Notation

Introduction

Ablation climate studies were made at two locations in North Greenland (Fig. 1 and Table 1) in the summers of 1993 and 1994. The studies were part of a 2 year programme on world sea-level changes supported by the European Union. North Greenland was chosen as the target because there is little information about ablation in the area, aside from a qualitative discussion by Reference FristrupFristrup (1951). The specific objectives of the studies were to collect daily ablation data and to compare ablation conditions with those found in West Greenland (Reference Braithwaite, Olesen and OerlemansBraithwaite and Olesen. 1989, Reference Braithwaite and Olesen1990). For example, the best available model of the mass balance and dynamics of the Greenland ice sheet (Reference Huybrechts, Letréguilly and ReehHuybrechts and others, 1991) still uses positive degree-day factors found in West Greenland, representing an extrapolation to the whole ice sheet that may not be valid because ablation climate conditions are not necessarily the same in all areas.

Fig. 1. Location map.

This is the first energy-balance study made in North Greenland. The field experiments were planned to save weight because it is very expensive to operate in this area. The basic approach is to measure the larger energy-balance components (radiation and ablation) as accurately as possible and to evaluate the smaller components (turbulent fluxes and conductive-heat flux into the ice) by indirect methods, requiring only light-weight equipment. By analogy with preliminary geological surveys, such an approach is termed a reconnaissance energy-balance study (Reference Konzelmann and BraithwaiteKonzelmann and Braithwaite, 1995), in contrast to very comprehensive studies in West Greenland (Reference Oerlemans and VugtsOerlemans and Vugts, 1993; Reference OhmuraOhmura and others, 1994), which is more accessible.

Energy Balance

The energy required for melting MLT is provided by the energy balance:

(1)

where CHF is the conductive-heat flux into the ice, SWR and LWR are the net short- and net longwave radiation fluxes, SHF and LHF are the turbulent sensible- and latent-heat fluxes, and ERR is the total error in the energy-balance equation. Defined as above, ERR can be regarded as an unknown, extra source of energy that absorbs the errors in the other terms. The latent heat released by freezing of rain water on to the glacier surface is neglected as being very small compared with other terms.

Table 1. Periods coverage and Locations of the two ablation–climate datasets: Kromprins Christiall Land (KPCL) alld HansTausen Ice Call (HTIC)

Ablation

The lefthand side of the energy-balance Equation (1) involves melt energy rather than ablation but it is not possible to measure melt directly. What can be measured, although somewhat inaccurately, is the ablation, which is the net loss of material Tram the glacier surface by melt and vapour transfer together. Although the latter may involve a large energy flux, it only causes a very small mass change. For example, to anticipate the results of the present study, the largest daily value of latent-heat flux is -71 W m⁻², which gives a mass loss of only 2kgm⁻² d⁻¹ by sublimation. Such a small change is not delectable as surface lowering and is negligible compared with the amount of melt. This is why this study, like others, treats ablation and melting as essentially identical in mass-balance terms and uses measured ablation to evaluate melt energy.

Daily measurements of ablation were made at two locations (Fig. 1): at the margin of the Greenland ice sheet in Kronprins Christian Land (KPCL) in 1993 and on an outlet glacier from the Hans Tausen Ice Cap (HTIC) in 1994.. Further details have been given by Braithwaite and others (in press).

Ablation was measured at ten stakes within an area of only about 100 m², located beside the climate and radiation stations on the ice. The ten stakes were read daily at close to 19 h UTC (about 17.15 h solar time in KPCL and 16.30 h solar lime at HTIC). At both sites, ablation crust was ubiquitous and an alternation between a white crusty surface and blue ice, as described by Reference Müller and KeelerMüller and Keeler (1969), was never observed. Data from the ten slakes were compared with each other to detect gross errors in the data, and erroneous data were discarded (one stake for KPCL 1993 and two stakes for HTIC 1994). The error standard deviation for daily ablation at the remaining stakes was about ±5 kg m ⁻² d⁻¹. This is further reduced to only about ±2 kg m⁻² d⁻¹ by averaging over the available 9 or 8 stakes.

Ice Temperature and Conductive-Heat Flux

Although Reference Braithwaite and OlesenBraithwaite and Olesen (1990) neglected the conductive-heat flux into the ice in West Greenland, it was expected that this term would be significant in North Greenland. As only a rotary drill was available for the 1993 fieldwork, it was only possible to install thermistors into the ice to a depth of 3 m to evaluate the heat flux while in 1994 thermistors were installed to 10 in with a portable steam drill.

Englacial temperatures were measured every day at both sites. The ice is very cold with the O deg isotherm only about 0.2-0.3 m below the ice surface (even with the possible help of radiation warming of the thermistor cables) but ice temperatures rose by about 0.2-0.3 K d⁻¹ within the top few metres.

The conductive-heat flux Q at any depth in the ice is proportional to the vertical temperature gradient:

(2)

where K is the thermal conductivity (2.1 W m⁻¹K⁻¹ and yis the depth below the ice surface. Note the différent sign convention to Reference PatersonPaterson (1994, p. 206), because we treat heat flux into the ice (away from the surface) as a heat sink.

Using Equation (2), the conductive-heat flux is calculated at depths midway between thermistors, whose initial depths are continually adjusted to lake account of the surface lowering due to daily ablation. Results for the HTIC 199 I dataset are plotted in Figure 2 where the curve represents a second-degree polynomial, and the odd-looking point clusters are the result of many points lying close together, only separated by about 0.02 m d⁻¹ due to ablation.

Fig. 2. Conductive-heat flux in the ice vs depth below the glacier surface, 2 July-5 August 1994 (days 183-217) at Hans Tausen lce cap (HT IC).

The inflection in the curve at nearly 8 m below the surface is probably an artefact of the polynomial and is not important for the present discussion. On the other hand, the intercept of the curve with the vertical axis is an estimate of the mean conductive-heat flux at the glacier surface, i.e. 18 W m⁻² in this case. Coincidentally, this is the same value found for KPCL 1993 (Reference Konzelmann and BraithwaiteKonzelmann and Braithwaite. 1995). The latter assumed a linear correlation of heat flux with depth, but to less than 3 m below the glacier surface, and inspection of Figure 2 shows that heat flux for the HTIC; 1991 dataset is also nearly linear within this depth range.

No doubt, the above method could be refined but it hardly seems worth it for present purposes. The conductive-heat flux CHF for both datasets is therefore assumed constant with a value of 18 W m⁻².

Radiative Fluxes

Due to the importance of radiative duxes in the energy balance, priority was given to accurate measurements of incoming radiation.

Global radiation and all-wave incoming radiation were measured directly with a Swissteco SS-25 pyranometer and a Swissteco ST-25 pyrradiometer, respectively, for the KPCL 1993 experiment, these instruments were mounted on land beside the base camp, while they were mounted on the ice at the glacier station in the HTIC 1994 experiment The 1993 configuration was chosen, because it was thought that it would be difficult to keep the instruments levelled if they were mounted on the ice. However, in 1994 the instruments were easily kept level by only small adjustments at least once a day. This is probably partly due to the low ablation rate, and partly due to the good design of the tripod instrument mounting.

The cosine error of the upfacing pyranometer was corrected for zenith angle >70° using a polynomial function whereby only part of the direct solar radiation is taken into account. Based on measurements made at ETH Camp (West Greenland) in June 1990, it was assumed that 70% of global radiation is caused by direct solar radiation (Reference Konzelmann and OhmuraKonzelmann and Ohmura, 1995). (Such an assumption is not needed if incoming global radiation is measured with two instruments, one with a shading ring and the other un-shaded, but this was not done in the present study in the interests of saving weight by only using one instrument.)

The longwave incoming radiation was then calculated as the difference between the all-wave incoming radiation and the global radiation, and compensated for the emission loss of the instrument (σT_i⁴), where σ is the Stefan-Boltz-mann constant and T_i is the temperature of the pyrradiometer in Kelvin. There is a possible underestimation of the all-wave incoming radiation due to thermal convection (Reference Ohmura, Gilgen, McBean and HantelOhmura and Gilgen, 1993) and the longwave incoming radiation was corrected accordingly. The remaining uncertainty in the incoming longwave radiation is estimated to be ± 10 Wm⁻² (Reference DeLuisi, Dehne, Vogt, Konzelmann, Ohmura, Keevallik and KärnerDeLuisi and others. 1993). The longwave outgoing radiation L¹ is calculated by:

(3)

where T₀ is the temperature of the glacier surface (273.5K for melting ice).

Shortwave incoming radiation, together with reflected radiation, was also measured in both years at the glacier station with a Swissteco SW-2 two-component pyranometer (albedometer). The instrument was mounted on a survey tripod al a height of about 1.2 m and was relocated every few days to sample as many types of surface as possible. Figure 3 shows variations in daily albedo within the immediate area covered by slake measurements in the HTIC 1991 experiment. The very high albedo in the first sample (days 191-194 for “light hummock”) was due to several days with snow, with maximum albedo 0.84 decaying to 0.59. There were also traces of snow on days 183, 197 and 199, which correspond to small peaks in albedo. Otherwise, albedo varies greatly between about 0.3 and 0.5, reinforcing the finding of Reference Konzelmann and BraithwaiteKonzelmann and Braithwaite (1995) for the KPCL 1993 experiment. Baggild and others (1996) have also measured larger-scale albedo variations from the ice margin, near to the site of the KPCE 1993 experiment, to the equilibrium line. (An oblique air photograph of the field area clearly showing albedo variations is on the from cover of Annals of Glaciology 23). Figure 3 undoubtedly shows albedo differences between different kinds of site but there are also large differences between different days at the same site. Aside from the effects of snow, albedo may also depend on whether the surface is fro/en or melting. It would be interesting to operate both moveable and fixed albedo stations in a future experiment.

Fig. 3. Variations of daily albedo between different sites, 2 July-5 August 1994 (days 183-217) at Hans Tausen Ice Cap(HTIC).

Turbulent Fluxes

The vertical turbulent sensible-heat flux SHF is expressed in flux-gradient form as:

(4)

where ρ is the density of air, c_p is the specific heat of air (1005 J kg^{−1 −l}), K_H is the coefficient of turbulent diffusivity, dT/dz is the vertical temperature gradient and Γ is the adiabatic lapse rate. As the present paper only deals with the air layer close to the glacier surface (instrument height 2 m) with large air-temperature gradients, Γ is neglected compared with dT/dz. In the present paper, turbulent fluxes towards the glacier surface are positive.

Equation (4) can be reformulated in terms of simple data for wind speed and temperature following Reference Ambach and KirchlechnerAmbach and Kirchlechner (1986) and Reference PatersonPaterson (1994, p. 60-66):

(5)

where ρ₀ is the density of air (1.29 kg m⁻³) at the standard atmospheric pressure b₀ (101 300 Pa). A is a dimensionless transfer coefficient, b is mean atmospheric pressure at the measuring site, and u and T are measured wind speed and air temperature at 2 m above the glacier surface.

Previous treatments (Reference Braithwaite and OlesenBraithwaite and Olesen, 1990; Reference Konzelmann and BraithwaiteKonzelmann and Braithwaite, 1995) assumed logarithmic profiles of wind speed and temperature in the near-surface boundary layer, which are valid for neutral conditions. However, the approach is extended here to log-linear profiles, which are supposed to be more appropriate for the strong stability that can occur over a melting ice surface.

Under these conditions, the transfer coefficient is given by:

(6)

where k is von Kármán’s constant (0.41), z is the instrument height (2 m), z_0U and z_0T are surface roughness for wind speed and temperature, α_U and α_T are empirical parameters for the wind and temperature profiles, and Λ is the scale height of Reference ObukhovObukhov (1971):

(7)

where T_k is the absolute air temperature (K), g is the gravitational acceleration and u* is the friction velocity for the log-linear profile given by:

(8)

The roughness lengths determine the magnitude of sensible-heat flux for neutral conditions, and the α parameters describe the reduction of sensible-heat flux with increasing stability. More research is needed to find the most appropriate values of these parameters to use in any particular situation. For the present study, Equation (6) is simplified as:

(9)

where z₀ is the effective roughness for sensible-heat flux and α = α_U = α_T Reference Morris and HardingMorris and Harding (1991) assumed the same roughness lengths for wind and temperature profiles. There is, however, ample evidence that they are different (Reference SverdrupSverdrup, 1935; Reference HolmgrenHolmgren, 1971; Reference Ambach and KirchlechnerAmbach and Kirehlechner, 1986; Reference Van den Broekevan den Broeke, 1996: Reference Hock and HolmgrenHock and Holmgren, 1996), and that roughness is not really constant with time either (Reference Greuell and KonzelmannGreuell and Konzelmann, 1994; Reference Plüss and MazzoniPlüss and Mazzoni, 1994), but it is not clear what values should be used in a particular case (Reference BraithwaiteBraithwaite, 1995). The effective roughness z₀ is here defined such that Equation (9) gives the same A value as Equation (6) and satisfies the inequality z_0U >z₀ >z_0T.

After some trial and error, a value of 10 ⁻³ m was adopted for z₀over an ice surface (Reference Van de Wal and Russellvan de Wal and Russell, 1994; Reference BintanjaBintanja, 1995; Reference Konzelmann and BraithwaiteKonzelmann and Braithwaite, 1995). There is also an extensive literature on α (Reference GarrattGarratt, 1992, p. 289) but this study follows Reference MunroMunro (1989) in assuming that α = 5 in stable conditions as proposed by Reference DyerDyer (1974). An apparent difficulty is that the transfer coefficient, and hence the sensible-heat flux, uses the Obukhov length Λ which, in turn, uses the sensible-heat flux. This vicious circle is avoided by an iterative procedure (Reference MunroMunro, 1989) whereby SHF is first calculated for z/ Λ = 0 (neutral case), then a new Λ is calculated from SHF, and an updated SHF is calculated from the new Λ, the whole procedure being repeated 2-3 times until Λ converges. Reference Greuell and KonzelmannGreuell and Konzelmann (1994) rejected this approach as “time consuming" but, to be fair, it does increase the total number of calculations in any modelling study by several times so that some workers may prefer a stability correction (without iteration) in terms of the Richardson number.

By analogy with the sensible-heat flux, the latent-heat flux is given by:

(10)

where L_v is the latent heat of vaporization, e is the vapour pressure at height z above the glacier surface and e₍₎ is the saturation vapour pressure at the glacier surface. The latter is a function of the surface temperature and is 611 Pa for a melting surface (Reference PatersonPaterson, 1994, p.65). We follow Ambaeh and Kirchleehner (1986), and Reference Greuell and KonzelmannGreuell and Konzelmann (1994), in distinguishing between condensation and sublimation, i.e. with latent heat L_v = 2.514 and 2.849 MJ kg⁻¹, respectively. When (e — e₀) is positive and T₀ = O deg, water vapour condenses as liquid water on the melting glacier surface with L_v = 2.514 MJ kg⁻¹. When (e — e₀) is negative, there is sublimation with L_v = 2.849 MJ kg⁻¹. Also, when (e — e₀)) is positive and T₀ O deg, there is condensation from vapour to solid ice with L_v ⁼ 2.849 MJ kg⁻¹.

Calculation of the Energy Balance

The full energy balance was calculated on an hour-to-hour basis. Aside from being physically more correct than a daily calculation, the hourly calculation of the turbulent fluxes has a hidden bonus. This is because the (unventilated) temperature sensors show clear signs of radiation heating: temperatures rise quickly if wind speeds drop below about 2ms⁻¹. This caused some concern until it was realized that, even if the temperature is erroneously high for a particular hour, it is multiplied by a correspondingly low wind speed for the same hour. The resulting error in the sensible-heat flux summed over any day is small because the largest contributions come from hours with high wind speeds.

For each hourly time-step, the glacier-surface temperature is initially assumed to be 273.15 K for calculation of longwave outgoing radiation, sensible-heat flux and latent-heat flux, and a trial value of hourly ablation is calculated. If the trial value is negative, it is assumed that the glacier surface is frozen, and the surface temperature is reduced in the model by 0.1 K in successive steps until the trial ablation for the hour becomes zero. This occurs quite often in both data-sets, even when the air temperature is positive, confirming that melting conditions cannot be assumed a priori or preset in models (Reference OerlemansOerlemans, 1991; Reference Van de Wal and RussellVan de Wal and Russell. 1991). Reference Braithwaite and OlesenBraithwaite and Olesen (1990) were ambiguous on this point as their paper implied that the surface temperature was preset at 0 deg but, in fact, a trial value of daily ablation is calculated to check for freezing temperatures. Reference KuhnKuhn (1987) suggested that melting conditions can prevail over a wide range of air temperatures, both negative and positive, but the present results suggest a definite tendency towards a frozen ice surface while air temperatures are still positive.

Table 2. Calculated energy balance, 8-27 July 1993 (days 189-208) at Kronprins Christian Land (KPCL). Units are W m⁻¹.

The hourly values of the computed energy balance are summed into daily totals in tables 2 and 3. The day refers to the 24 hour period from 20 h UTC on one day to 19 h UTC on the following day, because daily ablation is measured between these times. The error in the daily energy balance is then calculated as the difference between measured daily ablation and modelled daily ablation.

Sensitivity of the Model to Assumptions

The error in the calculated ablation can be used to judge the sensitivity of the model to diffèrent assumptions about roughness, albedo and the effect of stability (table 4).

For KPCL 1993, a roughness of 10⁻³ m and an albedo of 0.48 gives a smaller error than the other assumptions. However, for HTIC 1994, the error is not very sensitive to different choices of roughness because the sensible- and latent-heat fluxes are of roughly equal and opposite magnitudes. The weighted average of the albedo measurements in Figure 3 for HTIC 1994, excluding the few days with snow, is about 0.43 but a model ice albedo of 0.48 gives a lower error for HTIC 1994 as well as for KPCL 1993.

Table 3. Calculated energy balance, 2 July—5 August 1994 (days 183 217), at Hans Tausen Ice Cap (HTIC). Units are W m⁻²

Table 4. Error in calculating melt energy as a function of stability, surface roughness and albedo for two ablation-climate datasets: Kronprins Christian Land (KPCL) and Hans Tausen lce Cap (HTIC). Units are W m⁻²

The log-linear profile need not be true for real glaciers and ice sheets with sloping and inhomogenous surfaces (Reference Hock and HolmgrenHock and Holmgren, 1996), and should not be applied blindly Extra calculations of the turbulent fluxes were therefore made without taking account of stability, i.e. assuming logarithmic profiles instead of log-linear profiles, and the resulting errors are given in Table 4 for the case “Stability effect Off”. In both datasets, the mean errors are slightly more negative than in the case of “Stability effect On" but this can be offset again by choosing a smaller effective roughness. The effect of stability is therefore fairly small and the correctness of the stability assumption is not unequivocally demonstrated by this sensitivity analysis. The reason is probably that neither of the datasets involves very strong stability. This point is illustrated in Figure 4, which shows the exchange coefficient A as a function of wind speed u and air temperature (both at 2 m above a melting surface). For high wind speeds and the relatively low air temperatures that prevailed in both datasets, the exchange coefficient is quite high and fairly constant.

Fig. 4. Dimensionless exchange coefficient for sensible-heat flux. Temperature and wind at 2m above melting glacier surface.

The process of choosing model parameters to fit the data, i.e. “model tuning" to find the desired values of effective roughness and albedo, is not one to be undertaken lightly, For example, if the model is incorrectly specified, or if the data are wildly inaccurate, the model parameters found by tuning will be wrong. However, in the present case, the indicated values of both the effective roughness and albedo are highly plausible. For example, an effective roughness z₀ of 10 ⁻³ m is consistent with the larger z_0T values reported in the literature (Reference KuhnKuhn, 1979; Reference MorrisMorris, 1989; Reference Van den Broekevan den Broeke, 1996), if it is also combined with much smaller z_0U values in agreement with Reference SverdrupSverdrup (1935), Reference HolmgrenHolmgren (1971), Reference Ambach and KirchlechnerAmbach and Kirchlechner (1986), Reference Van den Broekevan den Broeke (1996) and Reference Hock and HolmgrenHock and Holmgren (1996). By the same token, an albedo of 0.48 is within the range of albedo values measured at both sites and may well be the “most representative" value.

Ablation Variations

The error in the calculated daily energy balance reflects errors in the data and in the modelling, and represents the accuracy with which ablation or melting can be calculated. The small mean values of the errors in tables 2 and 3 have no special significance because surface roughness and albedo values in the model are chosen to make the mean error small, i.e. by tuning the model (table 4). The standard deviations of the errors are also small and these are not directly affected by the tuning. For example, there is a strong correlation between measured and calculated ablation (Fig. 5) with an error standard deviation of only about ± 5 kg m⁻² d⁻¹.This is a lot lower than the ± 14—19 kg m⁻² d⁻¹ achieved in West Greenland (Reference Braithwaite and OlesenBraithwaite and Olesen, 1990). The reasons for the lower errors are discussed in the following section, but for the present it is enough that the error standard deviations are small compared with ablation variations. However, as should be clear from Figure 5, some very large daily errors can occur, which seem too large to be measurement errors and must be model errors. There is therefore still room for improving the model.

Fig. 5. Measured daily ablation and daily ablation calculated from the energy balance for Kronprins Christian Land (KPCL) and Hans Tausen Ice Cap (HTIC). Periods are 8-27 July 1993 at KPCL and 2 July-5 August at HTIC.

In Figure 6 the melt energy is compared with net radiation (the sum of short- and longwave radiation) and the total turbulence (the sum of sensible-and latent-heat fluxes). It is clear that ablation was generally high for KPCL 1993 because of high net radiation and high turbulence. However, day-to-day variations in net radiation are rather small and the ablation is mainly controlled by variations in turbulence, in agreement with Reference BraithwaiteBraithwaite (1981). By contrast, ablation was generally low for HTIC 1994, because both net radiation and turbulence are low, and the latter is even negative for several periods such that the net contribution of turbulence to melt energy is rather small. However, day-today variations in ablation for HTIC 1994 are in step with both turbulence and net radiation. For example, the ablation minimum at day 191 is caused by high surface albedo due to fresh snow that coincides with low temperature.

Although ablation is only measured on a daily basis, the diurnal variation in melt energy can be calculated with the energy-balance model (Fig. 6). Despite the high latitude with 24 hours daylight, there is a strong diurnal variation at both sites, which is mainly forced by variai ions in short-wave radiation and reinforced by nocturnal cooling of the ice surface by outgoing longwave rachat ion and sublimation. The energy-balance model frequently predicts a frozen glacier surface at night even when air temperatures are positive. This explains the frequent observation of ice in water-filled cryoconite holes until well into the day (the ice is usually above the water level in the holes, which has presumably dropped since the ice formed).

Fig. 6. Variations of daily melt energy, net radiation and turbulent fluxes for Kronprins Christian Land (KPCL) and Hans Tausen Ice Cap (HTIC). Periods are 8- 27 July 1993 at KPCL and 2 July-5 August at HTIC.

The displacement of the maxima in Figure 7 is mainly caused by the difference in solar noon due to the differing longitude of the two sites, i.e. about 13.40 and 14.30 UTC for KPCL and HTIC, respectively.

Comparison with West Greenland

The energy-balance studies in North Greenland are compared in tables 5 and 6 with two earlier studies from West Greenland (Reference Braithwaite and OlesenBraithwaite and Olesen, 1990). Differences reflect both different methods (table 5) and different glacier-climate conditions (table 6). The North Greenland data essentially cover July, while the West Greenland studies extend over June-August, The large sample sizes for the West Greenland studies represent overkill (there was a strong political motive to keep the data collection going as part of investigations for hydro-electric power in the late 1970s and early 1980s) but it is impossible to claim that the shorter North Greenland studies are completely representative: the ideal would be measurements over several seasons.

The albedo is higher for the North Greenland cases (table 4) than for those assumed for West Greenland. No explanation for this can be given here, but Bøggild and others (1996) and Reference Cutler and MunroCutler and Munro (1996) suggested that albedo is mainly controlled by debris inclusions in the ice, and the matter certainly deserves further attention. The apparently higher surface roughness for the North Greenland cases is not significant because different wind and temperature profiles are used. The log-linear profile for KPC IL and HTIC leads to reduced sensible-heat flux under stable condition but this could be offset again by choosing a higher effective roughness (Reference BraithwaiteBraithwaite, 1995). Judged subjectively, the local topography at Qamanârssûp sermia (QAM) was the roughest of the four cases and Hans Tausen Ice Cap (HTIC) the smoothest.

The errors in the energy balance are much lower for the North Greenland eases (KPCL and HTIC) than for the West Greenland sites (NBG and QAM). From Table 5, there could be several reasons for the greater accuracy. First, the energy-balance calculation is made every hour, including the check on surface temperature that actually shows a surprisingly large number of cases with a frozen surface while air temperatures are still positive. This effect is largely missed if the energy balance is calculated with daily data as in West Greenland (the data collections in the latter case were based on old-fashioned recorders and only analysed on a daily basis while the present study uses modern data loggers). Secondly, shortwave radiation is measured with better instruments (pyranometers), and longwave radiation is based on measurements (pyrradiometers) rather than estimated. Thirdly, the ablation measurements in North Greenland are made with a larger number of stakes (ten instead of three) with a careful check for errors (Braithwaite and others, in press).

Fig. 7. Diurnal variation in mean melt energy for Kronprins Christian Land (KPCL) and Hans Tausen Ice Cap (HTIC). Periods are 8-27 July 1993 at KPCL and 2 July-5 August at HTIC.

Table 5. Methodology of energy-balance studies at four sites in Greenland: Nordbogletscher (NBG), Qamanârssûp sermia (QAM), Kronprins Christian Land (KPCL) and Hans Tausen Ice Cap (HTIC)

The highest amount of net radiation was for the KPCL dataset (table 6) but this mainly reflects a long period of line and clear weather due to an anticyclone over Greenland (Geb and Naujokat, 1993) and may not be entirely typical. Otherwise, Qamanârssûp sermia (QAM) has higher net radiation than Nordbogletscher (NBG), because of a slightly more continental climate. Overall, net radiation accounts for 58-75% of the total energy sources for the four sites.

The KPCL dataset (table 6) has the largest sensible-heat flux, which is mainly due to the predominance of high wind speeds as air temperatures are fairly low. By comparison, Qamanârssûp sermia (QAM) has high sensible-heat flux due to both high wind speed and temperature. Sensible-heat flux was low at HTIC because both wind speed and temperature are low.

The relative roles of condensation and sublimation in the melt process has long been a point, of controversy in the snowmelt literature, and is important, because the first is a source of melt energy while the second takes energy that would otherwise be available for melting. In the 1930s, François Matthes stressed the importance of sublimation for snow ablation, as quoted and supported by Reference BeatyBeaty (1975), but this has been denied by Reference SharpSharp (1951). For the West Greenland sites, condensation and sublimation on average nearly balance (with some large daily latent-heat fluxes of both signs) compared with large sublimation at the North Greenland sites, amounting to 17 and 21 % of the total energy sinks. In percentage terms, the latter agrees well with measurements in northeast Greenland (Reference Lister and TaylorLister and Taylor, 1961), showing the dominance of sublimation, and qualitatively with a report from Peary Land, North Greenland (Reference FristrupFristrup, 1951). The predominance of sublimation over condensation is a general characteristic of ablation at lower temperatures, e.g. early in the melt season for all types of glacier (Wallon, 1948) or in more continental conditions (Reference Ohmura, Lang, Blumer and GrebnerOhmura and others, 1990; Reference Ohno, Ohata and HiguchiOhno and others. 1992). The ultimate expression of the dominance of sublimation over melting in the ablation process is reached in the “blue ice" areas of the Antarctic where there is no melting (Reference Bintanja and van den BroekeBintanja and van den Broeke, 1994).

Table 6. Mean energy balance at four sites in Greenland: Nordbogletscher (NBG), Qamanârssûp sermia (QAM), Kronprins Christian Land (KPCL) and Hans Tausen Ice Cap (HTIC)

The ablation energy is fairly low for the North Greenland sites if one takes account of their lower elevations compared to the West Greenland sites. Conductive-heat flux in West Greenland must be quite low but it is probably incorrect to neglect it completely as in Table 6. By contrast, conductive-heat flux accounts for 8 and 16% of the total heat source at the North Greenland sites. The overall impression is that ablation in North Greenland is relatively low, because both sublimation and conductive-heat flux use energy that would otherwise be available for melting.