GC-Net consists of 18 AWSs distributed around the ice sheet. We refer the reader to Steffen et al. (1996) for details but briefly summarise here. The first station (Summit) began operation in 1995, with others coming online at various times since then. The AWSs measure a range of meteorological variables, of which the temperature and pressure time series are the most complete. The GC-Net stations each have four temperature sensors (two different instruments mounted at two different heights); here we use data from the type-E thermocouple mounted at position 1 at all sites except NGRIP (North Greenland Ice Core Project), and Saddle during 2010–2016, for which we used data from the type-E thermocouple mounted at position 2. Measurements are taken hourly; we use these data to calculate daily maximum and mean values for compatibility with MAR output.

Our analysis focuses on 14 of the 18 stations; we found the remaining 4 stations to have temperature time series which were either too short or too patchy for robust statistical analysis. Figure 1 shows the data coverage at each of the 14 stations studied here, and Table 1 gives the total number of years of data available when gaps are excluded. We attribute these missing data to equipment failure and assume that it is unrelated to the occurrence of extreme high temperatures. As such we treat these data gaps as “missing at random” and ignore them in our analysis. Since most of the missing periods cover whole years, rather than just a summer or winter period, this assumption is reasonable.

The MAR model is an RCM developed and extensively evaluated to study the present Greenland climate and SMB from the beginning of the last century (Fettweis et al., 2017) as well as to perform future projections of Greenland Ice Sheet SMB for the last IPCC report till the end of this century (Fettweis et al., 2013). It is fully coupled with a snow energy balance model dealing with the energy and mass exchanges between surface, snow, ice and atmosphere. The MAR version 3.5 used here has been extensively evaluated in Fettweis et al. (2017) with daily in situ PROMICE-based AWS measurements over 2008–2010, daily satellite-derived melt extents over 1979–2010, and SMB measurements and ice cores over 1958–2010. We chose to use MARv3.5 in this study since this is the model version which was used to make the most recent set of estimates of future ice sheet change (Fettweis et al., 2013). We refer to Fettweis (2007) and Fettweis et al. (2013, 2017) for more details about MAR and its surface scheme.

Here, we use data from MAR simulations forced with the ERA-Interim reanalysis (e.g. Fettweis et al., 2017), and with the GCMs CanESM2 (Canadian Earth System Model), MIROC5 (Model for Interdisciplinary Research On Climate) and NorESM1 (Norwegian Earth System Model) over 1995–2015. CanESM2, MIROC5 and NorESM1 have been found to be the best models (with respect to ERA-Interim over 1980–1999) from the CMIP5 database over Greenland from which 6-hourly outputs were available (Fettweis et al., 2013). MAR is forced every 6 h at its lateral boundaries with temperature, humidity, wind and surface pressure. Sea surface temperature and sea ice extent are also prescribed into the MAR integration domain from the forcing data every 6 h. Hereafter we refer to MAR variants with forcing by Era-Interim, NorESM1, CanESM2 and MIROC5 as MAR–Era, MAR–Nor, MAR–Can and MAR–MIR respectively. MAR–Era data are available continuously during our study period (1995–2015 inclusive). For the GCM-forced model runs, we use historical simulations until 2006 and simulations performed under forcing by the Representative Concentration Pathway 8.5 (RCP8.5) climate change scenario (van Vuuren et al., 2011) thereafter. This is reasonable because observed greenhouse gas concentrations followed the RCP8.5 scenario during this period, and in any case the differences between the RCP scenarios during 2006–2015 are very small. For comparison with the GC-Net data we pick the MAR model grid cell (25 km by 25 km resolution) closest to the AWS location in terms of latitude and longitude of the cell centre. The MAR cell centre is typically at a lower elevation than the AWS, according to the MAR DEM and the measured elevation of the AWS, and so we apply a lapse-rate-based correction to MAR temperature data (0.71 ∘C per 100 m of elevation difference; Steffen and Box, 2001). We restrict the model time series at each station to periods where GC-Net data are also available.

Extreme value analysis provides a toolbox of methods for the identification and statistical modelling of extreme events (Coles, 2013), i.e. events that are unusually large or small when compared to the central behaviour of a dataset. For a given site and a given data type (observations, MAR–Era, MAR–MIR, MAR–Nor and MAR–Can), we identify the extreme events using a site- and type-specific threshold applied to the maximum daily temperature time series. To enable a fair comparison, the threshold is taken always to be the 90 % quantile of the dataset in question (Table 2), and an extreme event is deemed to start once the maximum daily temperature exceeds this threshold. The event ends after the temperature has been below the threshold for three consecutive days. This method of event identification is known as the runs method (Smith and Weissman, 1994). It follows that the durations, as well as both frequencies and magnitudes, of events are random. Note that here we take the magnitude of an event to be the largest of the daily maxima within that event.

Melting is most appropriately calculated as a function of the surface energy balance; however measurements of variables required to calculate the surface energy balance (e.g. net radiation, wind speed) are not consistently available at the GC-Net stations. Positive degree days are an estimate of the magnitude and duration of above-zero temperature events and are typically well correlated with melting (e.g. Braithwaite, 1995; Huybrechts et al., 1991). Here we calculate PDDs for both observed and modelled temperatures and take this to be a reasonable approximation for melt energy. Diurnal temperature variability is modelled using Eq. (1), and PDDs are calculated by integrating Eq. (1) with T>0 ∘C. T=Asinφt+B, where A is daily maximum temperature, B is daily mean temperature and φ is 1 day. Daily mean and maximum 2 m temperature are output by MAR; for GC-Net data, daily mean and maximum are calculated based on hourly data as detailed above.

We use independent definitions of the ablation, percolation and dry snow zones first identified in McMillan et al. (2016) using RACMO2.3 simulations of SMB and surface melt. Briefly, the area of the ice sheet lying below the equilibrium line in a majority of years between 2009 and 2014 is defined as the ablation zone. The area of ice where melt did not exceed 5 mm w.e. on any day during this period is defined as the dry snow zone, with the remainder being classed as the percolation zone. Using these definitions, we find areas of 0.23, 0.61 and 0.80 million km2 for the ablation, percolation and dry snow zones respectively.

We apply extreme value analysis to observed daily maximum temperatures from GC-Net in order to compile a statistical climatology of extreme temperature events on Greenland (Table 3). Each location is considered independently, and the timing of statistically extreme events is not necessarily contemporaneous between stations. Extreme events are characterised in terms of their frequency, duration and magnitude; we use “duration” and “magnitude” to refer to median values across all events observed/modelled. We assess these characteristics in the context of station geography, i.e. elevation, latitude and melt zone (see methods). Each of the three characteristics is dependent on elevation; however the nature of that dependence and the role that latitude and melt zone play in the relationship is different for each (Fig. 2). Extreme temperature events occur 4–8 times per year, and event frequency is negatively correlated with elevation in south Greenland; events become less frequent the higher the station is on the ice sheet. Event frequency is positively correlated with elevation in north Greenland/the dry snow zone (Fig. 2a). Events last between 5 and 10 days, and duration is positively correlated with elevation for all stations (Fig. 2b). However events tend to last longer (by ∼ 1 day) at stations in the dry snow zone/north Greenland than at stations at similar elevations in the percolation zone/south Greenland. Event magnitude is negatively correlated with elevation at all stations (Fig. 2c), but elevation has a stronger influence on event magnitude in the dry snow and ablation zones (-4.4 ± 0.3 ∘C km-1) than in the percolation zone (-1.8 ± 0.4 ∘C km-1).

We compare the degree to which MAR is able to capture the observed climatology of extreme events at GC-Net stations by repeating the same extreme value analysis with output from each of the MAR model variants (Fig. 3). In addition to considering each station independently, we also consider each model variant independently; i.e. there is no common event mask. This is because the GCM-forced model variants (MAR–MIR, MAR–Nor and MAR–Can) are designed to simulate climatic variability over typical climatic periods like 20–30 years, which is not necessarily contemporaneous with observed variability in a given time period. We exclude JAR2 (Jakobshavn Ablation Region 2) from the remainder of this analysis due to the large discrepancy in elevation between the station and the corresponding grid cell in MAR (316 m, Table 1) and the dependency we find between elevation and extreme event characteristics (Fig. 2). Whilst all of the four model variants typically simulate the duration of extreme events reasonably well (i.e. within 1 day per event), they underestimate event frequency at most of the stations (Fig. 3). This is most notable for the GCM-forced model variants MAR–MIR, MAR–Nor and MAR–Can, which underestimate event frequency by 1.12, 0.75 and 0.65 events per year respectively. Similarly, all of the model variants underestimate the observed event magnitude by more than half a degree at most of the stations (though notably not the two remaining in the ablation zone; in fact event magnitude at Swiss Camp is overestimated). In terms of the individual model variants, the MAR–Era simulation is best able to reproduce event frequency (-0.09 events on average), the MAR–ERA and MAR–MIR simulations are both best able to reproduce event duration (±0.04 days on average) and the MAR–Era simulation is best able to reproduce event magnitude (-0.76 ∘C on average). MAR–Nor is the poorest-performing model variant overall.

We assess the ability of the four MAR variants to reproduce temperature observed by the GC-Net more generally by comparing the mean and trend of the entire daily mean temperature time series at each station location (Table 4). We present aggregate statistics for the entire time period in order to account for the fact that the GCM-forced MAR variants are predicting climatic variability at the decadal scale. The number of years of data (including gaps in the time series) is given for each station in Table 1. Results are presented by melt zone, where values are an average of all stations in that zone, weighted by the number of years of data available for each station. Both MAR–Era and MAR–MIR overestimate mean daily mean temperature (i.e. the average of all of the daily means) by ∼ 1 ∘C, although this signal is dominated by a large discrepancy in the dry snow zone, where both model variants are too warm by ≥ 1.5 ∘C. Both model variants, however, show good agreement with the observations in the ablation zone (-0.24 and -0.34 ∘C respectively), which is where the most melting occurs. MAR–Can and MAR–Nor both underestimate temperatures overall and give better agreement with observations in general (-0.13 and -0.21 ∘C respectively), but they exhibit a poor performance in the ablation zone (both variants > 1 ∘C too cold). When considering only the summer (JJA) daily mean temperatures, with the exception of MAR–Can in the percolation zone, all MAR variants are too cold in all zones and overall. MAR–Can performs best overall in summer, with a bias of just -0.01 ∘C. All model variants reproduce observed trends in both all and summer temperatures to within 0.1 ∘C yr-1 (most within 0.05 ∘C yr-1). We evaluate the ability of MAR–Era to reproduce observed climate variability by comparing modelled vs. observed mean annual and mean summer (JJA) temperatures (Fig. 4). MAR–Era is well able to capture observed inter-annual variability in both. Mean annual temperatures are particularly well correlated, with Pearson's correlation co-efficient (r) values in the range 0.77–1.00. Inter-annual variability in mean summer temperatures is less well captured (r=0.62–94 if JAR2 is ignored). The low bias in summer temperatures described above is also evident at the inter-annual timescale in the MAR–Era simulation.

We assess the degree to which the raw Era-Interim output (i.e. not MAR forced with Era-Interim) captures extreme temperature events at GC-Net stations (Fig. 5). In comparison with the same data for MAR–Era, using the raw Era-Interim output yields a poorer match to observations at all sites except NASA-U and NGRIP. The average absolute bias in magnitude of extreme temperature events is 0.87 ∘C in MAR–Era and 1.81 ∘C in the raw Era-Interim data output. In general, Era-Interim underestimates temperatures during extreme events in a similar manner to MAR–Era. However Era-Interim overestimates temperatures in the Swiss Camp region and north-east of the ice sheet.

We use a positive degree-day sum (see methods) to approximate melt energy available during extreme and non-extreme conditions at each of the 13 stations (Fig. 6). We note that the difference in abundance of melt energy between adjacent melt zones is roughly an order of magnitude, with observed total PDDs per station of 617, 96 and 5 ∘C in the ablation, percolation and dry snow zones respectively. All MAR variants are able to reproduce this gradient. We find that the dependence of observed melt energy on statistically extreme temperatures also scales with elevation (r2=0.71; n=13); one-third and ∼ 95 % of all melting occur during extreme events in the ablation and dry snow zones respectively. MAR–Era is able to reproduce this pattern (r2=0.71), but the relationship is less clear in data from the GCM-forced variants (r2=0.23–0.43).

We compare differences in the total PDDs observed and predicted during the entire study period; all of the MAR variants are found to underestimate total PDDs (Table 5). During extreme events, we see a two-fold increase in the model bias for the MAR–Era, MAR–MIR and MAR–Can model variants; PDDs are underestimated by 26, 32 and 22 % during extreme events and 12, 18 and 10 % during non-extreme conditions respectively. In the MAR-Nor simulation, PDDs are underestimated to a greater degree during non-extreme temperature conditions. The relative influence of model bias during extreme events is spatially variable. In the ablation zone, the total bias during extreme events is comparable to that during non-extreme events except that the two biases are of the opposite sign; PDDs are overestimated in the ablation zone during extreme events and underestimated in the ablation zone during non-extreme events. Given the relative contribution of melting during extreme events to overall melting here however (just 33 %), this results in an underestimate overall of 5, 12, 22 and 7 % for MAR–Era, MAR–MIR, MAR–Nor and MAR–Can respectively. Conversely, in the percolation zone, PDDs are underestimated during extreme events and overestimated during non-extreme conditions. However again the signal observed during the dominant regime (i.e. 96 % of PDDs occur during extremes) leads to a large underestimate overall (52, 58, 84 and 40 % for the model variants as before). In the dry snow zone it is more difficult to partition the relative influence of extreme vs. non-extreme events on total PDDs because there is far less melting here: a PDD total of 5 ∘C per station over the entire study period. This is particularly of note for Summit and NGRIP stations which are high up and far inland on the ice sheet; very small amounts of melting are observed here, but no melting is modelled by any of the model variants.

Despite our relatively small sample, given the size of the ice sheet, we see clear relationships between extreme event characteristics and elevation, latitude and melt regime. It is not surprising that extreme temperature events exhibit a stronger magnitude at lower-lying locations, given the atmospheric temperature lapse rate, but it is interesting that this relationship is less strong for the five percolation zone stations than for stations in the ablation and dry snow zones. We speculate that this is a result of heat exchange at the snow surface moderating near-surface temperatures in this region; sublimation is a known energy sink in the percolation zone in the summer (Ettema et al., 2010). In south Greenland, extreme events at lower elevations tend to be more frequent and of shorter duration than those higher up on the ice sheet. Temperature anomalies can be associated with cloudiness (reflecting upwelling longwave radiation back down to the surface), and lower-lying stations are more likely to experience short-term periods of orographic cloud cover. This is particularly likely to affect west Greenland, which lies in the path of the prevailing summer circulation pattern and consequently receives moisture-laden onshore flow during the summer (Ohmura and Reeh, 1991). In north Greenland however, we see that extreme events become both longer-lasting and more frequent as elevation increases. Longer extreme temperature events are likely associated with high-pressure conditions which are relatively persistent. In fact, extreme melt years on Greenland have been attributed to an increase in the frequency and duration of high-pressure conditions promoted by wider-scale atmospheric pressure gradients such as the North Atlantic Oscillation and the Greenland Blocking Index (e.g. Nghiem et al., 2012; Hanna et al., 2013b; Lim et al., 2016; Hanna et al., 2016). Extreme temperature events are responsible for the vast majority of melt energy produced in the percolation and dry snow zones on the ice sheet but contribute a much smaller proportion to overall melt energy in the ablation zone. Because we only have data for two ablation zone stations which are located in close proximity, further work is required to assess whether this is a general property of the ablation zone or restricted to this location; temperatures in general are much warmer here, and extreme events are not required to generate melting.

All of the four MAR model variants underestimate the frequency of extreme events but simulate their duration well. This suggests that MAR is able to reproduce the persistence of conditions driving extreme temperature events when they arise in the model. All MAR variants underestimate the magnitude of extreme temperature events at most stations, in most cases by > 0.5 ∘C. This can be explained in part by a general low bias in modelled summer temperatures, although the magnitude of this bias is not sufficient to account for the magnitude of the data–model mismatch during extreme periods. For example, MAR–Era exhibits a bias of -0.35 ∘C during summer and -0.76 ∘C during extreme temperature events. The raw Era-Interim output also exhibits a low bias during extreme temperature events at most of the GC-Net stations, with notable exceptions being north-east Greenland and the most marginal stations at which temperature during extremes are overestimated. This suggests that the low bias we see in the MAR model during extreme periods could be an artefact of the forcing data. This is important because Era-Interim and the GCMs examined here are commonly used to force other regional- and local-scale models (e.g. RACMO2); their use is not restricted to MAR. The version of MAR which is analysed here (v3.5) is known to underestimate the atmospheric liquid water content and so cloudiness (Fettweis et al., 2017) which may also contribute to the cold bias in temperature extremes. However, we repeated the analysis with the most recent version of MAR (v3.7) in which a correction for this has been incorporated, and this yielded no noticeable difference in the result. All of the MAR model variants and Era-Interim overestimate event magnitude at stations in the ablation zone, JAR and Swiss Camp. We attribute this to difference in albedo between the bare ice in the ablation zone and the snow-covered surface at higher elevations. Energy exchange in bare-ice areas is generally more sensitive to sunny conditions; this likely explains why the biases are opposite in this area compared to the percolation and dry snow zones where the albedo is high enough to prevent this sensitivity.

Melt energy simulated by MAR is underestimated by 19, 25, 41 and 16 % when forcing is provided by Era-Interim, MIROC5, NorESM1 and CanESM2 respectively. However during extreme events, model biases in terms of melt energy are double those calculated during non-extreme, positive-temperature, conditions. This is important because approximately half of all melt energy is generated during extreme events. In general, the GCM-forced MAR simulations perform more poorly than the Era-Interim-forced simulation, with the exception of MAR–Can (bias = 16 % vs. 19 % for MAR–Era). We would expect the reanalysis-forced simulation to perform the best, given its assimilation of observations; however we note that the difference is not large.

We observe melt energy generated at the two highest/furthest inland stations in our sample, Summit and NGRIP, but none of the MAR variants simulate any melting at either of these stations during our study period. This is because extreme temperatures are underestimated by ∼ 1 ∘C by MAR at these stations (e.g. MAR–Era exhibits a bias of -0.91 at Summit and -0.76 at NGRIP). It is important to note that these are very small quantities and would not impact ice-sheet-wide estimates of melting; however melting is also important because of its role in ice sheet albedo: wet snow is less reflective than dry snow. A significant melt event can be defined as achieving > 1 mm w.e. day-1 (Franco et al., 2013), and with the exception of Summit in 2012 this was not achieved at either station during the study period. Nonetheless, as the climate warms, melting at these locations is likely to be more abundant, and properly capturing temperature variability here will become even more important.