Modelling Sediment Transport in the disastrous Flash Flood of November 2017 in Mandra (Attica, Greece)

<p> </p><p><strong>Abstract</strong></p><p>The flash flood in Mandra on the 15<sup>th</sup> of November 2017 was the third most disastrous “November” flood in Attica; it was characterized by heavy sediment and debris transport that can be easily observed in Figure 1.</p><p>We applied the Hydrologic Engineering Center's-River Analysis System (HEC-RAS) to model sediment transport using the Ackers-White sediment transport equation that is engraved in HEC-RAS to analyze sediment transport characteristics. The required input data were based on a limited number of available studies, which mainly include a survey performed by the Hellenic Centre for Marine Research in the coastal area of the Elefsis Bay where sediments were deposited after the catastrophic event. We compared the results of the model with calculations performed within a previous Thesis in 2018 using TELEMAC-2D and SISYPHE.</p><p>The present paper is based on the Diploma Thesis of the first author; it was performed within the project “National Network on Climate Change and its Impacts (CLIMPACT)” of the General Secretariat of Research and Technology.</p><p> </p><p><img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gepj.5d3d3b91860061319301161/sdaolpUECMynit/12UGE&app=m&a=0&c=bc7fbb3ecf180060dec33436ebc2faea&ct=x&pn=gepj.elif&d=1" alt=""></p><p>Figure 1. The greater area of Mandra (a) before and (b) after the flood event</p>

Solving the erosion transport equation on three dimensional catchments

<p>Modeling the kinematic wave equation and sediment transport equation enables a deterministic approach for predicting surface runoff and resulting sediment transport. Both the kinematic wave equation and the sediment transport equation are first order differential equations. Moreover the kinematic wave equation is a quasilinear problem. In many engineering applications this set of equations is solved on one-dimensional representative cross-sections. However, a proper selection of representative cross-section(s) is  cumbersome. On the other hand integrating this set of equations on real catchment topography  yields difficulties for standard variational methods such as continous Galerkin method. These difficulties are two-fold (1) the nonlinearity of the kinematic wave, and (2) the absence of diffusion term, which acts as a stabilization term for convection-diffusion equation. In a theory, the Peclet number of numerical stability reaches infinity. </p><p>In this contribution we will focus on a stable numerical approximation of this convection-only problem using least square method. With this method we are able to reliably solve both the kinematic wave equation and the sediment transport equation on computational  domains representing real catchment topography. Several examples representing real-world scenarios will be given.</p>

Finite volume scheme for numerical simulation of the sediment transport model

In this paper, we propose and apply a modified Rusanov scheme for numerical solution of the sediment transport model in one and two dimensions. This model consists of two parts, the first part is modeled by shallow water equations and the second part is described by the bed-load transport equation. The scheme consists of a predictor stage scheme including a local parameter of control. It is responsible for the numerical diffusion. To control this parameter, we use a strategy depending on limiter theory. In the corrector stage, we used special treatment of the bed to get a well-balanced discretization between the flux gradient and source term. Some numerical results are presented for the sediment transport equation in two forms called A-formulation and C-formulation. These results show that the finite volume scheme is accurate and robust for solving the sediment transport equation in one and two dimensions.

Robustness Analysis of Model Parameters for Sediment Transport Equation Development

Robustness analysis of model parameters for sediment transport equation development is carried out using 256 hydraulics and sediment data from twelve Malaysian rivers. The model parameters used in the analyses include parameters in equations by Ackers-White, Brownlie, Engelund-Hansen, Graf, Molinas-Wu, Karim-Kennedy, Yang, Ariffin and Sinnakaudan. Seven parameters in five parameter classes were initially tested. Robustness of the model parameters was measured on the statistical relations through Evolutionary Polynomial Regression (EPR) technique and further examined using the discrepancy ratio of the predicted versus the measured values. Results from analyses suggest (ratio of shear velocity to flow velocity) and (ratio of hydraulic radius to mean sediment diameter) to be the most significant and influential parameters for the development of sediment transport equation.

River Model Calibration Based on Design of Experiments Theory. A Case Study: Meta River, Colombia

Numerical models are important tools for analyzing and solving water resources problems; however, a model’s reliability heavily depends on its calibration. This paper presents a method based on Design of Experiments theory for calibrating numerical models of rivers by considering the interaction between different calibration parameters, identifying the most sensitive parameters and finding a value or a range of values for which the calibration parameters produces an adequate performance of the model in terms of accuracy. The method consists of a systematic process for assessing the qualitative and quantitative performance of a hydromorphological numeric model. A 75 km reach of the Meta River, in Colombia, was used as case study for validating the method. The modeling was conducted by using the software package MIKE-21C, a two-dimensional flow model. The calibration is assessed by means of an Overall Weighted Indicator, based on the coefficient of determination of the calibration parameters and within a range from 0 to 1. For the case study, the most significant calibration parameters were the sediment transport equation, the riverbed load factor and the suspended load factor. The optimal calibration produced an Overall Weighted Indicator equal to 0.857. The method can be applied to any type of morphological models.

A simple non-equilibrium bedload transport equation for the formation of dune in a shallowwater flow over an erodible bed

In this work, we consider the long-standing problem of capturing dune formation in an erodible-bed channel at subcritical speed by using a reduced order model of depth-averaged equations. The pioneering study by Reynolds [1] showed that the standard Saint-Venant-Exner equations are unconditionally stable at subcritical Froude number. Hence, the use of depthaveraged flow equations, which are commonly used by the hydraulic community, prevents the formation of bedforms as dunes. Recently, Cañada-Pereira & Bohorquez [2] have proposed a simple sediment transport formulation able to capture the formation of dune when coupled with the Saint-Venant equations. We replace the standard Exner equation with a non-equilibrium sediment transport equation that includes the following necessary ingredients: first, a phase shift in the particle entrainment rate; second, a particle diffusivity and an eddy viscosity. Subsequently, we solve the linear stability problem of an erodiblebed channel and show that the neutral curve properly captures the bed instability both in subcritical regime (i.e. dune) and supercritical flow (i.e. antidune and roll wave). Finally, we corroborate the capabilities of the model by means of non-linear numerical simulations which reproduce the growth of dune and antidune in agreement with experiments.

A New Approach to Model Numerically the Nonlinear Wave Propagation

In order to model nonlinear breaking waves with moving boundary and coastal sandbar migration; we presented a morphodynamic model, where hydrodynamic equations (free surface flows) and sediment transport equation are solved in a coupled manner. The originality lies in the development of an innovative approach, in which, we project the horizontal velocity onto a basis functions depending only on the variable z and we calculate analytically the vertical velocity and the nonhydrostatic pressure. The choice of basis depends on the problem under consideration. This model is numerically stable because there is no mesh in the vertical direction. This model is accurate because we can directly introduce functions that best fits the physical nature of the flow. Our model is validated through laboratory measurements carried out by Dingemans [1994, J. Comput. Phys. 231, 328–344], Cox and Kobayashi [2000, J. Geophys. Res. 105(c6), 223–236. and Dette et al. [2002, Coast. Eng. 47, 137–177].

Determination of Correlation Parameters of Near-Bed Sediment Flux

It is difficult to solve the near-bed sediment flux of suspended sediment transport equation under the non-equilibrium condition by theory analysis and numerical calculation. There are many variances, empirical coefficients and expressions undetermined. Bed shear stress is active methods to determine near-bed sediment flux. By comparing and analyzing of the research achievements, this paper provided the parameters spans, formulas of the variances and their correlations for determining the sediment flux, in the hope of promoting the sediment research.

The Erosion Analysis of the Muddy Tidal Flat Profile in Cangzhou City of Hebei Province

In order to analysis the variation and characteristic of the muddy tidal flat, this article provided the modified sediment transport equation (MSTE). It was proved to be true after verifying the measured data of 2000 and 2007 in the field, and it could be used to simulation calculation the muddy tidal flat. The results of study showed that the slope of the muddy tidal flat was increasing as 0.0020‰ / a from 1987 to 2010. It was eroded slowly, which was lower as 0.021‰ / a of the slope above the department of 0 m contour line. In the meantime, the slope was eroded increased as 0.022‰ / a of the slope below the department of 0 m contour line. It still below the equilibrium state of tidal flat in study area, and the slope would be further eroded steeply. The study results were very important on the protection of muddy tidal flat, and would provide practical reference on management and development in the near future.

MODELLING INFILTRATION ON GRAVEL BEACHES WITH AN XBEACH VARIANT

Coarse-grained beaches are particularly prevalent in the UK, composed of accumulations of either gravel, or mixed sand and gravel sediments. Understanding and predicting their morphological behaviour in response to short-term and long-term forcing has been the subject of recent research. Despite the focus on sandy beaches, it is important to understand that the balance of processes that govern different behaviour between sandy and gravel beaches. In this study we show how a public domain numerical model, XBeach, developed for sandy environments (Roelvink et al., 2009) can be modified for use in predicting the cross-shore profile changes of gravel beaches. Improvements investigated here include: use of Lagrangian interpretation of velocity in place of Eulerian for driving sediment movement; incorporation of Packwood’s (1983) pragmatic model of infiltration in the unsaturated area of the swash region; introducing of new morphological module based upon Soulsby’s (1997) sediment transport equation for waves and currents. These changes are suggested in order to significantly improve the application of this model to gravel beaches, especially with regard to swash velocity asymmetry which is responsible for development of the steep accretionary phase steep berm above waterline. The results from the model agree well with the measured experimental data and improve upon the results presented by Pedrozo-Acuña et al. (2006).