commit d6896552d938a8670a831612069f06624d2c1dad
parent f09c349adb4bea74c1b23c13ac19d6fa224ecee6
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Wed, 18 Dec 2019 16:59:03 +0100
Update results presentation and discussion
Diffstat:
2 files changed, 68 insertions(+), 25 deletions(-)
diff --git a/BIBnew.bib b/BIBnew.bib
@@ -1431,6 +1431,8 @@
Year = {2010},
}
+
+
@Article{Kjaer2006,
Title = {Subglacial decoupling at the sediment/bedrock interface: a new mechanism for rapid flowing ice},
Author = {Kj{\ae}r, K. H. and Larsen, E. and {van der
@@ -9177,7 +9179,7 @@ Winton and A. T. Wittenberg and F. Zeng and R. Zhang and J. P. Dunne},
volume = {9},
number = {1},
author = {P. Christoffersen and M. Bougamont and A. Hubbard and S. H. Doyle and S. Grigsby and R. Pettersson},
- title = {Cascading lake drainage on the Greenland Ice Sheet triggered by tensile shock and fracture},
+ title = {Cascading lake drainage on the {G}reenland {I}ce {S}heet triggered by tensile shock and fracture},
journal = {Nature Commun.}
}
@article{Palmer2015,
@@ -9187,7 +9189,7 @@ Winton and A. T. Wittenberg and F. Zeng and R. Zhang and J. P. Dunne},
volume = {6},
number = {1},
author = {S. Palmer and M. McMillan and M. Morlighem},
- title = {Subglacial lake drainage detected beneath the Greenland ice sheet},
+ title = {Subglacial lake drainage detected beneath the {G}reenland ice sheet},
journal = {Nature Commun.}
}
@article{Humphrey1993,
@@ -9198,10 +9200,9 @@ Winton and A. T. Wittenberg and F. Zeng and R. Zhang and J. P. Dunne},
number = {B1},
pages = {837--846},
author = {N. Humphrey and B. Kamb and M. Fahnestock and H. Engelhardt},
- title = {Characteristics of the bed of the Lower Columbia Glacier, Alaska},
+ title = {Characteristics of the bed of the {L}ower {C}olumbia {G}lacier, {A}laska},
journal = {J. Geophys. Res.: Solid Earth}
}
-https://doi.org/10.1680/geot.1996.46.2.197
@article{Tika1996,
doi = {10.1680/geot.1996.46.2.197},
@@ -9214,11 +9215,46 @@ https://doi.org/10.1680/geot.1996.46.2.197
title = {Fast shearing of pre-existing shear zones in soil},
journal = {G{\'{e}}otechnique}
}
-https://doi.org/
-https://doi.org/
-https://doi.org/10.7717/peerj.929/supp-1
-@misc{1,
- doi = {10.7717/peerj.929/supp-1},
- publisher = {{PeerJ}}
+@article{van_der_Meer2009,
+ doi = {10.1016/j.quascirev.2008.07.017},
+ year = 2009,
+ publisher = {Elsevier {BV}},
+ volume = {28},
+ number = {7-8},
+ pages = {708--720},
+ author = {J. J. M. van der Meer and K. Kj{\ae}r and J. Krüger and J. Rabassa and A. Kilfeather},
+ title = {Under pressure: clastic dykes in glacial settings},
+ journal = {Quat. Sci. Rev.}
+}
+
+@article{Knight2015,
+ doi = {10.1016/j.sedgeo.2015.01.002},
+ year = 2015,
+ publisher = {Elsevier {BV}},
+ volume = {318},
+ pages = {85--96},
+ author = {J. Knight},
+ title = {Ductile and brittle styles of subglacial sediment deformation: An example from western {I}reland},
+ journal = {Sediment. Geol.}
+}
+@article{Salamon2016,
+ doi = {10.1016/j.quascirev.2016.09.002},
+ year = 2016,
+ publisher = {Elsevier {BV}},
+ volume = {151},
+ pages = {72--87},
+ author = {T. Salamon},
+ title = {Subglacial conditions and {S}candinavian {I}ce {S}heet dynamics at the coarse-grained substratum of the fore-mountain area of southern {P}oland},
+ journal = {Quat. Sci. Rev.}
+}
+@article{Ingolfsson2016,
+ doi = {10.1016/j.earscirev.2015.11.008},
+ year = 2016,
+ publisher = {Elsevier {BV}},
+ volume = {152},
+ pages = {37--69},
+ author = {{\'{O. Ing{\'{o}}lfsson and {\'{I}}var Örn Benediktsson and A. Schomacker and K. H. Kj{\ae}r and S. Brynj{\'{o}}lfsson and S. A. J{\'{o}}nsson and N. J{\'{a}}kup Korsgaard and M. D. Johnson},
+ title = {Glacial geological studies of surge-type glaciers in {I}celand {\textemdash} {R}esearch status and future challenges},
+ journal = {Earth-Sci. Rev.}
}
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -259,7 +259,7 @@ Pulse perturbations of various shape in water pressure are also able to cause de
Pore-pressure diffusion and strain distribution with depth with a sinusoidal water-pressure forcing from the top.
The bed thickness is $L_z$ = 8 m, but here only the upper 4 m are shown.
The water-pressure forcing has a daily periodocity, and plot lines are one hour apart in simulation time.
- The horizontal green line marks skin depth from Eq.~\ref{eq:skin_depth}.
+ The full horizontal line marks the skin depth from Eq.~\ref{eq:skin_depth}, and the dashed line marks the expected maximum deformation depth from Eq.~\ref{eq:max_depth}.
}
\end{center}
\end{figure*}
@@ -280,14 +280,15 @@ Pulse perturbations of various shape in water pressure are also able to cause de
\section{Discussion}%
\label{sec:discussion}
This study has the specific aim of quantifying advective sediment transport under shear.
-As granular deformation is associated with finite length scales, it is crucial to include non-local terms in the granular model equations instead of applying earlier \emph{local} sediment models \cite<e.g.,>[] {daCruz2005, Jop2006, Forterre2008}.
+As granular deformation is associated with finite length scales, it is crucial to include non-local terms in the granular model equations instead of applying simpler \emph{local} sediment rheology models \cite<e.g.,>[] {daCruz2005, Jop2006, Forterre2008}.
However, the modeled sediment flux presented here may present an upper bound since we assume that there is a strong mechanical coupling between ice and bed.
-If the subglacial sediment bed is a thin layer of $\sim$10 cm or less, our model predicts that the sediment itself will be comparatively strong (bulk friction vs.\ bed thickness in Fig.~S2).
Overpressurization and slip at the ice-bed interface may cause episodic decoupling and reduce bed deformation.
Interface slip is observed both under contemporary ice streams \cite<e.g.,>[] {Engelhardt1998}, and in deposits from past glaciations \cite<e.g.,>[] {Piotrowski2001}.
-Still, we see the presented framework as a significant improvement of treating sediment advection in ice-flow models, but acknowledge that a complete understanding of the sediment mass budget requires improved models of ice-bed interface physics.
+A complete understanding of subglacial sediment transport requires further research of ice-bed interface physics.
+Furthermore, we assume that the onset of deformation is not affected by initial hardening caused by shear-zone dilation \cite<e.g.,>[] {Iverson1998, Moore2002, Damsgaard2015}.
-Without water-pressure variations, the sediment advection is stress dependent (Fig.~\ref{fig:validation}d), which is a prerequisite for instability theories of subglacial landform development \cite{Hindmarsh1999, Fowler2000, Schoof2007, Fowler2018}.
+In simulations without water-pressure variations, the sediment transport is dependent on the magnitude of the effective normal stress (Fig.~\ref{fig:validation}d).
+Such a dependence is a prerequisite for instability theories of subglacial landform development \cite{Hindmarsh1999, Fowler2000, Schoof2007, Fowler2018}.
From geometrical considerations, it is likely that up-ice sloping stoss sides of subglacial topography experience higher bed-normal stress than down-ice sloping lee sides.
With all other physical conditions being equal, our results indicate that shear-driven sediment advection would be larger on the stoss side than on the lee side.
Topography of non-planar ice-bed interfaces (proto-drumlins, ribbed moraines, etc.) may be transported and modulated through this spatially variable transport capacity, unless stress differences are overprinted by variations in water pressure \cite<e.g.,>[] {Sergienko2013, McCracken2016, Iverson2017b, Hermanowski2019b}.
@@ -304,8 +305,9 @@ As long as fluid and diffusion properties are constant and the layer is sufficie
\end{linenomath*}
where $D$ is the hydraulic diffusivity [m$^2$/s] and $P$ [s] is the period of the oscillations.
The remaining terms were previously defined.
-However, as the deformation pattern depends on both hydraulic properties and the forcing amplitude (Fig.~S3), the skin depth alone is insufficient to judge the occurence of deep deformation.
-We constrain an analytical solution for diffusive pressure perturbation to find the largest depth $z'$ containing a minimum of effective normal stress over the cause of a pressure-perturbation cycle (see Supplementary Information Text S2 for full derivation):
+Figure~\ref{fig:skin_depth}a shows the skin depth for water at 0$^\circ$C under a range of permeabilities and forcing frequencies.
+However, as the deformation pattern depends on both hydraulic properties and the pressure-perturbation amplitude (Fig.~S2,~S4), the skin depth alone is insufficient to judge the occurence of deep deformation.
+Therefore, we constrain an analytical solution for diffusive pressure perturbation to find the largest depth $z' = L_z - z$ that contains a minimum in effective normal stress over the cause of a pressure-perturbation cycle (see Supplementary Information Text S2 for full derivation):
\begin{linenomath*}
\begin{equation}
0 =
@@ -316,13 +318,7 @@ We constrain an analytical solution for diffusive pressure perturbation to find
\label{eq:max_depth}
\end{equation}
\end{linenomath*}
-Figure~\ref{fig:skin_depth}a shows the skin depth for water at 0$^\circ$C under a range of permeabilities and forcing frequencies, while panels~\ref{fig:skin_depth}b and~c show the maximum expected deformation depth from solutions to Eq.~\ref{eq:max_depth}.
-Minima in effective normal stress are increasingly difficult to create at larger depths through pure diffusion from the ice-bed interface.
-The deepest deformation occurs when the combination of forcing amplitude and skin depth is optimal.
-At higher skin depths, the lithostatic stress increase exceeds the pressure perturbation at depth.
-Conversely, deformation depth is restricted at lower skin depths because the pressure signal propagates too slowly through the bed relative to the forcing frequency.
-Coarse tills are more susceptible to deep deformation (Fig.~\ref{fig:skin_depth}a), but deep strain requires larger perturbations in water pressure (Fig.~\ref{fig:skin_depth}b,c).
-On the contrary, fine-grained tills are unlikely to undergo deep deformation, but deformation is still expected to occasionally occur away from the ice-bed interface.
+When using the same stress, hydraulic parameters, and pressure-perturbation amplitude, the analytical solution matches our NGF simulations well (dashed horizontal line in Fig.~\ref{fig:stick_slip_depth}).
\begin{figure}[htbp]
\begin{center}
@@ -336,7 +332,18 @@ On the contrary, fine-grained tills are unlikely to undergo deep deformation, bu
\end{center}
\end{figure}
-Lateral water input from lake drainage or hydrological rerouting at depth may be a viable alternate mechanism for creating occasional episodes of deep slip, in particular when horizontal bedding decreases vertical permeability \cite<e.g.,>[] {Kjaer2006}.
+Figure~\ref{fig:skin_depth}b and~c show the maximum expected deformation depth from solutions to Eq.~\ref{eq:max_depth} through pressure perturbations enforced from the ice-bed interface.
+Deep deformation occurs when the combination of forcing amplitude ($A_\mathrm{f}$) and skin depth (i.e.\ the $k/f$ ratio) is optimal.
+A combination of highly permeability and slow water-pressure forcing frequency results in a large skin depth (Fig.~\ref{fig:skin_depth}a), but the rapid pore-pressure diffusion is unlikely to overcome the lithostatic stress increase with depth.
+Conversely, low skin depths (i.e.\ relatively impermeable materials and/or fast water-pressure forcing frequencies) are associated with limited penetration distance into the bed, limiting the maximum deformation depth.
+For that reason, coarse and relatively permeabile tills are more susceptible to deep deformation due to larger associated skin depths (Fig.~\ref{fig:skin_depth}a), as long as the perturbation amplitude is sufficiently large (Fig.~\ref{fig:skin_depth}b,c).
+Fine-grained and relatively impermeable tills are unlikely to undergo deep deformation as pressure perturbations propagate at slower velocities.
+Albeit at shallower depths, deformation is still expected to occasionally occur away from the ice-bed interface in poor hydraulic conductors (Fig.~\ref{fig:skin_depth}b,c).
+
+Other water-pressure forcings may be additional mechanisms for deep deformation if they cause minima in effective stress at depth.
+For example, lateral water input from lake drainage or hydrological rerouting may also create episodes of deep slip, in particular when horizontal bedding decreases vertical permeability \cite<e.g.,>[] {Kjaer2006}.
+Water-escape structures are commonly observed in till deposits \cite<e.g.,> {vanDerMeer2009, Knight2015, Salamon2016, Ingolfsson2016}, which indicates that overpressurization of water within till beds may be extremely common.
+Since tills fail at their weakest spot, we suggest that subglacial deformation may not only be a patchy mosaic of deforming spots in the horizontal plane \cite<e.g.,> {Piotrowski2004}, but also at depth.
\section{Conclusion}%
