Contacts with larger values of Rr are found to produce contact contours with higher fractal dimension as calculated by a 2D box-counting method. Regions of true contact evolve through the formation of new microcontacts and their progressive merging, meanwhile the area distributions of contact island induced by various forces tend to obey similar Weibull distributions due to fractal nature in their surfaces. With increasing load, the power exponent converges to that of Hertzian contact, e.g., 1/3, independent of Rr. The dependence of normal contact stiffness (k) on applied normal force (F) is found to follow a power law over four orders of magnitude, with both alpha and beta being highly correlated with Rr and FD. The contact behaviour of rough spheres with a rigid flat surface is simulated using FEM to quantify the influences of surface structure and sphere morphology by focusing on contact stiffness and true contact area. These surfaces are described by two roughness descriptors, namely, relative roughness (Rr) and fractal dimension (FD). A series of spherical grain surfaces with distinguished roughness features are generated by means of Spherical Harmonics. Normal contact behaviour between non adhesive fractal rough particles is studied using a finite element method (FEM). Arctic shrubs cool permafrost in winter by acting as a thermal bridge through the snowpack, according to ground temperature observations and heat transfer simulations. The inclusion of these thermal bridging processes into climate models may have an important impact on projected greenhouse gas emissions by permafrost. The overall thermal effect is likely to depend on snow and shrub characteristics and terrain aspect. The thermal bridging effect is reversed in spring when shrub branches absorb solar radiation and transfer heat to the ground. This is despite a snowpack that is twice as insulating in shrubs. Observations from unmanipulated herb tundra and shrub tundra sites on Bylot Island in the Canadian high Arctic reveal a 1.21 ☌ cooling effect between November and February. Here, we use ground temperature observations and heat transfer simulations to show that low shrubs can actually cool the ground in winter by providing a thermal bridge through the snowpack. These shrubs are thought to have a warming effect on permafrost by increasing snowpack thermal insulation, thereby limiting winter cooling and accelerating thaw. ![]() Considerable expansion of shrubs across the Arctic tundra has been observed in recent decades.
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