern, laser-based
isotope measurement system on-site, this would probably be feasible in just
one summer season. If designed carefully, this set-up delivers the density
of the firn as well. Second is reconstruction of the input function: the
temperature, the precipitation events and – ideally – their isotopic
composition. In this way, the “virtual ice core” approach (van der Wel et al., 2011b) can be followed
to reconstruct the non-diffused firn profile, and, by comparing that profile
to the data, diffusivity can be calculated with high temporal/spatial
resolution. The results can then be compared to the output of the Johnsen et
al. (2000) model, and to a model containing both the firn diffusion and the
diffusion inside the grains. A valuable additional measurement would be
isotope measurements on vapour in firn air at various depths. In this way
the isotopic (dis)equilibrium could directly be assessed.
Summit would be the ideal spot for such an experiment: it has been in
operation since 1988, and surface temperature and precipitation amounts have
been logged since then. Furthermore, many scientific experiments run at
Summit each year, many of them including stable isotope measurements.
Such a detailed study would finally enable us to describe isotope diffusion
in firn in a reliable, quantitative way. The results of such a study would
especially be crucial for the use of differential diffusion to reconstruct
palaeotemperatures: the way the diffusion process behaves through the firn
layer determines the weighted average of the temperature that is conserved
in the differential diffusion signal. If the upper-few-metre diffusion is
less prominent than the Johnsen et al. (2000) model suggests, this weighted
average would be far less sensitive to the high summer day temperatures than
is assumed at present.
Acknowledgements
A substantial part of this project has been funded by the polar programme of
the Netherlands Organisation for Scientific Research (NWO) with project
numbers 851.30.015, 851.30.22 and 851.20.038-B, for which support we are grateful.
Staff and crew from CH2MHill Polar Services at Summit and Kangerlussuaq are
thanked for their enthusiastic and skilful assistance over the years. The
NSF is thanked for granting us access to the fantastic Summit infrastructure.
Thanks to Henk Snellen and Ellen den Ouden for their assistance in the
field. Laboratory technicians Berthe Verstappen, Janette Spriensma and Henk Jansen
are acknowledged for the isotope analyses, and Jenny Schaar for
assisting with the numerical code.
Edited by: J.-L. Tison
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