On-glacier meteorological measurements, as part of different research projects over the last decade, have been collected from three glaciers in the Interior Mountains of British Columbia and one large glacier in the St. Elias Mountains in the Yukon (Fig. ). The AWSs intermittently recorded data for glacier sites within different summer seasons between 2012 and 2019 (Table ). Five AWSs recorded local meteorological variables and energy and mass fluxes in ablation zones (Castle Creek Glacier, 2012; Nordic Glacier, 2014; Conrad Glacier, 2015, 2016; Kaskawulsh Glacier, 2019), while one AWS was set up in the accumulation zone of the Conrad Glacier in 2016. Topographic maps of these glaciers with the AWS locations are shown in Fig. .

All AWSs measured the following variables: incoming and outgoing components of shortwave and longwave radiation fluxes, 2 m air temperature and humidity, atmospheric pressure, 2 m wind speed and direction, liquid precipitation, temperature in the surface layer from the surface down to 4 m depth, and surface height changes as an indicator of solid precipitation and ablation at the site. In addition to these observations, high-frequency (20 Hz) measurements of wind speed, air temperature, and humidity were collected by sonic anemometers and gas analyzers to assess the turbulent heat fluxes through the eddy-covariance (EC) method. More details on the specifications of the sensors and accuracy control at each site are given in , , and . The meteorological sensors at all the sites, except Castle Creek Glacier, were housed on a quadpod, which provided a stable platform (where any tilt was monitored by an inclinometer) that lowered as the ice melted and maintained a nearly constant height of the sensors above the surface (Fig. ). All variables were saved as 1 min averages, except for rainfall, which was saved as 1 min totals, while the EC-derived turbulent fluxes were calculated as 30 min averages. A time-lapse camera in close proximity (∼30 m) to each AWS was used for a visual record of surface and atmospheric conditions during the observational period.

Castle Creek Glacier is located in the Cariboo Mountains and contributes meltwater to Castle Creek, a tributary of the Fraser River. The AWS on Castle Creek Glacier operated at the lower part of the glacier, which was gently sloping, with an approximate mean gradient of 7∘ (Fig. ). A melting ice surface was present during the observational period of 24 d in 2012, with some intermittent fresh snowfall events . Nordic and Conrad glaciers lie in the Purcell Mountains in eastern British Columbia and are located within the Columbia River basin. The surface slope at the location of the AWS on Nordic Glacier was 13 ∘, while 8 ∘ were observed for Conrad Glacier in the ablation area (AWS1) and 3 ∘ in the accumulation area (AWS2). Over the course of 46 d in 2014 at the Nordic Glacier site, a transitional snow surface was present for the first 4 d, with partial snow cover diminishing to a fully bare ice surface . A melting ice surface was present during observations for Conrad Glacier in 2015 and for most of the observational period in 2016 at the AWS in the ablation zone . At the AWS in the accumulation zone of Conrad Glacier, a snow surface was present throughout the observational period in 2016 and for the first 10 d at the AWS in the ablation zone . Kaskawulsh Glacier is located in the St. Elias Mountains and is part of the Kluane Icefield. The surface slope at the location of the AWS in the summer of 2019 was smaller than 2 ∘. Throughout the observational period, the ice surface was at the melting point .

Global climate reanalysis products combine modeled data with observations from across the world to provide a globally complete and consistent dataset of multiple climate variables of the recent past. ERA5 reanalysis provides hourly estimates of a large number of atmospheric, land, and ocean surface variables from 1950 to the present at a horizontal grid spacing of 30 km for the surface, as well as 37 pressure levels from 1 hPa (top level) to 1000 hPa bottom level;. ERA5-Land provides only surface variables on land at the interpolated 9 km grid spacing . These data are a refinement of the land component of the ERA5 reanalysis, with a higher spatial resolution forced by meteorological fields from ERA5. We use mainly the surface variables (details given below) from hourly ERA5 and ERA5-Land reanalysis. Hourly two- and three-dimensional ERA5 reanalysis data are also used to provide initial and lateral boundary conditions to the WRF model.

The Advanced Research WRF (ARW) dynamics solver is a non-hydrostatic atmospheric model, with fully compressible Euler equations, solved on an Arakawa C grid stagger in the horizontal and a terrain‐following hydrostatic pressure coordinate in the vertical . The model uses a time split integration, using a third-order Runge–Kutta scheme, with a smaller time step for the acoustic wave and gravity wave modes . We ran the WRF model, version 4.1.3, configured with four nested domains of 30 km (d1), 10 km (d2), 3.3 km (d3), and 1.1 km (d4) horizontal grid spacing, with the parent domain (d1) covering the bulk of North America and the northeastern section of the Pacific Ocean (Fig. ). The domains d1 and d2 are kept the same for the three glaciers in the interior of British Columbia (Castle Creek, Nordic, and Conrad), while d3 and d4 are set differently for each of the three glaciers in order to be centered at the AWS location. We use a one-way nesting approach, where WRF is first run for the outer domain and then iteratively fed into the nested domains as lateral boundary conditions. Since the outer domain has a larger grid spacing and time step than the nested domains, interpolations in both space and time are required. This process is repeated for each pair of nested domains. WRF is initiated at the beginning of the observational period for each summer season, while the first 24 h are discarded as a spin-up period. We chose 60 vertical levels, with a model top level at 50 hPa. We use a time step of 2.2 s for the innermost domain (d4) and save the selected set of variables as hourly and daily averages.

All WRF model runs use the same forcing (ERA5) and input data on land characteristics, such as topography and land categories (Tables , ). Examples of the land cover data used for WRF runs at Conrad and Kaskawulsh glaciers are shown in Fig. , while examples for the topography data are shown in Fig. S1 in the Supplement. Land cover data are taken from the European Space Agency (ESA) Climate Change Initiative (CCI) dataset but are converted to the 24 United States Geological Survey (USGS) land use categories implemented in WRF. Initially, the land category for a few grid cells overlapping with our glacier locations in the d3 and d4 domains did not correctly display the snow/ice category but showed the bare ground tundra or evergreen needleleaf forest category instead. These incorrect categories were manually corrected to the snow/ice land category. The elevation of the AWSs in reality differs from the elevation of grid cells representing these AWS locations in ERA5, ERA5-Land, and WRF (Table S1), with the smallest differences, as expected, for the d4 domain (1.1 km grid spacing) in WRF. As our sites are located in complex mountainous terrain, slope and shadow effects on shortwave radiation are activated in WRF. The sea surface temperature is updated daily in WRF, with hourly input data from ERA5 reanalysis. The WRF model was run on our department's high-performance computing cluster using three nodes (each with 20 cores) per glacier site.

The WRF model comes with various options for physics parameterizations , but previous glacier studies with WRF have used some parameterization schemes more often than others. For example, the most commonly used schemes in glacier studies include RRTMG , CAM , Dudhia and Goddard for radiation, the Grell 3D ensemble , the Kain–Fritsch and the Betts–Miller–Janjić schemes for cumulus convection, and the Morrison two-moment , the Thompson and the updated aerosol-aware Thompson–Eidhammer schemes for microphysics. The local closure Mellor–Yamada–Nakanishi–Niino (MYNN) level 2.5 and Mellor–Yamada–Janjić schemes, as well as the non-local closure Yonsei University scheme, are the ones most commonly used for the boundary layer, and the revised MM5 and Eta similarity schemes are most often used for the surface layer. The Unified Noah and Noah-MP land surface models are most commonly used in glacier studies. Noah-MP, which is a more sophisticated version of the Unified Noah model, includes multiple snow layers, representing percolation, retention, and refreezing of meltwater within the snowpack rather than in the snow–atmosphere and snow–soil interface, as is the case with the Unified Noah model . The WRF simulations over non-glacierized terrain are shown to vary substantially, depending on which of the two land surface models is used .

We chose our initial set of parameterizations based on those most commonly used in previous glacier studies e.g.,. This set of parameterizations represents our reference (REF) model configuration (Table ), while we also test different parameterizations as part of our sensitivity analysis. In this analysis, we perform 25 independent WRF runs, each with only one different parameterization scheme from those used in REF (Table S2). The different parameterizations are selected from a set of previously used ones in a range of WRF glacier studies, as well as a study that used WRF for hydrological modeling across western Canada . For each set of parameterizations, WRF is run for a period of 7 d (6 d after discarding 24 h of spin-up time) at the four sites, namely Conrad Glacier in 2015 and in 2016 (accumulation and ablation zone) and Nordic Glacier in 2014. The 6 d periods are selected randomly to represent different time windows throughout the early, middle, and late melt season.

We use these sensitivity runs to investigate whether there is a better configuration than REF, i.e., a best-performing configuration for our study sites. To this end, we evaluate the output from each sensitivity run against our AWS observations over the same 6 d period. The evaluation is performed for the meteorological variables relevant for the SEB modeling (described in Sect. 2.4). Our goal is to determine the best-performing sensitivity run in each category of physics parameterization schemes (radiation, cumulus convection, microphysics, planetary boundary, surface layer, and land surface model). We focus on the following two approaches:

minNRMSE configuration. We determine the best-performing sensitivity run in each category of physics parameterizations as the one with a minimum normalized root mean square error (NRMSE) in the modeled melt energy, where the reference data are the time series of modeled daily melt energy derived from the AWS data. The final optimal configuration, labeled minNRMSE, includes the best parameterization schemes from each of the categories.

Surface melt modeling through SEB accounts for the surface energy budget at the glacier–atmosphere interface and thus calculates the energy available for melt once the surface is at the melting point. Here we use a relatively simple SEB model that considers only the key contributors to total surface melt energy over a summer season at mid-latitude glaciers . The modeled energy available for melt, QM (Wm-2) at a given point on a glacier, is derived as 1QM=Kin(1-α)+Lin-σT04+QH+QL, where Kin and Lin are the incoming shortwave and longwave radiation, respectively, α is the surface albedo, and QH and QL are the sensible and latent heat fluxes, respectively. T0 is the glacier's surface temperature, and σ is the Stefan–Boltzmann constant. The outgoing longwave radiation is approximated using the Stefan–Boltzmann law with an emissivity set to unity, where T0 is set to 0 ∘C, as it is also confirmed with measurements at our glacier sites . All variables in the model are represented as their daily mean values. Fluxes are defined as positive (negative) when directed towards (away from) the surface. Once the surface temperature reaches 0 ∘C and stays at the melting point throughout the summer season, a positive QM in Eq. () drives melt.

Given our focus on the key seasonal SEB components, we neglect the ground heat flux and the heat flux from rain, since both have been shown to give negligible contributions to the total seasonal melt at mid-latitude glaciers , as well as at our study sites . The rain heat flux, however, can be a substantial contributor (up to 20 %) to daily melt energy on a day with extreme rainfall , but the uncertainty in the model used to assess the rain heat flux is relatively large . For these reasons, we neglect the heat flux in the SEB model but will include precipitation, both as rainfall and snowfall, in the evaluation analysis.

For the simplicity of the model, we also neglect empirical correction schemes commonly applied to the shortwave radiation fluxes, such as separation into direct and diffuse components, as in . These corrections, however, are shown to have minor effect on simulated seasonal melt at our sites in the interior of British Columbia . The turbulent heat fluxes are calculated using the bulk aerodynamic method as follows: 2QH=pp0ρacpCHUz(Tz-T0),3QL=0.622p0ρaLvCLUz(ez-e0), where Uz is the mean near-surface wind speed at height z, and Tz and ez are mean air temperature and vapor pressure at height z (2 m at our AWSs), respectively. e0 is the mean vapor pressure, ρa is air density, cp is specific heat capacity of air at constant pressure, and Lv is the latent heat of vaporization of snow or ice. p0 is the air pressure at standard sea level, p is the actual air pressure, and CH and CL are dimensionless exchange coefficients for sensible and latent heat, respectively. The exchange coefficients are parameterized following the Monin–Obukhov stability theory and depend on the surface roughness for momentum (z0v), temperature (z0T), and humidity (z0q), as well as on the atmospheric stability conditions in the surface boundary layer. On the one hand, we use constant values for these three roughness lengths for each site, which have been adopted from the EC-derived values determined from previous studies at these sites Table S3;. On the other hand, for the stability corrections and based on the assessed stability conditions, we use the functions applied previously in . The order of magnitude in these EC-derived values for roughness lengths (z0v=10-3 m; z0T=z0q=10-5 m) agree with commonly assumed values for glaciers in mid-latitudes . Vapor pressure ez at height z is calculated from the relative humidity RH at height z using the August–Roche–Magnus formula .

The primary goal of the evaluation analysis is to assess the performance of the SEB model, forced with either ERA5 or WRF data, in simulating seasonal melt energy at our sites. To do so, we evaluate the total simulated energy available for melt (QM; Eq. ) and the daily time series of QM, as calculated from the SEB model forced with the reanalyses (ERA5; ERA5-Land) and the WRF output, against the reference calculations when the same SEB model is forced with the AWS data. Thus, the input for the SEB model, i.e., the atmospheric variables Kin, Lin, T, RH, and U, are taken from (1) the AWS at each site, representing the reference or true values, (2) ERA5, (3) ERA5-Land, and (4) WRF at grid spacings of 3.3 and 1.1 km, using each of the three configurations (REF, minNRMSE, and TOPSIS). For the reanalysis and WRF, only the data from the grid cell covering each study site are used.

As we are interested in the evaluation of meteorological rather than surface variables (albedo and surface roughness), we use in situ observations of daily surface albedo and seasonally averaged roughness lengths in the SEB model. These surface variables could have been taken directly from the reanalysis and WRF; however, we found that these values can differ substantially from the observed ones throughout the observational period (Fig.  and Table ). The discrepancy between WRF and the observed albedo on glaciers, especially in the ablation zone, has also been noted in previous glacier studies . Thus, to avoid any evaluation biases originating in poorly assigned surface variables, we stick to the choice of using observed surface variables in the SEB model. We note that while we incorporate observed albedo into the SEB model, the inaccurately simulated albedo in WRF still influences the near-surface meteorological forcing fields. The observed daily surface albedo is calculated as the ratio of measured daily totals (in local daylight hours) of reflected and incoming shortwave radiation at each site. The incoming shortwave radiation at the surface is taken from these datasets without any further modifications (e.g., separation into direct and diffuse radiation).

Since the elevations of the grid cells from the reanalyses and WRF differ from the actual AWS elevations (Table S1), we perform a lapse rate correction on the temperature data from these datasets. Here we do so by calculating a daily averaged lapse rate from a regression between ERA5 temperature and geopotential height at multiple pressure levels for each glacier site. This time series of daily lapse rates is then used to correct the time series of daily 2 m air temperature (T) from the reanalyses and WRF over the observational period.

Near-surface wind speeds in the reanalyses and WRF are given at a height of 10 m above the surface, while the AWS wind data were measured at a height of 2 m above the surface. A common correction for the difference in wind speed heights is based on the assumption of a logarithmic wind profile e.g.,, which rarely takes place at our study sites, especially those in the interior of British Columbia, where katabatic flow with low (<3 m above surface) wind speed maxima prevails during a summer season e.g.,. The correction based on the logarithmic wind profile may therefore introduce an additional bias (underestimation) of wind speed relative to the observed wind speed at 2 m. We therefore chose not to correct for the height difference in the wind datasets. The remaining variables, Lin and RH, are also taken directly from the reanalysis and WRF without any modifications.

For each glacier site, we evaluate how closely ERA5, ERA5-Land, and WRF (1.1 and 3.3 km) resemble the observed components of the SEB, as well as the total energy for melt (QM) derived from the SEB model forced by AWS data. To do so, we use the same evaluation metrics as in the TOPSIS method (rsp, NRMSE, MAPE, and NNSE) and also add the normalized mean bias error (NMBE). While we evaluate the reanalysis and WRF performance in simulating day-to-day variability in those variables, our main focus is on evaluating their daily values as a mean over the whole observational period at each site.

In addition to the aforementioned variables, we also look into how well the reanalyses and WRF simulate the time series of daily precipitation (P), both in liquid and solid form. While an extreme rainfall event can present a strong contribution to the daily melt energy , fresh snowfall events over a summer season can substantially alter the glacier albedo and consequently the net radiative fluxes and the SEB e.g.,. Despite our choice to use the observed albedo in the SEB model, we look into how well the reanalysis and WRF capture the frequency of fresh snowfall events over the observational period at our sites. To differentiate between rainfall and snowfall, we use a simple model that relies on the temperature threshold of 0 ∘C; rainfall (snowfall) is assumed when the near-surface temperature at the given site is above (below) the threshold. We note that the overall quality of in situ precipitation measurements, based on tipping bucket rain gauges, is likely to be lower relative to the quality of other measurements at our sites . The rain gauges can have extensive underestimation of rainfall amounts (of up to 50 %), primarily due to the acceleration of airflow over the top of the gauge, with other error sources including splashing, and the finite time required for the buckets to reset between tips during heavy rain e.g.,.

Here we evaluate the performance of ERA5, ERA5-Land, and WRF (3.3 and 1.1 km) in simulating the selected variables (T, RH, P, U, Kin, and Lin) from the six study sites over the observational period. A summary of results based on the relative error and NRMSE is shown in Table , while the results based on other evaluation metrics are shown in the Supplement (Tables S4 and S5). Looking first at the results for the reanalysis data, we find that ERA5 and ERA5-Land yield a similar performance (difference of a few percent in NRMSE), with an overall slightly better performance, though not statistically significant (Table S5), by ERA5 over ERA5-Land. ERA5 and, similarly, ERA5-Land are found to simulate the mean daily radiative fluxes (Kin and Lin) relatively close to observations, with a relative error (overestimation) of 11 % in Kin and no relative error in Lin (Fig. ). The mean daily sensible heat flux from ERA5 is substantially underestimated (relative error of 87 %), mainly due to the substantial underestimation of mean wind speed (relative error of 64 %), despite the well-simulated lapse-rate-corrected mean daily near-surface air temperature (overestimated by 14 %). Similarly, the mean daily latent heat flux is also substantially overestimated. However, as the contribution of the latent heat flux to the total melt energy is small (<5 %), the large errors here reflect the differences in small numbers (e.g., 0.5 Wm-2 versus 3 Wm-2). Correlating the daily time series between ERA5 or ERA5-Land and the AWS-equivalent variables reveals that all correlations are statistically significant (p value <0.05), except for QL for ERA5 and except for U, QH, and QL for ERA5-Land (Table S4). On the one hand, the seasonally averaged total daily precipitation (P) from ERA5 is overestimated at some glacier sites (relative error of 130.3 % for Kaskawulsh 2019 and 84.5 % for Conrad 2016 AWS1), while being underestimated at other sites (relative error of -37.9 % for Conrad 2016 AWS2, -33.2 % for Conrad 2015, and -18.7 % for Nordic 2014; Figs. S2 and S3). On the other hand, the modeled time series of daily precipitation all show statistically significant correlation (p value <0.05) with the observed time series (Fig. S2). The frequency of days with heavy snowfall is overestimated in the ablation zones (Castle Creek 2012; Kaskawulsh 2019) and underestimated in the accumulation zone (Conrad 2016 AWS2). On average, ERA5-Land precipitation simulations perform worse than ERA5 (mean overestimation of 35.6 % in ERA5-Land versus 20.3 % in ERA5 across all sites).

The results from WRF reveal similar performance patterns to those for the reanalysis but with some differences, depending on the three configurations (REF, minNRMSE, and TOPSIS; Table ). For the REF configuration, the mean incoming longwave radiation is slightly underestimated (5 % for WRF at 3.3 and 1.1 km), while the mean sensible heat flux is substantially underestimated (43 % for WRF at 3.3 km and 64 % for WRF at 1.1 km; Fig. ). The REF configuration yields an overestimation in the mean Kin (12 % for WRF at 3.3 km and 19 % for WRF at 1.1 km), while the minNRMSE configuration gives an underestimation (16 % for WRF at 3.3 km and 11 % for WRF at 1.1 km) and TOPSIS has only a small relative error (4 % underestimation for WRF at 3.3 km and 1 % overestimation for WRF at 1.1 km). Correlating the daily time series between equivalent variables from WRF and AWSs reveals that all correlations are statistically significant (p value <0.05), except for U (Table S5). In contrast to ERA5 and ERA5-Land, WRF does yield statistically significant correlations (p value <0.05) for both QH and QL. WRF at 1.1 km underestimates the seasonally averaged total precipitation (P) for all glacier sites (relative errors ranging from -3.1 % for Conrad 2015 to -45.0 % for Kaskawulsh 2019 with the REF configuration), except for Conrad 2016 AWS1, where P is overestimated by 94.0 %. The modeled time series of daily precipitation shows statistically a significant correlation (p value <0.05) with the observed time series for all sites, except for Kaskawulsh Glacier (Fig. S2). WRF tends to overestimate the frequency of days with heavy snowfall in both the ablation zone (Castle Creek 2012, Kaskawulsh 2019) and the accumulation zone (Conrad 2016 AWS2; Fig. S3). Additionally, it also overestimates the frequency of days with light rainfall (<2.5 mm). On average, precipitation values from WRF at 3.3 km perform significantly worse than from WRF at 1.1 km (29.0 % versus -5.0 % relative error with the REF configuration; Table ).

When comparing the performance of the three WRF configurations at 1.1 km for the whole observational period at each study site, we find that no consistent pattern of outperformance or underperformance is found across the variables and glacier sites (Fig. ). Overall, there is a smaller spread in NRMSE across the sites for the minNRMSE configuration relative to the other two configurations, but even this finding does not hold for each variable (Table ). Notably, the simulation of RH at Kaskawulsh Glacier is particularly poor (NRMSE of 70 %) for both TOPSIS and REF, while for the other sites the NRMSE in RH does not exceed 50 %. Wind speed is another variable, with a large NRMSE (>30 % across all the sites) that is most pronounced in the ablation area of Conrad Glacier in 2016 (NRMSE of 57 %, while at almost the same location on Conrad Glacier in 2016 the NRMSE is much smaller, with 38 %). Despite the poor simulation of U, all three WRF configurations yield similar and statistically significant correlations (p value <0.05) between modeled and AWS-modeled daily QH values (Table S5). The results highlight relatively large variability in the WRF model performance across the study sites and observational period, as well as across the selected variables. For comparison, we also looked into the WRF performance as an ensemble mean across the three WRF configurations (Table ). To this end, we averaged the results from the three configurations (REF, minNRMSE, and TOPSIS) for each variable. Relative to at least two individual members, the ensemble mean has slightly improved performance (smaller relative errors) for T, RH, P, and Kin. Wind speed and turbulent heat fluxes still remain substantially underestimated.

Of the variables that play an important role in the SEB model, RH and U have, on average, the largest errors for the two reanalyses and WRF (Fig. ). The relatively poor simulation of wind speed and direction, in both reanalyses and WRF, reveals the inability of the models to capture the katabatic (downglacier) flow that prevails during summer months at the glacier sites. Failing to resolve the strong downslope wind speeds with maxima close to the glacier surface, the reanalysis and WRF substantially underestimate the wind speed (Fig. ). While WRF does resolve the wind speed better than the reanalysis, the underestimation of wind speed in WRF is still substantial (44 % in WRF at 1.1 km and REF run, relative to 64 % in ERA5). During episodes of synoptic storms, when the katabatic flow is interrupted, there is a slightly better agreement between the modeled and observed wind speed and direction across the glacier sites for both ERA5 and WRF (Fig. ). However, these episodes are relatively rare and too short-lasting to make any substantial difference in the overall model performance in simulating U.

We also investigated the use of surface QH and QL values, as outputted directly from the reanalysis and WRF into the SEB model, rather than calculating those fluxes with our bulk method. In WRF, these fluxes are derived through a local or non-local closure scheme in the planetary boundary and surface layers, depending on the parameterizations used . When QH is directly taken from ERA5, the NRMSE of QH is 83 %, which is twice as large as the original error when QH is calculated with the bulk method. In WRF at 1.1 km, the error in QH is increased from 31 % when the bulk method is used to 60 %, while the error for QL is increased from 21 % to 54 % with the REF configuration. For Kaskawulsh Glacier, the largest glacier among our study sites, the performance of simulated QH and QL directly from ERA5 is similar to or only slightly worse (few percent) than the performance based on the bulk method. Across all the sites, taking QH and QL values directly from ERA5 leads to an increased underestimation, from 6 % in the original estimate to 72 %, of the mean QM. For WRF at 1.1 km, the relative error in QM increased from 8 % in the original estimate to 17 %. These results justify our choice to assess the turbulent heat fluxes via the bulk method instead of taking them directly from the reanalyses and WRF.

Our sensitivity analysis to the choice of parameterizations in WRF consists of running the WRF model with the REF configuration over the selected 6 d period and study sites and altering only one physics scheme in the REF confirmation per run. This process yields in total 25 WRF independent runs (Table S2), including the one with the REF configuration, whose output is then evaluated against the AWS observations over the same sites and time windows, using NRMSE (Figs.  and S4). The larger the range of NRMSE across these runs, the larger the sensitivity to the choice of the schemes.

Altering the land surface model between Unified Noah and Noah-MP yields the largest impact, i.e., the largest range of NRMSE, in the simulations of RH (NRMSE in the range of 20 %–35 %) and T (NRMSE in the range of 20 %–29 %), followed by the simulations of U (NRMSE in the range of 38 %–42 %) and Lin (NRMSE in the range of 35 %–40 %). Altering the radiation scheme, where 12 different schemes were tested, made the largest impact on the simulation of Lin (NRMSE in the range of 34 %–50 %), while having a relatively small impact (<4 % range) on the simulation of all other variables. Altering the cumulus scheme, with three different cumulus schemes and three parameterization configurations that were each tested, made the largest impact on simulations of Lin (NRMSE in the range of 37 %–44 %) and RH (NRMSE in the range of 19 %–24 %), while having a relatively small impact (<4 % range) on the simulation of the remaining variables. The sensitivity to the choice of the four schemes for the planetary boundary layer is the largest for simulating Lin (NRMSE in the range of 40 %–51 %) and U (NRMSE in the range of 42 %–52 %), with relatively small sensitivity in other variables. Finally, none of these altered WRF configurations yields a strong impact on the calculated QM from the SEB model (Eq. ), where NRMSE is in the range of 12 %–15 % (Fig. ). Note that when different optimal configurations were used (REF, minNRMSE, and TOPSIS), the mean NRMSE for simulating QM over all the sites and observational period was in the range of 16 %–22 % for WRF at 1.1 km and 18 %–23 % for WRF at 3.3 km (Table ).

Looking at the performance of the 25 sensitivity runs, as well as the performance of the three optimal configurations, we identified the schemes for each category that consistently performed better in simulating the components of the SEB at our sites. For the microphysics, the best-performing scheme is the Thompson scheme, while for the planetary boundary and surface layers, the best-performing scheme is the MYNN Level 3 scheme. For the cumulus scheme, the results were less conclusive in terms of identifying only one scheme that consistently performed better. Instead, we found that two cumulus schemes performed better than others, namely the Betts–Miller–Janjić scheme that is switched “on” in all domains and the Grell 3D ensemble scheme that is turned “off” only in the innermost domain (d4) or the two inner domains (d3 and d4). For the radiation scheme, both the minNRMSE and TOPSIS method preferred the RRTMG scheme for longwave radiation and the Dudhia scheme for shortwave radiation. The Noah-MP land surface model gave better results than Unified Noah, in particular for the simulations of near-surface temperature and relative humidity (Fig. ). In both land surface models, the glacier surface albedo is calculated as a weighted average of land ice albedo and snow albedo, based on the snow cover fraction . However, we modified the current Noah-MP albedo parameterizations for land ice, as the default options were too high for our glacier sites; the ice albedo values were changed from 0.80 to 0.6 for the visible spectrum and from 0.55 to 0.3 for the near-infrared spectrum. No changes were applied to the albedo representations within Unified Noah.

In addition to the parameterization schemes, the WRF output is known to be sensitive to its “nesting” configuration, including the choice of domain boundaries and their size and grid spacing within. Due to the nature of our study domain, we could not follow the general recommendation for placing each of the domain boundaries outside of complex terrain . However, we assessed the sensitivity of the WRF output to small latitudinal and longitudinal shifts (by a few grid cells) of the domain boundaries for our two inner domains (d3 and d4) at the Castle Creek, Conrad, and Nordic glaciers. The results reveal a negligible difference in the WRF output at the study sites. Furthermore, changing the grid refinement ratio from the original 1:3 (30 km, 10 km, 3.3 km, and 1.1 km) to the 1:5 grid refinement ratio (30 km, 6 km, and 1.2 km) yielded slightly worse WRF results (up to a few percent difference in relative errors) in simulating the SEB components at our study sites.

Finally, we tested the sensitivity of our WRF simulations to the initialization setup. In addition to our original WRF runs, which have been initialized on day 1 of the simulation period and continuously run for the whole observational period (in addition to a 24 h spin-up period), we performed separate WRF runs that were re-initialized each day (in addition to a 24 h spin-up period each). Our results, as illustrated by the 6 d example for simulated temperature (Fig. ), revealed that after the initial 36 h, during which the two runs closely match each other, the runs differed by up to 4 ∘C at a given hour, which led to a difference of up to 2.5 ∘C (up to 40 % relative difference) for the daily averaged temperature. A similarly large sensitivity to the choice of initialization procedure was found for the other meteorological variables analyzed in this study.

In simulating the daily averaged QM from the SEB model, the results from the reanalyses and WRF with the REF configuration benefit from the cancellation of biases between the overestimation of Kin and the underestimation of QH (Table ; Fig. S5). For the reanalyses, the overestimation of Kin partly compensates for the underestimation of turbulent heat fluxes, resulting in a relatively good overall simulation of QM, which is underestimated with 6 % relative error for ERA5 and 10 % for ERA5-Land. This compensation of biases between Kin and QH has a lesser effect on the SEB model being forced by the WRF output because the partial cancellation of biases is only effective in the REF configuration, as it is the only among the three configurations that overestimates Kin. Thus, REF yields the lowest relative error for QM (underestimation of 5 % or WRF at 3.3 km and 8 % for WRF at 1.1 km), followed by TOPSIS (underestimation of 15 % for WRF at 3.3 km and 19 % for WRF at 1.1 km) and then minNRMSE (underestimation of 28 % for WRF at 3.3 km and 27 % for WRF at 1.1 km).

Looking at the time series of daily QM, ERA5 and ERA5-Land are shown to closely resemble the observed time series but fail at times to capture peak values of daily QM (correlation rsp of 0.86; Fig. ). Across all sites, the SEB model forced by ERA5 and ERA5-Land yields stronger correlations between the modeled and observed time series of QM than is the case for WRF data (rsp of 0.72 for WRF at 3.3 km and 0.74 for WRF at 1.1 km with the REF configuration; Fig. ), but all the correlations remain statistically significant at the 5 % confidence level.

While the model performance in simulating QM is similar across the study sites, the model forced with reanalyses yields the best performance for Kaskawulsh Glacier (nearly 0 % relative error for ERA5 and an overestimation by 1 % for ERA5-Land), while the worst performance is found for Nordic Glacier (QM underestimated by 15 % for ERA5 and 17 % for ERA5-Land). When the model is forced with WRF data, the site with the best performance in QM is Nordic Glacier (overestimated by 3 % for WRF at 3.3 km and no relative error for WRF at 1.1 km with the REF configuration), and the site with the worst performance is the station in the accumulation zone on Conrad Glacier in 2016 (underestimated by 18 % for WRF at 3.3 km and 16 % for WRF at 1.1 km). We find no dependence of the model performance on the size of glaciers in the sample or on their geographical location; however, our sample size is too small to allow for a robust analysis of these relationships. Finally, we find negligible differences between the SEB model performance when forced with the WRF at 3.3 km relative to 1.1 km (Table ).