Firn layer impact on glacial runoff: a case study at Hofsjökull, Iceland

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1 HYDROLOGICAL PROCESSES Hydrol. Process. 20, (2006) Published online in Wiley InterScience ( DOI: /hyp.6201 Firn layer impact on glacial runoff: a case study at Hofsjökull, Iceland Mattias de Woul, 1 * Regine Hock, 1 Matthias Braun, 2 Thorsteinn Thorsteinsson, 3 Tómas Jóhannesson 4 and Stefanía Halldórsdóttir 3 1 Department of Physical Geography and Quaternary Geology, Stockholm University, Stockholm, Sweden 2 Center for Remote Sensing of Land Surfaces, University of Bonn, Bonn, Germany 3 Hydrological Service, Orkustofnun (National Energy Authority), Reykjavik, Iceland 4 Icelandic Meteorological Office, Reykjavik, Iceland Abstract: A mass balance runoff model is applied to Hofsjökull, an 880 km 2 ice cap in Iceland, in order to assess the importance of the firn layer for glacial runoff. The model is forced by daily temperature and precipitation data from a nearby meteorological station. Water is routed through the glacier using a linear reservoir model assuming different storage constants for firn, snow and ice. The model is calibrated and validated using mass balance data and satellite-derived snow facies maps. Simulated mass balances and snowline retreats are generally in good agreement with observations. Modelled cumulative mass balance for the entire ice cap over the period 1987/1988 to 2003/2004 is 7Ð3 m, with uninterrupted negative mass balances since 1993/1994. Perturbing the model with a uniform temperature (C1 K)and precipitation (C10%) increase yields static mass balance sensitivities of 0Ð95 m a 1 and C0Ð23 m a 1 respectively. Removing the firn layer under otherwise likewise conditions results in almost unchanged total runoff volumes, but yields a redistribution of discharge within the year. Early summer discharge (June to mid August) is amplified by roughly 5 10%, whereas late-summer/autumn discharge (mid August to November) is reduced by 15 20% as a result of accelerated water flow through the glacial hydrological system. In comparison, applying a climate-model-based temperature and precipitation scenario for Iceland until 2050 results in higher runoff throughout the year, increasing total runoff by roughly one-third. The results emphasize the role of the firn layer in delaying water flow through glaciers, and the influence on discharge seasonality when firn areas shrink in response to climate-change-induced glacier wastage. Copyright 2006 John Wiley & Sons, Ltd. KEY WORDS temperature index model; glacier runoff; firn; glacier mass balance; climate change; Hofsjökull; Iceland INTRODUCTION The worldwide general retreat of glaciers during recent decades (Dyurgerov, 2002) has many implications operating on all spatial scales. These range from global effects on sea level and ocean systems (Dyurgerov and Carter, 2004), to regional and local effects on catchment hydrology (Dyurgerov, 2003; Hock et al., 2005). Glacier-melt-induced changes in runoff are of concern in areas such as Iceland, where glacier runoff is a major source for hydropower. Recent modelling experiments forced by model-generated climate scenarios indicate that total meltwater discharge from the Hofsjökull ice cap, Iceland, will increase by 50% until near the end of this century and decrease after that due to diminishing area of the ice cap, which is predicted to disappear within 200 years (Aðalgeirsdóttir et al., 2006). Several studies have found similar patterns with initially enhanced runoff volumes followed by runoff decline as the glaciers shrink (e.g. Jóhannesson, 1997; Braun et al., 2000; Ye et al., 2003). * Correspondence to: Mattias de Woul, Department of Physical Geography and Quaternary Geology, Stockholm University, Stockholm, Sweden. mattias.dewoul@natgeo.su.se Received 30 May 2005 Copyright 2006 John Wiley & Sons, Ltd. Accepted 18 November 2005

2 2172 M. DE WOUL ET AL. In addition to the effect on annual runoff volumes, glacier decline will affect the transport of water through the glacier, and thus seasonal and shorter-term discharge hydrographs (Hock et al., 2005). A glacier consists of firn (defined as snow that has survived at least one melt season), snow and ice, and thus three media with markedly different hydrological properties. In the accumulation area, the glacier ice is overlain by a firn layer often several tens of metres thick, whereas in the ablation area bare ice is exposed when the winter snow has melted. Although firn and snow behave hydrologically like porous groundwater aquifers with water percolating through interconnected pore spaces at speeds in the order of meters per hour (Schneider, 2000), ice is virtually impermeable to water, and water runs off the surface fast or enters the glacier via crevasses or moulins. From there, water flows mainly through well-defined passage systems with much larger travel velocities usually on the order of metres per second (Fountain and Walder, 1998). Consequently, the firn layer significantly delays water transport through the glacier by temporarily storing water in the firn aquifer, which is formed in a water-saturated zone above the impermeable ice firn transition. Under steady-state conditions, the firn area approximately coincides with the accumulation area, and covers roughly 50 60% of total glacier area (Dyurgerov, 2002), whereas the firn layer will be reduced or even vanish in a warming climate with enhanced melt, most rapidly for glaciers with a comparatively narrow altitude distribution (Braun et al., 2000). A retreat and thinning of the firn layer, and thus reduced water retention capacity, will accelerate runoff generation, amplifying peak discharges (Braun et al., 2000; Hock et al., 2005). Reduced winter discharge may have implications for water resource management when water levels fall beyond critical values, especially in regions with well-defined wet and dry seasons. The firn area is often not recognized for its effect on runoff regime, and to our knowledge there is no study explicitly investigating quantitatively the effect of the firn layer on glacial runoff. The purpose of this study is to assess the effect of the firn layer on glacial discharge. A distributed temperature index melt model is calibrated that is coupled to a linear reservoir discharge model forced by daily temperature and precipitation data from a meteorological station outside the ice cap. Mass balance observations and satellite-derived facies maps are used for calibration and validation. The model is then run with unperturbed climate data, but without a firn layer. This is intended as a theoretical exercise in order to assess the role of the firn layer in the runoff regime of the glacier, although our experiment of complete removal of the firn layer is not a likely scenario for Hofsjökull in the near future owing to its wide altitude distribution. But glacier disappearance, as predicted within the next 200 years (Aðalgeirsdóttir et al., 2006), will most likely be accompanied by gradual reduction and eventual disappearance of the firn layer. Complete removal of the firn layer has been observed on smaller alpine glaciers (e.g. Braun et al., 2000) as a result of prolonged negative mass balances in recent decades. The impact of the removal of the firn layer on annual and seasonal runoff is compared with the effects resulting from a change in the climate as specified by a climate-change scenario for Iceland until Finally, a uniform temperature and precipitation increase is applied to the meteorological data in order to assess static mass balance sensitivities and seasonal sensitivity characteristics. SITE DESCRIPTION Located in the central highlands of Iceland, Hofsjökull covers an area of 880 km 2 (in 2004), making it the third largest ice cap in the country (Figure 1). The summit is at 1790 m a.s.l., and outlet glaciers reach down to 600 m a.s.l. in the southern part and 850 m a.s.l. at the northern margins. The ice caps in the Icelandic highland are located in an area of maritime climate in the middle of the main track of low-pressure systems across the North Atlantic Ocean and, thus, receive large amounts of precipitation each year. Mass balance measurements on Hofsjökull were initiated in 1987 (Sátujökull), and the winter and summer mass balance of three ice-flow basins (Figure 1) has been monitored annually since 1988/1989 (Sigurðsson, 2001). Net mass balance (expressed in water equivalent) at the ice cap summit has varied between 5Ð31 m a 1 in 1991/1992 and 2Ð30 m a 1 in 2000/2001, averaging 3Ð35 m a 1 in the period 1987/1988 to 2003/2004.

3 FIRN LAYER IMPACT ON GLACIAL RUNOFF Sátujökull Langjökull Hofsjökull Vatnajökull 64 Hveravellir 0 50 km Blágnípujökull Þjórsárjökull km Figure 1. Location of Hofsjökull in central Iceland (left) with the meteorological station at Hveravellir, and a surface elevation map of the ice cap (right). The shaded areas outline the glaciers Sátujökull, Þjórsárjökull and Blágnípujökull for which mass balance data are reported (Sigurðsson, 2001). Dots mark mass balance stake locations The net mass balance of the monitored basins was positive in 1988/1989 and in the period 1990/1991 to 1993/1994. In the other years it was negative. The cumulative mass balance averaged over the monitored ice-flow basins of the ice cap in the period 1988/1989 to 2003/2004 was 8Ð3 m, which corresponds to a 4% decrease in the total ice volume in these areas. The bedrock and surface topography of Hofsjökull were surveyed in 1983 (Björnsson, 1988), and the map of the ice cap surface was later updated using results from global positioning system measurements in the summit region and aerial photogrammetry in the ablation area, as part of mass balance studies on the ice cap (Jóhannesson et al., 2004a). The average thickness of the ice cap is 215 m, with a maximum thickness of 750 m within a subglacial volcanic caldera located west of the summit. The surface and bedrock maps have made it possible to delineate ice catchment and water drainage basins within the ice cap (Björnsson, 1988). Currently, roughly 40% of the surface on Hofsjökull is covered by a firn layer up to 30 m thick (Thorsteinsson et al., 2002). Previous studies using degree-day glacier mass balance models have been conducted on Sátujökull (Jóhannesson et al., 1995; Jóhannesson, 1997), on Blöndujökull/Kvíslajökull, located on the western part of Hofsjökull between Sátujökull and Blágnípujökull, and on Illviðrajökull, located on the northeastern part of Hofsjökull between Sátujökull and Þjórsárjökull (Jóhannesson, 1997; Figure 1). Both the static and dynamic mass balance sensitivities of the glaciers were found to be in the approximate range 0Ð4 to 1Ð1 ma 1 K 1, depending on modelling assumptions (Jóhannesson, 1997). DATA Meteorological data Daily measured air temperature and precipitation data were taken from the meteorological station at Hveravellir ( N, W, 641 m a.s.l.) located about 30 km west of the Hofsjökull ice cap (Figure 1). Observations started in 1965, and the location is considered to be representative for the regional climate of

4 2174 M. DE WOUL ET AL. the Hofsjökull ice cap area (e.g. Jóhannesson et al., 1995). Mean annual temperature and precipitation for Hveravellir over the period 1987 to 2004 are 0Ð4 C and 740 mm respectively. Climate-change scenario The climate-change scenario developed for the Nordic countries within the framework of the Climate, Water and Energy (CWE) research project was adopted for this study (Rummukainen et al., 2003; Kuusisto, 2004). The scenario predicts climate change until 2050, with respect to 1990, based on regional climate model simulations forced by the Intergovernmental Panel on Climate Change (IPCC) B2 emission scenario (Houghton et al., 2001), and has previously been used for future predictions of Hofsjökull (Jóhannesson et al., 2004b; Aðalgeirsdóttir et al., 2006). Monthly temperature and precipitation changes for 2050 were used. Temperatures are projected to increase in 60 years by approximately 1Ð8 C in winter and 0Ð9 C in summer, with sinusoidal variation in-between. Owing to a lack of a clear seasonality in precipitation changes simulated by general and regional circulation models for the North Atlantic area, precipitation is assumed to increase by 5% per 1 C warming throughout the year, following Jóhannesson et al. (2004b). Mass balance data Mass balance is measured along three longitudinal profiles on the glaciers Sátujökull, Þjórsárjökull and Blágnípujökull (Figure 1), using standard techniques (Østrem and Brugman, 1991). Winter mass balance is determined in the first half of May by snow coring, and ablation is recorded in late September or early October from stakes drilled into the ice cap in spring. The measurements are carried out at over 30 fixed locations (Figure 1) on approximate flow lines, and each data point is assumed to be representative of the mass balance of a m altitude interval within each of the monitored ice-flow basins on the ice cap. From these data, width-averaged mass balances are derived for 100 m altitude intervals and then used to estimate area-averaged mass balances for the three ice-flow basins. The data for the period 1988/1989 (1987/1988 for Sátujökull) to 2003/2004 were used here (Sigurðsson, 2001). Satellite-derived snow facies maps For validation of modelled snowline retreat, a total of eight LANDSAT multi-spectral scenes (TM/ETMC, 30 m spatial resolution, path 219, row 15) acquired between 1994 and 2001 were retrieved. Emphasis was given to data from the ablation period. To extract the thematic information from the satellite images, a stepwise method was applied using a combination of techniques proposed by, for example, König et al. (1999) and Sidjak and Wheate (1999). All images were geometrically co-registered to an orthorectified master scene from the archive of the Global Land Cover Facility at the University of Maryland. A root-mean-square error below unity could be achieved for all images, guaranteeing a pixel-to-pixel match. During the preprocessing, three masks were subsequently generated. First, all glacierized areas were extracted using band 4, the normalized difference snow index and normalized difference vegetation index. Some snow-covered areas outside the glacier had to be removed manually. When the threshold approach did not capture all cloud features over the ice cap, cloud masking was performed using the thermal channel and some manual digitizing. Furthermore, cloud shadows were masked by another threshold on the principle component analysis image. All thresholds were selected by the operator for each image individually to optimize the results. For the classification process, an unsupervised ISODATA classification, with classes, was applied on each image (Mather, 1999). The classes were manually reviewed by the operator and then recoded to the desired four classes of snow, firn, ice and no data. MASS BALANCE AND DISCHARGE MODEL Mass balance model Ablation and accumulation are calculated at a daily resolution for each grid cell of a 100 m by 100 m digital elevation model. Ablation is modelled by a distributed temperature index melt model, which assumes

5 FIRN LAYER IMPACT ON GLACIAL RUNOFF 2175 a relationship between ablation and positive daily mean air temperatures, but which varies the degree-day factor as a function of potential direct solar radiation (Hock, 1999). Hence, air temperature is the only required meteorological input data for melt calculations. Melt M (mm day 1 ) at the glacier surface is calculated according to M D MF C r snow/ice I pot T T > 0 1 M D 0 T 0 where MF (mm day 1 C 1 is an empirical melt factor and r snow/ice (mm day 1 W 1 m 2 C 1 )isan empirical radiation coefficient, different for snow and ice to account for their differences in albedo; firn surfaces are treated as snow. I pot (W m 2 ) is the potential direct solar radiation at the inclined glacier surface and T ( C) is the daily mean air temperature, extrapolated to each grid cell using a constant lapse rate. I pot is time variant and is calculated as a function of top of atmosphere solar radiation, an assumed atmospheric transmissivity, solar geometry and topographic characteristics, such as shading, aspect and slope angles, and set to zero if the grid cell considered is shaded by surrounding topography. Although the effects of topography surrounding Hofsjökull are negligible, the ice cap itself exerts a topographic control on the distribution of solar radiation and the resulting spatial melt patterns, due to the effects of surface slope and surface aspect. By varying the degree-day factor according to I pot, a distinct spatial element is introduced considering these effects without the need of additional input data. The model has successfully been applied on several glaciers, e.g. by Schneeberger et al. (2001), Flowers and Clarke (2002), Schuler et al. (2005a,b) and snow-covered areas (Hock et al., 2002). The latter study discusses the model in further detail. Accumulation is modelled using a temperature threshold T 0 ( C) to discriminate snow from rain precipitation. A mixture of snow and rain is assumed in a transition zone ranging from T 0 1 C tot 0 C 1 C with a precipitation ratio of 50% snow and 50% rain at T 0. T 0 was set to 1 C in line with previous studies (e.g. Jóhannesson et al., 1995). Precipitation is adjusted by a precipitation correction factor to account for undercatch losses and then assumed to increase linearly with elevation. The following six model parameters (Table I) are optimized using observed mass balance stake readings: temperature lapse rate, melt factor MF, radiation coefficient for snow/firn r snow/firn, radiation coefficient for ice r ice, precipitation versus elevation gradient, and precipitation correction factor. Discharge routing Melt water and rainwater are routed through the ice cap using a linear reservoir approach. Despite its simplicity, the concept of linear reservoirs has proven highly efficient, and thus is widely used in accommodating the delay of water in the glacial hydrological system (Baker et al., 1982; Hock and Jansson, 2005; Schaefli et al., 2005). Following Hock and Noetzli (1997), the model used in this study comprises three different parallel linear reservoirs, referred to as the firn, snow, and ice reservoirs. Daily discharge for each reservoir is computed by Q t D Q t 0 e t t0 /k C I t [1 e t t0 /k ] 2 Table I. Calibrated model parameters Parameter Value Unit Temperature lapse rate 0Ð7 C/100 m Melt factor, MF 2Ð0 mm day 1 C 1 Radiation coefficient for snow r snow/firn 21Ð6 ð 10 3 mm day 1 W 1 m 2 C 1 Radiation coefficient for ice r ice 28Ð8 ð 10 3 mm day 1 W 1 m 2 C 1 Precipitation gradient 30 % per 100 m Precipitation correction factor 25 %

6 2176 M. DE WOUL ET AL. where Q t is outflow, I t is the inflow by melt and rain water, k is the storage coefficient corresponding to the mean residence time of the water in the reservoir, and t 0 is the time step preceding t. Total discharge is obtained by adding the outflows from the three reservoirs (firn, snow and ice). Daily discharge from the entire ice cap is computed assuming one fictitious glacier stream, although the ice cap is actually drained by several rivers originating from distinct glacier drainage basins. This procedure is justified because the purpose of the study was not to model the runoff of individual glacial rivers, but, rather, to assess the effect of the firn layer on the glacial discharge regime. Modelling partly glacierized drainage basins would require a fourth, groundwater flow, reservoir to be used, calibrated with downstream discharge measurements. Such a reservoir is excluded from this study because the focus here is exclusively on the glacial contribution to catchment runoff. Water of each grid cell is transferred to one of the three reservoirs according to surface characteristics (Figure 2). The firn reservoir is delineated by the area with a firn layer on top of the ice, no matter whether or not the surface is covered by last winter s, or fresh, snow (Figure 2a c). The snow reservoir refers to the snowcovered grid cells outside the area that is defined as the firn reservoir (Figure 2a and b). Since the overlying snowpack on the firn reservoir is relatively thin compared with the thickness of the firn layer, the additional retardation of water is small and, thus, snow-covered firn grid cells are regarded as firn (Figure 2a c). Water from grid cells with bare ice is transferred to the ice reservoir. The area of the firn reservoir is kept constant Winter Summer Late summer (a) (b) (c) Present firn extent Snow Q firn Q snow Q firn Q snow Q ice Q firn Q ice Firn Q total Q total Q total Ice Winter Summer Late summer (d) (e) (f) No firn layer Q snow Q snow Q ice Q ice Q total Q total Q total Figure 2. Schematic illustration of the linear reservoir concept using a firn, snow and ice reservoir on Hofsjökull. Delineation of reservoirs during present firn layer extent for (a) winter, (b) summer and (c) late summer during a negative mass balance year, and with the firn layer removed during (d) winter, (e) summer and (f) late summer. Q total is total discharge from the ice cap. Note that the thickness of the Q total bar is neither proportional to the number of active reservoirs, nor to total discharge

7 FIRN LAYER IMPACT ON GLACIAL RUNOFF 2177 throughout the simulation period (Figure 2a c), whereas the areas of the snow and ice reservoirs change progressively, according to snowline retreat as the melt season proceeds or whether fresh snowfall occurs. Storage coefficients are assumed constant but different for each reservoir, thereby accounting for the different water retardation properties of snow, firn and ice. The firn reservoir has the largest delay and, therefore, the highest coefficient, followed by that of the snow reservoir, with the lowest value attributed to the ice reservoir, reflecting that water runs off with very little delay. Owing to lack of data to determine, or calibrate, the storage coefficients, two sets of values were chosen, representing likely minimum and maximum values. Reported storage coefficient values k for glaciers ranging in size from 3 to 40 km 2 vary from 350 to 430 h for k firn, from 30 to 120 h for k snow, and from 4 to 45 h for k ice (Hock and Jansson, 2005). Since Hofsjökull is a much larger ice cap, the approximate average of these values is used as the minimum k-value for each reservoir (i.e. k firn D 400 h, k snow D 60 h, k ice D 20 h). A second set of k values is adopted as maximum values, with the value for k doubled for each different type of reservoir (i.e. k firn D 800 h, k snow D 120 h, k ice D 40 h). All results hereafter are reported for both sets in order to demonstrate the sensitivity of the model, and its outputs, to the choice of k. Firn layer extent was obtained from the satellite-derived snow facies map from 23 August 1998, and assumed constant (Figure 2a c), with the additional constraint that no firn was assumed below 1300 m a.s.l., based on observations. Analysis of further satellite images and other observations suggest that firn layer extent has not changed significantly during the simulation period. MODEL CALIBRATION AND EXPERIMENTS The model was calibrated by varying the six model parameters within reasonable limits until maximum agreement between modelled and measured mass balance was obtained at the 34 stake locations on the Hofsjökull ice cap (Figure 3; Table I). The data for the mass balance years 1987/1988 to 1994/1995 were used for calibration. The mass balance years between 1995/1996 and 2003/2004 were allocated as validation years, and the mass balance model was finally run over the entire mass balance period. The tuning of parameters for the calibration period followed a procedure where the winter mass balance was first computed individually for each mass balance year of the calibration period. The parameters related to snow accumulation (lapse rate, precipitation gradient and precipitation correction factor) were optimized. In a second step, the 6 Measured net mass balance (ma 1 ) r 2 = Modelled net mass balance (ma 1 ) Figure 3. Correlation between measured and modelled annual net mass balances at 34 locations on Hofsjökull ice cap for the calibration period 1987/1988 to 1994/1995

8 2178 M. DE WOUL ET AL. remaining parameters were optimized by maximizing agreement between modelled and observed annual net mass balances. Mass balance was extracted for each year matching the dates of measurements of summer and winter balances, based on an average date from the actual dates of measurements in the three different ice-flow basins (Sigurðsson, 2001). Glacial runoff for the entire ice cap was computed using the optimized set of parameters for the control run. In a second run, the model was applied without a firn layer, assuming otherwise likewise conditions (Figure 2d f). Although the experiment is not realistic for the near future of Hofsjökull, it is likely that the firn layer will be reduced substantially during this century if the equilibriumline altitude rises several hundred metres and the glacier experiences sufficiently prolonged glacier wastage as projected by Aðalgeirsdóttir et al. (2006). The experiment provides an upper bound on the impact of a reduction in the firn layer extent that will accompany such changes. The model was finally perturbed with the CWE climate-change scenario. Eight experiments were conducted, using all possible combinations of runs with or without firn layer, with present climate or CWE scenario, and for each set of k values. Since the temperature change for Iceland shows clear seasonality according to the CWE scenario, the model was also used to compute the static mass balance sensitivity of Hofsjökull by applying, over the entire period, a uniform 1 K increase in temperature and a 10% increase in precipitation to the meteorological data from Hveravellir. Following Oerlemans and Reichert (2000), the seasonal mass balance sensitivities were calculated, defined as changes in mass balance in response to changes in climate forcing during individual months. A total of 24 scenarios were produced, where, first, temperature was increased for each month individually, leaving the remaining months and precipitation unchanged (12 scenarios). Second, the procedure was repeated, but precipitation was increased while temperature was unperturbed (12 scenarios). Comparing the results with those of the control run allows one to assess how much each month contributes to the total sensitivity and, thus, how the sensitivity varies seasonally and, especially, during the main runoff season. RESULTS AND DISCUSSION Model performance Modelled snowline retreat patterns appeared to agree well with those derived from satellite data for the dates where such data were available (Figure 4). Modelled area-averaged mass balance for Hofsjökull generally agreed well with mass balances of Sátujökull, Þjórsárjökull and Blágnípujökull derived from the measurements (Sigurðsson, 2001). For the sake of readability, Figure 5 shows the observed values for the three flow basins along with the mass balance for the entire Hofsjökull ice cap, although these values are not directly comparable. Nevertheless, the variation with time coincides well with the measurements on all three glaciers measured, indicating that the model capturesinterannual mass balance variability well. Modelled cumulative mass balance for the entire ice cap over the period 1987/1988 to 2003/2004 is 7Ð3 m, and 6Ð8 m over the period 1988/1989 to 2003/2004, compared with an observed cumulative mass balance for the monitored ice-flow basins over the period 1988/1989 to 2003/2004 of 8Ð3 m. The modelled net mass balance for the entire Hofsjökull ice cap has been negative since 1993/1994, in agreement with observations (Figure 5). Part of the variance in Figure 3 is attributed to snow accumulation variability caused by factors other than elevation. The simple precipitation model does not, for example, capture the northwest to southeast horizontal precipitation gradient on the ice cap. This leads to a consistent geometrical distribution in difference between the modelled and measured mass balances. Including horizontal gradients, in addition to altitudinal gradients, captures a part of this variability (Aðalgeirsdóttir et al., 2006), but it is considered unlikely that such model enhancement would alter the results concerning the influence of firn on runoff seasonality. Runoff sensitivity to firn layer extent and climate change Modelled runoff shows a seasonal distribution typical of glacierized areas, with almost all runoff occurring during the melt season. Flow approaches zero during winter (Figure 6a). Modelled average specific runoff

9 FIRN LAYER IMPACT ON GLACIAL RUNOFF August August August 2000 Observed Snow Firn Ice Modelled Figure 4. Satellite-derived facies maps (top) with surface type (snow, firn and ice) in comparison with corresponding modelled surface conditions of Hofsjökull (bottom) for the entire 17-year period is 97 l s 1 km 2, of which 96% occurs during summer (defined as May to September). It must be borne in mind that the model only considers runoff from glacier melt and rainfall onto the glacier; groundwater from underlying substrate is not included, but this most likely sustains a continuous base flow throughout the winter whose rate is unknown. Removing the firn layer alters the discharge regime (Figure 6a) such that runoff is amplified during the first part of the melt season and reduced later in the season. Hence, runoff volumes are redistributed from late to early summer. This overall pattern is consistent for both sets of storage coefficients (k values), with a larger retardation effect for the second set of storage coefficients, as expected (Figure 6b). Averaged over all years, runoff volume between 1 June and 15 August increases by 6% (10%), ranging from 4 to 7% (7 to 12%) for individual years. Numbers in parentheses refer to simulation results using doubled k values (Equation (2)). During late summer to early winter (16 August to 1 December) the mean runoff volumes are reduced by 15% (19%), ranging from 5 to 23% (7 to 33%) for individual years. Maximum daily mean discharge for each year is enhanced on average by 18% (18%), ranging from 10 to 26% (13 to 27%) for individual years, as a direct consequence of faster runoff generation (Figure 7), where the numbers in parentheses again refer to simulations using doubled k values. Total runoff remains almost identical with and without a firn layer, indicating that melt conditions are similar. This is due to our assumption of unaltered climate conditions in each pair of simulations with and without a firn layer. Under present conditions, the higher parts of the glacier (roughly speaking those parts that lie above the present firn line) generally remain snow covered by the end of the melt season both in the model (cf. Figure 2c) and according to observations. Hence, no matter whether or not the firn layer is included in the model run, modelled melt will be similar because coefficients in the melt model are assumed equal for snow

10 2180 M. DE WOUL ET AL. 4 Winter mass balance 3 Mass balance (ma -1 ) Summer mass balance Net mass balance Mass balance (ma -1 ) Sátujökull (observed) Þjórsárjökull(observed) Blágnípujökull (observed) Hofsjökull (modelled) 1987/ / / / / / / / /04 Figure 5. Comparison between observed mean specific winter (top), summer (middle) and net (bottom) mass balance from the three glaciers Sátujökull (1987/1988 to 2003/2004), Þjórsárjökull (1988/1989 to 2003/2004) and Blágnípujökull (1988/1989 to 2003/2004), and modelled results for the entire Hofsjökull ice cap (1987/1988 to 2003/2004) and firn surfaces (Equation (1)). Under conditions that lead to reduced extent of firn and snow-covered areas, additional feedback mechanisms will act. Melt rates will accelerate as the area of bare ice increases due to firn-line retreat, and the duration that bare ice is exposed increases due to the shorter period of seasonal snow cover. Hence, melt rates accelerate, invoking additional amplification of discharge during summer. However, unaltered melt input in the experiment allows an assessment to be made of the effects of altered firn storage only. Consequential changes in runoff are not due to enhanced melt water volumes; rather, they result from altered storage characteristics in the glacier. Under present conditions, summer discharge peaks are dampened by storage of water in the porous firn layer. In the run without a firn layer, the retention capacity of the glacier is reduced and runoff generation is accelerated. Hence, discharge peaks are enhanced and storage of water in the glacier is depleted faster, so that glacier discharge is considerably reduced later in summer and autumn. Figure 6b compares the impact on runoff due to removal of the firn layer to the changes corresponding to the climate change scenario to Perturbing the model with the monthly CWE climate-change scenario, and assuming the present firn layer extent, enhances total melt water discharge from Hofsjökull by 34% for both sets of storage coefficients k. Figure 6b illustrates that, during early summer, runoff amplification by the effect of firn layer removal only (case 1, Figure 6b), can reach up to roughly half of the amplification resulting from the climate-change scenario to Since firn layer extent will most likely decrease under the climate conditions predicted by the CWE scenario, Figure 6b also includes results from a run including both CWE climate-change perturbation and removal of firn layer. The results show further amplification of early summer discharge, which reduces later in the melt season because of the effect of runoff shifting forward in the melt season as the firn layer vanishes. Mass balance sensitivity The CWE-projectedtemperature increase is higher in winter than in summer, but the mass balance sensitivity shows a clear seasonality in the opposite direction, as shown in Figure 8. A given temperature increase during

11 FIRN LAYER IMPACT ON GLACIAL RUNOFF 2181 (a) 400 Present firn layer No firn layer Q (m 3 s 1 ) (b) 120 Q (m 3 s 1 ) (1) No firn layer scenario (2) CWE climate scenario (3) No firn layer and CWE climate scenario 40 1 Jan 1 Apr 1 Jul 1 Oct 31 Dec Figure 6. (a) Modelled daily discharge Q from Hofsjökull ice cap averaged over the period 1988 to 2004 for two model runs assuming present firn layer extent and a scenario where the firn layer is removed; both runs using present climate conditions and lower set of storage coefficients k. (b) Differences in daily discharge 1Q between two model runs averaged over the period 1988 to 2004: (1) model results assuming removal of firn layer minus results assuming present firn layer, both runs using present climate conditions; (2) model results assuming CWE climate scenario minus results assuming present-day climate, both runs with present firn layer; (3) as (2), but both model runs without firn layer. Thicker and thinner lines refer to two different model runs using two different sets of storage coefficients in the linear reservoir discharge model Q (m 3 s 1 ) Year Figure 7. Maximum daily mean discharge Q for each year from Hofsjökull ice cap with present climate conditions but for a scenario where the firn layer is removed, for the lower (left-hand bars) and higher (right-hand bars) set of storage coefficients k. The darker parts of the bars indicate the amount by which daily mean discharge is amplified compared with daily mean discharge using present firn layer extent (lighter parts of the bar)

12 2182 M. DE WOUL ET AL. Dec Nov Oct Sep Aug Jul Jun May Apr Mar Feb Jan Mass balance sensitivity (ma 1 ) Figure 8. Seasonal sensitivity characteristics for Hofsjökull ice cap. The black bars represent the mass balance sensitivity (m a 1 )toac1 K temperature perturbation and the grey bars represent the mass balance sensitivity (m a 1 )toac10% precipitation perturbation applied to each month individually of the observed meteorological data from Hveravellir for the period summer has a much greater effect on mass balance than an identical change during winter. Hence, even small temperature increases in summer may have a considerable effect on mass balance and glacial runoff. The seasonal mass balance characteristic found on Hofsjökull is typical of maritime climates and similar to results obtained on Vatnajökull (de Ruyter de Wildt et al., 2003). Sensitivities have been shown to be higher on maritime glaciers characterized by high precipitation and large mass turnover compared with glaciers in continental environments (e.g. Oerlemans and Fortuin, 1992; de Woul and Hock, 2005). For the entire Hofsjökull ice cap, the static mass balance sensitivity to a uniform increase in temperature throughout the year by C1 Kis 0Ð95 m a 1,andC0Ð23 m a 1 due to an increase in precipitation by C10%; the latter thus compensates the temperature effect by approximately one-fourth. The results fall within the wide range of previously reported temperature sensitivities for various individual glaciers on Hofsjökull ice cap, ranging from 0Ð6 to 0Ð98 m a 1 K 1 (Table II). Although static mass balance sensitivities, in contrast to dynamic sensitivities (Oerlemans et al., 1998), ignore the effects of time-dependent glacier retreat and front variations, the concept of static mass balance sensitivities has, nevertheless, proven useful in studying regional and seasonal differences in the sensitivity of glaciers to climate change (Braithwaite and Zhang, 1999; de Woul and Hock, 2005). CONCLUSIONS A grid-based distributed temperature-index ice- and snow-melt model coupled to a linear reservoir discharge model was applied to Hofsjökull, Iceland, in order to assess the effect of the firn layer on the glacier discharge regime in comparison with the effect of climate change defined by a climate model scenario for the year Modelled cumulative mass balance for the entire ice cap over the period 1987/1988 to 2003/2004 is 7Ð3 m with uninterrupted negative balances for modelled mass balance for the entire Hofsjökull ice cap since 1993/1994, in agreement with observed negative mass balances from three monitored ice-flow basins on the ice cap. The model is also perturbed with a uniform temperature (C1 K) and precipitation (C10%) increase yielding static mass balance sensitivities of 0Ð95 m a 1 and C0Ð23 m a 1 respectively, in line with previous studies (Table II). An extreme case scenario where the firn layer is removed in the model, under otherwise similar conditions, results in a considerable redistribution of discharge over the year. Total summer runoff volumes

13 FIRN LAYER IMPACT ON GLACIAL RUNOFF 2183 Table II. Results from this and previous studies for static mass balance sensitivity for Hofsjökull ice cap and some of its outlet glaciers in response to an increase in temperature by 1 K and an increase in precipitation by 10% Glacier Mass balance sensitivity (m a 1 ) Meteorological station Reference C1 K C10% Hofsjökull ice cap 0Ð95 C0Ð23 Hveravellir This study Sátujökull 0Ð82 a C0Ð05 a Hveravellir de Woul and Hock (2005) Þjórsárjökull 0Ð98 C0Ð11 Hveravellir de Woul and Hock (2005) Blágnípujökull 0Ð78 C0Ð06 Hveravellir de Woul and Hock (2005) Blöndujökull/Kvíslajökull 0Ð6 Nautabú Jóhannesson (1997) Illviðrajökull 0Ð9 Nautabú Jóhannesson (1997) a Unpublished data. remain similar, but early summer runoff (June to mid August) is amplified on average by between 6 and 10% (depending on choice of model parameters), whereas late-summer/autumn runoff (mid August to November) is reduced by 15 to 19%. Such shifts result from accelerated water flow through a glacial hydrological system without a firn layer. Early in the season the melt water runs off faster, thus augmenting daily flows. Later in the season, discharge is generally lower due to the lack of outflow from water stored in the firn layer. In comparison, forcing the model with a temperature and precipitation increase as projected by a climate-change scenario for Iceland until 2050 and assuming the present firn layer extent results in a runoff increase throughout the year roughly amounting to one-third of annual average runoff. The results elucidate the role of the firn layer in glacial runoff regimes, and emphasize that, in addition to climate-change-induced augmentation of annual glacial runoff, a vanishing firn layer will strongly affect seasonality and peak discharges. Such changes will have implications for watershed management, flood protection and hydropower. Realistic predictions of future seasonality of runoff from glaciers need to consider the effects of diminishing firn layers. Modelling the decline of the firn layer in conjunction with mass balance, geometry changes and resulting runoff in response to climate-change scenarios is an important part of the prediction of future changes in glacial runoff seasonality. ACKNOWLEDGEMENTS This study is part of the GMES Northern View project, financed by the European Space Agency (ESA), and the CE (Climate and Energy) project, funded by Nordic Energy Research (NEFP). The meteorological data were provided by the Icelandic Meteorological Office. Comments by Oddur Sigurðsson, Bettina Schaefli, an anonymous reviewer and the scientific editor Gwyn Rees greatly helped to improve the paper. REFERENCES Aðalgeirsdóttir G, Jóhannesson T, Björnsson H, Pálsson F, Sigurðsson O The response of Hofsjökull and southern Vatnajökull, Iceland, to climate change. Journal of Geophysical Research in press. Baker DH, Escher-Vetter H, Moser H, Oerter H, Reinwarth O A glacier discharge model based on results from field studies of energy balance, water storage and flow. In Hydrological Aspects of Alpine and High-Mountain Areas, Glen JW (ed.). IAHS Publication No IAHS Press: Wallingford; Björnsson H Hydrology of Ice Caps in Volcanic Regions. Societae Scientiarum Islandica, Rit. 45. Societas Scientarium Islandica, University of Iceland: Reykjavík.

14 2184 M. DE WOUL ET AL. Braithwaite RJ, Zhang Y Modelling changes in glacier mass balance that may occur as a result of climate changes. Geografiska Annaler, Series A: Physical Geography 81(4): Braun LN, Weber M, Schulz M Consequences of climate change for runoff from alpine regions. Annals of Glaciology 31: de Ruyter de Wildt MS, Klok EJ, Oerlemans J Reconstruction of the mean specific mass balance of Vatnajökull (Iceland) with a seasonal sensitivity characteristic. Geografiska Annaler, Series A: Physical Geography 85: de Woul M, Hock R Static mass balance sensitivity of Arctic glaciers and ice caps using a degree-day approach. Annals of Glaciology 42: in press. Dyurgerov MB Glacier mass balance and regime: data of measurements and analysis. Meier M, Armstrong R (eds). INSTAAR Occasional Paper No. 55. Dyurgerov MB Mountain and subpolar glaciers show an increase in sensitivity to climate warming and intensification of the water cycle. Journal of Hydrology 282(1 4): DOI: /S (03) Dyurgerov MB, Carter CL Observational evidence of increases in fresh water inflow to the Arctic Ocean. Arctic, Antarctic, and Alpine Research 36(1): Flowers GE, Clarke GKC A multicomponent coupled model of glacier hydrology: 2. Application to Trapridge Glacier, Yukon, Canada. Journal of Geophysical Research 107(B11): DOI: /2001JB Fountain AG, Walder JS Water flow through temperate glaciers. Reviews of Geophysics 36(3): Hock R A distributed temperature-index ice- and snowmelt model including potential direct solar radiation. Journal of Glaciology 45(149): Hock R, Jansson P Modelling glacier hydrology. In Encyclopedia of Hydrological Sciences, Anderson M (ed.). Wiley: Chichester; Hock R, Noetzli C Areal melt and discharge modlling of Storglaciären, Sweden. Annals of Glaciology 24: Hock R, Johansson M, Jansson P, Bärring L Modelling climate conditions required for glacier formation in cirques of the Rasspautasjtjåkka massif, northern Sweden. Arctic, Antarctic and Alpine Research 34(1): Hock R, Jansson P, Braun L Modelling the response of mountain glacier discharge to climate warming. In Global Change and Mountain Regions A State of Knowledge Overview, Huber UM, Reasoner MA, Bugmann H (eds). Springer: Dordrecht; Houghton JT, Ding Y, Griggs DJ, Noguer M, van der Linden PJ, Dai X, Maskell K, Johnson CA (eds) Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press: Cambridge, UK/New York, NY, USA. Jóhannesson T The response of two Icelandic glaciers to climatic warming computed with a degree-day glacier mass balance model coupled to a dynamic glacier model. Journal of Glaciology 43(144): Jóhannesson T, Sigurdsson O, Laumann T, Kennett M Degree-day glacier mass balance modelling with applications to glaciers in Iceland, Norway and Greenland. Journal of Glaciology 41(138): Jóhannesson T, Aðalgeirsdóttir G, Björnsson H, Pálsson F, Sigurðsson O. 2004a. Response of glaciers and glacier runoff in Iceland to climate change. In Nordic Hydrological Conference 2004 (NHC-2004), Järvet A (ed.). Nordic Hydrological Programme: Tartu; Jóhannesson T, Aðalgeirsdóttir G, Björnsson H, Bøggild CE, Elvehøy H, Guðmundsson S, Hock R, Holmlund P, Jansson P, Pálsson F, Sigurðsson O, Þorsteinsson Þ. 2004b. The impact of climate change on glaciers in the Nordic countries. Report by CWE Glaciers group. CWE Report No. 3. König M, Winther J-G, Isaksson I Measuring snow and glacier ice properties from satellite. Reviews of Geophysics 39(1): Kuusisto E Climate, Water and Energy. A summary of a Joint Nordic Project CWE Report No. 4. Mather PM Computer Processing of Remotely-Sensed Images. An Introduction, second edition. Wiley: Chichester. Oerlemans J, Reichert BK Relating glacier mass balance to meteorological data by using a seasonal sensitivity characteristic. Journal of Glaciology 46(152): 1 6. Oerlemans J, Fortuin JPF Sensitivity of glaciers and small ice caps to greenhouse warming. Science 258(5079): Oerlemans J, Andersson B, Hubbard A, Huybrechts P, Jóhannesson T, Knap WH, Schmeits M, Stroeven AP, Van de Wal RSW, Wallinga J, Zuo Z Modelling the response of glaciers to climate warming. Climate Dynamics 14(4): Østrem G, Brugman M Glacier mass-balance measurements. A manual for field and office work. NHRI Science Report No. 4. NVE, Oslo. Rummukainen M, Räisänen J, Bjørge D, Christensen JH, Christenssen OB, Iversen T, Jylhä K, Ólafsson H, Tuomenvirta H Regional climate scenarios for use in Nordic water resources studies. Nordic Hydrology 34(5): Schneeberger C, Albrecht O, Blatter H, Wild M, Hock R Modelling the response of glaciers to a doubling in atmospheric CO 2 :a case study on Storglaciären, northern Sweden. Climate Dynamics 17(11): Schneider T Hydrological processes in the wet-snow zone of glaciers a review. Zeitschrift für Gletscherkunde und Glazialgeologie 36(1): Schuler T, Hock R, Jackson M, Elvehøy H, Braun M, Brown I, Hagen J-O. 2005a. Distributed mass balance and climate sensitivity modelling of Engabreen, Norway. Annals of Glaciology 42: in press. Schuler T, Melvold K, Hagen J-O, Hock R. 2005b. Assessing the future evolution of meltwater intrusions into a mine below Gruvefonna, Svalbard. Annals of Glaciology 42: in press. Schaefli B, Hingrau B, Niggli M, Musy A A conceptual glacio-hydrological model for high mountainous catchments. Hydrology and Earth System Sciences 9: Sidjak RW, Wheate RD Glacier mapping of Illecillewaet icefield, British Columbia, Canada, using Landsat TM and digital data. International Journal of Remote Sensing 20(2):

15 FIRN LAYER IMPACT ON GLACIAL RUNOFF 2185 Sigurðsson O Jöklabreytingar , og [Glacier variations in Iceland , and ]. Jökull 50: Thorsteinsson T, Sigurðsson O, Jóhannesson T, Larsen G, Drücker C, Wilhelms F Ice core drilling on the Hofsjökull ice cap. Jökull 51: Ye B, Ding Y, Liu F, Liu C Responses of various-sized alpine glaciers and runoff to climate change. Journal of Glaciology 49(164): 1 7.