Interactive comment on “ Air temperature variability over three glaciers in the Ortles-Cevedale ( Italian Alps ) : effects of glacier disintegration , intercomparison of calculation methods , and impacts on mass balance modeling ”

The authors present a new dataset from several high-elevation weather stations installed during summer 2010 and summer 2011 to study the air temperature distribution over three glaciers in the Italian Alps. This work aims to provide a comparison of different methods for calculating on-glacier temperature from off glacier data. The methods are commonly applied by mass balance models forced with off-glacier data and the pa-


Introduction and background
Air temperature exerts a crucial control on the energy and mass exchanges occurring at the glacier surface.It regulates the accumulation processes via the snowfall limit and the snowpack metamorphism (which affect redistribution phenomena), and regulates Introduction

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Full the ablation processes via turbulent fluxes and longwave radiation.It is also closely related to important feedbacks such as albedo, the mass balance-elevation feedback, and the glacier cooling effect, which changes as glaciers adjust their size in response to climatic fluctuations (Khodakov, 1975;Klok and Oerlemans, 2004;Paul et al., 2005;Raymond and Neumann, 2005;Haeberli et al., 2007;Fischer, 2010;Paul, 2010;Carturan et al., 2013).Distributed models of different complexity have been proposed for calculating the mass balance of glaciers under different climatic scenarios at a variety of spatial scales and with different purposes.The current concern about sea level rise and future availability of water resources stored in glaciers, under projected global warming scenarios, has led to increased efforts to develop models able to account for (i) direct effects of climate change, and (ii) reinforcing mechanisms which control glacier decay (Hock, 2005;Barry, 2006).
These models rely on accurate spatial calculation of input data, in particular air temperature, which affects not only their final performance but also the calibration of parameters and model generalizability.Indeed, wrong temperature estimates lead to wrong calibration and/or distortion of parameters, possibly hampering the applicability of models to ungauged catchments, despite the good knowledge achieved for individual processes (Savenije, 2001;Sivapalan, 2006).Charbonneau et al. (1981), for example, highlighted that issues in extrapolating meteorological input data are much more crucial than the possible choice between different approaches for modeling snow yields from a well-equipped catchment in the French Alps.Similarly, intercomparison projects of runoff models by the World Meteorological Organization (e.g.WMO, 1986) revealed that simple models provided comparable results to more sophisticated models, given the difficulties of assigning proper model parameters and meteorological input data to each catchment element.Machguth et al. (2008), analyzing model uncertainty with Monte Carlo simulations at one point on the tongue of Morteratsch Glacier in Switzerland, concluded that the output of well-calibrated models, when applied to extrapolate in time and space, is subject Introduction

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Full to considerable uncertainties due to the quality of input data.According to Carturan et al. (2012a), who compared three melt algorithms in a six-year application of an enhanced temperature-index model over two Italian glaciers, uncertainties in extrapolating temperature measurements from off-site data partly mask the peculiar behavior of each algorithm and do not allow definitive conclusions to be drawn.
Two main issues affect the correct estimation of air temperature distribution over glacial surfaces: (i) the absence of on-site weather stations in most operational model applications, and (ii) the development of a katabatic boundary layer (KBL) over the typically inclined glacier surfaces (van den Broeke, 1997).Several experiments with automatic weather stations deployed over glaciers demonstrated that general assumptions in extrapolating air temperature, based on the application of fixed lapse rates which account for the linear dependency of ambient (i.e.off-glacier) temperature on altitude, have serious limitations (e.g.Greuell et al., 1997;Strasser et al., 2004;Petersen and Pellicciotti, 2011).
In particular, these assumptions do not apply when katabatic flows and the KBL form, that is, during the ablation season on melting mid-latitude glacial surfaces, when the ambient temperature is higher than the surface temperature which cannot exceed 0 • C. Katabatic winds are gravity winds originated by the cooling of the near-surface air layers, resulting in density gradients which force a downward movement of the air under the effect of gravity.The two main processes affecting the temperature of the air during this downslope movement are the cooling due to the exchange of sensible heat and the adiabatic heating.The interplay of these processes has a twofold effect, consisting in lower on-glacier temperatures (the so-called glacier cooling effect), and lower temperature variability (the so-called glacier damping effect, also referred to as reduced climate sensitivity), compared to ambient conditions (Braithwaite, 1980;Greuell and Böhm, 1998;Braithwaite et al., 2002;Gardner et al., 2009).As a result, on-glacier lapse rates generally differ from average environmental lapse rates (i.e.−0.0065 • C m −1 ).Cooling and damping effects are not homogeneous over glacial surfaces, and mainly depend on the size and geometric characteristics, in particular the slope, of single glaciers, and Introduction

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Full on the specific position along the glacier.Generally, they are directly related to the size of glaciers and the fetch distance along the flowline, and inversely related to the slope of glaciers.The latest controls the prevalence of the cooling due to turbulent exchanges over the adiabatic heating of air forced to move downward by katabatic winds.Few methods have been proposed in the literature to model these processes, mainly due to the scarcity of glaciers instrumented for distributed measurements of air temperature.Among the first authors who measured the glacier cooling effect, defined as the temperature difference between an on-glacier and an off-glacier site with the same altitude, we can cite Schytt (1955) and Eriksson (1958), who detected temperature depressions ranging from 1.1 to 2.2 • C on Storglaciären (Sweden) and 3 to 4 • C on Skagastøl Glacier (Norway), respectively.Havens (1964) measured an average cooling effect ranging from 1.5 to 2.7 • C at a weather station located 1 km up-glacier from the terminus of White Glacier (Canada), recognizing maximum values during warm and sunny weather and minimum values during overcast and unsettled weather.
To our knowledge, the first attempt to parameterize the mean summer cooling effect at the firn line altitude was made by Khodakov (1975), who proposed a relationship with glacier length, based on temperature data obtained from mountain glaciers and ice sheets.Analyzing direct observations from glaciers in Caucasus, Pamir, Scandinavia, Thien Shan, and Altay, Davidovich and Ananicheva (1996) provided a simple relationship for calculating the mean summer temperature at the equilibrium line altitude (ELA) in function of the mean off-glacier summer temperature at the same altitude.The same authors suggested that the cooling effect is maximal at the ELA and decreases towards both the terminus and up-glacier (see details in Sect.3.4).
The first comprehensive glacio-meteorological experiment providing distributed temperature measurements was carried out in summer 1994 on Pasterze Glacier, Austria, and comprised five automatic weather stations (AWS) placed along a flowline.From this experiment, Greuell and Böhm (1998) developed a thermodynamic model for calculating air temperature in function of slope and distance along the flowline, accounting for sensible heat exchanges and adiabatic heating.Braithwaite et al. (2002) Introduction

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Full used an empirical approach and a formulation derived from data gathered in two Canadian Arctic glaciers (Sverdrup and White), similar to that proposed by Davidovich and Ananicheva (1996) but applied to monthly temperatures.Shea and Moore (2010) suggested empirical relationships based on piecewise linear regressions of on-glacier vs. ambient temperatures collected in British Columbia (Canada) between 2006 and 2008, for calculating (i) the threshold temperature triggering KBL development, and (ii) the glacier damping effect, as a function of elevation and flow path length (i.e. the "average flow distance to a given point starting from an upslope limit or ridge").
At present these methods have rarely been used by other authors, and they have not been compared using independent test sites.Petersen et al. (2013) tested the Greuell and Böhm (1998) model using a dataset of air temperature measurements from Haut Glacier d'Arolla, Switzerland, concluding that results of spatial extrapolations along the glacier are only a little better than using a constant linear lapse rate calculated between on-glacier data points.
The transferability of the proposed methods remains to be tested.In addition, it should be noted that many of them have been developed using temperature data collected from medium-to large-sized glaciers.As the glacier cooling effect and the damping effect depend on the size of glaciers, it is opportune to investigate the thermal effects of smaller ice bodies (< 0.5 km 2 ), which are widespread and increasing in number in mid-latitude mountain regions as a result of glacier shrinking and fragmentation.
In this work we present the results of a glacio-meteorological experiment, carried out in summer 2010 and 2011, deploying several automatic weather stations over three neighboring glaciers in the Ortles-Cevedale mountain group (Italian Alps).The study was focused on the variability of air temperature over the three glaciers, which differ in size, geometric characteristics, and reaction to climatic changes (Carturan et al., 2014).In this paper, we analyze the temporal and spatial behavior of air temperature and glacier cooling effect in the study area, testing different methods for calculating on-glacier temperatures from off-site data and evaluating their impact in mass balance simulations using an enhanced temperature-index model.Introduction

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Study area
The investigated glaciers are located in the Alta Val de la Mare (AVDM), Eastern Italian Alps (Fig. 1).This 36 km 2 experimental watershed is the subject of detailed studies concerning the impacts of climate change on the cryosphere and hydrology.The area has previously been selected for studying the behavior of meteorological variables at high altitude (Carturan et al., 2012b) and for developing an enhanced temperatureindex glacier mass balance model (Carturan et al., 2012a tion area and exhibit down-wasting and fragmentation in smaller units (Carturan et al., 2013), while La Mare Glacier still has an accumulation area and shows "active" retreat (Zanon, 1982;Small, 1995;Carturan et al., 2009).Long-term monitoring programs started in 1967 on Careser and in 2003 on La Mare.In the last 10 years, the glaciers have been the subject of investigations on snow accumulation, snow and ice ablation, point energy balance, and runoff generation (Carturan, 2010).Introduction

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Experimental setup
An automatic weather station (AWS) has been operating since July 2007 on the ablation area of La Mare Glacier (2973 m a.s.l.), measuring air temperature and relative humidity, wind speed and direction, incoming and outgoing shortwave and longwave radiation, and snow depth.The thermo-hygrometric probe is housed in a ventilated radiation shield.Data are sampled every 60 s, with 15 min means being stored in a Campbell Scientific CR1000 datalogger; the AWS is powered by a 25 W solar panel.Data were periodically downloaded with a portable laptop until July 2011.Since August 2011, a satellite modem has automatically transmitted data at three-day intervals (Abbate et al., 2013).On 3 July 2010 three Vantage Pro Plus (VPP) weather stations, manufactured by Davis Instruments, were placed along a longitudinal profile on La Mare Glacier at elevations ranging from 2709 m, close to the terminus, to 3438 m, near to the upper divide.Davis VPP stations are low-cost, commercial weather stations, characterized by a compact design and low weight, and can be moved rather easily along glaciers by few persons.Their thermo-hygrometric probe is shielded by a ventilated screen, which is important for air temperature measurements in high-radiation and/or low-wind speed conditions on glaciers (Georges and Kaser, 2002).Hourly mean data are stored in a Davis datalogger.During the experiment, the data were downloaded with a portable laptop every two weeks.The three VPP were removed on 23 September 2010.
On 7 July 2011 four VPP stations were deployed, two on Careser Glacier and two on La Mare Glacier.One weather station was re-positioned at 3438 m on La Mare Glacier because instrumentation failure occurred at that place in 2010, due to lightning damage.The other three weather stations were placed in areas where systematic errors in mass balance simulations were recognized by Carturan et al. (2012a), who applied a mass balance model using the standard environmental lapse rate for extrapolating air temperature from an off-glacier weather station, as commonly used in most model Introduction

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Full applications where on-glacier data are not available.The four VPP were removed on 12 September 2011.Table 1 reports the configuration of the weather stations operated on Careser and La Mare glaciers, whose location is shown in Fig. 1.Four off-glacier weather stations (Table 1) were also used in this study for the calculation of the glacier cooling effect in comparison to ambient temperature, and for testing various methods of calculation of on-glacier temperatures from off-site data.Two of them are part of the regional weather station networks (Bel_3328, at Cima Beltovo, 3328 m a.s.l.; Cog_1202, at Cogolo Pont, 1202 m a.s.l., Fig. 1).The other two weather stations consist of Hobo Pro dataloggers (Onset Computer Corporation) installed at Careser diga (Car_2607, at 2607 m a.s.l.) and close to Careser Glacier (Car_3051, at 3051 m a.s.l.).All these stations are far enough from the thermal influence of glaciers (minimum distance of 300 m from Car_3051 to the margin of Careser Glacier), and equipped with temperature probes housed in naturally ventilated radiation shields.Possible issues related to the use of different types of temperature sensors and radiation shields are addressed in the following section.

Data processing and accuracy assessment
For our analyses, hourly means were calculated from sub-hourly meteorological data.After being synchronized with local solar time, the data were checked for possible gaps, outliers, and inhomogeneities.The major gap concerned a few days in summer 2011 for the precipitation data at Careser diga, which were filled using the manual observations recorded by the personnel of the local hydropower company.Other gaps of 1-2 h occurred during the maintenance of weather stations, and were filled by linear interpolation.
The spatial density and type of weather stations used in this study were decided based on (i) the pre-existing network of regional AWSs and (ii) the logistic constraints affecting the access to the glaciers and limiting the number of research-grade AWSs which could be deployed.These limitations are common in mountain regions, and im-Introduction

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Full posed comparable or even lower densities of AWSs, as well as the use of different types of sensors with different radiation shields, in most similar studies on glaciers (e.g.Shea and Moore, 2010;Petersen and Pellicciotti, 2011;Petersen et al., 2013).
Intercomparison tests have been carried out in order to assess the impact of using different sensors and radiation shields for this study.The four VPP weather stations were run for some days within a 10 m radius, both before and after the glaciometeorological experiment, confirming the almost identical readings of air temperature, wind speed, and wind direction.Mean differences in air temperature data during the tests were lower than 0.20 • C (maximum SD = 0.16 • C).For comparison purposes, one VPP was run close to the AWS of La Mare Glacier in summer 2009, revealing mean differences in air temperature readings of 0.10 • C (SD = 0.12 • C).A further comparison was carried out in the summers of 2007 and 2008, running a VPP close to the Hobo Pro datalogger and close to a temperature sensor of the regional weather service installed at Careser diga.These two instruments, which have natural ventilation systems, showed mean differences of 0.10 respectively, compared to the aspirated VPP.Based on these results, no corrections were applied to the measured air temperatures.

Analysis of field data
The meteorological data collected by the weather stations were firstly analyzed calculating descriptive statistics for each of the two summers 2010 and 2011 and focusing on vertical lapse rates.Afterwards, the data were analyzed at hourly resolution focusing on the calculation of ambient (i.e.off-glacier) temperature, which is crucial for estimating on-glacier near-surface temperatures, and is required by all methods proposed in the literature for this purpose.Moreover, the correct estimation of the ambient temperature is an essential prerequisite for quantifying the site-specific cooling effect on glaciers, which is defined as "the difference between screen-level temperatures over glaciers compared to equivalent-altitude temperatures in the free atmosphere" (Braithwaite, 1980).Different combinations of lapse rates (i.e.fixed standard or hourly-variable Introduction

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Full obtained by linear regression of temperature vs. elevation) and subsets of weather stations were tested.
The spatial and temporal variability of the cooling effect was then investigated, plotting the average diurnal cycle of the cooling effect vs. average cycles of wind speed and direction, and drawing charts of the daily average cooling effect vs. daily temperature and precipitation recorded at Careser diga, in order to assess the role of different weather types in the glacial temperature regimes.

Calculation of on-glacier temperature from off-site data
The measured on-glacier temperatures served for testing five methods proposed in the literature for calculating the air temperature distribution over glacierized surfaces.The first three methods were only useable for mean summer calculations, while the Shea and Moore (2010) and Greuell and Böhm (1998) (from now on "S&M" and "G&B", respectively) methods could be used also for hourly temperature calculations, as they take into account the temporal variability of the cooling effect.
The first method (Khodakov, 1975) is expressed by the following: where ∆T ( • C) is the mean summer cooling effect at the firn line and L (km) is the "characteristic size" of the glacier, defined as "the distance between the ice divide and the start of the narrow tongue" of a mountain glacier.
The second method (Davidovich and Ananicheva, 1996) recommends the following equation: where T g ( • C) is the on-glacier mean summer temperature at the ELA and T ng is the off-glacier mean summer temperature ( • C) at the same elevation.The cooling effect is linearly reduced to 0.2 • C at the glacier terminus and to 0 Full A similar formulation was proposed by Braithwaite et al. (2002): where T Glacier and T Land ( • C) are monthly temperatures at the same elevation, the first on-glacier and the second off-glacier.S&M suggested the use of a piecewise regression model: where ) is the on-glacier temperature for site x at time t, T * ( • C) represents a threshold ambient temperature for KBL effects on T g , T 1 ( • C) is the corresponding on-glacier threshold temperature, k 2 (k 1 ) is the so called sensitivity of on-glacier temperature to ambient temperature (T a , • C) changes when T a is above (below) T * .Empirical transfer functions were obtained by S&M, relating the fitted coefficients (T * , k 1 and k 2 ) for each weather station used in their work to topographic attributes extracted from a digital elevation model (DEM): where β i are the coefficients of the transfer functions, Z (m) is the elevation, and FPL (m) is the flow path length, defined as "the average flow distance to a given point starting from an upslope summit or ridge" (Shea and Moore, 2010).T 1 is calculated as

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Full The G&B model assumes the presence of a katabatic wind, and therefore it applies when the ambient temperature is higher than the surface temperature.In these conditions the potential temperature Θ ( • C) at the distance x along the flowline (x = 0 at the top of the flowline) is calculated as: with where T 0 ( • C) is the temperature at x = 0, T eq ( • C) is defined as the "equilibrium temperature", x 0 and z 0 (m) are the location and elevation where the air enters the glacierwind layer, T cs ( where z(x) is the surface profile of the glacier.For all the described methods, the original formulations and parameters were tested unchanged against our experimental data.Possible modifications were evaluated for the S&M and G&B methods, as detailed in Sect. 4. The efficiency was evaluated by Introduction

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Full means of three different statistics: (i) the mean error (ME), (ii) the root mean square error (RMSE), and (iii) the efficiency criterion by Nash and Sutcliffe (N&S, 1970).The topographic information required to apply these methods was extracted from a 2 m×2 m DEM surveyed by LiDAR in late summer of 2006.

Mass balance modeling
The impact that the calculation of on-glacier temperatures according to different methods has on mass balance modelling was assessed using EISModel (Cazorzi and Dalla Fontana, 1996), which was already applied to Careser and La Mare glaciers by Carturan et al. (2012a).EISModel employs an enhanced temperature-index approach for computing melt, using the clear-sky shortwave radiation computed from the DEM as a distributed morpho-energetic index.Three melt algorithms (multiplicative, additive, and extended) have been implemented and can be used alternatively in EISModel.
In the present work we use the additive melt algorithm, which explicitly separates the thermal and radiative components: where TMF and RMF are empirical coefficients called the Temperature Melt Factor (mm h −1 • C −1 ) and the Radiation Melt Factor (mm h −1 W −1 m 2 ), T X ,t ( • C) is the air temperature at pixel X in hour t, CSR X ,t (W m −2 ) is the clear sky shortwave radiation and α X ,t is the surface albedo (spatially variable for ice and spatially and temporally variable for snow).calculated temperature from Careser diga via the standard ambient lapse rate (−6.5 • C km −1 ), (iii) calculated temperature according to the S&M method, and (iv) calculated temperature according to the G&B method.Option (ii) is commonly used in the absence of temperature data from glaciers (e.g.Gardner and Sharp, 2009;Michlmayr et al., 2008;Nolin et al., 2010).

Seasonal characteristics of temperature data
A close dependency on altitude has been detected for mean summer air temperature, both outside the glaciers and, remarkably, over them (Table 2, Fig. 2).Because of thermal inversions occurring at the lowermost weather station (Cog_1202) during the night and early morning, the vertical lapse rate was much higher above Car_2607 (−8.0 . At a given altitude, the on-glacier air temperature was systematically lower than ambient temperature, the difference decreasing with altitude.Lapse rates were also lower on the glaciers (−7.2 • C km −1 in 2010 and −6.7 • C km −1 in 2011), compared to high-altitude off-glacier weather stations, and close to the standard ambient lapse rate (−6.5 • C km −1 ).Much lower on-glacier lapse rates and fewer dependency of air temperature on elevation were found by earlier works (e.g.Greuell and Böhm, 1998;Strasser et al., 2004;Petersen et al., 2013).The average daily temperature range and the average SD are largest at the valley floor and both decrease with altitude, reaching their minima over the glaciers as previously reported, for example, by Oerlemans (2001).Hourly temperatures among different weather stations were highly correlated (r > 0.9, significant at the 0.001 level), with the remarkable exception of Cog_1202, at the valley floor, whose correlation with the other weather stations ranged from 0.65 to 0.75, peaking at 0.84 with Car_2607.Introduction

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Ambient temperature calculation
For the calculation of ambient temperature at the altitude of glaciers, which is crucial for the quantification of the glacier cooling effect, we tested the following methods: (i) use of a fixed standard ambient lapse rate (−6.5 • C km −1 ), (ii) use of a fixed calibrated lapse rate (seasonal mean value), and (iii) use of an hourly-variable lapse rate.Methods (ii) and (iii) were implemented using different combinations of off-glacier weather stations, calculating linear regressions of hourly temperature vs. altitude.The methods were tested removing alternatively Car_3051 or Bel_3328 from linear regressions and using them for validation.The results, displayed in Table 3, show that regardless of the method used, the inclusion of the lowermost weather station in linear regressions gives poorer results.At Car_3051, the method (iii) applied to Car_2607 and Bel_3328 works best, indicating that in our case hourly variable lapse rates is the most appropriate solution while interpolating temperatures between two weather stations.Conversely, method (ii) applied to Car_2607 and Car_3051 provides the best results at Bel_3328, which means that a fixed calibrated lapse rate is the most suitable option for extrapolations above our highest off-glacier weather station.

The glacier cooling effect
The cooling effect at each on-glacier weather station was calculated as the difference between the measured temperature and the ambient temperature at the same elevation, computed on the basis of the results described in Sect.4.2 (i.e.hourly-variable lapse rate below Bel_3328 and fixed calibrated lapse rate above it).The average seasonal cooling effect (Table 4) was maximal at Car-gl_3082 (−1. Figure 3 reports the mean daily cycles of the cooling effect and wind regime.A common pattern emerges, with minimum cooling at night and maximum cooling around noon or in the afternoon, coherent with the diurnal cycle of ambient air temperature and deriving temperature differences from the glacier surface.For five out of the seven monitored sites, the cooling occurred almost exclusively during daytime.Nighttime cooling took place only at Mar-gl_2973 and Car-gl_3082, which are the two sites with higher mean cooling.Down-glacier winds dominated on La Mare Glacier, with higher speeds compared to Careser Occidentale and Orientale glaciers, where up-glacier winds prevailed.The wind speed was at its maximum at night on La Mare, especially in 2010, while it was at its maximum in the afternoon on the two Careser glaciers.A peculiar behavior was found at the terminus of La Mare Glacier (Mar-gl_2709), where downglacier winds dominated at night, without a cooling effect, and were replaced by upglacier winds from mid-morning to late afternoon, when the cooling effect increased sharply.Wind data were not available at Mar-gl_3438, due to instrumentation failure, but we can argue that katabatic winds were not prevalent at this site, which is close to the crest, based on results published for similar locations in previous works (e.g.Greuell et al., 1997;Strasser et al., 2004).
Different weather conditions led to a considerable temporal variability of the glacier cooling effect during the two summer seasons of 2010 and 2011 (Fig. 4).Cooling was maximal during warm anticyclonic periods and nearly absent during cold unsettled weather.Differences among sites increased with warmer temperatures, whereas they nearly disappeared during cold and unstable periods.The highest variations occurred at Mar-gl_2973, Mar-gl_3215, Mar-gl_3140, and Car-gl_3082 while at Mar-gl_3438 and Car-gl_3144 there was a smaller temporal variability.A warming, rather than cooling, effect was observed on some days, mainly at the upper weather stations of La Mare Glacier.A close check on the wind and temperature data revealed that this was Introduction

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Full  The methods of Khodakov (1975), Davidovic and Ananicheva (1996) and Braithwaite et al. (2002), applicable to only seasonal temperatures, provided similar results in terms of mean errors, which were for the most part negative (i.e.excessive cooling effect).
The only method which accounts for the spatial variability of the cooling effect (Davidovic and Ananicheva, 1996) provided the worst results in terms of RMSE and N&S index, being correct in the lower ablation area of La Mare Glacier (Mar-gl_2709 and Mar-gl_2973) but strongly underestimating temperatures elsewhere.The least problematic site for all methods was Mar-gl_2973, whereas the most problematic sites for most methods were Mar-gl_3438, Car-gl_3144, and Mar-gl_3215 (i.e. the sites where the measured cooling effect was lowest).The terminus of La Mare Glacier was less challenging, except for the method of Braithwaite et al. (2002).Mean seasonal temperatures calculated from the hourly values obtained by the G&B and S&M methods (see the following section for details) matched the measurements better, with the mean errors among all the weather stations being closer to zero.The G&B method was the best at capturing the spatial variability of air temperature, even if significant underestimations persisted at the two sites with the lowest cooling effect (Mar-gl_3438 and Car-gl_3144).The S&M method was not so efficient, in particular at Mar-gl_2709, where the temperature was underestimated by 1.6 • C, and at Mar-gl_3438, where an overestimation of 0.9 • C occurred.Introduction

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Hourly temperature
According to the S&M method, piecewise linear regressions of on-glacier hourly temperature vs. ambient temperature at the same elevation have been calculated for each glacial weather station.The values of the parameters k 1 and k 2 (i.e.temperature sensitivities for ambient temperatures below and above the threshold temperature T * , respectively) were well aligned with the transfer functions proposed by S&M, using the FPL as predictor (Fig. 5).On the other hand, the transfer function for T * suggested by S&M, using station elevation as a predictor, could not be used in AVDM given the different geographic and climatic setting of the two study areas.We therefore propose to substitute Eq. ( 6) with the following function: which uses the FPL (m) rather than elevation as a predictor, thus being potentially more generalizable.The outlier already excluded by S&M was not included in our calculation of Eq. ( 16), nor was Mag-gl_2709, both due to under-sampling at below-zero temperatures.Figure 5 shows data points, transfer functions, and parameters.Calculated vs. measured temperature is shown in Fig. 6 along with related statistics.Four out of the five sites where the method works satisfactorily (ME < 0.5 • C in absolute value and N&S index > 0.87) have prevailing katabatic winds.On the contrary, lower performance affects sites close to the glacier margin (Mar-gl_3438 and, in particular, Mar-gl_2709), where katabatic winds are disrupted by valley winds or synoptic winds, and Car-gl_3082, where up-glacier winds prevail.
According to the G&B method, the location x 0 where the air enters the glacier wind layer, and the length scale L R , can be calculated by an exponential function which expresses the "climatic sensitivity" in function of the distance x along the flowline:

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Full Climatic sensitivities were calculated, comparing daily mean temperature at our onglacier sites to daily mean temperature at Car_3051, and have been added for comparison to the data displayed in Fig. 5 of the Greuell and Böhm (1998) paper.The results are shown in Fig. 7 and indicate a fairly good alignment of our data with the other glaciers' data and with the best fit calculated by G&B for the Pasterze weather stations.It therefore seemed appropriate to use the values of x 0 and L R calculated by those authors, that is, 1440 and 8340 m respectively.According to the G&B procedure, the hourly temperature above the freezing level was set equal to the ambient temperature (Sect.4.2).Below the freezing level, the glacier-wind model of G&B was applied, setting (i) x 0 = 0 if the freezing level was below the top of the flowline, and (ii) x 0 = 1440 m if it was above this point.z 0 was set equal to the freezing level in case (i) and equal to the altitude of the top of the flowline in case (ii).These settings are the same as those used in the G&B paper.Nevertheless, no corrections were applied to the computed temperatures, as was done by G&B, who applied a fixed offset of −0.74 • C.
Figure 8 displays the results of the G&B method.Calculated temperatures matched the measured temperatures fairly well and, as reported in Table 5, the efficiency statistics were better than for the S&M method, with a lower mean RMSE and a higher N&S index.Improvements were observed, in particular, at Mar-gl_2709, Car-gl_3082, and Mar-gl_3438, even if these sites lack predominant katabatic winds.A clear step is observable at Mar-gl_2709 and, slightly less obvious, at Mar-gl_2973 in both summer 2010 and 2011, attributable to the jump of x 0 from 0 to 1440 m when the freezing level exceeds the top of the flowline.

Mass balance modeling
EISModel applications using measured temperature datasets resulted in RMSE values well below the mass balance measurement error from ablation stakes readings (∼ 200 mm w.e., Thibert et al., 2008;Huss et al., 2009), thus confirming the good skill of the modeling tool.On the other hand, the RMSE was nearly double when calculated Introduction

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Full temperature datasets were used as input, and considerable differences also exist in the calibration parameters (Table 6).
The spatial distribution of modeling errors using temperature extrapolations from Car_2607 via the standard lapse rate (Fig. 9, scatterplots b1 to b4) replicated the findings of Carturan et al. (2012a) for the six previous years (2004 to 2009).In particular, the modeled vertical gradient of mass balance on La Mare Glacier in summer 2010 was lower than the observed one, in both calibration and validation runs, due to uneven errors in estimating air temperature (+0.77, +1.17, and +1.14 • C at Mar-gl_2709, Mar-gl_2973, and Mar-gl_3215 respectively).This dataset of overestimated temperatures led to significantly lower calibration parameters compared to the measured temperature dataset.Moreover, including critical points close to the lower margin of the glacier (Mar-gl_2709 in summer 2010) led to wrong calibration at the other two points, which are likely to have a higher spatial representativeness given the larger distance from the glacier margin.
The calibration parameters obtained with the G&B temperature dataset were closer to those obtained with the measured temperature dataset, as could be expected given the smaller errors in temperature estimations (Table 5, Fig. 8).In summer 2010, modeling results with the G&B temperature dataset were also the best among the three tested methods for air temperature calculation, in both calibration and validation runs.The same cannot be stated for summer 2011, due to the larger temperature underestimation at Mar-gl_3140 and Car-gl_3144.Similar errors occurring at Mar-gl_3438 did not impact mass balance estimations because they mainly happened at below-zero temperatures (Fig. 8).
The S&M temperature dataset led to the worst results in summer 2010 due to the strong underestimation of air temperature at Mar-gl_2709 (−1.6 • C).Calibrated parameters in 2010 were thus overestimated and led to mass balances that were too negative, on average, in 2011.On the contrary, when used for calibration, the data of 2011 led to parameters much closer to the measured temperature dataset, leading to correct

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Discussion
The temperature distribution and wind regime were found to be remarkably different for the three investigated glaciers (Tables 2 and 4, Fig. 3).The most significant differences were detected between La Mare Glacier, where the KBL and the cooling effect were clearly recognizable, and the Careser Occidentale Glacier, where the air temperature was not significantly different from the ambient temperature and where prevailing upglacier winds (i.e.valley winds) dominated.Differences were even more prominent during warm and stable weather (Fig. 4), brought by persistent anticyclonic systems.
In these periods, when the ablation is highest, the cooling effect is much more effective for example at Mar-gl_2973, causing a temperature depression of 2 to 3 • C compared to 1 • C at Car-gl_3144.These findings provide a first quantification for an important reinforcing mechanism during glacier decay, that is, the disintegration of parent glaciers into smaller units, which have reduced effectiveness in cooling the air above and in triggering katabatic flows.
The Car-gl_3082 site, on Careser Orientale Glacier, also displayed peculiar conditions compared to most weather stations operated on La Mare Glacier.On the one hand a prevailing up-glacier wind was recognized, but it cannot be attributed unequivocally to valley winds because the direction roughly corresponds to prevailing synoptic winds in the Ortles-Cevedale area (Gabrieli et al., 2011).On the other hand, although katabatic flows were generally absent, this site was the coldest in summer 2011, exhibiting a mean depression of 1 • C compared to the ambient temperature (Table 4).
In addition, during warm anticyclonic periods (as detected by inspection of reanalysis weather charts from www.wetterzentrale.de,last access: 31 October 2014) it displayed a cooling effect similar to Mar-gl_2973 and Mar-gl_3140, located in the middle part of La Mare Glacier.This is unusual for locations close to the top of glacier flowlines, which

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Full normally display a low cooling effect and high temperature sensitivity (e.g.Greuell and Böhm, 1998;Shea and Moore, 2010;Petersen et al., 2013).The efficient cooling at Car-gl_3082 could have been caused by the combination of adiabatic cooling of ascending air and cooling by loss of sensible heat due to the rather long fetch (780 m from the lower edge of the glacier), whereas in katabatic flows these two energy exchanges have opposite signs (i.e.loss of sensible heat and adiabatic heating of descending air).
A clear dependency of air temperature on elevation was found on La Mare Glacier, where the weather stations were placed along a longitudinal profile, exploring a large range of elevations (Fig. 2).The on-glacier lapse rate was higher than the standard ambient lapse rate, unlike in previous works which mostly report lower values, ranging from −2.8 to −8.1 • C km −1 and averaging −4.9 • C km −1 (Petersen and Pellicciotti, 2011, and references cited therein;Petersen et al., 2013).The high lapse rate measured on La Mare Glacier is likely due to its physical characteristics and to the specific location of weather stations.For example, Mar-gl_2973, which is located 2.13 km downslope from the upper margin of the glacier, displayed only a moderate cooling effect (−0.74 • C in 2010 and −0.90 • C in 2011), due to the presence of a steep slope causing adiabatic heating right above the weather station.An even more unusual behavior was measured at Mar-gl_2709, close to the terminus of the glacier.Here the cooling effect was detected only during daytime, with valley winds prevailing over katabatic winds, while at night the adiabatic heating of the air descending the steep tongue prevailed over the cooling due to turbulent exchanges.Besides the physical characteristics of the glacier, however, the steep lapse rates might also have been influenced by the high lapse rate measured outside the thermal influence of glaciers.
The specific reasons for the steepness of the high-altitude ambient lapse rates are not easy to identify.According to Marshall et al. (2007) and Minder et al. (2010), for example, they could have been caused by the prevailing synoptic circulation, local energy balance regime, persistence of snow cover, geographic position (windward or leeward with respect to the prevailing synoptic wind).Apart from these considerations, it has to be noted that the interpolation and extrapolation of ambient temperature at Introduction

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Full high altitudes, as a starting point for the computation of the on-glacier temperature fields, are strongly dependent on the availability and/or selection of suitable weather stations.As already suggested e.g. by Oerlemans, (2001), measurements from highaltitude weather stations are preferable to measurements from valley-floor sites, which are prone to thermal inversions and subject to high temperature oscillations during the day.
None of the five tested methods were able to fully reproduce the spatial variability of air temperature observed on the Careser and La Mare glaciers (Table 5).The "seasonal" methods generally underestimated temperature, in particular close to the edge of glaciers and in the small Careser Occidentale, because they have been developed using data from larger glaciers (e.g.Braithwaite et al., 2002) and/or they were conceived for applications at the ELA or at the firn line (e.g.Khodakov, 1975).The method by Davidovich and Ananicheva (1996), which explicitly accounts for the spatial variability of the cooling effect, was fairly effective in the lower ablation area of La Mare Glacier (Mar-gl_2709 and Mar-gl_2973), but underestimated temperature elsewhere.None of these three methods were able to differentiate between the "cold" Car-gl_3082 and the "warm" Car-gl_3144.
The good alignment of our data points with the transfer functions of Shea and Moore (2010), which can be seen in Fig. 5, is remarkable given the different characteristics of glaciers and geographic setting of the two study areas.This result points to a good generalizability of the S&M method, which we have tried to improve by implementing a transfer function for T * based on the FPL rather than on elevation.The S&M method was fairly successful at sites where the KBL was detected (Mar-gl_3140, Mar-gl_3215), that is, for the conditions under which the method has been implemented.Nevertheless, at Mar-gl_2973 it significantly underestimated the temperature, probably because it does not account for gradients upslope of the weather station, which causes a local prevalence of adiabatic heating.A larger error occurred at Mar-gl_2709, which is however influenced by valley winds and thermal emission from the surrounding bare rocks, determining high temperature sensitivity and unusual T * at such a long FPL (2896 m, Introduction

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Full Fig. 5).As already seen for "seasonal" methods, also with this method it was not possible to reproduce the temperature differences between Car-gl_3082 and Car-gl_3144, as expected, because they have similar values of down-glacier FPL (313 and 354 m, respectively).The G&B method provided the best overall results.Among sites with prevailing katabatic winds, the improvement was clearest at Mar-gl_2973, where the method was able to account for the combined effect of adiabatic heating and turbulent exchanges, which were regulated by the slope variations along the upstream flowline.On the other hand, it was worse than the S&M method at distinguishing between the two Careser glaciers (Table 5), and the better results in terms of lower mean errors at Mar-gl_2709, Mar-gl_3438 and Car-gl_3082, compared to the S&M method, are coincidental because at these sites the KBL was almost absent or not prevailing.Other combinations of parameters x 0 and L R have been tested to evaluate whether they are valid alternatives, for example for eliminating the artificial step in calculated vs. observed temperature at Mar-gl_2973 and Mar-gl_2709 (Fig. 8), caused by the jump of x 0 from 0 to 1440 m when the freezing level exceeds the top of the flowline.The tested combinations were: (i) x 0 = 0 m (constant) and L R = 8340 m, (ii) x 0 = 1440 m (constant) and L R = 8340 m, and (iii) x 0 = 1835 m (constant) and L R = 12 682 m.The last combination results from the best fit to AVDM data in Fig. 7, excluding the outlier Mar-gl_2709.We also tested the calculation using the unmodified ambient temperature.Tests indicate that at sites with almost no cooling effect (Mar-gl_3438 and Car-gl_3144) the unmodified ambient temperature or the combination (i) (x 0 = 0) provide the best results (mean errors < 0.2 • C in absolute value).At the four sites with prevailing KBL the best overall solution was (iii), but this combination is specific for the AVDM and not generalizable, due to the rather small size of our glaciers.At Mar-gl_2973, options (ii) and (iii) completely removed the step and provided the best statistics.At Mar-gl_3215, option (iii) provided almost identical results to a variable x 0 , while options (i) and (ii) led to excessive overestimations and underestimations, respectively.At Mar-gl_3140, the best option was (iii).These findings highlight site-specific and glacier-specific conditions which still need investigation in order to generalize the G&B procedure, possibly by including smaller or disintegrating glaciers in the datasets used for the generalization.Sites where the KBL no longer exists and is replaced by prevailing valley winds and/or synoptic winds also need to be included as they reveal important controlling mechanisms during glacier shrinking, which require modifications to the main G&B algorithms in order to be taken into account.
The results of EISModel applications underline the importance of correct on-glacier air temperature estimation for reliable mass balance calculations (Table 6, Fig. 9).Even small estimation errors induce significant distortions in calibration parameters and compromise model generalizability.The 2010 dataset on La Mare Glacier clearly demonstrates how single points, especially if they are displaced along altitudinal profiles, can affect the calibration of the model and its capability to account for the vertical gradients of the mass balance.This problem is clearly emphasized in our case study, with only three weather stations along the flowline of La Mare Glacier in 2010.The spatial representativeness of Mar-gl_2973 and Mar-gl_3215 is likely much higher than that of Mar-gl_2709, at the glacier terminus, which reflects the conditions close to the lower edge of glaciers.However, mass balance models should be improved in order to account for the decreased thermal offset in these areas and in smaller glacier units resulting from the fragmentation of larger glaciers, because they represent important processes involved in the response of glaciers to climatic changes.

Concluding remarks
The results of this work have interesting implications for the knowledge of glacier's reactions to climatic changes, and for their modeling.The main conclusions from this study are the following: Introduction

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Full  Full  Full  Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | on-and off-glacier) above the elevation where the mean summer temperature equals −4 • C.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | For a detailed description of the model we refer the reader to the work of Carturan et al. (2012a).The cumulated mass balance measured at ablation stakes drilled in close proximity to the glacial weather stations (AWS and VPP) served for model calibration and validation.We used alternatively each of the two summer seasons of 2010 and 2011 as an independent dataset for calibration/validation.Point-based EISModel calculations at the weather stations were run, using four temperature series: (i) measured data, (ii) Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 01 • C in 2011) and at Mar-gl_2973 (−0.74 • C in 2010 and −0.90 • C in 2011).Null or negligible cooling was detected at Mar-gl_3438, close to the top of La Mare Glacier, and at Car-gl_3144 on the small Careser Occidentale Glacier.Minor cooling occurred at Mar-gl_3215 (−0.27 • C in 2010), which was close to the balanced-budged ELA of the glacier, and at Mar-gl_3140 Discussion Paper | Discussion Paper | Discussion Paper | (−0.47 • C in 2011), in the upper ablation area.Notably, the narrow and steep terminus of La Mare Glacier experienced a significant cooling effect in 2010 (−0.65 • C).
Discussion Paper | Discussion Paper | Discussion Paper |ascribable to local föhn conditions, that is, forced adiabatic heating brought by strong northerly winds.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | mass balance estimations in summer 2010 with the exception of the already mentioned Mar-gl_2709.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Juncal Norte Glacier, Chile, J. Geophys.Res., 116, D23109, doi:10.1029/2011JD015842,2011.Petersen, L., Pellicciotti, F., Juszak, I., Carenzo, M., and Brock, B.: Suitability of a constant air temperature lapse rate over an Alpine glacier: testing the Greuell and Böhm model as an alternative, Ann.Glaciol., 54, 120-130, 2013Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .
Figure 1.Geographic setting of Alta Val de La Mare and location of the automatic weather stations.
Table 5 reports the seasonal temperatures calculated by the five different methods described in Sect.3.4 and their comparison with actual measurements on glaciers.

Table 1 .
Location, flow path length (FPL), period of observation and used variables for glacier and ambient weather stations * .The periods with common records are 3 July-23 September 2010 and 7 July-12 September 2011.

Table 4 .
Mean values of cooling effect, wind speed and wind direction recorded at the on-glacier weather stations.