Editing Glacier (section)

== Motion ==
{{Redirect|Ice flow|floating ice|Ice floe}}
[[Image:Stress-strain1.svg|thumb|upright=1.2|The stress–strain relationship of plastic flow (green section): a small increase in stress creates an exponentially greater increase in strain, which equates to deformation speed.]]
Glaciers move downhill by the force of [[gravity]] and the internal deformation of ice.<ref name="GreveBlatter2009">{{cite book|author1=Greve, R.|author2=Blatter, H. |s2cid=128734526 |year=2009|title=Dynamics of Ice Sheets and Glaciers|publisher=Springer|doi=10.1007/978-3-642-03415-2|isbn=978-3-642-03414-5}}</ref> At the molecular level, ice consists of stacked layers of molecules with relatively weak bonds between layers. When the amount of strain (deformation) is proportional to the stress being applied, ice will act as an elastic solid. Ice needs to be at least {{cvt|30|m|ft}} thick to even start flowing, but once its thickness exceeds about {{cvt|50|m|ft}}, stress on the layer above will exceeds the inter-layer binding strength, and then it will move faster than the layer below.<ref>W.S.B. Paterson, Physics of ice</ref> This means that small amounts of stress can result in a large amount of strain, causing the deformation to become a [[Plasticity (physics)|plastic flow]] rather than elastic. Then, the glacier will begin to deform under its own weight and flow across the landscape. According to the [[Glen–Nye flow law]], the relationship between stress and strain, and thus the rate of internal flow, can be modeled as follows:<ref name="Easterbrook">Easterbrook, Don J., Surface Processes and Landforms, 2nd Edition, Prentice-Hall Inc., 1999{{page needed|date=February 2014}}</ref><ref name="GreveBlatter2009" />

:<math>
\Sigma = k \tau^n,\,
</math>

where: 
:<math>\Sigma\,</math> = shear strain (flow) rate
:<math>\tau\,</math> = stress
:<math>n\,</math> = a constant between 2–4 (typically 3 for most glaciers)
:<math>k\,</math> = a temperature-dependent constant

[[File:Geirangerfjord (6-2007).jpg|thumb|upright|Differential erosion enhances relief, as clear in this incredibly steep-sided Norwegian [[fjord]].]]

The lowest velocities are near the base of the glacier and along valley sides where friction acts against flow, causing the most deformation. Velocity increases inward toward the center line and upward, as the amount of deformation decreases. The highest flow velocities are found at the surface, representing the sum of the velocities of all the layers below.<ref name="Easterbrook" /><ref name="GreveBlatter2009" />

Because ice can flow faster where it is thicker, the rate of glacier-induced erosion is directly proportional to the thickness of overlying ice.  Consequently, pre-glacial low hollows will be deepened and pre-existing topography will be amplified by glacial action, while [[nunatak]]s, which protrude above ice sheets, barely erode at all – erosion has been estimated as 5&nbsp;m per 1.2&nbsp;million years.<ref name=ngeo2008>{{cite journal | author =  Kessler, Mark A.| year =  2008| doi = 10.1038/ngeo201| title = Fjord insertion into continental margins driven by topographic steering of ice| journal = Nature Geoscience | volume =  1 | pages =  365 | last2 =  Anderson | first2 =  Robert S. | last3 =  Briner | first3 =  Jason P. | issue=6 | bibcode=2008NatGe...1..365K}} Non-technical summary: {{cite journal | author = Kleman, John | year = 2008 | doi = 10.1038/ngeo210 | title = Geomorphology: Where glaciers cut deep | journal = Nature Geoscience | volume = 1 | pages = 343 | issue=6|bibcode = 2008NatGe...1..343K }}</ref> This explains, for example, the deep profile of [[fjord]]s, which can reach a kilometer in depth as ice is topographically steered into them.  The extension of fjords inland increases the rate of ice sheet thinning since they are the principal conduits for draining ice sheets. It also makes the ice sheets more sensitive to changes in climate and the ocean.<ref name=ngeo2008/>

Although evidence in favor of glacial flow was known by the early 19th century, other theories of glacial motion were advanced, such as the idea that meltwater, refreezing inside glaciers, caused the glacier to dilate and extend its length. As it became clear that glaciers behaved to some degree as if the ice were a viscous fluid, it was argued that "regelation", or the melting and refreezing of ice at a temperature lowered by the pressure on the ice inside the glacier, was what allowed the ice to deform and flow. [[James David Forbes|James Forbes]] came up with the essentially correct explanation in the 1840s, although it was several decades before it was fully accepted.<ref>{{cite journal| title= A short history of scientific investigations on glaciers|year= 1987 |volume=Special issue |issue= S1 |journal=Journal of Glaciology|pages= 4–5|author=Clarke, Garry K.C.|bibcode= 1987JGlac..33S...4C |doi= 10.3189/S0022143000215785 |doi-access= free }}</ref>

=== Fracture zone and cracks ===
[[File:TitlisIceCracksDeep.jpg|left|thumb|Ice cracks in the [[Titlis]] Glacier]]

The top {{convert|50|m|abbr=on}} of a glacier are rigid because they are under low [[pressure]]. This upper section is known as the ''fracture zone'' and moves mostly as a single unit over the plastic-flowing lower section. When a glacier moves through irregular terrain, cracks called [[crevasse]]s develop in the fracture zone. Crevasses form because of differences in glacier velocity. If two rigid sections of a glacier move at different speeds or directions, [[Shear (geology)|shear]] forces cause them to break apart, opening a crevasse. Crevasses are seldom more than {{convert|150|ft|m|order=flip|abbr=on}} deep but, in some cases, can be at least {{convert|1000|ft|m|order=flip|abbr=on}} deep. Beneath this point, the plasticity of the ice prevents the formation of cracks. Intersecting crevasses can create isolated peaks in the ice, called [[serac]]s.
[[File: Chevron Crevasses 00.JPG|thumb|Shear or herring-bone [[crevasse]]s on [[Emmons Glacier]] ([[Mount Rainier]]); such crevasses often form near the edge of a glacier where interactions with underlying or marginal rock impede flow. In this case, the impediment appears to be some distance from the near margin of the glacier.]]
Crevasses can form in several different ways. Transverse crevasses are transverse to flow and form where steeper slopes cause a glacier to accelerate. Longitudinal crevasses form semi-parallel to flow where a glacier expands laterally. Marginal crevasses form near the edge of the glacier, caused by the reduction in speed caused by friction of the valley walls. Marginal crevasses are largely transverse to flow. Moving glacier ice can sometimes separate from the stagnant ice above, forming a [[bergschrund]]. Bergschrunds resemble crevasses but are singular features at a glacier's margins. Crevasses make travel over glaciers hazardous, especially when they are hidden by fragile [[snow bridge]]s.

Below the equilibrium line, glacial meltwater is concentrated in stream channels. Meltwater can pool in proglacial lakes on top of a glacier or descend into the depths of a glacier via [[Moulin (geomorphology)|moulins]]. Streams within or beneath a glacier flow in englacial or sub-glacial tunnels. These tunnels sometimes reemerge at the glacier's surface.<ref>{{cite news |url=http://www.nasa.gov/vision/earth/lookingatearth/moulin-20061211.html |title=Moulin 'Blanc': NASA Expedition Probes Deep Within a Greenland Glacier |publisher=[[NASA]] |date=2006-12-11 |access-date=2009-01-05 |archive-date=2012-11-04 |archive-url=https://web.archive.org/web/20121104182135/http://www.nasa.gov/vision/earth/lookingatearth/moulin-20061211.html |url-status=dead }}</ref>

===Subglacial processes===
[[File:Davies 2018 glacier sediment erosion rates.png|thumb|Erosion rates of subglacial sediment caused by the motion of different glaciers across the world <ref name="Davies2018">{{Cite journal |last1=Davies |first1=Damon |last2=Bingham |first2=Robert G. |last3=King |first3=Edward C. |last4=Smith |first4=Andrew M. |last5=Brisbourne |first5=Alex M. |last6=Spagnolo |first6=Matteo |last7=Graham |first7=Alastair G. C. |last8=Hogg |first8=Anna E. |last9=Vaughan |first9=David G. |date=4 May 2018 |title=How dynamic are ice-stream beds? |journal=The Cryosphere |volume=12 |issue=5 |pages=1615–1628 |doi=10.5194/tc-12-1615-2018 |doi-access=free |bibcode=2018TCry...12.1615D |hdl=2164/10495 |hdl-access=free }}</ref>]]

Most of the important processes controlling glacial motion occur in the ice-bed contact—even though it is only a few meters thick.<ref name=Clarke2005>{{cite journal | author = Clarke, G. K. C. | title = Subglacial processes | journal = Annual Review of Earth and Planetary Sciences | volume = 33 | issue = 1 | pages = 247–276 | year = 2005 | doi = 10.1146/annurev.earth.33.092203.122621| bibcode = 2005AREPS..33..247C }}</ref> The bed's temperature, roughness and softness define basal shear stress, which in turn defines whether movement of the glacier will be accommodated by motion in the sediments, or if it will be able to slide. A soft bed, with high porosity and low pore fluid pressure, allows the glacier to move by sediment sliding: the base of the glacier may even remain frozen to the bed, where the underlying sediment slips underneath it like a tube of toothpaste.  A hard bed cannot deform in this way; therefore the only way for hard-based glaciers to move is by basal sliding, where meltwater forms between the ice and the bed itself.<ref name=Boulton2006>{{cite book |doi=10.1002/9780470750636.ch2 |chapter=Glaciers and their Coupling with Hydraulic and Sedimentary Processes |title=Glacier Science and Environmental Change |year=2006 |last1=Boulton |first1=Geoffrey S. |pages=2–22 |isbn=978-0-470-75063-6 }}</ref> Whether a bed is hard or soft depends on the porosity and pore pressure; higher porosity decreases the sediment strength (thus increases the shear stress τ<sub>B</sub>).<ref name=Clarke2005/>

Porosity may vary through a range of methods.  
*Movement of the overlying glacier may cause the bed to undergo [[wikt:dilatancy|dilatancy]]; the resulting shape change reorganizes blocks.  This reorganizes closely packed blocks (a little like neatly folded, tightly packed clothes in a suitcase) into a messy jumble (just as clothes never fit back in when thrown in <!--this sentence only makes sense if the word "in" is repeated--> in a disordered fashion).  This increases the porosity.  Unless water is added, this will necessarily reduce the pore pressure (as the pore fluids have more space to occupy).<ref name=Clarke2005/>
*Pressure may cause compaction and consolidation of underlying sediments.<ref name=Clarke2005/> Since water is relatively incompressible, this is easier when the pore space is filled with vapor; any water must be removed to permit compression. In soils, this is an irreversible process.<ref name=Clarke2005/>
*Sediment degradation by abrasion and fracture decreases the size of particles, which tends to decrease pore space. However, the motion of the particles may disorder the sediment, with the opposite effect. These processes also generate heat.<ref name=Clarke2005/>

Bed softness may vary in space or time, and changes dramatically from glacier to glacier. An important factor is the underlying  geology; glacial speeds tend to differ more when they change bedrock than when the gradient changes.<ref name=Boulton2006/> Further, bed roughness can also act to slow glacial motion. The roughness of the bed is a measure of how many boulders and obstacles protrude into the overlying ice.  Ice flows around these obstacles by melting under the high pressure on their [[stoss (geography)|stoss side]]; the resultant meltwater is then forced into the cavity arising in their [[lee side]], where it re-freezes.<ref name=Clarke2005/>

As well as affecting the sediment stress, fluid pressure (p<sub>w</sub>) can affect the friction between the glacier and the bed. High fluid pressure provides a buoyancy force upwards on the glacier, reducing the friction at its base.  The fluid pressure is compared to the ice overburden pressure, p<sub>i</sub>, given by ρgh.  Under fast-flowing ice streams, these two pressures will be approximately equal, with an effective pressure (p<sub>i</sub> – p<sub>w</sub>) of 30&nbsp;kPa; i.e. all of the weight of the ice is supported by the underlying water, and the glacier is afloat.<ref name=Clarke2005/>

====Basal melting and sliding ====
[[File:Glacier cross-section.jpg|thumb|upright|A cross-section through a glacier. The base of the glacier is more transparent as a result of melting.]]
Glaciers may also move by [[basal sliding]], where the base of the glacier is [[lubrication|lubricated]] by the presence of liquid water, reducing basal [[shear stress]] and allowing the glacier to slide over the terrain on which it sits. [[Meltwater]] may be produced by pressure-induced melting, friction or [[geothermal heat]]. The more variable the amount of melting at surface of the glacier, the faster the ice will flow. Basal sliding is dominant in temperate or warm-based glaciers.<ref name="Schoof2010">{{Cite journal | last1 = Schoof | first1 = C. | title = Ice-sheet acceleration driven by melt supply variability | journal = Nature | volume = 468 | pages = 803–806 | year = 2010 | pmid = 21150994 | doi = 10.1038/nature09618|bibcode = 2010Natur.468..803S | issue=7325| s2cid = 4353234 }}</ref>

:&tau;<sub>D</sub> = &rho;gh&nbsp;sin&nbsp;&alpha;
:where &tau;<sub>D</sub> is the driving stress, and &alpha; the ice surface slope in radians.<ref name=Clarke2005/>

:&tau;<sub>B</sub> is the basal shear stress, a function of bed temperature and softness.<ref name=Clarke2005/>

:&tau;<sub>F</sub>, the shear stress, is the lower of &tau;<sub>B</sub> and &tau;<sub>D</sub>.  It controls the rate of plastic flow.

The presence of basal meltwater depends on both bed temperature and other factors. For instance, the melting point of water decreases under pressure, meaning that water melts at a lower temperature under thicker glaciers.<ref name=Clarke2005/> This acts as a "double whammy", because thicker glaciers have a lower heat conductance, meaning that the basal temperature is also likely to be higher.<ref name=Boulton2006/>  Bed temperature tends to vary in a cyclic fashion. A cool bed has a high strength, reducing the speed of the glacier.  This increases the rate of accumulation, since newly fallen snow is not transported away.  Consequently, the glacier thickens, with three consequences: firstly, the bed is better insulated, allowing greater retention of geothermal heat.<ref name=Clarke2005/>

Secondly, the increased pressure can facilitate melting.  Most importantly, τ<sub>D</sub> is increased.  These factors will combine to accelerate the glacier. As friction increases with the square of velocity, faster motion will greatly increase frictional heating, with ensuing melting – which causes a positive feedback, increasing ice speed to a faster flow rate still: west Antarctic glaciers are known to reach velocities of up to a kilometer per year.<ref name=Clarke2005/>
Eventually, the ice will be surging fast enough that it begins to thin, as accumulation cannot keep up with the transport.  This thinning will increase the conductive heat loss, slowing the glacier and causing freezing.  This freezing will slow the glacier further, often until it is stationary, whence the cycle can begin again.<ref name=Boulton2006/>
[[File:Lake_Vostok_drill_2011.jpg|thumb|Location and diagram of [[Lake Vostok]], a prominent subglacial lake beneath the East Antarctic Ice Sheet.]] 
The flow of water under the glacial surface can have a large effect on the motion of the glacier itself.  Subglacial lakes contain significant amounts of water, which can move fast: cubic kilometers can be transported between lakes over the course of a couple of years.<ref name=Fricker2007>{{cite journal| first1 = A.| last3 = Bindschadler| first2 = T.| last2 = Scambos| first3 = R.| first4 = L. | title = An Active Subglacial Water System in West Antarctica Mapped from Space| last1 = Fricker | journal = Science| last4 = Padman | volume = 315 | issue = 5818 | pages = 1544–1548 | date=Mar 2007 | issn = 0036-8075| pmid = 17303716 | doi = 10.1126/science.1136897| bibcode = 2007Sci...315.1544F| s2cid = 35995169}}</ref> This motion is thought to occur in two main modes: ''pipe flow'' involves liquid water moving through pipe-like conduits, like a sub-glacial river; ''sheet flow'' involves motion of water in a thin layer. A switch between the two flow conditions may be associated with surging behavior. Indeed, the loss of sub-glacial water supply has been linked with the shut-down of ice movement in the Kamb ice stream.<ref name=Fricker2007/> The subglacial motion of water is expressed in the surface topography of ice sheets, which slump down into vacated subglacial lakes.<ref name=Fricker2007/>

=== Speed ===
[[File:Wendleder 2024 Baltoro supraglacial acceleration.jpg|thumb|The formation of supraglacial lakes at Baltoro Glacier in April 2018 (top) had substantially accelerated its melting and motion in the following summer months (bottom)<ref name="Wendleder2024">{{Cite journal |last1=Wendleder |first1=Anna |last2=Bramboeck |first2=Jasmin |last3=Izzard |first3=Jamie |last4=Erbertseder |first4=Thilo |last5=d'Angelo |first5=Pablo |last6=Schmitt |first6=Andreas |last7=Quincey |first7=Duncan J. |last8=Mayer |first8=Christoph |last9=Braun |first9=Matthias H. |date=5 March 2024 |title=Velocity variations and hydrological drainage at Baltoro Glacier, Pakistan |journal=The Cryosphere |volume=18 |issue=3 |pages=1085–1103 |doi=10.5194/tc-18-1085-2024 |doi-access=free |bibcode=2024TCry...18.1085W }}</ref>]]
The speed of glacial displacement is partly determined by [[friction]]. Friction makes the ice at the bottom of the glacier move more slowly than ice at the top. In alpine glaciers, friction is also generated at the valley's sidewalls, which slows the edges relative to the center.

Mean glacial speed varies greatly but is typically around {{convert|1|m|ft|0|abbr=on}} per day.<ref>{{cite web |url=http://www.geo.hunter.cuny.edu/tbw/ncc/Notes/chap3.landforms/erosion.deposition/glaciers.htm |title=Glaciers |website=www.geo.hunter.cuny.edu |access-date=2014-02-06 |archive-url=https://web.archive.org/web/20140222172708/http://www.geo.hunter.cuny.edu/tbw/NCC/Notes/chap3.landforms/erosion.deposition/glaciers.htm |archive-date=2014-02-22 |url-status=dead}}</ref> There may be no motion in stagnant areas; for example, in parts of Alaska, trees can establish themselves on surface sediment deposits. In other cases, glaciers can move as fast as {{convert|20|–|30|m|ft|-1|abbr=on}} per day, such as in Greenland's [[Jacobshavn Glacier|Jacobshavn Isbræ]]. Glacial speed is affected by factors such as slope, ice thickness, snowfall, longitudinal confinement, basal temperature, meltwater production, and bed hardness.

A few glaciers have periods of very rapid advancement called [[Surge (glacier)|surges]]. These glaciers exhibit normal movement until suddenly they accelerate, then return to their previous movement state.<ref>[http://earth.esa.int/pub/ESA_DOC/gothenburg/154stroz.pdf T. Strozzi et al.: ''The Evolution of a Glacier Surge Observed with the ERS Satellites''] {{Webarchive|url=https://web.archive.org/web/20141111175824/http://earth.esa.int/pub/ESA_DOC/gothenburg/154stroz.pdf |date=2014-11-11 }} (pdf, 1.3 Mb)</ref> These surges may be caused by the failure of the underlying bedrock, the pooling of meltwater at the base of the glacier<ref>{{cite web|url=http://www.hi.is/~oi/bruarjokull_project.htm |title=The Brúarjökull Project: Sedimentary environments of a surging glacier. The Brúarjökull Project research idea|publisher=Hi.is |access-date=2013-01-04}}</ref>&nbsp;— perhaps delivered from a [[supraglacial lake]]&nbsp;— or the simple accumulation of mass beyond a critical "tipping point".<ref>Meier & Post (1969)</ref> Temporary rates up to {{convert|300|ft|m|-1|order=flip|abbr=on}} per day have occurred when increased temperature or overlying pressure caused bottom ice to melt and water to accumulate beneath a glacier.

In glaciated areas where the glacier moves faster than one km per year, [[glacial earthquake]]s occur. These are large scale earthquakes that have seismic magnitudes as high as 6.1.<ref name="people.deas.harvard.edu">[http://people.deas.harvard.edu/~vtsai/files/EkstromNettlesTsai_Science2006.pdf "Seasonality and Increasing Frequency of Greenland Glacial Earthquakes"] {{webarchive|url=https://web.archive.org/web/20081007062935/http://people.deas.harvard.edu/~vtsai/files/EkstromNettlesTsai_Science2006.pdf |date=2008-10-07 }}, Ekström, G., M. Nettles, and V.C. Tsai (2006) ''Science'', 311, 5768, 1756–1758, {{doi|10.1126/science.1122112}}</ref><ref name="TsaiEkstrom_JGR2007 2007">[http://people.deas.harvard.edu/~vtsai/files/TsaiEkstrom_JGR2007.pdf "Analysis of Glacial Earthquakes"] {{webarchive|url=https://web.archive.org/web/20081007050046/http://people.deas.harvard.edu/~vtsai/files/TsaiEkstrom_JGR2007.pdf |date=2008-10-07 }} Tsai, V. C. and G. Ekström (2007). J. Geophys. Res., 112, F03S22, {{doi|10.1029/2006JF000596}}</ref> The number of [[glacial earthquake]]s in Greenland peaks every year in July, August, and September and increased rapidly in the 1990s and 2000s. In a study using data from January 1993 through October 2005, more events were detected every year since 2002, and twice as many events were recorded in 2005 as there were in any other year.<ref name="TsaiEkstrom_JGR2007 2007"/>

=== Ogives ===
[[File:Forbes Bands on Mer de Glace in France.jpg|thumb|Forbes bands on the [[Mer de Glace]] glacier in France]]
Ogives or Forbes bands<ref>{{cite book|last=Summerfield |first=Michael A. |title=Global Geomorphology |year=1991 |page=269}}</ref> are alternating wave crests and valleys that appear as dark and light bands of ice on glacier surfaces. They are linked to seasonal motion of glaciers; the width of one dark and one light band generally equals the annual movement of the glacier. Ogives are formed when ice from an icefall is severely broken up, increasing ablation surface area during summer. This creates a [[swale (landform)|swale]] and space for snow accumulation in the winter, which in turn creates a ridge.<ref>{{cite book |last=Easterbrook |first=D.J. |title=Surface Processes and Landforms |publisher=[[Prentice-Hall]], Inc. |year=1999 |edition=2 |location=New Jersey |page=546 |isbn=978-0-13-860958-0}}</ref> Sometimes ogives consist only of undulations or color bands and are described as wave ogives or band ogives.<ref>{{cite web|url=http://pubs.usgs.gov/of/2004/1216/no/no.html |title=Glossary of Glacier Terminology |publisher=Pubs.usgs.gov |date=2012-06-20 |access-date=2013-01-04}}</ref>