CR
Cryospheric Sciences

# ice

## Image of the Week – Why is ice so slippery?

Ice can be slippery! [Credit: giphy.com]

Having spent most of my life in places where the temperature hardly ever falls below zero, my first winter in Sweden was painful. Especially for my bum, who met the ice quite unexpectedly. Reading the news this week, from reports of emergency services overwhelmed after so many people had slipped to a scientific study on how no shoes have a good enough grip, via advice on how to walk like a penguin, I understand I am far from alone in having a problem with ice. But why is ice so slippery anyway? This is what we will talk about in this Image of the Week.

## Did you know that you lacked friction?

To understand why one might fall sometimes, let us start with why one usually can walk without falling: friction! Friction is a resistive force that can have three causes:

• Surface roughness (think about sandpaper)

• Deformation (think about dragging a suitcase over a gravel path)

Each of these types of friction is nicely explained on this website, so I will concentrate on our walking question. Note that if you are standing still, it is a different story; then we are talking about static (instead of dynamic) friction. And everything is actually a bit more complicated than the distinction between the three causes, since adhesion and roughness are somehow related. I will not get into that, but if that stirred your interest, you could have a look at this paper. Anyway, back to walking.

The roughness of our roads and pavements, along with that of your shoes and their deformation ability, is, of course, crucial. But in the case of water after the rain or rotten autumn leaves, adhesion can be the deciding factor between casually walking and experiencing a sudden unexpected loss of altitude: not that much adhesion between your foot and what you walk on, but rather between what you walk on and the rest of the world. And that is exactly the problem with ice.

Frozen lake [Credit: Nilay Dogulu (distributed via imaggeo.egu.eu)]

## Water really is a weird material

Coming from a place where people rarely worry about ice, I had never heard the commonly accepted reasons why ice is slippery. A quick internet search informed me that a common belief is that ice is slippery because, by walking on it, we melt the very surface of the ice through the pressure of our weight and/or the heat of the friction. As a result, we end up with a dangerous layer of liquid water between our foot and the ice, lose adhesion, and … boom! A study published this summer has a different explanation: water in its solid form is made of chains of molecules attached to three other water molecules. But the chain has to stop somewhere, so, at the very surface, molecules are only attached to one or two others, and can, as a result, be easily detached from the rest of the ice. When that happens, they just hang around on top of the ice, “like marbles on a dancefloor“.

However, it cannot be seen as a layer of liquid water, rather as a gas, the authors of that new study say. Not that it makes a big difference when you are on the floor… The good (?) news is, this strange property of ice depends on temperature. They report that ice is the most treacherous at -7°C, but then becomes safer as the temperature decreases.

## EGU Cryosphere friendly advice: how to walk around -7°C

Personally, I avoid roads and pavements like the plague and walk on frozen paths and grass, which retain some roughness unless covered by a lot of snow. Since it is not always possible, adopt the technique of our favourite polar animal:

• go slowly

• move your foot next to each other, instead of in front of one another

• or give up and slide on your belly!

One of our favourite polar animals [Credit: Giuseppe Aulicino (distributed via imaggeo.egu.eu)].

Edited by Clara Burgard

## Image of the Week – Breaking the ice: river ice as a marker of climate change

Figure 1. Dates of ice breakup on Alaskan river reaches wider than 150 m calculated using Moderate Resolution Imaging Spectroradiometer (MODIS) data. [Credit: Wayana Dolan].

Common images associated with climate change include sad baby polar bears, a small Arctic sea ice extent, retreating glaciers, and increasing severe weather. Though slightly less well-known, river ice is a hydrological system which is directly influenced by air temperature and the amount and type of precipitation, both of which are changing under a warming climate. Ice impacts approximately 60 % of rivers in the Northern Hemisphere and therefore will be a clear indicator of climate change over the coming century.

## River ice terminology

First, I think it is important to get some quick vocabulary out of the way. There are three primary variables used to study large-scale trends in river ice:

• Ice freeze-up: The process of ice accumulation on a river reach (a segment of a river), usually during the autumn or winter.
• Ice breakup: The process of ice loss from a river segment. Breakup style is often related to a pulse of increased runoff from snow melt, known as the spring flood wave. Thermal breakup occurs when river ice melts prior to the arrival of the spring flood wave. It is a slow and relatively calm process. Alternatively, mechanical breakup occurs when ice on a river has not melted prior to the arrival of the spring flood wave. Mechanical breakups often cause severe ice jam floods, whereas thermal breakups are rarely associated with flooding events. You can observe an example of mechanical ice breakup and associated ice jam flooding in 2018 on the North Saskatchewan River at Petrofka Orchard on the video below [Credit: Planet Labs, Inc.].
• Ice cover duration: The length of time a river segment is ice-covered between freeze-up and breakup.

Now that we know these key phrases, let’s get to the good stuff!

## Why should you care about river ice?

Shifts in river ice cover duration can be used as an indicator for Arctic climate change due to its relationship with air temperature and precipitation (Prowse et al. 2002). Hotter air temperatures generally relate to earlier ice breakup, later ice freeze-up, and shorter ice cover duration. These trends in breakup and freeze-up have been observed over the past 150 years on multiple rivers in the Northern Hemisphere by Magnuson et al. 2000. Many arctic communities rely on ice roads, which often travel across frozen rivers, lakes, and wetlands. These roads are important for transporting food, fuel, and mining equipment, to predominately first nations people. They are also commonly used by people who live subsistence-based lifestyles for hunting and trapping during the winter months. If ice cover duration shortens, these roads will be stable for a shorter period each winter. Alternatively, longer ice-free seasons would allow for decreased shipping costs in many boreal and Arctic regions, which currently use ice breaking to clear shipping pathways (Prowse et al. 2011). Another trend observed in several large Arctic rivers is a shift from mechanical breakup to thermal breakup (Cooley & Pavelsky, 2016). While this change could lead to a decrease in ice jam flood damage to hydropower and other infrastructure, it could also cause a dramatic decrease in sediment and nutrient transport to near-river Arctic ecosystems such as floodplains and deltas.

Recent research has shown ice cover trends to be geographically complex and dependent upon variables such as air temperature, basin size, and precipitation (Bennett & Prowse, 2010; Prowse et al. 2002; Rokaya et al. 2018). However, many of these trends are poorly understood on a pan-Arctic scale.

## How do we measure changes in river ice?

From the early-1980s through the mid-2000s, satellites missions such as Landsat and the Moderate Resolution Imaging Spectroradiometer (MODIS) began allowing researchers to study ice on rivers in inaccessible areas. However, computing power limited the size and scale of rivers which could be observed. More recently, data processing through platforms like Google Earth Engine allow river ice to be studied on a much larger scale.

The University of North Carolina at Chapel Hill (UNC) has a working group which makes use of these new programs to study changes in pan-Arctic river and lake ice. My current project seeks to quantify historical river ice breakup and freeze-up using MODIS. We have developed an ice detection algorithm that has successfully been applied to all river reaches in Alaska wider than 150 m, limited by the 250 m spatial resolution of MODIS (Figure 1). Note that our detection algorithm can be applied to rivers which are slightly sub-pixel in width. I am currently working on calculating trends in this dataset and the expansion of the algorithm to pan-Arctic rivers, so that we can better identify which regions in the Arctic are changing the fastest. A quick glance at the dataset reveals that ice breakup is highly variable through time and space, even between upstream and downstream reaches of the same river. Internal variation in breakup dates within a given river may be caused by temperature gradients along the river profile, changes in elevation, as well as variation in the amount and type of precipitation. Additionally, preliminary work by UNC postdoctoral researcher Xiao Yang uses Google Earth Engine, Landsat, and MERRA-2 data to globally model river ice (Figure 2). This model can be applied to future climate change scenarios to see how river ice will change as the temperature warms. Keep an eye out for this paper in the next few months!

Figure 2. Preliminary results from modelling global river ice coverage using Landsat imagery, latitude, longitude, and surface air temperatures from MERRA-2. Colors refer to the percentage of the total river length in each area that is ice-covered each month (aggregated from 1984 to 2018) [Credit: Xiao Yang].

## Future outlook

River ice cover duration is expected to shorten as the climate warms. Shifts in ice breakup and freeze-up processes can impact sediment and nutrient delivery, Arctic transportation and hunting, and ice-related hazards. However, our preliminary results show that river ice breakup varies both spatially and temporally throughout Alaska (Figure 1). Ongoing research at UNC will allow researchers to identify areas of the pan-Arctic which are most vulnerable to river ice-related change.

## Further resources

Edited by Scott Watson

Wayana Dolan is a current M.S. student and future Ph.D. student at the University of North Carolina at Chapel Hill (USA) working with Dr. Tamlin Pavelsky. Her current research involves using remote sensing to study large-scale changes in river ice. She is passionate about any project that allows her to do Arctic fieldwork. Dolan also works with the WinSPIRE program – a summer research internship for female high school students in North Carolina. You can contact her by email or on twitter as @wayana_dolan.

## Image of the week – How hard can it be to melt a pile of ice?!

Snow, sub-zero temperatures for several days, and then back to long grey days of near-constant rain. A normal winter week in Gothenburg, south-west Sweden. Yet as I walk home in the evening, I can’t help but notice that piles of ice have survived. Using the equations that I normally need to investigate the demise of Greenland glaciers, I want to know: how hard can it be to melt this pile of ice by my door? In the image of this week, we will do the simplified maths to calculate this.

## Why should the ice melt faster when it rains?

The icy piles of snow are made of frozen freshwater. They will melt if they are in contact with a medium that is above their freezing temperature (0°C); in this case either the ambient air or the liquid rainwater.

How fast they will melt depends on the heat content of this medium. Bear with me now – maths is coming! The heat content of the medium per area of ice, $Q$, is a function of the density $\rho$ and specific heat capacity $c$ of the medium. Put it simply, the heat capacity is a measure of by how much something will warm when a certain amount of energy is added to it. $Q$ also depends on the temperature $T$ of the medium over the thickness $H$ of the boundary layer i.e. the thickness of the rain or air layer that directly impacts the ice.

Assuming that I have not scared you away yet, here comes the equation:

$Q = \rho c \int_{ice}^{H} T dz$

For liquid water (in this article, the rain): $\rho_{rain} \approx 1000 \: kg \: m^{-3}$, $c_{rain} \approx 3.9 \: kJ \: kg^{-1} \: K^{-1}$. For the ambient air: $\rho_{air} \approx 1.2 \: kg \: m^{-3}$, $c_{air} \approx 1.0 \: kJ \: kg^{-1} \: K^{-1}$. So we can plug those values into our equation to obtain the heat content $Q$ of the rain and of the air. We can consider the same temperature over the same $H$ (e.g. Byers et al., 1949), and hence we get $Q_{rain} \approx 3250 Q_{air}$.

Stepping away from the maths for a moment, this result means that the heat contained in the rain is more than 3000 times that of the ambient air. Reformulating, on a rainy day, the ice is exposed to 3000 times more heat than on a dry day!

The calculations have obviously been simplified. The thickness $H$ of the boundary layer is larger for the atmosphere than for the rain, i.e. larger than just a rain drop. At the same time, the rain does not act on the ice solely by bringing heat to it (this is the thermic energy), but also acts mechanically (kinematic energy): the rain falls on the ice and digs through it. For the sake of this blogpost however, we will keep it simple and concentrate on the thermic energy of the rain.

## How long will it take for the rain to melt this pile of ice then?

Promise, this will be the last equation of this blogpost! Reformulating the question, what is the melt rate of that ice? Be it for a high latitude glacier or a sad pile of snow on the side of a road, the melt rate $F_{melt}$ is the ratio of the heat flux from the rain $F_{Qrain}$ (or any other medium) over the heat needed to melt the ice. It indicates whether the rain brings enough heat to the ice surface to melt it, or whether the ice hardly feels it:

$F_{melt} = \frac{F_{Qrain}}{\rho_{ice}(L+c_{ice}\Delta T)}$

More parameters are involved

• $\rho_{ice} = 917 \: kg \: m^{-3}$ the density of the ice;
• $L = 335 \: kJ \: kg^{-1}$ the latent heat of fusion, defined as how much energy is needed to turn one kilogram of solid water into liquid water;
• $c_{ice} = 2.0 \: kJ \: kg^{-1} \: K^{-1}$ the heat capacity of the ice (see previous paragraph);
• $\Delta T$ the difference between the freezing temperature (0°C) and that of the interior of the ice (usually taken as -20°C).

But what is $F_{Qrain}$ I am glad you ask! This heat flux , i.e. $Q_{rain}/time$, is crucial: it not only indicates how much heat your medium has, but also how fast it brings it to the ice. After all, it does not matter whether you are really hot if you stay away from your target. I actually lied to you, here comes the final equation, defining the heat flux:

$F_{Qrain} = \rho_{rain}c_{rain}T_{rain}P$

We can consider that $T_{rain} \approx T_{air}$. We already gave $\rho_{rain}$ and $c_{rain}$ earlier. As for $P$, this is our precipitation, or how much water is falling on a surface over a certain time (given in mm/hour usually during weather bulletins). On 24th January 2018, as I was pondering why the ice had still not melted, my favourite weather forecast website indicated that $T_{air} = 5^{\circ}C$ (278.15 K) and $P = 1 \: mm/hour$.

Eventually putting all the numbers together, we obtain $F_{melt} \approx 3 \: mm/hour$. So that big pile on the picture that is about 1 m high will require constant rain for nearly 14 days – assuming that the temperature and precipitation do not change, and neglecting a lot of effects as already explained above. Or it would take just over one hour of the Wikipedia record rainfall of 300 mm/hour – but then ice would be the least of my worries.

The exact same equations apply to this small icy island, melted by the air and ocean [Credit: Monika Dragosics (distributed via imaggeo.egu.eu)]

In conclusion, liquid water contains a lot more heat than the air, but ice is very resilient. The mechanisms involved in melting ice are more complex than this simple calculation from only three equations, yet they are the same whether you are on fieldwork on an Antarctic ice shelf or just daydreaming on your way home.

### Other blogposts where ice melts…

Edited by Adam Bateson and Clara Burgard