In this study, we assess the role of altitude in determining the relative performance of temperature and precipitation as predictors of snowpack variability in Switzerland. The results indicate a linear relationship between altitude and the correlation of temperature (precipitation) with snowpack depth and duration. We identify a threshold altitude of approximately 1400 m a.s.l. (± 200 m, depending on the snow index considered), below which temperature is the main explanatory variable and above which precipitation is a better predictor of snowpack variability. The results also highlight that as climate warms, the altitude at which temperature is the main constraint on snow accumulation increases. This has important implications for the future viability of snow-dependent economic sectors in Switzerland, where projections indicate a continuous warming during the course of the 21st century.
 Snow is an important source of economic wealth in many mountain regions, including the Alps. From an economic perspective, winter tourism, and the viability of rural areas in which they are located, is dependent on winters with abundant snow [Elsasser and Bürki, 2002]. The snowpack also controls the timing and amount of seasonal runoff in alpine rivers and has a direct influence on the energy sector through hydropower [Rahman et al., 2012], which is the most important source of electricity in alpine countries [Romerio, 2002]. The decrease in the number of snow days in Switzerland since the late 1980s [Scherrer et al., 2004; Marty, 2008], and the expected decline in conditions appropriate for snow formation and retention under warmer climate conditions [Beniston et al., 2003b], are a source of concern for investors and policy makers on the future viability of these sectors.
 The weather conditions required for snow accumulation are well known: below-zero temperature and precipitation to trigger snowfall, and the persistence of low temperatures to maintain the snowpack. The dependence of snow on seasonal temperature makes the snowpack at midlatitudes highly vulnerable to climate warming. However, the conditions for snow accumulation in mountains are invariably linked to altitude and topography, and consequently the dependence of snow cover on climate is difficult to ascertain [Hantel et al., 2000]. The adiabatic gradient implies that temperatures decrease with height in mountains; in addition, topography enhances the uplift of moist air triggering condensation and precipitation [Barry, 2005]. Altitude is thus one of the most important geographic factors influencing changes in temperature and moisture at small spatial scales. Previous studies [e.g., Beniston, 2012; Laternser and Schneebeli, 2003; Marty, 2008; Scherrer et al., 2004] have reported on trends of decreasing snow depth and snowpack duration at low altitude sites associated with increasing temperature, and nonsignificant trends at high altitude sites. The explanation for the latter observation is that, despite atmospheric warming, at high altitudes, temperatures are still sufficiently low to enable snow accumulation during winter and spring; under these conditions, precipitation is a major factor determining the behavior of the snowpack. It is thus of interest to ascertain at what altitudes temperature is no longer a limiting factor for snow accumulation, and how altitude thresholds change in a warmer climate.
 The hypothesis of this study is that the role of temperature and precipitation in explaining snowpack variability in midlatitude mountains is strongly dependent on altitude. Testing this hypothesis involves determining the threshold altitude at which temperature or precipitation has a greater explanatory capability. Beniston  recently suggested a threshold at approximately 1500–2000 m a.s.l., but without implementing an objective method for locating the threshold. The objective of this study is to assess the possible location of the altitude threshold in Switzerland, by exploring the interactions between altitude, temperature, precipitation, and snowpack variability. We further explore how the altitude threshold has evolved over time, in relation to changing temperature conditions. The results are discussed in the context of temperature projections for Switzerland in the coming decades.
2 Data and Methods
2.1 Climate Data
 Data for daily snow depth (cm), air temperature (°C), and precipitation (mm) are from the climate database of the Swiss Federal Office of Meteorology and Climatology (MeteoSwiss). For the analysis of interactions between the variables to be investigated, we need to find a trade-off between the number of stations to be analyzed and the length of the data series. The selected stations cover the three main geographical areas of Switzerland: the Jura Mountains (north and west), the Swiss Plateau (center), and the Alps (south and east). These areas range in altitude from 316 m a.s.l. (Basel) to 2690 m a.s.l. in the Alps (Weissfluhjoch). The data for the 35 available time series span from January 1966 to December 2011. Very few data gaps are found, and these are generally isolated. The missing data are filled on a daily basis by performing least-squares regressions between the candidate series (series with gaps) and the reference series (series without gaps). When the correlation between candidate and reference series is R > 0.8, a linear regression is performed. The resulting equation is then used to calculate the value of the missing data.
2.2 Climatic Indices and Statistical Analyses
 The inter-annual variability in the duration and depth of the snowpack is compared with that of the climate variables (temperature or precipitation) to assess which of the two best predicted the snowpack variability. To achieve this, six snow indices and monthly and seasonal temperature and precipitation aggregations are computed. Snowpack duration is defined as the number of days between November and April that have a specified amount of snow. For this, we use an objective method based on percentiles, with every station analyzed having a unique threshold. As a measure of a “normal” snowpack (SD50), we determine the number of days per year between November and April for which the snow depth exceeds the long-term 50th percentile, whereas an “abundant” snowpack is defined as the number of days per year when the snow depth exceeds the long-term 90th percentile (SD90). The four other snow indices are the monthly (daily averaged) snow depth for January (DJan), February (DFeb), March (DMar), and April (DApr) for each year.
 Each snow index is then correlated with a number of climate indices using least-squares linear regressions following López-Moreno . The climate predictors for SD50 and SD90 are the seasonal aggregates of temperature (averages) and precipitation (sums) for November-April (TNov-Apr, PNov-Apr), December-April (TDec-Apr, PDec-Apr), November-March (TNov-Mar, PNov-Mar), and December-March (TDec-Mar, PDec-Mar). The climatic predictors for the monthly snow depth indices from January to April (DJan, DFeb DMar, and DApr) are the temperature and precipitation aggregates for the previous months, up to the previous November. For example, the predictors considered for DFeb are the temperature and precipitation in February (TFeb, PFeb), the average (sum) for temperature (precipitation) in January and February (TJan-Feb, PJan-Feb), the average (sum) for temperature (precipitation) in December, January, and February (TDec-Feb, PDec-Feb), and the average (sum) for temperature (precipitation) in November, December, January, and February (TNov-Feb, PNov-Feb). The best correlation between the snow index and the corresponding temperature and precipitation index is then selected. By plotting the values of the best correlations against the altitude of the site, we are able to assess the dependence of the model performance on altitude.
3.1 Temperature and Precipitation Versus Altitude
 Figure 1 shows that altitude plays an essential role in the way temperature and precipitation explains the variability of snowpack. Figure 1a shows the level of aggregation (number of months included in the computation of the temperature and precipitation indices) at which the best correlation between the snowpack depth and the climate indices is found. The boxplots represent the variability in the number of stations (n) that fall within each class. The pattern observed indicates that this aggregation level increases with altitude. In other words, at high altitudes, the snow depth correlates better with the aggregated climate of previous months, whereas at low altitudes, the snow depth of a given month is mainly dependent on the climate of that month. This pattern is more evident for precipitation (blue boxes) than for temperature (red boxes). Thus, seasonally aggregated precipitation (PNov-Jan for snow depth in January, PNov-Feb for snow depth in February, and so on) is the best predictor of snow depth variability at high altitudes, whereas the one-month aggregated precipitation is the best predictor at low altitudes (< 1000 m a.s.l.). In the case of temperature, the same pattern is observed for snow depth in February and March, but for April and January, no clear pattern is observed. Figure 1b shows the results of step-wise linear regressions between climate predictors and snow depth in February at three sites located at contrasted altitudes. At the low altitude site (Salen-Reutenen, 702 m a.s.l.), TFeb is the main variable explaining snow depth (R2 = 0.56), and the model performance significantly increases (R2 = 0.65) when precipitation (PFeb) is included. At the middle-high altitude site (Arosa 1.840 m a.s.l.), precipitation (PNov-Feb) is the main explanatory variable for snow depth variability (R2 = 0.54), and the inclusion of temperature (TNov-Feb) in the model significantly improves the model performance (R2 = 0.74). A similar result is obtained for the highest altitude site (Weissfluhjoch, 2690 m a.s.l.), although the effect of temperature is slightly weaker. These three examples show that temperature is the main driver of snowpack variability at low altitudes, but that its influence decreases with height, where precipitation then becomes the most important explanatory variable. The linear regressions undertaken for all sites and the various snow indices (duration and depth) provide similar results, as described below.
 Figure 2a plots the correlation coefficients between temperature (precipitation) indices and snow indices, as a function of altitude. For all indices, the magnitude and significance of the correlation coefficients show a clear relationship to the altitude of the site. The coefficients between temperature indices and the number of days of normal snowpack (SD50; upper left panel) are not significant for the high altitude sites, but are significant and robust for the low altitude sites. A linear relationship (R2 = 0.46) is observed between altitude and the magnitude of these coefficients. A similar pattern, but of opposite sign, is found for precipitation (i.e., low and nonsignificant coefficients between precipitation and SD50 for the low altitude sites, and high and significant coefficients for the high altitude sites; R2 = 0.45). Opposite linear relationships for the temperature and precipitation predictors as a function of altitude are also observed for the index derived from the number of days with an abundant snowpack (SD90, lower left panel), and for all indices of monthly snow depth. However, the strength of the relationships varies among indices. For example, a weak (but significant) relationship is found for snow depth in January (R2 = 0.26 and R2 = 0.25 for temperature and precipitation, respectively), while the strongest relationship is found for snow depth in March (R2 = 0.51 and R2 =0.57, respectively). Based on these results, it is possible to define an altitude threshold (or range) indicating which variable (temperature or precipitation) has more explanatory power with respect to snowpack variability. The point where the linear models intersect (within a 95% confidence interval) indicates the altitude threshold (ATh). Thus, below 1450 m a.s.l. (± 200 m, based on the confidence intervals), temperature is the best predictor of normal snowpack duration (SD50), but above that threshold precipitation becomes the best predictor. The ATh for the duration of abundant snowpack (SD90) is lower (1200 ± 200m). For the snowpack depth in January, the threshold is 1180 ± 210 m and gradually increases for each successive monthly snow index, reaching an altitude of 1540 ± 180 m for the snow depth in April. This increase in the ATh over consecutive months may be related to the successively warmer average conditions that occur in each month (the mean regional temperatures for January, February, March, and April are −2.9°C, −2.2°C, 0.8°C, and 4.1°C, respectively). It is a reasonable assumption that the altitude at which temperature becomes less important for snowpack variability increases with mean temperature conditions, given the altitudinal displacement of the zero-degree isotherm.
3.2 Displacement of the Altitude Threshold Over Time
 The length of the data series enables our analysis to be performed for consecutive time-slices, which facilitates the assessment of changes over time. This process is carried out based on the fact that mean temperatures in Switzerland have increased over recent decades [Beniston, 2012; CH2011, 2011]. The strong relationship between temperature and altitude suggests that a displacement in the ATh defined in this study should be expected over time. To confirm this, we perform linear regressions as in Figure 2a, but considering consecutive moving time-windows of 15 years (i.e., 1967–1981, 1968–1982, and sequentially to 1997–2011). The point where the temperature-snow and precipitation-snow linear models intersect for each moving time-slice is plotted in Figure 2b. In general, there is an increase (significant at p < 0.01; Mann-Kendall test) in the ATh with time for the various snow indices, except for snow depth in April. The ATh for SD50 increases by approximately 280 m, with the increase being more pronounced in the first half of the period. For SD90, there is also an increase, but it is more gradual, with < 150 m difference between the initial and final altitudes over the period considered. The difference in the ratio of increase of ATh between SD50 and SD90 suggests that the duration of abundant snowpack is constrained by temperatures up to a particular level, but is less sensitive to climate warming than the duration of the normal snowpack. The AThs for the January, February, and March snow depths also increase, although to different extents (220, 189, and 140 m, respectively). In contrast, DApr shows no long-term change, because of the decrease that occurs during the second half of the study period. This decrease, in the 1990s, is a common feature in the evolution of the ATh among the various snow indices. The graphs in Figure 2b also show the evolution of temperature (regionally and seasonally aggregated), for comparative purposes. The positive evolution of temperature during the study period is clear, (a net increase of approximately 1.2°C) and is similar to the 0.35°C/decade stated in the CH2011  report on global warming in Switzerland. Although the warming trend is obvious, we observe some periods of temperature decrease, such as in 1975–1985 and in the 1990s. Certain similarities in the evolution of both ATh and temperature can be seen, particularly the general increase, and the decrease in the 1990s. These similarities indicate a relationship between the altitudinal displacement of ATh and the observed temperature increase in the study area.
 A further displacement of the ATh is expected in coming decades if “greenhouse warming” occurs as projected [IPCC, 2007]. In a recent report on future climate projections for Switzerland [CH2011, 2011], the A1B IPCC emissions scenario indicates increases in the mean temperature for winter (spring) of roughly 0.5, 2.1, and 3.8°C (0.4, 1.9, and 3.6°C) for the 30-year averages centered on 2035, 2060, and 2085, respectively, relative to the mean temperature for the 1980–2009 period. The procedure used in the present study to investigate the relative weights of temperature and precipitation on snowpack variability does not enable projections of how the ATh may change in the future. However, based on the observed rates of ATh increase for the average temperature increase over the period 1967–2011, it is possible to extrapolate to global warming scenarios to estimate how ATh may increase in the future. According with projections for the IPCC A1B (nonintervention) scenario, the ATh for the duration of normal snowpack could increase to an altitude of 1600 m by 2035, and will exceed 2000 m by 2085. For the snow depth in January the ATh could reach 2000 m in 2060, and almost 2400 m by the end of the century. It must be emphasized that these figures are only estimates, and not projections.
 In this study, we address the ability of temperature and precipitation to explain snowpack variability in Switzerland. Our results show that the altitude of the site plays a critical role on how temperature and precipitation are able to reproduce the variability of the snowpack. It has been possible to conduct such a study thanks to the availability of data series spanning a wide range of altitudes and to the multivariate statistical approach utilized. Our method enables demonstrating that to accurately reproduce the variability of snowpack as a function of climate variables, no single climate predictor should be used in isolation. Rather, a range of indices that consider different levels of monthly aggregation are required. We find that there is a general relationship between the level of aggregation of the climate predictors and the altitude of the site (especially for precipitation), indicating that with increasing altitude, the climate conditions experienced in previous months become increasingly important in explaining snowpack behavior. This could explain why, in contrast to the findings of Scherrer et al.  who did not find precipitation to be well correlated with snow variability, we find numerous sites where precipitation does indeed explain large proportion of the snow variability, especially at high altitudes.
 The major highlight of this study is the observation of linear relationships between altitude and the potential for temperature and precipitation to largely explain snowpack variability. This relationship has already been suggested by different authors [Beniston et al., 2003a; Scherrer et al., 2004; Marty and Blanchet, 2011], based on indirect observations. In contrast, our method directly quantifies the strength of this relationship as well as the associated uncertainty. The observation of significant linear trends allows an estimation of thresholds that indicate at which altitude precipitation becomes a better predictor of snowpack variability than temperature. Below the threshold, temperature determines the snowfall-rainfall relationship, whereas at high altitudes, the abundance of snow in winter mainly depends on precipitation amount. The detected thresholds are not, however, an exact altitude limit, but rather a range of altitudes that reflect the uncertainties of the linear regressions. Although we focus on altitude, the role of other geographic factors (slope orientation, latitude, or longitude) that can drive temperature and precipitation gradients should be considered, as highlighted by Scherrer and Appenzeller . The strength of the linear relationship between climatic predictors and altitude found in the present study differs among the snow indices; for example, it is weaker for DJan than for the other indices. This may partly be attributed to the effect of geographic factors, such as those noted above. It must be stressed that very few summit stations show poor relations between the altitude and the correlation coefficients, which appear as “outliers” in the observed linear relationship. Such is the case of Säntis, where correlations between snowpack and precipitation are not as high as expected, considering the altitude of the station, 2502 m a.s.l. The same can be said of the Weissfluhjoch station at 2.690 m a.s.l., which only for SD50 shows better correlation for temperature than for precipitation. However, these are exceptions to the general rule found in this paper and do not invalidate the main conclusion of this study.
 We find that the altitude threshold has gradually changed over time, which appears to be related to increasing temperature at both intra-annual (from January to April) and inter-annual (climate warming) time scales. This is consistent with expectations, as the zero-degree isotherm rises gradually from January to April, and has been shown to have increased by almost 250 m in the Swiss Alps between 1958 and 2003 [Scherrer and Appenzeller, 2006]. Observations indicate that the increase in the altitude threshold is more sensitive to climate warming (more pronounced) for the duration of “normal snowpack”, than for the duration of the “abundant snowpack”, which is more dependent on the variability of precipitation. In practical terms, the results indicate that the altitude at which temperature is the main driver for snowpack increases as climate warms. This will have significant implications for snow-dependent economic sectors as well as for hydrology and ecosystems, if climate continues to warm. According to climate projections for Switzerland, the altitude threshold could reach 2000 m by the end of the 21st century, resulting in major economic problems for the numerous ski resorts that are located below this critical altitude. Other possible consequences of a change in the altitude threshold include shifts in hydrological regimes and changes in the behavior and functioning of mountain ecosystems.
 The aim of this study is to investigate temperature and precipitation as predictors of snowpack variability in Switzerland. Results show that temporal variability of snow at high altitudes is explained by the climatic conditions aggregated over preceding months, whereas at low altitudes, the snow depth of a given month is mainly explained by the climate of that month. The relationship between temperature or precipitation and snowpack variability has a linear dependency with altitude, i.e., the influence of temperature (precipitation) decreases (increases) with height. This relationship enables defining an altitude threshold below which temperature is the best predictor of snowpack variability and above which precipitation becomes the main explanatory variable. The altitude threshold is observed to increase between 1967 and 2011. This is clearly related to atmospheric warming in Switzerland in recent decades. Based on observations of its recent behavior, this threshold is likely to continue rising if climate in the region warms as projected by climate models.
 While the role of altitude in the climate-snow relationship is evident, a number of uncertainties persist. Further research is needed to explore the effect of other geographic factors to better understand the behavior of the snowpack under changing climatic conditions.
 This study was made possible thanks to financial support from the Spanish Government (Ministry of Education) through the postdoctoral program “Ayudas de movilidad postdoctoral en centros extranjeros (Orden EDU/2728 /2011, de 29 de septiembre)” and the project CGL2011-27536/HID: “Hidrologia nival en el Pirineo central español: variabilidad espacial, importancia hidrológica y su respuesta a la variabilidad y cambio climático”, funded by the Spanish Commission of Science and Technology, and FEDER.