Abstract
We study the probability for snow cover at a climate station. Connecting stations with the same probability yields the corresponding snow line (a figure between zero and unity). The climatological snow lines in the Alps are implicit in the state function of snow duration. This function, specified by just five parameters, depends upon the mountain temperature, a linear combination of the mean temperature over Europe and the 3D-coordinates of the stations. The influence of external parameters other than temperature (like snowfall, melting processes, station exposition) is treated as stochastic. The five state function parameters are gained for both winter (DJF) and summer (JJA) through a fit algorithm from routine snow depth observations in 1961–2010 in Austria and Switzerland. Any desired snow line is defined by a linear surface with a characteristic value of the mountain temperature. The snow line appears when there is a cut between the surface and the orography. Temperature sensitivity of snow cover duration, analytically derived from the state function, is extreme at the median snow line (snow probability 0.50). Alpine-wide mean altitude of the median snow line is 793(+ / −36)m in winter and 3.083(+ / −1.121)m in summer. The snowline field slopes gently from west to east across the Alps (downward in winter, upward in summer) and oscillates up and down with the seasons. The sensitivity of the median snowline altitude to European temperature over the five decades of Alpine data is 166 (±5) m/°C in winter and 123 (±18) m/°C in summer. Global warming causes the snow lines to shift upward with time; in parallel, the area of the Alps that is at least 50 % snow covered in winter shrinks by −7.0 (±4.1) %/10 years.
Highlights
The snow limit concept represents the intuitive notion that there is a well-defined transition between snowcovered ground and ground free of snow
In the geographical literature, Louis (1955) has analyzed the notion of the snow limit in detail; Louis considered, with focus upon the budgets of glaciers, the climatological snow limit as the position at which total snowfall and total ablation are in balance
With the mountain temperature τ and with χ(τ ), the error function serves as state function N to describe a relative seasonal snow duration, gained from snow data, without using t
Summary
The snow limit concept represents the intuitive notion that there is a well-defined transition between snowcovered ground and ground free of snow The position where this transition happens is often clearly visible in the field, in the mountains, sometimes locally with an accuracy of less than a meter. Connecting these positions yields the snow limit This concept has been applied from the daily time scale over monthly to annual and decade-long periods. This is in accord with general climatological experience (e.g., Laternser and Schneebeli (2003), Scherrer et al (2004), and Durand et al (2009)) With this qualitative background, Hantel and Maurer (2011) have developed the quantitative state function of snow duration for the coherent mountain region of the Alps, for the climate period 1961–2000.
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