The story in the news

Last week a little municipality of western Manitoba on the southern shores of the Dauphin Lake in Canada was caught in a media frenzy after homes in Ochre Beach were destroyed and seriously damaged by a wave of lake ice. The BBC titled 'Creeping wall of ice destroys homes in Canada' and other media showed dramatic pictures (here and here) and videos of what they sometimes inaccurately referred to as an 'ice tsunami'. In fact this natural phenomenon is commonly referred to as ice shove, Ivu, or shoreline ice pileup and can occur on the shore of almost any large body of water (see figure below) when sustained high winds set free-floating pieces of ice into motion. For me this event was a good excuse to talk about the mechanical properties of sea ice and the mechanism of ridge formation as I was asked to give a short presentation at our weekly Weather and Climate Discussion meeting (see also the WCD blog) at the Department of Meteorology of Reading University .

The power of sea ice

What the owners of these (now crushed) houses on the southern shore of the Dauphin Lake have experienced is very reminiscent of the early accounts made by the explorers of the heroic age of polar exploration. They have all testified of the enormous power of the sea ice and their stories are often tragic. On June 12 1881, the USS Jeanette, a few weeks after discovering two of the New Siberian Islands under the command of George Washington De Long was crushed by the ice and sank. In November 1915 and on the other side of the planet Ernest Shackleton describes how its ship, the Endurance, after being trapped by the ice and having drifted for nine months was also destroyed by the ice [Shackleton2010]: "Then on Sunday, October 24, there came what for the Endurance was the beginning of the end. [...] throughout the day we watched the threatening advance of the floes. At 6.45 p.m. the ship sustained heavy pressure in a dangerous position. [...] The shaded portions represent the pool, covered with new ice that afforded no support to the ship, and the arrows indicate the direction of the pressure exercised by the thick floes and pressure-ridges. The onslaught was all but irresistible. The Endurance groaned and quivered as her starboard quarter was forced against the floe, twisting the sternpost and starting the heads and ends of planking. The ice had lateral as well as forward movement, and the ship was twisted and actually bent by the stresses. She began to leak dangerously at once." One boat, the Fram, under the leadership of Fridtjof Nansen famously survived these high pressures due to its ingenious design and drifted with the ice for almost three years from Siberia to the other side of the Arctic Ocean and back to Norway.
Ice rubble pile formed in January 2006 at Barrow, AK as the result of an ice shove (www.gi.alaska.edu/snowice/sea-lake-ice/images/ice_events.html).
Sequential snapshots from a ridging numerical experiment performed by Hopkins. The ice thickness is 30 cm and each frame is 12 m x 20 m. The numbers on the top left corner are the time that has elapsed in seconds.

Modeling the ridging of sea ice

It is important to better understand the mechanism of ice ridging and to try to estimate the forces that the sea ice can generate in order to design adequate structures (ships, houses, paltforms...) in the polar environments. One of the most complete description of ice ridging of sea ice was given in a series of papers by Mark Hopkins [Hopkins1991, Hopkins1994, Hopkins2006]. Using a two-dimensional particle model Hopkins showed that the ridging process can be divided into four distinct stages. The first stage begins with an intact sheet of lead ice impacting a floe and ends when the sail reaches its maximum height (figure on the left). In the second stage the ridge keel deepens and widens. The stage ends when the maximum keel draft is reached. In the third stage the direction of growth is leadward creating a rubble field of more or less uniform thickness (this stage correspond to the ice advancing towards the house in Canada as shown here) . The third stage ends when the supply of thin ice is exhausted (or when the wind stops). In the fourth stage the rubble field is compressed between converging floes. The results of simulations establish the dependence of ridging energetics in the first and second stages on the thickness of the ice sheet and the amount of ice pushed into the ridge. The average profiles of the simulated ridges delineate the growth process in the first, second, and third stages. The energetics and profiles of the fourth stage were described by [Hopkins1998]. Lead ice extents of up to 1300 m are pushed into ridges to determine maximum sail heights, keel drafts, and ridging forces.

Ice ridging is an essential component of climate sea ice models

In contrast to what most people think the Arctic and Antarctic sea ice is for its most part in constant motion (as illustrated by the drift of the Fram) under the combined effect of the winds, ocean currents and internal forces in the ice (in addition to the usually more modest contributions from the Coriolis force and gravity force from sea surface tilt). The sea ice cover that is composed of a multitude of very thin blocks of ice (ice floes) follows in the Arctic two main large scale circulation patterns, the transpolar drift (from Siberia to the Fram Strait) and the Beaufort Gyre while in the Antarctic the ice follows a general cyclonic flow at the sea ice edge (further south) while along the coast of the continent it flows mostly anticyclonicaly. In order to understand the dynamic (and the thermodynamic) of the sea ice cover the mechanism of ice ridging must be correctly described in the models. Indeed as discussed in details inĀ [Martin2007b] ridges affect the momentum and the heat exchange between sea ice and atmosphere and ocean because they strongly increase the local surface roughness and thickness of the ice. Therefore, the sea ice drift and deformation interact with the climate system and its changes, and it is a key issue to both the remote-sensing and modelling community to provide products of good quality. Currently, in collaboration with researchers from NASA's IceBridge project (see figure on the right), I am investigating the impact of these ridges of the atmospheric and oceanic form drag on sea ice.

Preliminary results of the ridge detection algorithm developed by Nathan Kurtz from NASA's IceBridge project.

References

[Shackleton2010] E. H. Shackleton, South!: the story of shackleton's last expedition 1914 - 1917, Salzwasser-Verlag GmbH, 2010.
[Bibtex]
@BOOK{Shackleton2010,
title = {South!: The Story of Shackleton's Last Expedition 1914 - 1917},
publisher = {Salzwasser-Verlag GmbH},
year = {2010},
author = {Shackleton, E.H.},
pages = {--},
booktitle = {Historische Schifffahrt},
issn = {9783861952497},
owner = {mct},
timestamp = {2013.05.18},
url = {http://books.google.co.uk/books?id=xr4g1G4O-4IC}
}
[Hopkins1991] M. A. Hopkins, I. Hibler W. D., and G. M. Flato, "On the numerical simulation of the sea ice ridging process," J. geophys. res., vol. 96, iss. C3, pp. 4809-4820, 1991.
[Bibtex]
@ARTICLE{Hopkins1991,
author = {Hopkins, M. A. and Hibler, W. D., III and Flato, G. M.},
title = {On the Numerical Simulation of the Sea Ice Ridging Process},
journal = {J. Geophys. Res.},
year = {1991},
volume = {96},
pages = {4809--4820},
number = {C3},
abstract = {A two-dimensional particle simulation model of the sea-ice ridging
process is developed. In this model, ridges are formed from a floating
layer of rubble compressed between converging multiyear floes. The
energy consumed in ridge growth, including dissipation, is explicitly
calculated. A series of experiments are performed to establish the
dependence of the energy consumed in ridging on the velocity of the
multiyear floes and on the shape, the friction coefficient, and the
inelasticity of the rubble blocks. The experiments show that shape
and friction between ice blocks are the most significant factors
in determining the energy required to ridge ice. In large-scale sea
ice modeling, using a variable thickness approach, it is convenient
to parameterize total ridging work in terms of the increase of potential
energy. The results of the ridging simulations with block-shaped
rubble suggest that the total ridging work may be 4–5 times
the increase in potential energy. At the same time, an analytical
model of the ridging process is developed from classical Mohr-Coulomb-Rankine
theory for a cohesionless granular material. The predictions of this
model, using values of porosity and the passive pressure coefficient
derived from the ridge simulations, are in fair agreement with the
numerical experiments. However, several violations of the basic assumptions
underlying the Mohr-Coulomb-Rankine model are noted in the ridge
simulations.},
file = {Hopkins1991.pdf:Hopkins1991.pdf:PDF},
issn = {0148-0227},
owner = {mct},
publisher = {AGU},
timestamp = {2012.02.24},
url = {http://dx.doi.org/10.1029/90JC02375}
}
[Hopkins1994] M. A. Hopkins, "On the ridging of intact lead ice," Journal of geophysical research-oceans, vol. 99, iss. C8, 1994.
[Bibtex]
@ARTICLE{Hopkins1994,
author = {Hopkins, M.A.},
title = {On the ridging of intact lead ice},
journal = {Journal of Geophysical Research-Oceans},
year = {1994},
volume = {99},
number = {C8},
abstract = {The sea ice pressure ridging process is modeled using a two-dimensional
particle simulation technique. In this model, blocks are broken from
an intact sheet of relatively thin lead ice driven against a thick,
multiyear floe at a constant speed. The blocks of ice rubble accumulate
to form the ridge sail and keel. The energy consumed in ridge growth,
including dissipation, is explicitly calculated. A series of numerical
experiments are performed to establish the dependence of the energetics
on the thickness of the ice sheet and the friction between blocks.
The results suggest that the total energy required to create a pressure
ridge is an order of magnitude greater than the potential energy
in the ridge structure. A typical sea ice cover in the polar regions
contains a variety of ice thicknesses that evolve in response to
both dynamic and thermodynamic forcing. The variable thickness of
the ice cover is created by deformation, which simultaneously causes
formation of thick ice through ridge building and thin ice through
lead creation. Since the energy expended in deformation is largely
determined by the ridging process, an understanding of the energetics
of pressure ridging is critical in the determination of ice strength
on a geophysical scale.},
file = {Hopkins1994.pdf:Hopkins1994.pdf:PDF},
publisher = {American Geophysical Union},
url = {http://www.agu.org/journals/jc/v099/iC08/94JC00996/}
}
[Hopkins2006] [doi] M. A. Hopkins and A. S. Thorndike, "Floe formation in arctic sea ice," Journal of geophysical research-oceans, vol. 111, iss. {C11}, 2006.
[Bibtex]
@ARTICLE{Hopkins2006,
author = {Hopkins, Mark A. and Thorndike, Alan S.},
title = {Floe formation in Arctic sea ice},
journal = {JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS},
year = {2006},
volume = {111},
number = {{C11}},
month = {{SEP 13}},
abstract = {{{[} 1] The ice pack covering northern seas is composed of a mixture
of thick ridged and rafted ice, undeformed ice, and open water. Ice
motions determined from satellite remote sensing data show that deformation
of the pack takes place along the boundary of large floes. Eulerian
continuum sea ice models can simulate this behavior to a degree by
capturing the localization of gridded ice strength in some average
sense. However, using a discontinuous Lagrangian approach that explicitly
models ice floes and the interactions between them, it is possible
to simulate both the fracture process that creates floe boundaries
and the continued deformation along those floe boundaries. We have
developed a granular model of the central Arctic ice pack that consists
of thousands of individual grains that can freeze together, fracture
apart, and interact through ridging. Accelerations produced by passing
weather patterns and sustained quasi-steady deformation cause the
model pack to fracture apart into floes composed of one or more grains.
When the ice pack is nonuniformly accelerating due to passage of
a weather pattern, simulations show that the factors that influence
the size of the floes are the tensile strength of the joints between
grains, the gradient of the wind field, and the average size of the
individual grains. During sustained deformation the pack continues
to deform along existing floe boundaries while stresses build and
further fracture takes place. In quiet areas of the basin, fractures
refreeze. To explore the fracture process during sustained deformation,
we run 24-hour basin scale simulations at resolutions from 2.8 km
to 14 km. At the end of each simulation we construct a distribution
of floe areas. The cumulative distribution of floes at the large
end of the distribution is approximately the same at each resolution.
As we increase the resolution from 14 km to 2.8 km, the damage zones
between large floes become more localized. A log-log plot of the
cumulative floe size distributions obtained from the simulations
appears linear over several orders of magnitude.}},
address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
affiliation = {{Hopkins, MA (Reprint Author), ERDC CRREL, Hanover, NH 03755 USA.
ERDC CRREL, Hanover, NH 03755 USA. Univ Puget Sound, Dept Phys, Tacoma,
WA 98406 USA.}},
article-number = {{C11S23}},
author-email = {{mark.a.hopkins@erdc.usace.army.mil}},
doc-delivery-number = {{086AL}},
doi = {10.1029/2005JC003352},
file = {Hopkins2006.pdf:Hopkins2006.pdf:PDF},
issn = {{0148-0227}},
journal-iso = {{J. Geophys. Res.-Oceans}},
keywords-plus = {{SCALES LARGE; LEAD ICE; FRACTURE; MODEL}},
language = {{English}},
number-of-cited-references = {{20}},
publisher = {{AMER GEOPHYSICAL UNION}},
subject-category = {{Oceanography}},
times-cited = {{4}},
type = {{Article}},
unique-id = {{ISI:000240645400002}}
}
[Hopkins1998] M. A. Hopkins, "Four stages of pressure ridging," Journal of geophysical research-oceans, vol. 103, iss. C10, 1998.
[Bibtex]
@ARTICLE{Hopkins1998,
author = {Hopkins, M.A.},
title = {Four stages of pressure ridging},
journal = {Journal of Geophysical Research-Oceans},
year = {1998},
volume = {103},
number = {C10},
abstract = {The pressure ridging process is simulated using a two-dimensional
particle model. Blocks are broken from an intact sheet of relatively
thin lead ice pushed against a thick, multiyear floe at a constant
speed. The blocks of ice rubble accumulate to form the ridge sail
and keel. During the simulations the energy consumed in ridge growth,
including dissipation, is explicitly calculated. On the basis of
the results of simulations performed with the model, the ridging
process can be divided into four distinct stages. The first stage
begins with an intact sheet of lead ice impacting a floe and ends
when the sail reaches its maximum height. In the second stage the
ridge keel deepens and widens. The stage ends when the maximum keel
draft is reached. In the third stage the direction of growth is leadward
creating a rubble field of more or less uniform thickness. The third
stage ends when the supply of thin ice is exhausted. In the fourth
stage the rubble field is compressed between converging floes. The
results of simulations establish the dependence of ridging energetics
in the first and second stages on the thickness of the ice sheet
and the amount of ice pushed into the ridge. The average profiles
of the simulated ridges delineate the growth process in the first,
second, and third stages. The energetics and profiles of the fourth
stage were described by Hopkins et al. [1991]. Lead ice extents of
up to 1300 m are pushed into ridges to determine maximum sail heights,
keel drafts, and ridging forces.},
file = {Hopkins1998.pdf:Hopkins1998.pdf:PDF},
publisher = {American Geophysical Union},
url = {http://www.agu.org/journals/jc/v103/iC10/98JC01257/}
}
[Martin2007b] T. Martin, "Arctic sea ice dynamics: drift and ridging in numerical models and observations," PhD Thesis, 2007.
[Bibtex]
@PHDTHESIS{Martin2007b,
author = {Martin, T.},
title = {Arctic sea ice dynamics: drift and ridging in numerical models and
observations},
year = {2007},
file = {Martin2007b.pdf:Martin2007b.pdf:PDF},
publisher = {Alfred-Wegener-Institut f{\"u}r Polar-und Meeresforschung}
}