We installed an upGPR system within the perennial firn regime of the GrIS at the research site Dye-2 (Coordinates: 66.4779∘ N, 46.2856∘ W) next to Camp Raven, in April 2016 (Fig. ). The radar system consists of an IDS (Ingegneria dei Sistemi, Pisa, Italy) FastWave control unit with dual frequency 600/1600 MHz antennas. The whole aperture is powered by six 50 Ah batteries and two 60 W solar panels (Fig. b). We buried the radar antennas in a box approximately 4.5 m beneath the surface in April 2016. To enable observation of undisturbed snow and firn, we further excavated an additional 2 m cave sideways and fixed the antenna box at this position. The upGPR system is programmed to conduct measurements periodically at three different intervals: during summer time (15 April–14 August) every 30 min during the day (09:00–21:00 h) and every 1 h for nocturnal measurements; after 14 August until 14 October and from 1 March until 14 April every 3 h and from 15 October until end of February, we only record one measurement per day at 12:00 h. All times are given in local winter time (UTC -3 h). From 16 October 2016 until our next visit in April 2017, the radar stopped working due to technical problems. For analysis, we defined the start of upGPR measurements as 1 May 2016, when the installation pit was filled in and had had time to settle for 2 days.

Radar data were processed as described in . Snow surfaces in the resulting radargrams for both frequencies were determined using the “semi-automated picking algorithm” . All reflectors were automatically picked at the maximum amplitude per positive half cycle or minimum amplitude per negative half cycle, depending on the phase sequence of the respective reflector. However, for the same reflector, we consistently chose the same half cycle. The resulting radargram of the 1600 MHz system was used to pick the snow surface and the 600 MHz signal to determine the two-way travel time (TWT with mathematical symbol τ) to the target reflector. However, for periods with large amounts of melt affecting the snowpack and firnpack, the reflection from the snow surface for the 1600 MHz antennas diminished. We then also used the 600 MHz signal to pick surfaces for such periods and vice versa used higher frequency signal to determine the distance of the target reflector for some radar records. For all displayed radargrams, we generated a wave speed model for electromagnetic waves derived from core densities to convert measured TWT to height above the upGPR antennas. Since we only have density data available for May when we visited the site, the wave speed model is not updated during the season and certainly incorrect for radar reflections affected by liquid water. These inaccuracies have no influence on data analysis as will be shown in the discussion. The model is just used for visualization.

Two firn cores down to the depth of the radar antennas were drilled in 2016 and used for the installation of the target reflector (Fig. ). Core data were processed in 5 cm steps for average densities and stratigraphy was visually inspected on a 1 cm resolution. In May 2017, we drilled only one core down to 5.5 m depth in close proximity to the radar antennas but outside of the estimated footprint of the antennas (about 8 m away from the center of the antennas). Data were processed again with 5 cm resolution in density and 1 cm resolution in stratigraphy.

In 2016, in addition to the radar we also installed a thermistor string about 4 m away from the solar panel mast of the radar system (Fig. b). Thermistors were deployed at depths of 0.4 to 5.4 m every meter and additionally at 7.4 and at 9.4 m depth beneath the snow surface of 1 May 2016.

The bulk layer (Ls) above the antennas (Fig. ) has a layer thickness Ls‾=ΣLi‾, with i the individual layer from one horizon to the next layer above. Correspondingly, the bulk mass (bs) is the sum of the mass of all layers: bs=Σbi. To derive snow and firn parameters for Li, we use the target reflector at a fixed height above the surface similar to . With the known distance between target and antennas (d), the surface pick in measured TWT and the known relative dielectric permittivity of air (εa), we can simply calculate for the height of the target above the snow surface (dA). Since the target posts are drilled to the same depth as the radar antennas (Fig. a), we expect compaction of the radar and the target to be approximately equal. As a consequence, d remains constant. From simple subtraction, we obtain the bulk thickness of the snow and firn layer above the antennas Ls‾=d-dA. The retrieval of bulk firnpack parameters above the antennas relies on previously published assumptions and equations : we used the three phase mixing formula postulated by, for example, or with the exponent β=0.5 and the assumption of only three contributing volume fractions (air, ice and water: θa+θi+θw=1). For cold conditions with snow and firn temperatures below 0 ∘C (θw=0), the bulk density above the antennas can easily be determined. In contrast to conditions in seasonal snow described by , melting snow and firn on cold ice sheets can rapidly refreeze due to the underlying cold content. As a consequence, the assumption of a constant ice volume fraction after initial melt is invalid for ice sheets. Hence, melt and dry periods have to be treated differently. The resolution of the thermistor string with a 1 m spacing and the first thermistor at 0.4 m depth is not adequate to identify first occurrences of melt above the antennas. We use radar data instead for identification and timing of melt periods. Surficial melt produces strong changes in dielectric permittivity and, consequently, has an effect on radar response. The appearances of multiples or ringing in the radargram above the snow surface indicate those effects (Fig. ). This allowed for the determination of periods when melt is present. For such periods, we assume that (i) no lateral flow transported mass downslope (slope angle below 0.5∘); (ii) wind erosion after surficial wetting is not effective; (iii) evaporation and sublimation effects are negligible for wet snow surfaces; and (iv) no mass transfer from Ls to layers below is possible as long as percolation did not reach the location of the antennas. Those four assumptions lead to the fact that a decrease in height of Ls is compensated by a corresponding increase in wet snow density (ρs), since the total mass (bs) cannot diminish: bs=Ls‾ρs.

To reduce the effects of single outliers and uncertainties in the surface and target picks, we averaged the 37 radar measurements per day and analyzed subsequently for diurnal differences during melting periods. For calculating diurnal changes in ρs, we use Eq. () and determine the differences (ΔLs‾) from day i to i+1 in Ls‾: ρs,i+1=Ls,i‾ρs,i+ΔLs‾ρnifΔLs‾<0Ls,i‾ρs,iLs,i+1‾-1ifΔLs≥0, with the new snow density estimate ρn=120 kg m-3 being slightly larger than for Alpine sites .

In a second step, we set the obtained average values per day of ρs to be equal for each diurnal radar measurement. Since ρs in Eq. () describes the wet snow density, it is impossible to discriminate for individual volume fractions. Hence, we use the empirical equation of : εs=1+c1ρs+csρs2+c3θw+c4θw2, with c1=1.92×10-3, c2=4.4×10-7, c3=18.7, c4=45, ρs with units [kg m-3] and εs as the relative dielectric permittivity of snow to solve for θw.

We checked the reliability of the application of the three phase mixing formulation to gather snow density from defined relative dielectric permittivity ranges for snow and ice (εs=[1:3.2] in increments of 0.01) and applied the received values in Eq. (). In case the three phase mixing formulation and the empirically determined equations were compatible, we would receive a volumetric liquid water content of constantly θw=0. Figure  displays the estimated discrepancy in θw values. In order to correct for the observed discrepancies, we applied a quadratic correction on the resulting θw of Eq. (): θwc=θw-1.55×10-8ρs2+1.13×10-5ρs+4.10×10-6 (again with ρs in [kg m-3]).

Mass fluxes from snow above the previous summer horizon into firn are hereinafter defined as seasonal mass fluxes (SMFs with mathematical symbol F). Determination of SMF requires more iterations but can be accomplished with the applied setup as well. Two more layer definitions were necessary to prepare SMF analysis. First, we had to define a reference horizon, below which no temporal changes in stratigraphy are observable (Fig. , yellow line). Consequently, the total mass of the layer between the top of the antennas and the reference horizon did not change within the observation period. From the known height of the reference horizon and corresponding layer thickness (Ls,x‾), determined from core data, and the calculated ρs,x, we could then continuously calculate the amount of mass of the reference layer (bx), which results in the following: bx=Ls,x‾ρs,x.

The second horizon necessary to determine SMF is the previous summer surface. The assignment of the 2015 summer horizon is possible for both radar frequencies over the entire observation period (Fig. , white line). We chose to refer to the 600 MHz data (Fig. b), since both the surface reflection and the summer 2015 horizon are more predominant and persistent for this antenna configuration. It is possible that either the data processing or slightly different environmental conditions influenced radar acquisitions with the consequence that peaks in amplitude shifted by ±1 sample. During dry snow periods when no compaction of the layer between the reference horizon and the summer 2015 horizon (L15,x) was identifiable, we used the most frequently occurring TWT for both horizons to minimize effects of shifted peaks. To calculate the mass changes (b15) occurring within the snow layer above the previous summer surface (L15), we had to determine the mass flux (F15,x) into L15,x due to percolating melt water. To solve for b15, we simply subtracted b15,x together with the seasonal mass flux from the mass balance of the reference layer: b15=bx-(L15,x‾ρ15,x+F15,x).

L15,x‾ in Eq. () was simply determined using the recorded core data. We assumed that L15,x‾ remained constant over the entire observation period. It is certainly questionable whether this assumption is reasonable as will be discussed later. However, from measured TWT and L15,x‾, we could then calculate ρ15,x during periods with dry firn. The third term in Eq. (), F15,x corresponds to the gravitational liquid water content of L15,x, which can easily be converted from θw if the imaged radar volume is known. We used the same approach as described by . To assess the imaged radar volume for this layer, we applied the known radiation characteristics of the radar system. Refraction occurring at density transitions was neglected, since permittivity differences are small and consequently refraction ineffectual. However, for each event with percolating water reaching L15,x, the three phase mixing formula is underdetermined cf.,. Hence, to solve for θw, we used the same assumption as that θi remains constant after initial percolation into L15,x. This precondition will be discussed in the following as well.

Here we use the versions 3.7 and 3.8 of the regional climate model MAR, especially developed for simulating the GrIS surface mass balance. MARv3.7 is run at a resolution of 20 km and is forced by reanalysis NCEP1 (National Centers for Environmental Prediction, resolution of 2.5∘) over 1948–2016. MARv3.8 is run at a resolution of 15 km and forced by reanalysis ERA-Interim (ECMWF Interim Re-Analysis, resolution of approximately 0.75∘) over 1979–2016. Both reanalyses and the MAR model are described in detail in . In respect to MARv3.5 used in , the main improvements of MARv3.7 and MARv3.8 – apart from regular bugs corrections – are the increase in cloud life, partly correcting the cloudiness underrepresentation (and, hence, the infrared energy flux) as well as the excess of inland precipitation found in . The differences between MARv3.7 and MARv3.8 are mainly improvements in computing efficiency without significant modifications in the physics. The MAR snow model is based on an older version of the snow model Crocus using the “bucket approach” as water transport scheme discussed in . MAR is forced every 6 h by either NCEP1 or ERA-Interim reanalysis data. We decided to use daily outputs for comparisons.

All major density steps and ice lenses identified in the cores can be related to radar reflection events (Fig. a and b). Starting from the bottom, each ice lens corresponds to an amplitude increase in the radargrams. Since we buried the top of the antenna box within the significant ice crust at a 0.1 m height, only the decrease in density of that crust produced a reflection response (Fig. b). The next ice lens at 0.8 m height produced a strong reflection for both frequencies, while the double lens right above at 1.0 m only results in a significant signal amplitude increase in the 1600 MHz radargram (Fig. a). In firn, the vertical resolution of the 600 MHz antennas is roughly 17.7 cm and for the 1600 MHz antennas 6.6 cm . Destructive interferences diminish reflections appearing within shorter distance than the respective wavelength. However, the lens at 1.3 m appears again in both radargrams as a strong reflection. This reflection is marked as reference horizon. At about 2.0 m height, we identified another significant ice lens with densities exceeding 800 kg m-3. While for the 1600 MHz array (Fig. a), it is possible to track this horizon over the entire time period in the radargram, the reflection signal disappears in the 600 MHz data after the last liquid water percolations by mid-August (Fig. b).

The summer 2015 melt produced a remarkable double crust just below the recent snow accumulation at about 2.3 m above the antennas. Both radargrams in Fig.  show a clear reflection signal for this horizon. The 600 MHz data allow following this reflection throughout the whole summer season until fall 2016 (Fig. b).

Concerning the surface reflection, different behavior for both antennas could be observed as well. The 1600 MHz radargram (Fig. a) is incapable of producing a clear surface signal after strong melt affected the snowpack. In contrast, the 600 MHz data still show a clear surface signature. Such occurrences are in agreement with upGPR radargrams observed in seasonal snow . The use of a dual-frequency system is beneficial for such events. We still received a strong surface signal even after mid-July for the 600 MHz array (Fig. b).

The calculated layer thickness of the snow and firn column above the antennas Ls‾ was compared with data from two ultrasonic depth rangers. One of the ultrasonic transducers is located at a distance of about 60 m to the upGPR location being part of the FirnCover station and the other ultrasonic data were measured about 1 km west at the GCnet station . Fig.  displays all three curves. In perennial firn ultrasonic depth rangers measure only the distance of the instruments to the snow surface. Since no snow free conditions can be used to recalibrate the measurements, we adjusted both stations to match the height of the snow and firn column during installation for the start of upGPR measurements. Differences in between ultrasonic data and upGPR determined Ls‾ are 5.1 cm in comparison to GCnet data and 4.3 cm to results of the FirnCover station in root mean square deviation (RMS) over almost six months of observations.

Density values determined by radar could only be validated through available firn cores, which were drilled during time of visits. Table  displays density differences of core data and radar derived values for several different radar reflections, which could be attributed to distinctive layers in cores. As a third data set of validation, we can use the height of the target above the snow surface (dA, Fig. ). In May 2016 this height was measured manually to 1.80–1.86 m, due to surface roughness. In May 2017, we had to raise the target and measured dA to 2.69–2.70 m. Radar determined dA equal to 1.79 m in 2016 and 2.68 m in 2017 for the same date as the manual measurements.

In Fig. , determined changes in snow and firn from upGPR (Fig. a. extent of percolation, and Fig. c. changes in SWE, brown line and volumetric liquid water content, blue line) are compared with temperature data derived from the installed thermistor string (Fig. b). The radargram was additionally processed by horizontal filtering. All reflectors remaining constant over the observation period were thus removed. Such filtering enhances visibility of abrupt changes in stratigraphy such as those provoked by water percolation (Fig. a). In Fig. b, temperature data are interpolated for the upper four thermistors with the blue line on top indicating the snow surface. Isotherms for every 1 K are presented as black lines.

For the bulk snow and firn above the antennas, we observed two early peaks in melt in June causing percolation to reach down to 2.9 m height in early June and down to 1.8 m on 23 June. After a period of refreezing conditions from early July until mid-July, the strong melt event on 19 July caused deep percolation to a height of approximately 1.5 m with derived bulk θw approaching 1 vol %. Melt conditions lasted until early August when the next increase in melt caused the determined θw to exceed 1 vol % and water percolation to reach about 1 m above the antennas. After this peak, we observed rapid refreezing with fully refrozen snow and firn by early September.

Table  illustrates dates of local minimum for percolation above the radar antennas determined from the radargram and height above the antennas of the -1 ∘C isotherm. This isotherm was determined by linearly interpolating recorded snow temperatures. In general, radar-observed percolation matches well the temperature progression. Almost all liquid water occurrences in the radar data at the snow surface or below (indicated in the radargram by distinct multiples or ringing above the surface up to 7 m in air) correspond to heat waves penetrating into deeper layers of snow and firn. While the first stronger melt event by early June did not affect temperature records significantly, the next melt event for this season showed a clear signal in temperature data as well. The delay in temperature response by about five days in Table  is a consequence of the simple search for local minimum in height of the -1 ∘C isotherm. The primary decrease in height of that isotherm already occurred on 23 June at 21:00 h and consequently was delayed only by 20 h in comparison to upGPR results. However, the minimum height within the melt period of the isotherm was reached four days later. The strongest dips in water percolation for mid-July and early August 2016 match by 2–4 h for radar and thermistor string.

The measurements of percolation depths differ more significantly. The first percolation event, recorded by temperature data, are a mismatch with radar observed percolations by 1 m. However, the much stronger events in June and August show a coincidence of radar and temperature observations of 10–70 cm. Actual temperature records for the same day showed a maximum of -0.2 ∘C at a height of 1.0 m at 17:00 h (Fig. b). The given accuracy of the deployed thermistors is in the range of ±0.25 ∘C. Even though the minimum in height of percolation for the radar was detected four hours later (Table ), we detected percolation reaching a height of approximately 1.1 m in the radar data at 17:30 h the same day. Concerning determined θw data in Fig. c, it seems that any strong gradient in derived θw corresponds well with the timing of percolation of the warming signal for the temperature records.

Since all contributing volume fractions of the overlying snowpack and firnpack are determined, we can simply calculate for accumulation mass in the water equivalent as well. The bulk SWE over the antennas is presented in Fig. c (brown line). During wet snow conditions, the determined SWE remained stable or only slightly increased. Only after 1 September and before 1 June remarkable increases in snow accumulation were determined.

We could clearly identify a strong mass transfer from snow into firn below the 2015 summer surface (Fig. a and b). At least three melt events routed liquid water beneath this summer horizon (Figs. a, b, a and b), which was located at about 2.4 m above the antennas for May 2016. In total, we determined a mass flux of 56 kg m-2 from snow into firn (Fig. b). The three major percolation events occurred after mid-June and before mid-August. While the first event produced an outflow of roughly 6 kg m-2 water mass from the snow layer in three individual routing events within three hours, the percolations in July and August routed 27 and 23.5 kg m-2, respectively (Fig. b). L15,x experienced a volumetric liquid water content of up to almost 1 vol % at 10 August 2016, 18:00 h (Fig. a, blue line). At that day, both the thermistor data and radar observations obtain the maximum depth in percolation (Table ). The timing of all three data sets is within three hours difference.

The mass balance estimates for early May 2016 (b15) derived from the radar exceeds conventionally measured SWE values for the snow layer by roughly 100 kg m-2 (upGPR b15=438 kg m-2; b15 measured in the pit above the antennas: 335 kg m-2).

We use MAR outputs with a daily temporal resolution and two different forcings, which generate grid cells of 20 km (NCEP1) and 15 km (ERA-Interim), respectively. The radar, in contrast, provided point data on changes in total accumulation of up to every 30 min together with data on volumetric liquid water content, percolation and bulk density (Figs. , ). To quantify offsets of individual parameters, we averaged radar data to diurnal outputs to match the temporal resolution of MAR simulations.

The comparison of seasonal changes in accumulation in between simulation results and radar data (Fig. ) shows high agreement for both data sets. Uncertainty in radar determined SWE derives from the error in total height of snow (±4.3 cm, Sect. ) and the uncertainty in density estimates (±1 %, Table ) in an error propagation. Apart from the beginning of the time series in May, changes in SWE simulated in MAR with both forcings match radar observations very accurately. To assess the similarity between simulations and radar data, we calculate the Nash–Sutcliffe efficiency value (NSE) . NSE values of 1 indicate a perfect fit of the model with the data, while a NSE of 0 shows that the model fit is as good as simply the average value of the data. NSE for MAR NCEP1 simulations is at 0.75 and below 0 for ERA-Interim driven simulations for the whole data series. While NCEP1 driven simulations gradually approach changes determined from upGPR data over time, MAR with ERA-Interim forcing remain parallel to the radar line almost over the entire time series. We assume that the strong rise in SWE for upGPR data at 10 and 11 May 2016 is attributed to additional drifting caused by a shelter, which we created for digging the radar pit. Hence, deleting only the data point of 11 May (Δbs=35 kg m-2) from analysis lead to NSE values for MAR-NCEP1 of 0.53 and MAR-ERA of 0.95. Consequently, the temporal progression of changes in SWE is simulated in MAR with very high agreement to radar data using ERA-Interim forcings and acceptably well with NCEP1 forcing (Fig. ). However, the simulated significant increase in accumulation (by MAR-NCEP1) at 10 August is not reproducible by radar observations and distinctly smaller for ERA-Interim forced MAR.

For θw and bulk snow density above the reference horizon much more distinct differences in between simulations and radar determinations appear (Fig. a and b). Bulk density over the entire observation period is highly overestimated by MARv3.7 with NCEP1 forcing and significantly underestimated by MARv3.8 with ERA-Interim forcing for this specific location. Bulk density values of the NCEP1 forced simulation are exaggerating field data within the full observation period. While simulations overestimate ρx in the beginning by only 20 kg m-3, at the peak of the melt season, differences of almost 100 kg m-3 are commonly present (Fig. a). RMS deviations to upGPR derived ρx for MAR forced by NCEP1 reach 71.4 kg m-3. RMS values determined for ERA-Interim forced MAR simulations result in 51.2 kg m-3, which is only slightly better and still represents a deviation of roughly 10 % in comparison to mean ρx. Here, MAR models bulk density of the upper 2 m constantly too low.

MAR simulations with both forcings tend to exaggerate melt at Dye-2. This is especially the case for MAR being forced by NCEP1 reanalysis. For instance, the first spike in simulated θw for mid-May does not have an equivalent in radar data at all. Here, MAR simulations exaggerate the amount of melt and the duration. Documented changes in snow temperature (Fig. b) do not indicate such strong melt occurrences either. The subsequent simulated θw peaks correspond in timing but not in amplitude for MAR-NCEP1, while ERA-Interim forced MAR matches the amplitude but refreezes earlier. For the melting period lasting from 23 June until 3 July timing of the melt event agrees with radar derived data. Here, ERA-Interim forcing leads to a stronger overestimation in amplitude than NCEP1. Such occurrences are the opposite of the subsequent melt event starting at 19 July. While MAR-ERA data agree well in θw amplitude with radar, MAR-NCEP1 overestimates maximum θw by almost a factor of three. In consequence, refreezing is delayed for MAR-NCEP1 by 27 days. Since MAR-ERA misses the strong peak in melt (10 August), refreezing is simulated already for 15 August 2016 and thereby 18 days earlier than radar data indicates (Fig. b). Temporal offsets in between diurnal average values of θw≥0.3 vol % for the upGPR and NCEP1 forced simulations are always within maximum one day for the initiation of melt. However, duration of the periods with θw≥0.3 vol % differ by three days in mid-June and 31 days in late August/September 2016. For MAR-ERA, onset of melt reaching θw=0.3 vol % is delayed by three days in mid-June and otherwise within ±1 day. Refreezing of snow and firn to values below 0.3 vol % is usually predicted within an accuracy of ±1 day as well with the exception of mid-August, when MAR-ERA simulates a drop below the 0.3 vol % range 15 days too early.

Simulations of percolation depths for both model forcings are highly diverse and mainly disagree with upGPR determined data (Fig. ). Temporal agreement for the onset of melt is high for MAR-NCEP1 and upGPR percolation but percolation depths and timing of refreezing do not agree. For MAR-ERA, percolation depths are mostly underestimated over the course of the season and the strong melt in August is not captured, which leads to an earliness of refreezing. Both percolation simulations exceed radar determined percolations significantly for the first melt event in mid-May, which is in agreement with bulk θw predictions. For the following melt occurrences at mid-June, offsets in maximum percolation are rather small. Radar data reveal a height of infiltrating liquid water down to 2.85 m above the antennas, MAR-NCEP1 down to 2.82 m and MAR-ERA down to 3.07 m. Here, MAR-ERA has a slight delay in timing of water infiltration. The following melt event, lasting from late June to early July, results in much larger offsets of percolation depths. Deviations to radar data are at -1.08 m (MAR-NCEP1) and -0.76 m (MAR-ERA). For the major melt event (19 July–mid August), MAR-NCEP1 exceeds maximum percolation as observed by radar by at least +0.81 m and MAR-ERA underestimates water infiltration by -1.27 m. Such percolation offsets are in agreement with θw over- (MAR-NCEP1) and underestimation (MAR-ERA) as shown in Fig. . For both simulations, the speed of percolation is significantly underestimated for the onset of melt, when compared with upGPR data.

For the time period in between 3 August until 8 August, we observed refreezing conditions at the bottom of the percolation (Figs. a, ). However, MAR-NCEP1 simulates a stable percolation front with refreezing being simulated at the snow surface (Fig. ). ERA-Interim forced simulation correctly predicts refreezing from the bottom.

It is important to mention that the used wave speed model becomes incorrect when liquid water infiltrates snow and firn. Liquid water decelerates radar wave propagation significantly and, consequently, distance to reflections above the infiltration increase in measured TWT. However, snow pits and firn cores at the site can only be obtained when the instruments are visited once a year. For data analysis only measured TWT is used and, consequently, presented heights are not relevant. Still we consider a presentation of heights, even though they are partly incorrect after certain time periods, as being more intuitive and more supportive for readability. Percolation depths are unaffected from erroneous TWT conversions as they indicate the maximum height of dry snow and firn. In contrast to the ice lens at about 2 m height, the 2015 horizon and the snow surface, all layers below the reference layer (Fig. a and b) are basically unaffected by melt events and consequently do not show variations in TWT.

In Sect. , we described four assumptions required to enable data derivation for wet snow conditions: (i) no lateral flow transported mass downslope; (ii) wind erosion after surficial wetting is negligible; (iii) evaporation and sublimation effects are negligible for wet snow surfaces as well and (iv) no mass loss above the antennas is possible as long as percolation did not reach antenna height. Assumption (i) and (iv) induce each other and, hence, are discussed together. conclude that lateral redistribution of soil moisture is sensitive to slope angle. Here, we observed an area with an almost planar surface (< 0.5∘ slope angle). Consequently, lateral redistribution of liquid mass is considered negligible. Considering liquid water percolation, we recorded changes in firnpack stratigraphy every 30 min during daytime. For none of the records was water infiltration past the radar antennas identifiable. There is a slight chance that small amounts of water percolated in between two radar measurements below the depth of the antennas and refroze before the next radar scan. However, such infiltration would cause a release of latent heat at such depth during refreezing, which is not documented in the temperature data (Fig. b). Wind erosion of wet surfaces is assumed to have a negligible effect, since cohesion forces and bonds among grains are much stronger than for loose new snow . For the proof of assumption (iii), we used MAR outputs and quantified the effect of sublimation and evaporation during melting surfaces. For the time period in between 19 July and 19 August 2016, when strong melt affected the snow and firn at Dye-2 (Fig. ), MAR calculates an effect of evaporation being at 5 % of simulated SMB. Such an effect remains within the given uncertainty for radar derived SWE. However, MAR uses assumptions as well to estimate sublimation and evaporation. According to our knowledge, no experimental setup within the deep percolation zone of the GrIS exists to provide a more rigorous proof for assumption (iii).

Due to the fact that independent snow and firn temperature records of T≥-1 ∘C match percolation observed by radar very accurately and due to the high agreement between seasonal changes in SWE simulated with MAR and radar determined SWE development, we have strong reasons to trust results derived from radar data. In addition, calculated Ls‾ above the antennas is in close agreement with two time series of ultrasonic depth rangers. An error of 4–5 cm (< 1.5 % for a 3.4 m thick snowpack and firnpack) is below an observed uncertainty between manual measurements and snow depth sensors for a much smaller spatial offset in seasonal snow . For the presented data, conventionally measured bulk densities for specific layers agreed within ±1 % with radar derived densities for May 2016. In 2016, we had the opportunity to drill cores less than 2 m from the center of the radar antennas. Overestimation of bulk density of radar data in May 2017 cannot be directly attributed to increased uncertainties in radar derived parameters. Due to the fact that we did not want to influence snow and firn within the footprint of the radar antennas, we had to drill the core in 2017 about 8 m away from the center of the target reflector. Spatial variability in stratigraphy and Ls‾ caused difficulties in relating layers to radar reflectors and contributed to offsets for specific layer densities. The height of the target reflector above the snow surface could be determined with very high accuracies as well. Offsets in radar derived mass balance data (b15) of about 100 kg m-2 to manual observations can be attributed to difficulties in picking the reflection event seasonal snow above the summer horizon of 2015 in the radargram. Snow pits are usually just dug down to a remarkable crust, which is hardly penetrable with a shovel. The reflection response at this specific density gradient is masked by signal interferences with the reflection generated at the lower border of this crust, which represents the melt horizon of summer 2015. Correspondingly, including the observed ice lenses into SWE calculation of the pits results in a mass of 426 kg m-2 for early May. This reduces the offset to values obtained from upGPR to only 2.8 %.

The assumption of a fixed layer thickness in Sect.  for L15,x is based on the fact that during cold and dry conditions the TWT for both determined horizons remain at the same sample number within ±1 sample uncertainty. In addition, it is important to consider the respective firn layer to be part of a closed system. Neither evaporation, sublimation nor erosion can transfer mass. Due to rather small temperature gradients in perennial firn (here, approximately 3 K m-1 at maximum; Fig. b), water vapor transport mechanisms are small and consequently negligible. We presume that only compaction with a corresponding increase in ρs influence the measured TWT for dry conditions. Theoretically, it is possible that compaction is happening but the measured TWT remains constant. For instance, such conditions could be the case for the period until 19 June 2016 (Fig. ). The numerical approximation for a fixed TWT with varying ρs values ranging from 200–900 kg m-3 results in s=1.5×10-7ρs2-5.1×10-4ρs+1.4, with the strain s in meter and ρs in kg m-3. From this approximation it follows that a density increase for the observed layer of Δρs=+100 kg m-3 would only allow a compaction of about 3.7 cm for the reflector remaining at the same distance in TWT. For an observation period of one year, we observed maximum density increases of less than 30 kg m-3 per layer (Table ). Thus, the fixed layer thickness is a reasonable assumption for possible densification rates of that layer.

In addition, we assume the ice volume fraction to remain constant for the time period after water reached the respective layer and before refreezing is completed. Such an assumption is conceptually wrong in cold firn. Percolating water will refreeze and through the release of latent heat gradually increase the temperature of this layer. However, a gradual increase in θi is difficult to estimate from the given temperature resolution of the thermistor data. Consequently, we overestimate θw after initial percolation. However, only further increases in θw result in further increases in the amount of F15,x within the layer. Since F15,x remains stable after the first percolation event reaching L15,x (23 June) and after the third event (10 August), we expect the named overestimation to being of relevance only for the period in between 19 July and 10 August. As a consequence, for this time period of gradual warming (see Fig. b), the assumption of θi= const might lead to an overestimation of less than 10 kg m-2 for F15,x.

For the summer season 2016, we observed several major changes in snow and firn parameters. According to the radar records, a maximum volumetric liquid water content of θw≤2 vol % was observed for snow and firn above the reference layer (approximately 2 m beneath the snow surface). A maximum percolation depth throughout the season of 1.0 m height above the antennas, which corresponds to 2.3 m below the surface was recorded for 10 August. Deep percolation down to 10 m and more as proposed by for the here observed elevation range was not observed for the melt season in 2016. In terms of spatial extent of melt at the surface, this melt season is considered as above average (tenth in the 38-year satellite records) . All melt events together routed about 60 kg m-2 of mass into firn beneath the previous summer surface of 2015. This corresponds to roughly 40 % of liquid water, which were transferred into deeper layers, while about 60 % were retained against gravitational forces within the seasonal snow layer. model an average retention over the entire GrIS of 47 % with values reaching up to 75 % in the southeast of Greenland where rates of snow accumulation are largest. We did not observe major stratigraphic changes along the previous summer surface after the melt season 2016 as proposed by ; neither within the radargrams of both frequencies nor in the firn core of May 2017. However, a distinct increase in accumulation for the layer above the reference horizon and below summer 2015 was recorded from May 2016 (b15,x=484 kg m-2) to May 2017 (b15,x=534 kg m-2) of Δb15,x=50 kg m-2. This confirms the recorded mass transfer, despite of radar determined mass transfer being ∼ 12 % larger. Spatial inhomogeneities and inaccuracies in both measurement methods (uncertainty through use of θi= const, difficulties in layer attribution within firn cores) certainly contribute to this offset. Although, one should be very cautious of direct comparisons between annual firn cores, especially for individual layers, a general trend of mass increase could be confirmed by this core data. However, it is obvious that small scale changes appeared within the course of the melting period in 2016. In the layer bonded by the summer 2015 and the reference horizon, remarkable changes in reflection structure occur after percolation. Especially, the 600 MHz signal was influenced. A new reflector appeared right below the summer 2015 horizon and the reflection previously attributed to the significant ice lens at about 2 m height diminished with refreezing firn.

Concerning the mass balance of the snow layer above the summer horizon 2015 (b15) at Dye-2, we found an increase in accumulation of 84.4 kg m-2 for the time period of May until 30 September 2016. The simulated SMB in MAR resulted in 151 kg m-2 for the same time span with a simulated mass loss of only 7 kg m-2. Subtracting the mass flux of F15,x=56 kg m-2 of mass would result in an overestimation in MAR of b15 in comparison with radar data of roughly 12 %. This is in agreement with results presented by e.g., that model accuracies benefit from in situ data. For assessment of mass balance rates at Dye-2 without runoff and lateral redistributions at the current stage, it is of no relevance whether mass is transferred into firn beneath or remains within the seasonal accumulation layer. However, concerning lower elevation sites at the transition between accumulation and ablation area, the accurate assessment of residual water and outflow is critical for estimates on mass balances . The same appears for the formation of near surface layers of low permeability . Only monitoring and accurate determination of liquid mass being transferred into firn enables correct simulation of ice layer formations and future development.

Generally, regional climate model outputs are not compared with data from single point measurements and validation on time spans of days to several months is not common . It remains questionable whether such comparisons are fruitful or not, keeping in mind that the modeled snowpack is representing a mean state over an area of 20×20 km2 (15×15 km2). However, since conventional instrumentations such as lysimeters to measure snowpack outflow or snow pillows to determine changes in SWE are not applicable in perennial firn, upGPR offers an unique possibility to validate – on a temporally continuous basis – simulated snow and firn parameters with measurements and determine reliability of model results. Hence, we tested the performance of MAR on its upper end of accuracy.

In general, the performance of MAR with both forcings is very good especially for the timing of melt onset and simulated changes in SWE. After removal of one data point supposedly influenced by drifting, the agreement of seasonal SWE changes of upGPR data and simulations reach up to 0.95 in NSE values for the ERA-Interim forcing. Such NSE values indicate an almost perfect fit of simulation data. The temporal offset of melt simulated by MAR with respect to upGPR and thermistor results is mostly below one day, which is the temporal resolution of the model outputs. Such accurate performance of a regional climate model is encouraging since the model is not run with input data from the AWS nearby but forced at its lateral boundaries with atmospheric fields with a typical resolution of 100 km. As a consequence, the downsampling of MAR seems to be reasonably accurate. It should be remembered that we compare point measurements of specific parameters with an average snowpack over 20×20 km2 (15×15 km2) in area, which likely partially explains discrepancies.

Significant offsets between simulations and radar observations exist for the calculation of bulk density of the upper 2 m in snow and firn, which reach an offset of up to +100 kg m-3. In addition θw is overestimated for each melt event up to a factor of three in comparison to values derived for the upGPR. The general exaggeration of melt in the percolation zone by regional climate models has been described previously for another model as well . As a consequence of overestimation of density and θw for MAR run by NCEP1 forcing, water percolates too deep and refreezing is strongly delayed. The irreducible liquid water content of snow and firn is related to porosity . Snow and firn of higher density have less potential to retain liquid water and thus percolation is overreached. However, MAR forced by ERA-Interim has a tendency to exaggerate bulk volumetric liquid water content as well but with a lower amplitude. For two out of four melt events during the summer 2016, MAR-ERA predictions of θw are in agreement with radar data over a few days. However, MAR forced by ERA-Interim misses the peak of melt and percolation in August 2016 almost completely. For the moment when upGPR data obtain the highest percolation depths, MAR-ERA simulates refreezing in snow and firn. Here, problems with the reanalysis forcing might occur, which lead to a distinct underrepresentation of melt. Simulation of liquid water infiltration and percolation depths are coupled with the amount of melt being produced at the surface and the applied water transport scheme. The here used simple bucket approach is not capable of reproducing water infiltration as observed by radar and temperature data. Deviations of simulation results for percolation depths are rather erratic. This surveillance is in agreement with previous comparisons in seasonal snow e.g.,. The bucket approach is not capable of predicting heterogeneous infiltration and consequently, percolation is delayed at each onset of strong melt events but once melt has started is routing liquid water too fast in deeper snow . This study displays a very similar behavior of the bucket scheme to perennial firn as well. However, in contrast to seasonal snow, the cold content in firn forces refreezing from the bottom of water percolation as long as latent heat release is absorbed by the cold content of the surrounding firn. Hence, the typical water infiltration pattern of sharp dips in height as documented by radar and temperature data (i.e., Fig. ) is not reproduced in the model independent of used forcings. In addition, without adequate climate forcing, melt cannot be predicted in a correct manner. Neither of the two applied forcings for MAR enable correct prediction of full snowpack refreezing. Hence, we conclude that a model capable in modeling heterogeneous flow is required to assess water infiltration, retention and refreezing correctly.

As stated above, predicting individual parameters of the SMB for a point location of the GrIS is beyond the scope of regional climate modeling. Here, we used two different versions of MAR with two different resolutions. This already explains a large fraction of the observed discrepancies for the analyzed parameters density and melt. Since models are usually tuned to accurately reproduce SMB data, individual parameters such as bulk density or bulk liquid water content may result in variable offsets from in-situ data for different climate forcings. In addition, the initial conditions for summer 2016 for both ERA-Interim and NCEP1 are not exactly equal, which causes the model to adjust differently for the individual parameters. Next, clouds have a large impact on the energy balance of the percolation zone of the GrIS. Due to the positive feedback of melt and albedo, small differences in the timing of melt and the amount result in significant offsets for the used forcings. However, upGPR data can help to identify misconceptions in regional climate modeling and, consequently, support further improvements in simulations of temporal changes in snowpack and firnpacks.