Modelling snow accumulation and ablation

Using a snow-wedge model similar to that of Reference Fitzharris and GarrFitzharris and Garr (1995), the snow accumulation and ablation over Storglaciären is modelled daily from 1 January 1990 to 23 July 2006. Daily precipitation and average daily air temperatures are required for model input. Precipitation values from Kråkmo, Norway, are used, as no suitable continuous data are available from within the valley itself. Kråkmo is ~110km west of Tarfala across the Scandinavian Mountains (at 76 ma.s.l.). Reference Jansson and PetterssonJansson and others (2007) also use representative coastal Norwegian meteorological data when investigating snow deposition over the Kebnekaise massif. The temperature values are obtained from the Tarfala valley climate station, which is ~1 km northeast of the glacier at 1130 ma.s.l. (Reference HockHock, 1999). A linear 10% increase per 100 m is applied to the precipitation values (Reference Hock, Radiá and De WoulHock and Noetzli, 1997), and a lapse rate of 0.65˚C (100m)^–1 (Reference Barry and ChorleyBarry and Chorley, 1987) to the temperature values.

Using Equation (1), snow deposition (p) and snow ablation (a) are used to calculate the daily specific mass balance at each 100m elevation band (b _(z,d)), with d referring to day and z referring to the elevation band, which ranges from 1100–1199 to 1700–1799ma.s.l.:

The volume of snow deposited daily (p _(z,d)) depends on a threshold temperature (T _h) that is set at 1.5˚C to distinguish between solid and liquid precipitation (Reference HockHock, 1999):

Daily snow ablation at each elevation band (a _(z,d)) is calculated using a degree-day model (Reference BraithwaiteEquation (3)). Reference HockHock (1999) used a degree-day approach to simulate the dischar ge of Storglaciären for the 1993 and 1994 summer seasons. The maximum agreement between simulated and observed discharge was given by the highest R ² value, which in turn was correlated to the optimal degree-day factor. Though considerable diurnal and spatial variation was evident in the degree-day factors (f), it was found that the optimal ones for snow and ice were 5.5 and 6.5 mm^˚C^–1 d^–1 respectively for normal flow conditions (Reference HockHock, 1999). During low-flow conditions these changed to 4.5 and 7.5 mm^˚C^–1 d^–1. However, a time-averaged f of 3.2 mm^˚C^–1 d^–1 for snow was obtained from air-temperature and ablation measurements on the glacier surface for the same study period (Reference HockHock, 1999).

Within this current investigation, an initial degree-day factor of 5.5 mm^˚C^–1 d^–1 is used, as this is the higher optimal f for snow found in Hock’s (1999) study. This is then lowered to the 3.2 mm^˚C^–1 d^–1 time-averaged degree-day factor in order to obtain a better fit between model results and snowlines delineated from remotely sensed imagery and measured winter balances. Only snow ablation is simulated. Thus b _(z,d) is set at zero once the entire snowpack in a particular elevation band is completely melted, unless a fresh snowfall occurs.

Net specific snow accumulation (n _(z,d)) in mm water equivalent (mmw.e.) for each elevation band is calculated daily by cumulatively summing the daily specific mass balances. This is multiplied by the respective band area to give the daily net snow balance (B _z) in m³w.e. The daily net seasonal snow input to the glacier (B _G) in m³w.e. is calculated by adding B_z for all elevation bands. Annual snow accumulation (S _A) in m³ is calculated as the difference between maximum B _G at the end of winter and minimum B _G the previous autumn. By averaging annual snow accumulation over the glacier area, the winter balance (B _W) is calculated in mw.e. The amount of annual snowmelt (S _M) in m³ is also calculated, with the difference between S _A and S _M being the snow available for transformation to firn, termed here as net seasonal snow (S _N) in m³.

Mapping snow cover from remotely sensed imagery

Two aerial photographs (2 September 1990 and 9 September 1999), one Landsat 7 Enhanced Thematic Mapper Plus (ETM+) image (31 July 2002) and two Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images (15 April 2004 and 8 May 2004) are used. These are geometrically calibrated and the satellite imagery corrected for atmospheric interference. All are georeferenced to the Universal Transverse Mercator (UTM) World Geodetic System 1984 (WGS84) zone 34N projection within the programme ENVI version 4.2. A digital elevation model (DEM) of the catchment is also georeferenced to the common UTM zone. The DEM is then divided into seven 100m elevation bands ranging from 1100–1199 to 1700–1799ma.s.l.

The remotely sensed images are classified within the programme eCognition Professional (version 5.0). User-defined rules enable the distinction between areas of snow, ice and non-snow/ice, based on the spectral signatures of these regions as well as on aspect, slope and elevation information obtained from the DEM. All the classified images are then overlain onto the DEM. A transect is inserted from the névé to the snout of the glacier. The snowline altitude is obtained for each image as the point where the snowline intersects the transect. No account is taken of spatial variability across the glacier.

Validation of model results

The snowline elevations obtained from the image classifications are compared to the snowline elevations produced by the model. The model results are also compared with winter-balance (B _W) and net mass-balance (B _N) values measured annually at Storglaciären. Where discrepancies are identified between model results and observed data, the degree-day factor is lowered and the model run again.

Meteorological data

The total annual precipitation varies throughout the 16 year study period, from a maximum of 1877mm in 1992 to a minimum of 1223mm in 2000, with an average of 1429 mm. There is a slightly negative trend overall, though it is not statistically significant (p > 0.05).

There is considerable variability in the annual mean air temperature, fluctuating between a minimum of –3.90^˚C in 1998 and a maximum of –1.71^˚C in 2003. Over the study period there is an increase in temperature of 0.55^˚C (10 a)^–1. This is considerably higher than the globally averaged warming (0.13^˚C (10 a)^–1) for the period 1970–2005, though Arctic temperatures have increased almost twice as much as the global average in the past 100 years (Reference TrenberthTrenberth and others, 2007). This increasing trend is mainly due to a prominent increase in the maximum temperatures experienced during summer (Reference Linderholm and JanssonLinderholm and Reference Jansson, Linderholm, Pettersson, Karlin and MörthJansson, 2007). However, due to the variability in mean annual temperature the overall increase is not statistically significant (p > 0.05).

Snowline elevations

The model run with a degree-day factor (f) of 3.2mm ^˚C^–1 d^–1 simulates snowline elevations better than the model run with the degree-day factor of 5.5 mm^˚C^–1 d^–1, when compared to those the remotely sensed imagery identified (Table 1). This is because the lower degree-day factor reduces snow ablation, thus enabling the snow to persist for longer periods at lower elevations. As a result of this, the snowlines delineated from the images taken during and at the end of the ablation season (i.e. the 1990 and 1999 aerial photographs and the 2002 Landsat 7 ETM+ image) are more accurately simulated by the model run with the lower degree-day factor.

Table 1.

Snowline elevations (m a.s.l.) derived from remotely sensed imagery classifications and snow-wedge model results

Seasonal snow volumes

Decreasing the degree-day factor from 5.5 to 3.2 mm ^˚C^–1 d^–1 results in a marked increase in net seasonal snow input to the glacier (B _G), as shown in Figure 1. This is because the method used does not take into account the loss of snow from the snowpack as it transforms into firn and so produces a cumulative build-up of snow. The peaks and troughs of the plot in Figure 1 show the annual snow accumulation (S _A) and melt (S _M) respectively. The volume of snow available for transformation to firn is the base area under the troughs. Decreasing f increases the volume of snow available for transformation because snowmelt is reduced, thus leaving more snow on the glacier surface at the end of the ablation season.

Fig. 1.

Net seasonal snow input to glacier (B _G) (103^m3) for each year.

Figure 1 also shows the interannual variability in the amount of snow that falls, melts and is carried over to the next year in the form of net seasonal snow (S _N). The difference between the two model predictions of annual snow accumulation ranges from 6.4×103^m3 to 403.6×103^m3. The largest difference between the two model outputs occurs for estimations of the snow volume for 2006. This is a result of the model run with a higher f simulating a larger amount of snowmelt during the summer of 2005.

There is considerable variability in the amount of snow that falls each winter throughout the study period. The model results (using f = 3.2 mm⁸C^–1 d^–1) indicate that the early 1990s are characterized by large volumes of snow remaining on the glacier surface after the summer ablation season, which resulted in positive net seasonal snow volumes (Fig. 2). Following this, from the mid-1990s until 2000 there is a dramatic decrease in the net seasonal snow volumes. From 2001 to 2003, negative S _N values occurred, suggesting greater snow ablation than accumulation. This would have resulted in melting of old snow (firn/snow reservoir) as well as the seasonal snow. These results again indicate a decrease in the snow volume remaining on the glacier surface. However, 2004 and 2005 had positive net seasonal snow values. The model run with f = 5.5 mm^˚C^–1 d^–1 shows a similar pattern but with reduced net seasonal snow volumes, and the mid-1990s are characterized by negative seasonal snow values due to the higher ablation rates.

Fig. 2.

Net seasonal snow (S _N) modelled using the different degree-

The net snow balance (B_{z ,d}) for each elevation band is a function of the area of the band and its position in relation to the ELA. Therefore, the highest net snow balance occurs in the elevation band 1600–1699ma.s.l. for both model simulations, as this is the band with the largest area above the ELA (1485ma.s.l. according to Hock and Holmgren, 1996). Decreasing f produces markedly larger net snow-balance volumes in the elevation bands 1500–1599 and 1600–1699ma.s.l., meaning that more snow is present in the accumulation area of the glacier. This suggests that snow at the elevations closest to the ELA is most sensitive to changes in f and thus ablation processes.

Winter balance (b _w)

The winter balance results for the model run with f = 3.2 mm^˚C^–1 d^–1 are shown in Figures 3 and 5 and Table 2. Only the results from this model are further analyzed, as they show the closest fit with snowline elevations from the image classifications and measured winter balance values. The calculation of B _W was not possible for the year 1990, so this has been omitted. Figure 3 shows the interannual variability in winter balance over the study period.

Fig. 3.

Modelled and measured winter balance (mw.e.). day factors.

The greatest error between modelled and measured B _W is for the year 2000 and the smallest error is for 1999. A Mann– Whitney non-parametric t test was performed to see if there was a statistical difference between the measured and modelled winter balances. At the 95% confidence interval there is no significant difference between the two datasets (P = 0.24).

A regression equation was calculated in order to determine the nature of the relationship between measured and modelled winter balance. The resulting equation (Y = 0.34 + 0.845X) with an R ² value of 0.72 indicates that there is a moderate correlation between measured and modelled B _W. Outliers weaken the relationship, as the model does not accurately simulate the B _W for 1993, 2000 and 2001. Figure 4 indicates moderate precision of the model in predicting winter balance, as the slope of 0.85 for the data points is close to a slope of 1.0 (a perfect relationship).

Fig. 4.

Scatter plot of measured vs modelled winter balance (B _W), showing a 1 : 1 line.

Both plots in Figure 5 show that there is a negative trend in B _W over the study period, with the model simulating a slightly less negative trend than the measured trend. This decrease is winter balance occurs alongside an increase in the negativity of the summer balance, resulting in the occurrence of negative net mass balances, as shown in Table 2.

Fig. 5.

Measured B _W (a) and modelled B _W (b) both with regression line and equation overlain.

Table 2.

The winter-balance (mw.e.) results from the model (B _W(m)) run using f = 3.2 mm˚C^–1 d^–1 as well as the observed winter (B _W), summer (B _S) and net mass balance (B _N) and the ELA from Tarfala Research Station