Quantitative flood hazard assessment methods: A review

Flood hazard assessment is a fundamental step in flood risk mapping. Quantitative assessment requires hydrodynamic modelling of the flooding process in order to calculate the spatial distribution of suitable flood hazard indicators representative of flooding intensity and frequency, hence its potential to result in harm. Flood hazard indicators are usually defined by combining relevant flooding parameters, mainly flood depth and flow velocity, but also flooding arrival time, flooding duration, sediment or contamination load, and so forth. A flood hazard classification is commonly introduced to assign a hazard level to areas potentially subject to flooding. This article presents a systematic review of quantitative methods proposed in the scientific literature or prescribed by government authorities to assess the hazard associated with natural or anthropic flooding. Flood hazard classification methods are listed and compared by specifying their underlying approach (heuristic, conceptual, empirical), the exposed element which they were designed for (people, buildings, vehicles, etc.), and their fields of application (river overflow, dam-break, levee breach, debris flow). Perspectives and future challenges in quantitative flood hazard analysis are also discussed. This review aims to help modellers and practitioners to select the most suitable flood hazard assessment method for the case study of interest

Hydraulic hazard mapping in alpine dam break prone areas: the Cancano dam case

Dam-break hazard assessment is of great importance in the Italian Alps, where a large number of medium and large reservoirs are present in valleys that are characterized by widespread urbanized zones on alluvial fans and along valley floors. Accordingly, there is the need to identify specific operative approaches in order to quantify hydraulic hazard which in mountain regions inevitably differ from the ones typically used in flat flood-prone areas. These approaches take advantage of: 1) specific numerical algorithms to pre-process the massive topographic information generally needed to describe very irregular bathymetries; 2) an appropriate mathematical model coupled with a robust numerical method which can deal in an effective way with variable geometries like the ones typical of natural alpine rivers; 3) suitable criteria for the hydraulic hazard assessment; 4) representative test cases to verify the accuracy of the overall procedure. This contribution presents some preliminary results obtained in the development of this complex toolkit, showing its application to the test case of the Cancano dam-break, for which the results from a physical model are available. This case was studied in 1943 by De Marchi, who investigated the consequences of the potential collapse of the Cancano dam in Northern Italy as a possible war target during the World War II. Although dated, the resulting report (De Marchi, 1945) is very interesting, since it mixes in a synergistic way theoretical, experimental and numerical considerations. In particular, the laboratory data set concerning the dam-break wave propagation along the valley between the Cancano dam and the village of Cepina provides an useful benchmark for testing the predictive effectiveness of mathematical and numerical models in mountain applications. Here we suggest an overall approach based on the 1D shallow water equations that proved particularly effective for studying dam-break wave propagation in alpine valleys, although this kind of problems is naturally subject to "substantial uncertainties and unavoidable arbitrarinesses" (translation from De Marchi, 1945). The equations are solved by means of a shock-capturing finite volume method involving the Pavia Flux Predictor (PFP) scheme proposed by Braschi and Gallati (1992). The comparison between numerical results and experimental data confirms that the mathematical model adopted is capable of capturing the main engineering aspects of the phenomenon modeled by De Marchi

The propagation of gravity currents in a circular cross-section channel: experiments and theory

High-Reynolds number gravity currents (GC) in a horizontal channel with circular/semicircular side walls are investigated by comparing experimental data and shallow-water (SW) theoretical results. We focus attention on a Boussinesq system (salt water in fresh water): the denser fluid, occupying part of the depth or the full depth of the ambient fluid which fills the remaining part of the channel, is initially at rest in a lock separated by a gate from the downstream channel. Upon the rapid removal of the gate (‘dam break’), the denser ‘current’ begins propagating into the downstream channel, while a significant adjustment motion propagates upstream in the lock as a bore or rarefaction wave. Using an experimental channel provided by a tube of 19 cm diameter and up to 615 cm length, which could be filled to various levels, we investigated both full-depth and part-depth releases, considered the various stages of inertial-buoyancy propagation (in particular, the initial ‘slumping’ with constant speed, and the transition to the late self-similar propagation with time to the power 3=4), and detected the transition to the viscous-buoyancy regime. A first series of tests is focused on the motion in the lock while a second series of tests is focused on the evolution of the downstream current. The speed of propagation of the current in the slumping stage is overpredicted by the theory, by about the same amount (typically 15 %) as observed in the classical flat bottom case. The length of transition to viscous regime turns out to be TRe0.h0=x0/U (Re0 D .g0h0/1=2h0= c is the initial Reynolds number, g0 is the reduced gravity, c is the kinematic viscosity of the denser fluid, h0 and x0 are the height of the denser current and the length of the lock, respectively), with the theoretical D3=8 and experimental 0:27

Extension of the Galilean-Invariant Formulation of Bernoulli's Equation

Bernoulli’s equation is a famous, elegant fluid mechanics relation that, in its most popular version, relates pressure, velocity, and elevation changes along each streamline in a steady barotropic inviscid flow. Despite its simplicity and restrictive assumptions, this equation is a powerful and effective analysis tool in a variety of real-flow situations. However, the Bernoulli equation is unfortunately not Galilean-invariant, i.e., it does not satisfy the desirable property of remaining unchanged under a Galilean transformation between two inertial reference frames reciprocally moving with constant velocity. In a previous paper, the author presented a Galilean-invariant formulation of the Bernoulli equation, in which a new term is introduced in the definition of the Bernoulli constant. In the present technical note, this Galilean-invariant form of the Bernoulli relation is extended to (1) unsteady flow, (2) compressible flow, and (3) a noninertial frame of reference accelerating with constant rectilinear acceleration. Similar extensions are consolidated for the classic Bernoulli equation and treated in fundamental fluid mechanics textbooks. The use of the updated Galilean-invariant Bernoulli equation in these less-restrictive contexts is illustrated with typical engineering application examples. The results demonstrate that the extended version of the Bernoulli principle can also be applied along the same flow lines in a reference frame moving with constant velocity relative to another reference frame in which the conventional Bernoulli equation is valid, provided that the Bernoulli constant includes a suitable additional term

Analysis of the water surface profiles of spatially varied flow with increasing discharge using the method of singular points

Spatially varied flows with increasing discharge can be encountered in several hydraulic systems. The analysis of water surface profiles in such flow conditions is useful for the verification and design of these systems. In this paper, a comprehensive analysis of the possible flow profiles in non-prismatic trapezoidal channels is performed using the method of singular points, by taking into account bed slope and friction. Different cases are identified depending on whether singular points occur or not along the collecting channel. It is verified that a singular point can be of the saddle, nodal, or spiral type, and that two singular points may occur in special circumstances. Furthermore, water depth profiles may be non-monotonic, showing a minimum or a maximum. The method is applied to both a theoretical example and three experimental tests taken from the literature, and to a real-field case concerning the side spillway channel of a dam

New formulation of the two-dimensional steep-slope shallow water equations. Part II: Numerical modeling, validation, and application

Numerical models based on the two-dimensional (2D) shallow water equations (SWE) are commonly used for flood hazard assessment, although the basic assumption of small bottom slopes is not always strictly satisfied, such as in mountain areas. When terrain slopes are large, the steep-slope shallow water equations (SSSWE) are theoretically more suitable because the restrictive hypothesis of small bottom slopes is not introduced in deriving these equations. A new formulation of the 2D SSSWE, in which the water depth is measured in the vertical direction, and the flow velocity is assumed parallel to the bottom surface, is proposed in the companion paper (Part I). The pressure distribution on the vertical is assumed linear (yet non-hydrostatic), and the effect of flow curvature is neglected. In this paper, the new SSSWE are solved with an explicit MUSCL-type second-order accurate finite volume scheme using the centered FORCE method for flux evaluation. The SSSWE model is validated against existing experimental data of one-dimensional (1D) dam-break flows on sloping channels with fixed slopes. The numerical results of the SSSWE and SWE models are compared both in this benchmark test case and in other numerical tests, including a 1D dam-break flow moving on an adverse slope, a 2D dam-break flow spreading on an inclined plane, and a 2D dam-break flow propagating in a sloping parabolic channel. Finally, the two models are applied to the real-field test case of the Cancano dam (Adda River, northern Italy), which is characterized by very steep and irregular topography, especially in the upper portion of the valley. The results show that, on the whole, the SSSWE are more accurate in describing dam-break flows over steep topographies than the conventional SWE and predict less severe flooding with slower wave propagation. The two models are practically equivalent when bottom slopes are relatively small

Three-Dimensional Numerical Modelling of Real-Field Dam-Break Flows: Review and Recent Advances

Numerical modelling is a valuable and effective tool for predicting the dynamics of the inundation caused by the failure of a dam or dyke, thereby assisting in mapping the areas potentially subject to flooding and evaluating the associated flood hazard. This paper systematically reviews literature studies adopting three-dimensional hydrodynamic models for the simulation of large-scale dam-break flooding on irregular real-world topography. Governing equations and numerical methods are analysed, as well as recent advances in numerical techniques, modelling accuracy, and computational efficiency. The dam-break case studies used for model validation are highlighted. The advantages and limitations of the three-dimensional dam-break models are compared with those of the commonly used two-dimensional depth-averaged ones. This review mainly aims at informing researchers and modellers interested in numerical modelling of dam-break flow over real-world topography on recent advances and developments in three-dimensional hydrodynamic models so that they can better direct their future research. Practitioners can find in this review an overview of available three-dimensional codes (research, commercial, freeware, and open-source) and indications for choosing the most suitable numerical method for the application of interest

New formulation of the two-dimensional steep-slope shallow water equations. Part I: Theory and analysis

Two-dimensional (2D) depth-averaged shallow water equations (SWE) are widely used to model unsteady free surface flows, such as flooding processes, including those due to dam-break or levee breach. However, the basic hypothesis of small bottom slopes may be far from satisfied in certain practical circumstances, both locally at geometric singularities and even in wide portions of the floodable area, such as in mountain regions. In these cases, the classic 2D SWE might provide inaccurate results, and the steep-slope shallow water equations (SSSWE), in which the restriction of small bottom slopes is relaxed, are a valid alternative modeling option. However, different 2D formulations of this set of equations can be found in the geophysical flow literature, in both global horizontally-oriented and local bottom-oriented coordinate systems. In this paper, a new SSSWE model is presented in which water depth is defined along the vertical direction and flow velocity is assumed parallel to the bottom surface. This choice of the dependent variables combines the advantages of considering the flow velocity parallel to the bottom, as can be expected in gradually varied shallow flow, and handling vertical water depths consistent with elevation data, usually available as digital terrain models. The pressure distribution is assumed linear along the vertical direction and flow curvature effects are neglected. A new formulation of the 2D depth-averaged SSSWE is derived, in which the two dynamic equations represent momentum balances along two spatial directions parallel to the bottom, whose horizontal projections are parallel to two fixed orthogonal coordinate directions. The analysis of the mathematical properties of the new SSSWE equations shows that they are strictly hyperbolic for wet bed conditions and reduce to the conventional 2D SWE when bottom slopes are small. Finally, it is shown that the SSSWE predict a slower flow compared with the conventional SWE in the theoretical case of a 1D dam-break on a frictionless channel with fixed slope. The capabilities of the proposed model are demonstrated in a companion paper on the basis of numerical and experimental tests

3D CFD analysis of the performance of oblique and composite side weirs in converging channels

Conventional rectangular side weirs installed along prismatic open-channels may have low efficiency. One practical way to overcome this problem may be to insert the weir in the oblique side of a converging channel. In this paper, the performance of oblique straight side weirs or two-segment single-cranked side weirs inserted in rectangular converging channels are analysed through 3D computational fluid dynamics (CFD) for subcritical steady flow conditions. The numerical simulations were performed through a widely available software package by applying the VOF method to the Reynolds-averaged Navier–Stokes equations and adopting the Reynolds stress model for turbulence closure. The model is validated against experimental data previously obtained by the authors. The results provide insight into the features of the flow field and show the effect of the channel contraction rate on diversion efficiency. As regards the two-segment single-cranked weir, the “concave” arrangement has been verified as being more efficient than the “convex” one

Probabilistic Flood Hazard Mapping Considering Multiple Levee Breaches

Probabilistic methods are widely adopted for residual flood hazard assessment in flood-prone areas protected by levees. Such methods can consider various sources of uncertainty, including breach location and flood event characteristics, and allow for the quantification of the result confidence. However, the possible occurrence of multiple levee breaches during the same flood event is usually disregarded. This paper presents a probabilistic method based on levee fragility functions and basic probability rules to estimate the probability of selected breach scenarios, including multiple breaching events. The flood hazard classification is based on inundation variables calculated for flood events of different return periods. A combined 1D-2D hydrodynamic model is used for flood simulations. Probabilistic inundation extent maps and probabilistic flood hazard level maps are then created. Finally, probabilistic flood hazard estimates are summarized in a map of a suitable central tendency of the hazard level, coupled with a map of the Shannon entropy as uncertainty indicator. This pair of statistical maps provides concise and effective information on design flood hazard along with the associated uncertainty. The method was applied to a region located along the middle reach of the Po River (northern Italy). Similar central flood hazard estimates are obtained for the two sets of breaching events including or not multiple breaches. Considering multiple breaches led to higher uncertainty in central hazard level assessment. This result highlights the importance of considering multiple breaching events in flood risk management