Response of the ice cap Hardangerjøkulen in southern Norway to the 20th and 21st century climates

Glacier mass balance changes lead to geometry changes and vice versa. To include this interdependence in the response of glaciers to climate change, models should include an interactive scheme coupling mass balance and ice dynamics. In this study, we couple a spatially distributed mass balance model to a two-dimensional ice-ﬂow 5 model and apply this coupled model to the ice cap Hardangerjøkulen in southern Norway. The available glacio-meteorological records, mass balance and glacier length change measurements were utilized for model calibration and validation. Driven with meteorological data from nearby synoptic weather stations, the coupled model realisti-cally simulated the observed mass balance and glacier length changes during the 20th 10 century. The mean climate for the period 1961–1990, computed from local meteorological data, was used as a basis to prescribe climate projections for the 21st century at Hardangerjøkulen. For a projected temperature increase of 3 ◦ C from 1961–1990 to 2071–2100, the modelled net mass balance soon becomes negative at all altitudes and Hardangerjøkulen disappears around the year 2100. The projected changes in 15 the other meteorological variables could at most partly compensate for the e ﬀ ect of the projected warming.


Introduction
Glacier volume projections are required to assess the rate of sea level rise expected from ice wastage in a warmer future climate (e.g., IPCC, 2007;Meier et al., 2007;Bahr 20 et al., 2009). In order to obtain reliable estimates for a particular climate scenario, observed differences in glacier response for various glacier types and climatic regions first need to be understood.
In contrast to most other regions in Scandinavia and the global trend, the maritime glaciers in mainland Norway advanced in the late 20th century, following a series of glaciers is not only determined by the degree of warming, but also by the accompanying change in precipitation.
Regarding the spatial distribution of glaciers in southern Norway, the large glaciers (>25 km 2 ) are all situated relatively close to the coast, in a rather maritime regime. All these glaciers are ice caps, with a large and flat upper part and a number of steeper 10 outlet glaciers. Ice caps are particularly sensitive to climate change, because a small increase in the equilibrium-line altitude (ELA) can turn a large part of the accumulation area into ablation area (Nesje et al., 2008).
In this study, we determine the response of the ice cap Hardangerjøkulen in southern Norway to the observed climate in the 20th century and projected climate change 15 for the 21st century. Hardangerjøkulen is situated in the transitional zone between the maritime glaciers near the western coast and the more continental glaciers further inland (Andreassen et al., 2005;Giesen et al., 2009). We employ a spatially distributed surface mass balance model coupled to a two-dimensional (2-D) ice-flow model to assess the effect of climate fluctuations on Hardangerjøkulen. By using a spatially Introduction

Conclusions
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Interactive Discussion zone (1450 ma.s.l.) of the north-easterly outlet glacier Midtdalsbreen, providing all meteorological quantities needed to calculate the local surface energy balance (Giesen et al., 2008). This station was supplemented by a second AWS on the summit of Hardangerjøkulen (1860 ma.s.l.), which was in operation during the summer of 2005. Glacier length has been measured at Rembesdalsskåka during several intervals, 5 the first measurement dating from 1917. At Midtdalsbreen, glacier length has been measured annually since 1982 (Andreassen et al., 2005). The length measurements were combined with maps and dated moraines in the glacier forefields to reconstruct glacier length records for the 20th century, used for validation of the coupled model (data provided by H. Elvehøy, NVE, Oslo). 10 The last major advance of Hardangerjøkulen occurred around AD 1750, in the "Little Ice Age" (LIA). During this advance, almost all older moraines were overridden. Figure 2 shows the LIA extent for the north-eastern and south-western parts of Hardangerjøkulen, determined from terminal moraines (Andersen and Sollid, 1971;Nesje and Dahl, 1991;Nesje et al., 1994;Elvehøy et al., 1997). At some locations around the 15 ice cap, pre-LIA marginal moraines, deposited around 10 000 years before present (BP), are found just outside the LIA moraines (Nesje and Dahl, 1991). The history of Hardangerjøkulen between these two major advances was reconstructed from a series of terrestrial stratigraphic sections and lake sediment cores at the north-eastern side of the ice cap and one sediment core from the south-western side (Dahl and , 1997). Basal melt is assumed to be small compared to the high ablation rates at the ice cap surface.
The surface mass balance model is based on a model developed for Morteratschgletscher in Switzerland (Klok and Oerlemans, 2002). Thorough calibration of the model parameterizations was needed before the model could be applied at Hardan-5 gerjøkulen, where climatic conditions are different. Based on the AWS data from Midtdalsbreen, adjustments were made to the parameterizations for the surface albedo and the turbulent fluxes. Below we give a summary of the main model characteristics, for details of the calibration procedure and the values used for the model parameters, we refer to Giesen (2009), Ch. 5.

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The annual surface mass balance B (mw.e.) at each location in the model domain is determined by three processes where P snow is the amount of solid precipitation, M is the mass removed by ablation at the surface and S represents mass exchange with the air by sublimation or rime.
( 3) with L f the latent heat of fusion (3.34 × 10 5 Jkg −1 ) and ρ w the density of water (1000 kgm −3 ). Sublimation (S) is determined from the latent heat flux where L s (2.83 × 10 6 Jkg −1 ) is the latent heat of sublimation. The model only keeps track of changes in solid mass. When the surface is at the melting point, we assume there is meltwater available for vaporization.
Refreezing of rain and meltwater in the snowpack is not included in the model, 10 although ice formation has been observed in Hardangerjøkulen's accumulation area (Laumann, 1972). The available measurements are insufficient to determine the net effect of refreezing on the mass balance. Considering that substantial ablation occurs even at the highest altitudes (1-2 mw.e. according to the mass balance measurements), the amount of energy needed to heat the snowpack to the melting temperature 15 is much smaller than the total energy available during the summer season. The mass balance model computes the individual fluxes of the surface energy and mass balance at each grid cell, based on sub-daily records of air temperature, relative humidity, air pressure and cloudiness and daily precipitation. A seasonally varying lapse rate is used to extrapolate measured air temperatures to the altitude of the 20 AWS on Midtdalsbreen (Sect. A3), a constant lapse rate (6.5 Kkm −1 ) is used for subsequent extrapolation over the ice cap. Measured relative humidity is converted to water vapour pressure, for both water vapour and air pressure an exponential decrease with altitude is assumed. We assume that the observed cloud fraction is valid for the entire model domain. Interactive Discussion average for each daily or hourly interval as used in the model (Fig. 3). Air temperature has a sinusoidal seasonal cycle with a minimum in early February and a maximum in early August. The annual temperature range is 18 • C, similar to the annual range in the AWS measurements from Midtdalsbreen (Giesen et al., 2008). Daily mean relative humidity is higher than 70% through the year, with the lowest values in early June.

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Cloudiness and precipitation show a similar annual cycle with maximum values in autumn and minimum values in late spring and early summer. The mean summer temperature for 1961-1990 is about 1 • C lower than during the AWS period (2001)(2002)(2003)(2004)(2005), while winter precipitation was approximately 15% lower.

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To model future mass balances, we apply climate projections for southern Norway from the RegClim project (http://regclim.met.no). The projected changes in temperature and precipitation depend on the choice of the emission scenario, the climate model and the downscaling method. We therefore use a number of different projections as input to the model, to determine the variability in the ice cap response to different climate 15 changes. The climate projections give the change in air temperature, precipitation, cloudiness, air pressure and wind speed from the normal period 1961-1990 to 2071-2100. For the area around Hardangerjøkulen, the RegClim results indicate an increase in the annual mean temperature (∆T ) of approximately 3 • C from 1961-1990 to 2071-2100, with the largest changes in autumn and winter. Annual precipitation will probably 20 increase by approximately 10%, although an increase of ∆P = 70% is projected by one of the models (Räisänen et al., 2004). The projected increase in autumn and winter precipitation is larger than the annual mean change, while summer precipitation may decrease. Since the net mass balance on Hardangerjøkulen is probably more sensitive to temperature changes in summer and precipitation changes in winter, we 25 investigate the effect of a seasonal cycle in the climate projections compared to annual changes. The projected air pressure change is smaller than ±5 hPa, which is too small to have a notable effect on the calculated mass balance and is therefore not further 957 Introduction

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Printer-friendly Version Interactive Discussion investigated. Cloudiness is projected to change by less than 5% in all seasons. For present-day conditions, the effect of cloud changes on solar radiation is approximately compensated by a change in longwave radiation of the opposite sign. In a warmer climate, the balance between incoming longwave and solar radiation may change and the effect of cloud fraction changes may be different. The effect of a 5% increase in the 5 cloud fraction in combination with a temperature increase will therefore be investigated. The projected wind speed change is within ±6%, but the effect of such a change cannot be determined easily because wind speed is only indirectly incorporated in the turbulent exchange coefficient. By increasing the turbulent exchange coefficient by 10% along with a temperature increase, we use the model to obtain a rough estimate of wind 10 speed changes on the surface mass balance.

Climate projections in the model
All investigated future climate projections were incorporated in the same way in the model. Since the projections are defined as the change from the normal period 1961-1990 to 2071-2100, we assume a linear increase/decrease of the considered meteoro-15 logical variable by the projected amount from the middle of the first period (1976) to the middle of the second period (2086). As meteorological measurements are available until 2005, the climatological data is used from 2006 onwards. Hence, the imposed climate change is already larger than zero at the beginning of the future simulation (2006). We determined the effect of various changes in annual temperature, as well 20 as the combination of the most probable temperature increase (3 • C) with different increases in precipitation. The largest increase in both temperature and precipitation is projected for autumn and winter, but the timing of the maximum and minimum is uncertain. We therefore determined the effect of a sinusoidal variation with the maximum in mid-autumn (15 October) and the minimum in mid-spring, as well as a sinusoidal vari- 25 ation with the maximum in mid-winter (15 January) and the minimum in mid-summer. The amplitude of the oscillation is estimated from the RegClim results, where air temperature is varied by ±0.6 • C from a mean value of +3.0 • C and precipitation is varied TCD 3,2009 Hardangerjøkulen in the 20th and 21st century climates Interactive Discussion by ±15% from a mean change of +10%.

Results
In order to simulate the ice cap response to future climate projections, the effect of the present-day climate on the surface energy and mass balance should be well represented in the model. Therefore, we first compare the modelled surface energy and 5 mass balances with the AWS measurements on Midtdalsbreen and the mass balance measurements on Rembesdalsskåka. Ice dynamical effects were excluded in these model runs by keeping the topography fixed at the 1995 DEM. Subsequently, ice dynamics are included and we show the modelled response of Hardangerjøkulen to the observed climate of the 20th century and various climate scenarios for the 21st century.

Surface energy balance at the Midtdalsbreen AWS
The seasonal cycle of the surface energy balance at the Midtdalsbreen AWS is well captured by the model (Fig. 4a). Although the parameterizations for the individual fluxes were calibrated with the AWS measurements, this was often done separately for different atmospheric conditions (e.g., cloudy, clear-sky), not necessarily constraining 15 the integrated values. Furthermore, the calibration was performed with the meteorological values measured at the AWS, while the energy fluxes shown in Fig. 4a were calculated with local meteorological data. The model generally overestimates S net , while L net is too negative, which may indicate that cloud conditions at the local station are slightly different from the AWS site.

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For the period 1961-1990, all modelled energy fluxes are slightly smaller than for the warm 2001-2005 period (Fig. 4b). Using the control climate instead of the local meteorological records results in higher net solar radiation in several months; for the other fluxes the differences are small.
All surface energy fluxes increase or become less negative when the air temperature

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Interactive Discussion is raised by 3 • C, except for G, which remains close to zero (Fig. 4c). Because the winter snowpack with a high albedo disappears earlier in spring, the maximum in S net occurs earlier in the season and the largest increase in melt energy is simulated for June. The somewhat smaller increase in Q in the other summer months is mainly a result of larger turbulent fluxes and a small positive contribution by L net . Besides the increase This simulation shows how the surface energy fluxes at the Midtdalsbreen AWS are affected by an instantaneous temperature increase. For the future projection of Hardangerjøkulen, the air temperature is assumed to increase linearly in time and the ice cap surface will have lowered with respect to the DEM topography by the time the temperature has increased by 3 • C. The dynamic response will thereby further amplify the effect 15 of the warming on the surface energy balance.

Surface height at the Midtdalsbreen AWS
For all input data sets, the differences in modelled accumulation and ablation at the Midtdalsbreen AWS have been analysed separately, by first using the same (local) precipitation record in all runs and varying the set with other meteorological variables.

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This set, containing the air temperature, humidity, pressure and cloudiness records for a given input data set, is referred to as the "meteo" record. Similar results are obtained in the three runs ( Fig. 5a), hence modelled ablation at the AWS location does not deteriorate when the AWS measurements are replaced by a different "meteo" record; provided that the differences between the AWS and "meteo" records are accounted for 25 by a careful calibration. The variability between the results for the different data sets increases when the combination of "meteo" and precipitation records is used (Fig. 5b) Interactive Discussion measured snow depth is large in three of the five years, leading to the largest deviations from measured net ablation in these years. In 2003 and 2004, modelled snow depth is similar to the observed snow depth and measured net ablation is better reproduced. The modelled start of the melt season and the changes in ablation rate through the summer season agree well with the observations, again confirming that the modelled 5 energy fluxes are realistic and the differences with observations primarily originate from differences in precipitation. When the surface topography is not allowed to change, the accumulation and ablation modelled with the control climate are the same for all years (Fig. 5c). The comparison with measured surface height changes illustrates that the modelled start and end

Comparison with mass balance measurements
Modelled winter, summer and net mass balance for Rembesdalsskåka are compared 20 with NVE measurements for all 43 individual years (Fig. 6). The overall agreement between model results and measurements is good for the input data from both local stations and Bergen. The highest correlation coefficients (r) are obtained for the winter and net balance (Table 1), the interannual variability in the summer balance appears to be more difficult to simulate with the model. The best correlation is obtained by using 25 local input data; with Bergen input data, the winter balance is underestimated in the four wettest years. This could imply that the precipitation anomaly is larger in the surroundings of Hardangerjøkulen compared to Bergen. with Bergen input data is 0.19 mw.e. larger than the measured value, resulting in a higher than observed net balance in most of the years. Considering that no cloud observations are used for the simulations with data from Bergen, the model results are remarkably close to the measured values. There is little difference between the mass balance values modelled with either a constant or a responding surface topography, 5 suggesting that the modelled surface topography does not deviate much from the 1995 DEM. A comparison of two DEMs from 1961 and 1995 indicates that elevation changes over Rembesdalsskåka were generally smaller than +15 m (Andreassen and Elvehøy, 2001). We already showed that simulations with the control climate give seasonal energy 10 and mass balance variations at the AWS site on Midtdalsbreen that correspond well to the measurements, especially when considering that the period 1961-1990 was colder than 2001-2005. The control climate precipitation data were multiplied by a factor of 0.96 to match the modelled winter balance with the mean value from the NVE measurements over the period . The modelled summer and net mass 15 balance were not adapted in any way and correspond well to the mean NVE values, the difference is less than ±0.01 mw.e.

Spatial distribution of the mass balance
In Fig. 7 the spatial pattern of the modelled net mass balance is shown for the presentday topography (1995 DEM), together with the local mass balance deviation from the 20 altitudinal mean. We here show the mean values modelled with local data over the period ; the mass balance patterns are similar for other periods or input data, only the absolute values of the mass balance differ. The highest net mass balances are simulated for the upper ice cap with values around 1 mw.e (Fig. 7a). Mass balance values are slightly lower near the summit, 25 a result of the prescribed decrease in precipitation at the highest altitudes. There is little spatial variation in the accumulation area compared to the outlet glaciers, where the slopes are larger. The altitudinal deviations of the net mass balance mainly reflect vari-962 Introduction

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Printer-friendly Version Interactive Discussion ations due to the surface orientation and topography (Fig. 7b). Positive anomalies are found at steep north-facing slopes, where the surface orientation results in a reduction of direct solar radiation. Negative values mainly occur on the southern outlet glaciers, where the glacier surface is oriented towards the sun. Although surface slopes on Hardangerjøkulen are gentle compared to, for instance, glaciers in the European Alps, 5 topographic effects generate considerable spatial variability in the net mass balance. The differences can primarily be attributed to the angle of incidence for solar radiation, which varies with surface slope and aspect. Topographic shading, on the other hand, plays a minor role in the spatial pattern of the net balance as it mainly occurs at large solar zenith angles (in winter, morning and evening), when the amount of ablation is small. The precipitation gradient is less prominent in Fig. 7b, but on the plateau where slope effects are small, it is visible as generally positive anomalies in the south-west and negative anomalies in the north-eastern part of the ice cap.

Mass balance sensitivity
The changes in the surface mass balance corresponding to a 1 K change in air temper-15 ature (C T ) and a 10% change in precipitation (C P ) are often computed as a measure of a glacier's sensitivity to climate change. These static mass balance sensitivities C T and C P do not include ice dynamic effects and are defined as (Oerlemans, 2001): 20 We calculated C T and C P for the DEM topography, using local input data for the period . We obtained C T = −0.94mw.e.K −1 and C P = +0.30mw.e.  Rasmussen and Conway (2005) obtained C T = −0.64mw.e.K −1 and C P = +0.22mw.e.(10%) −1 , while De Woul and Hock (2005) report C T = −0.66mw.e.K −1 and C P = +0.28mw.e.(10%) −1 The larger sensitivity found in this study possibly results from differences in model types; while we used a distributed energy balance approach, Rasmussen and Conway (2005)  and C P = +0.28mw.e.(10%) −1 , almost identical to the values for the local data. These values suggest that at least a 30% increase in precipitation is needed to compensate 10 the effect of a 1 K temperature increase. The mass balance sensitivity for individual months is given by the seasonal sensitivity characteristic (SSC; Oerlemans and Reichert, 2000), where temperature or precipitation are only perturbed during one month at a time. We computed the SSC for Hardangerjøkulen, again using local input data for the period 1961-1990 (Fig. 8). The 15 largest changes in the net mass balance are obtained for a temperature change in the summer months. These are the months with the highest air temperatures, the largest surface energy fluxes and the transition from snow to ice albedos at the lower (June) to higher (August) altitudes and are therefore very sensitive to changes in the energy balance. In May and October, air temperatures are close to the threshold tempera-20 ture for snow. A small shift in temperature then directly enhances or reduces snow accumulation, significantly affecting the winter balance. The mass balance sensitivity to precipitation perturbations is largest in winter, when mass balance changes are dictated by the amount of solid precipitation. The lower mass balance sensitivity to precipitation changes in February compared to the surrounding months is not resulting 25 from the shorter length of this month; the sensitivities in Fig. 8 have been normalized to standard months of 30 days. For the period 1961-1990, the precipitation in February is clearly smaller than for the other winter months (Fig. 3).

Hardangerjøkulen in the 20th century
We now use the coupled model to simulate the ice cap evolution from 1905 to 2005. With the coupled model, the surface mass balance not only varies due to changes in climate, but also reacts to changes in the surface topography and ice cap extent induced by the mass balance history. When the coupled model is able to reproduce 5 the length change records of Rembesdalsskåka and Midtdalsbreen and the observed surface topography and ice cap extent, we can be confident that the model is able to simulate a realistic ice cap evolution for a given future climate scenario. Because there are no maps or outlines of Hardangerjøkulen available for the early 20th century, we use the 1904 ice cap modelled in the dynamic calibration (Giesen, 2009, Ch. 6) to prescribe the ice cap geometry at the beginning of 1905. Meteorological input data from Bergen are used until 1957, local meteorological data are used from 1958 onwards.
In 1905, the modelled margin of Hardangerjøkulen was located at an intermediate position between its maximum Little Ice Age extent and the present-day geometry 15 (Figs. 2 and 9). The ice cap decreased in volume until 1917, followed by a number of positive mass balance years that let the ice cap volume increase almost back to its 1905 volume (Fig. 10) and geometry (Fig. 9). Rembesdalsskåka is known to have advanced about 50 m between 1919 and the late 1920s, building a distinct moraine before retreating again (Faegri, 1936). This advance is smaller than the model res-20 olution (100 m) and is therefore not captured in the modelled length change record. The modelled frontal position of Rembesdalsskåka in 1928 corresponds well to the 1928 extent reported by Liestøl (1956). Midtdalsbreen is too large compared to the 1930 moraines identified by Andersen and Sollid (1971). After this small advance in the 1920s, a period with highly negative annual mass balances led to fast volume de-25 crease of Hardangerjøkulen until 1950 and an accelerated retreat of the outlet glaciers (Fig. 10) Interactive Discussion 1961, the ice thickness substantially decreased over the entire ice cap and the ice cap margin retreated everywhere along the outline of Hardangerjøkulen (Fig. 9). The modelled ice cap extent in 1961 corresponds quite well to the documented glacier outline for the south-western part of the ice cap; in the north-eastern part the modelled ice cap is too large (H. Elvehøy, personal communication, 2009). The period between 1961 5 and 1995 is characterized by steadily increasing net mass balances, culminating in the anomalously positive mass balance years in the late 1980s and early 1990s. An advance in the late 1990s is modelled for Midtdalsbreen, but not for Rembesdalsskåka, where the measured advance was significantly larger (Fig. 10). The length change measurements are however conducted at a different location than the end of the flow-10 line we used to determine the glacier length of Rembesdalsskåka. The model underestimates the length change of Midtdalsbreen through the entire 20th century. When we choose a smaller initial ice cap geometry to simulate the 20th century evolution of Midtdalsbreen, the length record is better reproduced. Hence, even for a century-long simulation, the initial conditions are important for the final result. 15 We find that the coupled model is well able to reproduce the observed variations of Hardangerjøkulen through the 20th century. The model performs somewhat less for the north-eastern part of the ice cap, probably a result of the initial ice thickness or the precipitation distribution, which is more uncertain for this area.

Hardangerjøkulen in the 21st century 20
The effect of different climate scenarios on the modelled ice cap mass balance and volume and the length of Rembesdalsskåka and Midtdalsbreen is shown in Table 2. All absolute and relative changes are given for the year 2086 with respect to a reference run with the unchanged control climate. By our definition of the climate projection, the projected change in climate for 2071-2100 occurs in 2086. The modelled volume and 25 length evolution through the 21st century are shown in Fig. 11  jumps in the lengths of Rembesdalsskåka and Midtdalsbreen prior to their disappearance occur because the ice disappearing last from the basins is situated at a distance from the head of the present-day glacier. Climate warming mainly affects the summer mass balance, but the winter balance also significantly decreases. A 10% precipitation increase along with the 3 • C tempera-10 ture increase has only a small effect on the projected volume and length changes. For a 50% precipitation increase, the ice cap disappears more slowly, but the effect of the temperature increase is by far not compensated. Even for a doubling of the precipitation (∆P = +100%), which may compensate a 3 • C warming according to the computed static mass balance sensitivities (Sect. 5.5), a significant reduction of Hardan-15 gerjøkulen's ice volume is projected for 2100. Apparently, non-linear effects associated with the much larger climate change than used to compute the mass balance sensitivities and the transient nature of the climate projections lead to more negative surface mass balances. A seasonally varying change in air temperature and precipitation with the maximum 20 change in autumn (15 October) does not lead to a notably different response of the ice cap (Table 2). However, when the maximum change occurs in winter (15 January), the winter balance remains more positive and the summer and net balance less negative, resulting in a slower decrease in ice volume and retreat of the outlet glaciers. Hence, the timing of the maximum change in temperature and precipitation does affect Introduction

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Printer-friendly Version Interactive Discussion snow accumulation or induce melt (Fig. 4). On the other hand, the smaller temperature increase from late spring to early autumn with respect to a constant annual change, leads to a higher winter balance and less summer ablation. Additional precipitation in winter further enhances this effect. For a maximum change in autumn, the mass balance is similar to the case without a seasonal cycle because opposite changes occur 5 in spring and autumn, when the sensitivity to temperature and precipitation changes is similar. An increase in the wind speed, simulated by a 10% increase in the turbulent exchange coefficient together with the 3 • C temperature increase, has a negligible effect on the modelled response of Hardangerjøkulen (∆V ice = −89% in 2086, instead 10 of −88%). A similarly prescribed cloud fraction increase of +0.05 also only slightly changes the model results (∆V ice = −91%). Apparently, the effect of the temperature increase on the incoming longwave radiation and the turbulent fluxes is much larger than changes induced by an increase in cloudiness or wind speed.
For one of the most probable scenarios according to the RegClim results (∆T = +3 • C 15 and ∆P = +10%), we discuss the modelled future changes in more detail. In the very near future, by 2010, the equilibrium-line altitude (ELA) is expected to be situated around 1740 ma.s.l. and only 35% of the total ice cap is located above the ELA (Fig. 12). However, the 2010 ice cap (Fig. 13) is very similar to the ice cap modelled for 1995 ( Fig. 9) and 2005, because the ice volume only just started to decrease after 20 reaching a maximum in the year 2000 (Fig. 10). Between 2010 and 2040, the net mass balance becomes negative at all altitudes (Fig. 12a) (Fig. 13). Because the ice layer at the high bedrock ridges is relatively thin (<100 m, Fig. 9), it has completely melted away by 2070, while ice still remains at the lower altitudes where the ice is thicker. By 2100, almost all ice has disappeared, thin ice layers only remain in the basins where the present-day ice is thickest. 5 The role of feedback processes in the response of Hardangerjøkulen was investigated by performing additional model simulations for ∆T = +3 • C and ∆P = +10% and excluding one process at a time.

Feedback processes
To determine the effect of the mass balance-altitude feedback, the mass balance distribution was computed on the 2005 topography for all years. In the first years, the 10 ice volume decrease is only slightly smaller when the mass balance-altitude feedback is excluded (Fig. 14), because the surface topography is still similar. By the year 2100, the ice volume difference has increased to almost 2 km 3 or 15% of the initial ice volume (2006). Subsequently, we completely turned off ice flow to assess to what extent volume 15 changes are determined by the local mass balance. Because the ice is no longer transported from high to low mass balance areas, thinning increases at the lower altitudes, while the change in ice thickness is reduced at the upper altitudes. As a result, the ice volume decreases more slowly than in the original simulation and attains almost exactly the same value in 2100 as in the simulation without mass balance-altitude feedback. Introduction

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Conclusions and discussion
A spatially distributed mass balance model was coupled to a two-dimensional ice-flow model to simulate the response of Hardangerjøkulen to projected climate change in the 21st century. By using a physically based mass balance model, projected changes in the meteorological variables could directly be incorporated in the model. Furthermore, the interactive coupling between the mass balance and ice-flow models ensured that feedback processes were included. The model was first validated with a simulation through the 20th century and was found to reproduce the evolution of Hardangerjøkulen as observed from changes in the glacier length and the surface topography. For the projected 3 • C warming, the model simulation indicated that Hardan-10 gerjøkulen will have almost disappeared by the end of the 21st century. The probable 10% increase in precipitation only slightly changed the modelled response; even a 100% precipitation increase could not fully compensate the effect of the temperature change. When the largest changes in temperature and precipitation were prescribed in winter, similar to the projections, the ice cap disappeared slower. However, none of 15 the probable changes in the other meteorological variables had such a large effect as a 3 • C warming.
Although we used a physically based model, there are still many factors adding uncertainty to the results. First of all, the future climate was modelled in a simple way. The interannual variability in the present-day climate of southern Norway is large, but 20 we prescribed the same annual cycle for every year. Moreover, the projected climate change was assumed to be constant or seasonally varying, while changes will most likely not be the same for different weather types. Secondly, the mass balance model contains several parameterizations which may be different for the future climate and ice cap. One example is the ice albedo, which was assumed to be constant in space and 25 time. In a warmer climate with less snowfall and a larger ablation area, more dust may accumulate on the ice surface, decreasing the albedo. A systematic lowering of the ice albedo has already been observed on Morteratschgletscher in Switzerland (Oerlemans , 2009). Still, lowering the ice albedo from 0.35 to 0.20 in the model simulation with ∆T = +3 • C and ∆P = +10%, only lead to a 5% larger volume decrease. The precipitation distribution and the snowpack structure were also simulated in a simple way and may not be correct for a warmer climate and a different ice cap topography. A high-resolution atmospheric model and a sophisticated snowpack model are needed 5 to improve the model in this respect, which is outside the scope of this study. Finally, increased meltwater production at the surface may enhance basal sliding and change the ice dynamics of Hardangerjøkulen. We expect that the warm, present-day ice cap already has an efficient drainage system and that this effect will therefore be small. By using a coupled model where the terms in the surface energy and mass balance are computed individually, the effect of climate change on the mass balance and geometry of Hardangerjøkulen was included in a realistic way. The largest uncertainties in the model results can therefore be ascribed to the large range in climate scenarios and not to the model design. We can conclude that, provided that a 3 • C warming indeed occurs in the 21st century and the precipitation increase is modest, Hardangerjøkulen 15 is bound to disappear within the next 100 years. The other maritime glaciers and ice caps in southern Norway have similar characteristics as Hardangerjøkulen and will probably also rapidly lose volume in the 21st century. A fast disappearance in a warmer climate has been projected for Nigardsbreen, an outlet glacier from the ice cap Jostedalsbreen, 130 km north of Hardangerjøkulen 20 (Oerlemans, 1997). Although he uses a simple mass balance representation and a flowline model, the results are similar. Only a small warming rate is needed for a significant decrease in ice volume, a simultaneous increase in precipitation only delays the glacier retreat. The more continental glaciers further inland have a more regular hypsometry and are situated at higher altitudes. These glaciers are less sensitive to 25 climate change and have a better chance to survive the 21st century, although largely reduced in size. Still, reconstructions of the Holocene glacier extent in southern Norway suggest that glaciers were absent in all glacierized regions during one or more periods in the early-/mid-Holocene, while air temperatures were probably lower than TCD Introduction

Conclusions
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Interactive Discussion the temperatures projected for the end of the 21st century. Applying the coupled model to a number of well-studied glaciers in different regions could give a more definitive answer on the future of the glaciers in southern Norway.
ice thickness distribution for the entire ice cap. The Norwegian Meteorological Institute is acknowledged for access to and use of their meteorological database eKlima. We thank NVE, in particular Hallgeir Elvehøy, for providing the mass balance and length change measurements.

A2 Bergen (1904-2005)
Before 1957, the nearest synoptic station with available data is the NMI station in Bergen ( Fig. 1 Bergen input data sets, respectively. When air temperature measurements were available for three-hour intervals, measurements were linearly interpolated to obtain hourly input data. For the data sets with three or four measurements per day, the daily cycle was approximated by a sine function fitted through the available measurements. Seasonally varying lapse rates for 5 temperature are necessary to correct for differences in the boundary-layer structure at the meteorological station and the glacier surface (Giesen et al., 2009). Separate lapse rates were applied for the local and Bergen data, determined from the difference in monthly mean values between the input data and the AWS measurements on Midtdalsbreen for the period 2001-2005. Values range between 6.5 and 9.7 K km −1 . Rela-10 tive humidity measurements were linearly interpolated between measurement times to create an hourly input data set. Air pressure input data were not interpolated to obtain hourly values, we only calculate the air pressure field at the measurement times. For the model runs with data from Bergen, we prescribe a seasonally varying air pressure at the AWS altitude with a sine function, based on the AWS measurements. The cloud 15 fraction input data were linearly interpolated between measurement times to create an hourly input data set. For runs with the Bergen data set, we prescribe the cloud fraction with a seasonally varying sinusoidal function derived from the AWS measurements. The daily precipitation sum from the input data is distributed evenly over the day in the model. As the measurement period at the NMI stations does not coincide with a 20 calendar day, we prescribe the precipitation sum measured between 6 and 06:00 UTC the following day on the first day, hence the record is shifted 6 h backward. For each precipitation data set (Slirå, Finse, Liset and Bergen), we determined a multiplication constant to relate measured precipitation to accumulation at the ice cap by fitting modelled to measured annual winter balance on Rembesdalsskåka for all overlapping 25 years. In this way, the total amount of winter accumulation is constrained to the measured winter balance, but interannual variations are preserved. Precipitation from Slirå and Finse is multiplied by 0.5 whenever the station temperature is above the threshold temperature for snow, to correct for overestimated values in summer resulting from  Table 2. Effect of different changes in air temperature (∆T ) and precipitation (∆P ) on the modelled winter (B w ), summer (B s ) and net (B n ) surface mass balance and ice volume (V ice ) of Hardangerjøkulen and the length of Rembesdalsskåka (L Remb ) and Midtdalsbreen (L Midt ) in the year 2086. The climate projections are prescribed as an annual and as a seasonally varying change, with the maximum on either 15 October or 15 January. All changes (∆) are given with respect to the reference run with the control climate for . The surface mass balance is the total surface mass balance over the modelled ice cap.  Modelled surface height at the AWS location on Midtdalsbreen with (a) variable "meteo" (air temperature, humidity, pressure and cloudiness) records and local precipitation, (b) both the "meteo" and precipitation records from the two data sets, and (c) the control climate (Ctrl) and the control climate with a 3 • C higher temperature, shown together with the measured surface height. The labels indicate the records used for the "meteo" and precipitation input in the order 'meteo'/precipitation. Introduction

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