As the GIS is located at high latitudes, it is not feasible to use aggregated day/night observations from ascending and descending orbits. L2 v1.0 data (without the subsequent enhancements to the algorithms, cloud masking and uncertainties) from the ESA LST_cci project were used, consisting of 1 km IST observations from AATSR on Envisat (only available until April 2012) and MODIS on the Aqua and Terra platforms . In addition, IST observations from the AASTI v2 L2 dataset, available multiple times per day with 4 km resolution, were included in the analysis . This dataset is generated using Global Area Coverage (GAC) retrievals from AVHRR on board the NOAA and Metop platforms. The AASTI dataset extends north of 50∘ N and south of 50∘ S, providing surface temperatures for sea ice, land ice, open water and marginal ice zone areas from 1982 to 2015. The satellite products assessed in this study are listed in Table .

The Programme for Monitoring of the Greenland Ice Sheet (PROMICE) data are provided by the Geological Survey of Denmark and Greenland . Surface temperatures are derived from upwelling longwave radiation measured by Kipp & Zonen CNR1 or CNR4 radiometers, assuming an emissivity of 0.97 . Only PROMICE data from the upper ablation and accumulation zones were used to ensure that data are only acquired over permanently snow- or ice-covered surfaces. Figure a shows the geographical distribution of the eight selected PROMICE stations and their elevation, also listed in Table .

The Operation IceBridge project conducts flight campaigns over the Arctic sea ice and the GIS, carrying various instruments including a thermal infrared radiometer, KT19, which observes in a similar IR frequency interval as the AVHRR channel 4 (9.6–11.5 µm). Surface temperatures are retrieved by measuring brightness temperatures and assuming a constant surface emissivity of 0.97. In total, IST retrievals from 27 IceBridge flights (version 2) starting at the end of March and ending on 16 May 2012 were used. Due to the high-resolution footprint of the KT19 instrument – approximately 15 m at 450 m above ground level  – which results in high variability in the observed radiometric surface temperature, IceBridge observations were averaged every kilometre to make them more comparable to the lower-resolution satellite data. The IceBridge observations were not screened for potential clouds; under the presence of clouds between the aircraft and the surface, the radiometer observes the usually colder cloud temperature instead of the surface.

L2 observations were aggregated on a fixed grid to Level 3 (L3) and combined using a statistical methodology similar to , resulting in L4 gap-free, merged and optimally interpolated (OI) daily fields with a 0.01∘ latitude and 0.02∘ longitude resolution. Prior to the optimal interpolation, an intermediate L3 super-collated (L3S) product was generated from the collation of all the L3 fields. The OI method is similar to the one from the high-latitude DMI SST (Danish Meteorological Institute sea surface temperature) processing scheme , which operates with anomalies from a first-guess field. In the current approach, a persistence-based method is applied, which uses the previous analysis field as the first-guess field. The IST observations from within 48 h (hours) of the analysis time are aggregated and interpreted as anomalies with respect to the first-guess field. The OI method, given statistical input such as a first-guess error variance or co-variance functions and uncertainties in the individual observations, finds the solution with the lowest errors for each grid point . The search radius for the OI method is set to 75 km, and the maximum number of satellite observations included in the optimal estimation is 16. A spatially and temporally varying dynamical bias correction has been applied to reference the MODIS products against the AASTI GAC data . This occurs when constructing the L3S product prior to generating the L4 IST product. The temporal window for the dynamical correction is 7 d (days), and the bias fields are smoothed over 500 km. Due to the limited temporal availability and sampling pattern (see Sect. ), AATSR data were not used for the generation of the L4 IST product.

The satellite products used in this study represent the clear-sky IST, as the IR satellite sensors cannot observe the surface through clouds. As a result, a clear-sky bias is usually observed when comparing averaged clear-sky surface temperatures against averaged all-sky temperatures . used PROMICE observations to estimate the clear-sky bias introduced when averaging using different temporal windows. Using a ​​​​​​​72 h averaging window, they found a clear-sky bias of -0.96 ∘C when PROMICE stations located in the middle or upper ablation zone and the accumulation zone were used. Here, this clear-sky bias of 0.96 ∘C has been added to the satellite products in order to provide an estimate of the corresponding all-sky daily IST fields, which can be compared to the all-sky ISTs observed by PROMICE and IceBridge.

The HIRHAM5 RCM simulates the climate of Greenland with a 5 km resolution . The RCM contains a simplified SMB model and a five-layer snow and ice subsurface scheme. The surface energy and water budget from the RCM (i.e. the radiative and turbulent heat fluxes and precipitation), evaporation and sublimation outputs are then used to force an offline SMB model with more and deeper layers and a more sophisticated treatment of snowpack processes to calculate the ice sheet SMB. The full model set-up is described in .

The Lagrangian set-up with 32 unequally spaced layers down to 100 m of water equivalent depth in the snow and glacier subsurface scheme is used . Assimilating an albedo product over bare glacier ice based on MODIS data can improve ice sheet surface melt estimates ; however satellite-derived albedo data are not available as far back in the past and suffer from other biases. Thus, the focus in this study was exclusively on IST assimilation without albedo data assimilation; for the latter an internally calculated albedo scheme was used. The SMB model calculates the accumulation of snow and ablation based on the surface energy balance by calculating a theoretical skin temperature. Since the skin temperature of ice cannot go above 273.15 K, i.e. the melting point, this is converted to energy available for melting surface ice. The skin temperature also influences deeper snowpack temperatures via diffusion.

Meltwater is assumed to run off immediately if bare glacier ice is exposed, but if there is snow on glacier ice, percolation into the deep layers and the associated latent heat released by refreezing in deeper layers is accounted for until the heat capacity and porosity of the layers is filled and no more percolation is possible. The sum of precipitation minus evaporation, sublimation and runoff of meltwater gives the daily SMB over the ice sheet.

For the control simulation, surface energy balance outputs from the RCM were used to calculate the IST and melt potential as normal. This control simulation was initially evaluated against the L4 IST data (not shown). For the simulation with assimilation of the L4 IST, HIRHAM5 RCM forcing was initially used to calculate IST, and if this was below -2 ∘C at a grid point for a given time step, the L4 IST product was assimilated. Therefore, at any given time step, the GIS IST output by the SMB model is a combination of the modelled and observed L4 IST. The threshold was chosen to filter out biases at higher temperatures observed within the L4 IST product compared with PROMICE weather station data. The L4 IST product is available once daily, yet modelled IST is dependent on the full surface energy balance and thus, highly variable in space and time; assimilating the L4 IST product inevitably introduces some biases. Therefore, the aim of this assimilation experiment is to act as a proof of concept for the potential ingestion of satellite-derived data into the model. For this reason focus is on the month of May when IST and surface melt are highly variable; then the inclusion of satellite observations is likely to have the highest added value in identifying surfaces close to the melting point.

Examples of the different L3 satellite products generated from the L2 datasets described in Table  are shown in Fig. . The L3 products are aggregated for 9 January 2012 – wintertime when cloud cover, impervious to IR radiation, is higher – into the L3S product (Fig. d), while after optimal interpolation, the L4 gap-free product (Fig. e) is produced for the same date. The coarser spatial resolution of AASTI (Fig. a) compared to MODIS (Fig. b) is visible, resulting in AASTI grid points with missing information, while MODIS daily aggregated L3 data offer superior coverage over the GIS. The sampling of AATSR (Fig. c) with its narrow swath and lower temporal resolution results in characteristic artefacts resembling the Envisat platform orbit. Such artefacts do not appear for either the MODIS or the AASTI products.

Figure  shows time series of mean daily ISTs and their standard deviation (shaded area) for 2012 from the aggregated AASTI L3, MODIS L3, AATSR L3, L3S and L4 IST. To estimate the mean daily IST for each dataset, a mask defining the Greenland Ice Sheet was applied, and all valid and available measurements were averaged to a daily value. Therefore, daily mean values shown in Fig.  are means over the entire area of consideration, and while the L4 IST product always has the same number of valid pixels used for the daily mean, the single-sensor products have a varying number of available measurements depending on data quality and cloud coverage. The L3S product is the combination of all single-sensor products, so its average is based on all available points from all single-sensor products.

MODIS and AATSR (when available) show lower ISTs in particular during winter and late autumn compared to the other products, with minimum MODIS ISTs of about -50 ∘C and the AASTI and L3S and L4 IST products reaching their lowest ISTs of -35 to -40 ∘C. All products, including the L4 IST, represent well the annual cycle with warming starting in early March and peaking in July, followed by cooling and a winter minimum at the end of December.

The mean monthly IST and its standard deviation for all L3 products and the L4 IST are shown in Fig. . AATSR was only available until the beginning of April; thus no monthly value was calculated. From January to March, mean monthly ISTs from MODIS (magenta) and AATSR (green) were similar and significantly lower than AASTI (blue), the L3S (cyan) and the L4 IST product (red) accompanied by a higher standard deviation. These differences decreased from April to June, yet MODIS consistently showed lower values and higher variability compared to AASTI and the derived L3S and L4 products, which consistently agreed throughout the year. All products showed a peak mean monthly value in July, while June was warmer than August. From January to March, mean monthly temperatures were comparable to November–December means, and standard deviations were of the same order.

Such differences and variabilities are also reflected in the mean seasonal and annual estimates, shown in Table  for the different L3 products (excluding AATSR) and the L4 IST product. The AASTI, L3S and L4 IST products showed higher, as well as similar, seasonal and annual means compared to MODIS. Discrepancies between the estimates ranged from 0.5 ∘C in winter to ∼ 1 ∘C in summer, between the AASTI, L3S and L4 IST products. MODIS was 3–8 ∘C colder, with discrepancies being smallest in spring. Mean annual IST over the GIS ranged from -22.1 ± 5.4 ∘C for the L4 IST to -27.9 ± 5.9 ∘C from MODIS.

The spatial variability in mean annual IST over the Greenland Ice Sheet for 2012 from the AASTI, MODIS, L3S and L4 OI products is shown in Fig.  along with the number of days with observations used to derive the means. For the MODIS and AASTI datasets, the intermediate L3 gridded products were used for the estimates; i.e. the original 1 km and 4 km L2 observations were re-gridded to the 5 km final grid. MODIS mean IST was significantly lower over the entire Greenland Ice Sheet compared to the AASTI estimates, although significantly more observations were available for the former. Mean IST from the L3S and L4 OI products appear more similar to AASTI mean estimates.

The primary reason for the lower LST_cci v1.0 MODIS and AATSR IST values, used in the present study, is the type of cloud masking applied in the first version of the data. No post-filtering or implementation of the cloud-masking techniques (later developed within the LST_cci for both instruments) were applied in the v1.0 of the data presented here, but only the standard operational cloud mask was used; this frequently failed to properly flag clouds, which are typically colder, resulting in lower surface temperature values. For the case of AATSR, in addition to the cold bias, there also was the sampling issue (see Fig. ) and the limited availability of data for the reference year 2012 (contact with Envisat was lost in April). Therefore, AATSR was not included in the final L3S and L4 IST product. With respect to the MODIS product, the pixel-to-pixel variability is smaller than for AASTI, mostly associated with the better coverage (see Fig. ), and it was thus decided to use it for the generation of the L4 IST product.

Figure  shows aggregated daily mean biases and standard deviations for the AASTI, MODIS, L3S and L4 IST product against the PROMICE stations (see Fig. a and Table ). Note that, for each day, all available PROMICE stations were used and that that number differs from day to day, as not all stations have availability for all days. The overall bias of AASTI data was -2.16 ± 3.89 ∘C, significantly smaller than -11.59 ± 7.48 ∘C reported for MODIS. The L3S product bias was -4.30 ± 5.80 ∘C, while the L4 IST product was also found cold with a mean bias of -4.04 ± 5.15 ∘C, i.e. 0.26 ∘C lower bias and 0.65 ∘C lower standard deviation compared to the L3S product. During summer, mean bias and standard deviation for AASTI was very stable and close to zero, which was not the case for MODIS. The L3S and L4 IST products also showed higher variability in the daily bias and standard deviation during summer, compared to AASTI, yet they appear more stable than MODIS, indicating the benefits of using the OI methodology to generate daily, gap-free IST fields. Furthermore, the lower bias and standard deviation of the L4 IST product against PROMICE stations, along with its better coverage, demonstrate its potential advantage over single-sensor products or daily aggregated fields.

When examining the performance of the L3 and L4 products individually for each PROMICE station (Table ), AASTI consistently had the lowest bias (from -3.24 to -1.34 ∘C) and standard deviation values (3.29–5.83 ∘C) for all stations, independent of altitude, type of ice sheet zone and geographical location. MODIS, beyond higher bias and standard deviation values, also showed higher variability, with biases ranging from -17.43 to -5.97 ∘C and standard deviations between 6.41 and 9.39 ∘C. Such behaviour provides additional evidence that the cold-bias issue stems from the early version of MODIS data used in this study and the cloud-masking approach implemented.

Other studies have shown similar cold biases in surface temperatures derived from MODIS . However, as shown in Sect. , the important contribution of the aggregated MODIS observations in achieving a proper coverage over the GIS justifies the dynamical bias correction of the MODIS product against the AASTI data described in Sect.  and its further use for the generation of the L4 IST product.

This higher variability in the MODIS product influenced the performance of both the L3S and the L4 IST product, where biases ranged from -8.61 to -0.62 ∘C and standard deviations from 3.68 to 7.42 ∘C. The overall performance using the PROMICE stations was -2.22 ± 4.32 ∘C for the AASTI, -11.9 ± 8.17 ∘C for the MODIS, -4.58 ± 6.47 ∘C for the L3S and -4.31 ± 5.78 ∘C for the L4 IST product. The stable performance of AASTI and the L4 IST indicated that no single station and its characteristics (location, altitude) influenced the validation statistics.

Using the 1 km averaged surface temperature observations from 27 IceBridge flight campaigns, starting in 30 March and ending in 16 May, mean bias (dots) and standard deviation (vertical bars) were estimated and are shown in Fig.  for AASTI, MODIS, L3S and the L4 IST. For most flights, AASTI observations were in agreement with the IceBridge observations, with overall zero bias (-0.01 ± 4.03 ∘C) and a very stable behaviour, as no major outliers occurred; biases ranged from -2.10 to 2.10 ∘C. MODIS was cold compared to the flight measurements, manifesting as a negative bias (-5.19 ± 4.8 ∘C) and with a pronounced variability during the period evident from the oscillating bias (from -14.15 to 2.20 ∘C) and standard deviation values (from 2 to 7.2 ∘C).

The L3S and L4 IST products (bottom panels of Fig. ) showed significantly lower bias and standard deviation compared to MODIS although with a similar, yet reduced, variability in the statistics depending on the campaign; biases ranged from -6.66 to 3.98 ∘C with standard deviations from 1.7 to 6.6 ∘C. Overall, the L3S product had a bias of -0.63 ± 4.27 ∘C, and the L4 IST had a bias of -0.61 ± 3.59 ∘C, i.e. the lowest standard deviation of all datasets considered, ∼ 0.44 and ∼ 0.6 ∘C lower than the AASTI and L3S product, respectively. As was the case for the PROMICE comparisons, the L4 IST product combined stability and robustness in its validation performance and along with its improved spatial coverage can be considered more relevant for applications, e.g. related to SMB modelling of the ice sheet.

An example of one IceBridge flight campaign is shown in Fig.  for 19 April 2012. Flight measurements, corresponding to the coloured flight path in Fig. b, averaged every 1 km as a function of distance covered during the flight (magenta) along with their standard deviation (shaded area), are shown along with values from the L4 IST product, extracted for the grid points corresponding to the flight path (blue line). The mean bias for that campaign was 0.40 ± 4.30 ∘C. This campaign, which started and ended on the western coast, covered various zones of the GIS, and the variability in the IST was intense as revealed by the 1 km averaged measurements. Beyond the warm bias during the first 800 km of the flight, the L4 IST captured the variability in the ISTs over the GIS remarkably well. As the IceBridge radiometer measures the radiometric surface temperature from an aircraft at an approximate height of 450 m a.g.l. without any cloud screening, the presence of clouds may explain the discrepancies for the first 800 km of the flight where the IceBridge data are significantly colder than the L4 IST.

In order to assess the impact of the high-resolution footprint of the IceBridge measurements on the validation statistics, i.e. 1 km averages over 5 km averages of the L3 and L4 IST products, the standard deviation of averaging raw measurements over different spatiotemporal windows minus the raw measurements were computed (not shown). This is an assessment of biases introduced from comparing flight data of very high resolution, i.e. resolving small-scale variability, against spaceborne sensors which, although referred to between 1 and 5 km grids, are known to resolve scales lower than their reference grid.

Using only IceBridge campaign data, averaging for different spatial windows, i.e. 1, 5 and 25 km, and subtracting raw measurements, the standard deviation values for each campaign were estimated (not shown). The largest component standard deviation was introduced when processing the raw data to 1 km averages, of the order of 2 ∘C. Depending on the campaign, an additional 0.1 to 0.6 ∘C of the standard deviation was attributed to the averaging from 1 to 5 km. When averaging from 1 to 25 km, differences in the standard deviation reached 0.9 ∘C while the mean difference in the standard deviation over all campaigns was averaging 0.22 ∘C from 1 to 5 km and 0.4 ∘C from 1 to 25 km. Thus, between 0.2 and 0.4 ∘C of the standard deviation in all comparisons against IceBridge campaigns (see Fig. ) can be attributed to the different spatial scales represented in the IceBridge data compared to satellite observations.

The validation of the AASTI, MODIS, L3S and L4 IST datasets showed that for both PROMICE and IceBridge, AASTI had an overall better performance, with lower biases and standard deviations. MODIS v1.0 data from the LST_cci project, used in this study, had a significant cold bias, associated with the less advanced cloud mask algorithm applied to this early version; this influenced the performance of the derived L4 IST product. Nonetheless, the better spatial coverage and higher resolution of MODIS rendered it crucial for the generation of the L4 IST product, and thus its inclusion was justified. A new, improved version of the MODIS L2P dataset, to be released by the LST_cci, is expected to result in better performance of the L4 IST OI product.

Monthly averages from the L4 IST product for 2012, shown in Fig. , indicate the extent of warming during the summer months where temperatures on the GIS ranged from -16 to 0 ∘C, especially during July and for most of the ice sheet. Similar ranges were reported in for the period 2000–2006 from MODIS LST products as well as in , using daily MODIS IST between 2000 and 2010.

The number of aggregated observations from AASTI and MODIS used to generate the L4 IST product (not shown) revealed a seasonal pattern where most observations were available between May and August, while the fewest observations were available from November to February. The northern part of the GIS was consistently observed fewer times compared to the central part. This spatial and temporal variability in the availability of observations from MODIS and AASTI is related to the availability of observations in the infrared which is limited by cloud cover.

The annual mean IST over the GIS for 2012 is shown in Fig. a, using the L4 IST product. Values ranged from -30 ∘C for the central part of the ice sheet and increased up to -8 ∘C for the terminal zones, particularly for latitudes south of 70∘ N. reported similar values using MODIS data between 2000 and 2006. Furthermore, the mean IST during the melt period May–August 2012 (Fig. b) estimated from the L4 IST product showed values ranging from -15 and up to 0 ∘C, in agreement with .

Melt days were defined as days for which the IST was -1 ∘C or higher, following . They were estimated for the period 1 May to 31 August, at each grid point over the GIS. Figure c shows the number of melt days from the L4 IST product, where white areas experienced 0 melt days and coloured areas indicate at least 1 melt day. Melting was observed over large parts of the GIS for more than 1 d​​​​​​​, while significant parts of the middle and lower zones experienced more than 30 d of melt conditions.

Figure  shows mean monthly IST values for May, estimated from the control (Fig. a) and updated simulation (Fig. b), i.e. including assimilation of the L4 IST product; the estimated anomaly is shown in Fig. c. May was selected, as it is the month when the onset of melting commonly occurs across much of western and southern Greenland; this is a challenging period for SMB models to simulate, and the use of IST observations can potentially have a positive impact on the simulated IST and consequently the amount of simulated melt (not directly assessed in this study).

When examining the simulated surface temperature, the updated simulation using the assimilation of the L4 IST, was generally warmer over a large part of the GIS, especially the east and north-east regions. The difference between the two mean May surface temperature estimates, computed by subtracting mean May surface temperature estimates of the control simulation from the one using assimilation of the L4 IST (Fig. c), highlighted the areas for which the control simulation was consistently colder by 2 ∘C or more, even up to 5 ∘C, extending to the north, south and east parts of the GIS. To the contrary, the control simulation showed warmer temperatures on the west and central part of the GIS, yet differences in this case did not exceed 1 ∘C, and only for small areas were they up to 3 ∘C.

Comparing the simulated surface temperatures against the PROMICE stations for May 2012 (Table ) showed that mean daily temperatures from both the control (top) and updated simulation (bottom), using assimilation of the L4 IST product, were colder compared to PROMICE station measurements. The bias was lower for the updated simulation (-1.14 ∘C) compared to the control simulation (-2.16 ∘C), yet the standard deviation was higher, 3.55 ∘C for the updated simulation compared to 2.9 ∘C for the control. Only at the TASU station did both simulations indicate warmer surface temperatures, but this needs to be assessed cautiously given the very few observations available in May 2012 at this station (not shown).

Figure  shows a comparison of surface temperatures with the IceBridge flight campaign measurements to assess the control (Fig. a) and updated simulation (Fig. b), with assimilation of the L4 IST product; a marked improvement with the assimilation of L4 IST data was found, with a reduction in both the bias and the standard deviation compared to the control. The reduced standard deviation for the IceBridge data comparison, as compared to PROMICE observations, was consistent with what was reported in Sect. .

An example of surface temperature measurements from one IceBridge flight and the associated surface temperatures from the SMB simulations is shown in Fig. , similar to what was shown for the L4 IST in Fig. . Flight measurements, averaged every 1 km, as a function of distance covered during the flight (magenta) and their standard deviation (shaded area) are shown along with surface temperature values from the SMB model control (green) and updated simulation using assimilation of the L4 IST product (cyan), extracted for the grid points corresponding to the flight path. For this specific flight, the mean bias and standard deviation with respect to the IceBridge measurements was -7.10 ± 6.74 ∘C for the control simulation and -0.80 ± 5.07 ∘C for the updated one.

The L4 IST product was shown to improve the SMB model simulated surface temperatures when compared to PROMICE stations and IceBridge flight campaign measurements, for the test case of May 2012, selected as the typical onset of the melting season. Experiments for other months of 2012 (not shown) indicated a neutral impact of the L4 IST product, providing more confidence in the existing SMB internal parameterisations for the simulation of surface temperature, for the least challenging periods.