KAN_U is part of the ∼ 20 AWSs comprising the Programme for Monitoring of the Greenland Ice Sheet (PROMICE) network (Ahlstrøm et al., 2008). Measurements include ambient air pressure, relative humidity and aspirated temperature (Ta) at 2.7 m height above the ice sheet surface, wind speed, and direction at 3.1 m height, as well as incoming and reflected solar/shortwave (ES↓, ES↑) and downward and emitted terrestrial/longwave (EL↓, EL↑) radiation components at 10-minute intervals. Accumulation and ablation are measured by two sonic rangers, one attached to the AWS and one on a separate stake assembly (Fig. 1b). Sensor specifications are listed in Table 1. The AWS transmits hourly measurements during the summer period and daily during winter (Citterio et al., 2015).

AWSs installed on glaciers are prone to tilt due to transient evolution of the ice or firn surface. The importance of accounting for pyranometer tilt has been discussed by MacWhorter and Weller (1991). AWSs located in accumulation areas are comparatively stable due to the accumulated snow on the base of the tripod. The maximum tilt registered by KAN_U was 3.0∘. A tilt correction for the solar radiation measurements is made after Van As (2011).

Two gaps in (sub-)hourly measurements exist due to a malfunctioning memory card, from 27 October 2010 until 22 April 2011 and from 26 October 2011 until 21 January 2012. During these periods, when only transmitted daily values are available, measurements from a second AWS, S10 erected on 17 August 2010 at ∼ 50 m distance from KAN_U, were used and adjusted by linear regression to eliminate systematic offsets due to different measurement heights. The overlapping records of the two time series revealed high cross-correlations and low root-mean-squared deviations (RMSD) for every measured parameter (Table 2). Due to technical issues with S10, EL↓, EL↑, and Ta measurement gaps from 9 February 2011 until 30 April 2012 were filled with a similar approach, using measurements from the AWS S9 located 53 km closer to the ice sheet margin. Any added uncertainty from using adjusted wintertime measurements will have minimal impact on the summertime results presented below.

The broadband albedo is the fraction of the incoming shortwave radiation reflected at the ice sheet surface and an important parameter in studying the changes in the accumulation area: α=ES↑ES↓. To verify its accuracy, albedo was compared for both AWSs KAN_U and S10 for the warm seasons (May–September) of 2010, 2011, and 2012 (Table 2). For hourly values, the RMSD for 2010 and 2011 was only ∼ 0.03. The RMSD for 2012 was 0.07 due to the higher spatial variability in surface reflectance after substantial melt.

The radiation budget at the ice sheet surface is given by the sum of solar and terrestrial radiation components: ER=ES↓+ES↑+EL↓+EL↑=ESNet+ELNet. Fluxes are here taken as positive when directed toward the ice sheet surface. By the inclusion of albedo and utilizing the Stefan–Boltzmann law, this can be rewritten as ER=(1-α)ES↓+εEL↓-εσTS4, with σ being the Stefan–Boltzmann constant (5.67 × 10-8 W m-2 K-4) and TS the surface temperature. The longwave emissivity ε for snow/firn is assumed equal to 1 (black-body assumption).

Various studies have applied SEB models in glaciated areas under different climatic conditions, such as the high Antarctic plateau (Van As et al., 2005) and the Greenland ablation area (Van den Broeke et al., 2008b, 2011). The energy balance at the atmosphere–surface interface is EM=ER+EH+EE+EG+EP, where EH, EE, EG, and EP are the turbulent sensible, turbulent latent, subsurface conductive, and rain-induced energy fluxes respectively.

Rainfall is assumed to be at melting-point temperature (T0 = 273.15 K), and thus EP is non-zero when Ts is below freezing: EP=ρwcwr˙T0-Ts, where cw is the specific heat of water (4.21 kJ kg-1 K-1 at 0 ∘C and 999.84 kg m-3) and r˙ is the rainfall rate. The rainfall rate is assumed to be non-zero under conditions of heavy cloud cover during periods with non-freezing air temperatures (see below).

The energy balance is solved for the one unknown variable Ts, which is limited to the melting-point temperature (273.15 K), and the imbalance in Eq. (4) is attributed to melt (EM). For sub-freezing Ts values all other SEB components are in balance and surface melt does not occur. EH and EE are calculated using the “bulk method” as described by Van As et al. (2005). This method uses atmospheric stability and thus depends on Ts, implying that Eq. (4) has to be solved iteratively.

The average surface roughness length for momentum z0 at this elevation would realistically be ∼ 10-4 m (Smeets and van den Broeke, 2008). During summer, the ice sheet surface melts occasionally, and thus smoothes while attaining a smaller z0 (∼ 10-5 m). Slightly increased roughness is expected during wintertime due to sastrugi, while drifting snow (Lenaerts et al., 2014) can increase z0 in cases up to 10-3 m. In the present study, z0 is kept constant at 10-4 m. A series of test runs showed that the results of this study were not very sensitive to the range of plausible z0 values. The scalar roughness lengths for heat and moisture are calculated according to Andreas (1987).

Subsurface heat transfer is calculated with 0.1 m spatial resolution (20 m depth; 200 layers) and is forced by temperature changes at the surface and latent heat release when water refreezes within the firn. Heat conduction is calculated using effective conductivity as a function of firn density (Sturm et al., 1997) and specific heat of firn as a function of temperature (Yen, 1981). The calculations are initialized using thermistor string temperatures from April 2009 and depth-adjusted firn core densities measured on 2 May 2012. The subsurface part of the model includes a percolation/refreezing scheme based on Illangasekare et al. (1990), assuming active percolation within snow/firn. Provided that there is production of meltwater at the surface, the amount of refreezing is limited either by the available pore volume or by the available cold content at each level. The scheme simulates water transport and subsequent refreezing as the progression of a uniform warming front into the snow/firn and is active for all melt seasons except for 2012. In 2012, surface run-off dominated water movement after 14 July, as clearly visible on Landsat imagery (not shown). This coincided with the surfacing of a 6 m thick ice layer in the model, which was also found in firn cores (Machguth et al., 2015). Consistent with these observations, we use 6 m of ice (density of 900 kg m-3) as a threshold that causes meltwater to run off horizontally, shutting down vertical percolation.

Solid precipitation is added in the model based on KAN_U sonic ranger measurements, assuming a rounded average snow density of 400 kg m-3 observed in snow-pit measurements. Although rain occurs infrequently at 1840 m a.s.l., a rain estimate is incorporated with prescribed precipitation rates for each year during hours with thick cloud cover producing EL↓ values that exceed black-body radiation using the air temperature (EL↓ > σTa4) and Ta is above freezing. Evaluating this against winter accumulation, the following precipitation rates were derived and prescribed to the rain calculation: 2.0 mm h-1 for 2009–2010 and 2012–2013, 3.5 mm h-1 for 2010–2011, and 0.5 mm h-1 for 2011–2012. Using this approach, the model produces liquid precipitation during the summer months only; by the end of the 5-year period it amounts to a total of 0.26 m w.e. (water equivalent), 15 % of the total precipitation over the 5 years. The contribution of rain in the energy balance is minor; the total energy added to the surface for the whole study period is approximately 1.15 MJ m-2, which could yield a total of 9 mm of melted snow.

The performance of the model in terms of ablation is illustrated by comparing simulated surface changes with the measured surface height changes due to ablation and accumulation (Fig. 2a). The model accurately reproduces the melt rates during every melt season, yet this validation does not cover the whole melt season. We found that the AWS tripod and stake assembly are prone to sinking somewhat into warm, melting firn during the second part of the melt season (note the measurement gaps). In a second model validation exercise, we compare simulated and measured Ts (inferred from the EL↑) in Fig. 2b and find they correlate well (R2 = 0.98) with an average difference of 0.11 ∘C and root-mean-squared error (RMSE) of 1.43 ∘C. Part of this difference can be attributed to the seemingly overestimated 10 % EL↑ measurement uncertainty as reported by the sensor manufacturer, which would yield a RMSE of 6.2 ∘C of Ts values.

For a study with a 5-year time span, it is useful to provide a longer temporal perspective. For this, we use the air temperature record from Kangerlussuaq airport observed by the Danish Meteorological Institute (DMI) since 1973 in support of aircraft operations (Cappelen, 2013). Full observational suite coverage is available since 1976. Monthly Ta from the airport correlates well with the KAN_U time series (R = 0.97), indicating that Kangerlussuaq measurements can be used for providing temporal perspective, despite the 160 km distance that separates the two measurement sites. Finally, we use the pixel nearest to KAN_U in 5-by-5 km re-gridded MODIS albedo product (MOD10A1) to investigate albedo variability over the 2000–2013 period.

The importance of katabatic and synoptic forcing on near-surface wind direction are roughly equivalent at the elevation of KAN_U (Van Angelen et al., 2011). The average wind direction is south-southeast (∼ 150∘; Fig. 3a). However, in a case study of the 2012/2013 winter (Van As et al., 2014), the prevailing wind direction was ∼ 135∘ (southeast), suggesting an influential katabatic regime in which air drains down-slope and is deflected by the Coriolis effect. Wind speed is higher during winter (Fig. 3b); annual average values are 6–7 m s-1, whereas summer (June–July–August) average values are around 5 m s-1 (Table 3). Winds exceeding 15 m s-1 occur primarily during the winter period and rarely exceed 20 m s-1 when averaged over 24 h. The barometric pressure of about 800 hPa exhibits an annual cycle with relatively high pressure in summer (Fig. 3c), favouring more stable, clear-sky conditions. The specific humidity also varies annually; it peaks in summer with annual average about 1.7 g kg-1.

The year 2010 was the warmest year of the record (Table 3), with the winter (December–January–February) of 2009–2010 being 4.0 ∘C warmer than the 2009–2013 average and the summer only being equaled by 2012 (-1.8 ∘C; Table 3). May 2010 was especially warm, at -6.2 or 5.1 ∘C above the 2009–2013 average. Positive Ta persisted during the end of the melt season resulting in a -1.1 ∘C monthly average for August. The high 2010 temperatures influenced surface ablation by inducing the early onset of melt. In 2010, ablation at KAN_U occurred from late April until early September, whereas, for instance, the 2009 melt season at KAN_U spanned early June until mid-August.

The average SMB over the period 1994–2010 at KAN_U is +0.27 m w.e. (Van de Wal et al., 2012). Melt at this elevation occurs during each melt season. The winter 2009/2010 accumulation of 0.25 m w.e. was relatively low, amounting to just 65 % of the 2009–2013 average (Table 4). During the 2010 melt season, all the snow that had accumulated since the end of the previous melt season ablated, including part of the underlying firn, resulting in the first negative SMB year on record (Table 4). The stake measurements from Van de Wal et al. (2012) document a 2-year surface height change of +0.42 m on average for 2008–2010 at the same location (S10), corresponding to +0.15 m w.e. assuming a snow-pit density of 360 kg m-3. From this estimate, we infer the winter and net SMB for 2009 to be +0.59 and +0.34 m w.e. respectively.

During winter 2011/2012, accumulation was similar to that in winter 2009/2010. In spring 2012, positive Ta was first recorded during April (at -12.8 ∘C April 2012 was the warmest April on record), followed by a relatively warm May (-8.6 ∘C). Ablation rates were already high in late May 2012 (7.2 mm w.e. day-1; Charalampidis and van As, 2015). June and July were the warmest of the 5-year record with -1.5 and -0.6 ∘C monthly average Ta respectively. With the summer of 2012 on average as warm as that of 2010, but the ablation period shorter by 39 days (Table 4), the summer SMB was -0.86 m w.e., making 2012 the most strongly negative SMB year (-0.61 m w.e.) to be recorded at this location (Van de Wal et al., 2005, 2012).

Solar radiation exhibits a strong annual cycle at this location above the Arctic Circle (Fig. 4a). In the absence of topographic shading or a significant surface slope (< 1∘) the day-to-day variability in incoming shortwave radiation at this elevation is dominated by cloudiness and the solar zenith angle. The highest daily ES↓ values occur in June and exceed 400 W m-2, while at the ELA they are just below 400 W m-2 (Van den Broeke et al., 2008a) due to more frequent cloud cover and a thicker overlying atmosphere. Whereas ES↓ increases with elevation from the ELA to KAN_U, ESNet obtains daily values of up to 100 W m-2 both at the ELA and at KAN_U, implying that solar energy input is regulated by surface reflectance.

Terrestrial radiation exhibits an annual cycle of smaller amplitude (Fig. 4a). The annual variations of the downward and emitted longwave radiation are governed by the temperature and emissivity variations of the atmosphere and the ice sheet surface respectively. Hence, the absolute magnitudes of both components are larger during the summer period. EL↓ fluctuations depend primarily on cloud cover. EL↑ is a sink to the SEB and during summer is limited by the melting surface with the maximum energy loss being 316 W m-2. This results in predominantly negative ELNet values throughout the year. The energy loss peaks during June and July.

The ER annual cycle displays an energy gain at the ice sheet surface during May to August and energy loss the rest of the year (Fig. 4b). This winter energy loss is primarily compensated by downward sensible heat flux. Calculated EH is typically positive throughout the year, with highest values in winter when ER is most negative, heating the ice sheet surface while cooling the atmospheric boundary layer (Fig. 4b). This facilitates the katabatic forcing and thus enhances wind speed and further turbulent energy exchange between the atmosphere and the ice sheet surface. The contribution of EH to melt is smaller than at lower elevations (Van den Broeke et al., 2011). The dominant melt energy source at KAN_U is therefore ER.

EE changes sign from winter to summer and is on average a small contributor to the annual SEB. During the summer period, EE is comparable to EH but with opposite sign, enabling surface cooling by sublimation and/or evaporation (Henneken et al., 1994). In winter, EE is directed mostly toward the cold ice sheet surface, resulting in heating from deposition.

The annually averaged EG is mostly negative and of the same magnitude as EE (3–4 W m-2) but with no distinct annual cycle. Melt seasons with substantial refreezing exhibit increased positive summer-averaged EG since the near-surface firn temperature is on average higher than Ts, leading to conductive heat transport toward the ice sheet surface. Low EG values in summer indicate limited refreezing in the firn just below the ice sheet surface.

EP is non-zero but still negligible in summer, when positive air temperatures occur and thus precipitation is liquid.

With the exception of August 2009, when predominantly clear skies caused ES↓ to be 40 W m-2 larger and EL↓ 36 W m-2 smaller than in the other years, monthly average values of ES↓ at this site are fairly invariant (difference < 25 W m-2; Fig. 5a). Often ER increases when clouds are present over an ice sheet; this is the so-called radiation paradox (Ambach, 1974), as it was observed in April 2012.

Figure 5b illustrates the annual cycle of monthly averaged albedo, excluding the winter months. From October to February shortwave radiation values are too low for accurate albedo estimation. Nevertheless, the albedo is expected to be characteristic of fresh dry snow values (0.8–0.9) during winter. High albedo persists until May due to fresh snow deposited on the ice sheet surface. An exception occurred during March and April 2013, when the monthly albedo of 0.78 suggests reduced precipitation input for a prolonged period and the presence of ageing dry snow on the ice sheet surface (Cuffey and Paterson, 2010). In the years 2009–2011 and 2013 the albedo gradually decreased beginning late May and during the summer due to the effects of relatively high temperatures and melt on snow metamorphism. During summer, albedo still exceeded 0.75. Although melt at KAN_U still occurs intermittently during August, such melt does not counteract the effect of snowfall events that increase the surface albedo.

The anomalously warm period in June and July 2012 (Fig. 3d) coincided with a larger decrease in surface albedo than in the other years. The combination of enhanced melting, heat-induced snow metamorphosis, and firn saturation reduced the albedo from 0.85 in April to 0.67 in July, reaching a value that is characteristic of soaked snow facies close to the lower elevation snow/firn line (Cuffey and Paterson, 2010). As a consequence, ESNet increased by approximately 25 W m-2 in June and July (32 %; Fig. 5c). This darkening thus functioned as an amplifier of melt (Box et al., 2012; Van As et al., 2013) and contributed to the large observed ablation (Table 4).

The largest longwave radiation surface emissions occurred during August 2010 and June–July 2012, approaching the theoretical limit of -316 W m-2 for a continuously melting ice sheet surface (Fig. 6b). The concurrent high EL↓ (Fig. 6a; Table 5) was related to high atmospheric temperatures. This caused summer ELNet in 2010 and 2012 to exceed its value in other years (Table 5; Van As et al., 2012). While summer ESNet was similar in 2009 and 2010, summer ER was 69 % larger in 2010 than in 2009, primarily due to the high atmospheric temperatures. During 2012, summer ELNet was similar as in 2010. The large summer ESNet resulted in summer ER 67 % higher than in 2010 (Table 5). The highest daily ER attained 100 W m-2 on 9 July and coincided with the start of a Greenland-wide warm event. On 12 July, nearly the entire ice sheet surface was reported to melt (Nghiem et al., 2012), followed shortly after by the highest meltwater discharge in 56 years on 12 July 2012, as inferred by the partial destruction of a bridge constructed over the Watson River in Kangerlussuaq in 1956. At KAN_U, well above the long-term ELA, not only a strongly negative SMB was recorded in 2012, but it was the only year with a positive annual radiation budget (ER = +4 W m-2; Table 5).

EH was largest during 2010 and smallest during 2011 (Table 5), the years of highest and lowest annual Ta respectively (Table 3). Sensible heat transfer toward the ice sheet surface was also low on average in 2012, owing to the cold winter months. The high July 2011 EH was due to warm air advection that occurred over a cold surface, yielding large near-surface temperature gradients and sensible heat exchange (Fig. 7a). During summer 2013, when air temperatures remained relatively low, the ice sheet surface exhibited the lowest sensible heat gain compared to the other melt seasons. In all, EH did not contribute to SEB interannual variability as much as the radiative components.

Summer EE values are correlated with summer atmospheric pressure (R = 0.96), which influences the gradients in near-surface specific humidity and wind speed. During summer 2012, pressure and specific humidity were relatively high (811 hPa and 3.7 g kg-1 respectively; Table 3), while the wind speed was reduced, thus contributing to the lowest absolute summer EE with the lowest cooling rates due to evaporation/sublimation. The maximum latent heat loss that year occurred in May. Thereafter, the moisture content in the near-surface air became relatively large, with EE decreasing in absolute value until July. Summer 2013 was conversely characterized by relatively low pressure and specific humidity (804 hPa and 2.8 g kg-1 respectively) resulting in high evaporation/sublimation rates especially in June and July (Fig. 7b).

Monthly EG values were small and displayed small interannual variability, especially in summer. The summers of 2010 and 2011 exhibited the most positive EG as a consequence of substantial refreezing (Fig. 7c), which influenced near-surface firn temperature gradients. Summer EG in 2009 and 2013 (Table 5) was lower due to the moderate melt seasons of smaller duration. Summer EG was lower in 2012 due to both a warm ice sheet surface conducting heat into the firn and the absence of refreezing.

The melt rates in 2009 and 2013 were similar. In both years the largest monthly EM occurred in July and did not exceed 30 W m-2 (Fig. 8). EM peaked similarly in 2010 and 2011, in June reaching about 20 W m-2 and in July exceeding 35 W m-2. May and August 2010 exhibited significant melt in response to the warm atmospheric conditions (Van As et al., 2012). Both 2010 and 2012 exhibited significant melt in May (10 W m-2). During summer 2012, EM far exceeded all other years, with a July value of 68 W m-2, leading to the largest ablation reported in Table 4.

The radiative fluxes dominate the interannual variability of melt at KAN_U, with variations in ELNet being most influential over the amount of available EM in the years 2009–2011 and 2013. In 2012, it was the large ESNet that mainly contributed to the melt anomaly.

Figure 9a, which depicts total monthly surface energy exchanges throughout the study period, illustrates that ESNet and ELNet dominate the SEB from May to September, while ELNet and EH dominate the SEB during the remainder of the year. During the years exclusive of 2012 considered here (2009, 2010, 2011, and 2013), the total summer energy input to the ice sheet surface was 620–650 MJ m-2 each year. During all years, the energy input peaked in July. For example, in July 2010 the total energy input reached 246 MJ m-2. By contrast, in 2012, the total summer energy input exceeded 770 MJ m-2, and in July it reached 304 MJ m-2. The 2012 total energy used for melt was 414 MJ m-2 (65 % higher than in 2010), of which 183 MJ m-2 was used for melt in July. Figure 9b illustrates the simulated mass fluxes at the ice sheet surface (note the different y axis scales for positive and negative values). A total of 40 kg m-2 of mass loss occurs on average by the sum of sublimation and evaporation during spring and summer. Conversely, deposition amounts to 10 kg m-2 each winter season. The total snowfall from April 2009 until September 2013 amounted ∼ 1500 kg m-2 (also Table 4). Up to the end of May 2012, all meltwater had accumulated internally through percolation into the firn, adding mass of 1158 kg m-2 (1020 kg m-2 from snowfall and 138 kg m-2 from rainfall). Due to an ice layer blocking vertical percolation in summer 2012, 444 kg m-2 ran off, removing approximately 38 % of accumulated mass since April 2009.

The total amount of meltwater generated at the ice sheet surface, equivalent to the sum of run-off and refreezing minus rainfall, amounted 1232 kg m-2 in 2012. As the calculated surface ablation was 860 kg m-2 (Table 4), 30 % (372 kg m-2) of the produced meltwater was melted more than once during the ablation season. This suggests that 416 kg m-2 (48 % of the total ablation or 34 % of the produced meltwater) was effectively retained in near-surface firn layers.

The first year on record during which surface ablation exceeded accumulation from the preceding winter at KAN_U was 2010 (Table 4; Van de Wal et al., 2012). Even though atmospheric temperatures were high and the impact on ablation was large in 2010, the response of the snow surface was much larger in 2012, when ablation was more than 3 times larger than the accumulation. In 2012, albedo decreased to ∼ 0.7 by mid-June (Charalampidis and van As, 2015), implying substantial metamorphosis of the snow surface, while in all other years this albedo was reached only in July or August. The albedo reduced even more on 10 July to ∼ 0.6, signifying the saturation of the ice sheet surface and the exposure of thick firn. Until 6 August, the albedo value corresponded to that of soaked facies close to the snow/firn line (Cuffey and Paterson, 2010). It should be noted that snowfall events increased the albedo during several periods in the summer season (Charalampidis and van As, 2015).

To quantify the impact of a relatively dark ice sheet surface on the SEB, the average annual cycle in albedo of all years excluding 2012 was used to replace the low 2012 albedo in dedicated sensitivity analysis. Figure 10a shows the albedo anomaly of 2012, which resulted in enhanced ablation in late May/early June (Fig. 10b). At the end of August, the ice sheet surface lowered an additional 0.64 m due to 58 % more melt energy compared to a situation with average albedo. The excess EM from the melt–albedo feedback amounted to 152 MJ m-2, while the excess ESNet supplied was 213 MJ m-2 (Fig. 10c). The remaining ESNet was consumed by other fluxes, primarily EH. As the total surface ablation of 2012 was 1.78 m of surface height change (Fig. 2) the remaining 1.14 m was primarily due to the warm atmospheric conditions and similar to 2010 (1.21 m). This sensitivity analysis implies that the location would have experienced a negative SMB in 2012 even without the melt–albedo feedback.

Model performance is limited by the accuracy of the instruments of KAN_U as given in Table 1. The radiometer uncertainties are the largest, based on what is reported by the manufacturer (10 % for daily totals, although this is likely to be an overestimate; Van den Broeke et al., 2004). Nevertheless, the accurate simulation of surface temperature and snow ablation rates (Fig. 2) throughout the period of observations provides confidence in both the measurements and the model.

The model exhibits considerable sensitivity to the subsurface calculations, suggesting importance of pore volume and firn temperature, and how much more complicated SEB calculations are in the lower accumulation area than for bare ice in the ablation area. The model is able to capture the seasonal variations of temperature in the firn and calculated temperatures are commonly within 3.6 ∘C of those measured with an average of -0.3 ∘C (Fig. 11a). The shallow percolation of a wetting front in the firn is estimated at depths of 1–3 m in the years 2009 and 2013 (Fig. 11b), while in the years of larger melt, pore volume until 10 m depth is affected, possibly overestimating the percolation depth given the relative temperature buildup in the simulated firn below roughly 5 m depth (Fig. 11a; Charalampidis et al., 2016). In particular for 2012, available simulated pore volume at ∼ 6 m is significantly affected by meltwater that percolates below the formed thick ice layer, which may indicate that the run-off threshold of a 6 m thick ice layer is an overestimate, highlighting the need for a better run-off criterion. Further investigation on this criterion and inclusion of water content held in the firn by capillary forces, saturation of the surface, and proximity of impermeable ice to the surface is necessary.

The fact that the subsurface calculations are initialized in 2009 by use of vertically shifted firn densities from a 2012 core does not influence the calculation of the surface energy fluxes and thus the outcome of this paper. Importantly, the timing that simulated run-off occurred in July 2012 is in agreement with satellite observations due to the run-off criterion, thereby providing confidence in realistic calculation of EG.

Although the subsurface calculations are on a vertical grid of 10 cm (see also Sect. 2.3), there is a progressive loss of detail in the density profile through time due to the interpolation scheme that shifts the column vertically when it needs to account for surface height variations (Fig. 11c). Increased spatial resolution requires a finer temporal resolution to avoid model instability. Although the calculated SEB would be unaffected, we accepted the loss of detail in density because increasing the spatial and temporal resolution would result in substantially increased computational time. Nevertheless, during each melt season, when it is important that refreezing is accounted for, no loss of detail is expected near the surface since the column is shifted almost continuously upward.

Rainfall is known to occur during summer on the higher elevations of the ice sheet (Doyle et al., 2015). The exact amount is unknown as in situ measurements for precipitation are rare and difficult to acquire on the ice sheet. Therefore, the rainfall calculated by our model should be considered a first-order estimate. Nevertheless, the amount of rain is expected to be small and its effect on the SEB is negligible, as shown by the model results.

It is possible that other factors than heat-induced snow metamorphism and the presence of surface water contributed to the 2012 albedo anomaly. Such could be aerosol particles or impurities at the snow surface, effectively reducing its albedo (Doherty et al., 2013). Also, in cases of extreme melt, microbial activity can develop at the ice sheet surface with the subsequent production of a dark-coloured pigment (Benning et al., 2014).

The Kangerlussuaq airport air temperature record since 1976 was used to provide a temporal perspective to the KAN_U air temperature in recent years (Fig. 12). The standard deviations reveal variability during the winter period of more than 10 ∘C while for the months of July and August standard deviations are ∼ 2.0 ∘C. The temperature measurements reveal that the region has been warming on average starting in 1996 (not shown). Figure 12c illustrates this for 2000–2013; e.g. the summers (JJA) were 1.2 ∘C warmer than in the reference period 1976–1999. The warm 2010 and 2012 summers have an anomaly value of +1.9 and +1.8 ∘C respectively. The high temperatures in recent years are most apparent for June when in 10 out of 14 years the 1976–1999 standard deviation is exceeded. A further increase of the regional temperatures, as anticipated by climate models, will likely further increase the frequency of large melt events and the extent of each melt season, leading to conditions similar to or more extreme than in 2012 (McGrath et al., 2013).

The MOD10A1 time series from the years 2000–2013 shows an albedo decrease of 0.05–0.10 during the 14 years of measurements in response to the increased temperatures (Fig. 13). In particular, May albedo reached record low values in 2010 and 2012. July albedo is considerably lower in the years 2007–2013 than it was in the first half of the record. The exceptional surface conditions in July 2012 were also captured by MODIS with the lowest monthly albedo (∼ 0.6) of the time series. The albedo in August is generally higher than in July due to snowfall, but the values remain sufficiently low to enhance melt. We note that part of the MODIS based albedo decrease could be the result of the declining instrument sensitivity of the Terra MODIS sensor (Wang et al., 2012; Lyapustin et al., 2014) though updated (through 2014) comparisons between MOD10A1 and ground observations from GC-Net data (Box et al. (2012); not shown) do not indicate an obvious or statistically significant difference.

Increased meltwater infiltration into the firn during events of increased melt has led to the formation of thick, near-surface ice lenses between 2 and 7 m, judging from the 2012 firn core (Machguth et al., 2015). This contrasts with the aquifers (i.e. liquid water storage) that are observed in the firn in southeast Greenland (Forster et al., 2013; Koenig et al., 2013; Kuipers Munneke et al., 2014). The southwestern ice sheet receives about one-third of the annual precipitation received in the southeast (Ettema et al., 2009). This results in reduced thermal insulation of the infiltrated water as well as reduced generation of pore volume. The subsequent shallow refreezing during recent years of enhanced melt has led to the formation of thick impermeable ice, ultimately enabling run-off in 2012 (Machguth et al., 2015).

The DMI measurements indicate that 2009 is representative of the reference period 1976–1999 (Fig. 11c; Van As et al., 2012). With respect to summer 2009, the radiation budget in summer 2010 was higher due to lower ELNet (Table 5; Sect. 3.3). In summer 2012, ELNet was the same while ESNet was larger than in 2010. Most of this ESNet excess was consumed by melting (Sect. 3.4). The melt–albedo feedback (Box et al., 2012) will contribute to the rise of the ELA in a warming climate (Fettweis, 2007; Van de Wal et al., 2012), and might transform the lower accumulation area into superimposed ice if warming prevails. We have shown that the melt–albedo feedback makes that warm summers can have great impact on melt and run-off in the lower accumulation area. Our results suggest that if warm atmospheric conditions persist in the future, the additional input of solar radiation at the ice sheet surface will be of higher importance to surface changes than atmospheric warming.