Sea Level Rise: How far, how fast?

A paper appeared in Science this week about sea level rise in the last interglacial (about 129-116,000 years ago). It has sparked the usual predictable headlines as it points out that during that period, sea level rose by about 6-9 metres but that that the ocean temperature as far as it can be reconstructed, is about what we see now, that is about 0.5C warmer than the preindustrial.

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Guardian reports on latest study

In a sense this isn’t that “new” – we’ve known about higher sea levels during the last interglacial for ages and that the global mean temperature was roughly 2C above the pre-industrial global mean. This is in fact one of the reasons for the Paris target (though some scientists speculate that it’s also pretty much already out of reach).

However, the sea surface temperature stuff makes it extra interesting as the ocean is a pretty big source of uncertainty in global climate models and mot models do not manage to reproduce modern day ocean temperatures all that well.

It should also be said that the last interglacial is only a good analogue for 2C world up to a point – it was warm because of enhanced solar input, not because of greenhouse gases as this plot from an Antarctic ice core, edited by the awesome Bethan Davies at the Antarctic Glaciers blog shows:

vostok_420ky_4curves_insolation_to_2004
Carbon dioxide (CO2), Methane (CH4) with reconstructed temperature from the Vostok Ice Core, taken in Eastern Antarctica. Enhanced with modern methane, CO2 and temperature measurements by Bethan Davies. Note that the “modern” value of CO2 here is from 2004. In 2017 it is currently measuring 403 ppm.

It’s also interesting to speculate where the water came from – the Greenland ice sheet was much smaller than today but it was still there and now “only” contains 7m of sea level rise today. So the complete disappearance of Greenland cannot explain the rise in global sea level. The small glaciers and ice caps of the world can’t contribute more than half a metre or so either. Therefore it has to be Antarctica contributing the most – East or West is the question and it really is a very very longstanding question.

The progress in the international polar year (IPY) in mapping the bedrock of Antarctic in the BEDMAP2 brought quite a few surprises, including the discovery of several very deep marine basins in the East that could potentially contribute a lot of water to sea level.

More recently, channels under the floating ice shelves of west Antartica, along with various modelling studies have proposed that the west could be much more unstable than thought. Actually this has been a very very longstanding problem in Antarctic science since at least the late 1970s when John Mercer first proposed the marine ice sheet instability hypothesis.

In any case, events in both Denmark and the UK have brought this problem home more sharply.

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The silent storm surge – coastal flooding in Copenhagen on the 5th January – the water in the harbour is not normally this high! Source: Brian Dehli, shared by DR 

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The “silent storm surge” in January 2017 around the coast of Denmark was  a hundred year event in many places, but as Aslak Grinsted points out, sea level rise makes a hundred year event a 20 year event with only a small rise.

Sea level will not rise equally everywhere, the fingerprint of Greenland ice sheet loss is felt largely in the Pacific, Antarctic ice melt will be felt in Europe. It matters where the water comes from. A point not generally appreciated.

So this new paper is also important, but it only underlines that we need to be able to make much much better estimates of how fast and how far the ice sheets will retreat, which is the justification for much of my own scientific research.

Finally, I think it’s probably necessary to point out that sea level is already rising. This was asked by a listener to Inside science, one of my favourite BBC radio 4 programmes/podcasts. I was a little surprised that an apparently scientifically literate and interested member of the public was not aware that we can measure sea level rise pretty well – in fact to an extent, the global warming signal is more easily detected in the ocean than in the global temperature record. This is because the ocean expands as it warms and there is ocean pretty much everywhere, whereas temperature observations are patchy and mostly on land. Clearly, scientists like myself are *still* not doing a very good job of communicating our science more widely. So here is the global mean sea level record to date, it’s updated pretty regularly here and on average, sea level is rising at about 3mm per year or 3cm per decade.

 

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Sea level variation measured by satellite since 1993 from NASA

When we look at tidal gauges,sea level rose about 20cm in the 2oth century

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Sea level rise in the 20th century measured by tide gauges, plot by NASA, data from CSIRO

The big uncertainties we have on whether or not this will accelerate in years to come is largely down to missing processes in ice sheet models that we don’t yet understand or model well – mostly calving by glaciers and ice shelves. I promised Steve Bloom a blog post on that at some point – I have a paper to finish and new simulations to run, but hopefully I’ll get round to that next.

UPDATE: I was made aware this morning of a new report from the European Environment Agency about climate change impacts and adaptation in Europe. In the report they state (correctly) that while the IPCC 5th Assessment Report suggested that in the 21st century the likely sea level rise will be on the order of half a metre, some national and expert assessments (I took part in a couple of these) had suggested an upper bound of 1.5 – 2m this century, for high emissions scenarios.

This is a big difference and would be pretty challenging to adapt to in low-lying countries like the Netherlands and Denmark, not to mention big coastal cities like London or Hamburg. It’s laso important to emphasise that it doesn’t jsut stop at the end of the century, in fact our simulations of the retreat of Greenland ice sheet suggest it’s only just getting going at the end of this century and the next century the rate of ice loss will really start to accelerate.

All of which is to say, there’s really a very good reason to act now to reduce our emissions. The EEA has also produced this very nice map of observed sea level rise in Europe over the last two decades based on  Copernicus environmental data.

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Check out how much the sea level is rising where you live… Source: European Environment Agency, data from Copernicus Marine Environment Monitoring Service

With the prospect of American federal funding for environmental observations being reduced or strongly constrained in the future, it’s really important we start to identify and support the European datasets which are the only other sources of environmental monitoring out there right now.

 

 

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Rain rain go away…

My 2 kids were singing the rain rain go away rhyme during last weekend’s epic rainfall in Copenhagen and it reminded me that I have not yet put up a post about a paper I was a co-author on this summer related to late summer/autumn rainfall and the effects on the Greenland ice sheet, so here goes….

Mostly when we think of precipitation in Greenland we think of snow in the winter, but it does rain quite a lot, as I know from personal experience (see photo taken as the clouds started to clear one September field season in Eastern Greenland…). This paper in Nature Geoscience by Sam Doyle and co-authors including myself shows that when rain falls on the ice sheet at the “wrong” time of year it can have a very far-reaching effect, causing the speed up of a large area across the ice sheet.

Rain clouds over the Stauning Alps of Eastern Greenland after the third day of rain... Exploratory mining camp tents in the foreground.
Rain clouds over the Stauning Alps of Eastern Greenland after the third day of rain…
Exploratory mining camp tents in the foreground.

The important caveat is that rainfall during the main part of the melt season is more or less evacuated away quickly. Glaciers – and the Greenland ice sheet is basically a very big glacier – develop a drainage system more or less analogous to large underground sewers during the melt season. These tend to close down during the colder accumulation season and reopen by the sheer pressure of water running through them when the melt season starts. Rainfall during that crucial late summer/early autumn period when the drainage is closing down and therefore less efficient at evacuating surplus liquid water is therefore not able to move away from the glacier very easily and forces its way through any way it can find.

During this period, most of the snow will have melted off the surface, leaving vast areas of bare ice. By contrast, rain on snow in the early part of the melt season when there is a thick snow pack is more likely to refreeze inside the snow. In late summer however, there will be a relatively short period between rain falling and accumulating in the glacier drainage system.

In practice this means the water makes its way to the bed of the glacier through moulins and englacial channels, where it more or less hydraulically jacks up the glacier over a large region, allowing the ice to flow to the margins faster. There may then also be a knock-on effect with increased calving of icebergs at outlet glaciers. in 2011, the field team were able to measure both the rain fall and the following cascade of processes in a range of different datasets as shown below:

Rainfall (a,b) over the ice sheet runs off the bare ice quickly as shown by discharge stations on a number of rivers in western Greenland (c). This triggers acceleration  across a wide area, shown by GPS stations on the ice sheet at 10 different locations (d). Figure taken from the paper
Rainfall (a,b) over the ice sheet runs off the bare ice quickly as shown by discharge stations on a number of rivers in western Greenland (c). This triggers acceleration across a wide area, shown by GPS stations on the ice sheet at 10 different locations (d). Figure taken from the paper

My contribution to the paper was in the form of some HIRHAM5 model runs for Greenland which show the last decade has seen a significant increase in rainfall events in the summertime compared with the previous decade. We chose as a study region the K-transect of weather stations in western Greenland. These are operated by Utrecht University and have a long time-series of data which previous work has shown our model can replicate quite nicely. The model is forced by the ERA-Interim reanalysis, a data set based on weather forecast models with real observations included in it run for the whole world so we are pretty confident the rainfall patterns are realistic. There are actually two interesting points illustrated in the picture below taken from the paper. Firstly that there is more rain falling and secondly that this rain is falling at higher elevations on the ice sheet, potentially causing a much wider area of the ice sheet to be affected by late-summer rainfall events.

The decadal change in rainfall events is partly due to a persistent North Atlantic Oscillation anomaly which has funnelled storms over the western edge of the ice sheet. There is also some evidence that the stratospheric Rossby waves have become more “wavy” over the same period, due to the increasing warming and vanishing sea ice in the Arctic. This hypothesis was articulated in a very nice paper by Francis and Vavrus but it remains a very open area of research as we just don’t have a lot of evidence right now.

We do know that the Arctic is one of the fastest warming regions on the planet and this will certainly have a knock-on effect on the Greenland ice sheet both in terms of melting and, perhaps, in the frequency of storms bringing rain over the ice sheet in the future. I am now preparing a new study to see if we see a signal along these lines in our future simulations of the Greenland domain.

Rainfall events at a weekly timestep over the K-transect in western Greenland  for two different decades and the difference between the two. The second decade has many more rainfall events that reach to a much higher elevation than the first decade.
Rainfall events at a weekly timestep over the K-transect in western Greenland for two different decades and the difference between the two. The second decade has many more rainfall events that reach to a much higher elevation than the first decade.

Conversion Factors

The official end of the hydrological year in Greenland (1st September to 31st August) means I am rather busy writing reports to give an overview of where the ice sheet is this year and what happened. I will try to write a quick blogpost about this in the next week or so (in case you’re curious here’s a quick plot to show the entire annual SMB, see also: http://polarportal.dk/en/groenlands-indlandsis/nbsp/isens-overflade/)

Daily and accumulated surface mass budget of the Greenland ice sheet, 31st August, 2015, last day of the hydrological year
Daily and accumulated surface mass budget of the Greenland ice sheet, 31st August, 2015
Anyway, as I find I am constantly switching between Gigatonnes (or indeed Gigatons), cubic kilometres and sea level equivalent, here is a quick and handy guide to converting different units of mass, for my own use as much as anyone else.

1 gigatonne is 1 billion metric tonnes  (or 1 milliard if you like the old British style, that is one thousand million).

However, on the Polar Portal we usually reckon everything in water equivalent. This is to save having to distinguish between snow (with a density between ~100 kg/m3 when freshly fallen and ~350 kg/m3 m when settled after a few days), firn (snow that has survived a full annual cycle with a density up to ~800 kg/m3) and glacier ice (anything from ~850 kg/m3 to 900+). Water has a density (at 4C) of 1000 kg/m3

1 gigatonne of ice will still weigh 1 gigatonne when it is melted but the volume will be lower since ice expands when it freezes.

1 metric tonne of water is 1 cubic metre and 1 billion metric tonnes is 1 km3 (a cubic kilometre of water)

A cubic kilometre of ice does not however weight 1 gigatonne but about 10% less because of the density difference.

100 gigatonnes of water is roughly 0.28mm of sea level rise (on average, note there are big regional differences in how sea level smooths itself out).

Finally, 1 mm sea level rise is 360 Gt of ice (roughly the number of days in a year) 

EDIT: – thanks to ice sheet modeler Frank Pattyn and ice core specialist Tas van Ommen on Twitter for pointing out I’d missed this last handy conversion. Interestingly and probably entirely coincidentally this is very close to the amount of mass lost by the Greenland ice sheet reported by Helm et al., 2014 for the the period January 2011 – January 2014 (pdf here) of 375 +/-24 km3 per year.

Over the last 10 years or so, Greenland has lost on average around 250 Gigatonnes of ice a year (Shepherd et al., 2012), contributing a bit less than a millimetre to global sea level every year with some big interannual variability. This year looks like it will be a comparable number but we will have to wait for the GRACE satellite results in a couple of months to fill in the dynamic component of the mass budget and come up with our final number.

Of course, gigatonnes and cubic kilometres are rather hard to visualise so we have skeptical science to thank for this post that tries. And as aside, Chris Mooney wrote a nice piece in the Washington Post on the difficulties of visualising how much ice is being lost which contains the immortal  line “Antarctica is clearly losing billions of African elephants worth of ice each year”.

A question of observation?

It’s been a while since I lasted posted anything, not for want of ideas but mainly lack of time. I shall try to catch up over the next few weeks. For now I was inspired to write an ultra-quick post about a very trivial question that came up at work today. I think it really captures how observational meteorology works (or should work).

Today, a colleague, John Cappelen, (also known as Mr. Greenland observational data), happened to mention in passing that on the 15th July this year, the weather station at Summit on the Greenland ice sheet had transmitted back to us in Copenhagen, a temperature observation of 2.5°C. This was during one of the highest melt periods this summer.

Automatic weather station operating at Summit, June 2015
The automatic weather station doing it’s thing at Summit, June 2015. Photo: DMI

Bearing in mind that Summit Camp is at roughly 3,216m, this is a pretty high measured temperature. In fact it would be rather noteworthy, especially as it occurred on one of the highest melt days of the summer. Temperatures above 0°C at Summit are not unknown and the record, during the famous summer of 2012 when around 95% of the ice sheet surface experienced melt, the water sweeping away a bridge on the Watson River near Kangerlussuaq, was 3.6°C.

Now, my colleague is a very experienced and careful scientist. He had checked the observations and the temperatures before and after this measurement were well below zero, so, my colleague asked, was there any reason to believe this measurement or can we assume an instrument failure of some kind?

My office mate in the Arctic and Climate Research section and I obligingly had a quick look at our Polar Portal Greenland ice sheet surface plots (see below) and at the melt extent plots that are updated daily on the DMI website. We had to conclude there was no evidence of melt that high on the ice sheet and there was also no reason to believe that a sudden sharp warming had occurred at Summit on this day based on DMI’s own weather forecast. We then turned to check the weather plots, also on the polar portal and based on data from the European Centre for Medium Range Weather Forecasting (the ECMWF – probably the best weather forecast modellers in the world).

Again, the anomaly plots showed rather cold conditions prevailing over the ice sheet during this period, though at the same time very high melt and low surface mass balance from the ice sheet due to the clear skies.

Graphs showing area of the Greenland ice sheet experiencing melt conditions, compared with the average (dark grey line) and range of past summers (1990-2012), for more detail see the DMI website
Graphs showing area of the Greenland ice sheet experiencing melt conditions, compared with the average (dark grey line) and range of past summers (1990-2012), for more detail see the DMI website
Temperature record from Summit Camp for the last month.
Temperature record from Summit Camp for the last month.

Fortunately, due to the American Summit Camp we have access to a back-up dataset very close to this location and after a quick web search John Cappelen was able to confirm that indeed this measurement was an error as the nearby station has not seen anything like that during the period in question (see right).

This kind of thing happens all the time and is therefore not at all newsworthy or interesting enough to write a publication about. However, when a recent record high temperature in the UK can lead to 2 critical articles in the Daily Telegraph and a particularly vigorous exchange on twitter for Met Office scientist Mark McCarthy, as well as this corrective piece on the Carbon Brief blog, perhaps we should be more vocal about just how careful and critical we as scientists are about observations, including the ones we decide to discard as well as the ones we keep.

Surface mass balance of the Greenland ice sheet on the 15th July 2015. Intense melting around the margins led to very negative SMB (the red colours) during this period.
Surface mass balance of the Greenland ice sheet on the 15th July 2015. Intense melting around the margins led to very negative SMB (the red colours) during this period.

Addendum: I was alerted by this tweet from Gareth Jones, also a Met Office scientist, to some slightly strange cherry picking in the blogosphere of climate records from a couple of DMI stations in Greenland. These have apparently been used to claim no climatic warming trend in Greenland over the 20th Century (I’m not going to link to it).

Screenshot of tweet

Anyone who is really interested in the observational data could try checking these reports by Mr Greenland observations himself instead, here is a quick summary: 

Mean annual temperature in Copenhagen, Torshavn (Faeroes) and selected DMI weather stations in Greenland from 1873 - 2014. Figure from DMI
Mean annual temperature in Copenhagen, Torshavn (Faeroes) and selected DMI weather stations in Greenland from 1873 – 2014. Figure from DMI

Calling all students…

I’m off to the UK next week for a workshop at Sheffield University where we will discuss the Surface Mass Balance of the Greenland Ice Sheet. The ISMASS workshop includes all the main modelling groups and observation groups who are involved in assessing surface mass balance in Greenland. I will be representing DMI’s Greenland SMB work there (not an easy task condensing it down to a 20 minute talk!).

In the course of preparing my presentation I have been making plots and figures and really investigating some exciting results. Sadly, I very rarely get the chance to spend time on this these days and I am keen to recruit students to assist in this work. Should any potentially interested students want to discuss this at Sheffield do let me know.

At the risk of spoilers in my presentation, here for example is one showing how different ways of characterising the surface snow pack affects our estimates for surface mass balance, and how the effects of the specific changes can be very different in different years.

Surface mass balance map plots of Greenland
Surface mass balance for the hydrological year (Sep -Aug) ending in 2012 and 2013 calculated using HIRHAM5 with 2 different surface schemes. The maps on the right show the difference between the 2.

As I mentioned I rarely get enough time to analyse the output from our runs and I would be very happy to hear from any students who are interested in doing a project on our simulations. We have lots of MSc and Bachelors projects already listed on our website at DMI but we are always happy to hear new ideas from students on related topics. I have terabytes of data from simulations I would like to be properly analysed and this could be very interesting given we are talking about Greenland and the Arctic in the present day and in the future. It’s a really nice opportunity to work with some cutting edge research. I am also happy to hear from students who would like to do a summer project and for the right candidate I would be able to look into a paid “studentmedarbejderhjælper” position for a few months, especially if you are already a trained computer science candidate….

If you are an undergraduate looking into an MSc, I urge you to consider Denmark. EU citizens usually qualify for generous support grants (rare these days!) as we have a shortage of candidates wanting to study in the sciences in Copenhagen. The research and teaching are world class and done in English at MSc level. The possibilities for projects in Greenland are literally endless.

If you want any more details or to talk about any of the possibilities, do get in touch!

Changes in SW Greenland ice sheet melt

A paper my colleague Peter Langen wrote together with myself and various other collaborators and colleagues has just come out in the Journal of Climate. I notice that the Climate Lab Book regularly present summaries of their papers so here I try to give a quick overview of ours. The model output used in this run is available now for download.

The climate of Greenland has been changing over the last 20 or so years, especially in the south. In this paper we showed that the amount of melt and liquid water run off from the ice sheet in the south west has increased at the same time as the equilibrium line (roughly analogous to the snow line at the end of summer on the ice sheet) has started to move up the ice sheet. Unlike previous periods when we infer the same thing happened this can be attributed to warmer summers rather than drier winters.

Map showing area around Nuuk
The area we focus on in this study is in SW Greenland close to Nuuk, the capital. White shows glaciers, blue is sea, brown is land not covered by ice.

We focused on the area close to Nuuk, the capital of Greenland, as we had access to a rather useful but unusual (in Greenland) dataset gathered by Asiaq the Greenland survey. They have been measuring the run off from a lake near the margin of the ice sheet for some years and made this available to us in order to test the model predictions. This kind of measurement is particularly useful as it integrates melt and run-off from a wider area than the usual point measurements. As our model is run at 5.5 km resolution, one grid cell has to approximate all the properties of a 5.5 km grid cell. Imagine your house and how much land varies in type, shape and use in a 5.5 km square centred on your house and you begin to appreciate the problems of using a single point observation to assess what is essentially an area simulation! This is even more difficult in mountainous areas close to the sea, like the fjords of Norway or err, around south west Greenland (see below).

Represent this in a 5.5km grid cell, include glacier, sea and mountain...  Godthåbsfjord near Nuuk in August
The beautiful fjords near Nuuk. Represent this in a 5.5km grid cell…

The HIRHAM5 model is one of very few regional climate models that are run at sufficiently high resolution to start to clearly see the climate influences of mountains, fjords etc in Greenland, which meant we didn’t need to do additional statistical downscaling to see results that matched quite closely the measured discharge from the lake.

Graph comparing modelled versus measured discharge as a daily mean from Lake Tasersuaq near Nuuk, Greenland. The model output was summed over the Tasersuaq drainage basin and smoothed by averaging over the previous 7 days. This is because the model does not have a meltwater routing scheme so we estimated how long it takes for melt and run-off fromt he ice sheet to reach this point.
Graph comparing modelled versus measured discharge as a daily mean from Lake Tasersuaq near Nuuk, Greenland. The model output was summed over the Tasersuaq drainage basin and smoothed by averaging over the previous 7 days. This is because the model does not have a meltwater routing scheme so we estimated how long it takes for melt and run-off from the ice sheet to reach this point.

We were pretty happy to see that HIRHAM5 manages to reproduce this record well. There’s tons of other interesting stuff in the paper including a nice comparison of the first decade of the simulation with the last decade of the simulation, showing that the two look quite different with much more melt, and a lower surface mass balance (the amount of snowfall minus the amount of melt and run – off) per year in recent years.

Red shows where more snow and ice melts than falls and blue shows where more snow falls than is melted on average each year.
Red shows where more snow and ice melts than falls and blue shows where more snow falls than is melted on average each year.

Now, as we work at DMI, we have access to lots of climate records for Greenland. (Actually everyone does, the data is open access and can be downloaded). This means we can compare the measurements in the nearest location, Nuuk, for a bit more than a century. Statistically we can see the last few years have been particularly warm, maybe even warmer than the well known warm spell in the 1920s – 1940s  in Greenland.

Graphs comparing and extending the model simulation back in time with Nuuk observations
Graphs comparing and extending the model simulation back in time with Nuuk observations

There is lots more to be said about this paper, we confirm for example the role of increasing incoming solar radiation (largely a consequence of large scale atmospheric flow leading to clearer skies) and we show some nice results which show how the model is able to reproduce observations at the surface, so I urge you to read it (pdf here) but hopefully this summary has given a decent overview of our model simulations and what we can use them for.

I may get to the future projections next time…

The Present Day and Future Climate of Greenland

Regional Climate Model Data from HIRHAM5 for Greenland

In this post I am linking to a dataset I have made available for the climate of Greenland. In my day job I run a Regional Climate Model (RCM) over Greenland called HIRHAM5 . I will write a simple post soon to explain what that means in less technical terms but for now I just wanted to post a link to a dataset I have prepared based on output from an earlier simulation.

Mean annual 2m  temperature over Greenland (1989 - 2012) from HIRHAM5 forced by ERA-Interim on the boundaries
Mean annual 2m temperature over Greenland at 5km resolution (1989 – 2012) from HIRHAM5 forced by ERA-Interim on the boundaries [Yes I know it’s a rainbow scale. Sorry! it’s an old image – will update soon honest…]

This tar file gives the annual means for selected variables at 0.05degrees (5.5km) resolution over the Greenland/Iceland domain.

I am currently running a newly updated version of the model but the old run gave us pretty reasonable and could be used for lots of different purposes. I am very happy for other scientists to use it as they see fit, though do please acknowledge us, and we especially like co-authorships (we also have to justify our existence to funding agencies and governments!).

This is just a sample dataset we have lots of other variables and they are available at 3 hourly, daily, monthly, annual, decadal timescales so send me an email (rum [at] dmi [dot] dk) if you would like more/a subset/different/help with analysis of data. This one is for the period 1989 – 2012. I have now updated it to cover up to the end of 2014. The new run starts in 1979 and will continue to the present and has a significantly updated surface scheme plus different SST/sea ice forcing and a better ice mask.

I have also done some simulations of future climate change in Greenland at the same high resolution of 5km using the EC-Earth GCM at the boundaries for RCP4.5 and RCP8.5 scenarios which could be fun to play with if you are interested in climate change impacts in Greenland, Iceland and Arctic Canada.

Mean annual 2m temperature change between control period (1990 - 2010) and end of the century (2081 - 2100) under RCP45 from HIRHAM5 climate model runs forced by EC-Earth GCM at the boundaries
Mean annual 2m temperature change between control period (1990 – 2010) and end of the century (2081 – 2100) under RCP45 from HIRHAM5 climate model runs forced by EC-Earth GCM at the boundaries.  This plot shows the full domain I have data for in the simulations.

This run should be referenced with this paper:

Quantifying energy and mass fluxes controlling Godthåbsfjord freshwater input in a 5 km simulation (1991-2012), Langen, P. L., Mottram, R. H., Christensen, J. H., Boberg, F., Rodehacke, C. B., Stendel, M., van As, D., Ahlstrøm, A. P., Mortensen, J., Rysgaard, S., Petersen, D., Svendsen, K. H., Aðalgeirsdóttir, G.,Cappelen, J., Journal of Climate (2015)

http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-14-00271.1 

PDF here

Finally I should acknowledge that this work has been funded by a lot of different projects:

Picture4