Multiscaling behavior of braided channel networks: An alternative formulation of Taylor's law variate transformations.

Braided channel networks exhibit a complex interplay between spatial and temporal dynamics. Their behavior is characterized by both simple and multiscaling patterns, and the mechanisms underlying the stochastic processes associated with this dynamics remain incompletely understood. Leveraging Taylor's pioneering work [Nature (London) 189, 732 (1961)NATUAS0028-083610.1038/189732a0], which unveiled scaling relations in a plethora of natural phenomena through what is now known as the Taylor power law (TPL), we propose a physical interpretation of braided channel systems. This interpretation utilizes a specific class of transformation functions applied to the mean of fluvial geomorphic variables measured along cross sections, namely, the number of wet channels, the average width of wet channels, and the entropic braiding index. By analyzing remotely sensed data of the Brahmaputra-Jamuna River in Bangladesh we obtain valuable insight into the spatiotemporal scaling of these geomorphological variables and gather a deeper understanding of the complexity of braided channel systems. Finally, through a direct analysis employing the TPL in conjunction with a fixed-mass multifractal algorithm, we prove that braided channel networks exhibit a multiscaling behavior.

Nonlinear shallow water investigation of atmospheric disturbances generated by strong seismic events.

The upper portions of the Earth's atmospheric layer, e.g., the ionospheric plasma layer, can be significantly affected by perturbations generated in the lower layers. In fact, all perturbations formed within the troposphere can easily propagate, not only horizontally within the layer but also vertically reaching the highest regions of the atmosphere far from the Earth's surface, as depicted by the Wentzel-Kramers-Brillouin (WKB) approximation of atmospheric waves. Because all perturbations generated in the atmospheric boundary layer must take into account the effects of the medium's nonlinearity and thus the effects of atmospheric turbulence, in this work the impact of a strong seismic event and the disturbances generated in the flow are analyzed by means of a fully nonlinear model which incorporates a simple parametrization of the seismic event and is based on the classical shallow water. A strict dependence was observed between the model control parameters and the vertical nonvanishing modes from the WKB approximation, and only few specific bands of excited modes are nonvanishing and can eventually propagate to the ionosphere. Moreover, the flow disturbance, generated by a seismic event, presents a multiscale nature characterized by two fixed wavelengths, and the excited modes are harmonics of such distinctive scales.

Fixed-mass multifractal analysis of river networks and braided channels.

A fixed-mass multifractal (FMA) analysis was used to investigate natural river networks and braided channels. In particular, while the study of natural river networks was performed with fixed-size algorithms (FSAs) in the past, the analysis of natural braided channels was not pursued before to our knowledge. Results showed the multifractal and non-plane-filling nature of all the digitalized data sets. Analysis of the digitalization step (constant or not) was performed and showed that it does not exert a strong influence on the assessed values of the Lipschitz-Hölder exponents and the support dimensions, even if a constant step permits better reconstruction of the right sides of the spectra, for negative moment orders of probabilities. The FMA approach presented two improvements with respect to the FSA one, in terms of oscillations of the scaling curves for negative moment orders of probabilities and of error bars. A more precise assessment of the multifractal spectra is of great importance in the development of multifractal models for the simulation of flood hydrographs.