We modelled the mass balances of eight glaciers in Scandinavia: Ålfotbreen (ALF), Rembesdalskåka (REM), Nigardsbreen (NIG), Storbreen (STO), Hellstugubreen (HEL), Gråsubreen (GR) in southern Norway and Engabreen (ENG) and Storglaciären (STORGL) in northern Norway and northern Sweden, respectively (Fig. 1). Storglaciären has the longest annual mass balance time series, beginning in 1946 and Engabreen has the shortest time series, initiated in 1970. For all glaciers, data until 2010 were considered. Glacier mass balance data are available at www.nve.no/bre (Kjøllmoen, 2011; Andreassen and Winsvold, 2012) and bolin.su.se/data/tarfala. For all glaciers, winter balances, summer balances and annual balances are available. Uncertainties of mass balance measurements and their possible sources are thoroughly discussed in Andreassen et al. (2005) and are estimated to between ±0.2 and ±0.4 m w.e. per year.

Cumulative mass balance changes are shown in Fig. 3. The three maritime glaciers Ålfotbreen (ALF), Rembesdalsskåka (REM), and Nigardsbreen (NIG) in southern Norway and the maritime glacier Engabreen (ENG) in northern Norway show positive cumulative annual balances between the initiation of the measurements and 2010 (Fig. 3). Mass balances are especially positive during the first half of the 1990s. The continental glaciers Storbreen (STO), Hellstugubreen (HEL), and Gråsubreen (GR) in southern Norway and the continental glacier Storglaciären (STORGL) in northern Sweden experienced negative cumulative mass balances between the start of the measurements and 2010. For these glaciers the mass balance loss was reduced in the first half of the 1990s.

We used meteorological data from the meteorological station Bergen-Florida to model mass balances in southern Norway. We decided to exclusively use precipitation data from Bergen-Florida for all glaciers in southern Norway since Bergen-Florida records the large synoptic weather systems and is not affected by local topographic effects that are affecting meteorological stations in the deep and narrow valleys closer to the glaciers studied (e.g. Nesje, 2005). For glaciers in northern Scandinavia, we used meteorological data from the coastal station Glomfjord available from the beginning of the mass balance series. The temperature measurements are continuous, but the precipitation series ends in 2003. We extended the precipitation series with data from the nearby Bodø meteorological station. The precipitation data from Bodø were scaled to the data from Glomfjord in the period of overlap (1953–2003) of the two data series.

To directly quantify the relative importances of summer temperature and winter precipitation on annual balances, we used a suite of three statistical models with increasing complexity and number of parameters that needed to be estimated: (i)

Linear models using a climate index as independent variable,

If the variance explained by two models was not significantly different, we favoured the simpler model, as it was more parsimonious.

As glaciers are mainly sensitive to summer temperatures and winter precipitation, models were run using one summer temperature and one winter precipitation as independent variables. We tested the influences of two summer temperatures, namely temperatures from May–September (T MJJAS) and temperatures from June–August (T JJA), and two winter precipitation variables, precipitation October to April (P ONDJFMA) and precipitation from November–March (P NDJFM) on annual glacier mass balances. This resulted in a total of four possible combinations of input variables. We chose the combination that resulted in the lowest Akaike information criterion (AIC).

The employed statistical models explained large proportions of the variance of annual mass balances (Table 1). For the maritime glaciers, the models explained more than 70 % of the variance. The variance explained for continental glaciers varied between 50 and 70 %. Table 1 shows input variables, model types, variance explained by the most parsimonious models and standard regression coefficients of linear models (i.e. the relative importance of summer temperature and winter precipitation) and their Bayesian credible intervals. Cross-validated r2 using leave-one-out cross-validation and h-block cross-validation were comparable to apparent r2. The only exception was Ålfotbreen, where an additive model was most parsimonious. Cross-validated r2 was reduced by 0.1, i.e. the variance explained was reduced by 10% and linear models had higher r2 under cross-validation. Cross-validated mean absolute deviations were also lowest for the models chosen, except for Ålfotbreen where again linear models yielded lowest mean absolute deviations.

For Storbreen, Engabreen and Storglaciären, the statistical models using climate indices as input variables were most parsimonious. These are the only glaciers where standard regression coefficients of linear models were not different (Table 1). Hence, linear models were also assigning about similar weights to summer temperature and winter precipitation for these three glaciers. For the maritime glaciers Rembesdalsskåka and Nigardsbreen, linear models indicated a higher relative importance of winter precipitation than of summer temperature, whereas for the continental glaciers Hellstugubreen and Gråsubreen, the relative importance of summer temperature was higher than the relative importance of winter precipitation. For the maritime Ålfotbreen, an additive model explained significantly (p< 0.05) more of the total variance than a linear model. The smooth terms of summer temperature and winter precipitation are shown in Fig. 2. The slope of the smooth for temperature was flatter than the slope of a linear model for below-average temperatures and steeper than the slope of a linear model for above-average temperatures. Hence the expected sensitivity of the annual mass balance for a change of 1 ∘C increased with increasing temperatures. In contrast, the slope of the smooth for precipitation was steeper than the slope of a linear model for below-average precipitation values and was flatter than the slope of a linear model for above-average precipitation levels. The expected sensitivity of the annual mass balance for a change in precipitation decreased with increasing precipitation.

Temporal changes of relative importance of summer temperature and winter precipitation are shown in Fig. 3b–i. The relative importance of winter precipitation, as indicated by standard regression coefficients of winter precipitation in 25-year running windows, was lowest at the end of the observation period. The relative importance of summer temperature, as indicated by standard regression coefficients of summer temperature in 25-year running windows, increased towards the end of the observation period (Fig. 3b–i).

Winter precipitation was more important than summer temperature for the annual balance of continental glaciers in southern Norway (STO, HEL, and GR) for the 25-year windows centred between 1977 and 1985. For STO, the period of higher relative importance of winter precipitation than relative importance of summer temperature was extended up to the 25-year window centred around 1990 (Fig. 3e). For the maritime glaciers in southern Norway, the Bayesian credible intervals of the standard regression coefficients (relative importances) were not overlapping for 25-year windows centred before 1990, but were overlapping for the last five running windows.

Storbreen indicated about equal importance of winter precipitation and summer temperature for 25-year windows ending prior to 1990 (Fig. 3e). The relative importance of summer temperature was higher than the relative importance of winter precipitation for 25-year windows centred in the first half of the 1970s for Storglaciären (Fig. 3i).

The mass balance models for years with above- and below-median NAO-index, respectively, were different in terms of variance explained and in terms of relative importance assigned to summer temperature and winter precipitation. They also differed from models covering the entire measurement period.

For years with above-median NAO, models for Ålfotbreen, Rembesdalsskåka, Nigardsbreen and Storbreen explained as much of the variance of the mass balance as models for the entire data series, whereas for Hellstugubreen and Gråsubreen, the variance explained was reduced compared to the models for the entire period. Interestingly, for Ålfotbreen standard regression coefficients for winter precipitation and summer temperature were not different. For the phase with below-median NAO-index, models for Ålfotbreen, Rembesdalsskåka and Nigardsbreen explained less of the variance than in the entire period and standard regression coefficients for precipitation and temperature were not different, whereas models for Gråsubreen and Hellstugubreen explained more of the variance than in the entire period, and together with Storbreen displayed a higher importance of summer temperature than winter precipitation. The two glaciers with long data series had an average mass loss of 0.54 m water equivalents per year (m w.e. yr-1) when the NAO-index was low, but an average gain of 0.03 m w.e. yr-1 for Storglaciären and an average loss of 0.08 m w.e. yr-1 for Storbreen with high NAO-index.

For all glaciers, except for ALF, the ratio sBs / sBa was lower in years with above-median NAO-index than for the entire data series and the ratio sBw / sBa was higher than for the entire data series for REM, STO, HEL, GR and STORGL (Fig. 4). For years with below-median NAO-index, the ratio sBs / sBa was higher than in the entire data series and sBw / sBa was lower than in the entire data series except for ALF and ENG (Fig. 4).

Correlations between NAO-index and winter and annual balance were different for the subsets of years with above and below-median NAO-index (Fig. 5). For glaciers in southern Norway, the correlation between NAO-index and winter and annual balance was higher than for the entire time series for years with above-median NAO-index and was lower than for the entire series for years with below-median NAO-index. For NIG, STO, HEL, GR, ENG and STORGL the correlation coefficients among NAO-index and Ba and Bw were not significant at the p< 0.05 level for the subset of years with below-median NAO-index. For ALF and REM the correlation between NAO-index and Ba was not significant (p< 0.05) for the subset of years with below-median NAO-index.

Changes in relative importances of winter precipitation and summer temperature were also found for the AMO+ and AMO- phases. The mass balance models for positive and negative AMO were differing for Storbreen in southern Norway (Table 1), whereas they remained unchanged for Storglaciären in northern Sweden. For Storbreen, the influence of winter precipitation was significantly higher than the influence of summer temperature with negative AMO-index, whereas the situation was opposite with positive AMO-index (Table 1). For both glaciers, the average annual mass balance was different in the two phases defined by positive and negative AMO indices: Storbreen lost an average of 0.5 and Storglaciären 0.48 m w.e. yr-1 when the AMO-index was positive, whereas the loss was reduced to averages of 0.15 and 0.02 m w.e. yr-1 for Storbreen and Storglaciären, respectively, when the AMO-index was negative. The AMO also affected the standard deviation ratios. For Storbreen, the ratios sBs / sBa and sBw / sBa were equal when the AMO was in its negative phase (Fig. 4). During the positive phase of the AMO, sBs / sBa was higher than sBw / sBa.

We used simple statistical models that are only taking into account summer temperature and winter precipitation to model annual mass balances. Even though these models are simplistic, they explain large proportions of the variance of annual balances, and are therefore appropriate to estimate relative importance of summer temperature and winter precipitation for annual balances. The model performance is increased for coastal maritime glaciers. This might have several reasons: (i) precipitation is highly variable in space and therefore precipitation from Bergen is possibly more appropriate for coastal glaciers than for continental glaciers. Still, using precipitation from meteorological stations closer to the continental glaciers did not improve the model performance for continental glaciers. (ii) Processes not represented in our model are more important in summer (radiation) than in winter (wind redistribution of snow).

Climate sensitivities of Engabreen (Schuler et al., 2005), Rembesdalsskåka (Giesen and Oerlemans, 2010) and Storbreen (Andreassen and Oerlemans, 2009) show that summer balances are largely unaffected by changes in precipitation, which suggest minor importance of summer precipitation for summer balance. Still other important components such as the direct effect of radiation are not entirely accounted for when only using summer temperature to model ablation. Our models do not take into account the hypsometry of glaciers, which might be important in transitional seasons, where accumulation and ablation can occur simultaneously on one glacier (e.g. Schuler et al., 2005). Although our models do not account for these processes we get coefficients of determination similar to the values found by Rasmussen and Conway (2005) who used degree day models and RMSEPs lower or comparable to RMSEPs found by Engelhardt et al. (2013). This good performance of statistical models is probably due to the distinct accumulation and ablation seasons on Scandinavian glaciers i.e. most accumulation occurring during winter and most ablation taking place during summer. In areas with less distinct accumulation and ablation seasons, statistical models using seasonally averaged climate variables will not perform well.

The application of statistical models using seasonally average climate as input variables seems especially interesting for two areas of application: (i)

Regions where only seasonal climate data are available (especially precipitation data) this problem can be overcome by using reanalysis data (e.g. Rasmussen and Conway, 2005). Rasmussen and Conway (2005) used reanalysis data for other reasons than lack of station data.

Our results showed, as also demonstrated in other studies (Andreassen and Oerlemans, 2009; Giesen and Oerlemans, 2010; Laumann and Nesje, 2009a, b, 2014; Oerlemans, 1992), that the annual glacier mass balance on near coastal, maritime glaciers was mainly controlled by winter precipitation and that the annual mass balance on the inland, continental glaciers was mainly controlled by summer temperature (Andreassen et al., 2005; Nesje et al., 1995). Hence, standard regression coefficients of linear models are shown to be good estimators of the relative importance of summer temperature and winter precipitation for annual balances. The relative importance as determined by standard regression coefficients display similar patterns as the standard deviation ratios presented by Andreassen et al. (2005) and are also shown in Fig 4. The exceptions are NIG and STO. For NIG, standard regression coefficients indicate higher relative importance of winter precipitation compared to summer temperature, but standard deviation ratios are similar. Standard regression coefficients suggest equal relative importance of summer temperature and winter precipitation for STO, whereas the standard deviation ratio sBs / sBa is higher than sBw / sBa. For both NIG and STO, climate sensitivities estimated by de Woul and Hock (2005) and Rasmussen and Conway (2005) using degree day models differ: de Woul and Hock (2005) estimate the precipitation increase needed to level a temperature increase of 1 K to be 30 and 50 % for NIG and STO, respectively, whereas Rasmussen and Conway found lower values of 25 and 28 %. Engelhardt et al. (2013) also modelled mass balances of NIG and STO using degree day models. Modelled annual balances showed a strong positive bias for NIG and a strong negative bias for STO. Hence assessing the relative importance of winter precipitation and summer temperature on annual balances of NIG and STO seems difficult.

As shown in this study, the relative importance of summer temperature and winter precipitation for annual balances is not constant in time. Temporal changes in relative importance of summer temperature and winter precipitation are consistent for all of southern Norway (Fig. 3), suggesting common large-scale forcing of the relative importance of summer temperature and winter precipitation.

Maritime glaciers had a consistently positive mass balance between 1988 and 1996 and continental glaciers were no longer loosing mass (Fig. 3a, Nesje et al., 2000; Andreassen et al., 2005; Nesje and Matthews, 2012). Looking at the 25-year windows centred between 1978 and 1984, we found that winter precipitation was more important than summer temperature for all glaciers including the continental glaciers in southern Norway, although the differences were not significant for the continental Gråsubreen. For the three continental glaciers in southern Norway, this phase was characterised by a marked decrease in relative importance of summer temperature and a marked increase in relative importance of winter precipitation.

In this phase, the AMO-index was consistently negative and the NAO-indexes were consistently positive between 1988 and 1996 (Fig. 3). In tendency, negative AMO indices were associated with reduced summer temperatures over Europe and positive NAO-indexes were associated with increased zonal flow in winter, entailing more winter precipitation in Northern Europe. Hence, the large-scale oceanic and atmospheric patterns were favourable for glacier growth.

As another example, in the 2000s all glaciers except Engabreen and Nigardsbreen generally experienced negative mass balances and mass balances of Engabreen and Nigardsbreen were at equilibrium. In this period, the importance of summer temperature for the annual mass balance was increased (Fig. 3), even though 25-year windows centred around 1997 still contained the years 1988–1996 with their transient mass surplus. The increasing relative importance of summer temperature and decreasing relative importance of winter precipitation for the annual balance at the end of the measurement period is consistent with more negative summer balances and less positive winter balances found for glaciers in southern Norway (e.g. Engelhardt et al. 2013). The AMO-index changed sign in the late 1990s and summer temperatures were in general higher than between 1985 and 1995.

For glaciers in the European Alps, Huss et al. (2010) found pronounced mass loss during phases of positive AMO-index and mass gain in phases of negative AMO-index, which is similar to findings in this study. The phases of increased glacier melt are, however, not simultaneous in the Swiss Alps and in Scandinavia. In the Swiss Alps, a pronounced mass loss lasting to the present day started in the late 1980s, whereas continental glaciers in Scandinavia lost mass between the start of the measurements and 1987 and all glaciers in Scandinavia lost mass after about 1998. This difference is most probably caused by the fact that changes in melt rates are most influential for mass balances in the Alps (Huss et al., 2010), whereas a decade with predominantly positive NAO-indexes began in the late 1980s (1988/1989 winter) associated with increased relative importance of winter precipitation for Scandinavian glaciers (Fig. 3). This is in line with Marzeion and Nesje (2012) who found a positive correlation between the NAO and glaciers in southern Scandinavia, while a weak anti-correlation was found for the western Alps. This anti-correlation was diminishing towards east. Six et al. (2001) point out that anti-correlations between glacier mass balances in the alps and Scandinavia are mainly found in decadally smoothed data and attribute this to the NAO, whereas only weak anti-correlations are found using annual data.

Clear differences are found between the subsets with above-median and below-median NAO-index. In winters with high NAO-index, stronger westerly flow and increased precipitation is expected (e.g. Wanner et al., 2001). The mass balance models of the maritime glaciers explained more of the total variance with high NAO-index and the relative importance of winter precipitation for the total mass balance was increased. This was according to expectations, as increased winter precipitation is expected to increase the importance of the winter precipitation for mass balance models.

For all glaciers, the correlation between NAO-index and winter and annual mass balance was higher for years with above-median NAO-index (Fig. 5). Additionally, the coefficient of determination between winter balance and NAO-index was decreased for the subset of years with below-median NAO-index (Fig. 5). This means that the reduction in coefficient of determination between NAO-index and annual balance was not only caused by an increased importance of the summer balance for the annual balance, but also by a loss of accordance between NAO-index and winter balance. This loss in accordance is only partly caused by lower accordance among precipitation in Bergen and winter balances, but mainly by a consistently decreased correlation between the NAO-index and precipitation in Bergen. Consequently the NAO-index is only a good predictor for winter balances of glaciers in southern Norway in years with above-median NAO-index. This is reiterating a find by Six et al. (2001), who do not recommend to model glacier mass balances solely based on the NAO-index. Unstable relations between the NAO-index and glacier length changes in Scandinavia as well as in the Alps were also found by Imhof et al. (2011).

For the two glaciers with long mass balance time-series, the influence of the NAO seemed equal to the influence of the AMO, as the difference between the average mass balances in the two NAO levels considered was about equal to the difference in the two AMO states. The AMO states only include consecutive years, whereas individual years were assigned to the NAO-index. The phase between ca. 1987 and 1995 with major mass gain for maritime glaciers and neutral mass balances for continental glaciers was characterised by negative AMO-index and predominantly positive NAO-index, that were both favourable for glaciers.

The relation between AMO and NAO seems rather complex and depends on the timescale considered (Li et al., 2013; Peings and Magnusdottir, 2014). On short timescales, the atmospheric NAO pattern influences the sea surface temperature, whereas on longer timescales, the sea-surface temperature AMO pattern drives the atmospheric NAO. Hence Li et al. (2013) find the NAO to lead the AMO by 16 years and state that the NAO is an excellent predictor for AMO and thereby Northern Hemisphere temperature, whereas Peings and Magnusdottir (2014) find “that the multidecadal fluctuations of the wintertime North Atlantic Oscillation (NAO) are tied to the AMO, with an opposite signed relationship between the polarities of the AMO and the NAO. Our statistical analyses suggest that the AMO signal precedes the NAO by 10–15 years”.

The association of negative AMO and positive NAO seems to be typical (Peings and Magnusdottir 2014), whereas positive AMO favours negative NAO and blocking situations. For the time period 1965–1998, with negative AMO, only 10 years have a negative NAO-index, whereas for the considerably shorter phase 1999–2010 already 6 years had a negative NAO-index. Hence, the two modes favouring glacier mass gain and mass loss, respectively, tended to occur simultaneously. However, the influence of AMO and NAO should not be overestimated, as similar weather patterns still result in different amounts of precipitation and in different levels of temperature (Jacobeit et al., 2003; Kuettel et al., 2011). Kuettel et al. (2011), for instance, attribute 60 % of the changes of winter precipitation over southern Norway between the periods 1900–1949 and 1950–1999 to changes within weather patterns and only 40 % to changes in frequencies of weather patterns.