The vulnerability of Pyrenean ski resorts to climate-induced changes in the snowpack

Winter tourism is the main source of income and the driving force of local development in many mountain areas. However, in recent years, the industry has been identified as being extremely vulnerable to future climate change. Although the Pyrenees has the largest ski area in Europe after the Alps, there are few detailed climate change vulnerability assessments on the ski resorts based in this region. This paper analyzes the vulnerability of the Pyrenean ski resorts to projected changes in the snowpack under various future climate scenarios. In addition, the study analyzes the sustainability of the snowmaking systems to offset the climate variability of natural snow cover. On average, the study predicts a shorter ski-season length, especially in low-altitude ski resorts in a moderate climate change scenario and for all ski resorts in a more intensive climate change scenario. However, a significant regional variability has been identified for the projected impacts at very short geographical distances within the studied area. Moreover, this paper shows that snowmaking cannot completely solve the problem for all ski resorts in the Pyrenees, as the measure can only act as a robust adaptation strategy in the region provided climate change is limited to +2 °C snowmaking.Peer ReviewedPostprint (author’s final draft

Finite difference Scheme with exact spectrum for the diffusion equation with piecewise constant coefficients in a layered medium

Maģistra darba mērķis - izstrādāt galīgo diferenču shēmu (metodi) ar precīzo spektru difūzijas vienādojumam. Darba ietvaros tika apskatīta taišņu metode Puasona vienādojumam. Tika iegūta taišņu metode ar precīzo spektru, kā arī pierādīta teorēma par precīzo taišņu metodi. Tika risināti daži piemēri, izmantojot iegūto teoriju. Difūzijas vienādojumam tika izstrādāta gan parastā taišņu metode, gan precīza spektra taišņu metode. Tika pierādīta teorēma par precīzo spektru, kā arī risināts viens piemērs.The aim of this Master's Thesis is to work out finite difference scheme (method) with exact spectrum for the diffusion equation. In this Thesis, method of lines for Poisson's equation is studied. Method of lines with exact spectrum was obtained, as well as the theorem about the method of lines with exact spectrum was proved. Using the obtained theory, Some problems were solved. Both: ordinary method of lines and method of lines with exact spectrum for the diffusion equation were obtained. The theorem on the exact spectrum was proved, as well as one preoblem were solved