commit 042c8f0aeaf76746a6f589808c1dc77907e2c45d
parent 01785de7c6046ebef202de071755e75b37d3a56d
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Thu, 14 Nov 2019 16:02:34 +0100
Remove Iverson2001 and Tulaczyk2000 references
Diffstat:
2 files changed, 5 insertions(+), 18 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -65,13 +65,6 @@ Deep deformation is most likely in tills with relatively high hydraulic permeabi
Fast glacier and ice-sheet flow often ocurrs over weak sedimentary deposits, where basal slip accounts for nearly all movement \citep[e.g.,][]{Cuffey2010}.
Basal sediments, called subglacial till, are diamictons commonly consisting of reworked sediments and erosional products \citep[e.g.,][]{Evans2006}.
Meltwater fully saturates the pore space, and variations in subglacial water pressure are common and can be caused by internal variability \citep[e.g.,][]{Kavanaugh2009} or external water input \citep[e.g.,][]{Andrews2014, Christoffersen2018}.
-%For example, large basal pressure variations can occur from daily meltwater input \citep[e.g.,][]{Andrews2014}, or through episodic drainage of ice-surface lakes \citep[e.g.,][]{Christoffersen2018} or subglacial lakes \citep[e.g.,][]{Palmer2015}.
-%The pore pressure relieves some of the overburden ice weight on the bed and reduces the compressive solid stress on the granular skeleton lowering Terzaghi's effective stress \citep{Terzaghi1943}.
-%Pore-pressure induced stress variations control the kinematics of the ice and sub-ice sediments, which in turn may feed back into the dynamics of the system.
-%The interplay of ice, water, and sediment is therefore important for glacier and ice-sheet dynamics, but remains poorly understood \citep[e.g.,][]{Clarke2005}.
-%
-%\citet{Boulton1979} presented the pioneering idea that sedimentary beds and hydrological processes can significantly influence glacier and ice-sheet flow and stability.
-%This idea sparked interest in understanding the associated sediment physics.
In-situ field observations demonstrate that deformation of this layer can contribute significantly to the glacier movement \citep[e.g.,][]{Boulton1979, Humphrey1993, Truffer2000}.
\citet{Boulton1987} argued that a viscous rheological model with mild stress non-linearity appropriately describes subglacial till deformation.
A viscous rheology implies that the stress required to deform the till is strongly dependent on how fast it is deformed.
@@ -480,21 +473,16 @@ Regardless of perturbation shape, the maximum deformation depth increases with i
\section{Discussion}%
\label{sec:discussion}
+In this study it is assumed that there is a strong coupling between ice and bed.
+However, overpressurization and slip at the ice-bed interface may cause episodic decoupling at the interface and reduce bed deformation, as observed under Whillans Ice Stream, West Antarctica \citep[e.g.,][]{Emgelhardt1998}, and in deposits from Pleistocene glaciations \citep[e.g.,][]{Piotrowski2001}.
+We see the presented framework as an important improvement of treating sediment advection in ice-flow models, but acknowledge that a complete understanding of the sediment mass budget requires improved models of sliding over sedimentary beds.
+
The stress-dependent sediment advection without variations in the pore pressure observed in Fig.~\ref{fig:strain_distribution} is relevant for instability theories of subglacial landform development \citep{Hindmarsh1999, Fowler2000, Schoof2007, Fowler2018}.
From geometrical considerations, it is likely that bed-normal stresses on the stoss side of subglacial topography are higher than on the lee side.
With all other physical conditions being equal, our results indicate that shear-driven sediment advection would be larger on the stoss side of bed perturbations than behind them.
Topography of non-planar ice-bed interfaces (proto-drumlins, ribbed moraines, etc.) may be transported and modulated through this variable transport capacity, unless stress differences are overprinted by spatial variations in water pressure \citep[e.g.,][]{Sergienko2013, McCracken2016, Iverson2017b, Hermanowski2019b}.
-Previously, \citet{Iverson2001} modeled the subglacial bed as a series of parallel Coulomb-frictional slabs.
-They demonstrated that random perturbations in effective stress at depth can distribute deformation away from the ice-bed interface.
-\citet{Tulaczyk1999} and \citet{Tulaczyk2000} demonstrated that Darcian diffusion of pore-pressure variations into the bed can distribute strain away form the ice-bed interface.
-However, these studies did not include non-local granular effects assosiated with granular deformation.
-We couple the water-pressure diffusion with a more complex sediment rheology than the above studies.
-The slight rate dependence (Fig.~\ref{fig:rate_dependence}) makes it relatively trivial to couple to ice-flow models, while retaining realistic sediment physics.
-Our numerical solution to pore-pressure diffusion can be forced with any water-pressure signal from the ice-bed interface.
-
At depth, the water pressure variations display exponential decay in amplitude and increasing lag.
-The skin depth is defined as the distance where the fluctuation amplitude of smooth forcings decreases to $1/e \approx 37\%$ of its surface value \citep[e.g.,][]{Cuffey2010}.
As long as fluid and diffusion properties are constant and the layer is sufficiently thick, an analytical solution to skin depth $d_\text{s}$ [m] in our system follows the form \citep[after Eq.~4.90 in][]{Turcotte2002},
\begin{linenomath*}
\begin{equation}
@@ -526,9 +514,8 @@ It is worth noting that to induce deep deformation the water pressure deviations
This means that minima in effective normal stress are increasingly difficult to create at larger depths through pure diffusion from the ice-bed interface.
Due to higher hydraulic permeability, coarse tills are more susceptible to deep deformation, but deep strain requires longer-lasting perturbations in water pressure (Fig.~\ref{fig:skin_depth}).
Contrarily, fine-grained tills are unlikely to cause deep deformation.
-\citet{Truffer2000} and \citet{Kjaer2006} both observed deep deformation in glacier settings with relatively coarse subglacial tills.
Lateral water input at depth may be a viable alternate mechanism for creating occasional episodes of deep slip, in particular when horizontal bedding decreases vertical permeability \citep[e.g.,][]{Kjaer2006}.
-TODO: LAKE DRAINAGE
+%TODO: LAKE DRAINAGE
\section{Conclusion}%
\label{sec:conclusion}
diff --git a/experiments/fig-rate_dependence.pdf b/experiments/fig-rate_dependence.pdf
Binary files differ.
