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Dynamical models for calculating snow avalanche motion have gained growingimportance in recent years for avalanche hazard assessment. Nevertheless, inherentuncertainties in their input-data specification, although well acknowledged, areusually not explicitly incorporated into the analysis and considered in the mappingresults. In particular, the estimate of avalanche release conditions is affected bystrong uncertainties when associated to a return period. These sources of error arenormally addressed through sensitivity analysis or conservative parameters estimate.However, each of these approaches has limitations in assessing the statistical implications of uncertainties. In the present paper the problem of release scenarios randomness is looked at following a Monte Carlo procedure. This statistical sampling-analysis method allows the evaluation of the probability distributions of relevant variables for avalanche hazard assessment – such as runout distance and impact pressure – once the release variables – essentially releasedepth and release length – are expressed in terms of probability distributions, accounting explicitly for inherent uncertainties in their definition. Both the theoretical framework of this procedure and its application to a real study case are presented. As initial step of this research in the present work the attention is mainly focused on flowing avalanches descending on open slopes. Therefore, the one-dimensional version of VARA dynamic models is usedfor avalanche simulations.

A mathematical model is applied to simulate two debris flows occurred in 1997 and 1998 in Italian Alpine valleys. The flows caused a casualty and significant damages to buildings and roads. The model considers a two-phase mixture of coarse sediments and interstitial fluid. The concentration of the finer solid fraction in the interstitial fluid is assumed to be negligible, so that this fluid acts as clean water. Assuming that the solids and the interstitial fluid move downstream with the same velocity, the flow of the mixture is described using a two dimensional depth averaged model with a unique 2D momentum equation and two mass balance equations for the mixture and the sediments, respectively. Erosion and deposition rates are computed with a modified version of the relationship developed by Egashira-Ashida. Differential equations are integrated with an upwind explicit finite-difference scheme. The total discharge hydrograph at the upstream sections of the alluvial fans was estimated by assuming equilibrium solid concentration values.

Debris flow is modelled using the equations governing the dynamics of a liquid-solid mixture. An upwind finite volume scheme is applied to solve the resulting differential equations in one dimension. These equations have a structure similar to those of the monophasic water flow, differing from them by the presence of some terms characteristic of the bifasic nature of the mixture, such as granular bed erosion velocity, sediment concentration, bed shear stress, etc. The model and the system of equations to be solved are presented with the description of the implementation of the upwind scheme for the resulting hyperbolic conservation system. The numerical method is first order in both space and time. The treatment of the source terms is specified in detail and some comparison with laboratory experiments are presented.

The simulation of the unsteady free-surface flow on infiltrating surfaces has many hydrological applications, including the study of overland flow, soil erosion and conservation, surface irrigation and contaminant transportation. The surface runoff is strictly connected to the infiltration through the soil surface; so, an independent simulation of the two processes, although very often adopted, may be unrealistic. This paper presents a mathematical model for simulating these interdependent surface and subsurface processes. The model is based on the two-dimensional shallow water equations, coupled with the one-dimensional Richards equation. These equations are integrated jointly, following the MacCormack scheme, which is an explicit, finite-difference scheme, accurate to the second order. The model can simulate initially dry surface conditions and variable initial soil water content, and can deal with space-variable characteristics (slope, roughness and soil hydraulic properties). The accuracy of the model is tested by comparing its results with analytical solutions and with experimental data. Finally, a numerical experiment carried out on a simple hypothetical catchment, both using the complete model and a simplified version, in which the Richards equation and the shallow water equations are solved in cascade, is discussed.

A mathematical model is used to interpret border irrigation tests carried out on plots sown with clover and maize, in order to evaluate the influence of the roughness coefficient compared with the parameters describing the hydraulic properties of the soil. The model simulates the surface runoff by integrating the unsteady motion equations of a gradually varied free surface flow according to a finite difference scheme of explicit type. In the momentum equation the convective inertia term is ignored. The infiltration is schematized through the physically based equation of Green and Ampt. Preliminary validation of the model is made on the basis of field data available in the literature. Border irrigation tests were carried out on 40 and 100 m long plots and measurements were made of advance times of the wave front and surface runoff volumes. The initial conditions were defined by measurement of the soil water content just before watering. The changes of the ground cover and the decrease of porosity along the soil profile owing to ploughing and to the formation of a plough sole are found to exert an important influence on the runoff. The sensitivity analysis of the model, carried out taking into account the wave front celerity, the discharge hydrograph at the end of the plot and the outflow volume, confirms the prevailing influence of roughness coefficient and natural hydraulic conductivity compared with the wetting front suction. According to the single-parameter perturbation technique, decreasing the values of roughness coefficient and hydraulic conductivity individually, compared with the calibration values, increases the computed outflow volumes by nearly 400% compared with experimentally measured outflows. Copyright 1995, 1999 Academic Press

A method for the evaluation of adequacy, distribution and application efficiencies of border irrigation is proposed. A mathematical model for the simulation of surface runoff and infiltration is applied in order to analyse the waterings carried out according to traditional practice in the lower Po valley and according to systematic, full and deficit irrigation, on plots cropped with clover ley and spring maize. In the application of the model, it is assumed that the water stored in the root zone may be identified with the readily available water. The computations make it possible to analyse the traditional parameters and to find their optimal values for a selected adequacy, i.e. for a selected percentage of the length-of-run adequately irrigated. The model shows that the traditional practice causes an over-irrigation and that significant water savings of nearly 11% may be made in comparison with the experimental values.