The modelled glaciers

Austre Brøggerbreen and Midre Lovénbreen are small glaciers with areas of approximately 6 km², located 3–5 km apart on the Brøggerhalvøya peninsula in northwest Spitsbergen (Fig. 1). A large body of glaciological information is available on these glaciers, including surface morphology, ice thickness measured by radio-echo sounding, and studies of their hydrological and thermal characteristics (e.g. Dowdeswell and others, 1984a, b; Liestøl, 1990; Hagen and Sætrang, 1991). Both glaciers span an altitudinal range between close to 0 and 700 m a.s.l., although neither actually reaches the adjacent fjord. The hypsometry of the two glaciers is somewhat different, Lovénbreen having a larger area at relatively higher elevations (Fig. 2).

Of particular significance for the present study is the long time series of mass-balance data that is available for

Fig. 1.

The Kongsfjorden area of northwest Spitsbergen showing the locations of Austre Brøggerbreen (AB) and Midre Lovénbreen (ML) and the weather station (Met.) at Ny-Ålesund. Glacier surface contours (50 m intervals) and spot heights are in metres. Shaded areas are moraine systems. The location of the study area within the Svalbard archipelago is inset.

the two glaciers (Hagen and Liestøl, 1990; Lefauconnier and Hagen, 1990). Both glaciers have experienced consistently negative balances since measurements began in 1966–67 for Brøggerbreen and in the following year for Lovénbreen (Fig. 3). Brøggerbreen has experienced only one positive balance season (1986–87) and Lovénbreen two (1981–82 and 1986–87). Each follows a similar pattern of interannual variation in net balance, but Lovénbreen, probably because more of its area is at a higher altitude (Fig. 2), experiences the less negative balance of the two. There has been a trend towards less negative mass balances over the period of observations (Lefauconnier and Hagen, 1990). It should be noted that superimposed ice plays a significant role in the mass balance of the two glaciers, making up 10–30% of the total.

Fig. 2.

Hypsometric curves of variation of area with altitude for Austre Brøggerbreen and Midre Lovénbreen (data from Norsk Polarinstitutt, 1979).

Climate

Meteorological data have been measured continuously in the Kongsfjorden area since 1969, with irregular measurements since 1950 (Steffensen, 1982; Hanssen-Bauer and others, 1990). The mean annual temperature at Ny-Ålesund is –6°C, with annual precipitation of 0.2–0.3 m year^–1 w.e. Mean monthly temperatures above zero occur from June to September, with an August value of 4.1°C at Ny-Ålesund (Fig. 1).

The ratio of precipitation between sea level (the Ny-Ålesund weather station) and the highest regions of the glaciers (approximately 700 m) is of the order of 1:3 (Liestøl, 1990). Hagen and Liesløl (1990) found that there is a relatively poor correlation (0.63) between winter precipitation (September–June) measured at Ny-Ålesund and snow accumulation over the whole glacier, because much of the accumulation over the glacier is associated with winds and snowdrifts. The variation of precipitation with altitude is accommodated by fitting a second-order polynomial to the observed values of snowfall with altitude (Liestøl, 1982, 1983, 1986; Hagen and Liestøl, 1987; Hagen, 1988). Examples are shown in Figure 4 for Austre Brøggerbreen in seasons 1980–81 and 1986–87, values being normalised with respect to data from Ny-Ålesund. Correlations of 0.95–0.99 between the fitted curve and the normalised data were obtained using this method.

The model

The energy-balance model is similar to that used in Oerlemans (1988, 1991, 1992). This model calculates the components

Fig. 3.

The winter, summer and net mass balances over the period (a) 1965–66 to 1989–90 for Austre Broggerbreen and (b) 1966–67 to 1989–90 for Midre lovénbreen (from Liesløl, 1990; personal communication from J. O. Hagen).

of the surface energy balance. It takes meteorological data, the area distribution with altitude of the ice mass, and parameters defining the global radiation as input values. The model has also been applied to the calculation of mass balances for glaciers in the Austrian Alps and in southern Norway (Oerlemans and Hoogendoorn, 1989; Oerlemans, 1992), and to the Greenland ice sheet (Oerlemans, 1991). As the model has been described in detail in Oerlemans (1992), only a brief summary will be given here. The mass balance of a glacier surface may be expressed as:

(1)

where M is the annual mass balance, f is the fraction of meltwater that refreezes instead of running off, B is the energy balance of the surface, L is the latent heat of melting, and P is the rate of precipitation in solid form. The term f is calculated using the ice-firn temperature in spring, which we approximate as the mean annual temperature. Surface layers at this temperature are then warmed through refreezing and latent heat release in the model.

The energy exchange between the atmosphere and the glacier surface is found from:

(2)

where a is the surface albedo, Q is the short-wave radiation reaching the surface, I _in and I _out are the incoming and outgoing long-wave radiations, and F_s and F_l are the sensible

Fig. 4.

Variations in snowfall with altitude for Austre Brøggerbreen in the seasons (a) 1980–81 and (b) 1986–87 (data from Liestøl, 1982; Hagen, 1988). Curves are second-order polynomials fitted to the data points.

and latent heat fluxes. The energy budget is thus divided into several components: solar radiation, long-wave radiation, turbulent energy fluxes and the refreezing of melt-water. The latent heat flux term is set to zero because of insufficient evidence on humidity over the glacier.

The solar radiation reaching the top of the atmosphere is found using the method of Walraven (1978). This radiation is then attenuated by absorption and scattering. Cloudiness, solar zenith angle and surface elevation are accounted for. However, the geometry of the glacier surface is not. Surface albedo is generated internally and is dependent upon the presence of snow, distance to the equilibrium line and the accumulated melt during the ablation season.

The long-wave component of the energy equation is divided between the outgoing radiation from the glacier surface and that incoming from the atmosphere. Outgoing radiation is set to a value of 316 W m^–2, that emitted by a black body at the melting point. The atmospheric long-wave radiation is in two parts: the contribution from a clear sky and that from clouds. The incoming radiation is calculated using the formulation of Kimball and others (1982). The radiation coming from clouds is transmitted in the 8–14 μm spectral band. Turbulent fluxes are proportional to the difference between the air and surface temperatures and humidity. The percolation and refreezing of meltwater is incorporated into Equation (1) of the model because, in Svalbard, superimposed ice contributes on the order of 10% to the annual accumulation (Hagen and Liestøl, 1990).

Nature of input meteorological data

There are three methods by which the required meteorological parameters may be applied to the model: (i) the use of

Fig. 5.

Measured and modelled mass-balance profiles for the period 1980–89: (a) Midre Lovénbreen; (b) Austre Brøggerbreen. The two modelled curves in (a) are obtained using daily meteorological parameters and the annual method of defining meteorological parameters. In (b) modelled results use the daily meteorological data from the Ny-Ålesund weather station.

long-term climate data (the global method); (ii) annual fils to measured data (annual method); (iii) daily inputs. The annual method has often been used (Oerlemans, 1991, 1992). This requires the annual temperature cycle to be expressed as a sinusoidal function. Precipitation is defined as constant throughout the year, with rain or snow every second day. Precipitation is assumed to fall as snow when the daily average temperature is below 2°C, and as rain above that value. All rainfall is assumed to rim off. Humidity and cloudiness are constant throughout the year, and set to the average annual value. The annual method is often adopted because daily meteorological data are either absent or only available from stations remote from the glaciers being modelled.

An alternative procedure is to use measured mean daily values for the meteorological parameters. We are able to take this approach because of the proximity of the Ny-Ålesund meteorological station to the glaciers being modelled (Fig. 1). We are therefore able to compare the results of energy-balance modelling using both annual fits to the meteorological data and observed daily values. In addition, we can compare both sets of mass-balance results, generated by energy-balance modelling, with the observed mass-balance data from the two glaciers.

Sensitivity to future warming

Modelling of climatic warming was carried out in two parts. The first series of tests applied global average values in response to a doubling of the CO₂ concentration, as predicted by various modelling efforts. Koster (1991) states that the global mean rise in temperature will be 1.5–4.5°C, with an average of 2.5°C. These values were each applied to the reference climate, and provided a test of the sensitivity of the glacier system to a wide range of warming scenarios. The results are presented in Figure 7. For a rise of 1.5°C, there is a calculated increase in the deficit in net balance of 0.77 m year^–1 (from –0.27 m year^–1 to –1.05 m year^–1) and an increase of 112 m in ELA (from 371 m to 483 m). In the most extreme case, of a warming of 4.5°C, the net mass balance will decrease by approximately 2.7 m year^–1 relative to to-day,

Fig. 7.

Modelled mass balance with altitude on Midre Lovénbreen determined from the use of modern reference climate data, and for increases in annual mean temperature of 1.5°, 2.5°, 3.5° and 4.5° C.

and the equilibrium line will rise to an elevation of over 700 m. This is greater than the highest elevations in the accumulation area of Lovénbreen and would therefore result eventually in the complete wastage of the glacier. In summary, changes on the order of –0.61 m year^–1 °C^–1 in net mass balance and 90 m °C^–1 in ELA are predicted from energy-balance modelling of valley glaciers in northwest Spitsbergen.

A second series of tests utilises values of climate change determined specifically for the Fennoscandian region, which are predicted to occur for a doubling in the atmospheric concentration of CO₂. They incorporate changes to both summer and winter temperatures, and to precipitation, in response to warming (Koster, 1991). Winter temperatures of +5° to 6°C and summer temperatures of +2° to 3.5°C are used, combined with precipitation increases of 10–50%. These changes were applied to the reference climate by use of a sinusoidal curve defined by the change in summer and winter temperature.

Examples of the results of modelling using these values for future climate changes are shown in Figure 8. In general, rises in summer temperature had an important effect on mass balance, whereas increases in winter temperature were of little significance. This is because the temperature is significantly below the melting point through most of the winter period, and raising it does not necessarily result in melting. When an increase of 2°C in summer temperature was applied, the increase in ablation was offset above about 600 m in elevation by an increase in precipitation by 50%, regardless of the change in winter temperature (Fig. 8). For this scenario, the equilibrium line rose by about 53 m. However, when the summer temperature was increased by 3.5°C, increased melting could not be offset anywhere on the glacier by even a 50% increase in precipitation, and the equilibrium line climbed 175 m relative to the modern reference climate (Fig. 8). When precipitation was either held at the reference climate value or increased by 10%, the ELA for a 3.5°C rise in summer temperature was found to be close to or above the highest points on the glacier, again resulting in the total wastage of the ice mass. Thus, depending on the relationship between temperature and precipitation, a warming of 3.5–4.5°C would be likely to

Fig. 8.

Modelled mass-balance profiles for Midre Lovénbreen over the decade 1980–89 compared with the modern reference climate. Different values represent (from left to right, separated by a slash) increase in winter temperature and increase in summer temperature, together with a 50% increase in annual precipitation in each case.

lead to the complete melting of Midre Lovénbreen, and of glaciers of similar hypsometry in Spitsbergen, if sustained through time (figs 7 and 8). In fact, because of the feedback between mass balance and ice surface elevation, glacier wastage is likely to take place at lower values of climate warming. The temperatures we present therefore indicate the maximum necessary for complete glacier wastage.

Past climate change: the Little Ice Age

Simões (1990) determined from ice-core data that the increase in temperature for the 20th-century average as compared with the previous three centuries was 1.5–2.2°C over the Svalbard archipelago, of which Spitsbergen is the largest island. These three centuries cover the most intense part of the climatic cooling associated with the Little Ice Age in Spitsbergen (e.g. Dowdeswell and others, 1990; Fujii and others, 1990; Simões, 1990). The modelling carried out to determine the mass balance under these cooler conditions involved an envelope of mean temperatures 0.5–3°C lower than today. Modelling was again restricted to Austre Lovénbreen, and results were compared with calculated mass balance for the modern reference climate (Fig. 9). In general, modelling predicts that cooling would result in an increase in net mass balance of approximately 0.30 m year^–1 °C^–1 and a decrease in ELA of approximately 77 m °C^–1 (Fig. 9).

Model calculations suggest that a decrease in the mean annual temperature of approximately 0.6°C or an increase of 23% in annual precipitation would result in a zero mass balance for Midre Lovénbreen (i.e. the glacier would be in equilibrium with the imposed climate). Using statistical correlations between meteorological and mass-balance data, Hagen and Liestøl (1990) found that a decrease in the average summer temperature of 1°C and a 50% increase in winter precipitation would result in a zero mass balance for Brøggerbreen and Lovénbreen.

Discussion

The sensitivity of ice masses to climatic change has also been modelled using an energy-balance approach for

Fig. 9.

Modelled mass balance with altitude on Midre Lovénbreen for past climate, using an envelope of cooler temperatures. Calculations using the modern reference climate are shown for comparison.

glaciers in southern Norway and the Alps, and for the Greenland ice sheet (Oerlemans, 1991, 1992). Changes in the net mass balance and ELA of glaciers in these areas for a 1°C warming are plotted in Figure 10, along with our results from Austre Brøggerbreen in northwest Spitsbergen. All values are plotted as a function of the annual precipitation in the highest part of the accumulation area. Oerlemans (1992) reports a clear relationship between annual precipitation and the predicted change in mass balance (Fig. 10b). However, he notes that there is no apparent link between precipitation and modelled change in ELA (Fig. 10a). The data for Austre Brøggerbreen, when plotted in Figure 10, are consistent with the trend in the relationship between mass balance and precipitation proposed by

Fig. 10.

Results of energy-balance modelling of glacier mass balance for a 1°C climatic warming, predicting changes in (a) ELA and (b) net mass balance linked to precipitation at the highest altitude on each glacier. Austre Brøggerbreen (BR) is compared with a part of the Greenland ice sheet (G), south Norwegian (SN) and Alpine glaciers (A) (data from Oerlemans, 1992).

Oerlemans (1992). This supports the conclusion that maritime glaciers are more sensitive to change in temperature and precipitation.

The implication of figure 10b for Svalbard in general is that glacier sensitivity to climate change will vary across the archipelago with the prevailing gradient in precipitation. Precipitation is greatest along the west coast of Spitsbergen, and decreases eastwards and with increasing altitude. We might therefore expect Austre Brøggerbreen and Midre Lovénbreen to be among the glaciers most sensitive to climate change in the archipelago, because of their location close to the west coast (Fig. 1).