1 Introduction

Major rivers in Europe such as the Po, Rhine, Rhone and Danube are fed by a network of tributaries that originates in the Alps, making this mountain chain a key element of the hydrological cycle. A shift in Alpine climatic regimes, particularly, winter precipitation and snow-cover duration, would impact heavily on the river systems originating in that area, affecting life and socio-economic structures of populations living within the mountains and downstream (Beniston et al. 1997). The strongest impacts would be not only on water availability for agriculture, industries and hydroelectrical power production but also on winter tourism that sensitively depends on a reliable snow cover throughout the skiing season (Fazzini et al. 2004).

In current general circulation climate models (GCMs), the complexity of mountain topography is difficult to represent and these areas remain poorly resolved, implying more coarse resolution and big uncertainties in climate predictions. To draw reliable conclusions on climate characteristics, climate change and its possible impacts on mountain areas, it is fundamental to relie on observational data representative of local scale. During the IPCC Second Assessment report (Watson et al. 1995), it was highlighted the need of understand and predict the effects of climate change on mountain regions with monitoring, experimental studies and modelling. Since then, a lot of works have been carried out on winter precipitation. A relevant number of studies were addressed to Swiss Alps: Laternser and Schneebeli (2003) evaluated long-term snow depth and duration trends in about 100 stations over the period 1931–1999; Beniston et al. (1997) linked the abundance or dearth of snow-cover over 1945–1995 period with the pressure fields over the Alpine region highlighting the dominant role of large-scale forcings in controlling the timing and amount of snow in the Alps. Scherrer et al. (2004) evaluated the trends in snowy days in the Swiss Alps and used a regression model to quantify the importance of mean temperatures, precipitation as well as large-scale climate variability to explain the observed trends. Marty (2008) evidenced a significant decrease in the number of snowy days induced by temperature increase since the end of the 1980s.

Concerning Austrian Alps Schöner et al. (2009) used the snow measurement network of the Sonnblick region to describe the temporal trend of snow-depth as well as its relation to climate change for a high-elevated site (2,400–3,100 m a.s.l.) of the European Alps. Hantel et al. (2000) and Hantel and Hirtl-Wielke (2007) studied the sensitivity of Alpine snow-cover duration as a function of the height and the mean temperature over Europe.

Regarding the French slope, Martin et al. (1994) used a numerical snow model to study the sensitivity of snow cover to changes in meteorological variables and Durand et al. (2009) draw the main climatic features of the French Alps through modeled snowfields at different spatial and temporal scales in the period 1958–2005.

Concerning Italian Alps, the information on winter precipitation variability is still scarce compared to the Swiss, French and Austrian sides. A general study considering the entire Alpine region over the 1971–1992 winters has been conducted by Quadrelli et al. (2001), who investigated also the links between snow precipitation and the North Atlantic Oscillation and the North Hemisphere blocking frequency. Valt et al. (2005) analyzed the Standardized Anomaly Index (SAI, Giuffrida and Conte 1989) of snow precipitation over the Southern Alps over the period 1920–2005 and highlighted a decrease of snow precipitation in the recent period (1985–2004). In particular, it has been carried out an in-depth analysis of snow climatology of two representative areas of Western and Eastern Italian Alps (Valt et al. 2008). Even though some regional studies have already been produced (Biancotti et al. 1998; Fratianni and Motta 2002; Fazzini and Gaddo 2003; Mercalli et al. 2008), this field can be still considered as underexplored due to the difficulty of finding long-term, continuous and homogeneous time series.

This work has been conducted in the frame of the Mediterranean climate Data Rescue (MEDARE) initiative, born under the auspice of the World Meteorological Organization, with the main goal of developing, consolidating and progressing climate data and metadata rescue activities across the Greater Mediterranean Region (GMR). In Western Italian Alps (Piedmont), the effort is addressed to recover historical climatic time series and enhance a unique and under-explored climatic dataset realized by the Ufficio Idrografico del Bacino del Po (Po basin Hydrographic Office), the ex-Servizio Idrografico e Mareografico Nazionale (National Hydrographic and Mareographic Service, SIMN), operational since 1920s up to 1990s and then merged to the Agenzia Regionale per la Protezione Ambientale (ARPA - Regional Agency for Environmental Protection) of Piemonte.

The data originally reported over bulletins were digitized, quality controlled, checked for homogeneity and then analyzed to investigate trends and interannual and decadal variability of snow and total precipitation over Western Italian Alps. Further analysis has been addressed to explore the connections between winter snow precipitation variability and the North Atlantic Oscillation, the dominant mode of the atmospheric variability over the North Atlantic (Hurrell 1995). Several previous studies were addressed to this subject but they obtained contrasting results; for example, Beniston and Jungo (2002) detected clear links between strongly positive (negative) modes of the NAO and extremes of moisture, temperature and pressure in Switzerland, especially for high-elevation sites; Schmidli et al. (2002) detected only weak and highly intermittent correlations between winter Alpine precipitation during the period 1901–1990 and the North Atlantic Oscillation Index; similar results were found by Bartolini et al. (2009) using a 20-km resolution precipitation dataset which covers all Europe. The availability of a historical high-quality dataset constitutes a unique opportunity to clarify the effects of large-scale forcings on local climate. In this work, the newly recovered instrumental long-term snow time series are used to obtain accurate and reliable information on the connections between high-frequency modes of climate variability and local winter precipitation in the area of study.

In summary, this paper aims to (1) investigate the temporal variability and trends of snow and total precipitation and compare the results to the existing bibliography, (2) determine the regularities, i.e., the periodic components embedded in the snow precipitation time series using two different methods, the Monte Carlo Singular Spectral Analysis (MCSSA) and MultiTaper Method (MTM) (Ghil et al. 2002) and finally (3) explore connections between oscillatory modes found for winter precipitation and the North Atlantic Oscillation (Hurrell 1995) and the Arctic Oscillation (Li and Wang 2003) for a better understanding of the influence of large-scale atmospheric forcings on the local climate. Finally, the outcomes of this study are drawn.

2 The data

The historical time series used in this study have been recovered from the paper archives of the Ufficio Idrografico del Bacino del Po now hosted at the ARPA of Piemonte and Lombardia. All the measurements are performed manually by the observers with rain gauges, graduated snow stakes and snow tablets.

The main parameters used in this study are the total snow depth and the total precipitation. As defined in Cagnati (2003) total snow-depth HS is the distance between the soil surface and the snow surface, measured along the direction normal to the ground. The total precipitation P is sum of liquid precipitation and melted snow. In some measurement sites, fresh snow precipitation (HN) is not systematically registered, so, to have continuous and comparable data, HN is calculated by subtraction of two consecutive HS values. With this procedure, the possible snow melting between two consecutive snowfalls in a 24-h period is neglected, appearently causing an underestimation of fresh snow precipitation. Nevertheless, the comparison between the available HN data directly measured with snow tablets and the corresponding HN derived by subtraction of consecutive HS values shows that these time series are almost identical except for few cases in which the differences are on the order of 2–3 cm, so the derived HN gives a good approximation of the real amount of fresh snow precipitation.

To have information on the amount of snow precipitation in term of water equivalent, it has been considered the solid precipitation fraction S/T defined as the ratio between the sum of daily precipitation when HN > 0 cm and the total P over a given time period. The advantage of using this parameter is that, being proportional to the amount of melted snow, it does not depend on snow density. On the other hand, a possible overestimation of solid precipitation can arise in case of mixed (rain + snow) precipitation. Other derived quantities are the number of days with precipitation PD (days when P > 0 mm) and the number of snowy days SD, defined as the number of days when solid precipitation HN > 0 cm.

For the purpose of this study, only stations located in the Alps were considered. The other criteria used for the selection of the stations have been the length, the continuity and the homogeneity of the series, the representativeness of different altitude ranges and the representativeness of different alpine sectors. The data finally analyzed refer to six stations covering the whole Piedmontese Alps and ranging between 960 and 2,177 m a.s.l. (Table 1; Fig. 1).

Table 1 Denomination, elevation, position and operational periods of the six measurement sites considered in this study
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Fig. 1
figure 1

Geographical position of the six stations selected for this study, located in Piedmont, NW Italy

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The two longest time series supply records of 85 years (1926–2010) and the shortest ones supply records of 60 years (1951–2010) and they are all continuous except for minor gaps. Other time series used for the analysis are the Winter North Atlantic Oscillation index (DJF NAO), representing the normalized sea-level pressure difference between Ponta Delgada (Azores) and Stykkisholmur/Reykjavik (Iceland) and the Winter Arctic Oscillation index (DJF AO), representing the normalized difference in zonal-averaged sea-level pressure anomalies between 35°N and 65°N. The two indexes are provided by the Climate Analysis Section (Hurrell 1995) and Li and Wang (2003).

3 Methodology

The daily rainfall, snow depth and fresh snow data collected by the observers and registered on the bulletins have been digitized together with all the eventual notes regarding the measurements or the instruments anomalies.

A parallel in-depth historical research has been carried out in order to acquire stations metadata. Particular attention has been addressed to possible relocations or changes undergone during the stations lifetime, which could reflect in inhomogeneities in the time series and relevant changes in the data not related to climatic factors [i.e. Aguilar et al. (2003), Venema et al. (2012)]. This inspection did not indicate relevant variations. The only exception is Alpe Devero station, where the manned observations stopped in 1991, about one year after the installation of an automatic station in the surroundings. In this case a careful control performed on the time series in the overlapping period 1991–1992 showed that the correlation coefficient exceeds 0.9 and the mean ratio between the automatic and the manual measurements exceeds 0.8: it was decided to join the two time series and to adjust them using the simple ratio method proposed by Thom (1958). The first stations daily values are multiplied by the ratio of total snow precipitation (average snow depth) at the two stations during the overlapping period. The ratios are computed separately for each month in order to avoid possible seasonal effects (Mekis and Hogg 1999). Concerning the station of Ceresole Reale, the manned observations of total precipitation end in 2002 and the joining with neighboring time series would have introduced large uncertainties, so it has been preferred to exclude the total precipitation time series from this analysis. All other stations are still manned then no artificial bias due to changes in the method of measurement has been introduced in the time series. Moreover the need of meteorological records in very peculiar areas in the surroundings of the barrages for hydroelectric power production let us believe, in the absence of other information, that the measurements were performed always in the same place. For these reasons, the precipitation and snow depth data have been considered homogeneous.

All the time series have been quality controlled to identify and eventually correct anomalous values and errors due to the observers or to the process of digitization. Precipitation time series used in this study have been quality checked using the RClimdex package (Zhang and Yang 2004) which highlights unresonable values (i.e., negative data, outliers exceeding n standard deviations, … , etc.). All the “suspect” data have been compared with those of the other stations and eventually discarded. For daily snow depth data, a technique has been developed for the purpose of this study. After a first visual check by plotting HS data against time to identify non-reasonable values, a procedure for the identification of the data outlying pre-fixed thresholds is applied to two derived time series: the snow accumulation HN(t) and the snow depletion d(t), derived from HS(t) as follows:

$$ d(t)= \left\{\begin{array}{lll} {\hbox{HS}}(t-1) - {\hbox{HS}}(t) & {\hbox{if}} &{\hbox{HS}}(t-1) - {\hbox{HS}}(t) > 0 \\ 0 & {\hbox{if}} &{\hbox{HS}}(t-1) - {\hbox{HS}}(t) \leq 0 \\ \end{array}\right. $$
(1)

where t is the time. Values of HN(t) and d(t) exceeding a given threshold (the 99th percentile calculated on non-zero values) are highlighted and the corresponding HS is first checked with the original value reported on paper bulletins, then evaluated in relation to temperatures and precipitation and finally compared with the corresponding values recorded in the neighboring stations, to check the reliability of abrupt changes in snow thickness. After the quality control, daily values have been aggregated over monthly and seasonal time scales. These data have been retained only if at least 80 % of the daily values were available (Klein Tank et al. 2002) and then a trend analysis has been performed. The significance of the trends has been evaluated with the non-parametric Mann–Kendall test at 95 % confidence level.

Searching the dynamical mechanisms underlying winter snow precipitation two different spectral methods have been used to separate oscillatory modes and regular behavior of the signal from the noise background: the MTM and the MCSSA. MTM (Thomson 1982; Percival and Walden 1993) separates harmonic (pure sinusoids) and anharmonic signals (phase and amplitude-modulated sinusoids) from continuous components (noise) of the spectrum, testing their significance against the null-hypothesis of white/red noise.

The Singular Spectrum Analysis technique (Vautard et al. 1992) uses the lag-covariance matrix of the data to derive a basis of empirical orthogonal functions (EOFs) onto which the original time series can be projected, making, thus, individual data components (modes) linearly independent. The EOFs in phase quadrature associated to paired eigenvalues of the lag-covariance matrix identify an oscillatory mode of the time series (Vautard and Ghil 1989). The Singular Spectrum Analysis has been firstly used to pre-filter the noisy part of the time series and to reconstruct the signal using the set of principal components that explain most of the signal variance. The Monte Carlo approach is used to establish whether the resulting time series is linearly distinguishable from red noise, described by an AR(1) process. The red noise coefficients have been determined from the original time series using a maximum-likelihood criterion. Based on these coefficients, an ensemble of surrogate red noise data has been generated (Allen and Smith 1996). The SSA has been finally applied to both data and surrogates and it has been tested whether the regular oscillations found in the signal are significantly different from the noise background (Ghil et al. 2002).

The oscillatory modes found through spectral techniques in winter snow precipitation have been related to large-scale forcings, represented by the North Atlantic Oscillation index (DJF NAO) and the Arctic Oscillation index (DJF AO), using the coherence analysis. The coherence analysis, or cross-spectral analysis, is used to identify similar spectral properties in the time series (high power in the same spectral frequency bands), thus, allowing to determine whether the variability of two distinct time series is inter-related in the spectral domain.

4 Results

4.1 Temporal variability of DJF snow precipitation (1933–2010)

The three longest snow records, Alpe Cavalli, Ceresole Reale and Entracque Lago Piastra representative of North, Central and South Piedmont, have been used to compare DJF snowfall HN, number of days with snow precipitation SD and average snow-depth HS over a common period 1933–2010 (Fig. 2). It has been applied a 5-year filter to avoid interannual fluctuations.

Fig. 2
figure 2

Temporal variability of 5-year averaged DJF cumulated snowfall (a), average snow depth (b) and number of snowy days (c) for the three longest records representative of North, Central and South Piedmontese Alps: Alpe Cavalli (1,500 m, dotted line), Ceresole Reale (1,573 m, dashed line) and Lago Piastra (960 m, solid line)

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Snow precipitation shows fluctuations of irregular period of about one decade, with relative maxima around 1940, 1950, 1960. The most prominent peak is registered in the 1970s, when average DJF cumulated snowfall was around 300 cm in all the three stations. The maximum has been followed by an absolute minimum around 1990, with snowfall amount reduced by 1/3. Then another complete fluctuation is registered and, in the last snow seasons, we are in a phase of increasing winter snow precipitation amount. Winter days with snow precipitation and average snow depth (SD and HS) have a similar pattern as the snowfall amount but they show more spread between stations because of both elevation and local factors. In fact, the Northern and Central stations located at about 1,500 m a.s.l. register higher SD and HS than the low-elevation station at 960 m a.s.l. Nevertheless, the difference between values registered at about 1,500 m is quite large, as the station located in North Piedmont has more frequent and abundant snowfalls and higher snow depth than the one located in Central Piedmont due to its exposition also to North and Northwestern perturbations (Biancotti et al. 1998).

Looking at the temporal evolution of snow parameters, snow depth at about 1,500 m a.s.l. presents large fluctuations that result stronger compared to the low-level station up to the 1970s. After the 1970s, the spread between high- and low-elevation stations decreased reducing the range of SD and HS variability at 1,500 m. To check significant variations in snow-precipitation characteristics, the analysis of the trends has been performed.

4.2 Trends in annual, seasonal (November–May), DJF and MAM total and solid precipitation (1951–2010)

This section presents the analysis of the total and solid precipitation trends comparing the results of all the six stations (five for total precipitation) over the common period 1951–2010. The analysis of annual records (Table 2) shows a general decrease in total precipitation (P) ranging between −0.1 and −4.7 mm/year although the trend is not statistically significant at 0.05 level. A negative trend in annual precipitation is registered also in the stations located in the Piedmontese plain (Torino, Asti, Vercelli) where the decrease ranges between −1 and −3 mm/year (Acquaotta et al. 2009).

Table 2 Annual trends in total (liquid + solid) precipitation P and precipitation days PD over the period 1951–2010
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The number of days with precipitation has a dipole pattern, with a statistically significant increase in Southern Piedmont [+0.4;+0.8 days/year] and a reduction in Northern Piedmont, in particular, in Alpe Devero (1,634 m a.s.l.), where rain is significantly less frequent by 0.3 days/year. So it seems that over the period 1951–2010 the rainfall amount and frequency in Northern Piedmont has non-significantly decreased while in Southern Piedmont more frequent but weaker precipitation events occur.

The analysis of total and solid precipitation trends over Piedmontese Alps has been conducted also over the snow season November–March (NM), over winter (DJF) and spring (MAM) 3-month period (Table 3).

Table 3 Winter (DJF), spring (MAM) and seasonal (NM) trends in total precipitation P (mm/year), number of days with precipitation PD (year−1), solid precipitation fraction S/T (mm/year), snow precipitation HN (cm/year), number of snowy days SD (year−1), and average snow-depth HS (cm/year)
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Similarly to what found for the annual time scale, the winter total precipitation has decreased in all the stations although, in general, the trend is not statistically significant, in agreement with Fratianni and Acquaotta (2011) who evaluated precipitation trends for Piedmontese stations located in the Po Valley. In spring, the sign of the total precipitation trend depends on the location of the station, while the days with precipitation are significantly more frequent in Southern Piedmont.

The most-relevant result is found for the snow depth: over the November–May snow season, it has been registered a significant decrease ranging between −0.2 cm/year in the lowest and most Southern station and −1.4 cm/year in the highest and most Northern station. A significant contribution to the snow-depth reduction is given by spring months in all the stations. Considering stations only located at comparable elevations, around 1,500 m a.s.l., the strength of the decrease grows moving Northward, so the Northern Piedmont is most subjected to the spring snow thickness reduction. Contrary to the expectations, the lowest station, situated in Southern Piedmont, suffers a smaller snow-depth reduction than the one located in Northern Piedmont above 2,000 m a.s.l. In winter, there is a similar pattern with a general snow-depth decrease that becomes larger and statistically significant moving toward Northern Piedmont. Globally, the complete NM snow season presents negative snow-depth trends associated with a decrease in the solid precipitation fraction and in the number of snowy days, especially in winter and in the Northern Piedmont. In spring, the solid precipitation fraction decreased as well but the trend is not statistically significant, suggesting that the snow-depth reduction is more related to the changes in the temperatures than in the total precipitation.

Further information on the temporal variability of snow precipitation can be inferred analyzing the time series in the frequency domain to find possible regular oscillations embedded in the signal. In the following paragraphs, the results of the spectral analysis are presented and discussed in relation to the variability of the large-scale atmospheric forcings.

4.3 Oscillation modes in DJF snow precipitation

Two different approaches have been used to separate the oscillatory modes of snow precipitation HN and snow-depth HS from the continuous noise background. The MTM estimates the power spectrum S(f) of the signal and the levels of confidence for a peak to be statistically significant from red/white noise. It distinguishes the harmonic peaks (corresponding to pure sinusoidal signals) from anharmonic peaks (phase and amplitude modulated sinusoids).

This method, applied to DJF accumulated snowfall in Entracque Lago Piastra data, allows to recognize one highly significant interannual harmonic peak centered at about f = 0.41 ± 0.02 cycles/year, corresponding to a period of about 2.4 years, significant above the 99 % confidence level. The power spectrum is shown in Fig. 3a, where the harmonic peak has been graphically highlighted by a square shape. The same 2.4-year periodicity is found for DJF average snow depth, together with another one at about f ∼ 0.18 cycles/year corresponding to a periodicity of about 5.6 years (Fig. 3b).

The Monte Carlo Singular Spectrum Analysis allows to identify the oscillatory modes of a signal detecting the couples of paired eigenvalues of the data lag-covariance matrix exceeding the level of confidence given by an ensemble of simulations of red noise (Allen and Smith 1996). The MCSSA applied to the same data of Fig. 3 allows to detect a couple of nearly equal eigenvalues significantly different from red noise at the same frequency found with MTM (Fig. 4).

Fig. 3
figure 3

MTM power spectrum (red line) of DJF cumulated snowfall (a) and average snow depth (b) in Entracque Lago Piastra station, Southern Piedmont. The estimated noise background and associated 90, 95, and 99 % significance levels are shown by the four smooth curves, in this order, from the lowest to the highest curve in the figure. The harmonic peaks at frequency f = 0.41 year−1 (graphically highlighted by squares) correspond to a periodicity of 2.4 years

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Fig. 4
figure 4

Monte Carlo Singular Spectrum Analysis (MCSSA) of DJF cumulated snowfall (a) and average snow depth (b) in Entracque Lago Piastra station, Southern Piedmont. The red squares represent the eigenvalues of the two signals plotted against the frequency, the vertical bars are the confidence limits within which lies the 95 % of the surrogate realisations of red noise. The paired eigenvalues at f = 0.41 year−1 burst the 95 % confidence level error bars and, thus, represent the 2.4-year period oscillatory mode

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This analysis has been performed on all the snow time series, taking into account that the longer is the record the longer is the periodicity that can be captured by spectral methods. A summary of the results is reported in Table 4. All the records present an oscillation whose period ranges from 2.4 to 2.7 years and it is confirmed by both MTM and MCSSA methods. In Lago Piastra, one of the longest records available since 1926, another oscillations is found at 5.6 years. This periodicity is probably too long to be identified using shorter (60 years) time series. As a consequence, the 2.3- and 2.7-year oscillations, which are common to all the time series, have been further analyzed, while the longer-period oscillations have been neglected.

Table 4 Oscillatory modes of DJF cumulated snowfall and average snow depth obtained using MTM method and MC Singular Spectrum Analysis (MCSSA)
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As the 2.3 and- 2.7-year modes are typical high-frequency modes of the North Atlantic/Arctic Oscillation Index, it has been explored if any relation can be established between this large-scale pattern and the local meteo/climatic conditions.

4.4 Correlation between winter precipitation and NAO/AO

The correlation between the winter snow and total precipitation time series (DJF HN, HS and P) and DJF NAO and AO has been investigated using the Spearman's rank correlation test, a non-parametric test that measures the statistical dependence between two variables. Spearman’s rank correlation coefficient ρ measures the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. In this way, the correlation coefficient is less sensitive to non-normality in distributions. A test to find out whether an observed value of ρ is significantly different from zero is performed using the 0.05 significance level threshold. The results of this analysis are reported in Table 5.

Table 5 Spearman’s rank correlation of DJF accumulated snow precipitation (HN), snow depth (HS) and total precipitation (P) with NAO and AO
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Looking at the correlation between the winter total precipitation and NAO/AO, it results that the influence of the large-scale forcing on Piedmontese Alps is not uniform in space. In particular, NAO significantly affects the total precipitation over Southern Piedmont, while in the North, the relation depends on local factors.

In the stations of Central and Southern Piedmont, snow precipitation and snow depth are significantly anticorrelated with the sea-level pressure difference over Atlantic Ocean: this confirms that positive phases of NAO/AO correspond to dry-air advection and mild temperatures over Mediterranean, causing unfavourable conditions for solid precipitation. On the contrary, negative phases of NAO/AO correspond to the advection of cold and moist air that impinges on the mountains and determines snowfall and longer persistence of winter snow cover at low-middle elevation.

In Northern Piedmont, snow depth is well significantly anticorrelated with large-scale patterns, while snow precipitation abundance seems controlled by local factors. Furthermore, a stronger snow precipitation-NAO dependence is registered at middle/low elevation probably due to the snow vulnerability in correspondence of the 0 °C isotherm: here, small changes in temperatures may force the precipitation to fall as rain instead of snow, while at higher elevation, this forcing is less marked.

The significant anticorrelation between snow depth and sea-level pressure difference over Atlantic Ocean remarks that the characteristics of the snow pack are linked to temperatures and precipitation not only in correspondence of the snowfall event but also over longer period prior and after the precipitation. So, it is clear that the mean winter conditions represented by NAO/AO index better describe the depth and the persistence of the snow mantle rather than the accumulated precipitation, that may be due to strong but isolated snowfalls. Finally, the strong links between NAO and snow depth in all the measurement sites and the weaker relation with solid and total precipitation suggest that NAO mainly controls snow depth via temperature, which affects the snow melt and the occurrence of liquid versus solid precipitation, and only secondarily via the total precipitation.

4.5 Relations between oscillatory modes of snow depth and NAO/AO

The winter NAO and AO time series have been tested for the presence of oscillatory modes using the MTM method. The considered NAO (AO) time series, extending since 1865 (1873), presents an oscillation with period of 2.3 years, at 95 % (99 %) confidence level. The NAO time series has other significant oscillations with 2.7- and 8.3-year period (Fig. 5).

Fig. 5
figure 5

MTM spectrum of DJF NAO (a) and AO (b). The estimated red noise background and associated 90, 95, and 99 % significance levels are shown by the four smooth curves, in this order, from the lowest to the highest curve in the figure. Harmonic and anharmonic significant peaks are highlighted

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The common periods of snow precipitation and NAO suggest to investigate if it is possible to establish a cause–effect relation between the large-scale circulation, represented by the index, and the local effects, i.e., the snow abundance and persistence. The coherence analysis is a common method to reveal interactions between the components of the climate system (i.e., Benner (1999); Rodriguez-Puebla et al. 2001) and it has been used here to explain the snow-depth variability in relation to the North Atlantic Oscillation.

The advantage of the coherency function over the correlation coefficient is that the former is a function of frequency, so it can show at which frequencies two time series are coherent and at which frequencies they are not. The coherency is expressed as a number ranging from 0 (no similarity) to 1 (perfect similarity).

For each couple of NAO and snow-depth records, the squared coherency between the two signals has been estimated. Table 6 reports the squared coherency peaks and the corresponding frequencies for all the stations. The squared coherency between NAO and snow depth reaches a maximum at the frequencies corresponding to about 2.3- and 2.7-year periods. The example of Alpe Devero is presented in Fig. 6.

Table 6 Squared Coherency between snow depth and NAO signal at frequencies of the snow-depth harmonics
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Fig. 6
figure 6

Coherence analysis on Alpe Devero snow depth and NAO signals. The coherency peaks correspond to the 2.3- and 2.7-year oscillations

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The final step in the coherence analysis is the determination of the confidence limits for the squared coherency estimates. For all frequencies, the limiting value of the squared-coherency (i.e., the level up to which squared coherency values can occur by chance) is given by:

$$ C^{2}_{k}=1-\alpha^{1/(n-1)} $$

where n = DOF/2 (called the equivalent degrees of freedom) is the number of independent cross-spectral realizations in each frequency band, and α is the level of significance (Thompson 1979).

In this case, the coherence estimate is computed from an average of six adjacent cross-spectral Fourier components (n = 6) and the 95 % confidence level for the squared coherency is C 2 k  = 0.45. The squared coherency between NAO and snow-depth time series in correspondence of the 2.3/2.7-year periods results C 2 > C 2 k for all the stations, so the signals are coherent at those frequencies.

In conclusion, as the time series have significant spectral peaks at the same frequencies and the signals are coherent, the local and global information constitute a true climate signal (Rodriguez-Puebla et al. 2001) and it is possible to establish a causality relation between the atmospheric large-scale patterns and the local climate. In particular, the NAO drives the 2.7- and 2.3-year period oscillations of snow precipitation.

5 Conclusions

This work gives a contribution to the understanding of winter precipitation characteristics over Western Italian Alps, through the recovery and analysis of long-term high-quality time series, spanning an 85-year period, from 1926 up to 2010. The investigation on temporal evolution of snow precipitation shows fluctuations with an irregular period of about one decade, with relative maxima around 1940, 1950, 1960, and the absolute maximum in the 1970s. Snow was abundant till the early 1980s, then a sequence of poor snow winters leads to the absolute minimum of the record in the 1990s. Now, we are in a phase of increasing winter snow precipitation amount. A similar investigation has been conducted over Switzerland (Laternser and Schneebeli 2003) considering individual winters and the results are comparable between the two sides of Alps.

This study outlines a significant decrease of snow depth in all the stations over seasonal (November–May) time scale in the period 1951–2010. The main contribution to this negative trend comes from spring when the snow-depth decrease is comparable to the one registered over the complete season. In particular, November–May trends range from −0.2 cm/year in the lowest (960 m a.s.l.) and most Southern station up to −1.4 cm/year in the highest (2,177 m a.s.l.) and most Northern station. At comparable elevation, around 1,500 m a.s.l., the strength of the snow-depth decrease grows moving Northward. Besides the strongest spring snow-depth reduction, the Northern stations suffer also a significant snow depth decrease during winter months, so, North Piedmontese Alps result the most sensitive to climate change.

The shallower seasonal snow depth cannot be explained only by a reduction in total precipitation, in general, not statistically significant. This is true especially in spring, when different stations present different behavior with increased or decreased precipitation. The fraction of precipitation falling as snow has significantly decreased in several stations, especially in winter, suggesting that the causes of the snow-depth reduction are mainly related to the temperature variations. Ciccarelli et al. (2008) analyzed a set of daily temperature time series in Northwestern Italy in the period 1952–2002 and found that average temperatures significantly increased of about 1 °C over the period of observation. The increase in daily temperature anomalies is particularly evident for winter months and it ranges from +0.018 °C/year for minimum temperatures and +0.036 °C/year for maximum temperatures. The higher temperatures registered in the last decades can explain the general negative trend in snow depth. Going into detail, Canevarolo et al. (2011) analyzed the temperatures recorded in two of the stations considered in this study, Alpe Devero and Lago Vannino, in the Northern Piedmont. They showed that the minimum (maximum) temperatures trend is +0.07 (+0.04) °C/year. Concerning Southern Piedmontese Alps, Fratianni et al. (2010) found that the minimum (maximum) temperature increased by +0.03 (+0.07) °C/year over the period 1930–2009 at comparable elevation as those considered in this work. Comparing the two studies it appears that in Northern Piedmont, the minimum temperature increased more than that in Southern Piedmont, causing a stronger snow-depth reduction. Furthermore, the analysis of the number of ice days (days with maximum temperature below 0 °C) in the extended winter season December–March in Piedmontese Alps (1957–2007) shows a statistically significant decrease that becomes strongest with increasing elevation, from −0.34 days/year at 1,000–1,500 m a.s.l. to −0.60 days/year at elevation above 2,000 m a.s.l. (Bovo et al. 2009). The high-elevation sites in Northern Piedmont have experienced the strongest increase in minimum temperature and the strongest decrease in the number of ice days, resulting the most vulnerable to snow-depth reduction and to climatic change. Low-elevation sites (below 1,000 m a.s.l.) are mainly affected by scarcer snow precipitation due to higher temperatures and consequent predominance of liquid respect to solid precipitation.

The dynamical mechanisms underlying winter snow precipitation over Western Alps have been explored by studying the existing relations between snow parameters and the NAO, i.e., the dominant mode of winter atmospheric variability in the North Atlantic (Hurrell 1995). A significant anticorrelation between snow depth and NAO in the entire region was found: negative (positive) NAO is favorable (unfavorable) to snow pack persistence. Snowfall amount is significantly anticorrelated mainly in Southern Piedmont at middle altitudes, where small changes in temperature and precipitation may largely affect snowfall frequency and amount. These results obtained using six long-term time series are in contrast with the findings of a similar analysis performed using a 20-km spatial resolution-gridded dataset (Bartolini et al. 2009). It follows the importance of using instrumental high-quality time series in assessing local climate features.

The spectral analysis performed on snow parameters allowed to determine periodic components embedded in the time series and to identify common 2.3/2.7 years oscillations (cycles) in NAO and snow precipitation. The approximate 2.5-year mode has been found also in annual rainfall series of Massachusetts (Kane and Teixeira 1991), in the annual and winter rainfall of Iberian Peninsula (Rodriguez-Puebla et al. 2001; Garcìa et al. 2002), and Belgrade (Tosić and Unkasević 2005). The coherence analysis showed that the circulation index and the local snow-depth oscillatory modes are synchronized, so, a further connection can be established between the atmospheric large-scale patterns (surface pressure fields, described by the NAO) and the local climate (precipitation, temperatures).

The description, understanding and prediction of the climatic variability has important applications in the downscaling of the Global Circulation Models output (Giorgi and Mearns 1991) and the present work contributed to this objective by exploring snow variability and deepening the knowledge on the connections between local weather and large-scale atmospheric circulation patterns. The current efforts in the improvement of the NAO seasonal forecast will have positive outcomes in seasonal snow and climatic prediction.