Francesco D'Asaro

Scaling properties of topologically random channel networks

Abstract The analysis deals with the scaling properties of infinite topologically random channel networks (ITRNs) fast introduced by Shreve (1967, J. Geol. , 75: 179–186) to model the branching structure of rivers as a random process. The expected configuration of ITRNs displays scaling behaviour only asymptotically, when the ruler (or ‘yardstick’) length is reduced to a very small extent. The random model can also reproduce scaling behaviour at larger ruler lengths if network magnitude and diameter are functionally related according to a reported deterministic rule. This indicates that subsets of rrRNs can be scaling and, although rrRNs are asymptotically plane-filling due to the law of large numbers, scaling ITRNs can also display fractional dimension.

Probability Distribution of Peak Discharge at the Hillslope Scale Generated by Hortonian Runoff

AbstractIn this work, the probability distribution of peak discharge at the hillslope bottom is determined hypothesizing a prevalent Hortonian mechanism of runoff production for a given rainfall duration. As is well known, the probability distribution of peak discharge depends on the probability of both the rainfall event as well as that of the antecedent soil moisture conditions. In particular, the probability of the rainfall event is calculated according to the familiar rainfall duration–intensity–frequency approach, whereas the ecohydrological method from the literature is used here to define the probability of the antecedent soil moisture conditions. The latter depends on a set of parameters describing the dynamic interactions between average climate, soil and vegetation. By using the Monte Carlo procedure, the peak discharge is derived for a given rainfall duration and for each antecedent moisture condition/rainfall intensity pair from a physical-based model from the literature, by coupling the analy...

Scale invariance properties of the peak of the width function in topologically random networks

Some scaling properties of the topological width function for an infinite population of networks obeying the random model are analyzed. A Monte Carlo procedure is applied to generate width functions according to the hypothesis of topological randomness. The probability distributions of both peak and distance to peak of the topological width functions, conditioned (1) on the network diameter λ and (2) on λ and parameter β=[log (2μ − l)]/log λ, are studied. The parameter β can be considered a shape factor of the network; indeed, low β values describe elongated networks, while high β values refer to fan-like networks. Scale invariance for both random variables is established in the first case by using λ as a scale parameter. Also in the second case, scale invariance is observed for both the peak and the distance to peak of the topological width function; in particular, the invariance property for the peak involves a scaling function which is directly related to the shape factor β, allowing determination of the statistical similarity between random networks indexed by the same β. Then, a coarse-graining procedure is applied to a set of 15,000 width functions with λ=512; a scaling behavior of peaks of the original width function and aggregated ones is observed over a wide range of aggregation scales. Consequently, a statistical self-similarity for the peaks is also observed, which involved the same β-related scaling function. Finally, possible implication of the present results on the hydrologic response, at the basin scale, is discussed.

River Conservation and Phytodepuration in a Mid-Mediterranean Streambed: A Sicilian Case Study

AbstractFor landslide mitigation purposes, a system of two screen dams was created along the main channel of the Capreria River in Sicily. The de facto constructed wetlands occasioned behind the flow-path barriers produced, for several years, an appreciable reduction of organic load of the upstream municipal wastewaters from the nearby town of Riesi, Italy. This coincidence inspires the prospect of promoting a multifunctional role for these slope-stabilization works, thereby allowing them to be viewed from an intriguing and innovative planning perspective.