An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

Potential drought stress in a Swiss mountain catchment-Ensemble forecasting of high mountain soil moisture reveals a drastic decrease, despite major uncertainties

Climate change is expected to profoundly influence the hydrosphere of mountain ecosystems. The focus of current process-based research is centered on the reaction of glaciers and runoff to climate change; spatially explicit impacts on soil moisture remain widely neglected. We spatio-temporally analyzed the impact of the climate on soil moisture in a mesoscale high mountain catchment to facilitate the development of mitigation and adaptation strategies at the level of vegetation patterns. Two regional climate models were downscaled using three different approaches (statistical downscaling, delta change, and direct use) to drive a hydrological model (WaSiM-ETH) for reference and scenario period (1960–1990 and 2070–2100), resulting in an ensemble forecast of six members. For all ensembles members we found large changes in temperature, resulting in decreasing snow and ice storage and earlier runoff, but only small changes in evapotranspiration. The occurrence of downscaled dry spells was found to fluctuate greatly, causing soil moisture depletion and drought stress potential to show high variability in both space and time. In general, the choice of the downscaling approach had a stronger influence on the results than the applied regional climate model. All of the results indicate that summer soil moisture decreases, which leads to more frequent declines below a critical soil moisture level and an advanced evapotranspiration deficit. Forests up to an elevation of 1800 m a.s.l. are likely to be threatened the most, while alpine areas and most pastures remain nearly unaffected. Nevertheless, the ensemble variability was found to be extremely high and should be interpreted as a bandwidth of possible future drought stress situations.

Cascading climate effects and related ecological consequences during past centuries

The interface between climate and ecosystem structure and function is incompletely understood, partly because few ecological records start before the recent warming phase. Here, we analyse an exceptional 100-yr long record of the great tit (Parus major) population in Switzerland in relation to climate and habitat phenology. Using structural equation analysis, we demonstrate an uninterrupted cascade of significant influences of the large-scale atmospheric circulation (North-Atlantic Oscillation, NAO, and North-sea – Caspian Pattern, NCP) on habitat and breeding phenology, and further on fitness-relevant life history traits within great tit populations. We then apply the relationships of this analysis to reconstruct the circulation-driven component of fluctuations in great tit breeding phenology and productivity on the basis of new seasonal NAO and NCP indices back to 1500 AD. According to the structural equation model, the multi-decadal oscillation of the atmospheric circulation likely led to substantial variation in habitat phenology, productivity and consequently, tit population fluctuations with minima during the "Maunder Minimum" (∼ 1650–1720) and the Little Ice Age Type Event I (1810–1850). The warming since 1975 was not only related with a quick shift towards earlier breeding, but also with the highest productivity since 1500, and thus, the impact of the NAO and NCP has contributed to an unprecedented increase of the population. A verification of the structural equation model against two independent data series (1970–2000 and 1750–1900) corroborates that the retrospective model reliably depicts the major long-term NAO/NCP impact on ecosystem parameters. The results suggest a complex cascade of climate effects beginning at a global scale and ending at the level of individual life histories. This sheds light on how large-scale climate conditions substantially affect major life history parameters within a population, and thus influence key ecosystem parameters at the scale of centuries.