CR
Cryospheric Sciences

# numerical modelling

## Image of the Week – (Un)boxing the melting under the ice shelves

The Antarctic ice sheet stores a large amount of water that could potentially add to sea level rise in a warming world (see this post and this post). It is currently losing ice, and the ice loss has been accelerating in the past decades. All this is linked to the melting of ice – not at the surface but at the base, underneath the so-called ice shelves which form the continuation of the Antarctic ice sheet over the ocean. These floating ice shelves (represented in color in our Image of the Week) are melted by ocean water from underneath. How can this process called ‘sub-shelf melting’ be included in ice-sheet models? One simple way is to divide the ice-shelf cavity into a number of ocean boxes. Let’s briefly see how it works.

## How to model sub-shelf melting in ice-sheet models?

There are three main ways to do so – which way is most suitable depends on the application:

1. The most elaborated approach is to use ocean models that resolve ocean dynamics underneath the ice shelves. However, they need a lot of computational power.

2. As an alternative, simple parameterizations in which melting is a function of the depth of the ice-shelf base can be used. However, such parameterizations are for many applications too simple…

3. Recently, intermediate approaches that include the basic ocean dynamics have been developed (e.g. Lazeroms et al., 2018; Pelle et al., in review). One such approach is the ocean box model (Olbers and Hellmer, 2010) that we extended for the use in an ice-sheet model. Our extension is called Potsdam Ice-shelf Cavity mOdel (PICO, Reese et al., 2018).

In the following, we take a closer look into the approach of PICO…

## “Boxing” the cavity circulation

In Antarctic ice-shelf cavities (i.e. the water below the ice shelves), in general, an overturning circulation transports ocean water from the sea floor along the ice-shelf base towards the calving front (see Figure 2). It is driven by the “ice-pump” (Lewis and Perkin, 1986): ice melting near the grounding line (separation between the grounded ice sheet and the floating ice shelf) reduces the density of the ambient water. It becomes buoyant and rises along the shelf base towards the ocean. Through this process, new water from outside of the ice-shelf cavity is “pumped” along the continental shelf towards the grounding line. This leads to the typical pattern of highest melting near the deep grounding lines and lower melting towards the calving front.

Figure 2: Schematic showing the ocean boxes following the ice-shelf base, with the first box B1 near the grounding line, and the last box Bn at the calving front. The arrows indicate the overturning circulation. The ocean water enters the cavity from box B0 which is at depth of the continental shelf, in front of the ice shelf. [Credit: Fig. 1 of Reese et al. (2018)]

By dividing the ice-shelf cavity into 2 to 5 ocean boxes, the transport of the overturning circulation is simplified while the sub-shelf melt pattern is captured. The open ocean conditions are simply represented by the ocean reservoir box B0 (Figure 2). And the circulation is driven by the differences in water density between the ocean reservoir (B0 in Figure 2) and the first box near the grounding line (B1 in Figure 2). The model computes sub-shelf melting successively over the ocean boxes, starting near the grounding line.

## Sub-shelf melting with PICO

Sub-shelf melting can vary a lot in-between ice shelves (Figure 1). Antarctic ice-shelf cavities can roughly be sorted into two types (Joughin et al., 2012). The first category are the cold cavities in which the ocean water is close to the freezing point and in which sub-shelf melting is generally low, about 0.1 meter per year. The second category are warm cavities which have a temperature of about 1 degree – that does not sound like much, but for an ice shelf, this feels like being in a sauna – and sub-shelf melting can easily exceed 10 meters per year. Small changes in ocean temperatures can hence have large effects on sub-shelf melting. An increase in sub-shelf melting thins the ice shelf, as for example observed in the Amundsen Sea region in West Antarctica (see this post). The ice shelves there are examples for warm cavities, and a cold cavity is, for instance, underneath the Filchner-Ronne Ice Shelf (see Figure 1 for the specific locations).

In reality, of course, things are much more complicated than simulated by our PICO model. For example, the Coriolis effect can influence ocean circulation in the cavities, sills in the bed can block access of warm water to the grounding line and so on…

## Applications of PICO

To summarize, PICO is a simple and efficient modeling tool that can capture the general pattern of sub-shelf melting observed in Antarctica today. Being implemented in the Parallel Ice Sheet Model, it is openly available, so if you got excited about what it can do and want to use it yourself, you’re welcome to download it!

Edited by David Docquier

Ronja Reese is a postdoctoral researcher at the Potsdam Institute for Climate Impact Research, Germany, in the group of Prof. Dr. Ricarda Winkelmann. She investigates ice dynamics in Antarctic with a focus on ice-ocean interactions and ice-shelf buttressing. She developed and implemented PICO together with Ricarda Winkelmann, Torsten Albrecht, Matthias Mengel and Xylar Asay-Davis. Contact Email: ronja.reese@pik-potsdam.de

## Image of the Week – Karthaus Summer School 2018

Beautiful and cozy Golden Rose hotel on the left; blissful and small Italian village, Karthaus, on the right [Credit: Rohi Muthyala].

Nearly every year since the late 90s, during the summer, the picturesque Karthaus has hosted 10-day glaciology course. This school is a platform for glaciologists to explore, learn and expand their knowledge base. This helps researchers become multi-faceted: to view glaciology from the perspective of those specializing in other backgrounds such as hydrology, geomorphology, oceanography, etc. which complement one another in defining glaciology. Along with the intense course work, one can wholeheartedly cherish the exotic food, cozy resort, spellbinding views and delicious wine!

## Time to learn

Day used to start at 8 am with a healthy breakfast and then we head out to Katharinaberg to attend the lectures. Morning session of the course composed of four lectures with coffee breaks in between to keep us alert. These lectures were on a gamut of topics including numerical and analytical modeling, continuum mechanics, glacier hydrology, mass balance of the ice sheets, thermodynamics of ice, geophysical methods, geodynamics, ice core analysis, polar oceanography and geomorphology, etc. Lectures began with basics in every topic and gradually evolved into complex concepts, enabling students understand the subject better, irrespective of their specialization. After four hours of lectures, we, surrounded by lustrous green hills, enjoyed a delicious three-course lunch.

Afternoon session was all about application of the concepts learned in the morning into numerical exercises and group projects. We were divided into 12 groups to work as a team for a group project. Each group was assigned a topic and a teacher to work with. Results from the group projects presented on the last day of the course, astonished me by the level of research we could accomplish in 10 days, showing the amount of knowledge gained through the program.

Outdoor afternoon session in Kartharinaberg [Credit: F. Pattyn]

## After school

School ended at 5 pm, leaving us with ample time to relax before dinner. While some students enjoyed it hiking, trail running and chilling in the sauna, I spent this time exploring Karthaus with a bunch of friends I made at the school and tried to capture the beauty of nature with my camera. Then was the best part of the evenings – a five-course dinner with lots of wine and stories from our fellow glaciologists. I have never had such an exotic five-course meal, which was so tasty that I couldn’t help but overeat. To top the delicious food, we had musical performances by Frank Pattyn and Johannes Oerlemans. I was amazed to know that most of the teachers have their own specialty with an instrument and that it’s a tradition at Karthaus to enjoy the evenings with their performances. After a two-hour long dinner, we moved to the bar next to the restaurant and continued our entertainment with games, wine and chatting. I wished there were more than 24 hours in a day to spend at Karthaus. This summer school is a complete package of education and entertainment.

Dinners at karthaus, with 5-course meal, wine and music (Frank Pattyn on Piano and Johannes Oerlemans on Bass) [Credit: Rohi Muthyala]

Entertainment after dinner with wine, games, chatting and as you can see, some map reading as well. Apparently, this year students are the most solemn group ever [Credit: Rohi Muthyala].

Adding to the fun, in the middle of the course, we had a day-off that most of us spent by going on an excursion to the Otztal Alps. A bus ride to Kuzras, a cable car to the top of Hochjochferner and hike down into the valley led us to the edge of the glacier where some stepped onto a glacier and/or entered an ice cave for the first time in their life. We stopped by Bellavista (Schonne Aussicht hut) for a hot meal and drinks before hiking higher onto the Italian Alps. Though we had been lucky with perfect clear skies throughout the course, we got a cloudy weather on our day-off to the Alps. Nonetheless, the experience of going well above the clouds in the cable car was the best start for the day.

Hiking on a cloudy day from the top of Hochjochferner gletscher to bellavista [Credit: Rohi Muthyala].

## All in all

This summer school would be an intense and beneficial experience for students in all stages of education. Be it a beginner in glaciology or an experienced final year Ph.D. student, I think the course has a lot to offer to every student. Especially to the students with no glaciology background, this could be a place to learn the basics and understand how to look for answers you are trying to find. With three years of experience going to Greenland for research as an Arctic hydrologist, I was still ignorant in some concepts (such as geomorphology, geodynamics, thermodynamics, etc) that are not directly related to my dissertation. This program opened paths for understanding those concepts in a productive way. I highly recommend this summer program to every graduate student studying glaciology and especially to those who are not from Europe, with few opportunities such as this to learn the basics in wide range of topics from glaciology.

Another best outcome of this course was the opportunity to interact with fellow students and build a network for future collaborations. AGU and EGU have been mostly exclusive, and this provided an opportunity for me (from an American university) to get to know my fellow researchers from other parts of the world. I would also like to highlight the women participation in this course (roughly 50%) and appreciate the organizing committee’s effort to encourage more women in this field. Huge thanks to the organizing committee and all the teachers for their effort in making this an incredible experience. Special thanks to the convener, Johannes Oerlemans, for coordinating such a quintessential summer school.

Class photo in Katharinaberg [Credit : W.J. van de Berg]

Edited by Violaine Coulon

Rohi Muthyala is a PhD candidate from Rutgers University (New Jersey, USA), working with Asa Rennermalm. Muthyala comes from a multidisciplinary background of atmospheric, environmental sciences and geography, and currently focuses her research on Arctic hydrology and hydrological modeling. Objective of her dissertation is to model surface hydrological processes influencing the transport of meltwater over the surface of Greenland ice sheet.

## Image of the Week – The shape of (frozen sea) water

Figure 1: Annual evolution of the sea ice area with two different floe shape parameters of 0.44 (red) and 0.88 (blue). The model is spun-up between 2000 – 2006 and then evaluated for a further ten years between 2007 – 2016 and the mean values over this period displayed by the thick lines. Thin lines show the results for individual years. [Credit: Adam Bateson]

Polar sea ice exists as isolated units of ice that we describe as floes. These floes do not have a constant shape (see here for instance); they can vary from almost circular to being jagged and rectangular. However, sea ice models currently assume that all floes have the same shape. Much focus has been paid to the size of floes recently, but do we also need to reconsider how floe shape is treated in models?

## Why might floe shape matter?

In recent years, sea ice models have started to examine more and more how individual floes influence the overall evolution of sea ice.

A particular focus has been the size of floes (see here and here) and the parameterisation of processes which influence floe size (see here for example). However less attention has been given to the shape of the floe. The shape of the floe is important for several reasons:

• Lateral melt rate: the lateral melt rate describes how quickly a floe melts from its sides. Two floes with the same area but different shape can have a different perimeter; the lateral melt rate  is proportional to the floe perimeter.
• Wave propagation: a straight floe edge will impact propagating waves differently to a curved or jagged floe edge. The distance waves travel under the sea ice and hence the extent of sea ice that waves can fragment will be dependent on these wave-floe edge interactions.
• Floe mechanics: an elongated floe (i.e. much longer in one direction than another) will be more likely to break from incoming waves if its longer edge is aligned with the direction the waves are travelling.

## How do models currently treat floe shape?

One approach used within sea ice models to define floe shape is the use is the use of a parameter, α. The smaller the floe shape parameter, the longer the floe perimeter (and hence, the higher the lateral melt rate). A standard value used for the parameter is 0.66 (Steele, 1992). Figure 2 shows how this floe shape parameter varies for some common shapes.

Figure 2: The floe shape parameters for some common shapes are given for comparison to the standard value of 0.66. [Credit: Adam Bateson]

The standard value of the floe shape parameter, 0.66, was obtained from taking the mean floe shape parameter measured over all floes greater than 1 km from a singular study area of 110 km x 95 km at one snapshot in time. Despite the limited data set used to estimate this shape parameter, it is being used for all sea ice throughout the year for all floe sizes. However, this would only be a concern to the accuracy of modelling if it turns out that sea ice evolution in models is sensitive to the floe shape parameter.

## Model sensitivity to floe shape

To investigate the model sensitivity to the floe shape parameter two simulations have been run: one uses a floe shape parameter of 0.88 and the other uses 0.44, chosen to represent likely extremes. The two simulations are run from 2000 – 2016, with 2000 – 2006 used as a spin-up period. Figure 1 displays the mean total ice area throughout the year and results of individual years for each simulation. Figure 3 is an equivalent plot to show the annual evolution of total ice volume for each simulation.

The results show that the perturbation from reducing the floe shape parameter is smaller than the variation between years within the same simulation.  However, the model does show a permanent reduction in volume throughout the year and a 10 – 20 % reduction in the September sea ice minimum. The impact of the floe shape is hence small but significant, particularly for predicting the annual minimum sea ice extent and volume.

Figure 3: Annual evolution of the sea ice volume with two different floe shape parameters of 0.44 (red) and 0.88 (blue). The model is spun-up between 2000 – 2006 and then evaluated for a further ten years between 2007 – 2016 and the mean values over this period displayed by the thick lines. Thin lines show the results for individual years.

## More recent studies on floe shape

In 2015, Gherardi and Lagomarsino analysed the floe shape behaviour from four separate samples of satellite imagery from both the Arctic and Antarctic. The study found different distributions of floe shapes in different locations, however there was no correlation between floe shape and size. This property would allow models to treat floe shape and size as independent properties. More recently, in 2018, Herman et al. analysed the results of laboratory experiments of ice breaking by waves. It was found that wave break-up influenced the shape of the floes, tending to produce straight edges and sharp angles.  These features are associated with a smaller floe parameter i.e. would produce an increased lateral melt rate.

## What next?

More observations are needed to identify whether the use of a constant floe shape parameter is justified. The following questions are important:

• Do further observations support the finding that floe size and shape are uncorrelated?
• What range of values for the floe shape parameter can be observed in reality?
• Do we see significant variations in the floe shape parameter between locations?
• Do these variations occur over a large enough scale that they can be represented within existing model resolutions?

Edited by Violaine Coulon and Sophie Berger

Adam Bateson is a PhD student at the University of Reading (United Kingdom), working with Danny Feltham. His project involves investigating the fragmentation and melting of the Arctic seasonal sea-ice cover, specifically improving the representation of relevant processes within sea-ice models. In particular he is looking at lateral melting and wave induced fragmentation of sea-ice as drivers of break up, as well as the role of the ocean mixed layer as either an amplifier or dampener to the impacts of particular processes. Contact: a.w.bateson@pgr.reading.ac.uk or @a_w_bateson on twitter.

## Image of the Week – A high-resolution picture of Greenland’s surface mass balance

The Greenland ice sheet – the world’s second largest ice mass – stores about one tenth of the Earth’s freshwater. If totally melted, this would rise global sea level by 7.4 m, affecting low-lying regions worldwide. Since the 1990s, the warmer atmosphere and ocean have increased the melt at the surface of the Greenland ice sheet, accelerating the ice loss through increased runoff of meltwater and iceberg discharge in the ocean.

## Simulating the climate with a regional model

To understand the causes of the recent ice loss acceleration in Greenland, we use the Regional Atmospheric Climate Model RACMO2.3 (Noël et al. 2015) that simulates the evolution of the surface mass balance, that is the difference between mass gain from snowfall and mass loss from sublimation, drifting snow erosion and meltwater runoff. Using this data set, we identify three different regions on the ice sheet (Fig. 1):

• the inland accumulation zone (blue) where Greenland gains mass at the surface as snowfall exceeds sublimation and runoff,

• the ablation zone (red) at the ice sheet margins which loses mass as meltwater runoff exceeds snowfall.

• the equilibrium line (white) that separates these two areas.

## From 11 km to 1 km : downscaling RACMO2.3

To cover large areas while overcoming time-consuming computations, RACMO2.3 is run at a relatively coarse horizontal resolution of 11 km for the period 1958-2015. At this resolution, the model does not resolve small glaciated bodies (Fig. 2a), such as narrow marginal glaciers (few km wide) and small peripheral ice caps (ice masses detached from the big ice sheet). Yet, these areas contribute significantly to ongoing sea-level rise. To solve this, we developed a downscaling algorithm (Noël et al., 2016) that reprojects the original RACMO2.3 output on a 1 km ice mask and topography derived from the Greenland Ice Mapping Project (GIMP) digital elevation model (Howat et al., 2014). The downscaled product accurately reproduces the large mass loss rates in narrow ablation zones, marginal outlet glaciers, and peripheral ice caps (Fig. 2b).

Fig. 2: Surface mass balance (SMB) of central east Greenland a) modelled by RACMO2.3 at 11 km, b) downscaled to 1 km (1958-2015). The 1 km product (b) resolves the large mass loss rates over marginal outlet glaciers [Credit: Brice Noël].

The high-resolution data set has been successfully evaluated using in situ measurements and independent satellite records derived from ICESat/CryoSat-2 (Noël et al., 2016, 2017). Recently, the downscaling method has also been applied to the Canadian Arctic Archipelago, for which a similar product is now also available on request.

## Endangered peripheral ice caps

Using the new 1 km data set (Fig. 1), we identified 1997 as a tipping point for the mass balance of Greenland’s peripheral ice caps (Noël et al., 2017). Before 1997, ablation (red) and accumulation zones (blue) were in approximate balance, and the ice caps remained stable (Fig. 3a). After 1997, the accumulation zone retreated to the highest sectors of the ice caps and the mass loss accelerated (Fig. 3b). This mass loss acceleration was already reported by ICESat/CryoSat-2 satellite measurements, but no clear explanation was provided. The 1 km surface mass balance provides a valuable tool to identify the processes that triggered this recent mass loss acceleration.

Fig. 3: Surface mass balance of Hans Tausen ice cap and surrounding small ice bodies in northern Greenland before (a) and after the tipping point in 1997 (b). Since 1997, the accumulation zone (blue) has shrunk and the ablation zone (red) has grown further inland, tripling the pre-1997 mass loss [Credit: Brice Noël].

Greenland ice caps are located in relatively dry regions where summer melt (ME) nominally exceeds winter snowfall (PR). To sustain the ice caps, refreezing of meltwater (RF) in the snow is therefore a key process. The snow acts as a “sponge” that buffers a large amount of meltwater which refreezes in winter. The remaining meltwater runs off to the ocean (RU) and contributes to mass loss (Fig. 4a).

Before 1997, the snow in the interior of these ice caps could compensate for additional melt by refreezing more meltwater. In 1997, following decades of increased melt, the snow became saturated with refrozen meltwater, so that any additional summer melt was forced to run off to the ocean (Fig. 4b), tripling the mass loss.

Fig. 4: Surface processes on an ice cap: the ice cap gains mass from precipitation (PR), in the form of rain and snow. a) In healthy conditions (e.g. before 1997), meltwater (ME) is partially refrozen (RF) inside the snow layer and the remainder runs off (RU) to the ocean. The mass of the ice cap is constant when the amount of precipitation equals the amount of meltwater that runs off. b) When the firn layer is saturated with refrozen meltwater, additional meltwater can no longer be refrozen, causing all meltwater to run off to the ocean. In this case, the ice cap loses mass, because the amount of precipitation is smaller than the amount of meltwater that runs off [Credit: Brice Noël].

In 1997, following decades of increased melt, the snow became saturated with refrozen meltwater, so that any additional summer melt was forced to run off to the ocean, tripling the mass loss.

We call this a “tipping point” as it would take decades to regrow a new, healthy snow layer over these ice caps that could buffer enough summer meltwater again. In a warmer climate, rainfall will increase at the expense of snowfall, further hampering the formation of a new snow cover. In the absence of refreezing, these ice caps will undergo irreversible mass loss.

## What about the Greenland ice sheet?

For now, the big Greenland ice sheet is still safe as snow in the extensive inland accumulation zone still buffers most of the summer melt (Fig. 1). At the current rate of mass loss (~300 Gt per year), it would still take 10,000 years to melt the ice sheet completely (van den Broeke et al., 2016). However, the tipping point reached for the peripheral ice caps must be regarded as an alarm-signal for the Greenland ice sheet in the near future, if temperatures continue to increase.

Data availability

The daily, 1 km Surface Mass Balance product (1958-2015) is available on request without conditions for the Greenland ice sheet, the peripheral ice caps and the Canadian Arctic Archipelago.

Edited by Sophie Berger

Brice Noël is a PhD Student at IMAU (Institute for Marine and Atmospheric Research at Utrecht University), Netherlands. He simulates the climate of the Arctic region, including the ice masses of Greenland, Svalbard, Iceland and the Canadian Arctic, using the regional climate model RACMO2. His main focus is to identify snow/ice processes affecting the surface mass balance of these ice-covered regions. He tweets as: @BricepyNoel Contact Email: b.p.y.noel@uu.nl

## Image of the Week – Supraglacial debris variations in space and time!

There is still a huge amount we don’t know about how glaciers respond to climate change. One of the most challenging areas is determining the response of debris-covered glaciers. Previously, we have reported on a number of fieldwork expeditions to debris-covered glaciers but with this Image of The Week we want to show you another way to investigate these complex glaciers – numerical modelling!

## Debris-covered glaciers

Debris-covered glaciers occur globally, with a great many being found in the Himalaya-Karakoram mountain range. For example, in the Everest Region of Nepal 33% of glacier area is debris covered (Thakuri et al., 2014). The response of debris-covered glaciers to future climate change in such regions has huge implications for water resources, with one fifth of the world’s population relying on water from the Himalayan region for their survival (Immerzeel et al., 2010).

Debris-covered glaciers respond to climate change differently to debris-free glaciers as the supraglacial debris layer acts as a barrier between the atmosphere and glacier (Reznichenko et al., 2010). The supraglacial debris layer has several key influences on the glacier dynamics:

• Glacier ablation (loss of mass from the ice surface) is enhanced or inhibited depending on debris layer thickness and properties – see our previous post.
• Supraglacial debris causes glaciers to reduce in volume through surface lowering rather than terminus retreat (typical of debris free mountain glaciers).

Understanding the influence of a supraglacial debris layer on mass loss or gain is, therefore, key in determining the future of these glaciers. The properties of supraglacial debris layers can vary in time and space both in debris layer thickness and distribution, as well as properties of the rocks which make up the debris (e.g. albedo, surface roughness, porosity, size and moisture content). It is these characteristics of the debris-cover which control the heat transfer through the debris and therefore the amount of thermal energy that reaches the underlying ice causing melting (Nicholson and Benn, 2006). In order to better predict the future of debris-covered glaciers we needs to be able to numerically model their behaviour. This means we need a better understanding of the variations in debris cover and how this affects the ice dynamics.

## How does a supraglacial debris layer vary in time and space?

Our Image of the Week (Fig. 1) shows a schematic of how debris distribution can vary spatially across a glacier surface and also this can change through time. The main inputs of debris are:

• Upper regions: snow and ice avalanches in the upper reaches of the glacier.
• Mid and Lower regions: rock avalanches and rock falls (Mihalcea et al., 2006).

These irregular mass movement events vary in frequency and magnitude, and therefore affect debris distribution across the glacier surface but also through time. The irregularity of them makes it really hard to predict and simulate! Luckily, debris transport is a little more predictable.

Figure 2: An ice cliff emerging out of the supraglacial debris layer on Khumbu Glacier, Nepal, with Nuptse in the background. [Credit: M. Gibson]

Debris is initially transported along medial moraines (glacially transported debris)  in the upper and mid-sections of the glacier, this is known as entrained debris. The various sources of entrained debris combine to form a continuous debris cover in the lower reaches of the glacier (Fig. 1). As a supraglacial debris layer is forming, such as for Baltoro glacier (Fig. 1), the boundary between the continuous debris layer and entrained debris sections progresses further upglacier over time.

Eventually transported debris will reach the terminus of the glacier and be deposited (Fig. 1), mainly due to a decrease in surface velocity of the glacier towards the terminus. However, once debris is deposited it doesn’t just sit there; debris is constantly being shifted around as ablation (surface melting) occurs. As ablation occurs the debris surface ablates unevenly, as the thickness of the debris layer is spatially variable. Uneven ablation, otherwise known as differential surface lowering, causes the glacier surface to be made up of topographic highs and lows, the latter of which sometimes become filled with water, forming supraglacial ponds (Fig. 1) . Another product of debris shifting is that ice cliffs, such as the one seen in Fig. 2, are exposed. These features are initially formed when englacial channels collapse  or debris layers slide (Kirkbride, 1993). All this movement and shifting means that not only do glacier models have to consider variation in debris layers across the glacier and through time, but also the presence of ice cliffs and supraglacial ponds. They are important as they have a very different surface energy balance to debris-covered ice. To complicate things further the frequency and area of ice cliffs and supraglacial ponds also vary through time! You see the complexity of the problem…

## Modelling spatially and temporally varying debris layers

Numerical modelling is key to understanding how supraglacial debris layers affect glacier mass balance. However, current numerical modelling often either omits the presence of a supraglacial debris layer entirely, or a debris layer that is static in time and/or space (e.g. Collier et al., 2013; Rowan et al., 2015; Shea et al., 2014). However, as outlined earlier, these supraglacial debris layers are not static in time or space. Understanding the extent to which spatiotemporal variations in supraglacial debris distribution occur could aid identification of when glaciers became debris-covered, glaciers that will become debris-covered glaciers in the future, and the timescales over which supraglacial debris layers vary. The latter is particularly relevant to numerical modelling as it would result in total glacier ablation being calculated more precisely throughout the modelling time period. Understanding the interaction between glacier dynamics and debris distribution is therefore key to reconstructing debris-covered glacier systems as accurately as possible.

Edited by Emma Smith

Morgan Gibson is a PhD student at Aberystwyth University, UK, and is researching the role of supraglacial debris in ablation of Himalaya-Karakoram debris-covered glaciers. Morgan’s work focuses on: the extent to which supraglacial debris properties vary spatially; how glacier dynamics control supraglacial debris distribution; and the importance of spatial and temporal variations in debris properties on ablation of Himalaya-Karakoram debris-covered glaciers. Morgan tweets at @morgan_gibson, contact email address: mog2@aber.ac.uk.