Commonly, three mechanisms of firn air transport are distinguished: molecular
diffusion, advection, and near-surface convective mixing. Here we identify
and describe a fourth mechanism, namely dispersion driven by synoptic-scale
surface pressure variability (or barometric pumping). We use published gas
chromatography experiments on firn samples to derive the along-flow
dispersivity of firn, and combine this dispersivity with a dynamical air
pressure propagation model forced by surface air pressure time series to
estimate the magnitude of dispersive mixing in the firn. We show that
dispersion dominates mixing within the firn lock-in zone. Trace gas
concentrations measured in firn air samples from various polar sites confirm
that dispersive mixing occurs. Including dispersive mixing in a firn air
transport model suggests that our theoretical estimates have the correct
order of magnitude, yet may overestimate the true dispersion. We further show
that strong barometric pumping, such as at the Law Dome site, may reduce the
gravitational enrichment of

The firn layer is the upper 50–120 m of consolidating snow found in the
accumulation zones of ice sheets and glaciers. Within this perennial snowpack
a network of connected pores exists that facilitates the movement of air. The
firn layer is a mixed blessing. On the one hand it complicates the
interpretation of ice core records via the gas age–ice age difference

Commonly, firn air transport models include three mechanisms of air movement

Diffusion effectively ceases at the lock-in depth, and consequently there is
no gravitational enrichment within the lock-in zone

The

Steady viscous fluid flow through a disordered porous medium leads to
dispersion

On the macroscopic level, dispersion can be described as a diffusive process
with a diffusivity

In this work we shall use published gas chromatography experiments by

Schematic depiction of dispersion. Fluid movement through a microscopically homogeneous, low-tortuosity porous medium (upper panel) is non-dispersive; fluid movement through a microscopically disordered porous medium (lower panel) disperses tracer molecules. Macroscopic fluid flow is from left to right.

Here we present a mathematical description of air pressure dynamics in polar firn, aimed towards understanding firn air movement in deep firn in response to surface pressure variations.

In hydrostatic equilibrium the firn air pressure

The continuity equation for macroscopic air movement within the firn is

Propagation of pressure variations into the firn at WAIS Divide.

Substituting Darcy's law into the continuity equation yields

Equation (

The approximation in Eq. (

In the numerical solutions presented here, Eq. (

In a first experiment we force the model with an atmospheric pressure

The response curves of Fig.

The firn transfer function of Fig.

Firn air pressure response at the WAIS Divide site.

The pressure variations described above are associated with net macroscopic
air movement in the firn column, a phenomenon known as barometric or
atmospheric pumping

The

Another source of macroscopic air movement in deep firn is the gradual
closure of the pore space by the densification process, which leads to an
upward air flow relative to the firn matrix

Here we revisit the published firn diffusion experiments by

Firn dispersivity.

The results at four representative sampling depths are shown in
Fig.

The slope of the fit represents

The firn dispersivity data are plotted in Fig.

Propagating the 95 % confidence intervals on the

Multiplying the experimental

The dispersivity

In this section we use the theoretical estimates of dispersive mixing
strength in a firn air model to investigate whether it is consistent with the
measured trace gas concentrations in air samples extracted from the pore
space. We use the NEEM

Next, using the CIC firn air model

The firn air data indicate that WAIS Divide has more dispersive mixing than NEEM, as also predicted by our
theoretical calculations. This should thus be considered a robust result.
While the theoretical estimates are of the correct order of magnitude, they
appear to overestimate the dispersion suggested by observed trace gas
concentrations. There may be several causes for this mismatch. First, to fit
the same tracer data, different firn air transport models require slightly
different diffusivity profiles

A site with strong barometric pumping is the Law Dome site in coastal eastern
Antarctica, where firn air has been sampled at the high-accumulation DE08
site

Model simulations and firn air data for the Law Dome
DSSW20K

A remarkable property of both Law Dome sites is that LIZ gravitational

In the first scenario (blue curves), we have eliminated both near-surface
convection and deep-firn dispersion to show the

In the third scenario (yellow curves), we attempt to fit the

Diffusion and dispersion in layered firn.

In all modeling scenarios so far we have assumed that molecular diffusion and
dispersion are both one-dimensional processes that vary smoothly with depth
and that occur independently without interactions between them. In reality, the pore space
is a three-dimensional network that is strongly impacted by density layering

Next we attempt to capture the dynamics of such a layered firn in our
one-dimensional model. In our fourth modeling scenario (green curves), we use
an idealized layered firn model, with alternating annual bands of diffusive
and dispersive mixing; details are shown in Fig.

Synoptic-scale barometric pumping strength for Greenland and
Antarctica using 6-hourly ERA-Interim reanalysis surface pressure values for
the period 1 January 2010 through 31 December 2011. The color scale gives the
root mean square of the pressure rate of change

There are probably three factors that contribute to the magnitude of
dispersive mixing at any given site.

The NEEM and WAIS Divide sites have comparable firn thickness and density
layering, and therefore the stronger barometric variability at the WAIS
Divide site results in stronger dispersive mixing at that site
(Fig.

Dispersive mixing influences the ice core record in several ways, the most
important of which is via the broadening of the gas age distribution. A
comparative firn model study at the NEEM site showed that the low-diffusion
lock-in zone environment contributes more to the broadening of the final age
distribution than the diffusive zone does

Dispersive mixing potentially has implications for the use of

The degree of isotopic gravitational enrichment of any given gas species in
the firn depends on the relative strength of molecular diffusion, which acts
to drive isotopic enrichment towards gravitational equilibrium, and
macroscopic transport processes (convection, advection and dispersion), which
act to erase the enrichment. Slow-diffusing gases such as krypton (Kr) and
xenon (Xe) will therefore always be less isotopically enriched than
fast-diffusing gases such as N

Here we define

Figure

Measurements on the WAIS Divide ice core

We propose here that

In this work we show that surface pressure variability on synoptic timescales
drives macroscopic air movement in the deep firn, which in turn leads to
dispersion of trace gases in the firn open porosity. The work resolves an
outstanding question regarding the nature of lock-in zone mixing deduced from
detailed firn air experiments at the north Greenland NEEM site

We present a mathematical description of the propagation of pressure
anomalies in polar firn. We find that pressure variations on the timescale of
order 1 h or slower are propagated to the firn–ice transition at full
amplitude; variations on shorter timescales are attenuated. Net
barometrically driven air movement is on the centimeter scale in the deep
firn, and on the meter scale in the upper firn; mean velocities are of the order of

We use published firn sample gas chromatography experiments to estimate the
dispersivity

We apply these theoretical estimates of dispersion in a firn air transport
model, and find that they overestimate the amount of lock-in zone
dispersivity needed to optimize the fit to firn air trace gas measurements;
this mismatch may be due to the fact that our firn dispersivity
parameterization is based on steady-flow conditions, whereas barometric
pumping induces a time-variable flow. We suggest that strong dispersive
mixing at Law Dome, Antarctica, in combination with firn layering, may halt
gravitational enrichment in

The dispersive mixing discussed here increases scientific understanding of
firn air transport, and has direct implications for the modeling thereof. The
ice core record is impacted by dispersive mixing primarily through the
widening of the gas age distribution. We propose that

NEEM and WAIS Divide firn air data are available with the original
publications

The authors wants to thank Roy Haggerty for fruitful discussions, the European Centre for Medium-Range Weather Forecasts (ECMWF) for making ERA-Interim reanalysis datasets publicly available, and the US National Science Foundation for financial support under NSF grant numbers ANT-0944343, ANT-1543267, and ANT-1543229. The authors appreciate the support of the University of Wisconsin–Madison Automatic Weather Station program (in particular Matthew Lazzara and Linda Keller) for the dataset, data display, and information, NSF grant number ANT-1245663. The authors hereby propose as a golden rule of ice core science: any time you have a new idea, Jakob Schwander already had that same idea several decades earlier. Edited by: Eric Wolff Reviewed by: C. Trudinger and one anonymous referee