melting ice caps science experiment

Mark the water level of each container with a permanent marker. Next, place the ruler along on the side of each container to measure the water depth in millimeters. Record these water levels as your first observation of sea level. 

As the ice on “land” and in the “sea” melt, what do you predict will happen? Where do you expect the melted ice water to go? 

Measure the water level again at regular intervals, such as at the same time every hour, until all the ice has melted. (Tip: Set a timer to go off every hour.) This could take several hours. At each interval, record the time and the water levels you observe. Optionally, you can continue to mark the levels on the side of the container to help you keep track. 

After the ice in both containers has melted, graph the water levels you recorded at each time interval for both containers. Plot the data points on a graph, with time on the x-axis and water level on the y-axis. Connect the “land ice” points. What do you notice? Connect the “sea ice” points. What do you notice? How did the sea levels change, or not change, in each container?

What might change if you conducted your experiment under different conditions (for example, both containers in a warmer or cooler location)?

Rising sea levels mean the volume of water in the sea has changed. 

The land ice melted and flowed down into the sea, adding more water to the sea and causing the volume of the sea to change. The melted land ice is a new addition to the ocean and causes a change in sea level over time (as your graph shows!).

Sea levels are rising due to melting ice from glaciers and ice sheets found on every continent except Australia. As water from melted land ice pours into the ocean, the volume of water in the global oceans increases. 

What about the melting sea ice? Ice is less dense than water, which is why it floats. When ice melts, the resulting water is denser, so a particular mass of what had been solid ice will have a smaller volume when it becomes liquid water. This change in volume offsets the small percentage of ice that is above the water's surface. Therefore, melting sea ice does not affect sea levels. 

Recent studies show that melting sea ice does have a small effect on sea levels: sea water's density is different from melting ice water because of its saltiness, and therefore, when floating sea ice melts into the ocean, it increases the sea level slightly.

Melting ice isn’t the only culprit for sea level rise. Other factors in the environment also cause sea level rise, including the effects of heating liquid water. When liquid water is warmed up, it increases in volume (takes up more space), while the actual amount of water (number of water molecules) stays the same. This is called thermal expansion , and it’s causing sea levels to rise as sea water is warmed by higher air temperature and expands, taking up more space. Investigate the effects of thermal expansion yourself by trying the Swelling Seas Science Snack .

Teachers can introduce this activity by asking students what they know about ice:  Have you noticed what happens to the water level in a glass of ice water as the ice melts? Where do they predict water will flow once the ice melts in this experiment? At the end of the activity, ask students how they interpret the results (graph) in terms of the actual phenomenon of sea level rise. Which contributes to rising sea levels: sea ice or land ice?

Encourage students to think about the real land/sea environment. Where would water flow as land ice melts? Would land ice or sea ice melt faster? Is global ice melting due to warming of air, land, seawater, or all of the above? Variables to consider include effects of heating of continental materials (soil and solid rock) versus water and air, flow of melting land ice vertically below ground versus horizontally into oceans, and whether land ice or sea ice is more abundant globally.

Students can think like scientists by discussing how well this model represents the sea and land in real life. What might be missing and what could be simplified to improve our understanding of what the model represents? One example of improving this experimental model would be for participants to have control of the temperature around the model. Increasing the temperature around the model throughout the course of the experiment could help represent climate change, and would produce a different rate of sea level rise.

This Snack is also a great opportunity to have students think about data collection and interpretation. How would they report their findings to others who did not conduct the experiment? How could this be explained to make it clear to others? What do the results mean for understanding causes of sea level rise? What does a graph of a horizontal line mean as an observation? How would changing a variable in the model affect the trend in the data (examples: slope of line changes, all values decrease/increase equally)?

For younger students, this could be set up as a demonstration or station, which a class can observe over the course of a school day, marking the sides of the containers with the water levels every hour.

This Snack is adapted from an activity developed by the NASA Jet Propulsion Laboratory.

Melting Ocean Ice Affects Sea Level – Unlike Ice Cubes in a Glass (NASA)

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13 min read

Warming Seas and Melting Ice Sheets

Jessica Evans

Public affairs officer.

Sea level rise is a natural consequence of the warming of our planet.

We know this from basic physics. When water heats up, it expands. So when the ocean warms, sea level rises. When ice is exposed to heat, it melts. And when ice on land melts and water runs into the ocean, sea level rises.

For thousands of years, sea level has remained relatively stable and human communities have settled along the planet’s coastlines. But now Earth’s seas are rising. Globally, sea level has risen about eight inches since the beginning of the 20th century and more than two inches in the last 20 years alone.

All signs suggest that this rise is accelerating.

While NASA and other agencies continue to monitor the warming of the ocean and changes to the planet’s land masses, the biggest concern is what will happen to the ancient ice sheets covering Greenland and Antarctica, which continue to send out alerts that a warming planet is affecting their stability.

“We’ve seen from the paleoclimate record that sea level rise of as much as 10 feet in a century or two is possible, if the ice sheets fall apart rapidly,” said Tom Wagner, the cryosphere program scientist at NASA Headquarters in Washington. “We’re seeing evidence that the ice sheets are waking up, but we need to understand them better before we can say we’re in a new era of rapid ice loss.”

Finding the Level

NASA has been recording the height of the ocean surface from space since 1992. That year, NASA and the French space agency, CNES, launched the first of a series of spaceborne altimeters that have been making continuous measurements ever since. The first instrument, Topex/Poseidon, and its successors, Jason-1 and -2, have recorded about 2.9 inches (7.4 centimeters) of rise in sea level averaged over the globe.

In the 21st century, two new sensing systems have proven to be invaluable complements to the satellite altimetry record. In 2002, NASA and the German space agency launched the Gravity Recovery and Climate Experiment (GRACE) twin satellites. These measure the movement of mass, and hence gravity, around Earth every 30 days. Earth’s land masses move very little in a month, but its water masses move through melting, evaporation, precipitation and other processes. GRACE records these movements of water around the globe. The other new system is the multinational Argo array, a network of more than 3,000 floating ocean sensors spread across the entire open ocean.

“To study sea level rise, the Jason series, GRACE, and Argo are the big three,” said oceanographer Josh Willis of NASA’s Jet Propulsion Laboratory, Pasadena, California, the project scientist for the upcoming Jason-3 altimetry mission.

Observations from the Jason series have revolutionized scientists’ understanding of contemporary sea level rise and its causes. We know that today’s sea level rise is about one-third the result of the warming of existing ocean water, with the remainder coming from melting land ice.

And it has shown precisely that the sea, of course, is not actually level. It varies as much as six feet (two meters) from place to place. And it is not rising evenly, like a bathtub filling with water. Currently, regional differences in sea level rise are dominated by the effects of ocean currents and natural cycles such as the Pacific Ocean’s El Niño phenomenon and Pacific Decadal Oscillation. As the ice sheets continue to melt, scientists predict their meltwater will overtake natural causes as the most significant source of regional variations and the most significant contributor to overall sea level rise.

Or as Willis put it: “You ain’t seen nothing yet.”

Watching Ice Melt

Not that long ago, in the early 1990s, scientists were not able to determine whether polar land ice was growing, shrinking, or in balance. Satellite and airborne missions, complemented by field measurements, have not only answered that question, but also provided the means for scientists to determine the mechanisms that are contributing to the growth and shrinkage of polar ice.

These advances in observing the world’s frozen regions have allowed scientists to accurately estimate annual ice losses from Greenland and Antarctica in only the last decade. We now know not only how much sea level is changing – as measured by satellite for the past 23 years – but we can determine how much sea level rise is caused by the loss of land ice.

In addition to the launch of the GRACE satellites in 2002, NASA also deployed the Ice Cloud and land Elevation Satellite (ICESat) from 2003 to 2009 to map changes in the height of the polar ice sheets using laser pulses. Other space agencies have used radar instruments to measure glacier speeds, as well as surface topography, such as the European Space Agency’s CryoSat-2 satellite. Airborne missions, like NASA’s Operation IceBridge, complement these measurements with instruments that map the bedrock topography beneath the ice, determine ice thickness and characterize its internal layers, and detect the depth of overlying snow. Combining these relatively recent – and unprecedented – measurements with longer-term satellite records and reanalyses of regional climate data  extends the record of ice sheet mass balance to more than 40 years.

Several studies have shown that different remote sensing methods for studying ice sheet mass balance agree well. GRACE’s record, spanning over a decade, shows that the ice loss is accelerating in Greenland and West Antarctica. Greenland has shed on average 303 gigatons of ice every year since 2004, while Antarctica has lost on average 118 gigatons of ice per year, with most of the loss coming from West Antarctica. Greenland’s ice loss has accelerated by 31 gigatons of ice per year every year since 2004, while West Antarctica has experienced an ice mass loss acceleration of 28 gigatons per year.

“Given what we know now about how the ocean expands as it warms and how ice sheets and glaciers are adding water to the seas, it’s pretty certain we are locked into at least 3 feet of sea level rise and probably more,” said Steve Nerem of the University of Colorado, Boulder, and lead of NASA’s new Sea Level Change Team. “But we don’t know whether it will happen within a century or somewhat longer.”

The Warming North

The Greenland Ice Sheet, spanning 660,000 square miles (an area almost as big as Alaska) and with a thickness at its highest point of almost 2 miles, has the potential to raise the world’s oceans by more than 20 feet. Situated in the Arctic, which is warming at twice the rate of the rest of the planet, Greenland fell out of balance in the 1990s, and is now shedding more and more ice in the summer than it gains back in the winter.

Download this video in HD formats from NASA Goddard’s Scientific Visualization Studio

“In Greenland, everything got warmer at the same time: the air, the ocean surface, the depths of the ocean,” said Ian Joughin, a glaciologist at University of Washington. “We don’t really understand which part of that warming is having the biggest effect on the glaciers.”

What scientists do know is that warming Arctic temperatures – and a darkening surface of the Greenland ice sheet – are causing so much summer melting that it is now the dominant factor in Greenland’s contribution to sea level rise.

Greenland’s summer melt season now lasts 70 days longer than it did in the early 1970s. Every summer, warmer air temperatures cause melt over about half of the surface of the ice sheet – although recently, 2012 saw an extreme event where 97 percent of the ice sheet experienced melt at its top layer.

Greenland’s glaciers have sped up, too. Though many of the glaciers in the southeast, west and northwest of the island that experienced quick thinning from 2000 to 2006 have now slowed down, others haven’t. A study last year showed that the northeast Greenland ice stream had increased its ice loss rate due to regional warming.

“The early 2000s was when some big things revealed themselves, such as when we saw the fastest glacier we knew of, the Jakobshavn ice stream in Greenland, double its speed,” said Waleed Abdalati, director of the Cooperative Institute for Research in Environmental Sciences, Boulder, Colorado, and former NASA chief scientist. “The subsequent surprise was that these changes could be sustained for a decade – Jakobshavn is still going fast.”

To answer the questions of how these glaciers will behave, how much they will contribute to sea level rise and how fast those changes will occur, scientists need better data on the bathymetry or geography of the ocean floor surrounding Greenland, said Eric Rignot, a glaciologist with NASA’s Jet Propulsion Laboratory and the University of California, Irvine.

“Bathymetry is critical for understanding how ocean waters circulate around Greenland, for projections and for understanding what we’ve been observing in the past few decades,” Rignot said.

Beginning with the deployment of research buoys in the waters around Greenland this summer, NASA is embarking on a three-year airborne and ship-based campaign to answer precisely these questions. OMG, Oceans Melting Greenland, seeks to understand the role of ocean currents and ocean temperatures in melting Greenland’s ice from below – and therefore better predict the speed at which the ice sheet will raise sea level.

Changes At The Southern End of The World

The Antarctic Ice Sheet covers nearly 5.4 million square miles, and area larger than the United States and India combined, and contains enough ice to raise the ocean level by about 190 feet. The Transantarctic Mountains split Antarctica in two major regions: West Antarctica and the much larger East Antarctica.

Though Antarctica’s contribution to sea level rise is still at less than 0.02 inches (0.5 millimeters) per year, several events over the past decade and a half have prompted experts to start warning about an the possibility of more rapid changes in the upcoming century.

The mountainous horn of the continent, the Antarctic Peninsula, gave one of the earliest warnings on the impact of a changing climate in Antarctica, when warming air and ocean temperatures led to the dramatically fast breakup of the Larsen B ice shelf in 2002. In about a month, 1,250 square miles of floating ice that had been stable for over 10,000 years were gone. In the following years, other ice shelves in the Peninsula, including the last remainder of Larsen B, collapsed, speeding up in the flow of the glaciers that they were buttressing.

In 2014, West Antarctica grabbed the spotlight when two studies focusing on the acceleration of the glaciers in the Amundsen Sea sector showed that its collapse is underway. While one of the studies said that the demise could take 200 to 1,000 years, depending on how rapidly the ocean heats up, both studies concurred that the collapse is unstoppable and will add up to 12 feet of sea level rise.

For the West Antarctic Ice Sheet, which largely rests on a bed that lies below sea level, the main driver of ice loss is the ocean. The waters of the Southern Ocean are layered: on top and at the bottom, the temperatures are frigid, but the middle layer is warm. The westerlies, the winds that spin the ocean waters around Antarctica, have intensified during the last decade, pushing the cold top layer away from the land. This allows the warmer, deeper waters to rise and spill over the border of the continental shelf, flowing all the way back to the base of many ice shelves. As the ice shelves weaken from underneath, the glaciers behind them speed up.

East Antarctica’s massive ice sheet, as vast as the lower continental U.S., remains the main unknown in projections of sea level rise. Though it appears to be stable, a recent study on Totten Glacier, East Antarctica’s largest and most rapidly thinning glacier, hints otherwise. The research found two deep troughs that could lead warm ocean water to the base of the glacier and melt it in a similar way to what’s happening to the glaciers in West Antarctica. Other sectors grounded below sea level, such as the Cook Ice Shelf, Ninnis, Mertz and Frost glaciers, are also losing mass.

“The prevailing view among specialists has been that East Antarctica is stable, but I don’t think we really know,” said Rignot. “Some of the signs we see in the satellite data right now are kind of red flags that these glaciers might not be as stable as we once thought. There’s always a lot of attention paid by the media to the changes we see now, but as scientists our priority remains what the changes could be tomorrow.”

On the other hand, weather models and reanalyses have shown that there has been an increase in snowfall along the coastline of Dronning Maud Land, which might counteract East Antarctica’s ice loss. But this may be a temporary shift – scientists can’t tell, because obtaining accurate field measurements of snow in Antarctica is extremely difficult. There are few weather stations and they might not provide representative measurements because snowfall in Antarctica doesn’t distribute evenly; the strong katabatic winds wipe some areas clean and make snow pile up in others. And satellite readings are not yet precise enough to detect small accumulation changes that would represent a difference of gigatons of mass when spread over East Antarctica’s huge surface.

As is the case for Greenland, researchers also working on Antarctica need better data on the Southern Ocean bathymetry and the pathways that warm waters can follow to reach the ice. And this kind of data, as well as snow accumulation and other ocean data, can’t be obtained remotely with enough precision, according to Ted Scambos lead scientist at the University of Colorado’s National Snow and Ice Data Center.

“We’ve learned so much from the satellites that we’ve been surfing the wave of new understanding for the last 20 years,” Scambos said. “But now, to go further, we have to try to get instruments on the ground while maintaining the ability we have with airborne and satellite missions to watch the ice sheet from a global perspective.”

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Melting Ice Science Experiment

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This is a fun, non-toxic project for kids of all ages, and the best part is you likely have everything you need at home. All you need is ice, salt, and food coloring.

You can use any type of salt for this project. Coarse salt, such as rock salt or sea salt , works great. Table salt is fine. Also, you could use other types of salt besides sodium chloride (NaCl). For example, Epsom salts are a good choice.

You don't have to color the project, but it's a lot of fun to use food coloring, watercolors, or any water-based paint. You can use liquids or powders, whichever you have handy.

• Food coloring (or watercolors or tempera paints)

Experiment Instructions

• Make ice. You can use ice cubes for this project, but it's nice to have larger pieces of ice for your experiment. Freeze water in shallow plastic containers such as disposable storage containers for sandwiches or leftovers. Only fill the containers part way to make relatively thin pieces of ice. The salt can melt holes all the way through thin pieces, making interesting ice tunnels.
• Keep the ice in the freezer until you are ready to experiment, then remove the blocks of ice and place them on a cookie sheet or in a shallow pan. If the ice doesn't want to come out, it's easy to remove ice from containers by running warm water around the bottom of the dish. Place the pieces of ice in a large pan or a cookie sheet. The ice will melt, so this keeps the project contained.
• Sprinkle salt onto the ice or make little salt piles on top of the pieces. Experiment.
• Dot the surface with coloring. The coloring doesn't color the frozen ice, but it follows the melting pattern . You'll be able to see channels, holes, and tunnels in the ice, plus it looks pretty.
• You can add more salt and coloring, or not. Explore however you like.

Clean Up Tips

This is a messy project. You can perform it outdoors or in a kitchen or bathroom. The coloring will stain hands, clothes, and surfaces. You can remove coloring from counters using a cleaner with bleach.

How It Works

Very young kids will like to explore and may not care too much about the science, but you can discuss erosion and the shapes formed by running water. The salt lowers the freezing point of water through a process called freezing point depression . The ice starts to melt, making liquid water. Salt dissolves in the water, adding ions that increase the temperature at which the water could re-freeze. As the ice melts, energy is drawn from the water, making it colder. Salt is used in ice cream makers for this reason. It makes the ice cream cold enough to freeze. Did you notice how the water feels colder than the ice cube? The ice exposed to the salty water melts faster than other ice, so holes and channels form.

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The ice is melting

In this set of four activities from the European Space Agency, students explore the impacts of global warming and melting ice on the Earth. They learn the difference between land ice and sea ice, and will investigate the respective effects of these melting. They then design their own experiment to examine how melting ice changes the temperature of the atmosphere. The project ends with learning about glaciers, and by looking at satellite images of a glacier to consider how much it has melted over a period of time.

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Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.

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Creative Ways to Use Graphic Novels in the Classroom! 🎥

16 Meaningful and Hands-On Climate Change Activities for Kids

How to teach about our changing planet.

Climate change is one of those important topics that can be hard to tackle in the classroom. Some teachers face opposition from parents, communities, or even school curriculum requirements that deny the existence or importance of climate change. But it’s vital to give kids the facts by using climate change activities that help them understand what’s taking place—and why it matters. Try some of these ideas with your students, accompanied with discussion about what kids can do to help keep our planet healthy for years to come .

1. Inspire your students to think locally

Climate change can feel like an insurmountable problem to many students. How can they have a meaningful impact on this global issue? The right resources can make all the difference in helping young people see how they can take action in their own community to make a real difference. This climate action resource kit from World Wildlife Fund’s Wild Classroom contains an informative slideshow as well as several lesson plans that are a perfect place to start.

2. Take part in the World’s Largest Lesson

In partnership with UNICEF, World’s Largest Lesson promotes use of the Sustainable Development Goals in learning so that children can contribute to a better future for all. Learn more about their videos, lessons, and resources here.

3. Understand the difference between climate and weather

One common refrain you might hear is, “It snowed 20 inches today, so explain how global warming is real.” That’s when it’s time to tackle the difference between weather (the current conditions) and climate (the average of those conditions over time in a particular region). Make an anchor chart like this one from Hayley Taylor on Pinterest . Then try a sorting activity to help kids understand the difference between the two. You can make your own cards, or find them on sites like Teachers Pay Teachers .

4. Measure temperatures to learn about the greenhouse effect

Global warming is a key component of climate change, and it’s caused in part by an enhanced greenhouse effect. Climate change activities like this one show kids just what that term means. Place two thermometers side by side in a sunny spot. Put one inside a covered glass jar, and leave the other one outside. Observe the temperatures after about 20 minutes to see which is higher. Learn more about this activity at Kid Minds.

5. Meet the greenhouse gases

Now that kids have seen the greenhouse effect in action, introduce them to the gases that make it happen. These fun trading cards of the six major atmospheric gases teach students what they are and where they come from. Each card has two sides, showing the positive and negative effects of that gas. Get the free printable cards from NASA here.

6. Make edible greenhouse gas models

Dive deeper into the chemistry of greenhouse gases by making edible models from toothpicks and gumdrops. Science Sparks has all the details.

7. Do a climate change word search

Try this free printable word search to reinforce the terms kids are learning during climate change activities. It’s part of this larger free lesson plan from Woo Jr .

8. Eat some Earth toast

Show kids how too much heat can make things (like deserts and other inland areas) hotter and drier with this fun edible experiment. Kids use milk paint to create “Earth” from bread, then bake it in a toaster oven to see what happens. Learn more from Left Brain Craft Brain.

9. Learn about conditions affecting ice melt

The accelerated melting of the polar ice caps and glaciers is of huge concern to climate change scientists. This simple experiment shows how ice in water melts faster than ice on land. Find out more from Science Learning Hub.

10. Explore how melting ice affects sea levels

The North Polar Ice Cap sits on water, while the South Polar Ice Cap is on land. Learn which of these two can cause sea levels to rise with this experiment, perfect for a science fair project. Get the how-to from Science Buddies.

11. Simulate melting polar ice caps and icebergs

Ice-melting experiments are very helpful climate change activities for seeing sea level rise in action, so here’s another one to try. If you’re unable to perform this one in person, show National Geographic’s video instead .

12. Discover how melting sea ice affects animals too

Humans aren’t the only ones affected by global warming and sea ice melt. In this experiment, kids try to help model polar bears stay afloat as the ice around them starts to melt. Learn more from Kitchen Counter Chronicle.

13. Trap particles to learn about air pollution

Particulates in the air are another cause of global warming and climate change. This experiment uses Vaseline and index cards to capture visible particulates from indoor and outdoor spaces, so students can compare them. Get the details at Education.com.

14. Water plants with acid solutions

Acid rain isn’t in the news as much these days, thanks to the incredible effectiveness of the EPA’s Acid Rain Program . It’s still good for kids to learn about, though, since when unchecked, it can do real damage to plants and the environment. Try this experiment, in which kids water plants with regular water and a lemon juice–water solution, to see the effects. Learn how it works from Education.com.

15. Play the Carbon Cycle Game

Carbon is another big contributor to global warming and climate change. Learn how the natural carbon cycle works, and how too much carbon throws the cycle off, with this free printable game from COSEE .

16. Track your carbon footprint

Good climate change activities should include action items kids and their families can take. Explore the term “carbon footprint” and then brainstorm ways to reduce it with this cute idea from Kitchen Counter Chronicle .

Ready to do your part? Check out our big collection of Recycling Activities for Kids .

Plus, check out 20 wild ways to explore animal habitats ., looking for more articles like this subscribe to our newsletters to find out when they’re posted.

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Summer of Science: Melting Polar Ice Caps

Being aware of your potential to impact the world  is an important lesson to learn and one that continues well into adulthood.  In this week’s Summer of Science experiments we’re broadening our ecological awareness and exploring how pollution impacts weather in the form of melting polar ice caps and acid rain. 

I think it’s important, and necessary, for children to understand and realize that the same things we’re studying in our experiments are happening in the world RIGHT NOW and eventually the end result of the experiment is going to be the end result for Earth if we don’t start changing our ways. And now, on to the experiment!

There’s no denying it, global warming is a major contributor to a number of ecological problems whose effects are far reaching.  Melting ice caps effect water levels, weather patterns, the ocean’s salt levels, below sea level islands, and the animals and people who make the coast their home.  In this experiment we’re going to melt our own ice caps and see what happens.

• handful of ice

Fill each glass with one cup of water and 10 drops of food coloring.

Now fill ONE glass with the handful of ice. 

To speed things up we sat both the glasses outside and waited for the ice to melt.

The water level difference between the two glasses should be obvious while the coloring is a little harder to see.

Explanation : To explain this experiment I just asked my kids a series of questions.  They got the point.

Imagine this glass of water is all the world’s oceans, what would’ve happened to low lying islands?  coastlines?  What about the polar bears and other animals who depend on the ice? What’s happened to the salt in the water?  Do the fish need the salt in the water to breathe?  Remember the water cycle?  If there’s more water on the Earth is that going to effect the weather?

Additional Reading: I recommend visiting the Natural Resources Defense Council to learn more about defending our Earth.

Hope you’ve been enjoying our Summer of Science Series!  If you’d like to learn more please Subscribe and take a moment to visit my Linky Party Page for some of the great places I share experiments like these!

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Key takeaway:.

Antarctica is losing ice mass (melting) at an average rate of about 150 billion tons per year, and Greenland is losing about 270 billion tons per year, adding to sea level rise.

Data from NASA's GRACE and GRACE Follow-On satellites show that the land ice sheets in both Antarctica (upper chart) and Greenland (lower chart) have been losing mass since 2002.

The GRACE mission ended in June 2017. The GRACE Follow-On mission began collecting data in June 2018 and is continuing to monitor both ice sheets. This record includes new data-processing methods and is continually updated as more numbers come in, with a delay of up to two months.

This is important because the ice sheets of Greenland and Antarctica store about two-thirds of all the fresh water on Earth. They are losing ice due to the ongoing warming of Earth’s surface and ocean. Meltwater coming from these ice sheets is responsible for about one-third of the global average rise in sea level since 1993.

Note: You now need to create an Earthdata account to access NASA's ice sheet data. Register here for free. Once logged in, click "HTTP" under the charts on this page to access the data.

Missions That Observe Land Ice

Gravity Recovery and Climate Experiment Follow-On (GRACE-FO)

NASA's IceBridge

ANTARCTICA MASS VARIATION SINCE 2002

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Science project, melting ice experiment.

Wanna see a magic trick? Magicians always make their tricks look like supernatural phenomena. But scientists can do “magic” tricks with explanations that are almost as cool as the tricks themselves.

In this experiment, we’re going to magically lift a piece of ice using only string and salt. Can we do it? Let’s find out.

Can you lift an ice cube out of water with just a piece of string and salt?

• 6 inches of string
• Fill the cup with cold water.
• Place the ice cube on the surface of the water.
• Lay the string across the top of the ice cube
• Pour salt on top of the ice cube and the string.
• Wait 5 minutes.
• Do you think the string will be able to lift the ice cube? If so, explain why. Use this time to write down your guess, also called a hypothesis, in your notebook.
• Gently pull the string on both sides and lift upwards.

The string will lift the ice cube out of the cup.

The string alone could probably never lift an ice cube out of the cup. However, salt elevates the temperature at which water freezes, causing the surface of the ice cube touching the string to rapidly melt. The salt quickly gets diluted into the rest of the water, causing the temperature at which the water can freeze to drop back down again. This allows water to quickly refreeze near the surface of the cube, trapping the string. Now, you’ll have no problem lifting the ice cube out of the water!

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Add to collection, create new collection, new collection, new collection>, sign up to start collecting.

Bookmark this to easily find it later. Then send your curated collection to your children, or put together your own custom lesson plan.

 / 

Researcher Andrea Spolaor holds an ice core recovered in Svalbard, Norway in April 2023. Scanderbeg Sauer Photography

The Race to Save Glacial Ice Records Before They Melt Away

As glaciers melt around the globe, scientists are racing to retrieve ice cores that contain key historical records of temperature and climate that are preserved in the ice. Researchers are also pushing to gather ancient relics locked in the ice before they are lost to warming

By Nicola Jones • July 1, 2024

When Margit Schwikowski helicoptered up to Switzerland’s Corbassière glacier in 2020, it was clear that things weren’t right. “It was very warm. I mean, we were at 4,100 meters and it should be sub-zero temperatures,” she says. Instead, the team started to sweat as they lugged their ice core drill around, and the snow was sticky. “I thought, ‘This has never happened before.’”

What Schwikowski couldn’t see yet, but would find later in the lab, is that it wasn’t just the surface that was affected: Climate change had penetrated the ice and trashed its utility as an environmental record. Warming weather had created meltwater that trickled down, washing away trapped aerosols that researchers like her use as a historical record of forest fires and other environmental events. Because of the melt, she says, “we really lose this information.”

Schwikowski, an environmental chemist at the Paul Scherrer Institut near Zurich, is the scientific lead for the Ice Memory Foundation, a collaborative group that aims to preserve glacial ice records before climate change wrecks them. Their goal is to get cores from 20 glaciers around the world in 20 years, and, starting in 2025, lock them away for long-term storage in an ice cave in the Antarctic — a natural freezer that will hold them at close to minus 60 degrees F (minus 50 degrees C). Since the program’s start in 2015 they have taken cores from eight sites , in France, Bolivia, Switzerland, Russia, Norway, and Italy. But the core attempted from Corbassière was a failure — and has the team wondering if they are already too late.

Studies show the pace of glacial ice loss has accelerated from a few inches per year in the 1980s to nearly 3 feet per year in the 2010s.

The team, watching in despair as ice cores melt and muddle, is not alone in seeing climate change wreaking havoc with scientific records — often in unexpected ways. Geologists who hunt for meteorites on the ice in Antarctica are finding their mission thwarted by warming temperatures. And while archaeologists who study the artifacts spat out by ice patches are seeing a bonanza of new finds, they are also racing to get to those objects before they rot. Other heritage sites are slumping into thawing permafrost .

What all these researchers have in common is a race to preserve what they can, while they can. When you are standing on a glacier that’s literally melting under your feet, says Schwikowski, “you really feel the urgency.”

Due to climate change, high mountain glaciers are now endangered, losing ice faster than they are gaining it. Studies of a few dozen well-monitored glaciers in the World Glacier Inventory have shown that the pace of glacial ice loss has accelerated from a few inches per year in the 1980s to nearly 3 feet per year in the 2010s. A 2023 model of some 215,000 mountain glaciers showed that nearly half of them could disappear entirely by 2100 if the world warms by just 1.5 degrees C, the ambitious maximum warming target of the Paris Agreement.

Researchers extract an ice core on an Ice Memory Foundation expedition to the Colle del Lys glacier in the Alps, October 2023. Riccardo Selvatico / CNR / Ice Memory Foundation

Glaciers have annual layers, just like tree rings. At the top, a single year might see a few feet of snow added to the surface. Hundreds of feet down, weight compresses ice that is thousands of years old into thin, flowing layers, where less than an inch may contain a century of snowfall.

This ice preserves all kinds of information from the time when it was deposited. A spike in lead pollution comes at the height of the Roman Empire. A drop in pollen reveals the collapse of farming during the Black Death. The Chernobyl accident left a layer of radioactive cesium . Black carbon and the sugars from burned cellulose map out changes in forest fire activity across the globe. The ratio of different oxygen and hydrogen isotopes in the water also reveals the air temperature of the time .

Many mountain glaciers have been cored and studied over the past decades. Since scientific methods and research questions change over time, researchers preserve some cores or sections intact for future reference — to study, say, the genetics of ancient DNA . The National Science Foundation Ice Core Facility in Colorado, for example, holds 82,000 feet of collected ice cores — mostly from Greenland and the Antarctic, but also from North American mountaintop glaciers.

The problem of glacial ice melting has been apparent for many years. “Everyone in our community is worried,” says a scientist.

The problem of glacial ice melting has been apparent for many years, says paleoclimatologist Ellen Mosley-Thompson of Ohio State University. In 2000, when she and her colleagues drilled to bedrock on Mount Kilimanjaro, they found the surface dated to the 1950s. The top 50 years of snow was gone. “Everyone in our community is worried,” she says.

Dorothea Moser, a PhD student who works on the ice core chemistry team at the British Antarctic Survey, says she has seen cores damaged by melt even in polar regions , including Greenland and coastal Antarctica. “I’ve got records from Young Island [in the Southern Ocean] that have been heavily melt affected,” she says. She is now working to see what kinds of information can still be salvaged from corrupted cores.

Moser warns that ice cores are highly vulnerable to increased melting through global warming. “This is why we need to retrieve them, where possible,” she says.

In 2015, glaciologist Jérôme Chappellaz of the Swiss Federal Institute of Technology and chemist Carlo Barbante of the University of Venice established the Ice Memory Foundation to capture archival cores from endangered mountain glaciers. “Ice Memory is attempting to answer the call of these glaciers before they disappear,” says Mosley-Thompson, who is not a member of the foundation.

Margit Schwikowski holds an ice core from the Corbassière glacier in the Alps, September 2020. Scanderbeg Sauer Photography

Less than a dozen teams around the world do coring work in high mountain settings, says Schwikowski — it takes skill and determination to haul the equipment up to these remote locations, she says, often in collaboration with mountaineers. Progress has been slow. And, just halfway into their collection effort, the work at Corbassière has shown it may already be too late to get pristine records from some sites.

The team only retrieved around 60 feet of core from Corbassière, rather than the 260 feet down to bedrock that they had hoped for, because the drill got stuck in melted-and-refrozen ice. And a comparison of this truncated 2020 core with a 2018 sample from the same spot showed that the record was corrupted. While the temperature record was preserved, the spikes of nitrate, sulphate, and ammonia they had seen in the 2018 core had, by 2020, washed away. The team thinks the cumulative effect of meltwater is to blame. Deeper ice may or may not be damaged, too.

The team has no idea how many other glaciers are affected: a core that the group took more recently from Svalbard in Norway was similarly muddled, says Schwikowski, while one taken from Monte Rosa in the Alps in 2021 seems to be intact. “I am afraid that most of them are already affected,” she says. “We will see what we can do.”

Human artifacts were only occasionally recovered from ice patches until the 1990s, when such finds sped up along with the rate of ice melt.

The loss of paleorecords in glacial ice is also distressing to archaeologists, who use those signals to help unravel the behaviors of past societies and the environmental conditions they faced. Of course, archaeologists also have another category of study material: human artifacts. To find these, they often look to ice patches — wind-blown snow drift accumulations that can be thousands of years old. Christian Thomas, an archaeologist with the Yukon Territory’s Department of Tourism and Culture, says such patches typically overlap with traditional summer hunting grounds, so ancient weapons are often found there.

The first documented find from an ice patch was an arrow in Norway during a particularly warm year in 1914. Discoveries were only random and occasional until the 1990s, when such finds sped up along with the rate of ice melt, says Lars Holger Pilø, co-director of the Secrets of the Ice program at Norway’s Department of Cultural Heritage. “We had no idea how intense the human use of the high mountains had been until all these artifacts started to emerge from the retreating ice,” he says. “In that way, we are unlikely beneficiaries of global warming.”

A 1,200-year-old birch distaff found near the shrinking Lendbreen ice patch in Norway. Espen Finstad / Secrets of the Ice

Since Pilø started his own work in 2006, he says the number of finds and sites has exploded, from a few hundred finds and less than 10 sites in 2006 to more than 4,000 finds from 69 sites in 2023. Some objects date back 6,000 years. They have found more arrows, clothing (including a 1,700 year-old Iron Age tunic and a 3,400 year-old Early Bronze Age shoe), and even prehistoric skis . Such items are often in pristine condition, “frozen in time” says Pilø. “But once they become exposed to the elements, the clock starts ticking fast, and they will [decompose and] be lost if they are not found and conserved.”

“Our ice patch sites are considered imperilled,” says Thomas, who doesn’t expect the ones in the Yukon to survive the next 20 to 30 years. Both in the Yukon and in Norway, scientists are on a quest to collect archaeological finds as quickly as possible.

While markers of human history are being erased, other researchers are worried, too, about access to markers of the solar system’s history: meteorites. These inch-sized chunks of the moon, Mars, or the asteroid belt contain vital evidence about the elemental composition of celestial objects and their origins. These rocks fall to Earth everywhere but are easiest to spot against white snow. Hundreds of meteorites fall over the vast surface of the Antarctic each year, and, over millennia, this has built up to an estimated stock of 300,000 to 850,000 space rocks sitting out on the ice. Researchers typically go out and collect about 1,000 a year, from “blue ice” fields where the meteorites are brought to the surface by ice flow and where no fresh snow falls to hide them.

By the end of the century, some 25 percent to 75 percent of the meteorites sitting on Antarctic ice could disappear from view.

Glaciologists Harry Zekollari and Veronica Tollenaar of the Université libre de Bruxelles set out to map the best places to hunt for these rocks, using an artificial intelligence model. Their work revealed that temperature is a major factor determining where meteorites can be found. The reason is simple: black rocks absorb heat from the sun. Even a brief spate of 16 degrees F (minus 9 degrees C) is warm enough for a meteorite to melt the snow beneath it, says Tollenaar, allowing it to sink — just as gravel thrown onto an icy driveway will drill down into tiny holes during the heat of the day.

The team estimates that some 5,000 meteorites sink out of sight this way each year and that every tenth of a degree Celsius of warming adds an additional 5,000 to the loss. By the end of the century, they predict, some 25 percent to 75 percent of the meteorites sitting on Antarctic ice could disappear from view, taking scientific information with them.

The Ice Memory Foundation is continuing on its mission to gather and store ice cores. But it’s hard going. Trips planned to take a core from Kilimanjaro in 2022, and in Tajikistan more recently, both fell through, says Schwikowski — it can be difficult to coordinate the necessary permits, people, and funding to get up these mountains and take samples away.

Geoff Hargreaves, curator at the National Science Foundation Ice Core Facility in Denver, Colorado. Jim West / Alamy Stock Photo

The team does have permission to store their ice cores in the Antarctic. This November they plan to ship a balloon to Concordia Station, the French-Italian research base in East Antarctica, where it will be blown up and snow piled on top to make an ice cave big enough to drive into. The ice cores are due to be shipped there at the end of 2025, where they will be stored in insulated boxes to keep the temperature steady. Such a cave should be stable for at least a decade, after which another, similar cave can be built if needed.

Of course, you don’t have to go to the Antarctic to find cold. There are plenty of freezers capable of maintaining such low temperatures, including the National Science Foundation ice core facility in Denver. But Schwikowski points out that these facilities use energy and are vulnerable to temperature fluctuations and even failure. In 2017, a rare double malfunction caused the Canadian Ice Core Archive freezer in Alberta to warm up to around 100 degrees F (40 degrees C) without triggering the right alarms. Several valuable core sections melted. In a separate event, Thomas says that they, too, lost ice when walk-in freezers in the Yukon failed.

Aside from logistical considerations, says Schwikowski, there’s a beauty to storing this ice in a place that sits outside of national ownership: “The Antarctic is a continent of peace and research.” She just hopes to get to the mountain glaciers quickly enough to store their ice. “It worries me a lot,” she says. “We are not so fast. It is not easy.”

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New Antarctic Ice Tipping Point Discovered as Study Says We've Underestimated Melting

Scientists have discovered a new tipping point toward "runaway melting" of Antarctic ice sheets, caused by warm ocean water intruding between the ice and the land it sits on, according to a study published on Tuesday.

While this type of melting has been previously studied, models used by the United Nation's Intergovernmental Panel on Climate Change (IPCC) to project the impact of global warming on the Antarctic have yet to factor in this phenomenon.

They have also systematically underestimated ice loss seen thus far, said the study, published in the journal Nature Geoscience .

As ocean temperatures rise due to human-caused global warming, Antarctic ice sheets are melting, threatening a rise in global sea levels and putting coastal communities at risk.

"Increases in ocean temperature can lead to a tipping point being passed, beyond which ocean water intrudes in an unbounded manner beneath the ice sheet, via a process of runaway melting," the study said.

Antarctic ice sheets sit atop the bedrock and extend beyond the coast to float on the sea.

Previous studies have shown that warm seawater is seeping into the "grounding zone" – where land and ice meet – and further inland from under the floating ice.

As the water warms, even by a fraction, the intrusion accelerates from short distances of 100 metres (330 feet) to tens of kilometres (miles), melting ice along the way by heating it from below, explained the study's lead author Alexander Bradley.

"Every 10th of a degree (of warming) makes these kind of processes closer, these tipping points closer," said Bradley, a researcher with the British Antarctic Survey.

The risk to sea-level rise comes when the accelerated melting outpaces the formation of new ice on the continent.

Some areas of Antarctica are more vulnerable to this process than others due to the shape of the land mass, which has valleys and cavities where sea water can pool beneath the ice.

The Pine Island glacier , currently Antarctica's largest contributor to sea-level rise, is at high risk of melting due to the slope of the land that allows in more sea water, the study said.

Scientific models need to be updated to take into account the element of melt to better predict the risk of sea-level rise in the future and prepare for it, Bradley said.

"And it really just stresses the need for urgent climate action in order to prevent these tipping points from being passed," he added.

© Agence France-Presse

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Environment

Warm water seeping under antarctic ice sheets may accelerate melting.

As ice melts beneath Antarctica, warm ocean water can intrude further inland and set off more melting, in what researchers say is an unrecognised tipping point

By James Dinneen

25 June 2024

Aerial view of an ice sheet in Antarctica

David Vaughan/BAS

Antarctica’s melting ice sheets may retreat faster as warm seawater intrudes underneath them. Warming ocean temperatures could also lead to a “runaway” feedback effect that allows warm seawater to push further inland, leading to more melting and faster sea level rise.

As the climate warms, the future of Antarctica’s vast ice sheets remains uncertain, with projections ranging widely for how rapidly they will melt and therefore how much they will contribute to sea level rise. One dynamic that researchers have only recently come to view as an important factor are intrusions of warm seawater beneath the ice.

“The intrusion mechanism is a lot more powerful than we previously understood,” says Alexander Bradley at the British Antarctic Survey.

Something strange is happening in the Pacific and we must find out why

Such intrusions occur due to the difference in density between the fresh water flowing out from beneath the ice sheet and the relatively warm ocean water where the ice meets the seafloor – an area known as the grounding line. This is difficult to directly observe as it occurs beneath hundreds of metres of ice, but simulations suggest the warm water could extend inland for kilometres in some places.

One model by Alexander Robel at the Georgia Institute of Technology in Atlanta and his colleagues found extensive intrusions could more than double the amount of ice loss from an ice sheet by adding heat from below and lubricating the flow of ice along the bedrock.

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Bradley and his colleague Ian Hewitt at the University of Oxford built on that model, accounting for how the changing shape of cavities in the ice as it melts would alter the flow of intruding seawater.

They found that when ocean water reaches a certain temperature threshold, it melts ice at the grounding line faster than can be replaced by the flowing ice. As this cavity grows, more seawater can flow beneath the ice sheet and intrude further inland in what amounts to a “runaway” positive feedback effect.

“A small change in ocean temperature leads to dramatic change in the distance that the warm water is able to intrude,” says Bradley. He says the ocean warming required to set off this effect is within the range of projections of what we might see this century, although the model is not yet able to make predictions about specific ice sheets and not all ice sheets are equally subject to such intrusions.

“That positive feedback can cause there to be much more intrusion than we thought possible,” says Robel. “Whether that will be a tipping point that will lead to unrestrained incursion of seawater under the ice sheet – that’s probably a stretch.”

Journal reference:

Nature Geoscience DOI: 10.1038/s41561-024-01465-7

• climate change /
• Antarctica /
• sea level rise

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• Published: 25 June 2024

Tipping point in ice-sheet grounding-zone melting due to ocean water intrusion

• Alexander T. Bradley   ORCID: orcid.org/0000-0001-8381-5317 1 &
• Ian J. Hewitt   ORCID: orcid.org/0000-0002-9167-6481 2  

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• Climate and Earth system modelling
• Cryospheric science
• Projection and prediction

Marine ice sheets are highly sensitive to submarine melting in their grounding zones, where they transition between grounded and floating ice. Recently published studies of the complex hydrography of grounding zones suggest that warm ocean water can intrude large distances beneath the ice sheet, with dramatic consequences for ice dynamics. Here we develop a model to capture the feedback between intruded ocean water, the melting it induces and the resulting changes in ice geometry. We reveal a sensitive dependence of the grounding-zone dynamics on this feedback: as the grounding zone widens in response to melting, both temperature and flow velocity in the region increase, further enhancing melting. We find that increases in ocean temperature can lead to a tipping point being passed, beyond which ocean water intrudes in an unbounded manner beneath the ice sheet, via a process of runaway melting. Additionally, this tipping point may not be easily detected with early warning indicators. Although completely unbounded intrusions are not expected in practice, this suggests a mechanism for dramatic changes in grounding-zone behaviour, which are not currently included in ice-sheet models. We consider the susceptibility of present-day Antarctic grounding zones to this process, finding that both warm and cold water cavity ice shelves may be vulnerable. Our results point towards a stronger sensitivity of ice-sheet melting, and thus higher sea-level-rise contribution in a warming climate, than has been previously understood.

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Heterogeneous melting near the Thwaites Glacier grounding line

Iceberg melting substantially modifies oceanic heat flux towards a major Greenlandic tidewater glacier

Suppressed basal melting in the eastern Thwaites Glacier grounding zone

There is growing evidence suggesting that ice-sheet models lack representation of important physical processes driving ice sheet retreat (for example, refs. 1 , 2 , 3 , 4 , 5 , 6 , 7 ), rendering their projections of sea-level rise less sensitive to climatic changes than they should be. Point-wise observations 1 , 2 suggest that ice-shelf basal melt rates are considerably smaller than those typically required by models to reproduce observed retreat rates. Moreover, ice-sheet models systematically underestimate recent ice loss 7 and struggle to reproduce observationally constrained sea-level highstands from previous interglacials 3 , 4 . Palaeoclimate ice-sheet reconstructions have largely been able to reproduce low-end estimates only when mechanisms to boost sensitivity to climatic forcing are invoked 8 , 9 , 10 . Recently, evidence from diverse sources has emerged suggesting that relatively warm ocean water can intrude long distances upstream of ice-shelf grounding lines 5 , 6 , 11 , 12 , 13 , 14 ; such long intrusions have dramatic consequences for sea-level-rise contributions from ice sheets 5 , 15 , making them a candidate mechanism to reconcile modelled and observed sea-level rise. Here we investigate how previously ignored feedbacks between melting and the confining ice geometry make this intrusion mechanism even more powerful.

Sea levels during previous interglacials can be considered analogues for future sea-level rise under anthropogenic influence 16 . During the Pliocene ( ∼ 3 million years before present), CO 2 levels were similar to present day 17 and temperatures 2–3 °C above pre-industrial levels 18 , but the global mean sea level (GMSL) was 6–40 m above present-day levels 4 . Such sea-level rise is only possible with a sizeable contribution from the Antarctic ice sheet 16 . Whereas proxy records suggest that such Antarctic ice loss occurred during previous interglacials (for example, refs. 19 , 20 , 21 ), ice-sheet models struggle to reproduce the corresponding ice-sheet retreat (for example, ref. 22 ).

Several palaeoclimate simulations 8 , 10 , 22 that attain low-end Pliocene GMSL estimates have gained interest because of their pessimistic Antarctic ice loss projections. To reconcile observational constraints, these models incorporate processes that increase their sensitivity to past climatic change, naturally rendering them more sensitive to future anthropogenic warming. Refs. 8 , 10 achieve low-end Pliocene GMSL by introducing a cliff-collapse mechanism, whereby sufficiently tall ice cliffs collapse, prompting rapid inland ice front retreat. However, these simulations have been questioned on both physical 23 , 24 and statistical 25 grounds. Ref. 22 obtained similar Pliocene GMSL using a model whose increased sensitivity results from a parameterization of basal melting in grounding zones, where grounded ice transitions into a floating ice shelf (Fig. 1 ). Flow of grounded ice is particularly sensitive to grounding-zone melting 15 , 26 , 27 , 28 , because melt-induced thinning there both reduces basal drag and provides a thinning perturbation that propagates through the shelf, reducing buttressing.

The grounding zone (dashed circle in top left) of marine-terminating ice sheets features networks of tunnels, channels and porous sediments through which water moves (centre). Layered intrusion models (cross section at right) consider this region as a two-layer system: freshwater, at the local freezing temperature T f , enters the zone with average velocity U ∞ , where it meets warm ocean water of temperature T O and salinity S O . Here V is the velocity of ice above the channel, H ∞ is the characteristic vertical length scale of the upstream subglacial network and θ is the local angle of the seabed. The two-dimensional model should be taken to represent an along-grounding-zone average of the complex three-dimensional drainage system in the centre panel; in particular, there will be areas where the ice remains in contact with the bed (that is, the model does not assume the ice is floating everywhere).

Specifically, the model in ref. 22 interpolates melting across model grid cells either side of the traditional ‘grounding line’, where the ice is at the hydrostatic floatation thickness. Although this respects the fact that areas between grid cells around the grounding line may be exposed to warm ocean water, it has little physical basis beyond; in practice, grounding zones are highly complex regions, with myriad features including local topographic highs (for example, ref. 29 ), porous till layers (for example, ref. 30 ) and channels on multiple lengthscales (for example, ref. 31 ) (Fig. 1 ). Freshwater is delivered to the ocean from the upstream grounded ice through this region; where freshwater meets the relatively warm, salty ocean water, the lower density freshwater rises, permitting the warm water to intrude upstream of the grounding line 11 . There is growing evidence of warm water intrusions from diverse sources including surface observations 12 , 13 , satellite data 6 , 14 and ice-shelf basal features 32 .

Recent near-grounding-zone observations 1 , 2 confirm that warm ocean water can reach cavity extremities. However, observations are unable to probe regions far upstream of the grounding line. A lack of direct observations beneath grounded ice sheets, combined with their importance in large ice-sheet models, means that models of the grounding zone are essential. Recently published grounding-zone models 5 , 11 treat the region as a porous, two-layer system with cold, fresh subglacial discharge overlaying warm, saline ocean water. These models predict that warm water can intrude significant distances (up to kilometres) upstream of ice-sheet grounding lines 5 , delivering excess heat for sub-ice melting. Ice-sheet models including the intrusion mechanism show that ice loss is highly sensitive to this intrusion length 5 , with kilometre length intrusions potentially doubling rates of ice loss. Grounding-zone melting via warm water intrusion has, therefore, been suggested as a physically based mechanism for explaining ice-sheet retreat during past warm periods 5 .

Crucially, however, existing models lack feedbacks between melting and the confining ice geometry. As grounding zones widen in response to melting, both primary factors controlling melt rates—the amount of warm water entering the grounding zone and flow speeds within it—will be affected. In particular, this feedback may strongly influence the distance warm water is able to intrude beneath ice sheets, with significant implications for ice dynamics. References 5 , 11 demonstrated that with no feedback between melting and geometry, the distance warm water can intrude depends on the slope of the ice base and can become infinite if the slope is sufficiently steep. Here we show that with the melt-geometry feedback included, the system exhibits a tipping-point behaviour as the parameters controlling the melt rate are varied, causing unbounded intrusions to develop even on a flat or down-sloping bed; this behaviour can be triggered by changes in external forcing, such as ocean temperatures.

Melting causes enhanced warm water intrusion

To understand how the melt feedback affects grounding-zone behaviour, and, in particular, the distance warm water is able to intrude, we coupled the layered intrusion model of refs. 5 , 11 with a common melt-rate model accounting for the dependence of melting on both temperature and flow velocity adjacent to the ice (Methods).

The modelled grounding-zone behaviour depends on four fundamental, dimensionless parameters ( Supplementary Information ):

Here U ∞ and H ∞ are a characteristic flow velocity and thickness of the upstream hydrological network (Fig. 1 ); V is the grounding-zone ice velocity; St is the Stanton number, the ratio between the thermal flux into the ice–ocean interface and the thermal capacity of the water, which effectively parametrizes exchange across a boundary layer at the ice–ocean interface 33 ( Supplementary Information ); c is the specific heat capacity of water; c d is a cross-sectional average drag coefficient between the water and the channel; c is the specific heat capacity of ocean water; \({{\Delta}}T={T}_\mathrm{O}+{{\varGamma}}{{{\mathcal{S}}}}_\mathrm{O}-{T}_\mathrm{D}\) is the thermal forcing, with T O the ocean temperature, \({{{{\mathcal{S}}}}}_\mathrm{O}\) the ocean salinity, Γ the freezing point slope with salinity and T D the local freshwater freezing temperature; \({\mathcal{L}}\) is the latent heat of fusion of seawater; θ is the local grounding-zone slope, assumed constant ( Supplementary Information ); \({g}^{\,{\prime} }=g(\,{\rho }_{0}-{\rho }_\mathrm{w})/{\rho }_\mathrm{w}\) is the reduced gravity, with ρ 0 a reference density and ρ w the local water density; and c i is a cross-sectional average drag coefficient between the two layers. A full model description, including a discussion of underlying assumptions, can be found in the Supplementary Information .

These parameters capture the complex ice–ocean interactions that occur in grounding zones: M (equation ( 1a )) is a dimensionless melt rate, describing the competing effects of increasing ocean temperature (increasing Δ T ) in promoting enhanced melting, and increased ice advection (increasing V ) in replacing this ice; S (equation ( 1b )) is a dimensionless bedslope, with positive (negative, respectively) S corresponding to retrograde (prograde) bedslopes—upward (downward) sloping in the direction of ice flow; F (equation ( 1c )) is the upstream Froude number, which describes the upstream hydrological network efficiency: efficient networks, with fast flow (high U ∞ ) through narrow confines (low H ∞ ) correspond to large F , whereas in inefficient networks (low F ), meltwater is transported slowly through wide channels; C (equation ( 1d )) is a dimensionless interfacial drag coefficient, describing the relative importance of drag between the two water layers and between the water and solid (ice/bed) boundaries.

Figure 2 shows how the intrusion distance, grounding-zone geometry, thermal driving and flow velocity change as the geometry evolves from an initially flat ice base and no seabed slope in two cases with similar ocean conditions: one with Δ T  = 2.3 °C and the other with Δ T  = 2.5°C (we consider the case of a variable bedslope later). Melting is concentrated at the channel entrance, where the flow velocity and thermal driving are highest (Fig. 2c,d,g,h ) and reduces with distance into the channel. As melting proceeds, the grounding-zone widens (Fig. 2b,f ), permitting more warm water to enter, increasing the average temperature (Fig. 2c,g ), and reductions in drag result in higher flow velocities (Fig. 2d,h ); these work in tandem to promote enhanced melting. When ice is replaced by advection sufficiently quickly (left panels of Fig. 2 ), the system reaches a steady state with melting balancing ice advection and drag balancing the gravitational force that results from a titled warm–cold interface. This equilibrium is reached on a timescale of days (Fig. 2a ). However, for marginally higher ocean temperatures, ice advection cannot balance melting and the grounding zone continually widens (Fig. 2e,f ). The feedback between geometry, hydrology and melting results in runaway warm water intrusion. This system displays a tipping-point-like behaviour: a small change in the ocean temperature (and thus parameter M ) results in a threshold being passed, across which a dramatic change in the modelled final intrusion length L occurs, from being bounded (Fig. 2a ) to being unbounded (Fig. 2e ). The timescale on which the grounding zone responds to melting is much shorter than that on which the grounded ice thickness responds to perturbations in melting; it is therefore reasonable to consider the late time behaviour, and we henceforth refer to the final intrusion length L as the intrusion length. The large increase in L , and thus melting beneath a large section of the grounded ice sheet, would have dramatic implications for the dynamics of a marine-terminating ice sheet 5 , 15 . Note, however, that we do not expect intrusions to penetrate indefinitely in practice, because processes not included in our model will play a role on long lengthscales and potentially stabilize the intrusion (see below).

a , e , Temporal evolution of the intrusion distance—the greatest upstream extent of the warm layer—for a thermal forcing of Δ T  = 2.3 °C (left) and Δ T  = 2.5 °C (right). For Δ T  = 2.3 °C, the intrusion distance tends towards a bounded value ( L  ≈ 110 m), indicated by the black dashed line, whereas for Δ T  = 2.5 °C, the intrusion becomes unbounded ( L  →  ∞ ) (note the different ordinate scales between the left and right panels). Translucent points in e show the data in a . b , f , Evolution of grounding-zone channel surface (solid curves) and warm–cold interface (dashed curves). Snapshots are shown at times 1, 5, 10, 50 and 100 days after initialization with a flat channel (the same initial condition is used in both cases). y is the distance to the seabed, which forms the base of the channel. Filled points indicate the intrusion distance and correspond to points shown in a as indicated by Roman numerals. In b , the dashed black line indicates the steady state intrusion distance L . c , d , g , h , Profiles of thermal driving ( c , g ) and ice-adjacent flow velocity ( d , h ) corresponding to the snapshots shown in ( b , f ). Solutions here correspond to a flat bed ( S  = 0), a fairly inefficient drainage system ( F  = 0.25) and C  = 0.1.

Grounding-zone melt as a generic tipping point

This tipping point is generic: for any hydrological network efficiency F , the intrusion length increases with the melt parameter M (Fig. 3 ) and there is a critical M above which the intrusion becomes unbounded (solid line in Fig. 3 ). Equivalently, for any M , there is a critical F , named F c , below which the intrusion becomes unbounded. Although less efficient networks (lower F ) correspond to lower upstream flow velocities (lower U ∞ , see equations ( 1a,b ) and ( 1c )), this is outweighed by reduced drag between the layers, resulting in higher flow speeds adjacent to the ice and a thicker warm water layer, both of which promote increased melting. The critical hydrological network efficiency F c is increasing with M (Fig. 3 ): higher melting is required to cross the tipping point for more efficient subglacial networks. This suggests that increases in the flow of water beneath ice sheets may act as a stabilizing control on their dynamics via reduced grounding-zone melting, contrasting the common belief that subglacial flow predominantly enhances ice loss via reduced basal friction 34 .

Regime diagram of dimensionless intrusion distance L /( H ∞ / c d ) as a function of upstream Froude number F and dimensionless melt rate M for C  = 0.1 and S  = 0, corresponding to a flat base. Coloured lines indicate the bounded–unbounded intrusion length transition for different values of C , as indicated. The red line indicates schematically the transition between the two values of M used in Fig. 2 .

The location of the transition between bounded and unbounded intrusions is relatively insensitive to the dimensionless drag coefficient C (Fig. 3 ). This provides support for our use of a two-dimensional model, because C encodes heterogeneity in the along-grounding-zone direction.

It is interesting to note that when the intrusion is bounded, the intrusion length L is fairly insensitive to the melt parameter M (Fig. 3 ). This suggests that early warning indicators 35 , which might indicate that a marine ice sheet is approaching such a grounding-zone melt tipping point as (say) the ocean temperature increases, may be hard to detect: an increase in the intrusion length would not appear as a detectable signal in ice dynamical observations until the tipping point is passed, propagating uncertainty into sea-level-rise projections 36 .

Widespread susceptibility to the tipping point in melting

Intrusion of dense seawater is ultimately gravity driven and therefore strongly modified by the grounding-zone bedslope. Retrograde bedslopes ( S  > 0) result in enhanced intrusion, whereas prograde bedslopes ( S  < 0) result in reduced intrusion, compared to a flat bed (Fig. 4a and Supplementary Fig. 8 ). Unbounded intrusion can occur with no melt feedback (equivalent to M  → 0), provided that the slope is sufficiently retrograde, under conditions described by ref. 5 . However, with melt feedbacks, unbounded intrusion can occur for any bedslope, including prograde (Fig. 4a ): when melting is sufficiently strong, the widening of the warm layer accompanying channel opening creates a gravitational driving force that overcomes the retarding gravitational effect from the bedslope, which is otherwise unfavourable for intrusion. The critical bedslope, S c , above which unbounded intrusion occurs, reduces with M (Fig. 4a ). Over large regions of parameter space, S c is negative (Supplementary Fig. 7 ): that is, our model suggests that unbounded intrusion may occur even on prograde bedslopes and particularly so for inefficient hydrological networks (low F ; Supplementary Fig. 7 ).

a , Dimensionless intrusion distance L /( H ∞ / c d ) as a function of dimensionless bedslope S for different M , as indicated by the colour bar. Filled circles indicate the critical slope S c , beyond which the intrusion becomes unbounded. The black dashed line indicates S  = 0, which delineates pro- ( S  < 0) and retrograde ( S  > 0) bed slopes. Data shown here correspond to F  = 0.5 and C  = 0.1. b , Curves of critical upstream Froude number F c , below which unbounded intrusion occurs, as a function of dimensionless slope S for different M , as indicated by the colour bar in a . c , Map of critical upstream Froude upstream number F c . Points indicate ice shelves in Antarctica (PIG = Pine Island Glacier, PSK = Pope–Smith–Kohler), determined from observations (see main text). Grey contours correspond to F c  = 0.3 and F c  = 0.7. Ellipses indicate errors in distributions used to generate values of S and M . Points on the inset indicate locations of those ice shelves in the main panel with corresponding colours.

Marine ice sheets grounded on retrograde bedslopes may be susceptible to the marine ice-sheet instability (MISI) (for example, refs. 37 , 38 , 39 ). Retreat of the West Antarctic ice sheet, many areas of which have grounding zones on retrograde bed slopes 40 , may be strongly controlled by MISI 41 . Our modelling suggests warm water intrusion is most likely on retrograde bedslopes, potentially enhancing MISI. Conversely, it is commonly assumed that prograde grounding lines are stable 38 , 42 ; our results suggest prograde grounding zones can also host substantial intrusions and have the possibility for a switch in behaviour as ocean temperatures change, potentially questioning their assumed stability.

In practice, hydrological networks beneath ice sheets are poorly constrained, making it difficult to determine their efficiency and thus F . However, M and S can be determined from observations (below). Therefore, to place our results in a present-day context, we consider the critical hydrological network efficiency, F c , which is shown as a function of M and S in Fig. 4c (as before, unbounded intrusion occurs for F  <  F c ). Assuming a uniform hydrological network efficiency for all ice shelves, F c is a proxy for susceptibility to passing the tipping point: regions of parameters space with darker (lighter, respectively) colours in Fig. 4c are more (less) susceptible to unbounded intrusions. Locations of key Antarctic ice shelves on this map are determined using the median of observations of grounding-line velocity 43 , basal slope 40 , ocean thermal forcing 44 and literature standard values for other parameters (Methods).

Despite a large spread in the data, particularly in the grounding-line slope, we find that on average, the rapidly accelerating 45 and thinning 46 Thwaites Glacier is the least susceptible of those ice shelves considered. This is perhaps surprising, given its high ocean forcing (Supplementary Fig. 5 ); however, its high grounding-line velocities (Supplementary Fig. 6 ) overcompensate for this melting potential. This highlights the stabilizing potential of high grounding-line velocities to warm water intrusion. However, Thwaites may be particularly sensitive to future changes: ice shelves corresponding to smaller M are more sensitive to changes in grounding-line slope (Fig. 4b ), which Thwaites may be exposed to as it maintains its present retreat 40 .

The Filchner and Amery ice shelves also have low susceptibility (Fig. 4c ). Compared to Thwaites, however, their low susceptibility results from low ocean forcing and strongly prograde bedslopes (Supplementary Figs. 4 – 6 ), respectively, rather than high grounding-line velocities. Pine Island, on the other hand, has high susceptibility; like Thwaites, it has high grounding-line velocities, but its grounding-line slope is higher (more retrograde), on average, and thus more favourable for intrusion (Supplementary Fig. 4 ). Pine Island is currently Antarctica’s largest contributor to sea-level rise; its high susceptibility to grounding-zone melting may represent another factor, in addition to a highly damaged ice shelf 47 and predicted future increases in ice-shelf melting 48 , 49 , which promotes its ongoing retreat. Both Getz and Larsen have similar susceptibility to Pine Island; although Getz has similar thermal forcing, its lower grounding-line velocities (higher M ) are balanced by reduced grounding-line slopes (lower S ). Larsen has high susceptibility owing to its low flow speeds (large M ): ice is not advected quickly enough to replace that removed by melting. More generally, these examples highlight the complex interplay between ice velocity, ocean forcing and bedslope in controlling melt in grounding zones of marine ice sheets.

Our results do not provide a prediction of which Antarctic ice shelves currently experience warm water intrusions but rather indicates their potential for such and their relative susceptibility. We speculate, however, that properties of subglacial hydrological networks may be inferred from our results; for example, recent observations of high melt upstream of the Thwaites grounding line 14 suggests this area may be in the unbounded intrusion regime. According to our modelling, such behaviour would require an inefficient subglacial network (Fig. 4c ), which is consistent with observations of ponding in distributed canals beneath Thwaites 50 .

We stress that completely unbounded intrusions are not expected in practice but rather the possibility of large, rapid, increases in intrusion distance and thus melting; on longer lengthscales, processes such as bedslope variations and melt feedbacks on channel temperature may suppress intrusion ( Supplementary Information ), and along-grounding-zone variations, not included in our model, may play an important role. Our model does not provide a prediction of the ice-dynamic response to unbounded intrusion, which requires a coupled ice-hydrology model to determine; increases in melting may lead to ice acceleration (increasing V ), potentially stabilizing the intrusion (effectively reducing M ). Finally, our model does not include tides. Grounding-zone characteristics may vary substantially over tidal cycles (for example, refs. 51 , 52 ), potentially affecting intrusion. As an ice shelf is raised in response to tides, water is forced into the grounding zone and evacuated as the ice shelf lowers. Given that grounding lines can migrate long (up to kilometre) distances over diurnal tidal cycles 51 , 53 , this has the possibility to create rapid flow in the grounding zone. In addition, the associated tidal flexure may lead to a modification of the grounding-zone geometry, potentially feeding back on intrusion, which is sensitive to the characteristic thickness of the subglacial environment 5 . Tidal currents may also modulate near-grounding-zone ocean circulation 2 , potentially altering flow boundary conditions on grounding zones and thus intrusion.

A complete treatment of grounding-zone flow on tidal timescales is beyond the scope of this work. However, when supplemented with a simple parameterization of tidal flow ( Supplementary Information ), our model still displays the tipping-point behaviour, with the location of the tipping point (in parameter space) modulated by the tidal amplitude (Supplementary Fig. 10 ). We find that tidal fluctuations can significantly enhance intrusion. This provides further motivation to better understand tidal influences on grounding zones, and, more generally, to develop high-resolution models of grounding zones and better constrain their characteristics via improved observations.

We have shown that feedbacks between subglacial water flow, melting and the confining ice geometry can result in increases in warm water intrusion into marine ice-sheet grounding zones, which would have implications for ice dynamics. In particular, we have identified a fundamental switch between bounded and unbounded warm water intrusions, occurring across a critical parameter threshold. The tipping point is generic: it exists for any marine-terminating ice sheet exposed to sufficiently warm ocean water, has sufficiently low grounding-line velocity or basal slopes or a sufficiently weak hydrological network. We have shown that the intrusion mechanism is stronger than previously understood, lending further credence to the theory that it is a physically based ‘sensitivity-boosting mechanism’ to reconcile the gap between observed and modelled sea-level rise in previous warm periods and the basal melt rates required to reproduce observed retreat. Current sea-level-rise projections for Antarctica and Greenland 54 are based on simulations that lack grounding-zone melting via intrusion and may therefore represent underestimates. Although our model is a simplification of the myriad complex processes occurring in grounding zones, the possibility of tipping points in grounding-zone melt and the universality of susceptible shelves warrants a continued research effort to better constrain grounding-zone processes both from models and observations.

Layered intrusion model

The layered intrusion model is identical to that of ref. 5 in the hard bed limit ( γ  → 0 in the nomenclature of ref. 5 ). This model builds upon that of ref. 11 and was verified experimentally therein. It is described in full detail in the Supplementary Information .

We couple the layered intrusion model to a simple model of melting,

where \(\dot{m}\) is the melt rate, \({\mathcal{L}}={3.35\times {10}^{5}}\;{\mathrm{J}\;{\rm{Kg}}^{-1}}\) is the latent heat of fusion of seawater, c  = 3.974 × 10 3 J Kg −1  °C −1 is the specific heat capacity of water and St is a combined Stanton number, which parametrizes combined exchange of salt and heat across a thermal boundary layer that forms on the ocean side of the ice–ocean interface 55 , 56 ( u * and τ are defined below). The Stanton number is fairly poorly constrained in general. In the results presented here, we take value St = 5.9 × 10 −4 ; this value is standard in the literature and was obtained from a fit to data obtained from beneath the Ronne ice shelf 57 .

Equation ( 3 ) results from the so-called ‘two-equation formulation’ of melting 55 in the limit of low diffusive heat flux (this is reasonable as freezing and internal temperatures of the ice are typically within a few degrees of one another 56 ) ( Supplementary Information ). The two-equation formulation is a simplification of the more detailed ‘three equation formulation’ 33 , 58 in which salt and heat exchange across the boundary layer at the ice-shelf base are considered separately rather than together as in the two-equation formulation. However, the two formulations have been shown to work equally well in several observational (for example, ref. 57 ) and numerical (for example, ref. 59 ) studies.

In equation ( 3 ), u * and τ are the velocity of the water adjacent to the ice–ocean interface and the thermal driving, respectively (the latter should not be confused with the thermal forcing Δ T ). We take u * to be the velocity of the fresh layer, which is the layer adjacent to the ice–ocean interface. The thermal driving is τ  =  T  −  T f , where T is the temperature adjacent to the ice–ocean interface (below) and \({T}_\mathrm{f}={T}_{\rm{ref}}+\lambda z-{{\varGamma}}{\mathcal{S}}\) the local freezing temperature, with T ref  = 8.32 × 10 −2  °C a reference temperature, λ  = 7.61 × 10 −4  °C m −1 the liquidus slope with depth, Γ  = 5.73 × 10 −2 the liquidus slope with salinity, \({\mathcal{S}}\) the local salinity and z the depth below sea level (more negative z corresponds to a greater depth) 60 .

We take a simple model for the channel temperature and salinity, assuming that the relevant temperature and salinity that drive melting are the depth-weighted average of the layer temperatures:

where ϕ is the column-wise proportion of the channel occupied by the freshwater layer ( Supplementary Information ), T D  = 0 and S D  = 0 are the temperature and salinity of the subglacial discharge layer, respectively, and T O and S O are the temperature and salinity of the warm ocean layer. The relations ( 4 ) and ( 5 ) capture the fact that the temperature and salnity in the channel increase with a greater proportion of warm, salty ocean water within it. Although entrainment between the two layers is not explicitly resolved, the column-wise averaging can be considered a simple proxy for mixing of the two layers. Observations also indicate that basal melting can occur where a cold fresh layer exists adjacent to an ice–ocean interface through double diffusive convection 52 , 61 .

Channel shape evolution

The dimensionless model equations (equations ( 19 ) and ( 20 ) in Supplementary Information ) are solved numerically in MATLAB. For a given channel shape, the layered intrusion equations are solved using the ODE15S routine. The equations are solved backwards from the downstream end of the channel, where we apply a perturbed boundary condition, setting the dimensionless freshwater layer thickness equal to \({\left[(1+\epsilon )F\right]}^{2/3}\) , where ϵ   ≪  1 ( Supplementary Information ). This perturbed boundary condition ensures that a singularity in the interfacial gradient is avoided at the downstream end of the channel 5 . In those results shown here, we use ϵ  = 10 −4 but verified that results are insensitive to this value, provided that the ϵ   ≪  1 condition holds. The intrusion equations are integrated backwards until either the freshwater layer occupies the entirety of the channel or the end of the numerical grid is reached (we use a sufficiently large numerical grid to ensure that the latter is only realized in the case of unbounded intrusion).

Having determined the interfacial shape, and thus velocity in the fresh layer and channel temperature, the melt rate is determined from equation ( 3 ). This melt rate is interpolated onto a regular grid with spacing d z (below) and the channel thickness timestepped according to the kinematic condition (equation ( 14 ) in the Supplementary Information ) using a first-order upwinding scheme 62 .

The numerical grid is made up of m blocks of n grid cells (giving a total number of grid cells of m  ×  n ); each block is of length L p  = 1 −  F 2 /4 − 3 F 2/3 /4, which is the intrusion distance in the limit of no interfacial drag ( C  = 0), a flat bed ( S  = 0) and no melting ( M  = 0) as described by ref. 5 ; the grid size is then d z  =  L p / n . In the results shown herein, we use n  = 100 and m  = 20, with the latter value being sufficiently large that the intrusion only reaches the end of the channel in the case of an unbounded intrusion.

Steady intrusion length

To determine the steady intrusion length L for a given set of parameters ( F ,  C ,  S ,  M ), we integrate the steady form of the coupled layered intrusion-melt equations (equations ( 24 ) and ( 25 ) in the Supplementary Information ) downstream from the nose of the wedge (where the freshwater layer occupies the width of the channel) using the ODE15S routine in MATLAB. At the nose, the problem is singular; to avoid this singularity, we linearize the problem about this point to determine the appropriate initial conditions ( Supplementary Information ). Solutions of this steady problem, which obtain the downstream boundary condition (dimensionless freshwater layer thickness =  F 2/3 ) in a finite distance correspond to true steady states; otherwise, no steady solution exists for this particular set of parameters, and the intrusion will be unbounded (Supplementary Fig. 2 ). In practice, we specify a finite end of the domain ℓ   ≫  1, and, if the solution does not obtain the downstream boundary condition before this point, we assume the intrusion is unbounded; in the results shown here, we take ℓ  = 10 5 , and results are insensitive to this value.

To determine the critical slope S c and critical Froude number F c shown in Fig. 4 , we apply a bisection method. The algorithm to do so is described fully in the Supplementary Information .

Parameter estimation

Values of parameters M and S for Antarctic ice shelves shown in Fig. 4 were determined from observations of ice velocity (for grounding-line velocity V ), thermal forcing (for Δ T ) and bedslopes (for θ ).

To determine grounding-line locations, we first obtain ice-shelf boundaries from Bedmachine V3 40 masks of ice-shelf location at 500 m resolution. Grid points within this mask corresponding to grounding-line and ice-shelf front positions were differentiated based on a floatation condition, relating to the floatation thickness ρ w / ρ i b , the ice thickness at which hydrostatic equilibrium is achieved, where ρ w  = 1,028.0 kg m −3 is the ocean density, ρ i  = 918.0 kg m −3 is the ice density and b is the bed elevation determined from Bedmachine V3 bed data 40 . Ice-shelf boundary points above 95% of floatation thickness were designated as grounding-line points, whereas the remaining points were designated as ice front points. Supplementary Fig. 9 shows grounding-line and ice front points for each of the ice shelves shown in Fig. 4 , indicating that this criterion does a good job at correctly identifying, and differentiating between, grounding-line and ice front points.

Ice velocities at grounding-line points were determined from NASA ITS_LIVE mosaics of 1985–2019 ice velocities 43 . We first put the data onto the same 500 m resolution grid used to determine grounding-line locations and then extract velocity components v  = ( v 1 ,  v 2 ) at these points (inset in Supplementary Fig. 9a ). Grounding-line ice velocities used to compute M are taken as the median of all grounding-line velocities within the individual ice shelf (Supplementary Fig. 6 ).

Grounding-line slopes were determined by first extracting bed data from Bedmachine V3 40 onto the 500 m grid. We then compute gradients of basal elevation,  ∇   b  = (∂ x b , ∂ y b ), where ∂ indicates a partial derivative, using second order finite differences. We then take the basal slope as the directional derivative in the direction of ice flow, that is

The value of \(\tan \theta\) used for each is shelf is then determined as the median of all grounding-line basal slopes for that particular shelf (Supplementary Fig. 4 ).

Thermal forcing is computed from maps of maximum thermal forcing between 200 m and 800 m in the water column from ref. 44 . For each ice front grid point on the 500 m grid, the thermal forcing associated with that point is computed as the mean of the maximum thermal forcing within a 1.5 km × 1.5 km square centred around the grid point; the thermal forcing of each ice shelf is then determined as the median over all well-defined ice front points in the shelf (Supplementary Fig. 5 ).

Having determined V , Δ T and \(\tan \theta\) from observations, M and S are computed using standard values from the literature. We take C d  = 10 −2 , which is consistent with a range of observations (for example, ref. 63 ), modelling (for example, ref. 48 ) and experiments (for example, ref. 64 ) of ice–ocean interactions, alongside \({\mathcal{L}}={3.35\times {10}^{5}}\;{\mathrm{J}\;{\rm{Kg}}^{-1}}\) , c  = 3.974 × 10 3 J Kg −1  °C −1 and St = 5.9 × 10 −4 as discussed above. The mean upstream flow velocity U ∞ is taken to be 1 cm s −1 , which is consistent with observations 65 , 66 and modelling 67 , 68 of subglacial flow beneath ice sheets.

Data availability

Data used to create the figures contained in this paper are available via Zenodo at https://doi.org/10.5281/zenodo.10895498 (ref. 69 ).

Code availability

Code to perform simulations and produce the figures contained in this paper are available via Zenodo at https://doi.org/10.5281/zenodo.10895498 (ref. 69 ).

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Acknowledgements

A.T.B. is supported by the Natural Environmental Research Programme (NERC) grant NE/S010475/1 and the PROTECT project, which received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 869304.

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A.T.B. conceived of the study and performed the analysis. A.T.B. and I.J.H. contributed to scientific discussion, interpretation of the results and wrote the manuscript.

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Bradley, A.T., Hewitt, I.J. Tipping point in ice-sheet grounding-zone melting due to ocean water intrusion. Nat. Geosci. (2024). https://doi.org/10.1038/s41561-024-01465-7

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Received : 11 May 2023

Accepted : 10 May 2024

Published : 25 June 2024

DOI : https://doi.org/10.1038/s41561-024-01465-7

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