原文網址：https://www.news.iastate.edu/news/2025/01/08/temperateice
當我們請Neal Iverson敘述最近發表於期刊《科學》(Science)有關冰川流動的研究論文時，他先介紹了兩則冰物理學的相關知識。
這張偏振光照片顯示了在愛荷華州立大學Neal Iverson的實驗室所進行的環剪儀實驗中，遭到變形的冰晶顆粒。實驗得出冰晶顆粒在過程中平均而言會變成三倍大，而且交界變得更加不規則。不同顏色代表的不同方位的顆粒。圖片來源：Neal Iverson
這位愛荷華州立大學地球、大氣與氣候科學系的特聘名譽教授首先說明冰川裡面有不同類型的冰：一部分的冰川剛好處於壓融溫度(pressure-melting
temperature)，因此強度較低且帶有水分。
他說這種溫帶冰(temperate
ice)就像是放在流理台上的冰塊，與檯面之間會有一灘融水。溫帶冰的性質一直以來都是個難以研究的課題。
冰川其它部分則是第二種又冷又硬的冰，就像還在冷凍庫裡面的冰塊一樣。一般的研究都是以這類冰為對象，模擬與預測冰川流動也是以其為基礎。
身為研究共同作者與計畫主持人的Iverson表示這篇新研究「溫帶冰的線性黏性流」(Linear-viscous
flow of temperate ice)探討的對象即為前者。
此論文描述了他們在實驗室如何進行試驗以及得到的數據，結果顯示了模擬冰川流動的經驗基礎——稱為格倫流動定律的方程式(Glen’s
flow law，名稱來自已故的英國冰物理學家John
W. Glen) ——套用到溫帶冰的時候應該要改變其中一個標準數值。
「隨著氣候暖化，冰層萎縮會對冰川造成更多應力，導致冰川的流速增加。當運用格倫流動定律預測流速會增加多少，代入新的數值會較易得到比之前小很多的結果，」Iverson解釋。這意味著模擬結果流到海洋的冰川會變少，海平面上升的幅度也較低。
溫帶冰的行為急需解釋
Iverson在學校的實驗室有座大型冰庫，打開便能看見一台9英尺高(約2.7公尺)的環剪儀。從2009年開始，Iverson便用它來模擬冰河的受力與運動。這台造價53萬美元的儀器由美國國家科學基金會(NSF)出資，當前研究的經費來源也是NSF。
Neal
Iverson實驗室的環剪儀
位在儀器中心的是一個寬約3英尺(約90公分)，厚7英吋(約18公分)的冰環。下方的液壓設備可以對冰環施加高達100噸的力量，以模擬800英尺厚(約245公尺)的冰河重量。周圍是有液體循環流動的水槽，能以近百分之一度為單位調節冰環的溫度。上方則用附有固定器的板子抓住冰環，然後接上電動馬達以每年萬分之一英尺的速度來轉動冰環。
為了執行這項計畫，研究人員對儀器做了點改造：他們在冰環底部也加上固定器，使得上方固定器旋轉的時候能對下方的冰環施加剪力。
團隊最近這篇研究論文的第一作者Collin
Schohn 之前為愛荷華州立大學的博士生，現在則是芝加哥BBJ
Group的地質學家。Schohn運用改造後的儀器接連進行了六個實驗，每個的持續時間為六週。他們也測量了冰的液態水含量，這是1970年代開始進行類似的實驗以來首次納入的項目。
「實驗包括了在不同的應力之下，讓冰的溫度位在該應力的熔點時將它們變形，」Schohn表示。
Iverson將實驗比喻成用手抓住貝果的上下兩半，然後往相反方向旋轉把夾在中間的奶油起司塗抹開來。
Iverson說實驗數據顯示冰的變形速度與應力的比例為線性關係。在傳統的想法當中，研究人員預期冰會隨著應力增加逐漸軟化，因此應力的增長應該會造成變形速度的增長幅度逐漸加大。
為什麼這很重要？
冰層邊緣與底部這些流速最快的部分，以及快速流動的山岳冰河會攜帶冰進到海洋而影響海平面，在這些地方的冰都是處在溫帶冰的狀態。「因此，精準模擬並預測冰川裡的暖冰如何流動，是個相當迫切的需求，」論文作者寫道。
重新把n值設為1.0
格倫流動定律的式子為：ϵ ̇=Aτ^n
這道方程式表達了冰受到的應力τ與變形速率ε ̇之間的關係，A則是依據冰的溫度所給定的常數。新的實驗顯示應力的指數n為1.0，而不是慣用的3或4。
作者寫道，「格倫最初進行的實驗以及後續許多實驗大部分的對象都是冷冰(cold
ice，-2℃以下的冰)。根據那些結果，好幾代的科學家在建立模型時，應力的指數n值皆採用3.0。」(他們也寫到其他對於「冰層裡的冷冰」的研究，甚至會把n設定成更高的4.0。)
原因一部分是「要在壓熔點的溫度下進行實驗相當困難，」論文共同作者Lucas
Zoet表示。他是威斯康辛大學麥迪遜分校的地球科學副教授，之前則是愛荷華州立大學的博士後研究員。身為計畫共同主持人Zoet在他的實驗室也建造了一個尺寸略小、外殼透明的環剪儀。
然而，Iverson實驗室的大尺度剪力變形實驗得出的數據，使他們對常用的n值提出了質疑。作者寫道：「在接近冰河底部與冰川邊緣的液態水含量與應力常用的估計值範圍內，溫帶冰的流動都是呈線性黏滯性(即n
= 1.0)。」
他們提出原因為微米到公分大小的冰晶顆粒在彼此之間的交界處會發生融化與再凍結的現象，其速率跟應力之間的比例應該也為線性。
新數據可以讓模擬人員「跟據實驗室證明出來的物理關係來建立他們的冰層模型，」Zoet表示。「對物理原理有更深的認識可以增加預測準確度。」
在研究人員的鍥而不捨之下才得出數據來支持新的n值。
「我們花了許多年來討論這項計畫，」Schohn說。「要付諸實行真的非常困難。」
Iverson最後說：「將所有的失敗與研發過程通通算進來，這趟旅程大概有10年這麼久吧。」
研究人員表示要更加精準地模擬冰河裡的溫帶冰，進而更加準確地預測冰河流動與海平面上升，如此漫長的過程是不可或缺的。
Researchers use
lab data to rewrite equation for deformation, flow of watery glacier ice
Neal Iverson started with two lessons in
ice physics when asked to describe a research paper about glacier ice flow that
has just been published by the journal Science.
First, said the distinguished professor emeritus of
Iowa State University’s Department of the Earth, Atmosphere, and Climate, there
are different types of ice within glaciers. Parts of glaciers are at their
pressure-melting temperature and are soft and watery.
That temperate ice is like an ice cube left on a
kitchen counter, with meltwater pooling between the ice and the countertop, he
said. Temperate ice has been difficult to study and characterize.
Second, other parts of glaciers have cold, hard ice,
like an ice cube still in the freezer. This is the kind of ice that has
typically been studied and used as the basis of glacier flow models and
forecasts.
The new research paper, “Linear-viscous flow of
temperate ice,” deals with the former, said Iverson, a paper co-author and
project supervisor.
The paper describes lab experiments and the resulting
data that suggest a standard value within the “empirical foundation of glacier
flow modeling” – an equation known as Glen’s flow law, named after the late
John W. Glen, a British ice physicist – should be changed for temperate ice.
The new value when used in the flow law “will tend to
predict increases in flow velocity that are much smaller in response to
increased stresses caused by ice sheet shrinkage as the climate warms,” Iverson
said. That would mean models will show less glacier flow into oceans and
project less sea-level rise.
An acute need to
account for warm glacier ice
Open the walk-in freezer in Iverson’s campus lab and
you’re looking at a 9-foot-tall ring-shear device that’s been simulating
glacial forces and movement since 2009. It was built with a $530,000 grant from
the National Science Foundation. The current study was also supported by NSF grants.
At the center of the device is a ring of ice about 3
feet across and 7 inches thick. Below the ring is a hydraulic press that can
put as much as 100 tons of force on the ice and simulate the weight of a
glacier 800 feet thick. The ice ring is surrounded by a tub of circulating
fluid that regulates the ice temperature to the nearest hundredth of a degree.
Electric motors attached to a plate with grippers above the ice ring can rotate
the ice at speeds of 1 to 10,000 feet per year.
For this project, researchers modified the device by
adding another gripper to the bottom of the ice ring so that rotation of the
upper gripper shears the underlying ice.
Collin Schohn, a former master’s degree student at
Iowa State who’s now a geologist with the BBJ Group based in Chicago and is the
first author of the group’s latest research paper, ran a series of six
experiments using the modified device, each experiment lasting about six weeks.
The experiments included measurements of the ice’s liquid water content,
something that hadn’t been done in these kinds of experiments since the 1970s.
“These experiments involved deforming the ice at its
melting temperatures and at various stresses,” Schohn said.
Iverson likened the experiments to grabbing a bagel
at the top and the bottom, then twisting the two halves to smear the cream
cheese in the middle.
The experimental data showed that ice deformed at a
speed that was linearly proportional to the stress, Iverson said. Traditional thinking
would have researchers expecting ice to soften with increasing stress, so
increments in stress would cause increasingly large increments in speed.
Why does all this matter?
Ice is temperate near the bottoms and edges of the
fastest flowing parts of ice sheets and in fast-flowing mountain glaciers, both
of which shed ice into oceans and influence sea level. “The need to model and
forecast accurately the flow of warm glacier ice is, therefore, acute,” the
authors wrote.
Resetting n to
1.0
Glen’s flow law is written as:
The equation relates the stress on ice, τ, to its rate
of deformation, ε ̇, where A is a constant for a particular ice temperature.
Results of the new experiments show that the value of the stress exponent, n,
is 1.0 rather than the usually assigned value of 3 or 4.
The authors wrote, “For generations, based on Glen’s
original experiments and many subsequent experiments mostly on cold ice (-2
degrees C and colder), the value of the stress exponent n in models has been
taken to be 3.0.” (They also wrote that other studies of the “cold ice of ice
sheets” have placed n higher yet, at 4.0.)
That was, in part, “because experiments with ice at
the pressure melting temperature are a challenge,” said Lucas Zoet, a paper
co-author, a former postdoctoral research associate at Iowa State and the Dean
L. Morgridge Associate Professor of geoscience at the University of
Wisconsin-Madison. Zoet, a co-supervisor of the project, has built a slightly
smaller version of the ring-shear device with transparent walls for his
laboratory.
But data from the large-scale, shear-deformation
experiments in Iverson’s lab raised questions about the assigned value for n.
Temperate ice is linear-viscous (n = 1.0) “over common ranges of liquid water
content and stress expected near glacier beds and in ice stream margins,” the
authors wrote.
They proposed that the cause is melting and
refreezing along the boundaries of individual, millimeter-to-centimeter scale
grains of ice, which should occur at rates linearly proportional to the stress.
These new data allow modelers “to base their ice
sheet models on physical relationships demonstrated in the laboratory,” Zoet
said. “Improving that understanding improves the accuracy of predictions.”
It took some perseverance to get the data supporting
the new value of n.
“We had been batting this project around for years,”
Schohn said. “It was really hard to get this to work.”
In the end, Iverson said, “considering all the
failures and development, this was about a 10-year process.”
A long process, the researchers said, that’s
essential for more accurate models of temperate glacier ice and better
predictions of glacier flow and sea-level rise.
原始論文：Collin M.
Schohn, Neal R. Iverson, Lucas K. Zoet, Jacob R. Fowler, Natasha
Morgan-Witts. Linear-viscous flow of temperate ice. Science,
2025; 387 (6730): 182 DOI: 10.1126/science.adp7708
引用自：Iowa State University. "Researchers use
lab data to rewrite equation for deformation, flow of watery glacier ice."
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