CR
Cryospheric Sciences

# Regular Author

## Image of the Week — Quantifying Antarctica’s ice loss

Fig. 1 Cumulative Antarctic Ice Sheet mass change since 1992. [Credit: Fig 2. from The IMBIE team (2018), reprinted with permission from Nature]

It is this time of the year, where any news outlet is full of tips on how to lose weight rapidly to  become beach-body ready. According to the media avalanche following the publication of the ice sheet mass balance inter-comparison exercise (IMBIE) team’s Nature paper, Antarctica is the biggest loser out there. In this Image of the Week, we explain how the international team managed to weight Antarctica’s ice sheet and what they found.

## Estimating the Antarctic ice sheet’s mass change

There are many ways to quantify Antarctica’s mass and mass change and most of them rely on satellites. In fact, the IMBIE team notes that there are more than 150 papers published on the topic. Their paper that we highlight this week is remarkable in that it combines all the methods in order to produce just one, easy to follow, time series of Antarctica’s mass change. But what are these methods? The IMBIE team  used estimates from three types of methods:

•  altimetry: tracking changes in elevation of the ice sheet, e.g. to detect a thinning;
•  gravimetry: tracking changes in the gravitational pull caused by a change in mass;
•  input-output: comparing changes in snow accumulation and solid ice discharge.

To simplify, let’s imagine that you’re trying to keep track of how much weight you’re losing/gaining. Then  altimetry would be like looking at yourself in a mirror, gravimetry would be stepping on a scale, and input-output would be counting all the calories you’re taking in and  burning out. None of these methods will tell you directly whether you have lost belly fat, but combining them will.

The actual details of each methods are rather complex and cover more pages than the core of the paper, so I invite you to read them by yourself (from page 5 onwards). But long story short, all estimates were turned into one unique time series of ice sheet mass balance (purple line on Fig. 1). Furthermore, to understand how each region of Antarctica contributed to the time series, the scientists also produced one time series per main  Antarctic region (Fig. 2): the West Antarctic Ice Sheet (green line), the East Antarctic Ice Sheet (yellow line), and the Antarctic Peninsula (red line) .

Antarctica overview map. [Credit: NASA]

## Antarctica is losing ice

The results are clear: the Antarctic ice sheet as a whole is losing mass, and this mass loss is accelerating. Nearly 3000 Giga tonnes since 1992. That is 400 billion elephants in 25 years, or on average 500 elephants per second.

Most of this signal originates from West Antarctica, with a current trend of 159 Gt (22 billion elephants) per year. And most of this West Antarctic signal comes from the Amundsen Sea sector, host notably to the infamous  Pine Island  and Thwaites Glaciers.

The Antarctic ice sheet has lost “400 billion elephants in 25 years”

But how is the ice disappearing? Rather, is the ice really disappearing, or is there simply less ice added to Antarctica than ice naturally removed, i.e. a change in surface mass balance? The IMBIE team studied this as well. And they found that there is no Antarctic ice sheet wide trend in surface mass balance; in other words Antarctica is shrinking because more and more ice is discharged into the ocean, not because it receives less snow from the atmosphere.

Floating ice shelf in the Halley embayment, East Antarctica [Credit: Céline Heuzé]

## What is happening in East Antarctica?

Yet another issue with determining Antarctica’s weight loss is Glacial Isostatic Adjustment. In a nutshell, ice is heavy, and its weight pushes the ground down. When the ice disappears, the ground goes back up, but much more slowly than the rate of ice melting . This process has been ongoing in Scandinavia notably since the end of the last ice age 21 000 years ago, but it is also happening in East Antarctica by about 5 to 7 mm per year (more information here). Except that there are very few on site GPS measurements in Antarctica to determine how much land is rising, and the many estimations of this uplifting disagree.

So as summarised by the IMBIE team, we do not know yet what the change in ice thickness is where glacial isostatic adjustment is strong, because we are unsure how strong this adjustment is there. As a result in East Antarctica, we do not know whether there is ice loss or not, because it is unclear what the ground is doing.

## What do we do now?

The IMBIE team concludes their paper with a list of required actions to improve the ice loss time series: more in-situ observations using airborne radars and GPS, and uninterrupted satellite observations (which we already insisted on earlier).

What about sea level rise, you may think. Or worse, looking at our image of the week, you see the tiny +6mm trend in 10 years and think that it is not much. No, it is not. But note that the trend is far from linear and has been actually accelerating in the last decades…

The IMBIE Team, 2018. Mass balance of the Antarctic Ice Sheet from 1992-2017. Nature 558, 219–222.

Edited by Sophie Berger

## Image of the Week – Antarctica: A decade of dynamic change

Fig. 1 – Annual rate of change in ice sheet height attributable to ice dynamics. Zoomed regions show (a) the Amundsen Sea Embayment and West Marie Byrd Land sectors of West Antarctica, (b) the Bellingshausen Sea Sector including the Fox and Ferrigno Ice Streams and glaciers draining into the George VI ice shelf and (c) the Totten Ice Shelf. The results are overlaid on a hill shade map of ice sheet elevation from Bedmap2 (Fretwell et al. 2013) and the grounding line and ice shelves are shown in grey (Depoorter et al. 2013). [Credit: Stephen Chuter]

Whilst we tend to think of the ice flow in Antarctica as a very slow and steady process, the wonders of satellites have shown over the last two decades it is one of the most dynamic places on Earth! This image of the week maps this dynamical change using all the satellite tools at a scientist’s disposal with novel statistical methods to work out why the change has recently been so rapid.

## Why do we care about dynamic changes in Antarctica ?!

The West Antarctic Ice Sheet has the potential to contribute an approximate 3.3 m to global sea level rise (Bamber et al. 2009). Therefore, being able to accurately quantify observed ice sheet mass losses and gains is imperative for assessing not only their current contribution to the sea level budget, but also to inform ice sheet models to help better predict future ice sheet behaviour.

An ice sheet can gain or lose mass primarily through two different processes:

• changes in surface mass balance (variations in snowfall and surface melt driven by atmospheric processes) or
• ice dynamics, which is where variations in the flow of the ice sheet (such as an increase in its velocity) leads to changes in the amount of solid ice discharged from the continent into the ocean. In Antarctica ice flow dynamics are typically regulated by the ice shelves that surround the ice sheet; which provide a buttressing stress to help hold back the rate of flow.

Understanding the magnitude of each of these two components is key to understanding the external forcing driving the observed ice sheet changes.

This Image of the Week shows the annual rates of ice sheet elevation change which are attributed to changes in ice dynamics between 2003 and 2013 (Fig. 1) (Martín-Español et al. 2016). This is calculated by combining observations from multiple satellites (GRACE, ENVISAT, ICESat and CryoSat-2) with in-situ GPS measurements in  a Bayesian Hierarchical Model. The challenge we face is that the observations we have of ice sheet change (whether that being total height change from altimetry or mass changes from GRACE) vary on their spatial and temporal scales and can only tell us the total mass change signal, not the magnitudes or proportions of the underlying processes driving it. The Bayesian statistical approach used here takes these observations and separates them proportionally into their most likely processes, aided by prior knowledge of the spatial and temporal characteristics for each process we want to resolve. This allows us reducing the reliance on using forward model outputs to resolve for processes we cannot observe. As a result, it is unique from other methods of determining ice sheet mass change, which rely on model outputs which in some cases have hard to quantify uncertainties.  This methodology has been applied to Antarctica and is currently being used to resolve the sea level budget and its constituent components through the ERC GlobalMass project.

## What can we learn from Bayesian statistical approach?

This approach firstly allows us to quantitively assess the annual contribution that the Antarctic ice sheet is making to the global sea level budget, which is vital to better understanding the magnitude each Earth system process is playing in sea level change. Additionally, by being able to break down the total change into its component processes, we can better understand what external factors are driving this change. Ice dynamics has been the dominant component of mass loss in recent years over the West Antarctic Ice Sheet and is therefore the process being focussed on in this image.

### Amundsen Sea Embayment : a rapidly thinning area

Since 2003 there have been major changes in the dynamic behaviour over the Amundsen Sea Embayment and West Marie Byrd Land region (Fig 1, inset a). This region is undergoing some of the most rapid dynamical changes across Antarctica, with a 5 m/yr ice dynamical thinning near the outlet of the Pope and Smith Glacier. Additionally the Bayesian hierarchical model results show that dynamic thinning has spread inland from the margins of Pine Island Glacier, agreeing with elevation trends measured by satellite altimetry over the last two decades (Konrad et al. 2016).

These changes are driven primarily by the rapid thinning of the floating ice shelves at the ice sheet margin in this region

The importance of ice dynamics  is also illustrated in Fig 2, which shows  surface processes and ice dynamics components of mass changes over the Amundsen Sea Embayment from the bayesian hierarchical model. Fig 2 demonstrates that ice dynamics is the primary driver of mass losses in the region. Ice dynamic mass loss increased dramatically from 2003-2011, potentially stabilising to a new steady state since 2011.

Fig. 2 – Annual mass changes due to ice dynamics (pink line) and SMB (blue line) for the period 2003-2013 from the Bayesian hierarchical model approach. Red dots represent mass change anomaly (changes from the long term mean) due to surface mass balance calculated by the RACMO2.3 model and allow for comparison with our Bayesian framework results. (calculated from observations of ice velocity and ice thickness at the grounding line and allow for comparison with our Bayesian framework results (Mouginot et al, 2014). [Credit: Fig. 9b from Martín-Español et al., 2016].

The onset of  dynamic thinning can also be seen in glaciers draining into the Getz Ice Shelf, which is experiencing high localised rates of ice shelf thinning up to 66.5 m per decade (Paolo et al. 2015) . This corroborates with ice speed-up recently seen in the region (Chuter et al. 2017; Gardner et al. 2018). We have limited field observations of ice characteristics in this region and therefore more extensive surveys are required to fully understand causes of this dynamic response.

### Bellingshausen Sea Sector :  Not as stable as previously thought…

The Bellingshausen Sea Sector (Fig 1, inset b) was previously considered relatively a dynamically stable section of the Antarctic coastline, however recent analysis from a forty year record of satellite imagery has shown that the majority of the grounding line in this region has retreated  (Christie et al. 2016). This is reflected in the presence of a dynamic thinning signal in the bayesian hierarchical model results near the Fox and Ferrigno Ice streams and over some glaciers draining into the George VI ice shelf, which have been observed from CryoSat-2 radar altimetry (Wouters et al. 2015). The dynamic changes in this region over the last decade highlight the importance of continually monitoring all regions of the ice sheet with satellite remote sensing in order to understand the what the long term response over multiple decades is to changes in the Earth’s climate and ocean forcing.

## Outlook

Multiple  satellite missions have allowed us to measure changes occurring across the ice sheet in unprecedented detail over the last decade. The launch of the GRACE-Follow On mission earlier this week and the expected launch of ICESat-2 in September will ensure this capability continues well into the future. This will provide much needed further observations to allow us to understand ice sheet dynamics over time scales of multiple decades. The bayesian hierarchical approach being demonstrated will be developed further to encompass these new data sets and extend the results into the next decade. In addition to satellite measurements, the launch of the International Thwaites Glacier Collaboration  between NERC and NSF will provide much needed field observations for the Thwaites Glacier region of the Amundsen Sea Embayment, to better understand whether it has entered a state of irreversible instability .

Data
The  Bayesian hierarchical model mass trends shown here (Martín-Español et al. 2016) are available from the UK Polar Data Centre. In addition, the time series has been extended until 2015 and is available on request from Stephen Chuter (s.chuter@bristol.ac.uk). This work is part of the ongoing ERC GlobalMass project, which aims to attribute global sea level rise into its constituent components using a Bayesian Hierarchical Model approach. The GlobalMass project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 69418.

References

Christie, Frazer D. W. et al. 2016. “Four-Decade Record of Pervasive Grounding Line Retreat along the Bellingshausen Margin of West Antarctica.” Geophysical Research Letters 43(11): 5741–49. http://doi.wiley.com/10.1002/2016GL068972.

Chuter, S.J., A. Martín-Español, B. Wouters, and J.L. Bamber. 2017. “Mass Balance Reassessment of Glaciers Draining into the Abbot and Getz Ice Shelves of West Antarctica.” Geophysical Research Letters 44(14).

Gardner, Alex S. et al. 2018. “Increased West Antarctic and Unchanged East Antarctic Ice Discharge over the Last 7 Years.” Cryosphere 12(2): 521–47.

Martín-Español, Alba et al. 2016. “Spatial and Temporal Antarctic Ice Sheet Mass Trends, Glacio-Isostatic Adjustment, and Surface Processes from a Joint Inversion of Satellite Altimeter, Gravity, and GPS Data.” Journal of Geophysical Research: Earth Surface 121(2): 182–200. http://dx.doi.org/10.1002/2015JF003550.

Mouginot, J, E Rignot, and B Scheuchl. 2014. “Sustained Increase in Ice Discharge from the Amundsen Sea Embayment, West Antarctica, from 1973 to 2013.” Geophysical Research Letters 41(5): 1576–84.

Paolo, Fernando S, Helen A Fricker, and Laurie Padman. 2015. “Volume Loss from Antarctic Ice Shelves Is Accelerating.” Science 348(6232): 327–31. http://www.sciencemag.org/content/early/2015/03/31/science.aaa0940.abstract.

Edited by Violaine Coulon and Sophie Berger

Stephen Chuter is a post-doctoral research associate in Polar Remote Sensing and Sea Level at the University of Bristol. He combines multiple satellite and ground observations of ice sheet and glacier change with novel statistical modelling techniques to better determine their contribution to the global sea level budget. He tweets as @StephenChuter and can be found at www.stephenchuter.wordpress.com. Contact email: s.chuter@bristol.ac.uk

## Image of the Week — Seasonal and regional considerations for Arctic sea ice changes

Monthly trends in sea ice extent for the Northern Hemisphere’s regional seas, 1979–2016. [Credit: adapted from Onarheim et al (2018), Fig. 7]

The Arctic sea ice is disappearing. There is no debate anymore. The problem is, we have so far been unable to model this disappearance correctly. And without correct simulations, we cannot project when the Arctic will become ice free. In this blog post, we explain why we want to know this in the first place, and present a fresh early-online release paper by Ingrid Onarheim and colleagues in Bergen, Norway, which highlights (one of) the reason(s) why our modelling attempts have failed so far…

## Why do we want to know when the Arctic will become ice free anyway?

As we already mentioned on this blog, whether you see the disappearance of the Arctic sea ice as an opportunity or a catastrophe honestly depends on your scientific and economic interests.

It is an opportunity because the Arctic Ocean will finally be accessible to, for example:

• tourism;
• fisheries;
• fast and safe transport of goods between Europe and Asia;
• scientific exploration.

All those activities would no longer need to rely on heavy ice breakers, hence becoming more economically viable. In fact, the Arctic industry has already started: in summer 2016, the 1700-passenger Crystal Serenity became the first large cruise ship to safely navigate the North-West passage, from Alaska to New York. Then in summer 2017, the Christophe de Margerie became the first tanker to sail through the North-East passage, carrying liquefied gas from Norway to South Korea without an ice breaker escort, while the Eduard Toll became the first tanker to do so in winter just two months ago.

On the other hand, the disappearance of the Arctic sea ice could be catastrophic as having more ships in the area increases the risk of an accident. But not only. The loss of Arctic sea ice has societal and ecological impacts, causing coastal erosion, disappearance of a traditional way of life, and threatening the whole Arctic food chain that we do not fully understand yet. Not to mention all of the risks on the other components of the climate system. (See our list of further readings at the end of this post for excellent reviews on this topic).

Either way, we need to plan for the disappearance of the sea ice, and hence need to know when it will disappear.

## Arctic sea ice decrease varies with region and season

In a nutshell, the new paper published by Onarheim and colleagues says that talking about “the Arctic sea ice extent” is an over simplification. They instead separated the Arctic into its 13 distinct basins, and calculated the trends in sea ice extent for each basin and each month of the year. They found a totally different behaviour between the peripheral seas (in blue on this image of the week) and the Arctic proper, i.e. north of Fram and Bering Straits (in red). As is shown by all the little boxes on the image, the peripheral seas have experienced their largest long term sea ice loss in winter, whereas those in the Arctic proper have been losing their ice in summer only. In practice, what is happening to the Arctic proper is that the melt season starts earlier (note how the distribution is not symmetric, with largest values on the top half of the image).

Talking about Arctic sea ice extent is an over simplification

Moreover, Onarheim and colleagues performed a simple linear extrapolation of the observed trends shown on this image, and found that the Arctic proper may become ice-free in summer from the 2020s. As they point out, some seas of the Arctic proper have in fact already been ice free in recent summers. The trends are less strong in the peripheral seas, and the authors write that they will probably have sea ice in winter until at least the 2050s.

So, although Arctic navigation should become possible fairly soon, in summer, you may need to choose a different holiday destination for the next 30 winters.

Melting summer ice. [Credit: Mikhail Varentsov (distributed via imaggeo.egu.eu)]

### But why should WE consider the regions separately?

The same way that you would not plan for the risk of winter flood in New York based on yearly average of the whole US, you should not base your plan for winter navigation from Arkhangelsk to South Korea on the yearly Arctic-wide average of sea-ice behaviour.

Scientifically, this paper is exciting because different trends at different locations and seasons will also have different consequences on the rest of the climate system. If you have less sea ice in autumn or winter, you will lose more heat from the ocean to the atmosphere, and hence impact both components’ heat and humidity budget. If you have less sea ice in spring, you may trigger an earlier algae bloom.

As often, this paper highlights that the Earth system behaves in a more complex fashion that it first appears. Just like global warming does not prevent the occurrence of unpleasantly cold days, the disappearance of Arctic sea ice is not as simple as ice cubes melting in your beverage on a sunny day.

Bhatt, U. S., et al. (2014), Implications of Arctic sea ice decline for the Earth system. Ann. Rev. Environ. Res., 39, 57-89

Meier, W. N., et al. (2014), Arctic sea ice in transformation: A review of recent observed changes and impacts on biology and human activity. Reviews of Geophysics, 52(3), 185-217.

Onarheim, I., et al. (2018), Seasonal and regional manifestation of Arctic sea ice loss. Journal of Climate, EOR.

Post, E., et al. (2013), Ecological consequences of sea-ice decline. Science, 341, 519-524

Edited by Sophie Berger

## Image of the Week – A Hole-y Occurrence, the reappearance of the Weddell Polynya

REMARK: If you’ve enjoyed reading this post, please make sure you’ve voted for it in EGU blog competition (2nd choice in the list)!

During both the austral winters of 2016 and 2017, a famous feature of the Antarctic sea-ice cover was observed once again, 40 years after its first observed occurrence: the Weddell Polynya! The sea-ice cover exhibited a huge hole (of around 2600 km2 up to 80,000 km2 at its peak!), as shown on our Image of the Week. What makes this event so unique and special?

## Why does the Weddell Polynya form?

The Weddell Polynya is an open ocean polynya (a large hole in the sea ice, see this previous post), observed in the Weddell Sea (see Fig.2). It was first observed in the 1970s but then did not form for a very long time, until 2016 and 2017…

Fig. 2: Map of the sea ice distribution around Antarctica on 25th of September 2017, derived from satellite data. The red circle marks the actual Weddell Polynya [Credit: Modified from meereisportal.de]

In the Southern Ocean, warm saline water masses underlie cold, fresh surface water masses. The upper cold fresh layer acts like a lid, insulating the warmer deep waters from the cold atmosphere. While coastal polynyas (see this previous post) are caused by coastal winds, open ocean polynyas are more mysteriously formed as it is not as clear what causes the warm deep water to be mixed upwards. In the case of the Weddell polynya, it forms above an underwater mountain range, the Maud Rise. This ridge is an obstacle to the water flow and can therefore enhance vertical mixing of the deeper warm saline water masses. The warm water that reaches the surface melts any overlying sea ice, and large amounts of heat is lost from the ocean surface to the atmosphere (see Fig. 3).

Fig. 3: Schematic of polynya formation. The Weddell polynya is an open ocean polynya [Credit: National Snow and Ice Data Center].

## Why do we care about the Weddell Polynya?

Overturning and mixing of the water column in the Weddell Polynya forms cold, dense Antarctic Bottom Water, releasing heat stored in the ocean to the atmosphere in the process. Antarctic Bottom Water is formed in the Southern Ocean (predominantly in the Ross and Weddell Seas) and flows northwards, forming the lower branch of the overturning circulation which transports heat from the equator to the poles (see Fig. 4). Antarctic Bottom Water also carries oxygen to the rest of the Earth’s deep oceans. The absence of the Weddell polynya could reduce the formation rate of Antarctic Bottom water, which could weaken the lower branch of the overturning circulation.

Fig.4: Schematic of the overturning (thermohaline) circulation. Deep water formation sites are marked by yellow ovals. Modified from: Rahmstorf, 2002 [©Springer Nature. Used with permission.]

## How often does the Weddell Polynya form?

The last time the Weddell Polynya was observed was during the austral winters of 1974 to 1976 (see Fig. 5). It was then absent for nearly 40 years (!) up until austral winter 2016. In a modelling study, de Lavergne et al. 2014 suggested that the Weddell Polynya used to be more common before anthropogenic CO2 emissions started rising at a fast pace. The increased surface freshwater input from melting glaciers and ice sheets, and increased precipitation (as climate change increases the hydrological cycle) have freshened the surface ocean. This freshwater acts again as a lid on top of the warm deeper waters, preventing open ocean convection, reducing the production of Antarctic Bottom Water.

Fig. 5: Color-coded sea ice concentration maps derived from passive microwave satellite data in the Weddell Sea region from the 1970s. The Weddell Polynya is the extensive area of open water (in blue) [Credit: Gordon et al., 2007, ©American Meteorological Society. Used with permission.].

The reappearance of the Weddell Polynya over the past two winters despite the increased surface freshwater input suggests that other natural sources of variability may be currently masking this predicted trend towards less open ocean deep convection. Latif et al. 2013 put forward a theory describing centennial scale variability of Weddell Sea open ocean deep convection, as seen in climate models. In this theory, there are two modes of operation, one where there is no open ocean convection and the Weddell Polynya is not present. In this situation, sea surface temperatures are cold and the deep ocean is warm, and there is relatively large amount of sea ice. The heat at depth increases with time, as it is insulated by the sea ice and freshwater lid. Then, eventually, the deep water becomes warm enough that the stratification is decreased sufficiently so that open water convection begins again, forming the Weddell Polynya. This process continues until the heat reservoir depletes and surface freshwater forcing switches off the deep convection. Models show that the timescale of this variability is set by the stratification, and models with stronger stratification tend to vary on longer timescale, as the heat needs to build up more in order to overcome the stratification.

In the end, the Weddell Polynya is still surrounded by some mystery… Only the next decades will bring us more insight into the true reasons for the appearance and disappearance of the Weddell Polynya…

Edited by Clara Burgard

Rebecca Frew is a PhD student at the University of Reading (UK). She investigates the importance of feedbacks between the sea ice, atmosphere and ocean for the Antarctic sea ice cover using a hierarchy of climate models. In particular, she is looking at the how the importance of different feedbacks may vary between different regions of the Southern Ocean.

## 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

## Image of the Week – Ice caps on Mars?!

Much like our Planet Earth, Mars has polar ice caps too, one for each pole: the Martian North Polar Ice Cap (shown on our image of the week) and the Southern Polar Ice Cap. Yet, their composition and structure reveals these ice caps are quite different from those of Planet Earth…

## Mars refresher

Planet Earth and planet Mars [Credit : NASA]

As a refresher, here are some Mars facts:

• Mars is the 4th planet from the sun.
• Its equatorial diameter is half the size of the Earth’s, but is bigger than our moon’s.
• Its mean surface temperature is -63°C (the Earth’s surface is around 14°C)
• Mars’ atmosphere is 96% carbon dioxide, less than 2% argon, less than 2% nitrogen and less than 1% other gases.
• Mars’ rotational axis has a tilt similar to Earth’s giving it four seasons as well .

For more detailed pictures and facts about Mars, go have a look on the NASA website here.

## What are these Martian ice caps like?

Like Earth, both of Mars’ poles are frozen. It is the only place in the solar system besides Earth where you can find permanent ice caps. These two Martian ice caps are primarily made of frozen water… but not only! During the winter season, the poles permanent bulk of “water ice” are covered by a seasonal layer of frozen carbon dioxide (commonly known as dry ice).

How come? Similar to Earth, during each pole’s respective winter, these ice caps experience continuous darkness for several months. The temperature becomes so cold (freezing point is -126°C !) that carbon dioxide in its atmosphere freezes and falls onto the ground, forming layers of dry ice. In the summer when the sun returns and temperatures warm, the dry ice begins sublimating back into the atmosphere. At the North pole almost all the dry ice turns back into gas and the ice caps shows its water ice, while a layer of frozen carbon dioxide always remains at the South pole. Seasonal variations can thus be observed like those on Earth.

Martian North (left) et South (right) poles [Credit: NASA ]

The northern ice cap on Mars is much bigger than the southern one. It is about 1,000 kilometers wide (roughly the width of Greenland at its widest point) while the South pole is only 350 kilometers in diameter. Yet… they both contain the same amount of ice! If all of this ice was to melt, Mars’ surface would be covered by an ocean that was 18 meters deep. They are thus the currently largest known water reservoirs on the planet.

## But… what are these spiral forms on Mars’ ice caps?!

The ice caps at both Martian poles show spiral throughs. According to the ESA, these unique features are the result of strong winds that spiral at the surface of the ice caps due to the same Coriolis effect that exists on Earth. This makes every fluid rotate to the right in the North Hemisphere and to the left in the South Hemisphere.

In the North Pole, one of these throughs, called Chasma Boreale, is particularly big. This 100-kilometer-wide and 2-kilometer-deep canyon roughly cuts the Northern Martian ice cap in half.

Chasma Boreale on the Northern ice cap [Credit: NASA ]

## Drilling ice cores on Mars?

The seasonal melting and accumulation of ice occurs while dust deposits, which explain why both Martian polar caps exhibit layered features. They are thus composed of layers of ice mixed with dust (in the scientific jargon, Mars ice caps are called “Polar Layered Deposits”). As for ice cores on Earth, information about the past climate of Mars might be “trapped” in these dust layers. These are essential if we want to find proof of a time when liquid water existed on Mars! Unfortunately, ice cores have not been drilled… yet!

Layers in North Martian Ice Cap (The more dust, the darker the surface) [Credit: NASA/JPL/University of Arizona ]

Edited by David Rounce

Violaine Coulon is a PhD student of the glaciology unit, at the Université Libre de Bruxelles (ULB), Brussels, Belgium. She is using a numerical ice sheet model to investigate the dynamics and stability of the Antarctic Ice Sheet for the past 1.5 million years.

## Image of the Week – Arctic changes in a warming climate

The Arctic is changing rapidly and nothing indicates a slowdown of these changes in the current context. The Snow, Water, Ice and Permafrost in the Arctic (SWIPA) report published by the Arctic Monitoring and Assessment Program (AMAP) describes the present situation and the future evolution of the Arctic, the local and global implications, and mitigation and adaptation measures. The report is based on research conducted between 2010 and 2016 by an international group of over 90 scientists, experts, and members of Arctic indigenous communities. As such, the SWIPA report is an IPCC-like assessment focussing on the Arctic. Our Image of the Week summarizes the main changes currently happening in the Arctic regions.

## What is happening to Arctic climate currently?

The SWIPA report confirms that the Arctic is warming much faster than the rest of the world, i.e. more than twice the global average for the past 50 years (Fig. 2). For example, Arctic surface air temperature in January 2016 was 5°C higher than the average over 1981-2010. This Arctic amplification is due to a variety of climate feedbacks, which amplify the current warming beyond the effects caused by increasing greenhouse gas concentrations alone (see the SWIPA report, Pithan & Mauritsen (2014) and this previous post for further information).

Fig.2: Anomaly of Arctic and global annual surface air temperatures relative to 1981-2010 [Credit: Fig. 2.2 of AMAP (2017), revised from NOAA (2015)].

This fast Arctic warming has led to the decline of the ice cover over both the Arctic Ocean (sea ice) and land (Greenland Ice Sheet and Arctic glaciers).

For sea ice, not only the extent has dramatically decreased over the past decades (see Stroeve et al. 2012 and Fig. 3), but also the thickness (see Lindsay & Schweiger, 2015). Most Arctic sea ice is now first-year ice, which means that it grows in autumn-winter and melts completely during the following spring-summer. In contrast, the multiyear sea-ice cover, which is ice that has survived several summers, is rapidly disappearing.

Fig. 3: Arctic sea-ice extent in March and September from the National Snow and Ice Data Center (NSIDC) and the Ocean and Sea Ice Satellite Application Facility (OSI SAF) [Credit: Fig. 5.1 of AMAP (2017)].

In terms of land ice, the ice loss from the Greenland Ice Sheet and Arctic glaciers has been accelerating in the recent decades, contributing a third of the observed global sea-level rise. Another third comes from ocean thermal expansion, and the remainder comes from the Antarctic Ice Sheet, other glaciers around the world, and terrestrial storage (Fig. 4, see also this previous post and Chapter 13 of the last IPCC report).

Fig. 4: Global sea-level rise contribution from the Arctic components (left bar), Antarctic Ice Sheet and other glaciers (middle-left bar), terrestrial storage (middle-right bar) and ocean thermal expansion (right bar) [Credit: Fig. 9.3 of AMAP (2017)].

Besides contributing to rising sea levels, land-ice loss releases freshwater into the Arctic Ocean. Compared with the 1980-2000 average, the freshwater volume in the upper layers of the Arctic Ocean has increased by more than 11%. This could potentially affect the ocean circulation in the North Atlantic through changes in salinity (see this previous post).

Other changes currently occurring in the Arctic include the decreasing snow cover, thawing permafrost, and ecosystem modifications (e.g. occurrence of algal blooms, species migrations, changing vegetation, and coastal erosion). You can have a look at the main Arctic changes in our Image of the Week.

## Where are we going?

The SWIPA report highlights that the warming trends in the Arctic will continue, even if drastic greenhouse gas emission cuts are achieved in the near future. For example, mean Arctic autumn and winter temperatures will increase by about 4°C in 2040 compared to the average over 1981-2005 according to model projections (Fig. 5, right panel). This corresponds to twice the increase in projected temperature for the Northern Hemisphere (Fig. 5, left panel).

Fig. 5: Autumn-winter (NDJFM) temperature changes for the Northern Hemisphere (left) and the Arctic only (right) based on 36 global climate models, relative to 1981-2005, for two emission scenarios [Credit: Fig. 2.15 of AMAP (2017)].

This Arctic amplification leads to four main impacts:

1. The Arctic Ocean could be ice-free in summer by the late 2030s based on extrapolated observation data. This is much earlier than projected by global climate models.

2. Permafrost extent is projected to decrease substantially during the 21st Century. This would release large amounts of methane in the atmosphere, which is a much more powerful greenhouse gas than carbon dioxide.

3. Mean precipitation and daily precipitation extremes will increase in a warming Arctic.

4. Global sea level will continue to rise due to melting from ice sheets and glaciers, ocean thermal expansion, and changes in terrestrial storage. However, uncertainties remain regarding the magnitude of the changes, which is linked to the different emission scenarios and the type of model used.

## What are the implications?

A potential economic benefit to the loss of Arctic sea ice, especially in summer, is the creation of new shipping routes and access to untapped oil and gas resources. However, besides this short-term positive aspect of Arctic changes, many socio-economic and environmental drawbacks exist.

The number of hazards has been rising due to Arctic changes, including coastal flooding and erosion, damage to buildings, risks of avalanches and floods from rapid Arctic glacier melting, wildfires, and landslides related to thawing permafrost. Furthermore, Arctic changes (especially sea-ice loss) may also impact the climate at mid-latitudes, although many uncertainties exist regarding these possible links (see Cohen et al., 2014).

## What can we do?

The SWIPA report identifies four action steps:

1. Mitigating climate change by decreasing greenhouse gas emissions. Implementing the Paris Agreement would allow stabilizing the Arctic temperatures at 5-9°C above the 1986-2005 average in the latter half of this century. This would also reduce the associated changes identified on our Image of the Week. However, it is recognized that even if we implement the Paris Agreement, the Arctic environment of 2100 would be substantially different than that of today.

2. Adapting to impacts caused by Arctic changes.

3. Advancing our understanding of Arctic changes through international collaboration, exchange of knowledge between scientists and the general public, and engagement with stakeholders.

4. Raising public awareness by sharing information about Arctic changes.

Edited by Scott Watson and Clara Burgard

David Docquier is a post-doctoral researcher at the Earth and Life Institute of Université catholique de Louvain (UCL) in Belgium. He works on the development of processed-based sea-ice metrics in order to improve the evaluation of global climate models (GCMs). His study is embedded within the EU Horizon 2020 PRIMAVERA project, which aims at developing a new generation of high-resolution GCMs to better represent the climate.

## Image of the Week – Of comparing oranges and apples in the sea-ice context

In the last fifty years, models and observations have enabled us to better understand sea-ice processes. On the one hand, global climate models have been developed, accounting for the sea-ice component in the climate system. On the other hand, satellite instruments have been developed to monitor the “real” sea-ice evolution. These satellite observations are often used to evaluate climate models. However, lately, doubts have arisen to whether comparing model output to observations is the most reasonable method. Are we sometimes comparing oranges to apples? To discuss this matter, sea-ice modelers and sea-ice observers met over three days in Hamburg earlier this month at the Workshop on improved satellite retrievals of sea-ice concentration and sea-ice thickness for climate applications.

## How do we measure past and current sea–ice changes?

The great advantage of satellites over in-situ measurements is that they measure changes in sea-ice concentration (fraction of ocean covered by sea ice in a given area) and sea-ice thickness in a continuous way with an almost complete spatial coverage of the polar regions (see this previous post) and with a high temporal resolution.
Of course, satellites do not directly measure sea-ice concentration. Rather, they measure the brightness temperature (left part of Fig. 2), which is a measure of the radiation emitted by the Earth’s surface and atmosphere, with passive microwave sensors (such as SSM/I). From this brightness temperature, it is possible to compute sea-ice concentration (see this article for further information). Microwave sensors are used because they can “see” the surface through clouds and during polar night, which is not possible with visible sensors (such as MODIS).

In a similar way, satellites do not directly measure sea-ice thickness. Rather, they measure sea-ice freeboard (right part of Fig. 2), i.e. the height of the ice above the sea surface, with different kinds of sensors (laser altimetry [e.g. ICESat], radar altimetry [CryoSat]). Sea-ice thickness is then retrieved through appropriate algorithms (see e.g. this article).

Fig. 2: Satellite measurement techniques that lead to the observed brightness temperatures and sea-ice freeboard [Credit: C. Burgard].

## Are the satellite retrievals accurate?

Each method of deriving sea-ice concentration or thickness from satellite measurements has its own uncertainties. For example, algorithms to retrieve sea-ice concentration use several assumptions about the state of the atmosphere and surface emissivity. Also, melt ponds and thin ice show up as lower concentration regions. Similarly, different assumptions about snow depth on ice and about sea-ice density impact the retrieved sea-ice thickness. Therefore, the sea-ice variables retrieved from satellite observations may deviate from their actual “real” state.

## How do we project future sea-ice changes?

In order to project the future sea-ice evolution, different climate models are used (see this article for example). These climate models are usually evaluated against satellite observations in order to assess their performance. While all models present biases compared to observations, it cannot always be concluded that this is necessarily a problem of the models as observations also have uncertainties as previously said. Therefore, the main discussions at the workshop in Hamburg (Fig. 3) were about reducing uncertainties in the comparison between observations and models.

## How can we better compare satellite observations and models?

The discussion in Hamburg was very lively as modelers and observers exchanged about how they actually reach the results they provide, explaining in detail their models and algorithms. It became rapidly clear that comparing observed sea-ice concentration to modeled sea-ice concentration might be like comparing apples to oranges under certain circumstances.

Thomas Lavergne, a researcher at the Norwegian Meteorological Institute, gave a presentation related to this discussion by presenting the picture that is our Image of the Week. The classical method up to now has always been to transform the measured satellite signal into a “satellite product”, a quantity that is directly computed by models (direction from right to left in the Image of the Week), so that we can compare this quantity to the corresponding model variable. As already mentioned, this can lead to assumptions and introduce errors into the observations, while one would expect observations to be the best representation of the “real” world.

Another possible approach, already well accepted in the community of weather forecasting, is to transform the model variables all the way into simulated brightness temperatures and compare these to satellite data (direction from left to right in the Image of the Week). The algorithms that transform model variables into simulated satellite quantities are observation operators. Although an active field of research, the observation operators for sea ice are not ready, and the comparison of sea-ice simulations to satellite observations will for the foreseeable future rely on satellite “products”.

At the workshop, Lavergne advocated for a middle-ground solution, where satellite products “take a step back” and climate models “take a step forward” using tailored observation operators. This would reduce the need for assumptions in the satellite products but still be manageable for modelers, and would most likely offer the best consensus for the two communities. This way, observed and modeled quantities can still be compared with each other and uncertainties introduced into the comparison can be reduced.

Fig. 3: Happy sea-ice observers and sea-ice modelers in Hamburg [Credit: Julika Doerffer, CEN, Universität Hamburg]

## Perspectives

The workshop aim was to bring together sea-ice observers and modelers. While no real consensus on the proposed approach was found, the reflection has been launched and probably deserves some more attention in the future in order to better compare sea-ice models and satellite observations. This might move the debate from an apple-to-oranges comparison to a pear-to-pear one. This will hopefully improve sea-ice models and satellite observations and improve future projections of sea-ice evolution.

With contributions by Thomas Lavergne and Clara Burgard

Edited by Clara Burgard and Sophie Berger

David Docquier is a post-doctoral researcher at the Earth and Life Institute of Université catholique de Louvain (UCL) in Belgium. He works on the development of processed-based sea-ice metrics in order to improve the evaluation of global climate models (GCMs). His study is embedded within the EU Horizon 2020 PRIMAVERA project, which aims at developing a new generation of high-resolution GCMs to better represent the climate.

## Image of the Week — Think ‘tank’: oceanography in a rotating pool

Miniature ocean at the Coriolis facility in Grenoble. [Credit: Mirjam Glessner]

To study how the ocean behaves in the glacial fjords of Antarctica and Greenland, we normally have to go there on big icebreaker campaigns. Or we rely on modelling results, especially so to determine what happens when the wind or ocean properties change. But there is also a third option that we tend to forget about: we can recreate the ocean in a lab. This is exactly what our Bergen-Gothenburg team has been doing these last weeks at the Coriolis facility, in sunny Grenoble.

## How to build your own miniature ocean

Take a 13m diameter (circular) swimming pool. Install it on a rotating platform, and start turning to simulate the Coriolis force, i.e. the impact of the Earth rotation on the flow. Fill it so that the water level reaches 90cm. Actually, the exact value does not matter and can be changed; just make sure that your tank width is an order of magnitude larger than your depth, and that you do not overflow everywhere on the lab floor. Congratulations, you have an ocean! But for now it is a bit boring.

Let’s add some stratification and density-driven currents. As we explained in a previous entry, all you need to do for that is change the temperature and/or salinity of your water. The people here at the Coriolis facility say that changing the salinity is easier than the temperature, so ok, put a source somewhere in your tank that will spit out salty water. Make it even more realistic: have some trough, underwater mountains, solid ice shelves etc. Or rather, some Plexiglas of the corresponding shape. Now you have a beautiful part of the ocean with realistic currents!

But how do you observe it? You can lower probes into the water at specific locations, as if you were doing miniature CTD casts in your miniature ocean. Or you can visualise the whole full-depth flow: add tracer particles to the water flowing from the source (in our case, biodegradable plastic), shoot lasers at it at various depth levels, and take high resolution pictures as you do so. Then, you can track the particles from one image to the next to infer their velocity, using a method called PIV.

By the way, it looks way neater than on this image – that one is just from our overview camera, for fun. [Credit: Céline Heuzé]

## What does it look like when you fire lasers at a large rotating tank?

In a nutshell, it looks like this:

The water flows from the source on the right of the image, towards the ‘ice shelf’ on the left. We are watching the scene from above, from our office that rotates with the tank. The laser successively illuminates several levels from the bottom of the channel to the water surface, revealing the changing structure of the flow with depth. In our real experiment, it took more than 10 minutes for the water to reach the ‘ice shelf’ – here, I have slightly accelerated it.

It is surprisingly peaceful and relaxing to watch. Well, there is tension and suspense regarding what the flow will do since this is, after all, why we are here. But otherwise you are in the dark, with particles shining all around you, in the silence except for the low-squeeking noise of the rotating tank, gently rocked by the vibrations of the platform, and there is not much you can do but wait and enjoy the view. You can also count how many undesired bubbles and dead insects floating at the surface you can see!

## Why do we need rotating tank experiments?

As we explained in this blog, the future of the Antarctic ice sheet is unknown due to marine ice sheet instability. We do not know under which conditions the floating ice shelves that block (‘buttress’) the big land-based ice sheet may collapse. In particular, we do not know what controls the flow of comparatively warm waters that melt the ice shelves:

•  under which conditions do these waters penetrate under the ice?
•  at which depths do they sit?
•  what are the impacts of stratification and the shape of the ice shelf itself?

These questions cannot easily be answered by going in the field. We would need access to many ice shelves, year round, and the ability to observe the flow everywhere –including under the ice– synoptically. Instead in the lab, we just need to adjust our flow speed, or the rotation speed of the tank, or the amount of salt in the source, and we are ready to observe!

The blog of the team: https://skolelab.uib.no/blogg/darelius/

Our blog post about the video game Ice Flows!, illustrating the marine ice sheet instability

Edited by Sophie Berger

## Image of the Week – ROVing in the deep…

Aggregates of sea ice algae seen from the ocean below by the ROV [Credit: Katlein et al. (2017)].

Robotics has revolutionised ocean observation, allowing for regular high resolution measurements even in remote locations or harsh conditions. But the ice-covered regions remain undersampled, especially the ice-ocean interface, as it is still too risky and complex to pilot instruments in this area. This is why it is exactly the area of interest of the paper from which our Image of the week is taken from!

## This is sea ice… seen from the ocean

Traditionally, only divers (and maybe seals, fish, krill, belugas, etc.) have been able to see what is happening just under the sea ice, in the ocean. That is no routine activity – I personally have not been in a fieldwork campaign involving a diver. It is extremely dangerous to dive in such cold waters, and the diver is limited to a small area around the entry hole, which might refreeze really fast. The most common method is to drill small holes from the top of the sea ice to the ice-ocean interface at specific locations instead, and collect the bottom of the resulting ice core. There are obvious problems with this method:

• drilling takes a lot of time and effort;
• you cannot drill everywhere, since it becomes unsafe if the ice is too thin (you still have to be standing on the ice to do the drilling);
• the location of your core has to be representative of what you are sampling.

This is why researchers are trying to more often use sea robots, which can take measurements over a large area while the researchers are safe somewhere else. But most robots that are now used to monitor the ocean are not adapted to ice-covered regions, and the few that are require a lot of specifically trained technicians to operate them and/or can only perform very specific tasks.

Our Image of the Week was taken by a new robot, “The Beast”, whose specificities are described in the recently published Katlein et al. (2017). In brief, it is ice-resistant, small, very manoeuvrable, can be operated by only one or two people from a cosy hut on the ice, and contains any possible sensor you can think of (even a small water bottle for sampling, and a net). It belongs to the family of Remotely Operated Vehicles (ROV), which means that it is connected to the operator by a cable – if anything goes wrong under the ice, just pull on the leash!

And thanks to ROVs, we can see (e.g. on this Image of the Week) that the thickness of the sea ice, hence the amount of light that goes through it and the whole sympagic communities vary a lot over small regions.

What the pilot sees when driving the ROV by a sea ice pressure ridge [Credit: Katlein et al. (2017)].

## Why do we need such observations?

1. Robustness: it will not totally replace the traditional ice coring, for some studies still need to get the actual ice. But it will ensure that the choice of locations make sense, or help extrapolate the localised coring results to a larger region.
2. Validation: for basin-wide studies, we need satellites. But satellite retrievals, especially those for sea ice thickness, still need in-situ measurements for validation. ROVs can provide more validation points than traditional point-coring for the same mission duration, hence ultimately improving algorithms.
3. Seeing is believing: for anything from outreach to future fieldwork preparation, videos captured by an ROV are an unvaluable tool. Ecologists can even see which species live there (or discover new ones).