A unique approach has been developed for explaining and forecasting the processes of flood and/or mudflow (debris) formation and their spread along riverbeds in mountainous areas, caused by flash increases in the water masses involved (considerably increasing in their expected level because of precipitation intensity) due to groundwater contributions. Three-dimensional crack-nets within the confines of unified rivershed basins in mountain massifs are a natural transportation system (as determined by some dynamic external stress factors) for groundwater, owing to hydrostatic/hydrodynamic pressure distribution, varied due to different reasons (e.g., earthquakes). This process reveals a wave nature characterized by signs of obvious self-organization, and can be described via the soliton model in nonlinear hydrodynamics on the surface propagation after a local exit of groundwater as the trigger type. This approach (and related concepts) might result in a more reliable forecasting and early warning system in case of natural water hazards/disasters, taking into account a groundwater-dominant role in some cases.

A model for the development of the city structure in the fractal approximation is proposed. To describe the dynamics of the development of an urban fractal, a diffusion approximation is used, which allows generating stochastic fractals based on models of directed percolation and diffusion-limited aggregation. The fractal dimensions are estimated.