Sensitivity of a distributed temperature-radiation index melt model based on a four melt season AWS record from Hurd Peninsula glaciers , Livingston Island , Antarctica

U. Y. Jonsell, F. J. Navarro, M. Bañón, J. J. Lapazaran, and J. Otero Departamento de Matemática Aplicada, E.T.S.I. Telecomunicación, Universidad Politécnica de Madrid, Av. Complutense, 30, 28040 Madrid, Spain Swedish Polar Research Secretariat, P.O. Box 50003, 104 05 Stockholm, Sweden Observatorio Meteorológico de Alicante, Agencia Estatal de Meteorologı́a (AEMET), C/ Regidor Ocaña, 26, 03011 Alicante, Spain


Background
Retreating and thinning glaciers have come at sharp focus in relation with increased atmospheric temperatures attributed to anthropogenic greenhouse emissions.Air temperature changes and their associated changes in meteorological conditions will, in different ways and to different extent, affect the various fluxes providing energy for heating and melting a glacier surface as part of an intricate system involving several feedback mechanisms (Ohmura, 2001).Surface energy balance (SEB) calculations using automatic weather station (AWS) data from glaciers aim to separate and Figures

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Full quantify the contributing fluxes and form a basis for understanding the coupling between meteorological conditions and glacier melt.As a prognostic tool for the response in energy fluxes, and eventually melt rates, to perturbations in meteorological conditions, SEB models have the advantage of being physically based but the disadvantage of involving a complicated extrapolation procedure to distribute the fluxes over the glacier surface (Hock, 2005).To overcome this complexity, the simpler temperatureindex models, based on the coupling between energy fluxes and temperature, are widely used.They perform best in environments where long-wave radiation and sensible heat are the dominating energy sources, as those fluxes are strongly coupled to temperature (Ohmura, 2001), while in environments dominated by solar radiation the model performance is reduced (Sicart et al., 2008).In many glaciated areas of the world, long-wave radiation is the major energy source for melt, but short-wave radiation plays a dominant role for the diurnal, daily and inter-seasonal variation of energy available for heat and melt (Greuell and Genthon, 2004).Therefore models including representations of a combination of temperature and short-wave radiation are commonly used (e.g.Hock, 1999;Pellicciotti, et al., 2005;Schuler et al., 2005;M öller et al., 2011).An increasing number of studies based on AWS data combined with glaciological mass balance data are continuously improving the understanding of glacier SEB and its geographical differences (e.g.Andreasssen et al., 2008;Giesen et al., 2008;Hulth et al., 2010).In this paper we present an AWS record extending over four melt seasons and its associated SEB from a region scarcely represented in the literature, namely the Hurd Peninsula on Livingston Island, South Shetland Islands, an archipelago parallel to the northwestern extreme of the Antarctic Peninsula (Fig. 1).The Antarctic Peninsula region has experienced a remarkable warming during the last decades (Vaughan et al., 2003;Turner et al., 2009).The 41-year long temperature record from Bellinghausen research station on King George Island, located about 90 km to the NE of Hurd Peninsula, shows a 0.25 • C per decade warming region on glacier dynamics (Rott et al., 1996;Rignot et al., 2004;Scambos et al., 2004;Pritchard and Vaughan, 2007), glacier extent (Rau et al., 2004;Cook et al., 2005), mass balance and melt rates (Braun and Hock, 2004;van den Broeke, 2005;Turner et al., 2005Turner et al., , 2009;;Vaughan, 2006) are key scientific questions for understanding the contribution of grounded ice losses from this region to future sea level rise.The Hurd Peninsula glaciers mass balance record (Navarro et al., 2011) is the only currently ongoing mass balance programme from the Antarctic Peninsula with both summer and winter balances listed at the World Glacier Monitoring Service, thus providing a particularly suitable field data source for studying the coupling between meteorological conditions and mass balance.
We use the AWS record to briefly outline the meteorological conditions at the site and to quantify the absolute fluxes and their relative contribution to melt.We also apply a distributed temperature-radiation index melt model, which is calibrated with in-situ mass balance data obtained using the glaciological method (Navarro et al., 2011).We compare the melt rates obtained from SEB and temperature-index model at the point scale, and use the four years of AWS data to compare the distributed modelled and measured melts.We use the calibrated model to analyze its sensitivity to changes in meteorological conditions.Furthermore, we present a novel approach to handle sub-daily albedo data that reduces the diurnal variations arisen due to measurement deficiencies but keeps the diurnal variations due to changes in cloud cover.

Physical setting
The Hurd Peninsula ice cap ( 62• 39-42 S, 60 • 19-25 W; Fig. 1) covers an area of about   (Navarro et al., 2009).The ice surface velocities of Johnsons glacier increase downstream from the ice divide, reaching annual-averaged values up to 65 m a −1 at the fastest part of the calving front (Otero et al., 2010), while the largest ice velocities for Hurd glacier are typically about 5 m a −1 (Otero, 2008).The Hurd Peninsula ice cap is a polythermal ice mass, showing an upper layer of cold ice, several tens of metres thick, in the ablation area (Molina et al., 2007;Navarro et al., 2009).The cold layer is rather uniform in Hurd glacier, while in Johnsons glacier the layer is more patchy.The Spanish Antarctic Station Juan Carlos I (JCI) is located very close to Hurd Peninsula ice cap (Fig. 1).Meteorological measurements are maintained in JCI all year round by an AWS, and are complemented by manual meteorological observations during the summer.In December 2006, an AWS was installed on the upper ablation area of Johnsons Glacier (Fig. 1).The latter provides the main meteorological data source used in this paper and will be further described in the next section.
The Hurd Peninsula ice cap is subjected to the maritime climate of the western Antarctic Peninsula region, with some particularities due to local conditions.The orography of Livingston Island alters the regional prevailing northwesterly dominating wind direction.At JCI and Johnsons Glacier the predominant wind direction is from NNE, followed by SSW (JCI), ENE (Johnsons Glacier).Average wind speeds are about 4 m s −1 , but gusts wind speeds above 30 m s −1 are frequent.The highest wind speeds come Introduction

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Full The cloudiness is high, with an average of 6/8 and, consequently, insolation is small, with 2 h day −1 of average insolation during summer and spring, though the cloud-free days during such seasons show a high irradiance.The relative humidity is very high, with average values above 80 % at JCI and 90 % on the glacier (unpublished data from Agencia Estatal de Meteorología, AEMET).
On the glacier, mass gain is dominated by direct snowfall and wind redistribution of snow, without any contribution from snow avalanches.The glacier ice hardly receives any debris from the surrounding mountains, except at the lowest elevations of its outlets.Tephra layers from the recent eruptions of the neighbouring Deception Island, however, are a common feature of these glaciers (Pall às et al., 2001).

AWS data record
The meteorological data used for SEB analysis and as input to the temperatureradiation index melt model was obtained from the AWS located on Johnsons glacier (62 • 40.266N, 60 • 21.672 W, 178 m a.s.l. at installation).The AWS (Table 1) was installed on the glacier on 16 December 2006, and the record used herein extends to 15 March 2010.During austral winters, major data gaps exist in the record due to energy shortage.However, for the melt seasons, which we focus on, the data gaps are minor.An ultra-sonic ranger was installed next to the AWS, and was used to measure the relative surface height changes caused by ablation or accumulation.Due to malfunctioning, the ultra-sonic ranger record includes major data gaps throughout the period of measurement.Introduction

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Full The data sampling and averaging intervals of the AWS logger differ between the summer seasons, when regular visits to the AWS are done from the nearby JCI research station, and the unmanned winter seasons.The majority of the data corresponds to the summer seasons, but still a portion was collected during winter mode of operation.Thus, temporal averages of the meteorological parameters are based on different number of readings.In case of missing data due to gaps or preposterous registrations, hourly averages are calculated down to the representation of at least one reading during the time interval; else linear interpolation between the adjacent time steps was made for gaps up to four hours.A gap in the temperature and relative humidity records due to sensor malfunctioning, spanning the period 16-24 December 2009 was replaced with temperature data from a T107 thermistor installed on the AWS and with RH data from JCI. Offsets calculated from data two days before and after the gap were applied.The temperature sensor was unventilated, which at high short-wave radiation fluxes and low wind speeds exaggerates temperatures and we therefore applied the correction to overheating suggested by Smeets (2006) on all air temperature data.

Correction of short-wave radiation and albedo
Large pseudo-diurnal variations in albedo (Fig. 2), α, may arise from the poor cosine response of the pyranometeres at high zenith angles and from an instrument set-up non-parallel to the glacier surface.The bias is mainly introduced by the upward facing sensor as incoming solar radiation flux is less diffuse compared to the outgoing (van den Broeke, 2004).As changes of surface conditions affecting α are of gradual nature, with the exception of snow falls, van den Broeke ( 2004) presented an approach to improve the accuracy of the incoming short-wave fluxes by filtering out diurnal variations using a 24 h running mean "accumulated" albedo, α d (Eqs. 1 and 2).This approach was subsequently adapted by others (Andreassen et al., 2008;Giesen et al., 2008).α d is calculated as the ratio between the sums of the instant (measured) outgoing flux, S r , and the measured incoming solar radiation flux, S i , with the timing of measurement Introduction

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Full as midpoint.A corrected incoming short-wave flux, S d , is there after calculated.
where t is time in hours (h).
Equation ( 1) produces a smooth diurnal signal of α d that leaves out the extreme values arisen from measurement shortcomings, which normally occur at high zenith angles.
As α d is based on the sums of the short-wave fluxes, the low fluxes occurring at high zenith angles reduces the impact of the measurement deficiencies on α d and S d .However, this approach filters out the rapid variations in α associated with changes in cloud cover also during midday hours when short-wave fluxes are high, which may have significant impact on SEB.The rapid variations are an effect of clouds absorbing radiation to a higher degree in the near-infrared spectra, leaving a higher portion of the visible wave lengths to reach the ground, for which the snow reflectance is higher.This effect is further enhanced by multiple reflections between the surface and the cloud base (Warren, 1982;Cutler and Munro, 1996).
With Eqs. ( 3) and ( 4) we present and use an extension of Eq. ( 1) which yields a corrected albedo, α c , and corrected short-wave flux, S c , that restore the effect of clouds reasonably well: (3) where λ is the slope of the linear relation between the change in instant albedo, α i , and the instant fraction of potential top of atmosphere radiation that reaches the ground, θ i , Introduction

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Full between two subsequent recording time steps (Fig. 3).The term restoring the effect of clouds is proportional to the difference between θ i and its corresponding 24 h running mean, θ d , and scaled by λ. θ i is calculated as where the top of atmosphere radiation, I toa , is given by I S is the solar constant (1366 W m −2 ), d and d m are the instant and mean Sun to Earth distance, and Z is the local solar zenith angle.A freely available Matlab code based on Reda and Andreas (2008) was used to calculate the required parameters.An iterative procedure is needed for solving Eq. ( 3) and subsequently Eq. ( 4) as Eq. ( 5) uses S c as input.The result normally stabilizes after less than five iterations.Regression analysis to obtain the linear slope λ was applied to each of the four seasonal data sets on all data when zenith angle was 80 • or less.The resulting four λ values were all within −0.09 ± 0.01 with corresponding r-values between −0.59 and −0.48.Consequently, λ was statically set to −0.09 in Eq. (3).The daily mean α will be the same regardless of using S i , S d or S c as incoming short-wave flux.Jonsell et al. (2003) found only a limited effect of clouds on α during ice conditions, probably because the multiple reflection of radiation will be limited due to lower α.The location of the AWS was snow covered during the period of data collection, with the exception of a few days at the end of the melt season 2006/2007, but still with α exceeding 0.55, and therefore we applied Eqs. ( 3) and ( 4) to the full data set.The rapid shifts in α c due to sudden changes in S c are well represented.During early morning and late afternoon hours an offset towards higher α c is present.This is due to reduced θ i caused by the longer atmospheric pathway and increased scattering of solar radiation at high zenith angles, and thus it is not primarily an effect of clouds.
However, during the morning and afternoon hours S c is small and the impact on SEB is Introduction

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Full  3) and ( 4) during midday hours, when S c is large, will have greater importance for SEB.

Energy balance calculation
We calculate SEB, using hourly mean AWS data, to investigate the absolute and relative contribution of the energy fluxes involved in glacier heating and melt.The energy balance condition at the glacier surface is represented by the equation Where S n is the net short-wave flux, L in and L out are the incoming and outgoing longwave fluxes, respectively, H is the sensible heat flux, and E is the latent heat flux, which summed up are expressed as the atmospheric energy fluxes, A, and must balance the sum of ground heat flux, G, and melt energy flux, M. A flux is considered to be positive when directed towards the surface.We do not quantify the energy from the sensible heat of rain fall due to lack of precipitation measurements on the glacier, but this term is generally small (Hock, 2005).The long-wave radiation components are, in contrast to their short-wave counterparts, treated separately.This division mirrors better their different physical nature and their different response to atmospheric and surface conditions (Ohmura, 2001).We use the bulk aerodynamic method based on Monin-Obukhov length following Hock and Holmgren (2005).No field measurements of the roughness length for momentum (Z 0w ) are available for the site.Although Z 0w is expected to vary with time (Brock et al., 2000;Hock, 2005), we use Z 0w as a constant-in-time model parameter to fit the SEB to the ablation rates estimated from the surface lowering registered by the ultra-sonic ranger.Conversion from surface lowering to mass loss was made by using depth density relations from snow pits dug in the area.The roughness lengths for heat, Z 0T , and moisture, Z 0e , are treated as functions of Z 0w following Andreas (1987).For stable stratification we use the stability functions by Beljaars and Holtslag (1991), and Introduction

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Full for unstable conditions the expression by Panofsky and Dutton (1984).The best fit was obtained using Surface temperature, T s , in • C, is calculated from L out assuming emissivity of unity: where σ is the Stefan-Boltzmann constant (5.67 × 10 −8 ).
When E is negative, the phase change is considered as sublimation, while when it is positive it is considered as condensation or as resublimation, depending on whether T s equals or is lower than 0 • C.
G could not be captured by any of the sensors of the AWS.On a perfectly temperate glacier G is by definition zero.The Hurd Peninsula glaciers are of polythermal type (Navarro at al., 2009) and during the melt season G will be directed to heat the cold surface layer.From other studies (see table in Ohmura, 2001) we conclude that the average G will be limited to a few W m −2 , but will occasionally be high due to the release of latent heat at refreezing of melt water upon the first onset of melt in the summer, and during subsequent recommences of melt-refreeze cycles.During the ablation season, melting conditions at the Hurd Peninsula glaciers are repeatedly interrupted by refreezing events.In other modelling approaches, the quantification of the energy compensation needed to reach melting conditions after a period of freezing and cooling of the surface (negative A) differs from full compensation (van de Wal and Russel, 1994) to no compensation (Hock and Holmgren, 2005).The latter means that, as soon as A turns positive, melting is resumed.Hock and Holmgren (2005) argued that the positive compensation flux will just be a part of the accumulated negative flux, because the latent heat from percolating refreezing melt water will make a significant contribution to the reheating of the cooled volume when melt conditions resume at the surface.
We consider the surface to be melting when T s > −0.melting at sub-zero T s can occur because of the ability of short-wave radiation to penetrate into the snow cover, where the thermal conductivity is low (Koh and Jordan, 1995).We consider that the surface is refreezing and cooling when A turns negative, and to be heated to resume to melt conditions when A is positive and T s < −0.5 • C. Thus G balances A during non-melting conditions.In practice this implies that the refreezing flux (negative A) is compensated by the positive flux of A when T s < −0.5 • C. Melt rates calculated via the energy balance are converted to water equivalent (w.e.) using the latent heat of fusion (334 × 10 −3 J kg −1 ).
Following Sicart et al. (2008), we describe the relative contribution of the energy fluxes to the variation of A as where r x is the correlation coefficient of flux x to A, and σ x ,σ A are their respective standard deviations.The sum of ρ x for all fluxes contributing to A is one.

Temperature index model description
We performed the surface melt modelling and the sensitivity analysis to perturbations in meteorological conditions using a grid-based distributed temperature-radiation index model following Hock (1999): conditions using θ i : where Z is the solar zenith angle, Ω is the solar azimuth, β is the surface slope angle and Θ is the surface aspect.We considered Z and Ω to be spatially constant in the study area, while we calculated β and Θ from a digital elevation model (DEM).The DEM has a grid cell resolution of 25 m and was obtained by kriging interpolation from 852 points surveyed in 2000/2001.The surrounding rock topography was digitized from Servicio Geogr áfico del Ej ército 1:25000 map for Hurd Peninsula (SGE, 1991).
A shaded grid cell implies that D is set to zero.We calculated the shading of grid cells by applying standard geometry on the DEM.When the AWS is shaded in the sunset, the preceding non-shaded value of θ i is used to calculate non-shaded grid cells, while the subsequent non-shaded value is used in the sunrise.
We initialized the model with a distributed snow cover thickness which is continuously reduced with the daily modelled melt and increased in case snow fall was registered by the ultra-sonic ranger.We distributed the snow fall following the mean accumulation pattern obtained from determining the mass balance by the glaciological method for the period 2001-2010 (Navarro et al., 2011).We obtained the initial snow cover grid of each season by interpolating snow depth measurements conducted simultaneously to the first stake height reading, and converting it into mass loss using the density measurements from three snow pits conducted at the beginning of the melt season.

Temperature-radiation index model calibration
The model calibration is based on comparing the mass balance, b, of a number of stakes obtained by the glaciological method (Navarro et al., 2011) and the model results for the grid cells corresponding to the stake positions.As Eq. ( 10) is set to compute melt during a specific period and not b, snow fall rates registered by the ultrasonic ranger (Fig. 4) were distributed over the glacier and subtracted from the modelled

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Full melt to produce comparable figures.We assumed a snow density of 300 kg m −3 for fresh snow.We converted the stake height differences into water equivalents using the density measurements from three snow pits at the beginning and the end of the melt season.As densification of the snow pack due to refreezing of melt water is expected during the melt season, the total mass loss at each stake in the end of the calibration period is given by the beginning of the season mass minus the end of the season mass.On average, the end of melt season densities were 14 % higher.Snow density is however expected to show local variations and introduces a source of error.Based on extensive density measurements during 2004-2010 on Johnsons and Hurd glaciers (Navarro et al., 2011), the relative double standard deviation of all measured snow densities was 13 % and provides an indication on the error involved.Where the model indicates ice at the surface, we used a density of 900 kg m −3 to convert into water equivalents.
Among the four seasons with data available from the AWS, we chose the period 29/11/2008-10/02/2009 as calibration period as it provided the best combination of the following criteria: number of stakes, length of calibration period, high ablation rates, and number of stakes on ice surface at the end of the period.For the calibration period 2008/2009 the total snowfall registered by the ultra-sonic ranger was 0.05 m w.e.
We calibrated the model parameters to obtain the least mean root square error between modelled and measured b (Fig. 5, Table 2), with the criteria that σ ice >σ snow to reflect the higher absorption of short-wave radiation on an ice surface.As pointed out by others (Hock, 1999;Schuler et al., 2007), the calibration of the current formulation of the model is not unambiguous as it is possible to find different sets of tuning parameters giving equally good fits to the observed data.Based on best performance in the subsequent validation of the model, we used m = 0.092 mm h

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Full For simple comparison, we set the periods of SEB analysis to a standard melt season 15 December-15 March, which corresponds to the period with most surface melt.Melt seasons are characterized by a mean temperature close to zero (Table 3).Hourly mean temperature rarely deviates more than ± 5 • C from zero (Fig. 6), due to the maritime setting of the glaciers.Maximum (minimum) hourly mean temperature during the four seasons was 6.8For all seasons the main energy source (sink) was L in (L out ) and the resulting mean long-wave net flux was negative.The net short-wave flux, S n , together with L in , show the highest inter-seasonal variations, but are opposing each other yielding a reduced variation in mean seasonal A to a maximum of 5 W m −2 , which is equivalent to 0.11 m w.e. of melt for a full melt season.The inter-seasonal variation in S n is driven, with similar weights, by the variations in α and S c .S n was for all seasons the individual source with best fit to A (Table 4) and was also, expressed as ρ, the flux having the highest influence on the variation of A. In 2009/2010 ρ was 120 %, as the variation was counteracted by L in .The generally negative coupling between L in and S n is mainly an effect of their different response to cloud cover.ρ for L in varies between the individual seasons from positive, through insignificant, to negative.This reflects the complex balancing of A as a response to the meteorological conditions and is exemplified in The negative coupling between L in and S n results in a high correspondence between net radiation, R, and A. R explains up to 82 % of the variation of A for an individual season.The turbulent fluxes, H and E , have, considering their low mean absolute values, a proportionally large impact on the variation of A that was largest in 2008/2009, when they together explain a third of the variance of A while the influence of S n was reduced.
The coupling between T air and the energy fluxes constituting A is the physical basis of the temperature-index models.T air was best correlated with A during the seasons 2006/2007 and 2008/2009, coinciding with the highest ρ of L in .T air and S n were slightly negatively or insignificantly correlated, with the highest correlation factor (−0.47) occurring in 2007/2008.The generally low correspondence between A and T air , in particular for 2007/2008 and 2009/2010, is discouraging for using a solely temperature-driven ablation model, both at point scale and distributed over the glacier.The degree of explanation for the variation of A when using a combination of T air and S n becomes similar for all seasons and is just slightly lower than the corresponding degree of explanation for R. In a combination where S n is substituted by D, thus corresponding to the input parameters in the temperature radiation-index model (Fig. 8), the degree of explanation is only slightly lower.Using a distributed model driven by D instead of S n reduces the complexity and avoids the source of error associated with introducing a spatial and temporal modelling of α that is required for a model driven by S n .

Model validation and sensitivity analysis
The calibrated model was run on three periods from other melt seasons for which corresponding stake measurements and data from AWS were available (Table 2).The period from season 2006/2007 is significantly shorter than the others because the installation of the AWS took place several weeks after the first stake reading of the season and thus the period of correspondence starts with the second set of stake readings of the season.
The modelled b generally agrees well with b obtained by the glaciological method (Table 2).
The difference is largest for season 2007/2008, when the model

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Full underestimates b by 0.14 m w.e., which is slightly larger than the typical error of the glaciological method (ca.0.1 m w.e.; Jansson, 1999).The scatter from a linear relation between observed and modelled b is large for the short validation period 2006/2007.This might be explained by the fact that during the validation period a large part of the surface at the position of the stakes changed from snow to ice conditions, and thus the actual more gradual transition between snow and ice compared to the model's binary set-up, may reduce the model performance.b in 2009/2010 was small because of a combination of little melt and extensive snow fall.The discrepancies between the modelled and the observed distributions of the snow fall possibly introduces a significantly larger error compared to the other years, which is exemplified by an outlier that was falsely modelled as ice surface for much of the period.The difference in seasonal mean T air and D is modest.A higher inter-seasonal variation, reflecting more contrasting weather conditions between the periods, would possibly have enhanced the validity test of the model.We analyzed the sensitivity of the model by applying perturbations to the calibrated model parameters, and to the meteorological parameters by manipulating the original AWS data corresponding to the calibration period.
Changes in m by ± 10 % produce a change in melt of a few percent (Fig. 9), while a similar change in δ snow/ice varies the total modelled melt by about ± 10 % (or ± 0.05 m w.e.).A change by ± 50 % in snow cover thickness over the entire glacier surface, that influences the temporal and spatial distribution of snow and ice represented in the model through variations in the use of δ snow or δ ice , changes the melt rates by less than 10 %.
We run the model with a step increase of 0.5 We perturbed the radiation climate represented in the model by changing θ i , as the other inputs to obtain D are not related to the meteorological conditions on the glacier.We run the model with a step change in θ i that, just as in the T air scenario, corresponds to half a standard deviation of the daily means (0.06).An increase in θ i (implying more direct solar radiation) leads to 15 % more melt (0.08 m w.e.), and a similar decrease in melt for a corresponding decrease in θ i .
T air and θ i are anti-correlated in the AWS record, meaning that under present climate a temperature increase is in general associated with a cloudier sky.Extrapolating this to a temperature increase driven by climate change implies that an increased melt due to higher temperature will to some extent be balanced by reduced direct radiation.However, climate change at these latitudes will probably be mainly driven by the associated changes in cyclonic activity and pathways, hence changes will neither be static nor solely impact a single meteorological parameter, and the model sensitivity as a predictive tool provides only a first level of understanding.

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Conclusions
We have used an AWS record located on Hurd Peninsula glaciers, Livingston Island, to analyse the SEB for four melt seasons (2006/2007-2009/2010).Further, we set up and run a temperature-radiation index model.The model was calibrated and validated with b obtained with the glaciological method.A novel correction method of α i , which adds the diurnal variation of clouds on a 24 h running mean α, is presented and adopted.
The advantage of the method is that the rapid and large variations during the high fluxes at midday in the short-wave balance are better reproduced.The following main conclusions can be drawn from our analysis: 1. S n is the most important individual energy flux impacting on the variation in A, but using the combined expression of the radiation fluxes, R, the degree of explanation increases and can account for 76-82 % of the variation in A. This high degree of explanation is due to a balancing of the generally anti-correlated fluxes S n and L in , which is mainly an effect of their different response to cloud cover.4. The model results show that these glaciers are very sensitive to air temperature changes.An increase (decrease) in temperature of 0.5 • C implies an increase (decrease) of the melt rates by about 56 % (44 %), which is an effect of the strong zero degree threshold for onset of melt.The high model sensitivity of these glaciers to temperature change are indicative, but it must be noted that it 5 only provides a first level of understanding of the response of the glacier mass balance to real climatic changes.
5. An increase (decrease) in the fraction of potential top of atmosphere radiation that reaches the ground, θ i , by half a standard deviation of its daily mean leads to an increase (decrease) of melt by 15 %.Introduction

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(
http://www.nerc-bas.ac.uk/icd/gjma/temps.html).The impact of the warming in the Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | an altitude range from sea level to about 330 m a.s.l.It is partly surrounded by mountains that reach elevations between 250 and 400 m.Hurd Peninsula ice cap can be subdivided into two main glacier systems, Johnsons glacier, a tidewater glacier, flowing north-westwards, that terminates on an ice cliff about 50 m in height a.s.l.extending approximately 500 m along the coast, and Hurd glacier terminating on land and mainly flowing south-westwards, with ice thickness tapering to Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | from East and North-East directions and are associated with deep westward facing low pressure systems passing north of Livingston Island.The annual average temperature at JCI during the period 2000-2010 was −1.1 • C, with average summer (DJF) and winter (JJA) temperatures of 2.8 • C and −4.4 • C, respectively, with maximum/minimum registered temperatures of 15.5 • C and −22.1 • C.
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 | limited, while the correction by Eqs. ( Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 5 • C and we set G constant to 5 W m −2 during melting.The temperature offset from zero degrees is made to allow for melting at depths below the surface skin layer that T s is representing.Sub-surface Discussion Paper | Discussion Paper | Discussion Paper | xy = T xy (D xy δ snow/ice + m), T xy ≥ 0 0 , T xy ≤ 0 (10) where M xy is the modelled melt at a specific grid cell.The melt factor, m, and the surface specific radiation factor, δ snow/ice , are model parameters obtained via calibration.The temperature at a specific grid cell, T xy , is given by the AWS temperature record with an offset based on altitude difference and air temperature lapse rate.D is a representation of the direct solar radiation flux and is distributed over the glacier surface depending on the angle of incidence of the solar beam, and scaled from clear-sky Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Fig. 7.During 2009/2010 the anti-correlation between S n and L in was strong and days with high daily mean A were in general associated with the outer ranges of S n compared to the season 2006/2007, when anti-correlation was weak and days with high A were in general associated with intermediate daily mean S n .The standard deviation of S c was higher in 2009/2010, indicating a season with more contrast between clear and cloudy days, which may explain the different modes.Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | which is of the same magnitude as one standard deviation of the summer mean temperature for the last 30 years from the nearest long-term temperature instrument record (Bellinghausen Station on King George Island) and close to half a standard variation of the daily mean T air for the calibration period.The corresponding modelled melt rates increased by 56 % to 0.81 m w.e.A temperature decrease of the same magnitude resulted in a reduction Discussion Paper | Discussion Paper | Discussion Paper |of melt by 44 % to 0.30 m w.e.There is a strong temperature threshold effect which is illustrated by the change in number of grid cells integrated over all the time steps where the model indicates melting conditions.For the temperature increase (decrease) scenario the change was +52 % (−54 %).Mean T air for the validation period 2009/2010 was 0.5 • C colder than that of the calibration season 2008/2009, while D and S n registered at the AWS were similar.The periods are of similar lengths and we note that the measured melt rate in 2009/2010 was 38 % lower than the melt measured in 2008/2009, which is close to the modelled response to a 0.5 • C temperature decrease on the 2008/2009 data.Because of the limited elevation range of the glacier, the entire glacier area experiences temperatures flickering around zero during summer time.This leads to a high sensitivity to temperature changes during the melt seasons.
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2.
The seasonal means of T air at the AWS site are close to zero during the four melt seasons, and due to the small altitude range of the glaciers their whole area shows temperatures flickering around zero degrees during the summer season.The poor correlation factors between daily mean T air and A questions the performance of a solely temperature-based melt model, both at point scale and distributed over the glacier, and supports the use of a temperature radiation-index model.A combination of T air with S n or D increases the correlation factor at the point scale.3. The modelled mass balance is in good agreement with that obtained by the glaciological method, showing differences model-observations generally below the typical error of the glaciological method (ca.0.1 m w.e., Jansson, 1999), with no sig-Discussion Paper | Discussion Paper | Discussion Paper | fluxes = R + H + E b -mass balance d and d m -instant and mean Sun to Earth distance D -representation of the direct solar radiation flux (according to Eq. 11) atmosphere radiation L in and L out -incoming and outgoing long-wave fluxes m -melt factor M -melt energy flux r x -correlation coefficient of flux x to A R -net radiation S c -corrected (according to Eq. 4) incoming short-wave flux S d -corrected (according to Eq. 2) incoming short-wave flux S i -measured incoming solar radiation flux S n -net short-wave flux = S c + S r S r -instant measured outgoing short-wave flux T air -air temperature T s -surface temperature X xy -value of variable X at a specific grid cell Z -solar zenith angle Z 0e -roughness length for moisture Z 0T -roughness length for heat Z 0w -roughness length for momentum α -albedo α c -corrected (according to Eq. 3) albedo α d -corrected (according to Eq. 1) albedo α i -instant albedo β -surface slope angle δ snow/ice -radiation factor of snow/ice λ -slope of linear relation between the change in α i and θ i , between two subsequent time steps Ω -solar azimuth ρ x -relative contribution of the energy flux x to the variation of A σ -Stefan-Boltzmann constant (5.67 × 10 −8 ) σ x -standard deviation of x θ i -instant fraction of potential top of atmosphere radiation that reaches the ground θ d -24 h running mean of θ i Θ -Discussion Paper | Discussion Paper | Discussion Paper | Otero, J., Navarro, F. J., Martín, C., Cuadrado, M. L., and Corcuera, M. I.: A three-dimensional calving model: numerical experiments on Johnsons Glacier, Livingston Island, Antarctica, J. Glaciol., 56, 200-214, 2010.Pall às, R., Smellie, J. L., Casas, J. M., and Calvet, J.: Using tephrochronology to date temperate ice: correlation between ice tephras on Livingston Island and eruptive units on Deception Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .
Fig. 1.Location of Hurd Peninsula, Livingston Island, with the position of Juan Carlos I Station (JCI), the AWS and the mass balance stakes in 2008/2009.
zero in the snouts of Sally Rocks, Argentina and Las Palmas.Two other basins are also part of the ice cap, both flowing eastwards towards False Bay.However, these are not included in this study because they are heavily crevassed icefalls preventing field measurements.The local ice divide separating Johnsons and Hurd lies between 250 and 330 m a.s.l.Hurd glacier has an average surface slope of about 3 • , though the

Table 2 .
Characteristics of model calibration and validation runs.

Table 3 .
Mean daily air temperature ( • C), energy fluxes (W m −2 ), α c and θ i with their standard deviations, for the four melt seasons.