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Research on Mathematical Models of Floods
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Research on Mathematical Models of Floods

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydrology".

Deadline for manuscript submissions: closed (31 August 2020) | Viewed by 44389

Special Issue Editors

Prof. Dr. Paolo Mignosa

E-Mail Website
Guest Editor
Department of Engineering and Architecture, Università degli Studi di Parma, 43121 Parma, Italy
Interests: mathematical models of floods; shallow water equations; dam break; hydraulic structures
Dr. Renato Vacondio

E-Mail Website
Guest Editor
Department of Engineering and Architecture, Università degli Studi di Parma, Parma 43121, Italy
Interests: Shallow water equations, Navier–Stokes equations, Smoothed particle hydrodynamics, Finite-volume schemes, Fluid–structure interaction, Urban porosity, Dam breach, GPU parallelization
Prof. Dr. Marco D’Oria

E-Mail Website
Guest Editor
Department of Engineering and Architecture, University of Parma, 43121 Parma, Italy
Interests: inverse problems in surface hydrology; hydraulics and groundwater modeling; impacts of climate change on meteorological variables and water resources
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, flood frequencies and flooding damage appear to be increasing, with worsening social and economic impacts. The development and application of mathematical models capable to predict floods are therfore essential for their management.

Models that solve the two-dimensional Shallow Water Equations (2D-SWE) on structured or unstructured grids have become nowadays a common tool, but there are still some challenges that have to be faced to obtain fast and accurate solutions for flood covering vaste areas. Some of them are the following:

  • Reduce the computational time even with high-resolution meshes: efforts have been made to increase the performance of models through MPI techniques or GPU parallelization, but there is still room for improvements on this topic;
  • Levee breaching modelization: coupling sub-models to simulate levee breaching due to overtopping or even piping in 2D-SWE models can increase the applicability of these models to real-world hazard mapping preparation;
  • Flood propagation in urban areas: there is a lot of work in this direction, for example in the analysis of urban areas through the porosity approach;
  • Applications to inverse problems: 2D-SWE start to be applied to solve inverse problems in surface hydrology, and this requires fast and stable models;
  • Simulation of structures: structures which interfere with floods (bridges, culverts, etc.) are often modeled as pure 1D internal b.c., despite their 2D (or even 3D) behavoiur;
  • Coupling hydrologic and hydraulic models to produce accurate and fast real-time forecasts of flood propagation;
  • Sediment transport models related to flood propagation;
  • Damage models to quantitatively assess the damages generated by floods in urban and agricultural areas;
  • Flood risk modification generated by climate change.
  • ……

Researchers working on these topics or on other topics dealing with 2D-SWE models are invited to contribute to this Special Issue.

Prof. Dr. Paolo Mignosa
Dr. Renato Vacondio
Dr. Marco D’Oria
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Water is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Floods
  • Shallow Water Equations
  • Urban floods
  • Dam break
  • Levee breaching
  • Inverse problems in surface hydrology
  • Hazard maps
  • GPU acceleration

Published Papers (10 papers)

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Research

20 pages, 7002 KiB  
Article
Application of HEC-RAS (2D) for Flood Hazard Maps Generation for Yesil (Ishim) River in Kazakhstan
by Nurlan Ongdas, Farida Akiyanova, Yergali Karakulov, Altynay Muratbayeva and Nurlybek Zinabdin
Water 2020, 12(10), 2672; https://doi.org/10.3390/w12102672 - 24 Sep 2020
Cited by 61 | Viewed by 8218
Abstract
The use of hydraulic models for carrying out flood simulations is a common practice globally. The current study used HEC-RAS (2D) in order to simulate different flood scenarios on the River Yesil (Ishim). Comparison of different mesh sizes (25, 50 and 75 m) [...] Read more.
The use of hydraulic models for carrying out flood simulations is a common practice globally. The current study used HEC-RAS (2D) in order to simulate different flood scenarios on the River Yesil (Ishim). Comparison of different mesh sizes (25, 50 and 75 m) indicated no significant difference in model performance. However, a significant difference was observed in simulation time. In addition, the inclusion of breaklines showed that there was a slight improvement in model performance and a shortening of the simulation time. Sensitivity analysis and the consequent manual calibration of sensitive parameters resulted in a slight improvement (an increase in the model accuracy from 58.4% for uncalibrated to 59.7% for calibrated). Following the simulations inundation maps for 10-, 20- and 100-year flood events were obtained. Hazard classification of the flood extents generated indicated that the settlements of Zhibek Zholy and Arnasay were flooded in all the simulated events. Volgodonovka village experienced flooding when a 100-year flood event was simulated. On the other hand, settlement No. 42 did not experience any flooding in any of the scenarios. The model results also demonstrate that the Counter-Regulator was not overtopped in the event of the 100-year hydrograph. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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20 pages, 6849 KiB  
Article
Performances of the New HEC-RAS Version 5 for 2-D Hydrodynamic-Based Rainfall-Runoff Simulations at Basin Scale: Comparison with a State-of-the Art Model
by Pierfranco Costabile, Carmelina Costanzo, Domenico Ferraro, Francesco Macchione and Gabriella Petaccia
Water 2020, 12(9), 2326; https://doi.org/10.3390/w12092326 - 19 Aug 2020
Cited by 57 | Viewed by 8093
Abstract
The Hydrologic Engineering Centre-River Analysis System (HEC-RAS), developed by the US Army Corps of Engineers, is one of the most known, analyzed and used model for flood mapping both in the scientific literature and in practice. In the recently released version (release 5.0.7), [...] Read more.
The Hydrologic Engineering Centre-River Analysis System (HEC-RAS), developed by the US Army Corps of Engineers, is one of the most known, analyzed and used model for flood mapping both in the scientific literature and in practice. In the recently released version (release 5.0.7), the HEC-RAS model has been enriched with novel modules, performing fully 2-D computations based on the 2-D fully dynamic equations as well as the 2-D diffusion wave equations; moreover the application of rainfall to each cell of the two-dimensional domain is now possible. Contrarily to the common applications for flood propagation in river reach, this specific module has never been analyzed in the literature. Therefore, the main purpose of this work is to assess the potential and the capabilities of the 2-D HEC-RAS model in rainfall-runoff simulations at the basin scale, comparing the results obtained using both the options (fully dynamic equations and diffusion wave equations) to the simulations obtained by using a 2-D fully dynamic model developed by the authors for research purposes. Both models have been tested in a small basin in Northern Italy to analyze the differences in terms of discharge hydrographs and flooded areas. The application of a criterion for hazard class mapping has shown significant variations between the two models. These results provide practical indications for the water engineering community in the innovative research field related to the use of 2-D SWEs at the basin scale. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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18 pages, 15342 KiB  
Article
Efficient Urban Inundation Model for Live Flood Forecasting with Cellular Automata and Motion Cost Fields
by Maikel Issermann, Fi-John Chang and Haifeng Jia
Water 2020, 12(7), 1997; https://doi.org/10.3390/w12071997 - 14 Jul 2020
Cited by 7 | Viewed by 2619
Abstract
The mitigation of societal damage from urban floods requires fast hydraulic models for emergency and planning purposes. The simplified mathematical model Cellular Automata is combined with Motion Cost fields, which score the difficulty to traverse an area, to the urban inundation model CAMC. [...] Read more.
The mitigation of societal damage from urban floods requires fast hydraulic models for emergency and planning purposes. The simplified mathematical model Cellular Automata is combined with Motion Cost fields, which score the difficulty to traverse an area, to the urban inundation model CAMC. It is implemented with simple matrix and logic operations to achieve high computational efficiency. The development concentrated on an application in dense urban built-up areas with numerous buildings. CAMC is efficient and flexible enough to be used in a “live” urban flood warning system with current weather conditions. A case study is conducted in the German city of Wuppertal with about 12,000 buildings. The water depth estimation of every time step are visualized in a web-interface on the basis of the virtual globe NASA WorldWind. CAMC is compared with the shallow water equations-based model ANUGA. CAMC is approximatively 5 times faster than ANUGA at high spatial resolution and able to maintain numerical stability. The Nash-Sutcliffe coefficient (0.61), Root Mean Square Error (0.39 m) and Index of Agreement (0.65) indicate acceptable agreement for water depth estimation but identify different areas where important deviations occur. The estimation of velocity performs considerably less well (0.34 for Nash-Sutcliffe coefficient, 0.13 ms − 1 for Root Mean Square Error, and 0.39 for Index of Agreement) because CA ignores momentum conservation. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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22 pages, 3858 KiB  
Article
Optimal Operation of Complex Flood Control System Composed of Cascade Reservoirs, Navigation-Power Junctions, and Flood Storage Areas
by Di Zhu, Yadong Mei, Xinfa Xu, Junhong Chen and Yue Ben
Water 2020, 12(7), 1883; https://doi.org/10.3390/w12071883 - 01 Jul 2020
Cited by 8 | Viewed by 2319
Abstract
As more and more water projects are built on rivers, the flood control operation becomes more complex. Studies on the optimal flood control operation are very important to safeguard human life and property. This study focused on optimizing the operation of a complex [...] Read more.
As more and more water projects are built on rivers, the flood control operation becomes more complex. Studies on the optimal flood control operation are very important to safeguard human life and property. This study focused on optimizing the operation of a complex flood control system composed of cascade reservoirs, navigation-power junctions, flood storage areas, and flood control points. An optimal model was established to jointly maximize flood peak reduction rates of downstream flood control points. A hybrid algorithm named the Dynamic Programming-Progressive Optimality Algorithm (DP-POA) was used to solve this model, and the middle and lower reaches of the Ganjiang River were selected as a case study. The results show that flood reduction at three downstream flood control points ranged from 1080 to 5359 m3/s for designed floods with different return periods, which increased by about 333~1498 m3/s in comparison with the conventional operation. Considering that the maximum water level of reservoirs using DP-POA and the conventional operation is the same, this indicated that DP-POA can make full use of the reservoirs’ flood control storage to reduce downstream flood peaks. In addition, the flood diversion volume of the flood storage area using DP-POA ranged from 0.33 × 108 to 1.79 × 108 m3 for designed floods with 200-year, 300-year, and 500-year return periods, which is smaller than that using the conventional operation. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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17 pages, 4728 KiB  
Article
Multipurpose Use of Artificial Channel Networks for Flood Risk Reduction: The Case of the Waterway Padova–Venice (Italy)
by Riccardo Alvise Mel, Daniele Pietro Viero, Luca Carniello and Luigi D’Alpaos
Water 2020, 12(6), 1609; https://doi.org/10.3390/w12061609 - 05 Jun 2020
Cited by 11 | Viewed by 3551
Abstract
Many rivers are increasingly threatened by extreme floods, and effective strategies for flood risk mitigation are difficult to pursue, especially in highly urbanized areas. A flexible and multipurpose use of the complex networks of artificial channels that typically cross these regions can play [...] Read more.
Many rivers are increasingly threatened by extreme floods, and effective strategies for flood risk mitigation are difficult to pursue, especially in highly urbanized areas. A flexible and multipurpose use of the complex networks of artificial channels that typically cross these regions can play a role in flood risk mitigation. A relevant example concerns the possible completion of a waterway from Padova to the Venice Lagoon, in North-Eastern Italy. Once completed, the waterway can boost shipping (which is considerably more climate and environment friendly than road transport), can lead to a urban re-composition of the territory and, serving as a diversion canal for the Brenta River, can reduce hydraulic hazard as well. The goal of the present work was to assess this last point. To this purpose, the 2DEF hydrodynamic model was used to reproduce the complex Brenta–Bacchiglione river network. This network includes river reaches, diversion canals, bed sills, pump stations, and control structures that assures the proper operation of the system in case of flood events. The mixed Eulerian–Lagrangian, semi-implicit formulation of the model provided accurate and computationally efficient results for subcritical regimes. The model results showed that the waterway can divert a significant part of the Brenta floodwaters toward the Venice Lagoon, thus reducing flood hazard in the Brenta River downstream of Padova. The benefits also extend to the Bacchiglione River, whose floodwaters can be diverted into the Brenta River through an existing flood canal; indeed, the waterway withdrawal produces a drawdown profile in the Brenta River that allows diverting larger flow rates from the Bacchiglione River as well. Finally, by conveying the sediment-laden floodwaters of the Brenta River within the Venice Lagoon, the waterway could contribute to counteract the generalized erosion affecting the lagoon. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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19 pages, 5504 KiB  
Article
An Assessment of the Influence of Uncertainty in Temporally Evolving Streamflow Forecasts on Riverine Inundation Modeling
by Youcan Feng, David R. Judi and Cynthia L. Rakowski
Water 2020, 12(3), 911; https://doi.org/10.3390/w12030911 - 23 Mar 2020
Viewed by 2369
Abstract
Continental-scale river forecasting platforms forecast streamflow at reaches that can be used as boundary conditions to drive a local-scale flood inundation model. Uncertainty accumulated during this process stems not only from any part of the forecasting chain but can also be caused by [...] Read more.
Continental-scale river forecasting platforms forecast streamflow at reaches that can be used as boundary conditions to drive a local-scale flood inundation model. Uncertainty accumulated during this process stems not only from any part of the forecasting chain but can also be caused by the daily variations in weather forcing that keeps evolving as the event advances. This work aims to examine the influence of the evolving forecast streamflow on predicting the maximum inundation for extreme floods. A diagnostic case study was made on the basis of a hindcast of Hurricane Matthew striking the eastern U.S. in 2016. The U.S. National Water Model was one-way coupled to a hydrodynamic inundation model through a developed automated workflow. Although the river forcing has significantly mismatched hydrographs versus observations, the simulated peak water surface elevations and maximum extents were validated to be comparable with the observations, which indicates that the inundation model may not be sensitive to the inherited uncertainty from the weather forcing. Moreover, the uncertainty of the forecast streamflow time series caused only one order of magnitude fewer variations in inundation prediction; this dampening effect may become clearer for extreme events with large areas inundated. In addition, the forecast total volume of stream discharge appears to be an important metric for assessing the performance of river forcing for inundation mapping, as a linear correlation between the total volume and the accuracy of the predicted peak water surface elevation and maximum extent was found, with the coefficients of determination all above 0.8. Extra best-practice experience of running similar operational tasks demonstrated the tradeoff between the cost and accuracy gain. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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27 pages, 16460 KiB  
Article
A GPU-Accelerated Shallow-Water Scheme for Surface Runoff Simulations
by Francesca Aureli, Federico Prost, Renato Vacondio, Susanna Dazzi and Alessia Ferrari
Water 2020, 12(3), 637; https://doi.org/10.3390/w12030637 - 26 Feb 2020
Cited by 26 | Viewed by 4336
Abstract
The capability of a GPU-parallelized numerical scheme to perform accurate and fast simulations of surface runoff in watersheds, exploiting high-resolution digital elevation models (DEMs), was investigated. The numerical computations were carried out by using an explicit finite volume numerical scheme and adopting a [...] Read more.
The capability of a GPU-parallelized numerical scheme to perform accurate and fast simulations of surface runoff in watersheds, exploiting high-resolution digital elevation models (DEMs), was investigated. The numerical computations were carried out by using an explicit finite volume numerical scheme and adopting a recent type of grid called Block-Uniform Quadtree (BUQ), capable of exploiting the computational power of GPUs with negligible overhead. Moreover, stability and zero mass error were ensured, even in the presence of very shallow water depth, by introducing a proper reconstruction of conserved variables at cell interfaces, a specific formulation of the slope source term and an explicit discretization of the friction source term. The 2D shallow water model was tested against two different literature tests and a real event that recently occurred in Italy for which field data is available. The influence of the spatial resolution adopted in different portions of the domain was also investigated for the last test. The achieved low ratio of simulation to physical times, in some cases less than 1:20, opens new perspectives for flood management strategies. Based on the result of such models, emergency plans can be designed in order to achieve a significant reduction in the economic losses generated by flood events. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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14 pages, 3073 KiB  
Article
Risk Analysis of Earth-Rock Dam Breach Based on Dynamic Bayesian Network
by Zongkun Li, Te Wang, Wei Ge, Dong Wei and Hanyu Li
Water 2019, 11(11), 2305; https://doi.org/10.3390/w11112305 - 03 Nov 2019
Cited by 34 | Viewed by 3848
Abstract
Despite the fact that the Bayesian network has great advantages in logical reasoning and calculation compared with the other traditional risk analysis methods, there are still obvious shortcomings in the study of dynamic risk. The risk factors of the earth-rock dam breach are [...] Read more.
Despite the fact that the Bayesian network has great advantages in logical reasoning and calculation compared with the other traditional risk analysis methods, there are still obvious shortcomings in the study of dynamic risk. The risk factors of the earth-rock dam breach are complex, which vary with time during the operation period. Static risk analysis, limited to a specific period of time, cannot meet the needs of comprehensive assessment and early warning. By introducing time factors, a dynamic Bayesian network model was established to study the dynamic characteristics of dam-breach probability. Combined with the calculation of the conditional probability of nodes based on the Leaky Noisy-Or gate extended model, the reasoning results of Bayesian networks were modified by updating the data of different time nodes. Taking an earth-rock dam as an example, the results show that it has less possibility to breach and keep stable along the time axis. Moreover, the factors with vulnerability and instability were found effective, which could provide guidance for dam risk management. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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12 pages, 1317 KiB  
Article
Risk Evaluation Model of Life Loss Caused by Dam-Break Flood and Its Application
by Wei Li, Zongkun Li, Wei Ge and Sai Wu
Water 2019, 11(7), 1359; https://doi.org/10.3390/w11071359 - 30 Jun 2019
Cited by 27 | Viewed by 3879
Abstract
The internal mechanism affecting life loss caused by a dam-break flood is complicated. On the basis of analyzing the risk formation path, a risk evaluation indicator system was established which included the hazards, exposure and vulnerability factors. Variable Fuzzy Sets theory was introduced [...] Read more.
The internal mechanism affecting life loss caused by a dam-break flood is complicated. On the basis of analyzing the risk formation path, a risk evaluation indicator system was established which included the hazards, exposure and vulnerability factors. Variable Fuzzy Sets theory was introduced into the risk evaluation of life loss risk grades and applied to eight collapsed dams in China. According to the sequence of the risk grades of these dams, the evaluation result was mainly consistent with the actual mortality ranking sequence, showing that the model could be effectively applied to the risk evaluation of life loss in dam-break events. Aimed at the problem of large differences in the downstream population distribution of dams in China, this manuscript suggested that 10,000 people should be the basis for the grouping operation of dams in the risk evaluation. These Variable Fuzzy evaluation models and grouping suggestions could help stakeholders to allocate the funds for dam reinforcement more accurately and provide a scientific basis for the study of dam-break life loss and dam risk management. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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11 pages, 2037 KiB  
Article
Improved Set Pair Analysis and Its Application to Environmental Impact Evaluation of Dam Break
by Meimei Wu, Wei Ge, Zongkun Li, Zening Wu, Hexiang Zhang, Juanjuan Li and Yipeng Pan
Water 2019, 11(4), 821; https://doi.org/10.3390/w11040821 - 19 Apr 2019
Cited by 46 | Viewed by 4113
Abstract
Despite the rapid development of risk analysis in dam engineering, there is a relative absence of research on the environmental impact of dam break. As a systematic theory, set pair analysis has a good effect in dealing with uncertainties, although the result is [...] Read more.
Despite the rapid development of risk analysis in dam engineering, there is a relative absence of research on the environmental impact of dam break. As a systematic theory, set pair analysis has a good effect in dealing with uncertainties, although the result is relatively rough and easy to distort. A connection degree of five grades and a generalized set of potential are introduced to improve traditional set pair analysis. Combined with the index system, the evaluation model of the environmental impact of dam break is established, which is based on generalized set pair analysis. Taking Sheheji Reservoir dam as an example, a comparison of evaluation results of fuzzy mathematics theory and generalized set pair analysis is made, which verifies the scientificity and practicability of the method proposed in this paper. The results show that the evaluation grade of the environmental impact of dam break at Sheheji Reservoir is serious, and appropriate management measures should be taken to reduce the risk. Full article
(This article belongs to the Special Issue Research on Mathematical Models of Floods)
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