Reply to comment by Lu et al. on “An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations”

This document addresses the comments raised by Lu et al. (2017). Lu et al. (2017) proposed an alternative numerical treatment for implementing the fully implicit friction discretization in Xia et al. (2017). The method by Lu et al. (2017) is also effective, but not necessarily easier to implement or more efficient. The numerical wiggles observed by Lu et al. (2017) do not affect the overall solution accuracy of the surface reconstruction method (SRM). SRM introduces an antidiffusion effect, which may also lead to more accurate numerical predictions than hydrostatic reconstruction (HR) but may be the cause of the numerical wiggles. As suggested by Lu et al. (2017), HR may perform equally well if fine enough grids are used, which has been investigated and recognized in the literature. However, the use of refined meshes in simulations will inevitably increase computational cost and the grid sizes as suggested are too small for real-world applications

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

Numerical models solving the full 2-D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large-scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2Haltwhistle Burn, UK

Efficient surface water flow simulation on static Cartesian grid with local refinement according to key topographic features

Aiming at improving the computational efficiency without accuracy losses for surface water flow simulation, this paper presents a structured but non-uniform grid system incorporated into a Godunov-type finite volume scheme. The proposed grid system can detect the key topographic features in the computational domain where high-resolution mesh is in need for reliably solving the shallow water equations. The mesh refinement is automatically carried out in these areas while the mesh in the rest of the domain remains coarse. The criterion determining the refinement is suggested by a dimensionless number with a fixed value of 0.2 after sensitivity analysis. Three laboratory and field-scale test cases are employed to demonstrate the performance of the model for flow simulations on the new non-uniform grids. In all of the tests, the grid system is shown to successfully generate high-resolution mesh only in those areas with abruptly changing topographic features that dominate the flooding processes. To produce numerical solutions of similar accuracy, the non-uniform grid based model is able to accelerate by about two times comparing with the fine uniform grid based counterpart

Hydrodynamic modelling of flow impact on structures under extreme flow conditions

Apart from the direct threat to human lives, the flood waves as a result of the rapid catchment response to intense rainfall, breaches of flood defences, tsunamis or storm surges may induce huge impact forces on structures, causing structural damage or even failures. Most existing design codes do not properly account for these impact forces due to the limited understanding of the underlying physical processes and the lack of reliable empirical formulae or numerical approaches to quantifying them. This paper presents laboratory experiments to better understand the interaction between the extreme flow hydrodynamics and the hydraulic structures and uses the measured data to validate a numerical model. The model solves the two-dimensional shallow water equations using a finite volume Godunov-type scheme for the reliable simulation of complex flow hydrodynamics. New model components are developed for estimating the hydrostatic and hydrodynamic pressure to quantify the flow impact on structures. The model is applied to reproduce two selected experiment tests with different settings and satisfactory numerical results are obtained, which confirms its predictive capability. The model will therefore provide a potential tool for wider and more flexible field-scale applications

Assessing slope forest effect on flood process caused by a short-duration storm in a small catchment

Land use has significant impact on the hydrologic and hydraulic processes in a catchment. This work applies a hydrodynamic based numerical model to quantitatively investigate the land use effect on the flood patterns under various rainfall and terrain conditions in an ideal V-shaped catchment and a realistic catchment, indicating the land use could considerably affect the rainfall-flood process and such effect varies with the catchment terrain, land use scenario and the rainfall events. The rainfall-flood process is less sensitive for the side slope than the channel slope. For a channel slope lower than the critical value in this work, the forest located in the middle of the catchment slope could most effectively attenuate the flood peak. When the channel slope is higher than the critical one, forest located in the downstream of the catchment could most significantly mitigate the peak discharge. Moreover, the attenuation effect becomes more obvious as the rainfall becomes heavier. The fragmentation of vegetation does not reduce the flood peak in a more obvious way, compared with the integral vegetation patterns with the same area proportion. The research can help more reasonably guide the land use plan related to flood risk

A coupled discrete element and depth-averaged model for dynamic simulation of flow-like landslides

Flow-like landslides commonly happen in mountainous areas and may threaten people's lives, damage their properties, and create negative impact on the environment. Computer modelling has become an effective tool to support landslide risk assessment and management. Models based on discrete element method (DEM) can capture micro-mechanical behaviour of soils, simulate large deformation and have been widely used for landslide simulations. However, these models are computationally too demanding for large-scale applications. On the other hand, depth-averaged models (DAM) have been well reported for simulation of flow-like landslides over large spatial domains due to its relatively high computational efficiency. To combine the advantages of both types of modelling approaches, this paper develops a novel landslide model by coupling a DEM model with a DAM for landslide simulation, in which the DEM component is employed to better simulate the complex landslide dynamics in the source area and the DAM is adopted to predict the predominantly convective movement in the runout and deposition zone. Finally, the new coupled landslide model is validated against several test cases, including a field-scale event. Satisfactory results have been obtained, demonstrating that the coupled model is able to reproduce the dynamic process of flow-like landslides

A coupled hydrodynamic and particle-tracking model for full-process simulation of nonpoint source pollutants

Nonpoint source (NPS) particulate pollutants are a major source of urban surface pollution. It is essential to better understand and model the dynamic process of NPS pollutants to inform the design of effective strategies for urban stormwater management and pollution control. This work presents a novel coupled hydrodynamic and particle-based model to simulate the full-process dynamics of NPS particulate pollutants from detachment, transport to deposition in urban areas. A particle-based approach is proposed to represent the physical processes of pollutant detachment and deposition. The transport of pollutant particles is simulated using a random-walk particle-tracking model, which can directly trace out the trajectories of individual particles and hence identify the pathways of pollutants. The new coupled hydrodynamic and particle-based stormwater quality model is successfully validated against several analytical and experimental test cases to demonstrate its capability in accurately simulating the full-process dynamics of NPS particulate pollutants in urban areas

A quantitative multi-hazard risk assessment framework for compound flooding considering hazard inter-dependencies and interactions

Multi-hazard risk assessment may provide comprehensive analysis of the impact of multiple hazards but still needs to resolve major challenges in three aspects: (1) proper consideration of hazard inter-dependency, (2) physically based modelling of hazard interactions, and (3) fully quantitative risk assessment to show the probability of loss. Compound flooding is a typical multi-hazard problem that involves the concurrence of multiple hazard drivers, e.g. heavy rainfall, extreme river flow, and storm surge. These hazard drivers may result from the same weather system and are thus statistically inter-dependent, physically overlayed and interacted in the same region. This paper aims to address the mentioned challenges and develop an integrated assessment framework to quantify compound flood risk. The framework is constructed based on the three typical components in disaster risk assessment, i.e. hazard, vulnerability and exposure analysis. In hazard analysis, joint probability and return period distributions of the three hazard drivers of compound flooding are estimated using Copula functions with hazard dependency analysis, which are then used to generate random multi-hazard events to drive a 2D high-performance hydrodynamic model to produce probabilistic inundation maps and frequency-inundation curves. Vulnerability and exposure analysis provides damage functions of the elements at risk, which are used to quantify multi-hazard risk with the frequency-inundation curves. The framework is applied in the Greater London and its downstream Thames estuary to demonstrate its capability to analyse hazard interactions and inter-dependencies to produce fully quantitative risk assessment results such as risk curves quantifying the probability of loss and risk maps illustrating the annual expected loss of residential buildings

Innovations towards the next generation of shallow flow models

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A deep learning technique-based automatic monitoring method for experimental urban road inundation

Reports indicate that high-cost, insecurity, and difficulty in complex environments hinder the traditional urban road inundation monitoring approach. This work proposed an automatic monitoring method for experimental urban road inundation based on the YOLOv2 deep learning framework. The proposed method is an affordable, secure, with high accuracy rates in urban road inundation evaluation. The automatic detection of experimental urban road inundation was carried out under both dry and wet conditions on roads in the study area with a scale of a few m2. The validation average accuracy rate of the model was high with 90.1% inundation detection, while its training average accuracy rate was 96.1%. This indicated that the model has effective performance with high detection accuracy and recognition ability. Besides, the inundated water area of the experimental inundation region and the real road inundation region in the images was computed, showing that the relative errors of the measured area and the computed area were less than 20%. The results indicated that the proposed method can provide reliable inundation area evaluation. Therefore, our findings provide an effective guide in the management of urban floods and urban flood-warning, as well as systematic validation data for hydrologic and hydrodynamic models