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\begin{document}

%\linenumbers

\title{Novel Threshold Behavior of Fluid Transport in Antarctic Sea Ice}


\author[1]{K. M. Golden}
\author[1]{A. Gully}
\author[2]{J. L. Tison}

\affil[1]{University of Utah, Department of Mathematics, 155 S 1400 E RM 233, Salt Lake City, UT $\;$ 84112-0090 $\;$ USA}
\affil[2]{Laboratoire de Glaciologie, CP 160/03, Universit\'{e} Libre de Bruxelles, 50, av. F. D. Roosevelt, 1050 - Bruxelles, Belgium}

%% The [] brackets identify the author to the corresponding affiliation, 1, 2, 3, etc. should be inserted.



\runningtitle{Novel Threshold Behavior of Fluid Transport in Antarctic Sea Ice}

\runningauthor{Golden et al.}

\correspondence{Professor Kenneth M. Golden \\ golden@math.utah.edu}



\received{}
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\firstpage{1}

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\begin{abstract}
Fluid flow through porous sea ice mediates a broad range of processes
which are critical to predictions of climate change, and the response of
polar ecosystems. We have made the first measurements 
of fluid permeability in Antarctic pack ice, and find that the 
granular sea ice there leads to strikingly different fluid transport 
behavior than in the Arctic. 
In particular, granular ice exhibits a percolation threshold,
the on$-$off switch for fluid transport,
for brine volume fractions around 10\% or higher, 
rather than 5\% observed in columnar ice.    
Tracer experiments on extracted sea ice blocks further support these results.  
%%%%%%%
%In addition, we speculate on the percolation threshold of different ice types based on compressed powder models. 
%%%%%%
Our findings shed new light on key processes such as
snow-ice formation, melt pond evolution, CO$_2$ exchanges, and nutrient
replenishment, and their parameterizations in global climate and
biogeochemical models.
\end{abstract}

%
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%\abstract{
% TEXT
% \keywords{TEXT}}
%


\introduction  %% \introduction[modified heading if necessary]
The polar sea ice packs form a key component
of Earth's climate system, and are sensitive   
indicators of climate change
\citep{Thomas:2008:SI,Serreze:S-1533}.
%\citep{Untersteiner:1986-GSI,Jeffries:1998:ASI,Untersteiner:1990:SDA,%
%Kattenberg:1986:GSP,Serreze:2000:OER,Sturm:SA-2003,Perovich:1999:YIG}.
They also host extensive algal and bacterial communities which sustain 
life in the polar oceans
\citep{Thomas:2008:SI,Fritsen:S-782}.
%\citep{Thomas:2003:SI,Fritsen:S-782,Lizotte:1998:ASI,Eicken:PB-3}. 
While global climate models generally predict declines in polar sea ice, 
they have significantly underestimated the dramatic losses observed 
in the summer Arctic ice pack \citep{Stroeve:GRL-2007,Boe:2009:NG}. 
On the other hand, 
Antarctic sea ice has increased overall, 
along with some significant regional losses
\citep{Zwally:2002:JRG,Zhang:2007:JC}.
 
Our focus here is on key sea ice processes that must be better understood
to improve the predictions of climate models and the future
of the polar ice packs, as well as the microbial communities that live there.
In particular, fluid flow
through porous sea ice helps control
the evolution of melt ponds and ice pack albedo \citep{Eicken:JGR-C08007}, 
brine drainage and the evolution of salinity profiles \citep{Weeks:1986:GSP,Eicken:GMP-02}, 
snow-ice formation, where sea water floods the 
ice surface and then freezes \citep{Maksym:JGR:2000,Powell:JGR-18327}, 
ocean-ice-atmosphere CO$_2$ exchanges \citep{Rysgaard:JGR:2009},
convection-enhanced thermal transport
\citep{Lytle:JGR-8853,Trodahl:JGR-11358}, 
and biomass build-up fueled by nutrient fluxes
\citep{Thomas:2008:SI,Fritsen:S-782,Lizotte:1998:ASI,Eicken:PB-3}.
For example, it is believed that ice-albedo feedback has played a 
significant role in the declines observed in the Arctic
\citep{Perovich:GRL-2008}. Snow-ice formation, on the other hand, 
may have helped in thickening the Antarctic sea ice pack
\citep{Maksym:JGR:2000,Powell:JGR-18327}, and may become
more important in the Arctic with increased precipitation
and thinning ice, so that it is more susceptible to flooding.


\begin{figure*} [t]               %\centering
\vspace*{2mm}
\begin{center}
\includegraphics[width=6cm]{Figure1chap6.eps}
\end{center}
   \caption{Comparison of {\it in situ} data on 
            the vertical fluid permeability $k$ (m$^2$) of 
            Antarctic sea ice (37 diamonds) 
           with a rigorous upper bound.}         
    \label{data_lognormal_pipe_bound}
       
\end{figure*}








The fluid permeability of sea ice, which depends strongly on its
brine microstructure, plays a key role in understanding
such processes, and in parameterizing them in large-scale models.
To date, columnar microstructures have received 
disproportionate attention, mostly due to their prevalence 
in Arctic sea ice and their importance in undisturbed ice growth 
\citep{Weeks:1986:GSP,Eicken:GMP-02,Light:2003:ETM}.
However, granular microstructures, which lack 
intragranular inclusions and exhibit a film of brine enveloping 
individual grains, are particularly important for
processes which are relevant to climate studies.
For example, granular ice is common in surface layers
in the Arctic \citep{Perovich:JGR-18327,Perovich:JGR:2009}, 
which directly underly the melt ponds 
controlling ice albedo.  
%It is potentially significant that 
Examination of the crystalline structure in sea ice from a 
recent trans-Arctic survey \citep{Perovich:JGR:2009} 
showed a striking increase in overall granular ice fraction, 
of just over 40\% compared to previous
observations of around 10\% \citep{Tucker:JGR:1999}.
In the Antarctic it has long been observed that 
granular ice
\citep{Jeffries:1994:AJ,Worby:1995:RR,Eicken:1998:AARS,%
Maksym:JGR:2000},  
accounts for a fraction of up to around 40\%
of the sea ice pack. Snow-ice in particular, with
granular microstructure itself, accounts for over a quarter
of the ice found in the Southern Ocean, with much higher
fractions in some regions \citep{Maksym:JGR:2008}. 
An accurate accounting of
%Incorporating snow-ice formation, melt pond evolution, gas exchanges,
%nutrient replenishment, and other 
sea ice processes involving fluid
flow in climate and biogeochemical models
relies on knowledge of the fluid permeability
of granular ice.





In \citep{Golden:S-2238} it was observed that
for brine volume fractions $\phi$ below about 5\%, columnar sea ice
is effectively impermeable to fluid flow, yet is increasingly permeable
for $\phi$ above 5\%. For a typical bulk salinity
of 5 ppt, this critical brine volume fraction
$\phi_c \approx 5\%$ corresponds to a critical temperature 
$T_c \approx -5^{\circ}$ C, which is known as the {\it rule of fives}.
The critical brine volume fraction was explained in terms of
the {\it percolation threshold} in a continuum model for 
compressed powders which has been used to understand the 
behavior of stealthy or radar absorbing materials.
In \citep{Golden:2007:GRL} a comprehensive theory for the
vertical fluid permeability $k(\phi)$ of columnar sea ice
was developed, and validated experimentally with
laboratory and Arctic field data. 
Micro-scale imaging methods based on 
X-ray computed tomography (CT) and 
pore structure analysis 
were also developed to provide detailed pictures of the brine
microstructure and the evolution of its 
connectivity with temperature \citep{Golden:2007:GRL,Pringle:JGR:2009}.


%Here, the novel behavior we find in the percolation threshold for fluid
%transport in granular ice is explained in terms of the compressed
%powder model \citep{Kusy:JAP-5301,Kusy:N-58}. By measuring the
%relative dimensions of the ice grains and the fluid inclusions
%in photomicrographs of granular sea ice, we obtain
%a percolation threshold of around 10\%, with the possibility 
%of even higher thresholds for more finely grained microstructures.  

%With this new percolation threshold, traditional percolation models are then applied to {\it in situ} Antarctic permeability data with excellent agreement.  Further, tracer studies are presented that vividly demonstrate a 10\% percolation threshold for granular ice.  






During September and October of 2007, we measured the
fluid permeability of first year Antarctic pack ice as participants
in the Australian Sea Ice Physics and Ecosystem Experiment (SIPEX),
aboard the icebreaker {\it Aurora Australis}. 
The study area was located off the coast of East Antarctica, between
115$^{\circ}$ E and 130$^{\circ}$ E, and 64$^{\circ}$ S
and 66$^{\circ}$ S. Permeability measurements were made at 8 of the
15 ice stations along the cruise track of the {\it Aurora}, and
we obtained 38 data points covering a range of depths, temperatures, 
salinities, and ice types. Full length cores were taken nearby
by our colleagues, usually
within a few meters of our location, and were later 
subjected to crystallographic and other analyzes. 
When we separated out the permeability data that were 
likely being influenced primarily by granular microstructures, 
we found that the critical threshold for fluid flow had
effectively doubled to around $\phi_c \approx 10\%$.
For a typical salinity of around 5 ppt, the corresponding critical
temperature is around $T_c \approx -2.5^{\circ}$ C
\citep{Frankenstein:JG-943}. Moreover, as predicted
by our percolation theoretic analysis in \citep{Golden:2007:GRL},
we find here that the {\it universal} lattice critical exponent of about 2 
for columnar ice in the Arctic still accurately describes the take-off 
of $k(\phi)$ above the threshold $\phi_c$ for granular sea ice
in the Antarctic.



The novel behavior we find in the percolation threshold for fluid
transport in granular ice is explained in terms of the compressed
powder model \citep{Kusy:JAP-5301,Kusy:N-58}. By measuring the
relative dimensions of the ice grains and the fluid inclusions
in photomicrographs of granular sea ice, we obtain
a percolation threshold of around 10\%, with the possibility 
of even higher thresholds for more finely grained microstructures.

We also extracted blocks of sea ice with a chain saw, 
turned them upside down, and poured cooled tracers into shallow channels
cut into the top surface of the block (which is actually the sea ice bottom).
Thin vertical slices were cut from blocks, which exposed the fluid fronts,
layers of different microstructures, and brine channels.
The tracers easily penetrated a highly permeable bottom layer, but stopped
when the fluid reached a depth characterized by a brine volume fraction
of about 10\%. 

%
%
%The novel behavior we find in the percolation threshold for fluid
%transport in granular ice is explained in terms of the compressed
%powder model \citep{Kusy:JAP-5301,Kusy:N-58}. By measuring the
%relative dimensions of the ice grains and the fluid inclusions
%in photomicrographs of granular sea ice, we obtain
%a percolation threshold of around 10\%, with the possibility 
%of even higher thresholds for more finely grained microstructures.

\begin{figure*} [t]               %\centering
\vspace*{2mm}
\begin{center}
\includegraphics[width=12cm]{Figure2chap6.eps}
\end{center}
   \caption{Microstructures of columnar ice in {\bf(A)} and granular ice in {\bf(B)}. 
            In {\bf(C)} we display the percolation threshold in the compressed powder
            model as a function of the ratio of the particle radii.}         
    \label{crystalline_microstructures}
       
\end{figure*}



\section{Analysis and Results}

We consider low Reynolds number flow of
brine of viscosity $\eta$ through sea ice.
The volume fractions of brine and ice are 
$\phi$ and $1-\phi$. 
The velocity and pressure fields in the brine
satisfy the Stokes equations for incompressible fluids.
Under appropriate assumptions 
\citep{Torquato:RHM-02},
the homogenized velocity $\vv(\xx)$ and pressure $p(\xx)$
satisfy Darcy's law and the incompressibility condition for the
velocity,
\begin{equation}
 {\vv} = - \frac{1}{\eta} \; \kk \; \nabla p,  \;\;\;\;\;\;\;
\nabla \cdot \vv = 0, 
\end{equation}
where $\kk$ is the permeability tensor, 
with vertical permeability k$_{zz}=k$ in units of m$^2$.






The {\it in situ} permeability data were collected using 
a hydrological bail test \citep{Freitag:JG-349}, where  
partial cylindrical holes were drilled vertically into 
the sea ice, and the cores removed. 
As water filled the hole, equilibrating to a known freeboard level, 
time series measurements 
of the height $h(t)$ of the rising water column or hydraulic head 
were taken, with $h$ in meters (m) and $t$ in seconds (s).   
The permeability of the ice underneath the borehole can be 
accurately estimated using the equation 
\begin{equation}                                 \label{eq2.2}
h(t) =  h(t_{0}) e^{-k_{exp}t(g\rho /\eta L)},
\end{equation}
with measured permeability $k_{exp}$ (m$^{2}$), 
ice thickness beneath the borehole $L$ (m), density $\rho$ (kg  m$^{-3}$), 
gravitational constant $g$ (m  s$^{-2}$), and initial time $t_0$.
To obtain the vertical component $k$ of the permeability, the data were corrected 
in two ways, using calculations in \citep{Freitag:JG-349}. First, we excluded 
the contribution from horizontal flow through the cylindrical sides of the holes, 
assuming a 10:1 ratio
of vertical to horizontal flow in sea ice \citep{Freitag:JG-349}. 
Then, based on simulations of the fluid
pressure field in the ice \citep{Freitag:JG-349}, we estimated the flow through
the bottom of the hole due exclusively to upward vertical flow directly beneath
the hole, yielding our measurements of the vertical permeability $k$ of sea ice.





%\begin{figure} [t]               %\centering
%\vspace*{2mm}
%\begin{center}
%\includegraphics[width=7cm]{Figure1chap6.eps}
%   \caption{Comparison of {\it in situ} data on 
%            the vertical fluid permeability $k$ (m$^2$) of 
%            Antarctic sea ice (37 diamonds) 
%           with a rigorous upper bound.}         
%    \label{data_lognormal_pipe_bound}
%       
%\end{figure}


%\begin{figure}[t]
%\vspace*{2mm}
%\begin{center}
%\includegraphics[width=8.3cm]{FILE NAME}
%\end{center}
%\caption{TEXT}
%\end{figure}



%
%We also extracted blocks of sea ice with a chain saw, 
%turned them upside down, and poured cooled tracers into shallow channels
%cut into the top surface of the block (which is actually the sea ice bottom).
%Thin vertical slices were cut from blocks, which exposed the fluid fronts,
%layers of different microstructures, and brine channels.
%The tracers easily penetrated a highly permeable bottom layer, but stopped
%when the fluid reached a depth characterized by a brine volume fraction
%of about 10\%. 




Rigorous bounds on bulk properties 
of composites, such as sea ice, provide benchmarks
which are useful in assessing data, and in connecting effective behavior
to mixture geometry \citep{Torquato:RHM-02}. 
In previous work \citep{Golden:2007:GRL,Golden:MM-801} 
we found rigorous upper bounds for $k$ based on an observed lognormal
distribution for the horizontal cross-sectional areas $A$ of 
of the brine inclusions \citep{Perovich:JGR-18327}.
In this case $Z=\ln{A}$ has a normal probability density
with mean $\mu$ and variance $\sigma^2$,
\begin{equation}                  \label{lognormal_distribution}
P(Z) = %(2 \pi \rho^2)^{-1/2}
     \frac{1}{\sqrt{2 \pi \sigma^2}} \;
         e^{-(Z-\mu)^2/2 \sigma^2}.
\end{equation}
The cross-sectional 
radius $a(\phi) = 7 \times 10^{-5} + (1.6 \times 10^{-4})\phi$ m
increases according to measurements of pore sizes with temperature
\citep{Perovich:JGR-18327,Bock:2005}.
The bound is a special case of optimal void bounds
\citep{Torquato:PRL-2004,Torquato:RHM-02}, and takes the form
\begin{equation}                  \label{pipe_bound_sigma}
k(\phi) \leq   \frac{\phi}{8 \pi} \; \langle A(\phi) \rangle \; e^{\sigma^2}.
\end{equation}
With variance $\sigma^2 \approx 1$
and $\langle A(\phi) \rangle=\pi a^2(\phi)$ as above \citep{Perovich:JGR-18327},
the {\it lognormal pipe bound} in (\ref{pipe_bound_sigma})
captures all our field data, 
as shown in Figure \ref{data_lognormal_pipe_bound} (one data point
where no fluid influx was measured is not shown on the
logarithmic scale). 




\begin{figure*} [t]               %\centering
\vspace*{2mm}
\begin{center}
\includegraphics[width=12cm]{Figure3chap6.eps}
\end{center}
   \caption{
            Comparison of {\it in situ} data on 
            $k$ (m$^2$) for 
            Antarctic sea ice 
           with percolation theory, displayed on a linear scale
            in {\bf(A)} and on a logarithmic scale in {\bf(B)}, where
           a statistical best fit (dotted line) of the data is shown 
           along with the prediction of percolation theory with 
           $\phi_c \approx 0.1$.}         
    \label{data_percolation_theory}
       
\end{figure*}


Based on previous analyzes of Arctic columnar sea ice \citep{Golden:2007:GRL}, 
we expected to see similar threshold behavior near a 5\% critical brine
volume fraction in Antarctic sea ice as well. However, initial analysis of
our permeability data did not show the expected behavior -- the 
threshold appeared to be ``smeared out,'' or stretched over a range
of $\phi$. Elementary analysis of the compressed powder model 
\citep{Kusy:JAP-5301}
we used to explain the rule of fives \citep{Golden:S-2238} shows
that granular microstructures should display higher thresholds
than columnar ice. As fluid flows into the borehole,
even a thin layer of granular ice beneath it can determine
the effective threshold behavior. 
Given the significant presence of granular ice
in our samples, 
we separated the permeability data into two categories,
those with primarily columnar ice under the bottom of the hole, 
and those with even a small amount (roughly a quarter) 
or more of granular ice under the hole. 
An image of the polycrystalline microstructure
of Antarctic columnar ice under cross-polarization is
shown in Figure \ref{crystalline_microstructures} (A), and
an image of granular ice is shown in (B). These samples were 
taken in the Bellingshausen Sea in October 2007 during 
the Sea Ice Mass Balance in the Antarctic (SIMBA) experiment.





In order to estimate the percolation threshold $\phi_c$ 
for fluid transport in 
Antarctic granular ice, we use a compressed powder model
\citep{Kusy:JAP-5301,Golden:S-2238}.
In this model, large polymer spheres of radius $R_p$ 
are mixed with much smaller metal spheres of radius $R_m$,
and then the mixture is compressed. 
The main parameter controlling the threshold is the
ratio $\xi = R_p / R_m$.
An approximate formula for the critical volume fraction 
for percolation of the small metal spheres 
is given by
$\phi_c=(1+\xi \theta / (4 X_c))^{-1}$, where $\theta$
is a reciprocal planar packing factor, and $X_c$
is a critical surface area fraction of the
larger particles which must be covered
for percolation by the smaller particles \citep{Kusy:JAP-5301}.
Values based on microstructural analysis 
giving good agreement with experiments are
$X_c=0.42$ and $\theta=1.27$.
This mixture geometry is roughly similar to the 
ice-brine microstructure of sea ice, where the 
ice grains have radius $R_i$ and the 
brine inclusions have radius $R_b$ (or half the thickness
of a brine film enveloping an ice grain), with 
$\xi = R_i / R_b$ in this case. We have estimated
a range of $\xi$ values from photomicrographs of 
granular microstructures,
and obtained a representative value of around 
$\xi \approx 12$, leading to a threshold value of
around $\phi_c \approx 10\%$, as illustrated
in Figure \ref{crystalline_microstructures} (C).
We remark that fine-grained columnar ice which displays
geometric similarity to classic granular ice can also
exhibit these higher percolation threshold values, and
that even finer grained frazil microstructures will likely
have even higher thresholds.  

%In Figure \ref{thresholds}, we display a range of measured $\xi$ values and mean $\xi$ values for different ice types.  Similarly to Figure \ref{crystalline_microstructures}, we see that the mean $\xi$ for small grained granular microstructures leads to a predicted threshold value of $\phi_c \approx 10\%$.



%\begin{figure}[t]                \centering
%\includegraphics[width=15cm]{Figure2chap6cc.eps}
%   \caption{Microstructures of columnar ice in {\bf(a)} and granular ice in {\bf(b)}. 
%            In {\bf(c)} we display the percolation threshold in the compressed powder
%            model as a function of the ratio of the particle radii.}         
%    \label{crystalline_microstructures}
%        
%\end{figure}





Percolation theory 
\citep{Torquato:RHM-02,Halperin:PRL-2391,Golden:PRL-2923} %,Golden:HPM-27
%Broadbent:PCPS-629,
has been used to model transport in disordered
materials where the connectedness of one phase,
like brine in sea ice,
dominates the effective behavior.
Consider the square ($d=2$) or cubic ($d=3$) network of bonds 
joining nearest neighbor sites on the integer lattice ${\mathbb{Z}}^d$.
%In the random pipe network,
The bonds are assigned fluid conductivities
$\kappa_0 > 0$ (open) or 0 (closed) with probabilities $p$ 
and $1-p$. 
%Groups of connected open bonds 
%are called open clusters. 
%The striking feature of this model is that 
There is a critical probability $p_c$, $0<p_c<1$,
called the {\it percolation threshold}, 
where an infinite, connected set of open bonds first appears.
In $d=2$, $p_c = \frac{1}{2}$, and in $d=3$,
$p_c \approx 0.25$. 
Let $\kappa(p)$ be the permeability 
of this random network
in the vertical direction.  
For $p < p_c$, $\kappa(p)=0$. For $p>p_c$, near the threshold  
$\kappa(p)$ exhibits power law behavior,
%\begin{equation}                    \label{critical_permeability}
$\kappa(p) \sim \kappa_0(p-p_c)^e$ as $p \rightarrow p_c^+$,
%\end{equation}
where $e$ is the permeability critical exponent.
%There was debate concerning the value of $t$ in three dimensions  
%over roughly three decades, 
%with a wide range of published 
For lattices, %$p_c$ depends on the type of lattice, while 
$e$ is believed to be {\it universal}, 
depending only on $d$, and is equal to $t$,
the lattice electrical conductivity exponent
\citep{Torquato:RHM-02,Halperin:PRL-2391,Golden:PRL-2923,Berkowitz:TPM-275}.
%In $d=2$ \citep{Stauffer-92,Sahimi-95}, $t \approx 1.3$.
In $d=3$, it is believed \citep{Torquato:RHM-02}
that $t \approx 2.0$, 
and there is a rigorous 
bound \citep{Golden:PRL-2923} that $t \leq 2$.
%The graph of $\kappa(p)$ in $d=2$ is illustrated 
%in the inset in Figure \ref{perc_field_data}.


\begin{figure*} [t]               %\centering
\vspace*{2mm}
\begin{center}
\includegraphics[width=12cm]{Figure4chap6.eps}
\end{center}
   \caption{Penetration of tracers into inverted blocks of sea ice.
            The fluid penetrated about 5 cm into the ice in {\bf(A)},
            about 10 cm in {\bf(B)}, and about 9 cm in {\bf(C)} and {\bf(D)}.
             In each case the descending fluid passed through 
            an initial layer a few centimeters deep of highly
             permeable ice of average brine volume fraction 
             in the range 18.5\% - 21.5\%, until reaching relatively impermeable
             ice with brine volume fraction of about 10\%, where it
            stopped flowing.             
            In {\bf(A)}, the temperature and brine volume decreased more rapidly,
            and the tracer stopped after 5 cm.
            In {\bf(B)} and {\bf(C)} the 10\% brine volume threshold was located about
            10 cm down, and in {\bf(D)} a tracer plume was also able to descend
            deeper through a large brine channel. }         
    \label{tracers}
       
\end{figure*}



Although $e$ can take non-universal values in the
continuum, it was shown \citep{Torquato:RHM-02,Halperin:PRL-2391}
that for lognormally distributed inclusions
the behavior is universal, with $e \approx 2$.
The scaling factor $k_0$ is estimated 
using critical path analysis and microstructural observations 
\citep{Golden:2007:GRL}.
Thus 
\begin{equation}                 \label{perc_theory}
k(\phi) \; \sim \; 3 \; (\phi - \phi_c)^2 \; 
\times  10^{-8}\;\; \mbox{m}^2,
\;\;\;\; \phi \rightarrow \phi_c^+,
\end{equation}
with $\phi_c \approx 0.1$ for granular ice.
In Figure \ref{data_percolation_theory} (A), 
we display the granular permeability data along with
the curve in (\ref{perc_theory}). In (B) we 
show in logarithmic variables the percolation theory 
prediction along with
a statistical best fit, for permeability data with
$\phi$ above 0.10, showing close agreement.







In Figure \ref{tracers} the results of our tracer experiments are shown,
where we poured fluid tracers into inverted sea ice blocks. In each case 
the fluid descended through a layer of highly permeable sea ice, and stopped
when it reached colder, impermeable granular ice (or fine-grained
columnar ice) of brine volume fraction around 10\%. These experiments 
vividly demonstrate that the critical threshold for fluid transport in 
Antarctic sea ice can be much higher than the 5\% brine volume fraction of classic columnar sea ice.

%\subsection{HEADING}
%TEXT
%
%\subsubsection{HEADING}
%TEXT








\conclusions  %% \conclusions[modified heading if necessary]
To date columnar ice has received disproportionate attention, mostly due to its prevalence in Arctic sea ice.  However, granular ice accounts for a fraction of up to around 40\% in the Antarctic.  Here we have observed that the presence of granular ice can significantly change the fluid permeability of sea ice.  A compressed powder model analysis for the smaller granular crystals indicates that the percolation threshold for the finer grained microstructure is $\phi_c \approx 10\%$.  %This new percolation threshold is then used to modify traditional percolation models for columnar sea ice.  
{\it In situ} granular sea ice data taken in Antarctica is then compared with a classic percolation model that has a percolation threshold of $\phi_c \approx 10\%$ and is in excellent agreement.  Additionally, we find here that the {\it universal} lattice critical exponent of about 2 for columnar ice in the Arctic still accurately describes the take-off of $k(\phi)$ above the threshold $\phi_c$ for granular sea ice in the Antarctic.  Further, tracer experiments presented here vividly demonstrate the inability of fluid to flow through a layer of granular ice (or fine-grained columnar ice) that has a brine volume fraction of $\phi \approx 10\%$.  %This work demonstrates the differences in fluid flow through sea ice for different ice types, which controls many key parameters in the polar ice packs.
This work displays that fluid flow through sea ice, which controls many key parameters of the polar ice packs, can vary greatly for different ice types.


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