The topological interconnection between grid, channel, and Peano networks is investigated by extracting grid and channel networks from high‐resolution digital elevation models of real drainage basins, and by using a perturbed form of the equation describing how the average junction degree varies with Horton‐Strahler order in Peano networks. The perturbed equation is used to fit the data observed over the Hortonian substructures of real networks. The perturbation parameter, denoted as “uniformity factor,” is shown to indicate the degree of topological similarity between Hortonian and Peano networks. The sensitivities of computed uniformity factors and drainage densities to grid cell size and selected threshold for channel initiation are evaluated. While the topological relation between real and Peano networks may not vary significantly with grid cell size, these networks are found to exhibit the same drainage density only for specific grid cell sizes, which may depend on the selected threshold for channel initiation.

We study the scale dependence of the saturated hydraulic conductivity K-s through the effective porosity n(e) by means of a newly developed power-law model (PLM) which allows to use simultaneously measurements at different scales. The model is expressed as product between a single PLM (capturing the impact of the dominating scale) and a characteristic function accounting for the correction because of the other scale(s). The simple (closed form) expression of the -function enables one to easily identify the scales which are relevant for K-s. The proposed model is then applied to a set of real data taken at the experimental site of Montalto Uffugo (Italy), and we show that in this case two (i.e. laboratory and field) scales appear to be the main ones. The implications toward an important application (solute transport) in Hydrology are finally discussed. Copyright (c) 2016 John Wiley & Sons, Ltd.

El estudio de la variabilidad espacial de específicas magnitudes que caracterizan el suelo no saturado es muy importante para la evaluación de los fenómenos de contaminación. La Geoestadística es una herramienta útil para la estimación de la variabilidad espacial de los parámetros considerados. El objetivo de este estudio es mejorara la comprensión de la variabilidad espacial de la dimensión fractal en las curvas de retención de agua, mostrando de esta manera el comportamiento de este parámetro en los puntos muestreados y de manera particular en los puntos donde no existen muestras. La evaluación de la dimensión fractal se calculó por el análisis de escalamiento obtenido a partir de algunos modelos fractales y la posterior comparación entre los resultados correspondientes.

This paper deals with the development of a 2D weakly compressible SPH model to simulate wave pressures acting on vertical and slotted coastal structures. Attention is devoted to investigate the diffusive term in the continuity equation in order to smooth out the high-frequency numerical noise in the pressure field. A hybrid formulation based on two literature diffusive models is proposed. The interaction between regular waves with vertical and perforated breakwaters is analyzed in time, space, and frequency domain. Numerical results are compared with laboratory experiments and other diffusive SPH formulations, varying the magnitude of the adopted diffusive term. On the basis of an error analysis, the results show that the hybrid formulation gives a better agreement with the experimental data for the majority of the investigated cases. Moreover, SPH simulations highlight nonlinear trends of dynamic pressures in correspondence with geometrical singularities, such as the holes of slotted walls, due to strong pressure drops induced by the flow motion.

The study of spatial variability of specific quantities characterizing the unsaturated soil is very important for the evaluation of polluting phenomena. Geostatistics is a useful tool for estimating the spatial variability of the considered parameters. The aim of this study is to improve the understanding of the spatial variability of the fractal dimension of water retention curves, showing the behaviour of this parameter in the site examined and particularly at the points where measures were not performed. The assessment of the fractal dimension was calculated by the analysis of scaling obtained from some fractal models and a comparison among the correspondent results was performed.

A fractal analysis of the soil retention and hydraulic conductivity curves is presented.The retention process is modeled by a two fractal regimes: one pertaining to high water content values, and another accounting for the low water content data.This significantly improves the physical insight of the retention process as compared with the case of one-fractal models.The fractal dimensions characterizing the two regimes are estimated by fitting the retention curve model upon real data, and subsequently they are used to determine the hydraulic conductivity which for the retention curve models of Mualem and Burdine, is obtained in closed form.The reliability of the model is tested against independent conductivity data collected in a field-scale campaign.

Hydraulic conductivity and effective porosity values for the confined sandy loam aquifer of the Montalto Uffugo (Italy) test field were obtained by laboratory and field measurements; the first ones were carried out on undisturbed soil samples and the others by slug and aquifer tests. A direct simple-scaling analysis was performed for the whole range of measurement and a comparison among the different types of fractal models describing the scale behavior was made. Some indications about the largest pore size to utilize in the fractal models were given. The results obtained for a sandy loam soil show that it is possible to obtain global indications on the behavior of the hydraulic conductivity versus the porosity utilizing a simple scaling relation and a fractal model in coupled manner.

Water retention curve (WRC) is analyzed by means of the fractal geometry approach. Three models accounting for the fractal distribution of either the pore and solid phase of unsaturated porous media have been considered. By using data collected during a field scale internal drainage, we determine the functional relationship between the WRC, and the fractal dimension(s). In particular, it is shown that the fractal scaling of the WRC is feasible provided that a large enough set of measurements at the lowest water contents is available.

The present work concerns the calculation of the infinitesimal porosity by using the Menger’s Sponge model. This computation is based on the grossone theory considering the pore volume estimation for the Menger’s Sponge and afterwards the classical definition of the porosity, given by the ratio between the volume of voids and the total volume (voids plus solid phase). The aim is to investigate the different solutions given by the standard characterization of the porosity and the grossone theory without the direct estimation of the fractal dimension. Once the utility of this procedure had been clarified, the focus moves to possible practical applications in which infinitesimal parts can play a fundamental role. The discussion on this matter still remains open.

A network analysis is used to investigate the low connections of natural river channels. At the basin scale, the river networks are analyzed according to the Horton-Strahler hierarchy. We propose a quantitative criterion for the average junction degree as a function of a fixed hierarchical order of the network and independent of the usual scaling laws. The numerical results of this analysis are compared with exact results of the Peano river network, showing differences of the order of 10(-3). This aspect is especially relevant for the characterization of transport and diffusion processes at the basin scale.

The complexity characterization of the porous media structure, in terms of the “pore” phase and the “solid” phase, can be carried out by means of the fractal geometry which is able to put in relationship the soil structural properties and the water content. It is particularly complicated to describe analytically the hydraulic conductivity for the irregularity of the porous media structure. However these can be described by many fractal models considering the soil structure as the distribution of particles dimensions, the distribution of the solid aggregates, the surface of the pore-solid interface and the fractal mass of the “pore” and “solid” phases. In this paper the fractal model of Yu and Cheng (2002) and Yu and Liu (2004), for a saturated bidispersed porous media, was considered. This model, using the Sierpinsky-type gasket scheme, doesn’t contain empiric constants and furnishes a well accord with the experimental data.

Previous observations on some natural river networks showed the similar values of the support fractal dimension and the information entropy in basins having similar source rocks. In the present work, lithologic control on river network multifractality is investigated through the reconstruction of the spectra belonging to two classes of different lithology: the plutonic-metamorphic class and the coherent sedimentary one. Two computational methods of the generalised fractal dimensions and multifractal spectra are illustrated and applied to river networks of the Calabria region (Southern Italy). It is shown that an increment of both the fractal dimensions and the Lipschitz-Hölder exponents of singularity occurs when passing from a coherent sedimentary to a plutonic-metamorphic river network. The importance of this finding emerges from the direct link between flood hydrographs and multifractal spectra, as expressed in the Multifractal Instantaneous Unit Hydrograph (MIUH): the increment of the multifractal parameters produces an increment of the flood peaks.

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.