All data used in this study has been collected at the location of the East Greenland Ice Core Project (EastGRIP) field site (75°37^′47^′′ N, 35°59^′22^′′ W). EastGRIP is located in the north-eastern part of the Greenland Ice Sheet (Fig. a), in the katabatic wind zone, and approximately 350 km NNE of Summit, the highest point of the ice sheet. The local time is set to UTC-2 and UTC-1 during daylight saving time. In this study, all times are given in UTC and the sign convention is positive for upward fluxes, corresponding to sublimation for the LHF. The observational data comes from three EC systems, installed upwind of the EastGRIP camp, an AWS that is part of the Programme for Monitoring of the Greenland Ice Sheet (PROMICE, station name “EGP”, ), and an AWS that is part of GC-Net (station name “EastGRIP”, ). Both AWSs are located in the vicinity of the EastGRIP camp with sufficient distance to rule out flow disturbance by the campsite (approximately 500 and 1000m distance for the GC-Net and PROMICE AWS, respectively). The three EC systems were installed at 2.15m height in a dedicated clean-snow area, set approximately 6m apart perpendicular to the dominant wind direction, with the instruments facing into the wind (Fig. b and c). The clean-snow area is a designated limited-access area oriented away from camp in the direction of the main wind direction to ensure undisturbed snow conditions.

We present observational data from the three EC systems sampled during the period from the 28 May until 31 July 2019. During this period, the PROMICE AWS recorded a mean air temperature of -10.2 °C, ranging from -25.9 to 1.3°C and a mean air pressure of 730hPa. The mean windspeed was 4.5ms-1, with a maximum of 13.7ms-1, an average direction of 254°, and strong directionality due to the katabatic winds (Fig. b). The specific humidity was on average 2.2gkg-1, ranging from 0.5 to 5.0gkg-1. A model comparison is done for the 4-year period from 2016–2019, during which both data from the PROMICE AWS and MAR simulation are available. During this period the PROMICE AWS recorded an average temperature of -27.6 °C, ranging from -63.3 to 1.3°C, a mean air pressure of 720hPa and an average windspeed of 5.3ms-1, with a maximum of 21.3ms-1. The average wind direction during this 4-year period was 242°, with 74% of the time the wind direction falling within the 200–280 ° sector. All values are based on hourly averaged data.

The data for the EC comparison comes from three individual EC setups. The first EC system is a combination of a CSAT3 sonic anemometer (Campbell Scientific) and a Krypton Hygrometer 20 (KH20, Fig. d, Campbell Scientific). Besides 2019, this EC system was also deployed at EastGRIP during the summers of 2016, 2017 and 2018 . The second EC system is the IRGASON (Campbell Scientific), hereafter used as reference system, which is a combined sonic anemometer and open-path gas analyser (Fig. e). The third system is the combination of a CSAT3 sonic anemometer and a Li-7500 (LI-COR) open-path gas analyser (Fig. f).

For all three EC systems, the air temperature measured by the sonic anemometer is used. To measure the humidity fluctuations, the IRGASON and Li-7500 both use infrared absorption, while the KH20 uses absorption of UV radiation, emitted by a krypton lamp. The IRGASON uses radiation at 2.7µm (absorption) and 2.3µm (reference); the Li-7500 uses absorption at 2.59 and 3.95µm as a reference; the KH20 uses 123.58nm along with a minor light at 116.49nm, both are absorbed by H2O and O2, and H2O concentration is computed from the combined signal of the two wavelengths. The combined systems of sonic anemometer and hygrometer will be referred to as EC-KH20, EC-IRGASON, and EC-Li-7500. The EC-IRGASON and EC-Li-7500 ran from the 28 May until 31 July 2019. The EC-KH20 was deployed for three fewer days and ran from the 29 May until 29 July 2019. During this period the EC systems sampled continuously at a frequency of 20 Hz. During the days around 29 June and the 1 July, a combination of snowfall and wind led to measurement issues and consequent gaps in the time series. On the night of 17 to 18 July, possible frosting of the instruments led to a gap in the time series from 18 July 2019, 00:00 UTC until 18 July 2019, 09:00. The KH20 has a gap in the data from 2 June 2019, 14:00 until 3 June 2019, 20:00.

Since the EC-KH20 has the longest data availability, the EC-KH20 flux observations from the summers of 2016 to 2019 are used to compare with the model simulations.

In this study data from two AWSs is used: the PROMICE AWS and the GC-Net AWS . The data from the PROMICE AWS is used to compute the LHF and SHF using the one-level bulk method. The two-level GC-Net data is only used for comparison with the PROMICE data to assess the data quality during winter.

The PROMICE AWS was installed on 1 May 2016 and has been collecting data uninterruptedly ever since. It measures single-level temperature, wind speed, relative humidity and up- and downwelling shortwave and longwave radiation at approximately 2m height above the surface, varying between 1.8 and 2.6m due to changes in snow height. Instrument specifications and uncertainties are described in . For the model comparison, it is assumed that the height is close enough to the 2m model output, that it does not need to be corrected (similar to in ). For specific case studies, the exact measurement height will be provided. The surface temperature is determined using the up- and downwelling longwave radiation and an emissivity of 0.97 . The sensitivity of the temperature gradient to the emissivity value is provided in Sect. S2. The surface specific humidity is determined using the surface temperature and assuming saturated conditions relative to ice. Inspection of the relative humidity, temperature and longwave radiation data obtained from the PROMICE station during the winter indicates unrealistic values at temperatures below -50 °C, i.e. that the relative humidity fully depends on temperature and that occurrences of low temperature (below -50 °C) take place without simultaneous radiative cooling. Thus, the data with temperatures below -50 °C is removed. Further discussion of the data quality in winter is provided in Sect. .

The GC-Net AWS measures air temperature, relative humidity and wind speed at two vertical levels typically separated by 1.2m (instrument specification and uncertainties described in ). The distance of the lowest level to the snow surface varied between 0.4 and 2.3m during the years 2016 to 2019 owing to snow accumulation, compaction and ablation. Instrument heights are provided in the relevant figures.

This study uses two different polar versions of RACMO, a hydrostatic model that combines the atmospheric dynamics of the High Resolution Limited Area Model (HIRLAM, version 5.0.3) with the physics package from the European Centre for Medium-range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) . The polar version of RACMO is developed and maintained at the Institute for Marine and Atmospheric Research Utrecht (IMAU) and uses specialised parameterisations to simulate the Arctic and Antarctic climate. Over the Greenland Ice Sheet and surroundings, RACMO is run on a 5.5km resolution, with 40 vertical layers. The simulations from both model versions are forced with 3-hourly ERA-5 reanalysis at the lateral boundaries and for both simulations, the output from the gridpoint closest to EastGRIP is analysed.

The oldest version of RACMO used in this study is RACMO 2.3p2 (, hereafter referred to as RACMO2.3), from which the three-hourly model output is analysed. In RACMO2.3 the ECMWF-IFS physics cycle CY33R.1 is used . The LHF and SHF are simulated using the bulk method, a constant roughness length for momentum (z0,m) of 1×10-3m and the parameterisation (presented in appendix ) to determine the roughness lengths for moisture (z0,q) and heat (z0,t) over snow surfaces. In RACMO2.3, the sublimation from blowing snow is included in the surface LHF.

The second version of RACMO is RACMO2.4p1 (, hereafter referred to as RACMO2.4), from which the hourly model output is analysed. One major difference with RACMO2.3 is that in RACMO2.4 the ECMWF-IFS physics package is updated to physics cycle CY47R.1 and the blowing snow scheme is improved, as described in . The upgraded physics cycle constitutes changes in the precipitation, convection, turbulence, aerosol and surface energy exchange schemes. RACMO 2.4 now uses the IFS radiation physics module ecRad, the new cloud scheme has more prognostic variables, and a multilayer snow module for non-glaciated regions is introduced. A fractional land–ice mask, as well as new and updated climatological data sets (such as aerosol concentrations), are used. The LHF and SHF in RACMO2.4 are simulated in the same way as RACMO2.3. However, sublimation from blowing snow is no longer directly included in the LHF but is stored as a separate variable, and only the surface sublimation is evaluated in this study. The implications of how blowing snow sublimation is handled in the model simulations are discussed in Sect. .

In a similar study by , turbulent flux simulations with the RCM MAR (e.g., ) were evaluated for the EastGRIP site using improved turbulent flux estimates from the PROMICE weather station and the EC-KH20. We show these results alongside the results for the RACMO evaluation in this study. The model data comes from the gridpoint closest to EastGRIP.

In all figures, MAR data is presented for the same periods as for RACMO, from between 2016 and 2019. MAR was run on a 30km horizontal and 30 vertical layer resolution, which is substantially coarser than in the RACMO simulation. Nonetheless, due to the smooth orography of the accumulation area of the Greenland Ice Sheet, we consider a direct comparison between both simulations for MAR and RACMO valid. As in RACMO, the MAR simulation is forced by the ERA-5 reanalysis product and turbulent fluxes are calculated using a one-layer bulk method with roughness lengths for moisture and heat calculated from the roughness length of momentum following . However, it should be noted that a constant roughness length of momentum of 1.3×10-4m was used for the MAR simulation, much lower than the value of 1×10-3m used in the RACMO simulation. Consequently, we would expect lower turbulent flux amplitudes for the MAR output compared to RACMO.

The calculation of fluxes using the EC method requires compliance with EC flux theory and adequate instrumentation. The EC flux technique assumes that transport is turbulence-dominated, with negligible contributions from (sub)meso motion timescales. The method further assumes homogeneity of the terrain, absence of convergence or divergence and stationarity. As the terrain upwind of the EC systems is flat and homogeneous, the EastGRIP field site is well suited for EC measurements. Thus, topography-driven transport regimes are assumed to be negligible and the transport therefore dominated by turbulence. The EC instrumentation was set up at 2m height to ensure measurements were performed in the atmospheric surface layer, which can be shallow in polar, snow-covered conditions.

The EC data is processed using the TK3 software from the University of Bayreuth . The raw data is filtered using consistency limits of -50 to 50ms-1 for horizontal wind speed (u), -10 to 10ms-1 for vertical wind velocity (w) and -80 to 30°C for air temperature (T) and spikes are removed using the MAD spike test applying a standard deviation of 3.5. For the EC-KH20 a high number of simultaneous spikes was detected in the measured T and w. These spikes have been removed based on the quality flags provided by the CSAT3. As the focus is on getting accurate fluxes rather than having a complete record, no interpolation is done for the missing values. The raw covariances are calculated using a 10 min averaging time, cross-correlation and planar fit correction and are corrected using the Moore , WPL , and the Tanner correction for the EC-KH20. The 10 min averaging time is chosen based on a modified version (using 30min instead of 4h) of the convergence test by to ensure the averaging time is suitable for the conditions, i.e. that it is long enough to capture all turbulent variations but does not include (sub)mesoscale effects. The correction is applied to correct for spectral losses and uses a transfer function based on the Kaimal spectrum , derived from the 1968 Kansas experiment. The use of the Kaimal spectrum for the correction of spectral losses is validated by comparing the shape of w, T, a, w′T′ and w′a′ (co)spectra to the shape of the Kaimal spectrum (Sect. S3). After the processing with the TK3 software, remaining outliers in the average flux data are removed by excluding time intervals where u was smaller than 1ms-1 or larger than 8ms-1, or when the absolute value of w was larger than 0.15ms-1 or the wind direction was between 20 and 110° (the direction in which the mounting installation obstructed the flow). Final outliers in the average flux data are removed based on visual inspection. This leaves 84% of the 10 min LHF and SHF intervals for the EC-IRGASON, 85% of the intervals for the EC-Licor-7500 and 86% of the intervals for the EC-KH20. An overview of the time series and the data removed in post-processing is provided in Fig. S4.

To obtain year-round measurements of the LHF and SHF to compare to the regional model output, the turbulent heat fluxes are calculated from the PROMICE AWS observations using the bulk method. We evaluate both the bulk-calculated LHF and SHF provided in the published PROMICE data product , as well as re-calculated LHF and SHF using site-specific roughness lengths, against the EC data in summer. Similar to , we calculate the SHF and LHF using the one-level bulk method, with equations 4 and 5 described in (note the added minus results from the sign convention used in this study): 1aSHF=ρCpκ2uln⁡zuz0,m-ψuTs-Tln⁡ztz0,t-ψt1bLHF=ρLsκ2uln⁡zuz0,m-ψuqs-qln⁡zqz0,q-ψq Here ρ is the air density, Cp the specific heat capacity of air at constant pressure, k = 0.4 the Von Kármán constant, u the wind speed, T and Ts the temperature measured at 2m and at the surface, respectively, Ls the latent heat of sublimation, and q and qs are the corresponding specific humidities. The surface specific humidity is derived from the surface temperature following the equations in , using the equilibrium vapour pressure over ice and assuming saturated conditions. zu, zt and zq are the measurement heights of the wind speed, temperature and humidity and z0,m, z0,t and z0,q the roughness lengths of momentum, heat and moisture. ψu and ψq are the stability correction functions for momentum and moisture, following under stable conditions and the Businger–Dyer expressions, described in , under unstable conditions. ψt and ψq are assumed to be the same.

Stable conditions: 2aψu=-0.7ζ+0.75ζ-50.35exp⁡-0.35ζ+0.7550.352bψq=ψu Unstable conditions: 3aψu=2ln⁡1+x2+ln⁡1+x22-2tan⁡-1(x)+π23bψq=2ln⁡1+x22 where ζ=z/L, L is the Monin-Obukhov length, x=(1-γζ)1/4 and γ=16 is an empirically derived constant .

The bulk flux formulations require a value for the roughness lengths. For the bulk calculation done by PROMICE a fixed z0,m = 1×10-3m is used for the entire Greenland Ice Sheet together with the parameterisation of (S&vdB) to determine z0,q and z0,t, which are assumed equal. Literature values of roughness lengths above a snow surface cover a wide range of 1×10-1–1×10-5m . To ensure a robust comparison between bulk and EC methods, we use two different methods for determining z0,m, z0,t and z0,q. The first uses z0,m based on our EC measurements and the parameterisation for z0,q and z0,t, which are assumed equal. The second method uses z0,m, z0,t and z0,q obtained from the EC measurements. The data from the EC-IRGASON is used, because this system requires no separation correction and provides the most accurate humidity measurements (see Sects.  and S3). It is assumed that the turbulence properties are similar for the other setups, due to the limited separation of 6m and the homogeneous terrain. The values for z0,m, z0,t and z0,q are estimated using Monin-Obukov similarity and calculated from the measured EC-IRGASON fluxes and the vertical gradients from the PROMICE AWS following : 4az0,m≃zexp⁡κu(z)u*+ψmzL,u*=u′w′‾2+v′w′‾21/44bz0,q≃zexp⁡κa(z)-asa*+ψmzL,a*=-w′a′‾/u*4cz0,t≃zexp⁡κT(z)-TsT*+ψhzL,T*=-w′T′‾/u* Here z is the height of the EC or PROMICE instruments above the snow surface, which are both 2.15m during the measurement campaign in 2019. u(z) is the 2m PROMICE wind speed and u* is the friction velocity, the value of which is based on the EC-IRGASON measurements and provided by TK3. The stability functions are the same as for the bulk calculation. w′a′ is the EC-IRGASON covariance of the absolute humidity. Thus, 2m and surface saturated specific humidity obtained from the PROMICE AWS are converted to absolute humidity. w′T′ is the EC-IRGASON covariance and T(z) and Ts are the 2m and surface temperature from the PROMICE AWS. Similar to u*, the a* and T* are turbulent humidity and temperature scales. The 10 min EC-IRGASON data is averaged to hourly values, to match the PROMICE time resolution. The value for the roughness lengths is then determined by filtering the values for neutral conditions (-0.02 < z/L < 0.02) and for z0,m for sufficient wind (U > 3ms-1) and taking the median. The median is taken due to the large range of magnitude in the results, making the mean unsuitable (see Fig. ). This gives the following values: z0,m = 1.3×10-4, z0,q = 5.7×10-7 and z0,t = 2.9×10-4m. The value for z0,m is similar to the roughness lengths of 1.6×10-4m recorded by in the katabatic wind zone in Antarctica.

RACMO2.3 and RACMO2.4 provide the windspeeds at 10m height and in the middle of the lowest layer (also at approximately 10m height), respectively. The windspeeds are interpolated to 2m height, using the logarithmic wind speed profile and the stability correction functions following the sign convention in . The surface specific humidity is derived from the surface temperature following the equations in , using the equilibrium vapour pressure over ice and assuming saturated conditions.

The comparison of the LHF measured by the three EC systems over the period 28 May to 31 July 2019 is presented in Fig. . It is noteworthy that contrary to the commonly assumed stable atmospheric boundary layer over snow surfaces, in 18%, 21% and 21% of the 10 min time intervals measured by the EC-IRGASON, EC-Li-7500 and EC-KH20, respectively, the conditions were unstable (z/L<-0.02). The 8 d time series (Fig. a–d) illustrate the diurnal fluctuation of the LHF and the dependence of LHF on specific humidity. Besides following the same general trend and diurnal cycle, Fig.  confirms that the three EC systems measure similar sub-hourly LHF variations. Hence, we assume that these observed LHF variations are accurate representations of actual LHF with high signal to noise ratio. Direct comparison of the three instruments (Fig. e and f) demonstrates high levels of correspondence with correlation coefficient r = 0.97 to 0.98, an absolute bias, indicating the mean difference, of 0.2Wm-2, and an RMSE between 1.2 and 1.5Wm-2. However, the slope of 1.16 in Fig. e indicates a substantial difference in the LHF measured by the EC-Li-7500 compared to the EC-IRGASON and EC-KH20 (not shown). This suggests that though the EC-Li-7500 measures the equivalent mean flux as the other two EC systems, it slightly overestimates the amplitude of the daily LHF.

The difference in the LHF measured by the EC-Li-7500 and the two other EC systems can be explained by the humidity measured by the Li-7500 as shown in Fig. . A comparison with the PROMICE AWS (Fig. ), shows an offset in specific humidity between the PROMICE hygrometer and Li-7500. Apart from this offset, a drift over time in the humidity measured by the Li-7500 can clearly be identified (Fig. b). This indicates an incorrect and varying sensitivity of the Li-7500, which explains the overestimated LHF measured by the Li-7500 and is likely due to an instrumental problem. In an EC-comparison study by in California, in which a.o. an IRGASON and Li-7500A are compared, a similar instrumental problem is reported. In their study the Li-7500A measured 14% higher humidity variances than the IRGASON, resulting in a 10 %–28% higher LHF than the IRGASON. In their study, the issue was resolved after instrumental repair and recalibration.

A comparison of the SHF measured by the three EC systems (see Fig. ) shows even higher agreement between the EC systems than the LHF. The SHFs measured by the three EC systems again follow the same diurnal cycle and have similar sub-hourly variations. The direct comparison of the fluxes also indicates a very good agreement between measurement systems (r = 0.98, an absolute bias of less than 0.5Wm-2, an RMSE between 1.6 and 1.9Wm-2, and slopes of 1.0).

Estimates of the LHF and SHF based on the bulk method in the PROMICE data product are overestimated (Fig. ), as can be seen by the slopes greater than 1 (Fig. a and e) and the overestimated amplitude in Fig. d and h. The overestimated flux magnitudes indicate that the roughness length z0,m = 1×10-3m used in the assessed time period is too high for the EastGRIP location. Using the same z0,m for both the LHF and SHF and assuming z0,q = z0,t, leads to a larger overestimation of the LHF than the SHF, with a slope of 2.22 as compared to 1.35 (Fig. a and e). A separate analysis of only the positive and negative fluxes results in similar slope values (Sect. S5), but similar to the bulk deposition is slightly more overestimated than bulk sublimation. Using a similar parameterisation for z0,t, z0,m = 1.3×10-4m based on our EC measurements, and assuming z0,q = z0,t, improves the correspondence with the EC data (Fig. b and f), especially the SHF. However, a slightly overestimated LHF remains (slope = 1.44 and absolute bias = 2.44Wm-2). Using the parameterisation by no other z0,m value could be found that provides good fits between both calculated SHF and LHF bulk fluxes and the EC data (see Sect. S6). Therefore, we use z0,m = 1.3×10-4 and z0,q = 5.7×10-7 and z0,t=2.9×10-4m, derived from the EC measurements (see Sect. ). We note that z0,t is larger than z0,m and that z0,t is two orders of magnitude larger than z0,q. This is not consistent with previous findings where z0,q and z0,t are often assumed to be smaller or approximately the same as z0,m, and z0,q and z0,t having the same or nearly identical values . Using the above roughness lengths, we find that the bulk method provides similar LHF and SHF values as the EC-Irgason (absolute bias of 0.79 and 0.67Wm-2, respectively, Fig. c and g) and these values are therefore used in the rest of this study and assumed constant. It is expected that the roughness length of a snow surface varies seasonally, e.g. through higher winds in winter that promote surface snow structure change . However, as no EC measurements were conducted during the winter, we only evaluate the estimated bulk fluxes during the summer (daylight) period. We assume that using the improved roughness lengths the calculated bulk fluxes provide reliable estimates during the winter as well. This is supported by a sensitivity study using roughness lengths up to one and two orders of magnitude smaller or larger than the original values (following ), showing that the exact value of the roughness length has limited influence on the estimated flux during the winter (see Sect. S7).

Intercomparisons between the simulated LHF from the RACMO and MAR models and observations are shown in Fig. . We note that there is a large spread between models and the observations in the seasonal cycle (Fig. a). The monthly averaged bulk LHF from the AWS varies between 2.6 and -0.9 W m⁻². The difference between the monthly averaged models and observations is up to 2.1 and -1.7 W m⁻² in June and October, respectively. Except for RACMO2.3 in summer and RACMO2.4 in June, the RCMs underestimate the LHFs year-round. Figure b shows the cumulative sum of the LHF over the 3.5 years of our measurements, expressed as a mass flux. While the cumulative mass flux from the AWS is approximately net zero after three complete years, simulations using MAR and RACMO2.4 result in a net deposition, with a total difference of 25 and 38mmw.e., respectively. RACMO2.3 shows overestimated sublimation and a total of -5 mm w.e. by the end of the three years. The time series in Fig. c shows that both the models and observations have similar diurnal cycles of the LHF in summer, although the amplitudes differ. In winter (Fig. d) there is a large difference between the models and the observations. MAR and RACMO2.4 episodically show strongly negative fluxes (of -7 to -13 W m⁻²), while the bulk flux from the AWS remains close to zero (between 1 and -2 W m⁻²). RACMO2.3 shows partly opposite flux results of MAR and RACMO2.4 and simulates a positive LHF, whereas the other two simulate a negative flux.

A direct comparison between model output and observed LHF is complicated by the sublimation of drifting snow, which, when it occurs, varies strongly with height and can reach significant heights above the surface . In the observations presented here, by locally moistening and cooling the air, blowing snow sublimation would violate the constant flux assumption in the EC measurements and bulk flux calculations. RACMO2.3 has an idealised drifting snow scheme , in which the associated vertically integrated sublimation is fully added to the surface latent heat flux, potentially explaining the overestimated sublimation in this model. In RACMO2.4 the drifting snow scheme is improved and moisture from drifting snow sublimation is added directly to the associated atmospheric model layers . Given the strong vertical variations in drifting snow sublimation, here we only use the surface latent heat flux from RACMO2.4 for comparison to our observations, which may lead to underestimated sublimation. The daily drifting snow sublimation from RACMO2.4 against the PROMICE windspeed is shown in Sect. S9. In MAR, the drifting snow routine was not activated for this comparison.

The comparison of SHF from observations, the bulk method and the RCMs is shown in Fig. . When comparing the seasonal cycle based on monthly means (Fig. a), the models have a slightly lower to similar SHF compared to the observations in summer, but simulate considerably more negative SHF values in winter. A monthly difference between the SHF of the models and observations in winter is between -20 to -33Wm-2 (Fig. a). The SHF time series in Fig. b and c show a similar pattern as the LHF comparison. During the summer the models and observations show similar diurnal cycles but differ in amplitude and hour-to-hour variations (Fig. b). In winter a large difference between the SHF from the models and observations can be seen, with strongly negative hourly fluxes of up to -62 to -86 W m⁻² from the models and a flux close to zero (-2 to 1 W m⁻²) from the estimates from the bulk method applied to AWS data (Fig. c).

We compare our results from the three EC systems in the polar conditions of the Greenland Ice Sheet to the performance of similar EC systems under non-polar conditions from earlier studies. In a verified and calibrated EC system was used to validate 84 EC systems of the AmeriFlux network, which are spread out over the North American continent, hence covering a wide range of environments. They reported a relative instrumental error of 3.06 ± 15.60% for the SHF and 1.72 ± 10.58% for the LHF, for the systems using an open path gas analyser. also compared different EC systems, using a combination of a CSAT3A, Gill 3R-50, IRGASON and Li-7500 A, in California. For the SHF, they generally find a slope between 0.92 and 1.09, with an intercept between -0.22 and 0.92Wm-2 (in one case, they report an intercept of 7.17Wm-2) and for the LHF a slope between 0.96 and 1.07 and an intercept between -0.2 and -0.01 W m⁻². compared six different sonic anemometers, CSAT3, Gill HS-50 and R3, METEK uSonic-3 Omni, R. M. Young 81000 and 81000RE, in southern Germany. Good agreement was found for the SHF with a slope between 0.98 and 1.02 and an intercept between 1.2 and -2.5 W m⁻². A comparison study by , was carried out in a cold desert environment in northwestern China using an IRGASON and a Windmaster Pro. They found a slope of 1.11 and an intercept of 1.22Wm-2 for the SHF. Finally, a comparison study by was done in Oregon, comparing eight different sonic anemometers (a-Probe, k-Probe, CSAT3, R3, DA-600 (TR61A), SAT-550, USA-1 and RM81000), where they found -1 to 8% difference in the SHF.

For the cold polar conditions reported on here, we find an inter-instrument variability for the SHF with r = 0.98, slope = 1.0, intercept = 0.4Wm-2, bias between 0.4 and 0.5Wm-2 and an RMSE between 1.6 and 1.9Wm-2. For the LHF is r between 0.97 and 0.98, slope between 1.01 and 1.16, intercept between -0.1 and -0.2 W m⁻², bias between -0.2 and 0.2Wm-2 and an RMSE between 1.2 and 1.5Wm-2. This inter-instrumental variability is consistent with the above-mentioned campaigns in non-polar conditions. Hence, we conclude that the accuracy and precision of EC SHF and LHF measurements carried out on the top of the Greenland Ice Sheet are comparable to EC measurements carried out under less challenging conditions. Our measurements and their high level of correspondence provide confidence in the quality of EC systems deployed under harsh polar conditions. However, systematic biases with the EC method, due to boundary layer characteristics in polar conditions cannot be ruled out, such as the influence of the katabatic wind maximum, and during (sub)meso motions , which both typically take place under very stable conditions and can cause the transport to deviate from a fully turbulence-dominated regime.

Our comparison between the EC measurements and the SHF and LHF deduced from the bulk method confirms the generally accepted uncertainties and challenges that come with using the bulk method in polar conditions. Known major limitations of MOST are the underpinning assumptions, i.e. high Reynolds number flow, steady state conditions and flat homogeneous terrain, in combination with the uncertainties in the universal functions describing the non-dimensional flux-gradient relationships . In this study, we also highlight the strong dependence of the calculated fluxes on the value of z0,m and the parameterisation used to obtain z0,q and z0,t. Different roughness lengths and parameterisations can lead to strong over- or under-estimation of the diurnal flux amplitude which has large consequences for the calculated net and total fluxes. Our results underline that uncertainty from using the bulk method can be greatly reduced by having a period of combined AWS and EC measurements in which not only z0,m is determined but also the fluxes are directly compared. Further improvement of the accuracy of the bulk method might be achieved by also having EC measurement during winter, making year-round evaluation of the roughness length possible.

The two orders of magnitude difference between the derived z0,t and z0,q explain the different accuracy of the bulk LHF and SHF when it is assumed that z0,q = z0,t (Fig. a, b, e, f). Comparing a filtered selection of all the measured z0,t and z0,q values during our campaign with different parameterizations shows that the measured z0,t is consistently higher than the parameterised z0,t and the measured z0,q is consistently lower than z0,t (Appendix , Fig. ). We note that the calculation of the roughness lengths is based on MOST and the accuracy of the temperature and humidity gradient measured by the PROMICE AWS. Our result implies that the parameterisation for z0,t and the common assumption that z0,t is equal to z0,q, which is used in most models and datasets, might not be valid over the entire Greenland Ice Sheet.

There is a large difference between the wintertime SHF/LHF values simulated by the RCMs and the bulk flux calculations (Figs.  and ). It is not possible to reconcile those discrepancies within the measurement uncertainties and hence this indicates either large systematic biases in models, issues with the measurements, assumptions related to the measurements or a combination of those. Intercomparison of the independent 2m temperature and wind speed measured by the PROMICE and GC-Net AWS show similar characteristics. During Arctic winter, conditions are mostly quasi-saturated, resulting in the specific humidity predominantly being dependent on air temperature, and the uncertainty in the relative humidity is unlikely to have a significant impact on the fluxes. The most important observational uncertainty is therefore that of the surface temperature, which is derived from the measured upward longwave radiation. This is especially important since the surface temperature is key for determining the near-surface temperature gradient, which determines the difference between flux results from the model simulation and observations (see Sect.  and Fig. ). We note that the net longwave radiation is close to zero for long periods spanning several days to over a week (Fig. a). The near-zero net longwave radiation sometimes coincides with low temperatures (T < -50 °C), conditions normally associated with a surface based temperature inversion rooted in longwave radiative cooling . Times when T < -50 °C are therefore also removed from the data (Sect. ). While we are observing near zero net long wave radiation, it is important to note that a zero net longwave radiation could also be explained by frosting of the sensor, which leads to artificial neutral conditions and SHF/LHF values close to zero (Fig. b). Measurements from both Summit in Greenland , the katabatic wind zone in Antarctica and modelling studies show that neutral conditions are uncommon during winter time. To explore whether frosting obstructs the radiation sensor, we compare the near-surface temperature gradient estimated from the PROMICE AWS with the near-surface air temperature gradient obtained from the two independent GC-NET AWS temperature measurements installed at two different heights (Fig. e and f). One can notice two important findings: (1) The independently observed temperature gradients by the single-level PROMICE and two-level GC-NET AWS are generally approximately similar and an order of magnitude smaller than the modelled temperature gradient (see Figs. i and for all winter months). (2) Features in the synoptic-scale variability of the near-surface temperature gradient are observable in both AWS datasets (see Sect. S10, Figs. S10 to S15 for other winter months).

A second line of evidence supporting the radiation sensor measurements can be deduced from the shallow near-surface (10cm) snow temperature, which is less prone to measurement uncertainties (Fig. c and d). Due to the thermal mass of the snow, it is not to be expected that the magnitude of the temperature gradient deduced from the near-surface snowpack temperature (T2.6-TSnow, Fig. d) is equivalent to the temperature gradient deduced from the snow skin surface (T2.6-TSurf, Fig. e). However, we note the general good agreement in the evolution of the sign of the temperature gradient based on the snowpack (T2.6-TSnow) and skin surface temperature (T2.6-TSurf). For example, when colder air is present, the air temperature is lower than the snow surface (e.g. 10 to 15 January 2019) and vice-versa (e.g. 1 to 10 January). Interpretation is, however, not straightforward, as the thermal inertia of the snowpack leads to a delayed response to surface forcing, and snow temperature reflects a delayed and smoothened pattern of the air temperature, reflecting a mixture of heat exchange between air, surface and subsurface at longer time scales.

Altogether, based on our assessment of observations and models, we cannot decide with strong certainty whether modelled or observed wintertime SHF/LHF values are closer to reality, and any conclusions based on either data source should be drawn with care. The large model-data discrepancy and our discussion here illustrate the outstanding requirement to resolve this question for areas with wintertime conditions such as the EastGRIP location, and the need for more direct observations of the near-surface temperature gradient.

Assuming that observational uncertainty cannot fully explain the difference with the modelled fluxes during winter, we explore potential shortcomings in the model simulations of either the air temperature or the snow surface temperature. The time series in Fig.  of the LHF, SHF and driving variables (seasonal cycle provided in Sect. S12) show that, while the wind speed in all three models is similar to the observed wind speed, both the humidity and temperature gradient are much larger than the observations. This means that the larger modelled magnitudes of LHF and SHF in winter result from a larger near-surface temperature gradient and therefore also a larger humidity gradient in the models. Since EastGRIP is located centrally in the modelling domain of both MAR and RACMO, we assume the impact of ERA5 forcing at the lateral boundaries to be small. With the tentative assumption that the observed surface temperatures are correct, the evaluated climate models simulate a too strong stability in this part of the ice sheet during winter. This conclusion is supported by a comparison of the near-surface temperature gradient measured by both the PROMICE and the two-level GC-Net AWS and the three RCMs over all winter months (see Fig. ). The too strong stability in the models implies that the processes driving the surface gradients are not yet accurately modelled and parameterised. This persistently larger near-surface temperature gradient during winter can have a considerable impact, as the LHF and SHF are important for obtaining an accurate SMB and closing the SEB. As seen in Fig. b small differences in LHF estimates can lead to large differences on longer timescales. Although studies suggest that the contribution of the LHF might switch to net mass loss in the future , most RCMs simulate the LHF to be a positive contributor to the SMB to date. In fact, by correcting the MAR model with summer observations at EastGRIP, find the LHF to be a negative SMB contributor in their simulations. They propose that the difference in LHF between the model and observations during summer arises from a negative bias in downwelling longwave radiation, as also found by , from the cloud scheme, while the winter bias may be caused by vertical mixing through katabatic winds that is not represented in the model . Similar to , we find that RACMO in winter also overestimates deposition compared to AWS observations at EastGRIP, probably a result of too low surface temperatures caused by a negative bias in incoming longwave radiation . This raises the important question of whether both established RCMs face systematic errors in the representation of the surface boundary layer on ice sheets during winter. Besides their importance for obtaining an accurate SEB and SMB, which are used for sea level rise estimates, accurately simulating surface fluxes is also important for other fields of study such as the interpretation of water isotope climate proxies from the snowpack and ice cores . Underscoring the need for better knowledge and model representation of the surface near-stability during winter on the Greenland Ice Sheet, both by improving model parameterisations and increasing the number of observations. This includes obtaining direct observations of the surface temperature, but also observations of blowing snow, to better understand and parameterise the impact of blowing snow sublimation on the heat fluxes.