Mauro Fiorentino

This study aims to conceptualize natural drainage networks as genuine complex networks. To overcome the limitation imposed by the regular connectivity structure of the traditional planted binary tree model—commonly employed to represent the planar configuration of fluvial systems—we introduce a line graph transformation. This mapping converts a planted binary tree into a plane tree, which can be regarded as a special class of loopless, directed graph characterized by inhomogeneous topology. From a geomorphological standpoint, our transformation naturally induces a hierarchical basin ordering that reflects the pioneering Gravelius stream order, offering insights into this scheme by projecting the hierarchy of tributary rivers onto a purely topological space. The application of complex network theory provides an explanatory perspective on river networks, yielding experimental findings that complement and extend established results in the geomorphological literature. In particular, our analysis of six catchments in southern Italy reveals previously unrecognized regularities, including a family of exact scaling laws and a surprisingly smooth width-type function that closely fits a Gamma distribution. These scaling laws emerge as power-law probability distributions for both the in-degree of nodes and the size of their in-components, which capture the scale invariance of tributary river lengths and drainage areas in tributary basins, respectively, thereby expanding the pantheon of known fluvial laws. Notably, these distributions represent sample distributions drawn from the complete populations of upstream lengths and drainage areas, with the sampling induced by our mapping through the selection of fluvial quantities corresponding to topologically well-defined elements of the plane tree. On the theoretical front, our approach is grounded in a model of directed, uncorrelated random graphs with arbitrary degree distributions. Among other things, by applying the generating function formalism to uncorrelated plane trees we derive an analytical expression for the distribution of drainage areas in tributary basins as a function of the distribution of tributary river lengths. By relying on average cluster properties, we predict the scaling exponent of the former distribution to be exactly 2 in the limit of large system sizes—a result that aligns well with both our empirical observations and previous findings in the complex network literature. Beyond the first-order approximation inherent in the model, our mapping also offers a coherent framework for interpreting the correlation structure consistently observed across all examined drainage networks.

Floods and landslides are two distinct natural phenomena influenced by different conditioning factors, though some environmental triggers may overlap. This study applied eXtreme Gradient Boosting (XGBoost) to develop susceptibility maps for both phenomena, using a unified approach based on the same geospatial predictors. The approach integrated topographical, geological, and remote sensing datasets. Flood event data were collected from institutional sources using multi-source and high-resolution remotely sensed data. The landslide inventory was compiled based on historical records and geomorphological analysis. Key conditioning factors such as elevation, slope, lithology, and land cover were analyzed to identify areas prone to floods and landslides. The methodology was applied to the Basento River basin in Southern Italy, a region frequently impacted by both hazards, to assess its vulnerability and inform risk management strategies. While flood susceptibility is primarily associated with low-lying areas near river networks, landslides are more influenced by steep slopes and geological instability. The XGBoost model achieved a classification accuracy close to 1 for flood-prone areas and 0.92 for landslide-prone areas. Results showed that flood susceptibility was primarily associated with low Elevation and Relative Elevation, and high Drainage Density, whereas landslide susceptibility was more influenced by a broader and balanced set of factors, including Elevation, Drainage Density, Relative Elevation, Distance and Lithology. The resulting susceptibility maps offered critical approaches for land use planning, emergency management, and risk mitigation. Overall, the results demonstrated the effectiveness of XGBoost in multi-hazard assessments, offering a scalable and transferable approach for similar at-risk regions worldwide.

The present work pursues theoretical and empirical objectives. With regards to the former, it is demonstrated that the natural tendency to uniformity of both the probability distribution of a city to have a certain number of inhabitants and that of a person to reside in a town of a given number of citizens leads to a competition between their information entropies, which provides the power law distribution as the most probable one for city size. It is also shown that Zipf's law reflects the significant control of the existence of interconnections between cities on the self‐organization of their size. With regards to the empirical objectives, based on population data of European countries and Italian municipalities, the theoretical approach proposed is validated. At the Italian scale, city distribution is shown to be a power law for cities above 10,000 inhabitants. In the 20 Italian regions, the breakpoint in the distribution is generally lower. Finally, the geographical control on city distribution is discussed based on the results achieved in some regions.

Monitoring Surface Soil Moisture (SSM) and Root Zone Soil Moisture (RZSM) dynamics at the regional scale is of fundamental importance to many hydrological and ecological studies. This need becomes even more critical in arid and semi-arid regions, where there are a lack of in situ observations. In this regard, satellite-based Soil Moisture (SM) data is promising due to the temporal resolution of acquisitions and the spatial coverage of observations. Satellite-based SM products are only able to estimate moisture from the soil top layer; however, linking SSM with RZSM would provide valuable information on land surface-atmosphere interactions. In the present study, satellite-based SSM data from Soil Moisture and Ocean Salinity (SMOS), Advanced Microwave Scanning Radiometer 2 (AMSR2), and Soil Moisture Active Passive (SMAP) are first compared with the few available SM in situ observations, and are then coupled with the Soil Moisture Analytical Relationship (SMAR) model to estimate RZSM in Iran. The comparison between in situ SM observations and satellite data showed that the SMAP satellite products provide more accurate description of SSM with an average correlation coefficient (R) of 0.55, root-mean-square error (RMSE) of 0.078 m³ m⁻³ and a Bias of 0.033 m³ m⁻³. Thereafter, the SMAP satellite products were coupled with SMAR model, providing a description of the RZSM with performances that are strongly influenced by the misalignment between point and pixel processes measured in the preliminary comparison of SSM data.

High and low flows and associated floods and droughts are extreme hydrological phenomena mainly caused by meteorological anomalies and modified by catchment processes and human activities. They exert increasing on human, economic, and natural environmental systems around the world. In this context, global climate change along with local fluctuations may eventually trigger a disproportionate response in hydrological extremes. This special issue focuses on observed extreme events in the recent past, how these extremes are linked to a changing global/regional climate, and the manner in which they may shift in the coming years.

The goal of this paper is to introduce the first clear-water scour model based on both the informational entropy concept and the principle of maximum entropy, showing that a variational approach is ideal for describing erosional processes under complex situations. The proposed bridge–pier scour entropic (BRISENT) model is capable of reproducing the main dynamics of scour depth evolution under steady hydraulic conditions, step-wise hydrographs, and flood waves. For the calibration process, 266 clear-water scour experiments from 20 precedent studies were considered, where the dimensionless parameters varied widely. Simple formulations are proposed to estimate BRISENT’s fitting coefficients, in which the ratio between pier-diameter and sediment-size was the most critical physical characteristic controlling scour model parametrization. A validation process considering highly unsteady and multi-peaked hydrographs was carried out, showing that the proposed BRISENT model reproduces scour evolution with high accuracy.

In this paper, considering time-averaged velocity as a random variable, two-dimensional (2D) velocity distributions in open-channel flow have been derived based on the Shannon entropy concept and the principle of maximum entropy. The velocity distributions so derived have limited practical use, since they contain too many parameters that need to be experimentally calibrated and hence are not convenient to apply. This work develops a new entropy-based approach for deriving a 2D velocity distribution in open-channel flow, thereby investigating a rectangular geometric domain. The derived distribution is parsimonious, and the values determined using the proposed distribution are found to be in good agreement with the experimentally-measured velocity values.