Abstract

Mountain glaciers in China are an important water source for both China and adjoining countries, and therefore their adaptation to glacier change is crucial in relation to maintaining populations. This study aims to improve our understanding of glacial vulnerability to climate change to establish adaptation strategies. A glacial numerical model is developed using spatial principle component analysis (SPCA) supported by remote sensing (RS) and geographical information system (GIS) technologies. The model contains nine factors—slope, aspect, hillshade, elevation a.s.l., air temperature, precipitation, glacial area change percentage, glacial type and glacial area, describing topography, climate, and glacier characteristics. The vulnerability of glaciers to climate change is evaluated during the period of 1961–2007 on a regional scale, and in the 2030s and 2050s based on projections of air temperature and precipitation changes under the IPCC RCP6.0 scenario and of glacier change in the 21st century. Glacial vulnerability is graded into five levels: potential, light, medial, heavy, and very heavy, using natural breaks classification (NBC). The spatial distribution of glacial vulnerability and its temporal changes in the 21st century for the RCP6.0 scenario are analyzed, and the factors influencing vulnerability are discussed. Results show that mountain glaciers in China are very vulnerable to climate change, and 41.2% of glacial areas fall into the levels of heavy and very heavy vulnerability in the period 1961–2007. This is mainly explained by topographical exposure and the high sensitivity of glaciers to climate change. Trends of glacial vulnerability are projected to decline in the 2030s and 2050s, but a declining trend is still high in some regions. In addition to topographical factors, variation in precipitation in the 2030s and 2050s is found to be crucial.

Abstract

The pseudospectra is a powerful tool to study the behavior of dynamic systems associated to non-normal matrices. Studies and applications have increased in the last decades, thus, its efficient computation has become of interest for the scientific community. In the large scale setting, different approaches have been proposed, some of them based on projection on Krylov subspaces. In this work we use the idea proposed by Wright and Trefethen to approximate the pseudospectra of a matrix A using a projection Hm of smaller size. Additionally, we propose a domain decomposition of the interest region into subregions which are assigned to a set of processors. Each processor calculates the minimal singular values of matrices (zI − Hm) where z = x + yi represents a point of the corresponding subregion. We conduct a numerical experimentation comparing the results with those on the literature of the topic. In all cases the proposed scheme shows a reduction in CPU time with respect to the sequential version, achieving from 41x to 101x.

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