0 Physical energy balance and degree-day models of summer ablation on Langjökull ice cap, SW-Iceland Sverrir Guðmundsson Helgi Björnsson Finnur Pálsson Hannes H. Haraldsson Science Institute, University of Iceland National Power Company of Iceland RH-20-2003 1 CONTENTS 1. INTRODUCTION........................................................................................................................ 2 2. OBSERVATIONS........................................................................................................................ 2 3. METHODS ................................................................................................................................... 4 3.1. ENERGY BUDGET DURING THE MELTING SEASON ..................................................................... 4 3.2. DEGREE-DAY MODELS ............................................................................................................. 5 4. RESULTS ..................................................................................................................................... 6 4.1. VARIATION OF THE ENERGY BUDGET DURING THE ABLATION SEASON ..................................... 6 4.2. VARIATION OF THE ENERGY BUDGET WITH ELEVATION ........................................................... 9 4.3. EMPIRICAL ABLATION MODELS (DEGREE-DAY) ...................................................................... 11 4.4. SENSITIVITY OF THE SUMMER MELTING TO CLIMATE CHANGES .............................................. 13 5. CONCLUDING REMARKS .................................................................................................... 18 ACKNOWLEDGEMENTS .......................................................................................................... 18 REFERENCES............................................................................................................................... 19 2 1. INTRODUCTION Langjökull is the second largest ice cap in Iceland (925 km2 in area), located at ~64.7°N and ~20.4°W in southwest Iceland (Fig. 1). The range in elevation is from 450 to 1450 m a.s.l., with an average height of 900 m a.s.l. The surroundings of Langjökull comprise lava, sand, and proglacial lakes. The major rivers draining the ice cap are Hvítá in Borgarfjörður and Hvítá in Árnessýsla. A significant part of the glacial meltwater drains directly into groundwater (Sigurðsson, 1990). Measurements of annual summer and winter balance ( bs and bw ) have been conducted at points along flowlines on Langjökull since 1996 (Björnsson and others, 1997; 1998a; Pálsson and others, 2000, 2001). Each year snow cores have been drilled in April-May through the winter layer and profiles of density measured. The summer balance was derived from observations in September-October of profiles of density and readings at stakes and wires drilled into the glacier in April-May (see Björnsson and others, 1998b). The glacial-meteorological observations were initiated in 2001. Two automatic weather stations (AWSs) at the southern outlet Hagafellsjökull (Fig. 1) collected meteorological data that allowed calculation of the surface energy budget. Two AWSs, located outside the ice cap (Fig. 1), were used to obtain empirical relationships between temperatures within and outside the glacier. This paper presents observations of melting and calculations of the energy balance at Hagafellsjökull during the ablation season 2001. The energy balance is related to the mass balance of the glaciological year 2000-2001. Simple empirical degree-day models are used to relate the summer ablation to temperature observations. Both the energy balance and the degree-day models are used to evaluate glacial- hydrological response to possible climate changes. 2. OBSERVATIONS Two automatic weather stations (AWSs) were operated at Hagafellsjökull during the ablation season 2001: at 490 m (G490) and 1060 m a.s.l. (G1060) (Fig. 1; Guðmundsson and others, 2002). The AWSs measured the incoming ( Qi ) and outgoing ( Qo ) solar radiation, incoming ( I i ) and outgoing ( I o ) long-wave radiation, and wind speed ( u ), wind direction ( WD ), air temperature ( T ) and relative humidity ( r ) at 2 m above the surface, and the melting rate ( h ) of the surface by a sonic echo sounder (Fig. 2; Figure 1. Location of automatic weather stations. Table 1). Air temperature was also recorded by (a): Locations at Hagafellsjökull (G490 and two AWSs outside the glacier: at 299 m a.s.l. on G1060), at Söðulhólar (S299) and north of Söðulhólar (S299) and 474 m a.s.l. north of Mt. Skjaldbreiður (S474), see Table 2 for locations Skjaldbreiður (S474) (Fig. 1). and elevations. Black dots: points of mass balance The meteorological instruments were stakes. Langjökull (L) and Vatnajökull (V) ice caps are shown on the inset map of Iceland. (b): Cross- operated on the glacier from the late April to the section of the profile in (a). beginning of October 2001, fully covering the ablation season (Table 2). All instruments were 3 calibrated in Reykjavík, in April 2001 and 2002. The AWSs were visited at the end of June and beginning of September 2001, to ensure that they were working properly. Data were missing at both the AWSs for about 10 days at the end of May (Table 2) due to an overflow in memory storage. Further, continuous records of the melting rate were not available after June 26 in the upper station and after August 11 at the lower station due to malfunction in the sonic echo sounders. However, observations of the total accumulated ablation up to September 2 at Figure 2. Upset of the AWSs at Hagafellsjökull. the upper station, and October 5 at the lower The meteorological instruments were mounted on one, were used to linearly reconstruct the melt a mast that followed the melting surface (always at ~2 m above the surface) and the sonic echo rate patterns over the periods when the sonic sounder on a mast, drilled several metres into the records were missing (Fig. 3a). glacier (independent to changes of the glacier Air-pressure and vapour-pressure were surface). Parameters are defined in section 2 and not measured on the glacier. The air-pressure the accuracy of instruments in Table 1. ( P (a ) ) was calculated as a sample mean of an observed air-pressure ( P(a0 ) ) at several reference stations outside the glacier by the experimental equation 5.25 0.0065(a − a 0 ) P(a) = P(a 0 ) 1 − (1) T (a 0 ) + 273 where a and a0 are the altitudes of the AWS on the glacier and the reference station, respectively. This relationship has been proven to apply successfully at various locations outside and inside the Vatnajökull ice cap (e.g. Björnsson and Guðmundsson, 1997; see Fig. 1 for location). The vapour- pressure was calculated as e = r ⋅ e s / 100 , where r is the measured relative humidity and the saturation vapour-pressure in Pa is given by the equation T es = 611.213 exp 17.5043 . (2) T + 241.2 Table 1. Observed meteorological parameters at the automatic weather stations; instruments and accuracy. Parameters are defined in section 2. Observation Equipment Accuracy T, r Vaisala HMP35 0.2°C, 2% WD , u R.M.Young 5°, 0.1 m s-1 Q , Q , I , I Kipp & Zonen CNR1 3%, 3%, 3%, 3% i o i o h SR50 max(1 cm, 0.4%) Table 2. Coordinates of the AWS´s and observation periods. See Fig. 1 for location. Location in ° Elevation Observation No data latitude, longitude m a.s.l. interval 2001 available G1060 64.592 N, 20.425 W 1060 19.4. – 5.10. 21.5. – 28.5. G490 64.494 N, 20.437 W 490 20.4. – 5.10. 21.5. – 29.5. S474 64.448 N, 20.676 W 474 1.1. – 31.12. S299 64.341 N, 20.909 W 299 1.1. – 16.12. 4 3. METHODS The radiation components were measured directly and the turbulent energy exchange calculated from one-level measurements of wind, temperature and humidity. Empirical models were derived relating the surface- melting rate to air temperature (degree-day models). 3.1. Energy budget during the melting season The energy budget at the melting surface can be written as Mc = R + Hd + Hl (3) where R = Qi − Qo + I i − I o is the net- radiation calculated from the observed radiation components, and H d and H l are the vertical eddy flux of sensible and latent heat, respectively. We assume that the heat supplied by rain is negligible. An eddy flux model Figure 3. Energy budget at Station G490 along with taking account of the stability of the boundary surface melt rates. (a): Surface melting. (b): Daily layer (Monin-Obukhov) was used to calculate values of the total energy supplied for melting, H d and H l (e.g. Björnsson, 1972; calculated through Eqs. (3) and (7). (c): The time series in (b), filtered by a three-day moving average. Guðmundsson, 1999, p. 3-6). The model can (d): Energy components filtered by a three-day be simplified for one-level measurements as moving average. The parameters are explained in section 3 T ( z) − T ( z0 ) H d = ρ1c p k 02 u ( z ) , (4) z (ln( z ) − ln( z 0 ) + β ) 2 L ρ1 e( z ) − e( z 0 ) H l = Lv k 0 u ( z )(0.622 2 ) , (5) P z (ln( z ) − ln( z 0 ) + β ) 2 L where T (z ) , u (z ) and e(z ) are the air temperature in °C, wind-speed in m s-1 and vapour-pressure in Pa, respectively, at the height z above the surface. The roughness parameter of the surface ( z 0 ) is defined as the height where the wind-speed is zero. For a melting glacier surface T ( z 0 ) ≈ 0 °C and e( z 0 ) ≈ 611.213 Pa. The parameter k 0 = 0.4 is the von Kármán constant, c p = 1010 J kg-1K-1 is a specific heat capacity of air at constant pressure, Lv = 2.5 ⋅ 10 6 J kg-1 is the latent specific evaporation heat, and the constant β lies within the interval 6 to 7. The air density is given as ρ1 = ρ 0 ( P / Po ) , with ρ 0 = 1.29 kg m-3, P0 = 1.013 ⋅ 10 5 Pa and P as the air pressure in Pa. The Monin-Obukhov length is expressed for one-level measurements and z >> z 0 as 5 1 L = −A + (6) B with A = βz /(ln( z ) − ln( z 0 )) and B = ( g / T0 )(T ( z ) / u 2 ( z ))(ln( z ) − ln( z 0 )) , where g = 9.8 m s-2 is the acceleration of gravity and T0 = 273.15 K. Values of the roughness coefficient z 0 Table 3. Applied values of surface roughness ( z 0 ). for various surface conditions (Table 3) were z 0 mm ln( z 0 ) adopted from experience of numerous detailed New snow 0.1 -9.2 studies of the energy budget on Vatnajökull Melting snow/firn 0.7 -7.3 during the period 1996-2000 (unpublished data; Ice in an ablation zone 1 -6.9 see Fig. 1 for location) using one- and two-level Monin-Obukhov eddy flux models with stability factor. The total energy supplied for melting, was estimated directly from the observed daily melting rate ( h ) as M m = h ⋅ Ll ⋅ ρ (7) where ρ is the glacier surface mass density and Ll = 3,3 ⋅ 10 5 J kg-1 the latent heat of melting. Thus, we estimate the total energy with two independent and complementary methods with aid of Eqs. (3) and (7), i.e. from the observed weather parameters and direct observation of the melting rate. The high consistency between the calculated energy with the two methods, both variations and the total amount (Fig. 3b-c, Table 4) supports the evaluation of the roughness coefficients in Table 3. 3.2. Degree-day models We have considered four regression models between observed specific ablation rate ( a s ) and the number of degree-days. The models are written as Table 4. Monthly averages of the energy components and weather parameters. Data were missing at both G490 and G1060 for ~10 days at the end of May (Table 2). See definition of parameters in sections 2 and 3. Month H H R M Q α T u l d c i W m-2 % of W m-2 % of W m-2 % of W m-2 W m-2 % °C m s-1 Mc Mc Mc G490 May 0.1 0 17.2 30 40.3 70 57.4 183 67 2.3 5.3 June 13.8 7 50.0 24 145.9 69 209.8 217 20 3.8 5.3 July 24.3 10 60.3 26 147.8 64 232.5 164 7 5.4 4.5 Aug. 30.8 13 76.5 32 128.2 55 235.5 151 7 5.6 5.0 Sept. 26.8 17 67.2 42 64.6 41 158.6 78 7 4.9 4.7 G1060 May 0.3 2 1.0 6 14.4 92 15.7 227 83 -1.3 7.0 June -0.7 -1 7.1 13 46.3 88 52.7 280 72 0.7 5.5 July 6.7 8 18.0 20 64.7 72 89.3 215 64 2.1 4.2 Aug. 10.6 9 24.0 21 80.3 70 115.0 174 37 2.4 5.0 Sept. 8.1 15 17.3 31 30.2 54 55.6 77 38 1.1 6.2 6 t2 a s = ddf 1 TG+ , (8) t1 t2 a s = ddf 2 (TS + d ) + , (9) t1 + t2 ∆T a s = ddf 3 TS + (hG − hS ) , (10) t1 ∆h t2 a s = ddf 4 (TS + γ (hG − hS ))+ . (11) t1 The sums are taken over the period from day t1 to t 2 of the ablation season where ddf 1 to ddf 4 are scaling coefficients that remain constant with time but vary for snow and ice/firn, TG is temperature at an elevation hG on the glacier, TS is temperature at a weather station outside the + glacier of elevation hS (here S474) and stands for degree days. Mean temperature difference + between these sites is d = TG − TS . Thus, (TS + d ) + is an estimate of TG . Equation (11) ignores the high lateral temperature gradients between the melting glacier surface and the surrounding low albedo areas and uses the constant lapse rate γ = 0.6 × 10 −2 °C m-1. The term ∆T ∆h is the temperature gradient between two stations outside the glacier (here S299 and S474), and is often used to estimate γ . 4. RESULTS We relate the summer balance to the weather parameters and surface albedo. The total energy supplied for melting was derived at the two stations on Hagafellsjökull from the observed ablation and calculated from the meteorological observations. Calculations were done at daily, monthly and seasonal time scales. The obtained energy components are used to evaluate the performance of the empirical degree-day models for calculation of the ablation. The sensitivity of the energy budged to possible future temperature changes are investigated. 4.1. Variation of the energy budget during the ablation season The ablation season started at the end of April at the lower weather station (G490 at 490 m a.s.l.) and in late-May at the higher station (G1060 at 1060 m a. s. l.) but terminated at the beginning of October at both stations (Guðmundsson and others, 2002). In general the net-radiation made the highest contribution to the total energy (Fig. 3-5 and Table 4-5), but was equalled or surpassed by peaks in latent and sensible heat during occasional spells of high temperatures and strong winds (Fig. 4a-b). Typically the daily variation in the energy budget was slightly more correlated to the eddy fluxes than the net-radiation (Table 6, Fig. 6a-b and 7g-h). This correlation changed however both with time and elevation during the summer (Fig. 6a-b and 7g-h). In June and July the net- energy was mainly correlated to the net-radiation at the lower station (Fig. 3c-d, 4b-d and 7h), where the albedo remained constantly low but the cloud cover was variable. At the higher station, the cloud cover was generally lower and variations in the net-energy more related to the eddy fluxes than the radiation (Fig. 7g). 7 Table 5. Observed summer balance ( bs ) and energy components on Hagafellsjökull over the ablation season 2001. The parameters are explained in section 3. Hl Hd R Mc bs -2 -2 -2 -2 -1 kW m % of kW m % of kW m % of kW m m a of m a-1 of Mc Mc Mc water water G1060 0.79 8 2.12 21 7.14 71 10.05 2.60 2.36 G490 2.89 11 8.62 31 16.18 58 27.69 7.35 7.35 Table 6. Correlation of calculated daily values of total energy ( M c from Eq. 3), with M m (Eq. 7), DDM1 from Eq. (8), DDM2 from Eq. (9), DDM3a from Eq. (10) with a constant ∆T ∆h , DDM3b from Eq. (10) with the observed daily mean for ∆T ∆h , DDM4 from Eq. (11), temperature at the glacier ( TG ), temperature north of Skjaldbreiður ( TS ), net radiation ( R ) and eddy fluxes ( H d + H l ). Mm DDM1 DDM2 DDM3a DDM3b DDM4 TG TS R Hd + Hl G1060 - 0.84 0.87 0.74 0.56 0.90 0.74 0.81 0.71 0.75 G490 0.95 0.74 0.80 0.80 0.80 0.81 0.66 0.77 0.68 0.74 During the ablation season the net-radiation was controlled by the incoming short-wave radiation and albedo (Fig. 4b-e, Fig 5c-h and Table 4) as the incoming long-wave radiation was only slightly varying and outgoing long-wave radiation fairly constant at 315 W m-2 (Fig. 4d, 5e-f and 6c-d). The time of exposure of the dirty low albedo summer surface (Guðmundsson and others, 2002, p. 113), is evident in the radiation records (Fig. 4b-e and 5c-h). When the summer surface was exposed on 11 June (Julian day 162) at G490, the albedo dropped to ~7%, and to ~37% on 18 August (day 230) in the firn at G1060. Because of the large drop in the albedo when the summer surface is exposed, small winter balance tends to cause high summer melting (Fig. 8). Similar trends have been found on Vatnajökull during the period 1996-2000 (Björnsson and others, 2001a, p. 13; 2001b; see Fig. 1 for location). At the beginning of the ablation season, in May and June, the melting at G1060 was mainly kept up by the net-radiation (88-92% of the total energy; Fig. 5a and Table 4). Despite the high albedo the net-radiation reached ~15-50 Wm-2 on average due to high sun elevation (Table 4 and Fig. 5c,e,g). The temperature varied around 0 °C and the eddy fluxes were only ~0-6 Wm-2 on average (Fig. 5c,i). Daily fluctuations in the energy budget were both due to variations in heat fluxes and radiation (Fig. 6a and 7g). Cloud cover in the SW-Iceland was considerably below average in June 2001 and above average in July 2001 (Jónsson, 2001). This is reflected in the monthly values of incoming short- and long-wave radiations on the glacier (Fig. 5e-f). The highest net-radiation was measured during July-August at G1060 and June-August at G490 (Fig. 5c-h and Table 4). During July-August, the two warmest summer months, high eddy fluxes were also observed at both the AWSs (Fig. 5c-d, 5i-j and Table 4). At the lower station (G490), high temperatures and strong katabatic wind-flow resulted in the eddy fluxes ( H d + H l ) contributing ~35-45% to the total-energy, almost equalling the net-radiation supported by the high solar radiation ( Qi ) of ~150-165 Wm-2 and albedo of only 7% (Fig. 5b and Table 4). 8 Figure 5. Monthly averages of the energy budgets at Stations G1060 and G490, compared with weather parameters and albedo. The parameters are explained in sections 2 and 3. Figure 4. The energy components at G490 in comparison with weather parameters and albedo, displayed as three-day moving averages. (a): Temperature ( T ) and wind speed ( u ). (b): Energy components (identical to Figure 3d). (c): The net radiation in (b), separated into short-wave ( Qi − Qo ) and long-wave ( I i − I o ) components. (d): Incoming and outgoing short- and long-wave radiation components. (e): Albedo. components at September 2001 was remarkably warm Figure 6. Variation of the daily energyfor each month. stations G1060 and G490, calculated in SW-Iceland, ~2-2.5 °C above average (a-b): Standard deviation ( σ ) of daily values of the (Jónsson, 2001). On the glacier the mean total-energy ( M ), net-radiation ( R ) and the eddy c temperatures were 4.9 °C and 1.1 °C at 490 fluxes ( H d + H l ). (c-d): Standard deviation of daily and 1060 m a.s.l., respectively (Fig. 5i-j and Table 4). As typical, stronger winds blew over values of the incoming ( Qi ) and outgoing ( Qo ) short- Iceland in September than during the summer wave radiation and incoming ( I i ) and outgoing ( I o ) months of June-August (Fig. 4a, 5i-j and long-wave radiation. Table 4; Guðmundsson and others, in preparation). Hence, melt-rates were high due to the eddy fluxes despite the low solar radiation (Fig. 3, 4b-d, 5a-f and Table 4). The eddy fluxes varied considerably duing September (Fig. 6a-b) and they correlated strongly with the net-energy (Fig. 7g-h). 9 Figure 7. Comparison of physical and empirical models for estimating the glacier melt rate. The values in (a- d) have been filtered by a three-day moving average. Left y-axis: melting. Right y-axis: energy supplied for melting. (a-b): M c ≥ 0 (Eq. 3) compared to ablation calculated by Eqs. (8-9), using temperatures on and outside the glacier, respectively. (c-d): Residuals between M c /( ρL1 ) ≥ 0 and the ablation estimated by Eqs. (8) (Profile G) and (9) (Profile S). The mean values ( µ ) and standard deviations ( σ ) of the residuals are also given, with subscripts referring to the two profiles G and S. (e-f): Correlation of M c ≥ 0 with the ablation calculated by Eqs. (8) (Profile G) and (9) (Profile S). (g-h): Correlation of M c with net radiation ( R ) and eddy fluxes ( H = H d + H l ). The values in (e-h) are calculated for each day based on samples extending from 15 days before to 15 days after (providing a moving window of 31 days). Values from Table 6 are shown as marks on the y-axis in (e-h). 4.2. Variation of the energy budget with elevation A good agreement was found at Hagafellsjökull between observed summer balance ( bs ) and the total energy ( M c ) calculated by Eq (3) (Fig. 9b and Table 5). The total ablation calculated from the meteorological observations ( M c ) in G1060 was, however, slightly higher than that obtained from the in situ stake measurements of the summer balance ( bs ). Similar discrepancy has been observed in AWSs at higher elevations on Vatnajökull (unpublished data; see Fig. 1 for location) where snowfall is frequent during the summer. Snow, which falls and melts during the summer, is not detected by the measured total summer balance ( bs ) but the calculated M c includes energy supplied for melting this snow. 10 Figure 8. Mean winter- ( bw ), summer- ( bs ) and annual net-balance ( bn = bw + bs ) of the ablation areas of Hagafellsjökull (excluding mass balance data from the accumulation zone). All the energy components entering the glacier increased downglacier (Fig. 9b and Table 5). The long-wave radiation increased due to higher cloud covers at lower elevations on the glacier (Björnsson and others, 2000), and the low albedo compensated for the reduced global radiation (Fig. 9b-d). The turbulent latent- and sensible heat fluxes were Figure 9. Variation of the energy budget at Haga- kept up by katabatic wind flows and the fellsjökull over the entire ablation season 2001, as increasing air temperatures downglacier (Fig. related to elevation and compared with weather 9b,e). During the ablation season, solar parameters, albedo and observed winter ( bw ) and radiation heats up the low-albedo areas summer ( bs ) balances. The y-axis remains the outside the ice cap generating high lateral same for every subplot. ELA and GT: altitude of temperature gradients between the melting the equilibrium line and the glacier terminus, glacier surface and the surrounding areas (Fig. respectively, in the year 2001. (a): Relative 9e and 10a-b), producing katabatic wind contribution of the energy components. (b): Energy downslopes the glacier (Fig. 9e; budget in comparison to the winter and summer balances. Lower x-axis: power supplied for Guðmundsson and others, 2002). The average melting. Upper x-axis: corresponding water wind speed was similar at both the AWSs on equivalent units. (c): Means for Qi , Qo , I i and Hagafellsjökull (~5-6 m s-1), however, slightly increasing upglacier (Fig. 9e). I o . (d): Mean albedo. (e): Mean T and u . Lower -1 In general, the relative contribution of x-axis: T in °C. Upper x-axis: u in m s . The parameters are explained in sections 2 and 3. the energy components to melting was similar for the two stations on the glacier: ~60-70% Table 7. Degree-day factors of the models in Eqs. (8), (9) and (11), optimised by figuring in the entire observations from the ablation season of 2001. i and ii: Parameters observed before (for snow) and after (for ice/firn) exposure of the summer surface, respectively. The mean temperature difference is given between both the Stations G1060 and S474 (G1060), and G490 and S474 (G490) ddf1 ddf 2 ddf 4 d mm °C -1 mm °C -1 mm °C -1 °C i ii i ii i ii G1060 10.6 11.3 7.9 9.3 5.3 6.0 -4.98 G490 9.1 11.1 9.9 10.2 6.3 8.1 -1.54 11 Figure 10. Variation of hour-mean values of air temperatures at Hagafellsjökull ( TG at G490 and G1060) with temperature outside the glacier north of Skjaldbreiður ( TS at S474). (a-b): TG at G1060 and G490, respectively. The scatter values in (b) are separated into southern and northern (katabatic) wind-flows in (c) and (d), respectively. The models in Eqs. (12-13) are shown as imprinted grey lines in (a), (c) and (d). The x- axis are the same for all the subplots. from radiation and 30-40% from turbulent fluxes (Fig. 9a and Table 5). Upglacier in the accumulation area the relative contribution of the net-radiation is expected to increase and there radiation contributes to melting even though the eddy fluxes are negative (Fig. 9b,e). Such results have been obtained in the accumulation zones of Vatnajökull (Björnsson and others, 2001a; 2001b). 4.3. Empirical ablation models (degree-day) The empirical models described by Eqs. (8-11) were applied for the ablation season of 2001 for the two sites on Hagafellsjökull (G490 and G1060 at 490 or 1060 m a.s.l.), and the two AWSs outside the glacier (S299 and S474 at 299 and 474 m a.s.l.). The optimised degree-day factors ( ddf 1 , ddf 2 , ddf 4 ) and the mean temperature difference ( d ) of the ablation season 2001 are given in Table 7. The ddf 3 parameter of Eq. (10) is not given, since the model predicted ablation poorly at the higher station G1060. Higher ddf parameters were needed to describe the melting of ice/firn than snow (Table 7). Guðmundsson and others (2003) found similar results for ddf 4 when applying the model on Vatnajökull ice cap (see Fig. 1 for location), but in their case, lower values of ddf 1 and ddf 2 were needed to describe melting of ice/firn than snow. 4.3.1. Stability of the ddf parameters The empirical relationship between melting and temperature described by the ddf parameters is typically assumed to depend entirely on conditions at the glacier surface and was derived separately for snow and ice/firn surfaces. Assuming constant albedo (no surface changes) during the period of June through August, the lower solar radiation and increased heat fluxes (Fig. 5c-f) resulted in reduced scaling factors (black lines in Fig. 11). This indicates that the degree-day factors are sensitive to seasonal changes in the weather (time dependent), especially at the higher station, G1060 (Fig. 11). The high ddf parameters in May (Fig. 11) are to be explained by the 12 Figure 11. Changes in ddf 2 (a,b) and ddf 4 (c,d) according to Eqs. (9) and (11), presented in relation to albedo and to time for the locations G1060 and G490 Black lines: experimental monthly values of ddf parameters obtained from the daily ablation calculated by Eq. (3) using observed weather data from 2001 and assumed constant albedo values (shown at the ends of the lines). Thick grey line: observed monthly values of ddf 2 and ddf 4 in 2001, accompanied by the corresponding observed monthly albedo percentages. relatively strong contribution of net radiation to melting (Fig. 11). As for the snow-ice transition, its impact depends on its timing because of the seasonal variation in energy fluxes. For example, a drop in the albedo at G1060 from 50% to 30% in June-July would increase ddf 2 from ~12 mm to 16 mm per °C (Fig.11a). In contrast, the same decline in albedo during July-August would actually reduce ddf 2 . The parameter ddf 4 has a lower value, varies more gradually and is less sensitive to changes in the weather parameters and to the timing of the snow-ice transition than ddf 2 (black lines in Fig. 11); hence, ddf 4 comes nearer to depending solely on conditions at the glacier surface. Furthermore, the typically strong contribution of net radiation in May, combined with the strong winds and relatively warm temperatures of September 2001, significantly affected ddf 2 , but not ddf 4 (Fig. 11a,c). Another justification for assuming time-independent scaling factors is that the reduced solar radiation and increased heat fluxes as summer proceeds jointly counteract the lowering of albedo (Fig. 5), which explains the slightness of developments in the observed monthly values for ddf 2 and ddf 4 at both stations (grey lines in Fig. 11). 4.3.2. Degree-day models to predict the ablation 2001 The predictions of the empirical models and the physical energy exchange model were compared on a daily basis (Fig. 7a-f and Table 6). The degree-day models described the seasonal variations in ablation at G490 and G1060 (Fig. 7a-b and Table 6) but did generally not predict satisfactorily the daily values (Fig. 7a-d). However, the models produced some reasonable predictions of the daily ablation at Hagafellsjökull during periods with high correlation between the total energy and the eddy fluxes. Exceptions from this are seen in periods when the eddy fluxes were more controlled by wind speed than temperature, e.g. in the middle of July 2001 at G1060 13 (Fig 7e,g). Better agreement was obtained between the observed daily ablation and predictions of Eqs. (8, 9 and 11) at the higher (G1060) than at the lower (G490) station (Fig. 7a-f and DDM1, DDM2 and DDM4 in Table 6). The best predictions were obtained at both the stations applying Eqs. (9) and (11) that uses temperature observations outside ( TS ) rather than inside ( TG ) the glacier (Fig. 7e-f and Table 6). Equation (11) that uses the constant lapse rate ( γ ), gave slightly better results than Eq. (9) that uses the absolute temperature difference d (DDM2 and DDM4 in Table 6). Guðmundsson and others (2003) obtained similar results of using Eq. (11) on Vatnajökull ice cap, but the performance model in Eq. (9) was much poorer than in our case for Langjökull. It should though be noted, that due to the damping effects off the melting glacier, the TS projected to a higher elevation with a constant lapserate, is neither a resample of the absolute values or variations of the temperature at the same elevation within the boundary layer of the glacier (Figs. 9e and 10a,b). The better performance of using TS rather than TG was particularly evident at the lower station. Further, from the end of May through July the melting was mainly driven by the incoming solar-radiation ( Qi ) (Fig. 4 and 7h), which was better reflected by TS than TG . The models that uses temperature form outside the glacier (Eqs. 9-11) did almost equally well in estimating the daily ablation at the lower station. In contrast, Eq. (10), that uses temperature gradient between two stations from outside the glacier, failed at the higher station (Table 6), particularly when observed daily means of ∆T ∆h were used instead of constant value. The standard deviation of the residuals between daily values of the observed and calculated ablation at the higher station with Eq. (10) was σ L 1 = 13 mm d-1 of water using a constant value, and σ L 2 = 25 mm d-1 of water when applying daily values of ∆T ∆h . This is much higher than σ G = σ S = 5 mm d-1 of water obtained when using Eqs. (8), (9) and (11) (Fig. 7c). The poor performance of Eq. (10) is partly explained with a very low correlation and negative that was found between hourly mean values of the temperature difference between the glacier and the surrounding non glacierized areas ( d ), and the temperature gradient ∆T ∆h observed between two stations outside the glacier, or –0.29 and –0.18 at G490 and G1060, respectively. 4.4. Sensitivity of the summer melting to climate changes Both the energy balance model and the degree-day models have been used to study the glacier mass balance response to a prescribed climate change. This was done by calculating the sensitivity of the melting rate and the equilibrium line altitude (ELA) at Hagafellsjökull to given regional temperature changes ( ∆TS ) outside the ice cap (at S474). An empirical relationship between the changes in air temperature outside the glacier and the temperature and katabatic wind speed over the glacier were included in the calculations of the eddy fluxes. 4.4.1. Empirical relationships between temperature inside and outside the glacier and katabatic wind Piecewise-linear regression of the data in Fig. 10, relating the temperature T (z ) = TG at the height z = 2 m above the melting ice surface at the two sites G490 and G1060, to the temperature ( TS ) at S474 gave the relationships TS − 4.51; TS < 4.51 TG = , (13) 0.53TS − 2.38; TS ≥ 4.51 14 TS − 0.37; TS < 3.67 or 85° ≤ WD ≤ 275° TG = , (14) 0.28TS + 2.28; TS ≥ 3.67 and (WD ≥ 275° or WD ≤ 85°) for G1060 and G490, respectively, where WD is the observed wind direction (Fig. 2). The temperature TS does not reflect the variations of the temperature TG used in the energy budget calculations (Eqs. 4-5), and hence, it is not preferable to use Eqs. (13-14) to calculate TG as a function of TS . Instead, the equations were used to quantify possible variation of TG ( ∆TG ) due to a given global temperature changes ( ∆TS ) (Figs. 12a and 13a). Katabatic wind flow is important when calculating the energy balance (Eqs. 4-5). The katabatic wind down the glacier outlet is expected to be driven by the temperature gradients between the glacier and the surroundings of the ice cap (Figs. 9e and 14a), similar to that observed on Vatnajökull (Guðmundsson and others, 2003; see Fig. 1 for location). Due to the damping effects of the melting glacier, the temperature gradient between the glacier and its surrounding areas changes with changed global temperature (Fig. 14a). We adopt the linear expression ∆uV uV = TV + c = 0.94TV + 3.67 , (15) ∆TV which was derived for data on the summer means of uV (in m s-1) and TV , observed at AWSs at 1200 and 1100 m a.s.l. at the northeasten and western Vatnajökull, respectively, 1994-2001 (data from Björnsson and others, 2001a; 2001b and Guðmundsson and others, 2003). We use the ratio ∆u / ∆TG = ∆uV / ∆TV = 0.94 to obtain a plausible change in the wind-speed ( ∆u ) with ∆TG (or ∆TS ) at the two sites on Hagafellsjökull (Figs. 12b and 13b). 4.4.2. The energy balance for scenarios of climate changes The sensitivity of the glacier mass balance to climate changes was studied by computing the eddy fluxes at the two stations on Hagafellsjökull, for temperature variations ( ∆TS ) of –5 to 5 °C from the observed values of TS in 2001. Changes in the albedo (net-radiation) are indirectly integrated because the winter balance ( bw ) was assumed to be equal to that observed in 2001 and by melting the winter snow the mean is significantly altered. The observed solar radiation ( Qi ), incoming ( I i ) and outgoing ( I o ) heat radiation were assumed to be equal to that observed in 2001. The results (Fig. 12-14) are shown as averages over a fixed ablation period close to that of 2001. The various energy components (Fig. 12e-f and 13e-f) were calculated for each ∆TS both by assuming constant wind speed (the same as observed in 2001) and the wind speed depending on TS (Fig. 12b and 13b). Assuming I i and bw to be constant may underestimates R and the total energy ( M c ) when ∆TS >0 °C, and vice versa if ∆TS < 0 °C. Increased regional temperature would reduce bw (as long as winter accumulation does not increase), lower the summer mean albedo increasing the global radiation absorbed by the glacier and extend the ablation season. Assuming constant I i (rather than proportional to TS4 ) leads to at most ~10% and ~30% errors in the total energy at the lower (G490) and higher (G1060) station, respectively, for | ∆TS | ≤ 3 °C. The assumption of constant bw , was cautiously estimated to cause at the most an error in M c of ~10-15% and ~20% 15 Figure 12. Weather parameters and energy components at G1060 as functions of assumed regional temperature changes at S474, as well as comparisons of the total energy balance components provided for melting with predictions from the empirical degree-day models in Eqs. (8), (9) and (11). All parameters represent averages over a period equal to the observation season in 2001. Lower x-axis: temperature at S474 ( TS ). Upper x-axis: changes ( ∆TS ) from TS in 2001 (a): Temperature ( TG ). (b): Wind speed. (c-d): Relative contribution of the energy components in (e) and (f), respectively. (e-f): Energy budget using only the temperature changes in (a) and the combination of the temperature and wind-speed changes in (a) and (b), respectively. Left y-axis: sum of power supplied for melting. Right y-axis: water equivalent units. (g-h): M c from (e) and (f), respectively, compared to the melting rate a s from Eqs. (8), (9) and (11). Left y-axis: melting. Right y-axis: corresponding power needed for the melting. (i): Albedo. (j): Day of the year (left y- axis) and the corresponding month (right y-axis) when surface melting reaches the summer surface from the previous year. Black profiles are calculated using only the temperature changes in (a) and light-grey profiles using the combination of temperature and wind-speed changes in (a-b). The summer surface does not become exposed at G1060 when ∆TS ≤ −2 °C. 16 Figure 13. The variation in weather parameters and energy components at G490 that would accompany assumed regional temperature fluctuations at S474, and comparisons of the total energy balance components provided for melting with predictions from the empirical degree-day models in Eqs. (8), (9) and (11). All parameters represent averages over a period equal to the observation season in 2001. See the caption with Fig. 12 for explanations of the subplots. at G490 and G1060, respectively. This error would be less than 5% when -3 °C ≤ ∆TS ≤ 5 °C at G490 and negligible at G1060 when ∆TS ≤ −2 °C because the summer surface would not be exposed (Fig. 12j). Increased melting with rising global temperature ( TS ) would be due to increased eddy fluxes rather than higher net-radiation (Fig. 12c-f and 13c-f), albeit earlier exposure of the summer surface and subsequently reduced albedo (Fig. 12i-j, 13i-j and 14c). An increase of the global temperature by 3 °C and assuming constant wind speed would increase melting by ~60% (from ~2.6 to ~4.3 m a-1 of water) at 1060 m a.s.l. and ~30% (from ~7.2 to ~9.4 m a-1 of water) at 490 m 17 a.s.l. (Fig. 12e, 13e and 14b). Assuming katabatic wind to increase proportional to TG , ablation would increase by ~90% (from ~2.6 to ~5.1 m a-1 of water) at 1060 m a.s.l. and ~70% (from ~7.2 to ~12.5 m a-1 of water) at 490 m a.s.l. (Fig. 12f, 13f and 14b). Lowering the air temperature by 3 °C, the reduction in melting would be similar whether we account for changes in wind speed or not (Fig. 12e-f, 13e-f and 14b); ~50% and ~60-70% at 1060 and 490 m a.s.l., respectively, Predicted changes in the equilibrium line altitude (ELA) with ∆TS are shown in Fig. 14d. The ELA on Hagafellsjökull was observed at ~1140 m a.s.l. in 2001 ( ∆TS = 0 °C) but is estimated at ~1000 m and ~1300 m a.s.l. for ∆TS of –3 °C and 3 °C, respectively. Assuming constant bw we may underestimate the rise in ELA for ∆TS > 0 °C, and underestimate the descent subsequent to cooling. The summer balance bs (or M c ) varies non-linearly with elevation (Fig 14b). The bending of the ELA profile for extreme values of ∆TS (grey circles in Fig. 14d), reflects the impact of the wind-driven eddy fluxes. For extreme cooling they become a sink of energy. 4.4.3. Comparison of the physical and empirical models for temperature changes A performance of the degree-day models was tested by using a comparison with the results from the physical energy balance model. The degree-day models are more reliable at the higher than the lower stations (Fig. 12g-h and 13g-h). Reasonable agreement was obtained between the complete model of physical energy balance and equations (8), (9) and (11) at G1060 when –3 °C ≤ ∆TS ≤ 3 °C (Fig. 12g-h), and this also applied to G490 for –4 °C ≤ ∆TS ≤ 2 °C, assuming a wind speed proportional to temperature (Fig. 13h). At the higher station, the models in Eqs. (8) and (11) are closer than Eq. (10) in simulating the influence of the assumed wind speed changes (Fig. 12h). The empirical models diverged increasingly from the physical ones as the temperature departed from the reference temperatures of 2001 (Figs.12g-h and 13g-h), especially at the lower warmer station (G490). Figure 14. Predicted changes in meteorological parameters and ELA due to a prescribed deviation ( ∆TS ) from the mean summer temperature of 2001 at S474, as a function of elevation. The parameters represent averages over a period equal to the observation season in 2001. The y-axis stays the same for all the subplots. ELA: equilibrium line altitude in 2001. GT: altitude of the glacier terminus. The results in (b-d) are obtained by assuming temperature changes only (black lines) and by assuming changes in both temperature and wind speed (grey lines). (a): Changes in air temperature. (b): Changes in the energy balance (summer balance). Lower x-axis: power supplied for melting. Upper x-axis: the water equivalent. Here bs is the observed summer balance in 2001. (c): Albedo values, (d): ELA. Lower x-axis: mean values of TS during the observation season. Upper x-axis: corresponding changes ( ∆TS ) of TS . The shifts in ELA were derived using the winter balance at the ELA of 2001, i.e. b w = − bs as seen in (b), and a linear extension of the inferred values for Mc in (b). 18 5. CONCLUDING REMARKS Energy balance studies described the summer ablation 2001 successfully. This applied to temporal and spatial variations. In the beginning of the ablation season the temperature was close to the melting point, the albedo high and the energy components were small and the eddy fluxes even negative. Some ablation took place through radiation even at air temperatures below the melting point. During the warmer summer months (June/July-August) ablation was both due to high eddy fluxes and net-radiation, that contributed ~50-70% to the total energy. September was unusually warm and strong autumn winds produced high eddy fluxes and considerable melting in spite of low global radiation. This would describe conditions of warmer autumns and winter months. In general, the input of energy from all components was highest in the terminus due low albedo and high temperature. The relative contribution of the net-radiation to the total input was however higher in the accumulation area, albeit higher albedo in the ablation area; increasing from 60% at the terminus to 70% at the equilibrium line and frequently 100% on the highest parts of the glacier. Temporal variations in the melting, however, were more due to fluctuations in the eddy fluxes than radiation, at all elevations. Seasonally changes in the melting were reasonably described with empirical degree-day models. A linear extrapolation of the mean temperature outside the glacier is not a satisfactory estimate of the mean temperature on the glacier. Temperature gradients outside and inside the glacier differ. A regression model applying the temperature observations outside rather than inside the glacier did best describing the ablation. This was most obvious when the melting mainly varied with global radiation, which contribution was better described by air temperature at the low albedo surroundings while this information tends to be smoothed out in the temperature signals over the melting glacier. The optimised regression coefficients derived for the climate conditions in 2001 cannot be expected to apply in general. They may vary with the relative contribution of the radiation and eddy flux components. The turbulent fluxes are influenced by the temperature difference between the glacier and the surrounding areas, which drive katabatic wind. Further measurements would be required to gain experience of how well degree-day models may describe seasonal changes in ablation for various glacier surface characteristics and the melting for given scenarios of climate changes. Global warming would lead to extended ablation season in the spring and the autumn, even increased ablation during the winter. Enhanced melting may lead to earlier exposure of the low albedo summer surface and increased net-radiation. In that respect the winter balance is important for the mean albedo of the subsequent summer and the summer melting. The turbulent fluxes would increase. Increased temperature difference between the glacier and the surroundings would generate stronger katabatic wind downglacier. Application of the energy balance model for studies of the melting for given scenarios of climate changes would require continued work on the relationship between global warming and the katabatic flow. ACKNOWLEDGEMENTS This work was supported by the National Power Company of Iceland, the Nordic project Climate, Water and Energy (CWE), The University of Icleand Research Fund and the EU projects Icemass (ENV4-CT97-0490) and Spice (EVK2-CT-2002-00152). 19 REFERENCES Björnsson, H, 1972. Bægisárjökull, north Iceland. Result of glaciological investigations 1967- 1968. Part II. The energy balance. 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