JMA-NHM employs flux form equations in spherical curvilinear orthogonal coordinates as the governing basic equations. Saito et al. (2006) demonstrated that JMA-NHM outperforms the JMA's previous hydrostatic regional model in predictions of synoptic meteorological fields and quantitative forecasts of precipitation. Although JMA-NHM is used mainly for operational daily weather forecasts around Japan, the model can also be used for long-term climate simulations (Murata et al., 2015). Recently, JMA-NHM was applied to support a field expedition in the GrIS (Hashimoto et al., 2017), and the model setting used on that occasion was used in this study. A double-moment bulk cloud microphysics scheme was used to predict both the mixing ratio and the concentration of solid hydrometeors (cloud ice, snow, and graupel), and a single-moment scheme was used to predict the mixing ratio of liquid hydrometeors (cloud water and rain). In addition, ice crystal formation in the atmosphere was simulated by using an up-to-date formulation that depends on temperature. Following Hashimoto et al. (2007), we did not employ the ice-saturation adjustment scheme and the cumulus parameterization used in the original configuration. The turbulence closure boundary layer scheme was formulated following the improved Mellor–Yamada level 3 (Nakanishi and Niino, 2006). For atmospheric radiation, the transfer function in longwave radiation was computed by a random model developed by Goody (1952), and shortwave radiation was computed by diagnosing the transfer function following Briegleb (1992).

The multilayered physical snowpack model SMAP was developed for the seasonal snowy areas of Japan by Niwano et al. (2012, 2014). SMAP calculates the temporal evolution of broadband snow albedos in the UV-visible, near-infrared, and shortwave spectra as well as the internal physical parameters of snowpack such as temperature, density, grain size, and grain shape. Because the model incorporates the physically based snow albedo model (PBSAM) developed by Aoki et al. (2011), in principle it can explicitly assess the effects of snow grain size and impurity concentration (black carbon and dust) on snow albedo. SMAP calculates vertical water movement in snow and firn by employing the detailed Richards equation (Richards, 1931; Yamaguchi et al., 2012). SMAP is also equipped with a bucket scheme to calculate vertical water movement in snow and firn, in which liquid water exceeding the maximum prescribed water content descends to the adjacent lower layer (Niwano et al., 2012). Because a bucket scheme is used in most existing polar RCMs (Reijmer et al., 2012), we investigated whether the Richards equation scheme improves the GrIS SMB (see Sect. 4.7).

Niwano et al. (2015) applied SMAP to the SIGMA-A site (Aoki et al., 2014b), on the northwestern GrIS and demonstrated that when forced by the measured surface meteorological data, the model reproduced the temporal evolution of the physical conditions in near-surface snow (Yamaguchi et al., 2014) during the record surface melt event of summer 2012 (Nghiem et al., 2012; Tedesco et al., 2013; Hanna et al., 2014). The authors modified the original model settings only for the effective thermal conductivity of snow and the surface roughness length for momentum. In this study, we started with the same model settings described by Niwano et al. (2015). Because this was the first attempt to perform year-round regional simulations of the GrIS with SMAP, we were obliged to make adjustments for three snow/firn/ice physical processes: new snow density (density of falling snow), ice albedo, and effects of drifting snow.

To validate NHM–SMAP, we employed hourly surface meteorological data obtained with the AWSs from the SIGMA (Aoki et al., 2014a; Niwano et al., 2015), GC-Net (Steffen and Box, 2001; Box and Rinke, 2003), and PROMICE (Ahlstrøm et al., 2008; van As et al., 2012) projects, as listed in Table 1 and shown in Fig. 2a. The properties we sought to validate were 2 m air temperature, 2 m water vapor pressure, surface pressure, 10 m wind speed, downward shortwave and longwave radiant fluxes, snow/firn/ice surface temperatures, surface albedo, and snow surface height change. Our selection of AWSs was based on the availability of high-quality data in adequate quantities during the study period and the elevation difference between the AWS site and the topographic model in NHM–SMAP (Sect. 2.3.1). To compare the in situ measurements and the NHM–SMAP results, we used modeled data for the grid cell nearest to each AWS. Differences in elevation were not corrected in NHM–SMAP, although elevation differences greater than 200 m were not allowed. From GC-Net stations, only 2 m air temperature, surface pressure, 10 m wind speed, and downward shortwave radiant flux were taken. From PROMICE stations, all the properties except for surface height change were acquired, and SIGMA stations provided all the properties. Because the sensor heights changed over time depending on accumulation and ablation, we calculated the 2 m air temperature, 2 m water vapor pressure, and 10 m wind speed from the measurements by using the flux profile calculation module of SMAP (Niwano et al., 2012). Erroneous values were rejected after visual inspection, and temporal gaps left by the rejected data were not filled by interpolation.

For the extent of the surface melt area in the GrIS, we used the daily composite of satellite data developed by Mote (2007, 2014). This data set, which was created from measurements by the Special Sensor Microwave Imager/Sounder (SSMIS), offers a daily record of surface and near-surface melting on the GrIS with 25 km horizontal resolution. Hanna et al. (2014) utilized this data set to evaluate recent changes in the GrIS melt area.

The SMB of the GrIS calculated by NHM–SMAP for the study period was evaluated by using data provided by PROMICE (Machguth et al., 2016) as well as ice core data from the SIGMA-D (Matoba et al., 2015) and SE Dome (Iizuka et al., 2015) drilling sites (Table 2 and Fig. 2b). Most of the PROMICE stations are in the ablation area, whereas SIGMA-D and SE Dome are in the accumulation area. Recently, SMB data from PROMICE were used for the validations of MAR (Fettweis et al., 2017), and the 1 km horizontal resolution GrIS SMB product statistically downscaled from the daily output of RACMO2.3 (Noël et al., 2016) and ERA-Interim (Wilton et al., 2017). The validation sites were selected on the same basis as AWSs: data availability and an elevation difference less than 200 m between the site and the model. By employing the provided information for measurement periods at each site, the NHM–SMAP calculated SMB for each exact corresponding period were retrieved.

Table 3 lists the model performance for 2 m air temperature during the study period at each AWS depicted in Fig. 2a. Average ME and RMSE at all sites were improved for the online simulation by 1.4 ∘C (p<0.01) and 0.7 ∘C (p<0.1), respectively. Notable overestimates by the model (ME reached 6.6 ∘C at Summit, for example) were corrected in the online configuration (ME was within 2.3 ∘C at all sites). These results suggest that the surface analysis provided by JRA-55 is of inadequate quality in the GrIS and that SMAP improves the results through the use of more realistic snow/firn/ice physical conditions. This result in turn suggests that making every day an atmospheric spinup period (6 h; Sect. 2.3.2) longer than 6 h can improve the performance of NHM–SMAP. Finding an appropriate spinup period in the GrIS is a future issue to be dealt with. The following discussion focuses on results from the online simulation.

Figure 3a displays a year of observed and modeled 2 m air temperature at SIGMA-A, from 1 September 2013 to 31 August 2014. The observed seasonal cycle was well reproduced by NHM–SMAP (R2=0.95; Table 3); however, overestimation of the model was especially evident during winter (November to March), when measured 2 m air temperature sometimes reached below -30 ∘C; this characteristic was found at all sites. The scatter plot of measurements versus model simulations for the whole study period at SIGMA-A (Fig. 3b) also displays this tendency. A possible reason for this discrepancy is that JRA-55 overestimates the surface temperature. The JMA Climate Prediction Division (CPD), which operationally develops JRA-55 data, recognizes that JRA-55 tends to overestimate winter surface air temperature in the polar region owing to inadequate treatment of energy exchanges between the atmosphere and the snow/firn/ice surface, especially under very stable atmospheric conditions: a failure that also affects the reproducibility of the surface inversion layer and results in underestimation of the lower tropospheric temperature (Shinya Kobayashi, personal communication, 2017). Further investigation of this issue would require conducting further NHM–SMAP simulations forced by other reanalysis data sets like ERA-Interim, as done by Fettweis et al. (2017), which was beyond the scope of this study. At the same time, extending the atmospheric spinup period discussed above can also resolve the issue, because simulation results are expected to be less susceptible to a parent reanalysis data.

Tables S1 and S2 indicate statistics for the model performance in terms of 2 m water vapor pressure and surface pressure. To summarize, R2 for both parameters was acceptably high (more than 0.84), and ME and RMSE were reasonable. Relatively large biases and RMSE as well as relatively low R2 were found for 2 m water vapor pressure at sites TAS_U, QAS_L, and QAS_U. This result suggests that NHM–SMAP forced by JRA-55 cannot adequately reproduce absolute water content in the southeastern GrIS. According to Hanna et al. (2006), the southeastern GrIS is characterized by high accumulation rates attributed to prevailing easterly winds, frequent cyclogenesis in and around Fram Strait, and relatively high moisture availability when source air originates over a warm ocean. Stations TAS_U, QAS_L, and QAS_U are very close to the margin of our model domain (Fig. 1). Therefore, the use of a larger model domain that includes all of Svalbard may improve model results by resolving frequent cyclone activity in and around Fram Strait. Surface pressure was well simulated by NHM–SMAP, because R2 was very close to 1.0 except for Summit. Even at Summit, ME and RMSE were still reasonable when they were compared with those obtained at other sites (Table S2). The reason why R2 at Summit was relatively low should be investigated in the future. The slightly larger ME and RMSE for surface pressure found at SIGMA-B, SCO_U, QAS_L, QAS_A, and NUK_U can be attributed to relatively large elevation differences between the actual topography and the topographic model (-165, 176, 85, 104, and 85 m, respectively), as indicated in Table S2.

Orr et al. (2005) and Moore et al. (2016) pointed out that topographic flow distortion commonly induces high-speed low-level winds in the southern GrIS including tip jets, barrier winds, and katabatic flows. They also noted that an atmospheric model of Greenland would need a horizontal resolution of about 15 km to characterize the impact of topography on the regional wind field and climate; however, even at this resolution, features of the wind field would be under-resolved. Therefore, we investigated the reproducibility of a strong wind event observed at the TAS_U site (Fig. 2a) during the study period, when a maximum 10 m wind speed of 46.9 m s-1 was recorded at 17:00 UTC on 27 April 2013. A comparison of measured and simulated data (Fig. 4a) shows that the 5 km resolution NHM–SMAP successfully reproduced the strong wind event but underestimated its maximum wind speed by about 5 m s-1. In the figure, 10 m wind speed from the parent JRA-55 reanalysis with a horizontal resolution of TL319 (∼ 55 km) is depicted. Clearly, JRA-55 could not reproduce the strong wind event and the advantage of a high-resolution nonhydrostatic atmospheric model is successfully demonstrated. A comparison of measured and modeled 10 m wind speeds at TAS_U during the whole study period indicates that the model tended to underestimate high wind speeds (> 30 m s-1) but overestimated relatively low wind speeds, resulting in ME, RMSE, and R2 of 2.5 m s-1, 4.3 m s-1, and 0.68, respectively (Fig. 4b). At other sites, absolute values for ME and RMSE were smaller than those at TAS_U, and R2 ranged widely between 0.13 (SCO_U) and 0.78 (KAN_U) (Table S3).

These results confirm that it is difficult for atmospheric models to reproduce surface wind fields in the southern GrIS. This problem may be solved by updating the boundary layer scheme (Sect. 2.1) and increasing the horizontal resolution. In addition, a simple treatment of the surface roughness length for momentum (Niwano et al., 2015) may also affect surface wind speed estimates, as suggested by Amory et al. (2015). NHM–SMAP can provide synoptic weather data during strong wind events. Figure 4c, depicting the estimated surface wind speed field at 17:00 UTC on 27 April 2013, shows that strong wind speeds were simulated near the southeastern margin of the GrIS. This surface strong wind event corresponds to the Køge Bugt Fjord katabatic flow reported by Moore et al. (2016).

The downward shortwave and longwave radiant fluxes are important elements of the GrIS surface energy balance. During 30 June to 14 July 2012, Niwano et al. (2015) visited SIGMA-A (Fig. 2a) and witnessed the record surface melt event (Nghiem et al., 2012; Tedesco et al., 2013; Hanna et al., 2014). They reported mainly clear-sky conditions until 9 July and cloudy conditions with occasional heavy rainfall after 10 July. NHM–SMAP successfully reproduced the observed temporal evolution and diurnal variation of downward shortwave radiant flux at SIGMA-A from 1 to 15 July; however, it tended to underestimate slightly when clouds appeared (Fig. 3c). This tendency was typical during the whole study period, as shown by Fig. 3d and the ME value of -13.5 W m-2 listed in Table S4, although the signs of ME differ from place to place. RMSE ranged from 56.0 W m-2 (KPC_U) to 127.3 W m-2 (KAN_L) and was close to values reported by Ohtake et al. (2013) when the operational version of JMA-NHM was validated using hourly data from Japan, and relatively accurate RMSEs were obtained in the northern GrIS (Table S4). The underestimation in cloudy conditions may arise from effects in the cloud radiation scheme or in the reproducibility of cloud amounts and types by the model.

Although the tendencies of ME for downward shortwave radiant flux vary from place to place, ME for the downward longwave radiant flux had a similar tendency across the GrIS, ranging from -25.1 W m-2 at SIGMA-A to -10.8 W m-2 at KAN_M (Table S5). Underestimates of downward longwave radiant fluxes at SIGMA-A were especially large during winter (November to January when observed values reached less than about 200 W m-2) in the record from 1 September 2013 to 31 August 2014 (Fig. 3e) and over the whole study period (Fig. 3f). This characteristic was also found at other sites. One possible reason for this discrepancy is that the parent JRA-55 underestimates lower tropospheric temperatures, especially during winter (see Sect. 4.1). In addition, uncertainty in the winter cloud amount, low-level liquid clouds (Bennartz et al., 2013), and thin clouds (Cox et al., 2014) may affect the results. Improving the model would require detailed in situ measurements of cloud amount, cloud type, and atmospheric profiles as well as intercomparisons with satellite remote sensing data like that of Van Tricht et al. (2016). A model intercomparison like that done by Inoue et al. (2006) would also aid a deeper understanding of the limitations of current polar RCMs. On the other hand, observation data for downward longwave radiant flux can also have errors, especially during the winter period due to riming, which may act to increase measured values. In SIGMA-A, measured 2 m air temperature often decreased to about -40 ∘C during the 2013–2014 winter (Fig. 3a). Although such reductions in 2 m air temperature during March and April 2014 were followed by significant reductions in downward longwave radiant flux (Fig. 3e), they did not synchronize in December 2013 and January 2014. These results suggest that observed downward longwave radiant flux, especially during December 2013 and January 2014, were affected by riming and forced to increase. A reliable quality control technique for automatic downward longwave radiant flux measurements in the polar region should be developed in the future to perform not only model validation accurately but also climate monitoring.

We assessed the surface energy balance of the GrIS simulated by NHM–SMAP in terms of surface temperature and albedo. Measured and simulated snow surface temperature at SIGMA-A from 1 September 2013 to 31 August 2014 agreed well, especially from May to October; however, overestimates were obvious at temperatures below about -20 ∘C (Fig. 3g), much like the pattern for 2 m temperature (Sect. 4.1). As listed in Table S6, the model overestimated surface temperature at all sites except NUK_U, where 2 m temperature was also underestimated (Table 3). Therefore, the temporal evolution of simulated surface and 2 m temperatures followed the same pattern. Both ME and RMSE for surface temperature were slightly larger than those for 2 m temperature (Table 3); however, they are reasonable because they were almost the same as those obtained in Japan (Niwano et al., 2014). It is difficult to ascertain which physical process affected the model tendency because that would require us to investigate the complicated atmosphere–snow/firn/ice coupled system simulated by NHM–SMAP. One possible cause of the model's overestimation of surface temperature is overestimation of the surface wind speeds when they are relatively low (see Sect. 4.2), which acts to heat the surface through increases in sensible heat flux. Of course, overestimation of 2 m temperature by the model (see Sect. 4.1) especially during winter (November to March) may also contribute to the error. For a deeper insight, each physical scheme related to this problem should be investigated by standalone tests utilizing detailed in situ measurements.

NHM–SMAP could not adequately reproduce surface albedo. The model tended to overestimate surface albedo, especially in the ablation area (Fig. 5a). Similarly, the RMSE increased at lower surface elevations (Fig. 5b). The model performance was best at SIGMA-A, in the accumulation area, and worst at QAS_L in the ablation area, the most southerly station in this study (Table S7). ME and RMSE at these two stations during months of the study period when the sun appeared (Fig. 5c and d) show that model performance was uniformly good at SIGMA-A, covered with snow throughout the year, but both ME and RMSE suddenly increased after June at QAS_L. These results imply that our version of NHM–SMAP has difficulty simulating high-density firn and ice. Alexander et al. (2014) and Fettweis et al. (2017) reported that this is also the case for the MAR model. Tedesco et al. (2016) argued that the discrepancy between measured firn/ice albedo trends and trends modeled by MAR can be explained by the absence in MAR of processes associated with light-absorbing impurities. The dark microbe-rich sediment called cryoconite significantly reduces the surface albedo in the ablation area (Takeuchi et al., 2014; Shimada et al., 2016). Therefore, future models should consider this process as well as the possibility that NHM–SMAP overestimates snowfall during the summer period. In any case, it is necessary to conduct in situ measurements in the ablation area to confirm what is happening in reality.

If a polar RCM can calculate changes in surface height realistically, it can be used to partition volume changes supported by satellite altimetry observations into mass changes related to SMB and ice dynamics (Kuipers Munneke et al., 2015). Therefore, we compared the modeled changes in hourly snow surface height with in situ measurements obtained at SIGMA-A and SIGMA-B. Because the SIGMA AWSs started operation in the summer of 2012 (Aoki et al., 2014a), comparisons were performed for the 2012–2013 and 2013–2014 mass balance years (September to August). On the whole, the model captured the trend of measured changes, but underestimations were apparent for both sites and years (Fig. 6). At SIGMA-A, ME, and RMSE were -0.19 and 0.21 m for 2012–2013 and -0.13 and 0.17 m for 2013–2014. At SIGMA-B, ME and RMSE were -0.24 and 0.26 m for 2012–2013 and -0.04 and 0.12 m for 2013–2014. These scores are still acceptable in comparison to the SMAP validation results for seasonal snowpack in Japan (Niwano et al., 2014). As discussed in Sect. 4.7, SMB at the SIGMA-D site, located near SIGMA-A and SIGMA-B, is well reproduced by the model. Therefore, the underestimation can be attributed mainly to overestimation of simulated snow density, as mentioned in Sect. 4.4. Schemes for new snow density and the viscosity coefficient of snow in the polar region may need to be upgraded by performing detailed laboratory experiments.

The area of surface melt in the GrIS was extensive in the summer of 2012, setting a new record on 12 July 2012 (Nghiem et al., 2012; Tedesco et al., 2013; Hanna et al., 2014). At present, the melt area extent in the GrIS is commonly diagnosed from satellite data (Mote, 2007, 2014; Nghiem et al., 2012; Hall et al., 2013). A polar RCM that can simulate the melt area extent realistically would enable us to investigate atmospheric and snow/firn/ice physical factors controlling the melt area extent within the same RCM framework, as was done by Fettweis et al. (2011). We compared the simulated daily melt area extent with the data of Mote (2007, 2014) during 2012 and 2013.

The daily melt area extent simulated by NHM–SMAP was diagnosed from hourly snow/firn/ice surface temperature data and water content profiles. First, the daily maximum surface temperature was extracted at each grid point. If the value reached 0 ∘C and the top model layer contained water at the time when the maximum surface temperature was recorded, we considered the grid point to have experienced surface melt. Figure 7 shows that the simulated results matched the data well (R2 was 0.97 and 0.94 for 2012 and 2013, respectively), and NHM–SMAP successfully reproduced the record melt event around 12 July 2012, at which time the simulated melt area extent reached 92.4 %. The following year was relatively cold, as suggested by the maximum observed melt area extent of 44 %, and the model successfully replicated the satellite-derived results. It appears that NHM–SMAP can reliably and consistently simulate surface melt extent in the GrIS. Figure S1, which shows observed and simulated total numbers of surface melt days in 2012, supports this argument.

We evaluated the simulated SMB for the GrIS by using the PROMICE stake measurements and the ice core data obtained at SIGMA-D and SE Dome (Table 2 and Fig. 2b). During the study period, 55 measurements were available, and comparison results are presented in Fig. 8. In addition, simulated SMB data from MAR v3.5.2 forced by JRA-55 (Fettweis et al., 2017) were employed as reference information. The geographic patterns of accumulation and ablation simulated for the 2011–2012, 2012–2013, and 2013–2014 mass balance years by NHM–SMAP are depicted in Fig. S2.

The default version of NHM–SMAP employs the Richards equation to calculate vertical water movement in snow and firn. However, most polar RCMs employ a simpler scheme in which the maximum amount of water retained against gravity (irreducible water content) controls the vertical water movement (Reijmer et al., 2012). The irreducible water content is typically set at 2 % or 6 % of the pore volume, depending on the chosen modeling strategy. The lower of these values can induce more rapid transport of water towards lower layers, mimicking the piping process. To examine the adequacy of the Richards equation for GrIS SMB estimates, we performed sensitivity tests in which the Richards equation scheme was replaced by bucket schemes with irreducible water contents of 2 and 6 %. The tests employed only the standalone SMAP simulations forced by the atmospheric field calculated by the online version of NHM–SMAP, which implies that interaction between the atmosphere and the snow/firn/ice was not considered. In the sensitivity tests, profiles for snow/firn/ice physical conditions were reset at the beginning of the 2011–2012, 2012–2013, and 2013–2014 mass balance years by referring to the simulation data from the online version of NHM–SMAP. It means that feedbacks, which have a timescale of more than a year, are not considered. In the accumulation area where the observed SMB was positive, the simulated SMB agreed well with measurements during the study period regardless of the choice of vertical water movement scheme; however, the model did not capture large mass losses in which observed SMB reached values lower than -4 m water equivalent (m w.e.). The model tended to overestimate SMB in the lower part of the ablation area. In the default simulation, ME, RMSE, and R2 were 0.75 m w.e., 1.07 m w.e., and 0.86, respectively. With the bucket scheme, these scores worsened slightly, to 0.82 m w.e., 1.12 m w.e., and 0.85 for the case of 6 % irreducible water content and to 0.95 m w.e., 1.26 m w.e., and 0.85 for the case of 2 % irreducible water content. The Richards equation generally allows more water retention than the bucket scheme (Yamaguchi et al., 2012), which may result in higher near-surface density. In turn, more impermeable ice can form near the surface and induce runoff from the near-surface layer. On the other hand, lower irreducible water content forces rapid transport of water towards lower layers as expected, which acts to prevent the formation of ice layers and thus surface mass loss. To confirm the discussion, the GrIS-area-integrated daily melt and refreeze rates were investigated (Fig. 9). In the figure, results for the 2011–2012 mass balance year are shown, whereas results for other mass balance years are depicted in Fig. S3. During the 2011–2012 mass balance year, simulated daily melt rates were almost the same among the results from Richards equation scheme and two bucket schemes (Fig. 9a); however, refreeze rates from the control Richards equation scheme were much lower compared to other results (Fig. 9b), which is evidence for the abovementioned more impermeable ice in the results from Richards equation scheme. The same characteristics could be found in other mass balance years (Fig. S3).

Although the Richards equation scheme contributed to improved SMB estimates by NHM–SMAP, the model still produced significant overestimates, especially in the ablation area. Deviations between the measurements and the default model simulation results became larger where the measured SMB was smaller. As presented in Sect. 4.1, the online version of NHM–SMAP successfully reproduced 2 m air temperature at SIGMA-A during summer. Because surface mass loss during the summer is affected by near-surface (2 m) temperature, model performance in terms of simulating JJA 2 m air temperature at each AWS on the GrIS were re-examined (Table S8). As indicated in the table, significant or systematic errors were not found, and obtained ME and RMSE were around -0.2 and 2.1 ∘C, respectively. Therefore, a possible cause is overestimation of surface albedo by NHM–SMAP, especially in the ablation area (Sect. 4.4). According to the PROMICE data in the ablation area, ice albedo often decreases to around 0.2 during summer. Therefore, additional model sensitivity tests, in which ice albedo is set to 0.2, were performed. Obtained results indicate that simulated SMB did not change significantly compared to the control Richards equation setting (Fig. 8), suggesting that overestimation of surface albedo by NHM–SMAP can be attributed mainly to overestimates of snowfall as pointed out in Sect. 4.4. In addition, it is possible that even at 5 km resolution, NHM–SMAP cannot resolve the complex topography in the ablation area. Recently, Noël et al. (2016) demonstrated that statistical downscaling of individual SMB components from 11 km resolution RACMO2.3 to a 1 km ice mask and topography (Howat et al., 2014) can improve SMB estimates owing to the correction of modeled surface elevations. Moreover, Wilton et al. (2017) showed generally favorable results from a 1 km statistical downscaling of reanalysis data, with results generally comparing well with MAR and RACMO RCM output. On the other hand, MAR v3.5.2 with a horizontal resolution of 20 km is generally able to resolve the ablation zone well (Fettweis et al., 2017). A possible cause of this success can be attributed to the introduction of a subgrid mask, which is not employed by NHM–SMAP. It appears that statistical downscaling or further dynamical downscaling or introduction of the subgrid mask is inevitable that more realistic SMB estimates are obtained.

Using the SMB estimates from NHM–SMAP, we calculated the temporal evolution of accumulated SMB over the entire GrIS during the 2011–2012, 2012–2013, and 2013–2014 mass balance years. We set the area of the GrIS and peripheral glaciers at 1.807×106 km2, as explained in Sect. 2.3.1. The 2011–2012 and 2012–2013 mass balance years present a strong contrast as warm and cold years, respectively. According to simulation results by MAR v3.5.2 forced by JRA-55 (Fettweis et al., 2017), which uses the bucket schemes with an irreducible water content of 8 %, the GrIS SMB during the 2011–2012 mass balance year was relatively low (147 Gt year-1), then increased greatly in 2012–2013 (473 Gt year-1) and decreased slightly in 2013–2014 (403 Gt year-1). Our model, which tends to simulate lower SMB compared to MAR v3.5.2, produced a similar sequence in those years, with accumulated SMBs at the end of each mass balance year of -23, 420, and 312 Gt year-1 (Fig. 10a). In each of these years, the differences in these estimates emerged after the beginning of June.

Figure 10b–e show the accumulated totals of each SMB component in Eq. (6) for the same three mass balance years. They make it clear that the differences in the yearly estimates can be attributed almost entirely to the differences in runoff amounts (Fig. 10c), the differences in P, SUs, and SUds being relatively small. As mentioned, NHM–SMAP overestimated SMB especially in the ablation area, which implies that the runoff amount is still underestimated. Future studies should upgrade the model physics in the ways mentioned above, then clarify how much the current version overestimates SMB across the entire GrIS. At the same time, it is imperative to validate the simulations of each SMB component in Eq. (6). In a comparison of SMB components from four reanalysis data sets and the MAR model, Cullather et al. (2016) found that large variations exist for all of the SMB components.

In light of the importance of the runoff amounts for our SMB estimates, we again investigated the sensitivity of our SMB simulations to the three different vertical water movement schemes. The results clearly showed that the vertical water movement scheme made a notable difference to our GrIS-wide SMB estimates: for the relatively warm 2011–2012 mass balance year, the accumulated SMBs were -23, 113, and 174 Gt year-1 for the default setting and the bucket schemes with irreducible water contents of 6 and 2 %, respectively (Fig. 11a). Even in the other two relatively cold years, the SMB estimates deviated by as much as 100 Gt year-1 (Fig. 11b and c). Clearly, the percolation and retention of water in snow and firn plays an important role in estimates of the present-day SMB for the GrIS.