The study area is located in the La Laguna catchment in the Chilean Coquimbo region, close to the Argentinian border (Fig. a). To assess the sensitivity of the models to the representation of snow physics and meteorological forcing, we use data from the Tapado AWS, a permanent meteorological tower since 2009 located close to the terminus of the Tapado Glacier at 30∘ S, 69∘ W; 4306 m a.s.l. (Fig. c). The site shows a complex topographic setting with average (maximum) wind speeds of 4.2 m s-1 (>15 m s-1) in 2017 and little precipitation (< 200 mm a-1) that falls as snow during fewer than 10 events per year. Precipitation events mainly occur during the winter season (>90 %) . Therefore the area surrounding the AWS is only covered with snow in austral winter. At this elevation, vegetation is extremely sparse.

The meteorological forcing data consisted of hourly mean values of air temperature (TA), relative humidity (RH), incoming shortwave radiation (S↓), incoming longwave radiation (L↓), wind speed (WS), wind direction (WD), and air pressure (PA) measured by the AWS (Figs. b, , Table ). Precipitation forcing (P) consisted of hourly data by a Geonor rain gauge (Fig. b). This gauge is an unshielded, unheated weighing bucket precipitation gauge filled with anti-freeze liquid and oil to prevent freezing and evaporation, respectively. During the snow season, defined as the period with snow on the ground (i.e. between 10 May and 6 November 2017), the station recorded meteorological observations continuously except for the TA and RH, for which gaps have been filled using three nearby AWSs (Fig. c, Sect. ).

Hourly snow depth (SD), reflected shortwave radiation (S↑), and six-hourly means of snow water equivalent (SWE) were also recorded at the station and used for model calibration and evaluation. SWE was measured with a CS725 sensor by Campbell Scientific, which passively detects the change in naturally emitted terrestrial gamma radiation from the ground after it passes through snow cover. It provided two independent SWE observations measuring both potassium and thallium gamma rays . The uncertainty given by the manufacturer is ±15 mm from 0 to 300 mm and ±15 % from 300 to 600 mm, but differences of up to 82 mm w.e. between potassium and thallium gamma ray measurements at ∼300 mm w.e. were measured. The manufacturer suggests that the output with the higher count is generally the most reliable, which were the potassium gamma rays measurements (Kevin L. Randall, Campbell Scientific Web Request (case:83574), personal communication, 2018). We display both data sets and estimate an uncertainty of ±25 mm for this data set.

The period between 5 May and 30 November 2017 has been covered to model the snow evolution in the austral winter, as this was a season where SWE data were available to validate the models. Since continuous data are required for both snow models, preprocessing was necessary to fill the gaps in the TA and RH data sets (23 June, 11:00, to 31 October, 10:00 CLT, due to sensor failure) and to correct the wind-induced undercatch in the precipitation data. Therefore, TA and RH data were interpolated based on lapse rates from nearby AWSs (Agua Negra (4774 m a.s.l.), Llano de las Liebres (3565 m a.s.l.), and La Laguna (3209 m a.s.l.; Fig. c).

For TA, a daily temperature lapse rate was calculated using TA measured at La Laguna and Paso Agua Negra AWSs (1565 m elevation difference) between 2014 and 2017. We fitted a sinusoidal trend over these lapse rates for the four-year period and found daily lapse rates with a maximum of -6.9 ∘C km-1 in winter and a minimum of -8.0 ∘C km-1 in summer. These daily lapse rates were subsequently applied to TA observations of Llano de las Liebres AWS, which is the only AWS that covers the entire period of missing data in 2017. For RH a similar approach was applied using the lapse rate of the daily dew point temperature between the Paso Agua Negra and La Laguna AWSs and applying it to data measured at the Llano de las Liebres AWS. Dew point temperature was converted to RH following . Evaluation of this lapse rate interpolation, based on 1638 overlapping observations at Tapado, shows an uncertainty (i.e. RMSE) of 2.8 ∘C and 9.97 % for TA and RH, respectively.

Since the precipitation observations were directly influenced by wind, an undercatch in the precipitation gauge is likely e.g.. As there are different possibilities to correct for this, the assimilation and correction of precipitation data are explained in Sect. .

To assess the sensitivity of both models to parameterisation choice and input uncertainty, we applied a four-step approach. First, we set up both models similarly to allow later comparisons (Sect. ). Second, we designed the most ideal setup for both models to acquire a precipitation data set that corrects for the underestimation of precipitation. Third, we varied the parameterisation settings of each model to determine the effect of parameterisation choice (Sect. ). Last, we implemented forcing biases (Sect. ) to evaluate the sensitivity of the models to the meteorological forcing uncertainties. The combination of sensitivity analysis to model parameterisations and meteorological forcing allowed the evaluation and comparison of the two models (Sect. ).

Model evaluation consists of comparing the model output of SD, SWE, and albedo with the corresponding observations. For the idealised case this consists of evaluating the RMSE and R2 between the modelled and the observed SD to acquire precipitation data that approach the correct mass balance. For the parameterisation uncertainty, this consists of evaluating the RMSE and R2 between the modelled and the observed albedo to select the best reference for each model (i.e. 40 for SNOWPACK and 12 for SnowModel). In this case, it is chosen to only compare between modelled and observed albedo, as this ensures the best possible net shortwave radiation term in the energy balance equation. The forcing uncertainty is evaluated by comparing the differences of end of snow season. Last, the differences in ablation processes of the parameterisations are shown.

The assimilated precipitation data sets markedly differ between SNOWPACK and SnowModel (blue lines, Fig. e and f). For clarity Fig.  only shows the results of the idealised simulations for the z0 value of 1 cm; the results for z0 of 1 cm and 1 mm are displayed in Sect. S2. For SNOWPACK, 8 out of 10 runs with z0=1 cm crashed, thus only two simulations are shown. The reason for these crashes has not been further investigated.

Assimilation of SD in SNOWPACK results in SWE that approximates the PSWE (Fig. ), leading to assimilated precipitation amounts of 2.55 to 3.02 times the observed precipitation and a good correspondence with the observed SD (i.e. RMSE between 9.2 and 11.5 cm and R2 between 0.90 and 0.93, calculated with the observed and simulated SD; Fig. a).

Assimilation of SWE in SnowModel only adjusts the precipitation between 22 and 27 June and between 7 and 12 August. The amount of precipitation is not adjusted at the beginning of the season; thus, the assimilated data by SnowModel still lead to an underestimation of the SD and SWE (Fig. b and d). The missing adjustment of the SWE is probably caused by SnowModel taking a maximum of 99 SWE observations; the observations do not exactly align with the precipitation events, which leads to correction factors of one (i.e. no change) to the precipitation data. The assimilated precipitation is approx. 1.6 times larger than the observed precipitation and the agreement between modelled and observed SD is better for SNOWPACK than for SnowModel (i.e. RMSE between 7.1 and 17.1 cm and R2 between 0.19 and 0.90 calculated with the observed and simulated SD; Fig. b).

Both models overestimate the SWE between mid-July and September when PSWE was given as input (red lines in Fig. c and d). This is likely caused by an overestimation of the PSWE at the end of June. Only small amounts of precipitation are observed at the precipitation gauge, but the observed SWE distinctly increases probably due to snow drift, as strong winds were also observed. A similar thing occurs at the end of September. The models markedly increase the amount of precipitation (between 97 and 137 mm w.e.) in the assimilation runs, but only small amounts of precipitation and strong winds were observed. This is related to a strong melt in September, not simulated by the model, along with models trying to get the SWE and SD to the observational levels. The strong melt in September is caused by a sudden decrease of the albedo (observations in Fig. e and f), as it is likely that the snow got covered with dust after some days with strong wind at the end of September, but the simulations overestimate the melt caused by this albedo decrease. Likewise, high wind speeds and a strong decrease of SWE and SD are observed mid-July, which is likely due to snow erosion that is not considered in our simulations. The overestimation of and the need for SWE as validation data are indications that the PSWE is not a valid precipitation data set for our simulations, but it is also unfeasible to select one of the assimilated precipitation sets by SNOWPACK as the amount of precipitation markedly increases at the end of September and we want to use SD as validation data.

Therefore, three different precipitation corrections depending on WS or on TA and WS were applied to the observed precipitation (see Sect. S3). Equation (12) from with WS corrected to gauge height using a logarithmic wind profile e.g. and a z0 of 0.01 m is used as precipitation data (Pcor) in the further study, as this correction approaches the PSWE and shows an increase in precipitation of 2.35 times the observed precipitation at the end of the season.

Evaluation of simulated SD and SWE based on various parameterisations shows that both models are in good agreement with observations (Fig. ), although they overestimate SWE at the beginning of the season (May/June). The correction of the precipitation with the equation from overestimates the precipitation in this period and also leads to an overestimation in the simulations.

For SNOWPACK, the spread of the simulated SD from the 40 different parameterisations (20 simulations for z0=1 mm and 20 for z0=1 cm) is the largest at the end of the snow season (i.e. October) (Fig. a). The date of snow-free surface is the earliest at 8 October and exceeds the simulated period (i.e. after 30 November), depending on parameterisation choice, and covers the observed date of snow removal (i.e. 16 October). The different SNOWPACK parameterisations (equations in Sect. S1) show a mean SD difference of 32 cm (which corresponds to 28.9 % of the total SD) between the minimum and maximum simulated SD (Fig. a), with a maximum of 127 cm observed at 27 June. For the SWE, this corresponds to a mean difference of 98.3 mm w.e. (i.e. 28.2 % of the total SWE) (Fig. c). The large modelled SD spread in May and June can be explained by the different density parameterisation choices as it is not apparent in the SWE simulations (Fig. a and c). The rapid decrease (3–8 cm d-1) of snow depth until July, caused by compaction of the snowpack, is simulated by the majority of fresh snow density parameterisations, while only one fresh snow density parameterisation models a more moderate compaction (i.e. the bold red line has a moderate slope, compared to the light red lines in Fig. a, until July). From July onward, the measured snow depth decreases 10 centimetres per 25 d, which is only simulated by the fresh density parameterisation that simulated moderate compaction before July. Snow density measurements were unavailable in 2017 and the observed snow density in Fig. g is calculated with SWE/SD. The observed snow density is only shown until the end of August, as the calculation led to unrealistic decreasing snow densities after August. This is likely caused by higher readings at the SD sensor than at the SWE sensor, as those sensors were placed on different sides of the meteorological tower or to a bias of the SWE sensor in the ablation season as explained by .

The albedo evaluation (Fig. e) and corresponding statistics (Sect. S4) highlight one parameterisation choice that outperforms all other parameterisations (i.e. RMSE of 0.09 (–) and R2 of 0.86 calculated with the observed and simulated albedo) in terms of snow compaction after snowfall events, end of snow season, and albedo evolution (Fig. e). Therefore this simulation with a z0 of 1 cm is selected as the reference simulation (represented in bold lines in Fig. ) for the forcing uncertainty simulations.

For SnowModel, the largest SD spread of the 12 ensembles (six for every z0; equations in Sect. S1) occurs at the end of the simulated snow season (i.e. August, September, and October) with complete snow removal between 21 October and 12 November (i.e. 22 d) (Fig. b). The mean SD difference between the parameterisations is 20 cm (i.e. 18 % of the total SD), with a maximum of 152 cm at the first snowfall event (12 May), while for SWE the mean difference is 57 mm (i.e. 19.2 % of the total SWE) with a maximum of 317 mm w.e. at 12 August (Fig. d).

Quantitative analysis (Sect. S4) shows best performance scores for the time-evolution albedo approach in combination with the reference snow density parameterisation and a z0 of 1 cm (RMSE of 0.150 (–) and R2 of 0.600). Therefore, these are used as the reference simulation (bold line in Fig. ).

Comparison of the SNOWPACK and SnowModel output shows similar SD variations attributed to snow density parameterisations that simulate low density snowfall with notable subsequent compaction (Fig. g and h). In reality, this happens at Tapado until June, followed by a different regime with denser fresh snow and less compaction. The biggest difference between the models, however, is the result of the albedo parameterisations. Where SnowModel relies on two albedo models based on TA and albedo ranges, SNOWPACK relies on empirical relations calibrated with measurements in Switzerland and not adapted to the arid Tapado climate. Nevertheless, the albedo of the reference run of SNOWPACK performs well in a semi-arid area. Last, the simulations by SnowModel all approximate the end of snow season within a period of 22 d, whereas the simulations at the end of season noticeably diverge for SNOWPACK. This is likely caused by TA being above the freezing point at the end of October, resulting in a fast melt simulated for all ensembles by SnowModel.

Ablation rates (Fig. ) show that sublimation is the dominant mode of mass loss in both models until September (i.e. cold period), followed by melt from September to the end of the season (i.e. end of November, and called the melting period). Note that for SNOWPACK, the first day of snow-free surface of the reference run is 11 October and for SnowModel is 27 October.

For SNOWPACK, the spread of the averaged sublimation rates corresponding to the ensemble runs from the first day of snow to 20 September have a minimum of 1.41 and a maximum of 2.96 mm w.e. d-1 (Fig. a). During the cold period, when no melt occurs, the sublimation amounts mainly depend on the z0, with sublimation rates ranging between 1.40 and 3.18 mm w.e. d-1, but this is mainly clustered according to the implemented z0. At the end of the season, the total sublimation ranges between 153 and 364 mm w.e. (corresponding to 36.2 % to 86.0 % of the total ablation, again strongly depending on the z0). During the melting period, the ensemble runs show a large spread of melt rates ranging between 0.97 to 17.7 mm w.e. d-1. The total amount of runoff is between 28.9 and 236 mm w.e. for SNOWPACK, and this model also simulates evaporation, which contributes between 2.5 % and 10.2 % of total ablation (Fig. a).

For SnowModel, sublimation differences between the parameterisations are similar (Fig. b) with average sublimation rates from the first day of snow to 20 September ranging between 1.27 and 2.79 mm w.e. d-1. At the end of the winter season the sublimation totals range between 154 and 342 mm w.e. (which corresponds to 36.4 % to 80.7 % of the total ablation). The runoff is between 81.7 and 269 mm w.e. A closer analysis of Fig. b shows that SnowModel's output clusters into four groups, where the grouping is determined by the albedo parameterisation and z0 with limited influence of fresh snow density parameterisations. The two lower clusters are linked to the z0 value of 1 mm. The differences between clusters for different z0 values increase as the difference in albedo between the parameterisations increase at the end of June.

While the ensemble parameterisation simulations do not lead to significant differences in the modelled end date of the snow season (i.e. difference of 22 d), the albedo parameterisation and z0 value directly impact the proportion of sublimation versus melt to the total ablation (Fig. b and d). During the cold period, simulations considering the lowest albedo and z0 of 1 cm (the reference simulation) lead to a higher sublimation rate (Fig. b). Indeed, a lower albedo increases the energy absorbed by the snowpack, and as the temperature is below the freezing point, this energy leads to an increase in the sublimation. A higher z0 enhances this process even more as this leads to a more negative latent heat flux. Second, the increase of net shortwave radiation also affects the physical properties of the snowpack resulting in an increase of compaction (Fig. b and h). The snow density of the snowpack is therefore higher, which directly affects the thermal conductivity of the upper snow layers . Surface temperature variation is directly linked to the latent heat flux and therefore to sublimation, explaining the different sublimation ratios simulated depending on the albedo parameterisations and z0 values.

In contrast to SnowModel, the albedo parameterisation in SNOWPACK does not affect the sublimation but noticeably influences the melting rate (Fig. c), which can be attributed to the more complex characteristics of this model. SNOWPACK allows refreezing and evaporation of melting snow within the snowpack, which can lead to a longer melt season, whereas calculated evaporation leads to a lower amount of runoff from melt. Also, SNOWPACK considers a more complex representation of snow physics, such as the grain size and microstructure, which directly impacts the albedo and can help to explain the wide diversity of melt simulations.

Our results show the importance of model parameterisations and model forcing over the snow model choice, despite the limited model options chosen for the ensemble approach, and the large differences in the two model complexities chosen in this study. This conclusion, found here in an arid environment, is in agreement with the studies performed in other alpine areas .

The representation of turbulent fluxes is an important variable to consider to simulate sublimation and in snow models this is commonly based on the bulk method; the Richardson number is often used, together with the Monin–Obukhov similarity theory, to evaluate the atmosphere stability e.g.. Here, only the Richardson number is used as both models offered this option and the uncertainty associated to the turbulent fluxes parameterisation is only considered by implementing two different z0 values, while it can have major implications in surface energy balance modelling e.g.. While the stability function cannot be compared between the two models chosen in this study, the sensitivity of SNOWPACK to the six possibilities available in the current version is low (i.e. max SD bias of a few centimetres; results not shown). In a study over Brewster Glacier in New Zealand, pointed out the importance of the stability functions to properly simulate the heat fluxes with low wind speed and large temperature gradients and also that the modelled latent heat fluxes were unaffected by the choice of exchange coefficient parameterisation. The present study takes place in a dry and windy environment without a large temperature gradient and this helps to explain the small differences observed related to the different atmospheric stability functions. The turbulent fluxes parameterisation is sensitive to the z0 value and observations, such as eddy covariance measurements, are essential to accurately parameterise the turbulent fluxes e.g..

Due to the absence of such measurements, the variability of this value over time e.g. and due to other values in the literature at other locations showing a wide variety (two orders of magnitude) of snow roughness length , it was decided to use two different values for z0 (1 mm and 1 cm). Similar sensitivity ranges for SNOWPACK and SnowModel were found (e.g. Fig. ), along with similar sublimation rates, but this directly depended on the value for z0. For both models, a z0 of 1 cm led to better simulations (Figs. , ), but as applied more often, this can also be seen as optimising parameter e.g.. In future work, the z0 can be evaluated with eddy covariance measurements.

The biggest differences between the models are found as the snow settles and therefore depends on the snow density parameterisation. The challenge in this study was that the snow settling showed two distinct regimes. From May to mid-June, high compaction rates were found, whereas the compaction afterwards was more moderate. SNOWPACK is able to model both moderate and high compaction, depending on the parameterisation chosen, but the mode of compaction remains the same over the season. SnowModel simulates high compaction rates for all parameterisations, which is correct for the start of the season but an overestimation after mid-June. These compaction rates implicate changes in the thermal conductivity of the snowpack and thus changes in the melting. The different snow density parameterisations in SNOWPACK are still being developed and improved e.g., but an improvement of snow density parameterisations in semi-arid regions shows a demand for snow density measurements, as deriving density from SWE/SD measurements is biased over direct density observations using manual measurements .

Subsequently, the albedo parameterisation appears to be an important parameter to be properly assessed (Figs. , ), as also reported by the studies performed in alpine regions . This can be surprising at first glance as in the semi-arid Andes the ablation is mainly driven by the sublimation and the albedo parameterisation is generally crucial to accurately simulate the melt. However, according to the results presented here, the two models agree with the larger sensitivity to the albedo parameterisation. The impact of parameterisation choice differs for the two models as the uncertainty is directly related to the difference in snow physical representation and the characteristics of the models. Indeed, the range of the ensemble approach simulated by SNOWPACK is higher than that simulated by SnowModel, which is directly related to both higher number of parameterisation possibilities for SNOWPACK and more complex physical representation of the processes.

Likewise, results presented here show that the main sensitivity remains in the forcing uncertainty, in agreement with previous studies . For instance, found that the models of different complexity (temperature-index models versus physical models) show similar ability to reproduce daily observed snowpack runoff, and concluded that forcing uncertainties are the greatest factor affecting model performance, rather than model parameterisations. However, as mentioned by , simulated SD and SWE are critically sensitive to the relative magnitude of errors in forcing. and also mentioned that precipitation bias (or correction of the undercatch of the precipitation gauge) was the most important factor, in agreement with the findings of our study.

Finally, pointed out that no universal “best” model exists and model performance directly depends on calibration of the models to the specific study site. Here, similar conclusions can be drawn for both alpine and semi-arid environments, namely that the choice of model structure and parameterisations, along with a specific calibration of the parameterisations for the study site, has a major impact on the performance.

The sensitivity study of the two models to the forcing is done by adding a bias to the meteorological variables with ranges derived from the literature. It was also possible to add random noise to the data, but this does not necessarily preserve the physical consistency and would lead to low sensitivity of the models (results not shown), as random noise counterbalances each other, which has also been investigated by . It would also have been possible to apply a random perturbation e.g. using a first-order auto-regressive model . However, the forcing bias does not affect the conclusion of the relative comparison of the two models, which only requires the exact same forcing as input to be relevant. For the same reason, the choice of method applied for the forcing correction (i.e. for precipitation) and reconstruction (i.e. for the TA and RH) would not affect the conclusions of the model comparison. However, due to the precipitation uncertainty related to measurements errors and also because the sensor locations may not be representative of the area, different ways to correct the precipitation data were proposed. and already outlined that the snow cover is spatially heterogeneous even at very small scales due to topographic and microclimatic effects on accumulation, redistribution, and ablation processes, introducing an uncertainty in validation data. We also show that in any case, due to (i) the question of the sensor location representativity of the area, (ii) the precipitation undercatch because of the wind, and (iii) the high sensitivity of models to precipitation uncertainty, this study highlights the complexity and necessity of accurately measuring precipitation. Additionally, possible corrections depend on the availability of observations, but this study was restricted to not using SWE and SD as forcing, as these parameters were needed as validation data. Therefore, we chose a precipitation correction that overestimates snowfall at the start of the season, but does not capture the increase of SD and SWE in mid-June, resulting in a good agreement between simulated and observed SWE from the beginning of July (e.g. Fig. ).

The ensemble approach with different parameterisations is built considering limited parameterisation options, contrary to other studies where a large number of physical options are considered e.g.. In our case, choosing snow models with different physical complexities limits the number of calibration possibilities, as the parameterisation of the same variables are chosen for the comparison. Thus, some parameterisations, such as the choice of atmospheric stability correction only available in SNOWPACK, were excluded and this model is calibrated following the same options found in SnowModel (Sect. ).

Testing different albedo parameterisations is chosen as (i) different options are possible in both models and (ii) previous studies concluded that the largest absolute uncertainties originate from the shortwave radiation and the albedo parameterisations e.g.. The sensitivity test to different fresh snow density parameterisations was also chosen as previous studies identified this parameterisation as a significant uncertainty in model calibration e.g.. Finally, energy balance models are known to be sensitive to z0, especially in cold and dry regions where sublimation is the main ablation process e.g.. However, due to this important sensitivity and the absence of measurements to properly calibrate this value, two values for z0 were implemented, but this still might underestimate the possible range of z0 values.

Otherwise, despite the choice of limiting the parameterisation options, SNOWPACK's sensitivity to model parameterisations is evaluated based on 40 simulations, whereas SnowModel's evaluation is based on only 12 simulations. However, the difference of the number of simulations does not impact the conclusion, as the width of the spread of different parameterisations was not quantitatively assessed.

Among the possible settings of the model, the snow transport option has not been activated, while the option is available in both models. However, due to the strong wind speed characteristics of the study area and Fig. , snow transport is expected to be considerable. Yet, snow transport estimation remains out of the scope of this study, which was focused on energy balance comparisons mainly to assess differences in sublimation rates. Also, in a study performed in the Pascua-Lama catchment, a region to the north of Tapado AWS, highlighted that the inclusion of SnowTran3D does not change the fact that the model is unable to capture the small-scale snow depth spatial variability (as captured by in situ snow depth sensors). Finally, snow transport in SNOWPACK can only be simulated in the three-dimensional domain with SD as forcing, which then could not be used as validation data. However, due to the importance and complexity of modelling snow transport, properly assessing its impact could be assessed in future work.