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In this chapter we apply hierarchical Bayesian modeling to describe fatigue crack growth. Due to the special pattern of crack growth data, we propose a nonparametric model which is based on a minimum of probabilistic assumptions. We put a (prior) probability model on an unknown growth curve by considering a grid of time points and assuming that the increments between such grid points are independent exponential random variables, with expectations proportional to the length of the grid interval. The nonparametric structure enables us to arrive at a model which is both flexible enough to be fitted to different sets of growth data and, at the same time, enables us to interpret different parts of the model in an intuitively plausible manner. A Markov chain Monte Carlo method is adopted for the numerical computation. Numerical results show that our model behaves well in both being fitted to the data and in predicting future observables.
The identified glide cracks on at least two measuring positions, indicating extreme glide rates and, therefore, strong negative effects on juvenescent trees. To prevent glide rates of a magnitude such as this requires a mature forest with at least 300 stems/ha.
Glide cracks (Fig. 2) result from rapid gliding (In der Gand and Zupancic 1966). Gliding snow sluffs are small avalanches that slide on the ground and which occur when there is rapid snow gliding (In der Gand and Zupancic 1966).
Glide crack in a forest clearing. The picture was taken in Dec. 1992 in a south-facing larch stand nearby the Kaserstattalm, Stubai Valley, Tyrol. The larch trees on the right side are characterized by Säbelwuchs [sweep of the bole] which is a typical indicator of trees having been affected by snow gliding in previous years
Snow gliding can have negative effects on forest plants; the so-called Säbelwuchs [sweep of the bole] is a typical indicator of trees having been affected by snow gliding in previous years. However, juvenescent trees may also be uprooted from the ground, with several authors describing this type of damage to juvenescent trees (Höller et al. 2009). According to In der Gand (1968b), plants can be uprooted as a result of snow gliding and the accompanying tensile forces. He found that growth of young plants is adversely impacted by the force released from glide cracks (Fig. 2) and gliding snow sluffs, and it is therefore necessary to prevent the extreme glide rates caused by these events in order to protect afforestations. 2ff7e9595c
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