The Snowline Climate of the Alps 1961–2010

Theor Appl Climatol (2012) 110:517–537 DOI 10.1007/s00704-012-0688-9 SPECIAL ISSUE The snowline climate of the Alps 1961–2010 M. Hantel · C. Maurer · D. Mayer Received: 14 October 2011 / Accepted: 30 April 2012 / Published online: 7 July 2012 © The Author(s) 2012. This article is published with open access at Springerlink.com Abstract We study the probability for snow cover at sons. The sensitivity of the median snowline altitude to a climate station. Connecting stations with the same European temperature over the five decades of Alpine probability yields the corresponding snow line (a figure data is 166 (±5) m/◦Cinwinterand123(±18) m/◦Cin between zero and unity). The climatological snow lines summer. Global warming causes the snow lines to shift in the Alps are implicit in the state function of snow du- upward with time; in parallel, the area of the Alps that ration. This function, specified by just five parameters, is at least 50 % snow covered in winter shrinks by −7.0 depends upon the mountain temperature, a linear com- (±4.1) %/10 years. bination of the mean temperature over Europe and the 3D-coordinates of the stations. The influence of external parameters other than temperature (like snowfall, 1 Introduction melting processes, station exposition) is treated as stochastic. The five state function parameters are gained The snow limit concept represents the intuitive notion for both winter (DJF) and summer (JJA) through a that there is a well-defined transition between snow- fitting algorithm from routine snow depth observations covered ground and ground free of snow. The position in 1961–2010 in Austria and Switzerland. Any desired where this transition happens is often clearly visible in snow line is defined by a linear surface with a character- the field, particularly in the mountains, sometimes lo- istic value of the mountain temperature. The snow line cally with an accuracy of less than a meter. Connecting appears when there is a cut between the surface and these positions yields the snow limit. This concept has the orography. Temperature sensitivity of snow cover been applied from the daily time scale over monthly duration, analytically derived from the state function, to annual and decade-long periods. For example, it is extreme at the median snow line (snow probability has been used by Hann (1883) and various subsequent 0.50). Alpine-wide mean altitude of the median snow authors. Further, in the geographical literature, Louis line is 793(±36)m in winter and 3.083(±1.121)m in (1955) has analyzed the notion of the snow limit in summer. The snowline field slopes gently from west detail; Louis considered, with focus upon the budgets to east across the Alps (downward in winter, upward of glaciers, the climatological snow limit as the position in summer) and oscillates up and down with the sea- at which total snowfall and total ablation are in balance. A worldwide map of the snow limit (in relation to the tree line) has been provided by Hermes (1955). B · M. Hantel ( ) C. Maurer We have recently (Hantel and Maurer (2011)) stud- Theoretical Meteorology Research Forum, Berggasse 11/2/3, 1090 Vienna, Austria ied the snow limit concept in the more general con- e-mail: [email protected] text of the snow line. The basis of the snow line is the relative seasonal snow duration, obtained from D. Mayer daily routine measurements of the snow depth at a Institute of Meteorology and Geophysics, University of Vienna, Althanstrasse 14, climate station. We interpret this as the probability to 1090 Vienna, Austria encounter snow cover. Connecting stations with the 518 M. Hantel et al. same probability yields the corresponding snow line (a only the daily snow depth at the climate stations (plus, figure between zero and unity—see also the equivalent of course, the 3D-station coordinates); other possi- definition in the Dictionary of Earth Science, Parker ble input parameters (e.g., local station temperature, (1997)). The snow limit is adopted for the specific value snowfall, quantities describing the melting process, or of 50 %; we refer to it as the median snow line.Atthe the exposition of a climate station to radiation) are median snow line, the probability to encounter snow is not used. In Section 4, we present standard (“naive”) equal to the probability to encounter no snow. statistics without reference to the model. The model There is a physical reason for the significance of results come in Section 5 for the entire Alpine region this boundary. The median snow line should be located andinSection6 for the selected Alpine valleys. Trend where the sensitivity to temperature is extreme. In high estimates are discussed in Section 7. An outlook is given and cold mountain regions with sizeable snow cover, in Section 8. the snow duration should be insensitive to an external large-scale warming or cooling; a similar reasoning ap- plies to warm climate stations in the lowlands where 2 Review of the model there is no snow cover at all. Extreme temperature sensitivity should be found somewhere in between. This The snowline model as we want to use it here (Hantel is in accord with general climatological experience (e.g., and Maurer (2011)) is based upon a snow cover model, Laternser and Schneebeli (2003), Scherrer et al. (2004), originally designed for Austrian data by Hantel (1992), and Durand et al. (2009)). further developed in paper I (Hantel et al. (2000)), With this qualitative background, Hantel and Maurer extended to Swiss data in paper II (Wielke et al. (2004) (2011) have developed the quantitative state function along with Wielke et al. (2005)) and applied to all-Alps of snow duration for the coherent mountain region data in paper III (Hantel and Hirtl-Wielke (2007)). The of the Alps, for the climate period 1961–2000. The unifying concept is the hypothesis that the seasonal corresponding theory yields a formula for the state snow cover at a climate station is primarily controlled function which implies the definition of the snow lines by the seasonal surface air temperature of the station. and implies further that the snowline f ield is controlled The station temperature, however, can eventually be by the mountain temperature, a linear combination of replaced by the montain temperature, a linear combi- European temperature and 3D-station coordinates. nation of the area mean surface temperature T over In this study, we want to corroborate these results, Europe and the 3D-station coordinates. In this section, with the following innovative components. First, we will we review three different applications of the model, present evaluations for the 50-year climate epoch in schematically sketched in Fig. 1. 1961–2010, both for winter (DJF) and summer (JJA), for the Alpine region consisting of Austria (A) and 2.1 Laboratory model (see Fig. 3 of Hantel Switzerland (CH); the results will be quite well in accord and Hirtl-Wielke (2007)) with our previous evaluations. Further, we will describe and implement a modified fitting algorithm to derive In the physical laboratory (first column of Fig. 1)with the parameter estimates for the state function; this actual temperature ϑ, we observe two phases ν of theoretically improved method does not much change pure water: liquid water (ν = 0)forϑ above t = 0 ◦C the results but in addition yields statistically sound 0 and ice (ν = 1)forϑ below t . The probability P to estimates of the explained variance (Appendix 1). Fi- 0 encounter ice is equal to the ensemble average ν.We nally, we will extend the mean snowline surfaces, valid further assume that there are stochastic temperature for the entire Alpine region, into a couple of selected fluctuations, normally distributed, with ensemble mean individual valleys; this may demonstrate the applicabil- ϑ and standard deviation . For this setting, P is ity, including its limits, of the present approach to the controlled by the temperature parameters as follows: climate of a local station. The paper is organized as follows: In the next section, P(ϑ,)= (χ) with χ = (t0 −ϑ)/. (1) we give a skeleton review of the model, stratified into its different levels of application. Data management is is the Gaussian error function defined as (Bron- covered in Section 3. In accord with our basic hypoth- stein et al. (1999)): esis (i.e., the dependence of the snowline field solely upon the mountain temperature), we use as observed χ 1 −ϑ2/ temperature data only the mean seasonal temperature, (χ) = √ e 2dϑ. (2) 2π averaged over Europe, and as observed snow data ϑ=−∞ The snowline climate of the Alps 1961–2010 519 Fig. 1 of Hantel and Hirtl-Wielke (2007) for Austrian stations and in Fig. 5 of Hantel and Maurer (2011)for all-Alps stations, both for the winters (DJF) of 1961– 2000. This type of plot reveals the dependence of the snow duration upon station temperature. However, the altitude dependence of temperature at the climate stations is mixed with the large-scale climate temperature of Europe. It follows that snowline information cannot be gained from N(t). 2.3 Alpine-wide model (see, e.g., Fig. 6 of Hantel and Maurer (2011)) In order to identify snow lines, we note that the station temperature t is influenced by the large-scale climate process, represented by the European temperature T and by local effects, represented by the position (x, y, z) of the climate station. This suggests to introduce the mountain temperature: τ = T + ax + by+ cz. (4) Fig. 1 Poster of different model versions. The unifying theoretical concept is a Gaussian error function (χ). It serves as an exact description of ice probability P with χ(ϑ,ε) in the The model in Eq.

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