Energy balance and melting of a glacier surface

Transcription

1 Energy balance and melting of a glacier surface Vatnajökull 1997 and 1998 Sverrir Gudmundsson May 1999 Department of Electromagnetic Systems Technical University of Denmark Science Institute University of Iceland 0

2 Table of contents Introduction 2 1. Energy budget formula and eddy flux models Energy budget Direct measurement of the total energy One-level eddy flux model for neutral air conditions Two-level eddy flux model with stability factor Experimental values for the surface roughness 6 2. Measurements 7 3. Energy budget on Vatnajökull 1997 and Brúarjökull 1997 (1210 m a.s.l.) Brúarjökull 1997 (918 m a.s.l.) Köldukvíslarjökull 1997 (1100 m a.s.l.) Brúarjökull 1998 (1200 m a.s.l.) Tungnaárjökull 1998 (1445 m a.s.l.) Köldukvíslarjökull 1998 (1100 m a.s.l) Dyngjujökull 1998 (1200 m a.s.l.) Comparison of eddy flux models Stability calculations Result of applying eddy flux model with stability Result 58 Conclusion 62 References 63 Appendixes 64 A. Data recovery 64 B. Air pressure 66 C. Estimation of daily ablation 66 D. The roughness parameter z

3 Introduction Automatic weather stations have been operated on Vatnajökull since 1994, to describe weather conditions and ablation and its connection to weather outside the glacier. In 1996 a two years glacial-meteorological experiment were started on the glacier in cooperation between the University of Iceland and the University of Utrecht, Netherlands. The main purpose was to improve the understanding of relation between glacier behavior and climate changing. This assignment was continued in 1998 as a two years multinational research project. Knowledge of energy balance is needed to understand the relationship between the glacier behaviour and climate changing. For this purpose, automatic weather stations capable of measuring the energy budget have been operated on Vatnajökull since The energy budget has been calculated for the summer of 1996 [1]. In this report, result of calculating the energy budget of the summers of 1997 and 1998 are presented. Two models were used to calculate the transfer of latent and sensible heat. The first approach uses one-level model for neutral air conditions given in [2]. The model has an advance of being relatively simple. The airflow at the glacier is typically not neutral. A model using one or two level measurements and an estimation of the eddy flux stability in [3] was tested on meteorological data from 1996 and A great advance of the later model is much less sensitivity to the surface roughness than the model for neutral air conditions. 2

4 1. Energy budget formula and eddy flux models 1.1. Energy budget Equations for energy budget at the surface are given in (1), (2) and (3). The energy budget can be written as: M + G = Q Q + I I + H + H + H, (1) i o i o d l v where Q i and Q o are the incoming and reflected solar radiation, respectively, I i and I o the long wave radiation from the atmosphere and the glacier respectively, H d and H l are the vertical eddy flux of sensible heat and latent heat, respectively, and H v is the heat supplied by rain. The total short wave radiation can also be written as Q i + Q o = Q i (1-α), where α or albedo is the reflection coefficient of the surface. The sum of the right hand site in (1) is the energy used for warming up the surface layer G and the energy that melts the glacier surface M. Here H v is assumed to be negligible and energy components are calculated for the melting season, which gives G=0. This gives the energy budget formula for a melting surface as: M (2) c = R + H d + H l, where R=Q i (1-α)+I i -I o is the net radiation and M c is the total energy. In this report the energy budget is calculated as flux density in W/m 2. The automatic meteorological stations measured either directly the net radiation R or the radiation parameters Q i, Q o, I i and I o Direct observation of the total energy The distance from the surface to a fixed height was directly measured by a sonic echo sounder and the ablation (h in mm/day of water) calculated from the distance measurement and an estimated density of the melting glacier surface. The measured total energy M m is written M m = h L ρ, (3) k 1 k 2 where L=3.3x10 5 J/kg is the latent heat of melting, ρ=10 3 kg/m 3 is the density of water, k 1 =1000 mm/m and k 2 =86400 s/day One-level eddy flux model for neutral air conditions The first approach was to use the one level model given in [1, 2] where H d and H l is derived for neutral airflow conditions. The transfer of sensible heat in a neutral conditions, for a given height z above the surface, can be written as H d 2 T ( z) T ( z0 ) = ρ 1c pk0 u( z), 2 (4) (ln( z) ln( z )) 0 3

5 where T(z) and u(z) are the temperature and wind-speed respectively at the height z, c p =1010 J kg -1 K -1 is a specific heat capacity at constant pressure, k 0 = 0.4 is the von Kármáns constant, ρ 1 is the density of air, z 0 is the roughness parameter of the surface or the height where the wind-speed is zero. For a melting glacier T(z 0 ) = 0 C. The air density can be written as ρ 1 = ρ 0 (P/P 0 ), where ρ 0 = 1.29 kg/m 3, P 0 = 1.013x10 5 Pa and P is the air pressure in Pa. The transfer of latent heat in a neutral conditions for a given height z above the surface can be written as H l 2 ρ 1 e( z) e( z0 ) = L k0 u z)(0.622 ), (5) v P (ln( z) ln( z )) ( 2 0 where L v = 2.5x10 6 J/kg is the latent specific evaporation heat and e(z) and e(z 0 ) are the vapour pressures at the heights z and z 0 respectively. The parameter e(z) was not measured directly but calculated as e(z) = r(z)e s /100, where r(z) is the observed relative humidity in % and e s is the saturation vapour pressure given in [1] e s T( z) ( T( z)) = exp T( z) (6) For a melting surface e 0 = Pa. For a ordinary conditions, the airflow to the glacier is not neutral. The eddy flux model (in (4) and (5)) was used as an approximation since the measured total energy M m in (3) can be used as calibration of M c in (2). The net radiation (R) is measured directly and hence the task is to find H d and H l. This was done by finding values for ln(z 0 ) that gave a good consistency between M c and M m. The results of applying this model to data from Vatnajökull 1997 and 1998 are presented in chapter 3. This model has also been tested on a meteorological data from Vatnajökull glacier 1996 with good result [1] Two-level eddy flux model with stability factor Two-level eddy flux model with stability factor was tested and compared to the model for neutral air conditions. The model is described in details in [3]. Transfer of sensible heat in a stable condition is given by H d θ ( z2 ) θ ( z1) = ρ 1c k0u, (7) p x z2 z1 ln( z2 ) ln( z1) + β L where ρ 1, c p and k 0 are the same constants as used in (4) and (5), β [6,7] and z 1 and z 2 are heights above the surface (z 2 > z 1 ). The parameter θ is the potential temperature in Kelvin,written as dθ ( z) dt ( z) = + dz dz g c p, (8) 4

6 5 where g = 9.8m/s 2 is the gravitational acceleration and u x the friction velocity with z 0 as the surface roughness and L the Monin and Obukhov length in meters, written for z 2 >> z 0 as with T 0 =273.15K. The factor L is a function of the air stability; decreasing with increased stability. Transfer of latent heat in a stable condition is given by where e(z) is given by (6). The model in (7) to (11) can be simplified for one-level measurement by setting z 2 = z and z 1 = z 0, with β(z-z 0 )/L β(z)/l and θ(z)-θ(z 0 ) T(z)-T(z 0 ) which simplifies (7), (8), (9) and (11) to and respectively. The Monin and Obukhov length becomes, ) ln( ) ln( ) ( L z z z z u k u x β + = (9) )), ( 4 1 (1 2 1 A C B B A L = (10), ) ln( ) ln( z z z A = β, ) ln( ) ln( )) ln( ) (ln( ) ( ) ( ) ( z z z z z u z z T g B = θ θ, ) ln( ) ln( ) ( z z z z C = β, ) ln( ) ln( ) ( ) ( ) ( L z z z z z e z e P u k L H x v l + = β ρ ρ (11) ) ) ln( ) (ln( ) ( ) ( ) ( L z z z z T z T z u k c H p d β ρ + = (12) ) ) ln( ) (ln( ) ( ) ( ) )(0.622 ( L z z z z e z e P z u k L H v l β ρ ρ + = (13) (14) B A L 1 + =

7 The only difference between (4) and (12) is the denominator which has changed from (ln(z)-ln(z 0 )) 2 to (ln(z)-ln(z 0 )+S) 2, where S = βz/l. The same is achieved by comparing (5) and (13) except the air density ρ 1 is used in (13) but not in (5). The estimated air pressure at all meteorological stations on Vatnajökull 1996, 1997 and 1998 was always within around 800 to 900 mbar on average an slowly varying, which resulting in ρ 1 =ρ 0 (P/P 0 ) 1. Thus, ρ 1 is negligible in energy budget calculation at Vatnajökull. The stability factor S 0 when the air fluxes gets more neutral which leads to the model given in (4) and (5). The process of finding optimal value for ln(z 0 ) in (4) and (5) (leading to a good consistency between M m and M c ) can be regarded as a process of finding an optimal value of ln(z 0 )+S in (12) and (13). The models in (7) to (14) were tested for two meteorological stations on Vatnajökull 1996 and 1997 (see Chapter 4) Experimental values for the surface roughness Table 1.1 shows some experimental values for z 0 taken from [2]. Those values will be used for comparison to the results obtained with the eddy flux models. Table 1.1. Experimental values of z 0 from [2]. z 0 [mm] ln(z 0 ) Smooth ice New snow (not melting) Fine-grained melting snow Ice in a ablation zone Coarse snow with sastrugi

8 2. Measurements Automatic weather stations (AWSs), capable of measuring the energy budget, have been operated on Vatnajökull since 1996; three during the summers of 1996 and 1997 and five Energy components have been calculated for 1996 and results for 1997 and 1998 are presented in this report. Figure 2.1 shows a schematic plot of an AWS. The equipments were mounted on a mast that followed the surface while melting; always at a fixed height above the surface. The stations measured either superlatively the radiation parameters or directly the net radiation at 2 m above the surface. Air temperature, humidity and wind-speed were measured at one to six levels. All the stations measure the wind-direction at 2 m above the surface and the ablation directly by using an ultrasonic echo sounder, mounted on a mast that is drilled several meters into the glacier (always at a fixed height independent of the glacier surface changes). The echo meter was located several metres from the meteorological masts. Figure 2.2 shows the location of the automatic meteorological stations on Vatnajökull 1997 and For the summer of 1997, the three stations measuring the energy components at Brúarjökull (1210 m a.s.l.), Brúarjökull (918 m.a.s.l.) and Köldukvíslarjökull (1100 m. a.s.l) are labelled as BRU, EYB and KOK respectively. and the 1998 stations at Brúarjökull (1200 m a.s.l.), Köldukvíslarjökull (1100 m a.s.l.), Dyngjujökull (1200 m a.s.l.), Tungnaárjökull (1445 m a.s.l.) and Tungnaárjökull (1100 m a.s.l.) are labelled as R5, R2, R6, R3 and R4 respectively. Figure 2.1. A schematic plot of an AWS. 7

9 Figure 2.2. Location of AWSs on Vatnajökull the summers of 1997 and The lines on the glacier are icedivides. 8

10 Meteorological observation from Brúarjökull 1996 (1140 m a.s.l.) and Brúarjökull 1997 (1210 m a.s.l.) are used for evaluation of models in section 1.4. The air pressure was measured at two AWSs 1997 and 1998, Grímsfjall 1710 m a.s.l. (ESH) and Jökulheimar 675 m a.s.l. (JOK), and used to calculate the air pressure at other locations, see appendix B. The AWSs observations were like following: Brúarjökull 1996 (1140 m a.s.l.) All the radiation components were measured directly and the air temperature, humidity and wind-speed at 1 m, 2 m, 4 m and 6 m above the surface. Brúarjökull 1997 and 1998 (1210 m a.s.l.) All the radiation components were measured directly and the air temperature, humidity and wind-speed at 1 m, 2 m, 4 m and 6 m above the surface. Brúarjökull 1997 (918 m a.s.l.) The solar radiation and the reflected solar radiation were measured. The net radiation was measured directly and the air temperature, humidity and wind-speed at 1 m, 2 m and 4 m above the surface. Köldukvíslarjökull 1997 and 1998 (1100 m a.s.l) All the radiation components were measured individually and air temperature, humidity and wind-speed at 1 m, 2 m and 4 m above the surface. Dyngjujökull 1998 (1200 m a.s.l.) All the radiation components were measured directly and the air temperature, humidity and wind-speed at 1 m and 2 m. Tungnaárjökull 1998 (1445 m a.s.l.) All the radiation components were measured directly and the air temperature, humidity and wind-speed at 1 m. Tungnaárjökull 1998 (1100 m a.s.l.) The solar radiation and the reflected solar radiation were measured. The net radiation was measured directly and the air temperature, humidity and wind-speed at 1 m, 2 m and 4 m above the surface. Further details about the observed meteorological parameters, equipment and location of the meteorological stations are given in Appendix A. No data is available from Tungnaárjökull 1998 (1100 m a.s.l.) after the middle of May and therefore no data were used from that station. An accurate calibration of all the equipment were carried out in Cawbau in Holland 1996 and in Reykjavík in April 1997 and April The results were used to calibrate the measurements from Vatnajökull 1997 and Daily ablation was calculated by using the measured distance from the echo sounder to the surface and an estimated mass density model. Direct daily measurements of density in the top surface layer are available from 1996 and were used to estimate the mass density model. Further details about the distance 9

11 measurement and the ablation calculation are given in Appendix C. The meteorological parameters were sampled at 10 minutes intervals. One-hour averages were calculated for all the parameters and used for the energy balance calculation. 10

12 3. Energy budget on Vatnajökull 1997 and 1998 This chapter presents result of energy budget calculation for three sites on the glacier 1997 and four The one-level model, given in equation (4) and (5) in chapter 1, was used to the transfer of turbulent sensible and latent heat. The energy budget was calculated within the ablation season. The beginning of the ablation season for each of the site is definite as the day when the daily average of air temperature exceeds freezing point. The end of the ablation season is then defined to be the last day with average above freezing point. It takes around four days at the beginning of the ablation season for the glacier top layer to reach melting point [1]. Experiences of using echo sounder for ablation observations indicate that the changes in distance are not always due to melting at the same moment. The surface can sink as a result of previous hours or days of melting. To account for this, the result from energy budget calculations is displayed as a three-day moving average. Plots showing energy budgets for different sites are plotted in the same scale to make comparison easier. The glacier surface can be inhomogeneous during some periods, especially below the equilibrium line after the surface from the previous ablation seasons is exposed. At that time, water channels can be formed and sand and volcanic ash liars can be found on the surface. This affects the albedo and can lead to discrepancy between M m and M c during some periods Brúarjökull 1997 (1210 m a.s.l.) The AWS at Brúarjökull 1997 (1210 m a.s.l.) was located a little above the equilibrium line at the northeastern part of Vatnajökull. Figure 3.1 (a) and (b) shows daily average of the meteorological parameters measured in 2m above the surface. Figure 3.1 (a) shows also profile over the melting and the estimated daily ablation. The ablation season for this site varied from 24 of May to 8 of September (day 144 to 251). The ablation season was not continuous but interrupted by one long and few short cold periods. The net radiation was probably strong enough to keep the surface at melting point at short cold periods. The winter accumulation was measured as 250cm. Hence; the ablation did reach the summer surface around 24 of July (day 205) according to the profile over the surface melting. Day 205 is marked with a dashed line on some of the subplots in figure 3.1 (a) and (b). The surface consisted of firn after day 205. Brúarjökull was visited at the end of July At that time sand had been blown over the glacier surface. The surface was inhomogeneous and a water-pool was located under the meteorological mast but not under the echo sounder. According to the albedo profile, the surface is likely to have been covered with dust from the end of June. 11

13 Figure 3.1. (a). Meteorological parameters. Brúarjökull 1997 (1210 m a.s.l.). 12

14 Figure 3.1. (b). Meteorological parameters. Brúarjökull 1997 (1210 m a.s.l.). 13

15 Energy components The energy components were calculated from 29 of May to 3 of June and 20 of June to 6 of September (day 149 to 154 and 171 to 249). Figure 3.2 shows a comparison of M c and M m and how the total energy was separated into H d, H l and R. The previous year summer surface was exposed at day 205 and is marked on the plot. The plot shows also three-day moving average of air temperature and wind-speed. A good consistency is obtained between the measured and calculated total energy until the end of July. Large differences are found between M m and M c at the end of July and at the middle of August (pointed out on the plot in figure 3.2 and labelled as number 1). The timing of the first large difference corresponds directly to the time when the weather station was visited at the end of July. At that time the equipment, measuring the reflected solar radiation, was located above water and does therefore not include observations of reflected solar radiation from the glacier. Other discrepancy show also too high net radiation and are therefore most likely to be also due to water collected under the meteorological station. Figure 3.3 shows the energy components normalised to the calculated total energy M c. The ablation is mainly produced by the net radiation R; around 90% in June and July. The sensible and latent heat reached around 40-50% of the total energy at the beginning and the end of August, as a result of having spells of high windspeeds and temperatures. Table 3.1 shows averages of energy components for June, July and August and total average over the ablation season. The table shows also the total average with the abnormal days, pointed out in figure 3.2, removed. Total averages shows that around 84% of the melting was produced by radiation and 11% and 5% by sensible and latent heat, respectively. Those numbers varied within the ablation season. Table 3.1. Average of energy components in June, July and August and total averages. Total is average over all the days calculated. Total* is average over all days calculated excluding abnormal days. Brúarjökull 1997 (1210 m a.s.l.) R H d H l M c M m Number of days June July August Total Total*

16 between M c and M m. Figure 3.2. Energy component, air temperature and wind-speed. Brúarjökull 1997 (1210 m a.s.l.) 15

17 Figure 3.3. Energy components normalised to M c. Brúarjökull 1997 (1210 m a.s.l.). Table 3.2 shows the values of ln(z 0 ) (or ln(z 0 )+S) that gave a good consistency between M c and M m. According to table 1.1 a typical value of ln(z 0 ) for melting snows should lie around 7.3. Lower values in table 3.2 indicate a stable air flux conditions. Table 3.2. Values observed for ln(z 0 ). Brúarjökull 1997 (1210 m a.s.l.) Day-number ln(z 0 ) (or ln(z 0 )+S) Surface type Winter snow Winter snow Firn New snow Firn Firn/New snow Correlation between measured total energy and other parameters Table 3.3 shows correlation of measured and calculated parameters to the total energy M m. The correlation was calculated for the same days considered for the energy calculation, where days showing abnormal consistency between M m and M c were excluded. This was done for daily average and three-day moving average. Figure 3.4 compares M c and M m for daily and three-day moving average. The correlation between M m and R is 0.7 for daily average but 0.79 between M m and M c. This indicates that more parameters than net radiation alone are needed to describe the energy budget, even though the melting was mainly produced by the radiation. Table 3.3. Correlation between measured total energy M m and meteorological parameters. Days having abnormal consistency between M c and M m have been removed. Number of days are N = 64. Brúarjökull 1997 (1210 m a.s.l.) Correlation between M m and M c T T + u T u R Q i I i r H d H l Daily average Three-day moving average

18 Figure 3.4. Comparison of measured and calculated total energy M m and M c for daily and threeday moving average. Brúarjökull 1997 (1210 m a.s.l.) 3.2. Brúarjökull 1997 (918 m a.s.l.) The meteorological station on Brúarjökull 1997 (918 m a.s.l.) was located within the ablation zone at the northeastern part of Vatnajökull, at a step inclination close to the glacier border. Figure 3.5 (a) and (b) shows daily average of meteorological parameters at 2 m above the surface and (a) the results from the echo sounder and the estimated daily ablation. The ablation season lasted from 23 of May to 8 of September (day 143 to 251). The ablation season was interrupted by some cold periods. Net radiation was however high enough to keep the surface at melting point during short cold period. Annual winter accumulation was measured as 200 cm. The surface reached the previous year summer surface around 11 of July (day 192 marked with dashed line on some of the subplots in figure 3.5). After day 192, the ablation consisted of a melting of ice. The effect of melting onto the summer surface is clearly evident from the reflected short wave radiation, albedo, net radiation and ablation. The surface around the station was homogeneous and consisted of ice with small grains when the station was visited in the end of July. 17

19 Figure 3.5. (a). Meteorological parameters. Brúarjökull 1997 (918 m a.s.l.). 18

20 Figure 3.5. (b). Meteorological parameters. Brúarjökull 1997 (918 m a.s.l.) Energy components The energy components were calculated from 29 of May to 3 of June and 18 of June to 6 of September (day 149 to 154 and 169 to 249). Figure 3.6 shows a comparison of the measured and calculated total energy M m and M c, respectively, and how the total energy is separated into H d, H l and R. Day 192 is also marked on the energy plot. The figure show also a comparison of the energy components to air temperature and wind-speed profiles. The equipment used to measure the net radiation is less accurate than equipments used for radiation observations at the other sites of the glacier. 19

21 Figure 3.6. Energy component, air temperature and wind-speed profiles. Brúarjökull 1997 (918 m a.s.l.) 20

22 Figure 3.7. Energy components normalised to M c. Brúarjökull 1997 (918 m a.s.l.). Good consistency is assessed between M m and M c. Some of the discrepancies can be explained by the inaccurate net radiation equipment. Also some large differences are found right before the melting reached the ice surface and is explained by different surface conditions between the location of the meteorological station and the echo sounder. Figure 3.7 shows a plot of the energy components normalised to M c. Contribution from net radiation varied around 50-90% of the total energy and more for some days. At the end of July and middle of August, the latent and sensible heat increased as a consequence of high air temperature and wind-speed. Table 3.4 show averages of the energy components for June, July and August and total average. On average 68% of the ablation was produced by net radiation and 24% and 8% by sensible and latent heat respectively. The table shows that those numbers varied within the ablation season. Table 3.4. Averages of energy components in June, July and August and total averages. Brúarjökull 1997 (918 m a.s.l.). R H d H l M c M m Number of days June July August Total Table 3.5 shows the values of ln(z 0 ) (or ln(z 0 )+S) that gave a good consistency between M c and M m. According to table 1.1 a typical values of ln(z 0 ) for melting snows should lie around 7.3 and 6.9 to 5.1 for ice in an ablation zone. Much lower values in table 3.5 indicate a large stability factor. Table 3.5. Values observed for ln(z 0 ). Brúarjökull 1997 (918 m a.s.l.) Day-number ln(z 0 ) (or ln(z 0 )+S) Surface type Winter snow Winter snow Ice Ice Ice 21

23 Figure 3.8. Comparison of measured and calculated total energy M m and M c for daily average and three-day moving average. Brúarjökull 1997 (918 m a.s.l.) Correlation between measured total energy to other parameters Table 3.6 shows correlation of measured and calculated parameters to the measured total energy M m. The correlation was calculated for the same days as considered for the energy calculation. This was done by using daily averages and three-day moving averages. Figure 3.8 compares measured and calculated total energy for both daily average and three-day moving average. The correlation of M m to R, T and H l is around 0.7, showing that the fluctuations in the energy budged are also due to air temperature, despite the net radiation being larger on average. The correlation is highest between M m and M c, or 0.89 for daily average. Table 3.6. Correlation between measured total energy M m and meteorological parameters. Number of days are N = 87. Brúarjökull 1997 (918 m a.s.l.). Correlation between M m and M c T T + u T u R Q i r H d H l Daily average Three-day moving average

24 3.3. Köldukvíslarjökull 1997 (1100 m a.s.l.) Köldukvíslarjökull is located at the western part of Vatnajökull. The AWS was located within the ablation zone of the ice-sheet. Figure 3.9 (a) and (b) shows daily average of meteorological parameters at 2 m above the surface, sinking of the surface and estimated daily values of ablation. The ablation season lasted from May 24 to the end at September 8, day 144 to 251. The ablation season was interrupted by one short cold spell. The winter accumulation was measured as 120 cm and the ablation reached the previous year summer surface at June 27 (day 178). After day 178, the ablation consisted of melting of ice. Day 178 is marked on some of the plots in figure 3.9. The exposed summer surface affected the ablation, outgoing solar radiation, albedo, and net radiation. When the AWS was visited at the end of July, the surface consisted of ice with dirtcones, sand and exposed ash layers at some of the nearest areas surrounding the station. Water channels were found on the glacier surface. When the station was visited at the end of the ablation season, a 50 cm dirt-cone was located below the echo sounder. According to the melting profile, the melting below the echo sounder did most likely reach the top of the dirt-cone around the days (8 to 10 of August). Hence, the measured ablation after day 220 do not describe the melting of the glacier surface Energy components The energy components were calculated from 29.5 to 3.6. and from to (day 149 to 154 and 169 to 227). Figure 3.10 shows a plot of the energy components and comparison of measured and calculated total energy components M m and M c. The day 178 when the ablation reach the summer surface is marked on the plot and also day 222. The figure shows also profiles of air temperature and windspeed. The large difference in observed M m and M c around day 178, marked as number 1 on the plot, is most likely to be due to different characteristics in the surface between the echo sounder and the meteorological mast during this period. This is in accordance with having the surface close to the summer surface at that time. The large difference in M m and M c, marked as number 2 on the plot, is a result of having dirtcone bellow the echo sounder during this period. The green profile, or M c, is therefore more likely describing the correct ablation for days 222 to 227. Figure 3.11 shows the energy parameters normalised to the calculated total energy M c. At the beginning of the ablation season, only around 50% of the ablation is produced by radiation. Around 90% of the ablation is due to radiation at the end of June and the beginning of July. The energy contributions from sensible and latent heat increased again at the end of the ablation season. 23

25 Figure 3.9. (a). Meteorological parameters. Köldukvíslarjökull 1997 (1100 m a.s.l.). 24

26 Figure 3.9. (b). Meteorological parameters. Köldukvíslarjökull 1997 (1100 m a.s.l.). 25

27 Figure Energy component, air temperature and wind-speed profiles. Köldukvíslarjökull 1997 (1100 m a.s.l.) 26

28 Figure Energy components normalised to M c. Köldukvíslarjökull 1997 (1100 m a.s.l.). Table 3.7 shows the averages of the energy components within June, July and August and total average over all days calculated. Average for August and total average were also calculated when days 223 to 227 were excluded, labelled as August* and Total*. Total averages show that around 75% of the melting was produced by radiation and 18% and 7% by sensible and latent heat respectively. Table 3.7. Average of energy components in June, July and August and total averages. Total is average over all the days calculated. The August average excludes days 223 to 227. Total* is average over all days calculated excluding days 223 to 227. Köldukvíslarjökull 1997 (1100 m a.s.l.) R H d H l M c M m Number of days June July August August* Total Total* Table 3.8 shows the values of ln(z 0 ) (or ln(z 0 )+S) that gave a good consistency between M c and M m. According to table 1.1 typical values of ln(z 0 ) for melting snows should lie around 7.3 and around 6.9 to 5.1 for ice in an ablation zone. It is interesting to note that the lowest values for ln(z 0 ) are found when the contribution from air temperature and wind-speed are high and lower values correspond to time intervals having high contribution from net radiation. This can be explained by adding the stability term S to ln(z 0 ). S is low when wind-speeds and temperatures arise high and high for more stable conditions. Table 3.8. Values observed for ln(z 0 ). Köldukvíslarjökull 1997 (1100 m a.s.l.) Day-number ln(z 0 ) (or ln(z 0 )+S) Surface type Winter snow Winter snow ice ice ice New snow/ice 27

29 Figure Comparison of measured and calculated total energy M m and M c for daily average and three-day moving average. Köldukvíslarjökull 1997 (1100 m a.s.l.) Correlation between measured total energy and other parameters Figure 3.12 shows the consistency between the measured and the calculated total energy. Table 3.9 shows correlation between M m and other meteorological parameters. The correlation was calculated for the days used in the energy budget calculation. Days showing abnormal consistency between M m and M c are not included in the correlation calculations. No measured parameter shows high correlation to the measured ablation. The correlation between measured and calculated total energy is though 0.87 for daily average and 0.95 for three days in moving average. Correlation to H d and H l gets lower when more days are used in the moving average. It should be noted that the days used in the correlation calculation are only 47, which can make the results inaccurate. Table 3.9. Correlation between measured total energy M m and meteorological parameters. Days having abnormal consistency between M c and M m have been removed. Number of days are N=47. Köldukvíslarjökull 1997 (1100 m a.s.l.). Correlation between M m and M c T T + u T u R Q i I i r H d H l Daily average Three-day moving average

30 3.4 Brúarjökull 1998 (1200 m a.s.l) The meteorological stations Brúarjökull 1998 (1200 m a.s.l.) and Brúarjökull 1997 (1210 m a.s.l.) were located at the same site at Vatnajökull. The station was located close to the equilibrium line of Brúarjökull outlet. Figure 3.13 (a) and (b) shows profiles of meteorological parameters measured in 2m above the surface. Figure 3.13 (a) show also profiles of the surface melting and the estimated daily ablation. The climate was colder on average at Brúarjökull 1998 than The ablation season 1998 was from May 21 to September 6 (day 141 to 249). The ablation season was discontinuous and interrupted by both long and short cold periods. This can be seen from the air temperature record. The largest period varied from day 151 to 161 (May 31 to June 10). The period from day 151 to 161 had very low air temperature and low net radiation. Therefore, some of the melting water from the beginning of the ablation season did probably freeze again during this cold period. This might also have happened for other cold short periods within the ablation season but most often the net radiation was strong enough to keep the surface at the melting point. The annual winter accumulation was measured as 209cm with firn below. The ablation did reach the summer surface at day 217 (5 of August) according to the melting profile in figure 3.13 (a). Day 217 is marked on some of the profiles in figure The effect of reaching the summer surface can be seen on the profiles of albedo and net radiation. Brúarjökull was visited at the end of July and at that time, the surface was rather clean and homogenous Energy components The energy components were calculated from May 22 to 31 and June 14 to September 6 (day 142 to 151 and 165 to 249). Figure 3.14 shows a plot of the energy budget and comparison to air temperature and wind-speed. Day 217, when the ablation reached the summer surface is marked on the energy budget plot. A good consistency was gained between the measured and calculated total energy, except for days 228 to 239. This period is pointed out in figure 3.14 and marked as number 1. The measured total energy was much lower than the calculated total energy for those days. The melting at this period corresponds to 25cm of the surface. It is possible, that the ablation consisted of melting of a thick ice-lens instead of firn, with mass density of 0.9g/cm 3 instead of 0.65g/cm 3. Ice-lenses, cm thick, have been detected at this site of Vatnajökull. Also the summer of 1997 was unusual and some water-pools were formed like mentioned in section 3.1. Figure 3.14 shows M m calculated with mass density of 0.90g/cm 3 for the days 228 to

31 Figure 3.13 (a). Meteorological parameters. Brúarjökull 1998 (1200 m a.s.l.) 30

32 Figure 3.13 (b). Meteorological parameters. Brúarjökull 1998 (1200 m a.s.l.) 31

33 Figure Energy component, air temperature and wind-speed profiles. Brúarjökull 1998 (1200 m a.s.l.). 32

34 Figure Energy components normalised to M c. Brúarjökull 1998 (1200 m a.s.l.). Figure 3.15 shows a plot of the energy components normalised to M c. The contribution from net radiation varied from 75% of the total energy and up to over 200% for some cold days. The contribution from sensible and latent heat was up to 50% of the total energy for days around the two days number 183 and 242. This was a consequence of combination of high air temperature and wind-speed and is seen from the profiles in figure Table 3.10 show averages of the energy components within June, July and August and total averages. The total averages were calculated for all days included in the energy calculation and also when days 228 to 239 are excluded, labelled as Total and Total* respectively. On average, around 88% of the total ablation was produced by radiation and 10% and 2% by sensible and latent heat respectively. The contribution of the heat fluxes varied within the ablation season. Average over the measured days in June indicate that around 107% of the total ablation was due to net radiation, 2% by sensible heat and 5% by latent heat. Table Average of energy components within June, July and August and total averages. Total is average over all the days calculated. Total* is average over all days calculated excluding days 228 to 239. Brúarjökull 1998 (1200 m a.s.l.) R H d H l M c M m Number of days June July August Total Total* Table 3.11 shows the values for ln(z 0 ) (or ln(z 0 )+S) that give a good consistency between M m and M c. Low values in the table could indicate stable air fluxes during some of the time periods and higher values more neutral conditions. Table Values observed for ln(z 0 ). Brúarjökull 1998 (1200 m a.s.l.) Day-number ln(z 0 ) (or ln(z 0 )+S) Surface type Winter snow Winter snow Winter snow Firn Firn/New snow 33

35 Figure Comparison of measured and calculated total energy M m and M c for daily average and three-day moving average. Brúarjökull 1998 (1200 m a.s.l.) Correlation between measured total energy and other parameters Figure 3.12 compares the measured and calculated total energy for daily average and three-day moving average. Table 3.12 shows correlation between M m and other meteorological parameters. The same days was used in energy budget calculation and the correlation calculation. The correlation between M m and R is 0.62 when using daily average, even though on average, 88% of ablation were produced by R. Higher correlation is achieved between M m and H d and M m and H l, or 0.70 and 0.64 respectively for daily average. The reason for correlation of 0.67 with air temperature and wind-speed combination is evident when profiles are compered in figure It can bee seen that even though the parameter R was high, there were days when the ablation is affected more by air temperature and wind-speed. The correlation coefficients suggest also that H d and H l were important in the energy budget, even though the ablation was mainly produced by radiation. Table Correlation between measured total energy M m and meteorological parameters. Number of days are N=95. Brúarjökull 1998 (1200 m a.s.l.) Correlation between M m and M c T T + u T u R Q i I i r H d H l Daily average Three-day moving average

36 3.5 Tungnaárjökull 1998 (1445 m a.s.l) Tungnaárjökull 1998 (1445 m a.s.l) was located at the western site of Vatnajökull above the equilibrium line. Figure 3.17 (a) and (b) show daily average of meteorological parameters in 2m above the surface. The melting profile and the estimated daily ablation is also shown in (a). The ablation season varied from May 22 to September 6 (day 142 to 249). At this site the climate is cold and the air temperature varied around 0 C during the ablation season. Some of the melting water from the beginning of the summer did probably freeze again during a cold spell from May 31 to June 21 (day 151 to 172). This might also have happened at other short cold periods, but it is also possible that the contribution from radiation did manage to keep the surface at freezing point. The winter accumulation was measured as 280cm. The melting did not reach the summer surface. Tungnaárjökull was visited at the end of July, and at that time the surface was rather homogeneous snow, but the covered by of some fine light-brown dust at some spots Energy components Figure 3.18 shows three-day moving average of energy components and how the total energy is separated into R, H d and H l. The figure show also comparison to three-day moving average of air temperature and wind-speed. The energy components were calculated from May 22 to June 2 and from June 14 to September 6 (day 142 to 153 and 165 to 249). A good consistency was found for all days except the periods pointed out with number 1 and 2 in figure The air temperature was below 0 C and the net radiation was low at the time pointed out as number 1. The surface can have been frozen at that time. The energy budget formula, given in (2) in chapter 1, does not hold under those conditions. Also the assumption of having T 0 =0 C for the model given in (4) and (5) in chapter 1 does not hold under those conditions. This could explain some of the discrepancy. The interval pointed out as number 2 in figure 3.18 corresponds to day 170 to 190. A good consistency was found between M m and M c for day 170 to 190, when the outgoing solar radiation increased by 5% to 10. The direct ablation measurement and the meteorological mast were located with several metres distance. This may be explained by more dust cover surrounding the meteorological mast than at the surface surrounding echo sounder during the day 170 to 190. This would have given a difference in the reflection coefficient (albedo) at the two spots. Figure 3.18 shows the results when Q o have been increased by 10% for day 170 to 190. Figure 3.19 shows R, H d and H l normalised to the measured net radiation M c. The plot shows that the contribution from radiation varied from 70% of the net energy up to over 200%. Contributions from latent and sensible heat were mostly low and negative for some days. Contribution from H d and H l did go up to around 75% of the net energy at the end of the ablation season, as a consequence of combination of high temperature and wind-speed. 35

37 Figure 3.17 (a). Meteorological parameters. Tungnaárjökull 1998 (1445 m a.s.l.). 36

38 Figure 3.17 (b). Meteorological parameters. Tungnaárjökull 1998 (1445 m a.s.l.). 37

39 Figure Energy component, air temperature and wind-speed profiles. Tungnaárjökull 1998 (1445 m a.s.l.). 38

40 Figure Energy components normalised to M c. Tungnaárjökull 1998 (1445 m a.s.l.) Table 3.13 show averages of the energy components within June, July and August and total average over all day used in the energy calculation. On average 96%, 8% and 4% of the ablation was produced by net radiation, sensible heat and latent heat respectively. In June the contribution were 115%, 3% and 18% from R, H d and H l respectively, but 77%, 15% and 8% in August. Table Average of energy components within June, July and August and total averages. Tungnaárjökull 1998 (1445 m a.s.l.) R H d H l M c M m Number of days June July August Total Table 3.14 shows the values of ln(z 0 ) (or ln(z 0 )+S) that gave a good consistency between M m and M c. The values are low compered to the melting snow value of 7.3 given in table 1.1, except for days At most of the days from 142 to 237, the climate was rather still and cold on average but for days the combination of air temperature and wind-speed was high. The air flux stability should be high for still and cold climate but more neutral for higher air-temperature and wind-speed combination. This could explain the values achieved for z 0 in table Table Values observed for ln(z 0 ). Tungnaárjökull 1998 (1445 m a.s.l.) Day-number ln(z 0 ) (or ln(z 0 )+S) Surface type Winter snow Winter snow Winter snow Winter snow Winter snow Winter snow 39

41 Figure Comparison of measured and calculated total energy M m and M c for daily average and three-day moving average. Tungnaárjökull 1998 (1445 m a.s.l.) Correlation between measured total energy and other parameters Figure 3.20 compares between the measured and the calculated total energy for daily average and three-day in moving average. Table 3.15 shows the correlation between measured total energy and meteorological parameters. The same days were used in correlation and energy calculation. No direct measured parameter shows high correlation to M m. The highest correlation is achieved between M m and M c or 0.78 for daily average. It is interesting to note that correlation between M m and R is only 0.45 for daily average but 0.61 between M m and H d and 0.69 between M m and H l. This is evident from figure R produced 98% of the ablation on average. Thus net energy was mainly controlled by radiation. Small changes in the total energy profile were on the other hand more controlled by H d and H l. The shape of the total energy profile is therefore more like the shape of the sensible and latent heat profiles, which explain the higher correlation for those parameters. Table Correlation between measured total energy M m and meteorological parameters. Number of days are N=97. Tungnaárjökull 1998 (1445 m a.s.l.) Correlation between M m and M c T T + u T u R Q i I i r H d H l Daily average Three-day moving average

42 3.6. Köldukvíslarjökull 1998 (1100 m a.s.l.) The meteorological stations Köldukvíslarjökull 1998 (1100 m a.s.l.) and Köldukvíslarjökull 1997 (1100 m a.s.l.) were located at the same site. The station was located within the ablation zone of Köldukvíslarjökull outlet. Figure 3.22 (a) and (b) shows daily average of meteorological parameters measured in 2m above the surface. Figure 3.22 (a) shows also the measured melting profile and the estimated on-day ablation. The ablation season was from May 21 to September 7 (day 141 to 250) and was interrupted by one long and few short cold periods. Some of the meltwater, from the beginning of the ablation season, did probably freeze again within the long cold period from May 31 to June 11 (day 151 to 162). The meltwater did probably not freeze at other short cold periods, because of high net radiation. The annual winter accumulation was measured as 50 cm. The weather station was visited 25 of July (day 206). At that time around 250 cm had melted of the surface. The surface consisted of cm winter snow at the meteorological station and the echo sounder was located above ice surface shaped by a water channel. More of the surface was therefore melted below the echo sounder or around 290 cm. According to the photograph, the winter accumulation was probably cm. Accumulation measurements from other sites close to the station do also support this result. The radiation equipment was also located over ice-surface affected by a small water channel. The shape of the water channels indicated that the channel below the echo sounder was formed much earlier than the channel below the radiation equipment. Figure A photograph taken at the meteorological station Köldukvíslarjökull 1998 (1100 m a.s.l.) at the July 25 (day 206). At that time, the surface beneath the echo sounder, pointed out as number 1, was made of melting of ice surface that had been shaped by a water-channel. The surface surrounding the meteorological station, pointed out as number 2, consisted of snow. 41

43 Figure 3.22 (a). Meteorological parameters. Köldukvíslarjökull 1998 (1100 m a.s.l.) 42

44 Figure 3.22 (b). Meteorological parameters. Köldukvíslarjökull 1998 (1100 m a.s.l.) 43

45 The melting did reach the summer surface around July 25 (day 206) according to figure After that day, the ablation consisted of melting ice. Day 206 is marked on some of the subplot in figure The effect of reaching the summer surface can be seen on the profile over albedo Energy components The energy components were calculated from May 21 to June 3 and from June 8 to September 8 (day 141 to 154 and 159 to 249). Figure 3.23 shows plot of the measured and calculated energy and how the energy separates into net radiation, sensible heat and latent heat. Profiles of three-day moving average of air temperature and wind-speed are also shown. Day 206 (25 of July) is marked on the energy budget plot. A good consistency was gained between M m and M c, except for day 170 to 195 and 227 to 237, pointed out as number 1 and 2 respectively. The most probably reason for the discrepancy for day 170 to 195, is high difference in albedo between the meteorological mast and the echo sounder. Better fit was gained when the outgoing solar radiation was increased by 20% for those days. This indicates a lower albedo or darker surface at the meteorological mast than below the echo sounder during this period. Higher values for M m than M c at day 193 to 198 could be explained by the differences in melting of the dark water channel surface below the echo sounder and the snow surface at the meteorological mast. The reason for the discontinuity at day 227 to 237 is not evident. One explanation might be dirt-cones and sand that be exposed up with the melting at this site. Figure 3.24 shows a plot of M c, R, H d and H l normalised to M c. The contribution from R varied from 50% to 150% of the net energy for most of the ablation season. High wind-speed and air temperature in the end of August and the beginning of September increased the contribution from H d and H l up to 70%. Table 3.16 shows averages of the energy components within June, July and August. The table shows also total averages, both for all calculated days and when day 181 to 195 and 227 to 237 are excluded. Those averages are labelled as Total and Total* respectively. On average 77% of the total ablation were produced by radiation, 20% by sensible heat and 3% by latent heat. The contribution of the heat component varied within the ablation season. (Fig ) Table Average of energy components within June, July and August and total averages. Total is average over all the days calculated. Total* is average over all days calculated excluding days 181 to 195 and 227 to 237. Köldukvíslarjökull 1998 (1100 m a.s.l.) R H d H l M c M m Number of days June July August Total Total*

46 Figure Energy component, air temperature and wind-speed profiles. Köldukvíslarjökull 1998 (1100 m a.s.l.). 45

47 Figure Energy components normalised to Mc. Köldukvíslarjökull 1998 (1100 m a.s.l.) Table 3.17 shows the values of ln(z 0 ) (or ln(z 0 )+S) that were used to gain consistency between M m and M c. Most of the values are lower than expected and could be explained by stable air conditions. Table Values observed for ln(z 0 ). Köldukvíslarjökull 1998 (1100 m a.s.l.) Day-number ln(z 0 ) (or ln(z 0 )+S) Surface type Winter snow Winter snow Winter snow Ice ice Correlation between measured total energy and other parameters. Table 3.18 shows calculated correlation between M m and other observed and calculated parameters. The correlation was calculated for the same days used in the energy calculation excluding days showing abnormal discrepancy between M m and M c. Most of the ablation was generated by R, or around 77%, but the correlation between M m and R is only 0.48 for daily average. Correlation between M m and H d and M m and H l is higher or 0.68 and 0.65 respectively for daily average. The reason for this is evident from the energy profiles in figure The net radiation controlled the net energy on average, but most of its variation was produced by sensible and latent heat. The highest correlation is achieved between M m and M c, or 0.79 for daily average and 0.92 for three-day moving average. Figure 3.25 shows the consistency between M m and M c for daily average and three-day moving average. Table Correlation between measured total energy M m and meteorological parameters. Number of days are N=83. Köldukvíslarjökull 1998 (1100 m a.s.l.) Correlation between M m and M c T T + u T u R Q i I i r H d H l Daily average Three-day moving average

48 Figure Comparison of measured and calculated total energy for daily average and three-day moving average. Köldukvíslarjökull 1998 (1100 m a.s.l) 3.7. Dyngjujökull 1998 (1200 m a.s.l) The meteorological station Dyngjujökull 1998 (1200 m a.s.l) was located at the northwestern site of Vatnajökull. The station was located within the ablation zone of Dyngjujökull outlet. Figure 3.26 (a) and (b) shows one day average of meteorological parameters in 2m above the surface. Figure 3.26 shows also the melting profile and the estimated daily ablation. The ablation was from May 20 to September 5 (day 140 to 248) and was interrupted by few cold periods. It is likely that some of the meltwater from the beginning of the ablation season did freeze again in long cold period from May 30 to June 11 (day 150 to 162). This did probably not occur at other short cold periods because of high net radiation. The annual winter accumulation was measured as 183 cm with ice below. The ablation did therefore reach the summer surface between 25 to 28 of July (day 206 to 209). Day 209 is marked on some of the plots in figure It is evident from figure 3.26 how this affected the ablation, outgoing short wave radiation, net radiation and albedo. Figure 3.27 show two photographs taken at the meteorological station 26 of July (day 207). The photographs are taken around the days when the surface was reaching the summer surface. At this site of the glacier, like at the ablation zone of Köldukvíslarjökull, the surface may consist of dirt-cones and sand layers after the ice is exposed. The albedo profile in figure 3.26 (a) indicates that the radiation equipment were located over dark area of sand from July 31 to September 6 (day 212 to 249). This is consistent with the surface conditions shown in figure It is also possible that something similar did happened below the echo sounder. 47

49 Figure 3.26 (a). Meteorological parameters. Dyngjujökull 1998 (1200 m a.s.l.) 48

50 Figure 3.26 (b). Meteorological parameters. Dyngjujökull 1998 (1200 m a.s.l.) 49

51 Figure Two photographs of the surface at Dyngjujökull 1998 (1200 m a.s.l.) at 26 of July. The surfaces pointed out as number 1 is below the radiation meters and number 2 below the echo sounder Energy components The energy budget was calculated from May 21 to May 30 and from June 11 to September 7 (day 141 to 150 and 162 to 250). Figure 3.28 shows a plot of the energy budget and three-day moving average of air temperature and wind-speed. Day 209, when the ablation reached the summer surface is marked on the energy plot. Good consistency between M m and M c was not attained for most of the days used in the energy budget calculation. The best consistency between M m and M c was gained for the beginning of the ablation season to the end of June and also for some days around the middle of July and at the end of the ablation season. The reason for the poor relationship between measured and calculated net energy for days 183 to 194, pointed out as number 1 in figure 3.28, is not evident. One possible reason could be that some slush was formed at the meteorological mast or at the echo sounder during this period. The discrepancy, for M m and M c, from day 212 to 249 can be explained by the photograph in figure 3.27 and the albedo record in figure 3.26 (b). The surface below the radiation meter did probably consist of dark sand surface at this period. The reflected coefficient can therefore have been much lower at surface surrounding the meteorological mast then at the surface surrounding the echo sounder. If so, the measured net radiation can not be used directly to describe the measured ablation M m during this period. Figure 3.29 shows R, H d and H l normalised to M c. The contribution from R varies from 65% of the net energy and up to over 200% until the end of August. At the end of the ablation season, the contribution from H d and H l goes up to 50% of the total energy as a consequence of combination of high air temperature and wind-speed. 50

52 Figure Energy component, air temperature and wind-speed profiles. Dyngjujökull 1998 (1200 m a.s.l.) 51

53 Figure Energy components normalised to Mc. Dyngjujökull 1998 (1200 m a.s.l.) Table 3.19 show averages of energy components within June, July and August and total average over all days used in the energy calculations. A good consistency is only gained for the averages of M m and M c in June. The reason for this is evident from figure According to the total average values for R, H d, H l and M c, around 90% of the total energy was produced by net radiation and around 10% and 0% by sensible and latent heat respectively. Those numbers varied within the ablation season. Table Average of energy components within June, July and August and total averages. Dyngjujökull 1998 (1200 m a.s.l.) R H d H l M c M m Number of days June July August Total Table 3.20 show the values used for ln(z 0 ) (or ln(z 0 )+S) that were used in the energy calculations. Most of the values are very low. Some of the explanation could be air stability. Another reason can be that darker surface at the meteorological mast gives an overestimation of R when it is used for the surface surrounding the echo sounder. Therefore, low values are needed to force H d and H l down and keep consistency between M m and M c. The total energy M m and M c, observed between two measured spots, can be different as a consequence of difference, in radiation absorption. Under these conditions, both M m and M c can represent correct net energy. Table Values observed for ln(z 0 ). Dyngjujökull 1998 (1200 m a.s.l.) Day-number ln(z 0 ) (or ln(z 0 )+S) Surface type Winter snow Winter snow Winter snow Winter snow Ice 52

54 Figure Comparison of measured and calculated total energy M m and M c for daily average and three-day moving average. Dyngjujökull 1998 (1200 m a.s.l) Correlation between measured total energy and other parameters Comparison of measured and calculated total energy is given in figure 3.30 for daily average and three-day moving average. Table 3.21 shows the correlation between measured total energy and other observed and calculated parameters. The correlation was calculated for the same days used in the energy budget calculations. No parameters show high correlation to M m for daily average. The correlation between M m and M c is only 0.55 for one day average but goes up to 0.87 for three-day moving average. Low correlation between M m and R could be a consequence of difference in the surface albedo between the meteorological mast and the echo sounder. Table Correlation between measured total energy M m and meteorological parameters. Number of days are N=99. Dyngjujökull 1998 (1200 m a.s.l.) Correlation between M m and M c T T + u T u R Q i I i r H d H l Daily average Three-day moving average

55 4. Comparison of eddy flux models In chapter 3, results of applying one-level model for neutral air conditions were presented for meteorological stations at Vatnajökull 1997 to Results of estimating the surface roughness for this model indicate that the eddy fluxes were stable on general. More reasonable values were attained for the surface roughness at all the meteorological stations at Vatnajökull 1996 [1]. A model using one level or two level measurements and an estimation of the eddy flux stability was tested on data from Brúarjökull 1996 (1140 m a.s.l.) and Brúarjökull 1997 (1210 m a.s.l.). This model is given in equation (7) to (14) in chapter 1. This chapter presents result of applying this model. The results are compared with the results given in section 3.1 and 3.4, for one-level neutral eddy flux model. Data from Brúarjökull 1996 (1140 m a.s.l.) and Brúarjökull 1997 (1210 m a.s.l.) were used for several reasons. The data from 1996 is expected to represent more neutral air fluxes than data from 1997 or This gives an opportunity to investigate two different air flux conditions. All measurements and calibration on Brúarjökull 1996 (1140 m a.s.l.) were done in solicitude manner, which makes the data more reliable. Brúarjökull 1996 (1140 m a.s.l.) and Brúarjökull 1997 (1210 m a.s.l.) were located at similar sites with one year difference. The data from 1998 have only been calibrated for measurements in 2m above the surface and was therefore not used for the two-level model Stability calculations The Monin and Obukhov length L was estimated for the two sites, by using several combinations of heights. Figure 4.1 show a comparison of using two-level and onelevel measurements to estimate L at Brúarjökull 1996 (1140 m a.s.l.). The heights z 1 =2m and z 2 =4m, and z 1 =z 0 and z 2 =2m were used for the two estimation respectively. Figure 4.2 show the same for Brúarjökull 1997 (1210 m a.s.l.). L is inverse as a function of stability. Comparison of figure 4.1 and 4.2 shows that L was higher on average at Brúarjökull 1996 (1140 m a.s.l.) than at Brúarjökull 1997 (1210 m a.s.l.). The air conditions were therefore more neutral on average1996 than Very good consistency was attained for Monin and Obukhov lengths calculated from different two-level height combination. The results achieved by using only one-level estimation of L did though show some differences from the others. This is partly evident from figure 4.1 and Results of applying eddy flux model with stability The stability model was tested by using both one level and two levels. The best result was achieved when two levels were used to calculate the sensible heat H d and one level to calculate the latent heat H l. In both cases, two levels were used to calculate the length L. A two level model was also tested for H l but without success. One explanation for this could be a systematic error in the calibrated humidity profiles measurements. This could be a consequence of using an incorrect method to calibrate the humidity profiles. 54

56 Figure 4.1. One-hour samples of the Monin and Obukhov length L. Brúarjökull 1996 (1140 m a.s.l.). Figure 4.2. One-hour samples of the Monin and Obukhov length L. Brúarjökull 1997 (1210 m a.s.l.). The two levels used to calculate H d were z 1 =2m and z 2 =4m and the one level for H l was z=2m. Comparison of energy profiles attained by the neutral model and the stability model is given in figure 4.3. Figure 4.3 (a) shows the result of finding the energy components at Brúarjökull 1996 (1140 m a.s.l.) with one-level neutral model and (b) with the stability model. The same is shown for Brúarjökull 1997 (1210 m a.s.l.) in figure (c) and (d) respectively. Table 4.1 shows then comparison of the averages of the energy components shown in figure 4.3, calculated by the two models. 55

57 Figure 4.3. (a) and (b) shows energy components on Brúarjökull 1996 (1140 m a.s.l.). (c) and (d) shows energy components on Brúarjökull 1997 (1210 m a.s.l.). In (a) and (c) a one-level neutral model was used to calculate H d and H l. In (b) and (c), one and two levels were used to calculate H l and H d, by using model including stability. All the plots are plotted on the same scale. It is evident from figure 4.3, that similar consistency is attained between M m and M c for both the models. Some differences are though in the calculated sensible and latent heat, like for example in August 1996 and at the beginning of August The results from the two models are close to being the same on average according to table 4.1. Table 4.1. Comparison of total averages of the energy components calculated by one-level model for neutral conditions and a model for one- to two levels with stability. Brúarjökull 1996 (1140 m a.s.l.) R H d H l M c One-level model for neutral conditions Model for one and two levels with stability Brúarjökull 1997 (1210 m a.s.l.) One-level model for neutral conditions Model with stability Number of days 56

58 Table 4.2 shows the values of the surface roughness z 0 at Brúarjökull 1996 (1140 m a.s.l.), that were used for the two models. Table 4.3 shows the same for Brúarjökull 1997 (1210 m a.s.l.). The roughness used at Brúarjökull 1996 is close to be the same in both cases, as a result of nearly neutral air flux. Unreasonable values of estimated roughness for Brúarjökull 1997 are changed to reasonable values when using model with stability parameter instead of a one-level neutral model. It is to be expected to have the surface roughness increasing during the ablation season and decreasing for snow. This was attained for the roughness estimation at both the sites, when the stability model was used. It was noted that the model with stability was much less sensitive for variation in the roughness parameter than the model for neutral conditions. Table 4.2. The surface roughness z 0 used for the two models. Brúarjökull 1996 (1140 m a.s.l.) Model for neutral conditions Model with stability Surface Day-number ln(z 0 ) z 0 [mm] ln(z 0 ) z 0 [mm] type Winter snow Winter snow Winter snow Winter snow Table 4.3. The surface roughness z 0 used for the two models. Brúarjökull 1997 (1210 m a.s.l.) Model for neutral conditions Model with stability Surface Day-number ln(z 0 ) z 0 [mm] ln(z 0 ) z 0 [mm] type Winter snow Winter snow Winter snow Firn New snow Firn Firn/New snow 57

59 5. Results The energy budget was calculated for seven meteorological stations on Vatnajökull, three from 1997 and four from This was done by using one-level model to estimate the sensible and latent heat. Results for each station are given in chapter 3. It was shown that it is possible to justify the result from the one-level model, since the calculated total energy can be compared to directly measured total energy provided for melting the glacier. This chapter shows some comparison of the energy budget from each of the meteorological stations. Figure 5.1 shows a comparison of the energy components at Vatnajökull 1997 and 1998, when three-day average is used to display the results. The figure shows how the energy budget characteristics can vary within the ablation season, from one site to another and between years. The energy budget is mostly controlled by radiation on average. The contribution from sensible and latent heat is highest for days that combined high air temperature and wind-speed. Table 5.1 compares the total averages from each of the meteorological station. The total averages are calculated for all days used in energy budget calculations. Large differences between M c and M m for some of the stations are explained in chapter 3. The table shows also values for H l +, H l -, H d + and H d -, where H l and H d stands for the latent and sensible heat respectively. The plus sign indicates sum over all positive values normalised to the total number of days and the minus sign is the same for negative values. Those numbers show the average positive and negative eddy fluxes at each station. The most of the total eddy fluxes are negative the cooler the local climate gets. The total average values for M c, R, H d and H l are plotted as bars in figure 5.2 (a). It can be seen that the total energy budget was higher at the summer of 1997 than Figure 5.2 (a) shows also that the ablation is not only depended on the elevation but also on the horizontal position at the glacier. Table 5.1. Total average of energy components on Vatnajökull 1997 and N is number of days. B.u.97: Brúarjökull 1997 (1210 m a.s.l.); B.l.97: Brúarjökull 1997 (918 m a.s.l.); K.97: Köldukvíslarjökull 1997 (1100 m a.s.l.); B.98: Brúarjökull 1998 (1200 m a.s.l.); T.98: Tungnaárjökull 1998; K.98: Köldukvíslarjökull 1998 (1100 m a.s.l.); D.98: Dyngjujökull 1998 (1200 m a.s.l.). H l + H l - H l H d + H d - H d R M c M m N B.u B.l K B T K D

60 Figure 5.1. Comparison of energy budget on Vatnajökull 1997 and The energy profiles are plotted for three-day moving average. All the plots are plotted on the same scale. 59

61 (a) (b) Figure 5.2. Comparison of total energy budget at Vatnajökull 1997 and (a) shows the total averages of the energy components for each weather station. (b) shows the energy components normalised to the calculated total energy. B.u.97: Brúarjökull 1997 (1210 m a.s.l.); B.l.97: Brúarjökull 1997 (918 m a.s.l.); K.97: Köldukvíslarjökull 1997 (1100 m a.s.l.); B.98: Brúarjökull 1998 (1200 m a.s.l.); T.98: Tungnaárjökull 1998; K.98: Köldukvíslarjökull 1998 (1100 m a.s.l.); D.98: Dyngjujökull 1998 (1200 m a.s.l.). The total averages of the energy components normalised to the calculated total energy are shown in table 5.2. Figure 5.2 (b) shows the table values plotted as bars. The contribution of radiation is high for all the stations or from 68% to 96% of the total energy. The climate was colder on average the summer 1998 than This makes the contribution higher from R at the sumer1998 than 1997 for most of the stations. Figure 5.2 shows that the net radiation is highest on average for station located below the equilibrium line as consequence of low albedo when the surface consist of ice. The latent and sensible heat is also highest for those stations due to warmer local climate. The contribution from the net radiation is though highest for stations located above the equilibrium since the latent and sensible heat are low on average at those sites. Table 5.2. B.u.97: Energy components normalised to the calculated total energy. Brúarjökull 1997 (1210 m a.s.l.); B.l.97: Brúarjökull 1997 (918 m a.s.l.); K.97: Köldukvíslarjökull 1997 (1100 m a.s.l.); B.98: Brúarjökull 1998 (1200 m a.s.l.); T.98: Tungnaárjökull 1998; K.98: Köldukvíslarjökull 1998 (1100 m a.s.l.); D.98: Dyngjujökull 1998 (1200 m a.s.l.). H l H d R M c N [%] [%] [%] [%] B.u B.l K B T K D