Comparing Measured Incoming Shortwave and Longwave Radiation on a Glacier Surface with Estimated Records from Satellite and Off-Glacier Observations: A Case Study for the Forni Glacier, Italy

: The development of methods for quantifying meltwater from glaciated areas is very important for better management of water resources and because of the strong impact of current and expected climate change on the Alpine cryosphere. Radiative ﬂuxes are the main melt-drivers, but they can generally not be derived from in situ measures because glaciers are usually located in remote areas where the number of meteorological stations is very low. For this reason, focusing, as a case study, on one of the few glaciers with a supraglacial automatic weather station (Forni Glacier), we investigated methods based on both satellite records and o (cid:11) -glacier surface observations to estimate incoming short- and long-wave radiation at the glacier surface (SW in and LW in ). Speciﬁcally, for SW in , we considered CM SAF SARAH satellite gridded surface solar irradiance ﬁelds and data modeled by cloud transmissivity parametrized from both CM SAF COMET satellite cloud fractional cover ﬁelds and daily temperature range observed at the closest o (cid:11) -glacier station. We then used the latter two data sources to derive LW in too. Finally, we used the estimated SW in and LW in records to assess the errors obtained when introducing estimated rather than measured incoming radiation data to quantify glacier melting by means of an energy balance model. Our results suggest that estimated SW in and LW in records derived from satellite measures are in better agreement with in situ observations than estimated SW in and LW in records parametrized from observations performed at the closest o (cid:11) -glacier station. Moreover, we ﬁnd that the former estimated records permit a signiﬁcantly better quantiﬁcation of glacier melting than the latter estimated ones.


Introduction
The global warming period temperature increase has been particularly strong in the Alpine region, which has recorded a significantly higher temperature trend than Earth's average one (see, e.g., [1]). The strong temperature trend, together with high vulnerability to climate change, has strongly enhanced the impact of global warming in high-elevation areas of this region that in the last decades have experienced relevant environmental changes. These changes are particularly strong in glacierized areas because glaciers have lost a relevant fraction of their volume with a wide range of impacts, including significant changes in the amount and in the seasonality of meltwater discharge [2]. Expected temperature increase for the next decades will further strengthen the current changes with dramatic impacts on the Alpine cryosphere [3].
outlines (compared to Landsat TM ones) (see [42]) and to cover a wide and complex region such as the Alps with a few scenes acquired within a few weeks or even days. Remote sensing also permitted glacier surface flow velocity to be mapped at the regional scale by using a multiple-sensor approach [43] to describe glacier dynamics and its changes. Moreover, satellite imagery has permitted the description of glacier darkening (see [44]), an ongoing phenomenon that is largely affecting glaciers worldwide and thus increasing ice melt. By analyzing remote sensing data, glacier surface conditions (i.e., supraglacial debris cover occurrence and depth) were described over large areas [34,45,46], and their recent changes, witnessing an actual darkening, were quantified [47]. Glacier darkening is also evident from the analysis of glacier albedo. Satellite images permitted the description of glacier albedo [48][49][50], which is diminishing in the Alps [51] due to increasing debris and black carbon deposition. Furthermore, remote sensing highly improved snow cover mapping, thus permitting researchers to describe snow depletion and to compute more accurately the water budget of a mountain catchment [52][53][54][55][56][57][58][59][60].
Widely used satellite data sets for Europe concerning the variables considered in this paper are the gridded surface solar irradiance fields SARAH-2.1 [61,62] and the corresponding cloud fractional cover fields COMET Ed. 1 [63,64] that are available among climate products from EUMETSAT Satellite Application Facility on Climate Monitoring (CM SAF-https://www.cmsaf.eu). One of the most interesting features of these products is that in EUMETSAT CM SAF, the generation of long-term data sets is pursued with the goal of obtaining data records suitable for the analysis of climate variability and potentially for the detection of climate trends. This is not an easy issue, especially for areas like Italy that have experienced relevant changes in the atmospheric transparency over the last decades [65].
In spite of their wide availability, satellite observations are not easy to use for the detection of cloudiness and solar radiation over high-elevation areas because snow coverage is not always correctly distinguished from clouds, resulting in an enhanced cloud optical depth and subsequently in an overestimation of cloudiness and an underestimation of surface solar irradiance, particularly under clear-sky conditions [61,66].
In this context, we focus, as a case study, on the Forni Glacier (Stelvio National Park, Italian Alps) where since September 2005 an on-glacier automatic weather station has been continuously running [49,[67][68][69], and we use the radiation data recorded at this site to (i) search for parametrizations that allow estimating cloud transmissivity at a glacier surface from meteorological data acquired in the area surrounding the glacier (i.e., at an off-glacier weather station) or from COMET cloud fractional cover fields, (ii) investigate the ability of these parametrized values to estimate the incoming shortwave and longwave radiation over the glacier surface (SW in and LW in ), and (iii) study the impact of introducing estimated incoming shortwave and longwave radiation in the application of an energy balance model applied to calculate daily glacier melt. For shortwave incoming radiation, we also test the benefits of using SARAH−2.1 gridded surface solar irradiance fields instead of estimated SW in .
The paper is organized into six sections. After the introduction (Section 1), Section 2 presents the study area and the data. In Section 3, we illustrate the methods for estimating incoming shortwave and longwave radiation and for quantifying glacier melt. The results of the analyses are reported in Section 4. In Section 5, we discuss our findings. Finally, we report the conclusions of the paper in Section 6.

Forni Glacier and the Meteorological Stations
Forni Glacier is one of the largest glaciers in Italy (ca. 11.34 km 2 , [70]) covering an elevation range from about 2600 to 3670 m a.s.l. It is located inside an extensive natural protected area (Stelvio National Park).
In September 2005, the first on-glacier meteorological station in Italy (AWS1 Forni; Figure 1) was set up at the lower sector of the eastern tongue of this glacier [6]. The WGS84 coordinates of AWS1 Forni were 46 •    AWS1 Forni is equipped with sensors for measuring air temperature (T gl ) and humidity (by means of a naturally ventilated shielded sensor), wind speed and direction, air pressure, the four components of the radiation budget (incoming and outgoing short-and long-wave radiation at the glacier surface-SW in-gl , SW out-gl , LW in-gl , LW out-gl ), liquid precipitation (by means of an unheated precipitation gauge), and snow depth (Campbell SR50 and Sommer USH8 sonic ranger sensors) (see also Senese et al. [6]). AWS Forni SPICE is equipped with a snow pillow and a barometer for measuring the snow water equivalent (SWE) (see also Senese et al. [70]). Both AWS1 Forni and AWS Forni SPICE are supported by four-leg stainless steel masts (5 and 6 m high, respectively) standing on the ice surface. The meteorological variables are sampled every 60 s, and the acquired data are averaged every 60 min (snow depth (Campbell SR50), wind speed and direction, and air pressure), every 30 min (air temperature, relative humidity, solar and infrared radiation, and liquid precipitation) or every 10 min (snow depth (Sommer USH8) and SWE). All data are recorded in a flash memory card, including the basic distribution parameters (minimum, mean, maximum, and standard deviation values).
In the Forni Glacier area, there is also a station located near the dam of the Frodolfo stream (46 • 25 12.64 N, 10 • 33 45.35 E, 2180 m a.s.l., Figure 1) at a distance of about 3 km from the on-glacier station. This off-glacier station is included in the meteorological network of Lombardy Environmental Agency (ARPA Lombardia), and it measures only air temperature (daily minimum, mean, and maximum values). Hourly temperature data are available from 2006 to 2009 and from June to August.

Incoming Shortwave Radiation Satellite Data
For incoming shortwave radiation satellite data (SW in-SARAH ), we used CM SAF Surface Solar Radiation Data Set, Heliosat, Edition 2.1 (SARAH 2.1) [62] based on the geostationary Meteosat satellite series. SARAH 2.1 data are available at daily resolution over the 1983−2017 period and they are provided on a regular 0.05 • × 0.05 • grid (at the Forni glacier, the extension of this grid cell is 3.8 km in the east-west direction and 5.6 km in the south-north one): we considered the closest (about 0.8 km) grid-point (46 • 24 00 N and 10 • 36 00 E, Figure 1) with respect to the AWS1 Forni station. As reported in the validation report, the SARAH 2.1 dataset has been compared with the Baseline Surface Radiation Network (BSRN) data showing a bias of 1.5 W m −2 and a mean absolute difference of 11.7 W m −2 (below the target accuracy value of 20 W m −2 and below the optimal accuracy of 12 W m −2 ). Moreover, an extensive analysis of temporal variability and trends in Europe was performed and discussed in detail by Pfeifroth et al. [61]. The comparison between the daily AWS1 Forni incoming shortwave radiation (SW in-gl ) and the corresponding data from SARAH (SW in-SARAH ) over the summer months (June to August) of the 2006-2009 period ( Figure 2A, Table 2) highlights a rather good agreement. The mean difference is 2.0 W m −2 , the mean absolute difference is 34.9 W m −2 , and the common variance is 73%, corresponding to a correlation index of 0.85. In order to allow a better comparison between the considered datasets, the bisector lines are also shown in the two panels.

Cloudiness Satellite Data
For cloudiness, we considered the data from the CM SAF Cloud Fractional Cover dataset from Meteosat First and Second Generation (COMET) [63,64]. COMET data are available at daily resolution over the 1991−2015 period and they are provided on a regular 0.05 • × 0.05 • grid: we considered the closest (about 3 km) grid-point (46 • 22 30.0 N and 10 • 34 30.0 E, Figure 1) with respect to the AWS1 Forni station.
COMET fractional cover data are expressed as the percentage of the sky covered by clouds, with values between 0 (clear sky) and 100 (overcast sky). As reported in the validation report [63], these data fulfilled the optimal accuracy and precision requirements (mean bias error of −0.2%, bias-removed root-mean-square error of 16.5%) when they were compared with 237 SYNOP reference sites. However, in order to evaluate their goodness over an area characterized by a complex orography like a glacier, we assessed their agreement with daily data from Bernina Pass (46 • Figure 1) and considering all days in the summer months (from June to August) of the 1991−2014 period, which is the one in common to the two datasets. It showed a bias-removed root-mean-square error of 0.16 and a common variance of 74%.

Methods
In this section, we first list the indicators we used to evaluate the errors of the adopted models. Then, we introduce cloud transmissivity (Section 3.2) and present the parametrizations we used to estimate this variable from daily temperature range data acquired at the off-glacier Frodolfo dam station (Section 3.3). Then, we present the methods we used to link cloud transmissivity to cloudiness (Section 3.4) and to estimate incoming shortwave (SW in ) and longwave (LW in ) radiation over the glacier surface (Section 3.5). Then, we present the energy balance model we applied to quantify the amount of melting (Section 3.6). Finally, we explain how we performed the comparison of glacier melt obtained from observed and estimated SW in and LW in records (Section 3.7).
MBE (the mean of the differences between estimated and measured values) highlights any systematic bias, while MAE (the mean of the absolute differences between estimated and measured values) gives evidence of the accuracy of the estimated values. RMSE (square root of the quadratic mean of the differences between estimated and measured values) is again a measure of the accuracy of the estimated values but is more sensitive to outliers. BRRMSE is calculated as RMSE, but the estimated values are corrected for bias before RMSE calculation. Finally, R 2 is the common variance (the correlation coefficient is the square root of the common variance) between the estimated and the measured values, and it shows how much of the variability of the measured values is reproduced by the estimated ones.

Cloud Transmissivity at AWS1 Forni
Cloud transmissivity (τ-comprised between 0-1) is a factor that reduces the potential SW in of a quantity, which depends on the amount and type of clouds [15,71,72]. A value of τ = 1 corresponds to a clear sky with no clouds, whereas τ = 0 means that no shortwave radiation reaches the surface at all. However, an overcast sky usually has τ > 0 [71,72], with different values for different cloud types. For example, Anslow et al. [72] used τ = 0.4 for completely cloudy conditions for South Cascade Glacier (Washington, DC, USA).
We derived daily τ (τ gl ) from the 2006−2012 AWS1 Forni daily mean SW in-gl dataset and following Senese et al. [17]: where SW in-CS is the potential clear-sky mean SW in for the considered day at the AWS1 Forni site (W m −2 ) calculated following the approach proposed by Senese et al. [17].

Cloud Transmissivity Parametrization from Daily Temperature Range
We tested different models from linear regression to models of enhancing complexity (see Table 1) to parametrize τ by means of the daily temperature range (difference between maximum and minimum daily temperature) acquired at the off-glacier Frodolfo dam station (∆T dam ). Specifically, we used the temperature measured at the off-glacier Frodolfo dam station instead of the temperature measured at the glacier surface because the latter one can be affected by the microconditions of the lowest air layers over the glacier. In fact, the low ice/snow temperature can cause, especially in summer, temperature inversions above the glacier, and melting conditions can affect the relative humidity values of the air over the glacier. Both phenomena (i.e., lower surface temperature and melting surface) do not influence the air conditions outside the glacier, while they can affect the conditions around the station. Table 1. Models adopted to test the parametrization of cloud transmissivity (τ) by means of the daily temperature range acquired at the off-glacier Frodolfo dam station (∆T dam ).

Model Equation
Linear We considered 2006 and 2008 (from June to August) for the calibration phase and 2007 and 2009 (from June to August) for the validation one. We evaluated the performance of the different models comparing the parametrized τ values with those from Equation (1) (τ gl ). The obtained results showed very similar performance of the different methods, with MBE and MAE respectively equal to 0.006 and 0.109 for the exponential method and 0.019 and 0.111 for the other methods. The common variance turned out to be 42% for all the methods, corresponding to a correlation index of 0.65. Considering the very similar results obtained with the different models, we decided to use the linear method for our analysis considering that increasing the complexity of the adopted method does not produce any significant difference in the results. The obtained relation between τ and ∆T dam is as follows:

Cloud Transmissivity and Cloudiness
We linked τ to n by means of the approach proposed by Sauberer [73] and Konzelmann et al. [74] using the following relation: This relation was found by Sauberer [73] and Konzelmann et al. [74] through the analysis of global radiation data from Austrian climate stations (Alps) and can be used also for other sites with similar climate conditions using the altitude of the considered point. In particular, if we consider the altitude of the AWS1 Forni site (2631 m a.s.l.), Equation (3) becomes τ = 1 − 0.24 n − 0.37 n 2 (4) or n = −0.12 + 0.12 2 Moreover, we also calibrated the following relation between τ and n using τ values obtained at AWS1 Forni (τ gl ) and n from satellite data (n COMET ) and focusing on 2006 and 2008 (from June to August) data: τ = (0.99 ± 0.04) − (0.41 ± 0.15) n − (0.08 ± 0.15)n 2 (6) or n = −0.41 + 0.41 2 + 4(0.08)(0.99 − τ) 2(0.08) The comparison with τ gl values, performed by means of 2007 and 2009 (from June to August) data, showed that the agreement is comparable for τ values obtained from Equations (4) and (6). Specifically, MBE values are 0.014 and 0.016, MAE values are 0.104 and 0.097 and common variances are 51% and 53% for the former and the latter equation, respectively.
Considering that the results are comparable (or slightly better for equation calibrated by means of COMET data), we will present the results obtained using Equations (6) and (7) in the remaining part of the paper, even if all the results have also been obtained using τ and n obtained from Equations (4) and (5).

Estimated Incoming Shortwave and Longwave Records
We used τ estimated by means of ∆T dam (Equation (2)) and τ estimated by means of n COMET (Equation (6)) in Equation (1) to get two derived records of incoming shortwave radiation (SW in-∆T and SW in-COMET , respectively) at AWS1 Forni.
We considered both n estimated by Equation (7) and n from satellite data (n COMET ) to get derived records of incoming longwave radiation (LW in-∆T and LW in-COMET , respectively) at this site. Specifically, we calculated LW in following the approach reported in Senese et al. [17]: LW in = ε CS 1 − n 2 + ε CL n 2 σT 4 gl (8) where ε CL is the emissivity for overcast sky (0.976) [75], σ is the Stephan-Boltzmann constant (5.67 × 10 −8 W m −2 K −4 ), and n is the cloudiness that can be obtained either from τ by applying Equation (7) (giving LW in-∆T ) or from COMET data (giving LW in-COMET ); ε CS is the emissivity for clear sky and is given by [74] ε CS = 0. 23 where RH gl is the relative humidity acquired by AWS1 Forni.

Glacier Melting
We applied the energy balance model to quantify the amount of melting. Specifically, according to Senese et al. [6] we used the following relation: where M EnBal is the snow/ice melt (kg m −2 or meters of water equivalent (m w.e.)), SW out is the reflected solar radiation, LW out is the longwave radiation emitted by the surface, SH and LE are the sensible and latent heat fluxes, respectively, and Lm is the latent heat of melting (3.34 × 10 5 J kg −1 ). SW out and LW out are measured by AWS1 Forni, and SH and LE are calculated by applying bulk aerodynamic formulas as reported by Senese et al. [6]. All the fluxes are defined as positive when directed towards the surface. Melting occurs as soon as the surface temperature is at 0 • C and the numerator is positive [6,77]. Senese et al. [6] compared the melt amount derived from the energy balance model to field measurements at a selection of ablation stakes located near AWS1 Forni. They reported an excellent agreement between the measured and the modeled cumulative melts (about 3% underestimation), supporting the usefulness of the energy balance computation in assessing the actual melt amount at this site.

Comparison of Glacier Melt Amount from Observed and Estimated SW in and LW in
We investigated how much the results of Equation (11) change when estimated values are used for incoming shortwave and longwave radiation instead than measured ones (SW in-gl and LW in-gl ). Specifically, we performed this analysis only for daily average values as the estimated shortwave and longwave radiation records are available at this resolution. We also used a shortwave incoming radiation record from satellite data (SW in-SARAH ) and checked the advantages and disadvantages of using it in Equation (11) instead of the parametrized SW in records.
The comparisons were performed (see Table 3) by first introducing parametrized or satellite values in only one of the two incoming radiation terms and then by introducing them in both the shortwave and the longwave terms. The agreement between the melting records obtained with observed and parametrized/satellite radiation was estimated according to the error indexes presented in Section 3.1 and considering as reference the daily melt record obtained by considering SW in-gl and LW in-gl in Equation (11). Table 2 Table 2). The common variance of measured and estimated SW in values is 66% for SW in-COMET and 51% for SW in-∆T , while corresponding values for LW in are 76% for LW in-COMET and 51% for LW in-∆T , respectively ( Table 2). The comparison of LW in-COMET and LW in-gl is also shown in Figure 2b. Overall, statistical indicators ( Table 2) show better performance for incoming radiation values obtained from cloudiness satellite data than for corresponding values obtained from daily temperature range measured at the closest off-glacier station. However, SW in-COMET has significantly lower performance than SW in-SARAH when it is compared with SW in-gl . Table 2. Mean bias error (MBE), mean absolute error (MAE), root mean square error (RMSE), bias removed root mean square error (BRRMSE), and common variance (R 2 ) obtained comparing estimated daily shortwave incoming radiation (SW in-∆T and SW in-COMET ) and longwave incoming radiation (LW in-∆T and LW in-COMET ) values with corresponding values measured at AWS1 Forni (SW in-gl and LW in-gl ). For comparison, we also report the same results presented in Section 2 for the comparison between SW in-gl and SW in-SARAH .  Table 3 shows the main results obtained comparing the values from Equation (11) applied using different combinations of estimated incoming radiation data (SW in-∆T , SW in-COMET , SW in-SARAH , LW in-∆T , and LW in-COMET ) with those from the same equation applied using measured incoming radiation data (SW in-gl and LW in-gl ). Table 3. MBE, MAE, RMSE, BRRMSE, and R 2 obtained comparing daily melt from Equation (11)  These results highlight that parametrizing LW in introduces a smaller error in the modeled melting than parametrizing SW in . In fact, when parametrizing LW in only, the explained variance with M(SW in-gl ,LW in-gl ) is 98% when the parametrization is performed by means of cloudiness satellite data (M(SW in-gl ,LW in-COMET )) and 96% when it is performed by means of daily temperature range data (M(SW in-gl ,LW in-∆T )). In both situations, the modeled melting is underestimated with respect to M(SW in-gl ,LW in-gl ), showing an MBE of about −0.002 m w.e. per day. On the contrary, when parametrizing SW in only, the modeled melting shows a much lower explained variance with M(SW in-gl ,LW in-gl ). Specifically, the explained variance with M(SW in-gl ,LW in-gl ) turns out to be 75% if satellite solar radiation data are used (M(SW in-SARAH ,LW in-gl )), while it reduces to 58% and 44% if SW in is obtained from cloudiness satellite data (M(SW in-COMET ,LW in-gl )) and daily temperature range data (M(SW in-∆T ,LW in-gl )), respectively. Parametrizing SW in only, the resulting MBE is always positive and equal to 0.001 m w.e. per day in the first case (M(SW in-SARAH ,LW in-gl )) and 0.003 m. w.e. per day for the other two cases (M(SW in-COMET ,LW in-gl ) and M(SW in-∆T ,LW in-gl )).

MBE
Considering the case in which neither SW in-gl nor LW in-gl are used in Equation (11), the best result is obtained when SW in is obtained from satellite solar radiation and LW in is parametrized by means of cloudiness satellite data (M(SW in-SARAH ,LW in-COMET )). In this case, the common variance with M(SW in-gl ,LW in-gl ) turns out to be 73%, corresponding to a correlation index of 0.85. Using only cloudiness satellite data, the common variance of the modeled melting (M(SW in-COMET ,LW in-COMET )) with M(SW in-gl ,LW in-gl ) reduces to 62% (corresponding to a correlation index of 0.79), and when using only daily temperature range data it reduces to 55% (corresponding to a correlation index of 0.74).
The MBE values for all the situations range between 0.000 and 0.001 m w.e. per day. Figure 3 shows the comparison of the progressive cumulative daily melting (m w.e.) curves for the four years of the 2006-2009 period obtained from M(SW in-SARAH ,LW in-COMET ) and M(SW in-gl ,LW in-gl ). The figure gives evidence that the agreement is good not only for the seasonal cumulated values but also for the single days. The days with the greatest disagreement are those which present high albedo values (due to fresh snow): they are probably interpreted as cloudy days by satellite measures. These periods are most evident in the first days of the June-August period when the glacier at the AWS1 Forni site is often covered by snow.

Discussion
The radiation record best fitting with measured short-wave incoming radiation values is indeed that of SARAH 2.1, which shows the lowest MBE and MAE (2.0 and 34.9 W m −2 , respectively) and the highest common variance (73%). However, the very low bias we find cannot be generalized trivially to other glacier sites, because both ground-based and satellite radiation measures can be significantly biased in complex orography contexts. In fact, on one hand, ground-based measures can be underestimated by shading or overestimated by reflected radiation from surrounding snow-covered surfaces; on the other hand, satellite measures can be underestimated due to high albedo of snow-covered ground being incorrectly interpreted as cloudiness [66]. These issues are fortunately not so relevant for the AWS1 Forni site because the station exposure ensures limited shading in summer, and fresh snow events that cause high albedo over a relevant fraction of the SARAH grid-cell are not frequent. However, such problems can make a comparison between ground-based and satellite solar radiation measures in complex orographic contexts very problematic.
Unfortunately, for LW in SARAH 2.1, data are available only at monthly resolution, thus not permitting the same comparison. However, satellite data are also found to be the best solution for modeling LW in when COMET cloudiness data are used compared to ∆T dam . Therefore, our results suggest that satellite input data show better performance compared to surface observations from a close off-glacier site for the estimation of on-glacier incoming radiation. The good performance of on-glacier incoming radiation data obtained by means of satellite records is also evident when they are used in Equation (11) instead of on-glacier incoming radiation measures: in this case, in fact, the use of estimated radiation values does not introduce any bias in the daily melt record, and MAE and RMSE correspond to 8 and 10 mm w.e. per day, respectively.
Interestingly, parametrizing LW in only introduces a slight underestimation of the estimated melt, whereas parametrizing SW in only involves a slight overestimation of it. In addition, parametrizing LW in only entails much higher common variance than parametrizing SW in only when the melt record is compared with the one obtained using measured incoming radiation data in Equation (11).

Conclusions
In this paper, focusing on one of the few glaciers with a supraglacial automatic meteorological station (Forni Glacier), we have investigated several methods of estimating incoming short-and long-wave radiation at a glacier surface by means of satellite records and/or off-glacier surface observations. Moreover, we have compared the daily melt records for four summer seasons (2006-2009) obtained when incoming estimated radiation data are used in an energy balance model with those obtained from the same model when correspondent on-glacier measured data are used.
The analyses have highlighted that the use of satellite data gives indeed much better estimations of on-glacier short-and long-wave incoming radiation that the parametrization of off-glacier surface observations. Moreover, as the reliability of the results of the energy balance model depends on the input data, satellite records also give better results for the estimation of glacier melt, suggesting that satellite data should be preferred over off-glacier surface observations whenever on-glacier measured radiative fluxes are not available.
The results we found for the Forni glacier cannot be generalized trivially to other glacier sites, because both satellite data and ground-based measures can be significantly biased in complex orography contexts. The former can in fact be influenced by high albedo of snow-covered ground being incorrectly interpreted as cloudiness, whereas the latter can be affected by shading and/or by reflected radiation from surrounding snow-covered surfaces. Such problems can make a comparison between ground-based and satellite solar radiation measures in complex orographic contexts very problematic.
In spite of these potential problems, the case study discussed in this paper highlights that satellite observations are a very important resource for better monitoring and modeling of glacier melt processes; they will become even more important in the future as the availability and quality of these observations are becoming more relevant every day.
An example where satellite data can represent a precious resource is the Central Karakoram National Park (CKNP, Pakistan) where about 700 glaciers are located, covering an area of about 4600 km 2 . Previous studies estimated the fresh water derived from the CKNP glaciers by applying an enhanced T-index model, which is easier when compared to the energy balance one [78,79]. Taking into account the methodology proposed in this paper could lead to more reliable SW in and LW in modeling and thus to more accurate meltwater quantification. Another example is represented by a hydrology study focused upon the Maipo River in Chile [80], a semi-arid area with mostly dry summer and rain in winter and where snow and glacier melt accounts for up to 70-80% of summer runoff. In this case, introducing SW in and LW in modeled by means of the methodology proposed in this paper could also facilitate a more reliable quantification of snow/ice melting. The Hindu Kush and Himalayan (HKH) chain is a final example of areas where remote sensing can play a crucial role in providing data to compute ice-and snowmelt. This area is the origin of 10 major river basins and encompasses over 4.2 million km 2 area [81]. The HKH area and the Tien Shan mountains form the largest area of permanent ice cover outside of the North and South Poles (hence the occasional reference to the HKH as the "Third Pole"). For this area, the methodology proposed in this paper could also lead to more reliable modeling of incoming radiation and thus to more accurate quantification of ice-and snowmelt.
This work has explored parameterizations of radiative fluxes as a crucial component of the summer glacier energy balance. In the future, it might be interesting to investigate such fluxes for the whole year because snowmelt processes at the glacier surface also occur before June [77]. Detecting the occurrence of snowmelt is important, for instance, in studying snow avalanches [82] or permafrost phenomena [83]. Moreover, the correct assessment of snow ablation in addition to ice ablation is also fundamental in studies aimed at computing the hydrological budget or the glacier mass balance [4].