Two-dimensional Shallow Water Model Research Articles

Selection of urban flood shelter locations based on risk assessment

Within the framework of global climate change, there is a recurring occurrence of floods and waterlogging disasters, which pose significant risks to human lives and overall safety. The phenomenon of urbanization has led to an increased vulnerability of cities to flood disasters. Evacuation serves as a viable strategy for adapting to climate change, managing intense precipitation events, and mitigating the impact of flood disasters. Hence, the meticulous choice of shelters has emerged as a crucial element in enhancing the effectiveness of evacuations. Nevertheless, the process of choosing shelters sometimes neglects to consider the potential for flooding and has not undergone thorough testing. Hence, the objective of this research is to systematically choose shelters within the central metropolitan region, incorporate flood risk considerations into the shelter site model, and assist cities in mitigating the consequences of floods resulting from climate change. To begin with, employ a two-dimensional shallow water model in order to replicate instances of intense precipitation and produce data on flood inundation. Subsequently, the simulation results are utilized to assess the flood risk using the entropy weight approach. This risk is then incorporated into the multi-objective optimization model to determine the optimal shelter placement. Ultimately, the ABM model was employed to create a simulation of crowd evacuation in urban areas, confirming the efficacy of shelter selection and thoroughly examining the influence of various shelters on the efficiency of community emergency evacuation. The study's findings indicate that a total of 26 shelters were chosen within the study area using a multi-objective methodology, ensuring the inclusion of all affected populations. The utilization of multi-objective models in the selection of shelter places has been shown to enhance evacuation efficiency, as confirmed by the ABM model. The simulation findings indicate a decline in the population's death rate from 1.94% to 0.98%, an increase in the evacuation rate from 97.4% to 98.4%, and a reduction in the number of casualties by 133 individuals.

A Shallow-water Model Exploration of Atmospheric Circulation on Sub-Neptunes: Effects of Radiative Forcing and Rotation Period

Sub-Neptune-type exoplanets are abundant in our Galaxy yet have no solar system analogs. They exist in a broad range of stellar forcing and rotational regimes that are distinctly different from solar system planets and more commonly studied hot Jupiters. Here we present simulations that explore global atmospheric circulation of sub-Neptunes generated with a two-dimensional shallow-water model, SWAMPE. We explore the circulation regimes of synchronously rotating sub-Neptunes with a focus on the interaction of planetary rotation rate and radiative timescale in a variety of stellar insolations. In highly irradiated, short-timescale regimes, our models exhibit high day–night geopotential contrasts. As the timescales become longer, the geopotential contrasts and longitudinal variability decrease, while temporal variability increases. The transition from day-to-night flow to jet-dominated flow is primarily driven by the radiative timescale. Strong- and medium-forcing regimes exhibit transitions between day-to-night flow and jet-dominated flow at similar points in the parameter space. The weak-forcing regime differs owing to comparatively stronger rotational effects. Planetary rotation period dominates in determining equator-to-pole geopotential contrast. Our simulations exhibit higher time variability when either radiative timescale or rotation period is long.

Joint assimilation of satellite soil moisture and streamflow data for the hydrological application of a two-dimensional shallow water model

Data assimilation (DA) in physically-based hydrodynamic models is conditioned by the difference in temporal and spatial scales of the observed data and the resolution of the model itself. In order to use remote sensing data in small-scale hydrodynamic modelling, it is necessary to explore innovative DA methods that can lead to a more plausible representation of the spatial variability of the parameters and processes involved. In the present study, satellite-derived soil moisture and in situ-observed streamflow data were jointly assimilated into a high-resolution hydrological-hydrodynamic model based on the Iber software, using the Tempered Particle Filter (TPF) for the dual estimation of model state variables and parameters. Twelve storm events occurring in a 199 km2 catchment located in NW Spain were used for testing the proposed approach. A 3-step procedure was followed: (1) sensitivity analysis of the model parameters; (2) joint assimilation of soil moisture and discharge data to estimate correlations between observations and model parameters; (3) joint assimilation of soil moisture and discharge data using an initial set of particles and parameter standard deviations derived from prior information. The numerical model correctly reproduces the observed data, with an average Nash-Sutcliffe efficiency (NSE) value of 0.74 over the 12 events when the prior information is used. The approach described is shown to be most efficient with storm events that produce isolated peak discharges.

Monsoon Depression Amplification by Horizontal Shear and Humidity Gradients: A Shallow Water Perspective

Abstract Transient, synoptic-scale vortices produce a large fraction of total rainfall in most monsoon regions and are often associated with extreme precipitation. However, the mechanism of their amplification remains a topic of active research. For monsoon depressions, which are the most prominent synoptic-scale vortex in the Asian–Australian monsoon, recent work has suggested that meridional gradients in zonal wind in the vortex environment may produce growth through barotropic instability, while meridional gradients in environmental humidity have also been proposed to cause amplification through coupling with precipitating convection. Here, a two-dimensional shallow water model on a sphere with parameterized precipitation is used to examine the relative role played by these two environmental gradients. By systematically varying the meridional moisture gradient and meridional wind shear for both weak, quasi-linear waves and finite-amplitude isolated vortices, we show that rotational winds in the initial vortex are amplified most strongly by meridional shear of the environmental zonal wind, while vortex precipitation rates are most sensitive to environmental moisture gradients. The growth rate in the presence of both gradients is less than the sum of growth rates in the presence of isolated gradients, as the phase relation between moisture and vorticity anomalies becomes distorted with increasing shear. These results suggest that background meridional gradients in both zonal wind and environmental humidity can contribute to the amplification of vortices to monsoon depression strength, but with some degree of decoupling of the dry rotational flow and the moist convection.

Um modelo acoplado 2D-3D de bacia hidrográfica-lago com uma estrutura de processamento paralelo

ABSTRACT Modeling catchment-lake interactions is computationally demanding, usually requiring coupled numerical models and parallel processing capabilities. However, models with these requirements are still rare. In this paper, we developed a coupled 2D-3D model for lake catchments using a parallel scheme that leverages processing power of GPU and multiple CPUs. The model allows for hydrodynamic simulation applications considering diffuse water flows at the interface between the catchment and the lake. We coupled the Environmental Fluid Dynamics Code (EFDC) with a two-dimensional shallow water model and test it on the Peri Lake Catchment in southern Brazil. The results revealed the ability of the model simulate lake water levels as well as the diffuse inputs of water and solutes, providing the possibility of its use in lake and reservoir water management.

Performance of conservative and non-conservative two-dimensional shallow water models in wavy riverbed

The conservativeness, stability, and robustness of the numerical models applied in braided river systems is primarily influenced by morphological complexities adverse, flow pattern and the channel roughness. Two-dimensional flow modelling over an undulating bed profile is critical on account of the existence of subsequent wet-dry regions in the flow domain. This work provides the applicability of the conservative and non-conservative form of two-dimensional unsteady flow equations in braided river system. Both models are solved by TVD McCormack predictor corrector finite difference method and applied in the Brahmaputra River near Majuli Island, Assam India. The computed outputs are compared with the field observed results for validation. Results indicate a satisfactory agreement between the computed and measured value. Two statistical indices are used in the model performance evaluation.

Self-similar solutions of shallow water equations with porosity

Simulated free surface transients in periodic urban layouts have been reported to be self-similar in the space-time domain when averaged on the scale of the building period. Such self-similarity is incompatible with the head loss model formulae used in most porosity-based shallow water models. Verifying it experimentally is thus of salient importance. New dam-break flow laboratory experiments are reported, where two different configurations of idealized periodic buildings layouts are explored. A space-time analysis of the experimental water level fields validates the self-similar character of the flow. Simulating the experiment using the two-dimensional shallow water model also yields self-similar period-averaged flow solutions. Then, the Single Porosity (SP), Integral Porosity (IP) and Dual Integral Porosity (DIP) models are applied. Although all three models behave in a similar fashion when the storage and connectivity porosities are close to each other, the DIP model is the one that upscales best the refined 2D solution.

Hydraulic Modeling of Bridges in Two-Dimensional Shallow Water Models

Hydraulic Modeling of Bridges in Two-Dimensional Shallow Water Models

Assessment of pre-simulated scenarios as a non-structural measure for flood management in case of levee-breach inundations

Levee breach inundations can entail large flood losses due to the high concentration of exposed assets in levee-protected floodplains and, sometimes, to the inadequacy or absence of early warning systems for this type of events. Since real-time modelling is computationally expensive and presents several uncertainties, which might prevent obtaining a reasonably accurate forecast of the flood propagation, an alternative methodology for the prompt prediction of flooded area, maximum depths, and arrival times during a real event was proposed. The strategy is based on the use of a database of pre-simulated scenarios of levee-breach inundations, obtained adopting a high-resolution two-dimensional shallow water model. The paper aims at the a posteriori assessment of the usefulness of this strategy. To this end, the December 2020 event on the Panaro River (Italy) is thoroughly analyzed. In the study area, the strategy had already been implemented before the event, and pre-simulated scenarios were consulted during the emergency. Post-event observations are also available for the ex-post model validation. The database was obtained considering two inflow synthetic hydrographs and a discrete number of breach locations, and unavoidable differences between real events and hypothetical scenarios were to be expected. However, for this case study, the closest levee-breach scenario in the database (in terms of breach position and inflow) provided reliable predictions of flood extent and maximum depths for the actual inundation. The pre-simulated database also helped identifying some critical spots, where effective emergency operations (sandbagging) helped protecting an urban district during the event. As accurate real-time forecasts of levee-breach inundations are yet to come, a database of pre-simulated scenarios is proven as an effective “surrogate” method for civil protection purposes.

Performance of conservative and non-conservative two-dimensional shallow water models in wavy river bed

Performance of conservative and non-conservative two-dimensional shallow water models in wavy river bed

SW2D-GPU: A two-dimensional shallow water model accelerated by GPGPU

Shallow water models are used for simulating flood and lake hydrodynamics. However, the computational cost of those models is often high and require high performance computing. We present the SW2D-GPU: a two-dimensional shallow water model accelerated by General Purpose Graphics Processing Unit. The model is implemented in parallel using CUDA C/C++. We exemplify the use of the model with two case studies: (i) Flood simulation in an urban area and (ii) water level simulation in a lake catchment. We have included potential evaporation in the formulation which expands its application to water level simulations in lakes and reservoirs. The SW2D-GPU model is approximately 34 times faster than its equivalent sequential version. The model can be run in any computer equipped with a NVIDIA GPU. Integrated simulations of surface waters in lake watershed and simulations of floods caused by dam break are some of the potential applications.

Modelling Weirs in Two-Dimensional Shallow Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

Numerical Investigation of a Flash Flood Process that Occurred in Zhongdu River, Sichuan, China

In 2018, a flash flood occurred in the Zhongdu river, which lies in Yibin, Sichuan province of China. The flood caused many casualties and significant damage to people living nearby. Due to the difficulty in predicting where and when flash floods will happen, it is nearly impossible to set up monitors in advance to detect the floods in detail. Field investigations are usually carried out to study the flood propagation and disaster-causing mechanism after the flood’s happening. The field studies take the relic left by the flash flood to deduce the peak level, peak discharge, bed erosion, etc. and further revel the mechanism between water and sediment transport during the flash flood This kind of relic-based study will generate bigger errors in regions with great bed deformation. In this study, we come up with numerical simulations to investigate the flash flood that happened in the Zhongdu river. The simulations are based on two-dimensional shallow water models coupled with sediment transport and bed deformation models. Based on the real water level and discharge profile measured by a hydrometric station nearby, the numerical simulation reproduced the flash flood in the valley. The results show the flood coverage, water level variation, and velocity distribution during the flood. The simulation offers great help in studying the damage-causing process. Furthermore, simulations without considering sediment transport are also carried out to study the impact of bed erosion and sedimentation. The study proved that, without considering bed deformation, the flood may be greatly underestimated, and the sediment lying in the valley has great impact on flood power.

Nonlinear Shear Effects of the Secondary Current in the 2D Flow Analysis in Meandering Channels with Sharp Curvature

In order to analyze the shear effect of secondary currents on the flow structures in a meandering channel, this research developed a two-dimensional shallow water model, which included the dispersion stress term accounting for the shear effect in the vertical velocity profile. A new equation for the vertical velocity profile that included nonlinear shear effects was derived from the equation of motion in the meandering channel with sharp curvature. Using the experiment data obtained from large-scale meandering channels, the ratio of the depth over the radius-of-curvature was incorporated into the shear intensity of the secondary flow in the proposed equation. Comparisons with the experimental results by previous research showed that the computed values of the primary velocity distribution by the proposed model showed better fit with the observed data than the simulations with linear models and models without secondary flow consideration. The simulated results in the large-scale meandering channels demonstrated that simulations with the nonlinear secondary flow effect added into modeling gave higher accuracy, reducing the relative error by 19% in reproducing the skewed distributions of the primary flow in meandering channels, particularly in the regions where the effects from spiral motion were strong, due to sharp meanders.

Local-inertial shallow water model on unstructured triangular grids

Two-dimensional shallow water models are widely used for flood risk assessment. Application of these models to large-scale urban areas significantly increases the computational cost as it requires high-resolution simulations to capture the complex hydrodynamic processes. Hence, simplified models that are based on local-inertial formulations have been proposed by different researchers. Although these models are successful in simulating floods, their applications are limited by the use of structured grids and instability issues. Structured grids do not have the flexibility of providing different mesh resolutions to model the computational domain. Importantly, in the case of structured grids, the use of a single grid or the combination of finer and coarser grids inevitably increases the overall computational time. To overcome all these problems, an unstructured grid-based local-inertial model is developed. The performance of the model is rigorously evaluated by solving analytical test cases and simulating an urban flood in Glasgow, UK. Finally, the model is applied to simulate a catastrophic flood event that occurred in Chennai, India. The simulated water depths and inundation extents are compared with observed data or full-2D model results. The investigations show that the developed model has the potential for simulating floods on a large-scale with high-resolution grids at a comparatively lower computational cost than its predecessors for a similar range of accuracy.

Flood Simulation by a Well-Balanced Finite Volume Method in Tapi River Basin, Thailand, 2017

Flood simulation of a region in southern Thailand during January 2017 is presented in this work. The study area covers the Tapi river, the longest river in southern Thailand. The simulation is performed by applying the two-dimensional shallow water model in the presence of strong source terms to the local bottom topography. The model is solved numerically by our finite volume method with well-balanced property and linear reconstruction technique. This technique is accurate and efficient at solving for complex flows in the wet/dry interface problem. Measurements of flows are collected from two gauging stations in the area. The initial conditions are prepared to match the simulated flow to the measurements recorded at the gauging stations. The accuracy of the numerical simulations is demonstrated by comparing the simulated flood area to satellite images from the same period. The results are in good agreement, indicating the suitability of the shallow water model and the presented numerical method for simulating floodplain inundation.

Flux closures and source term models for shallow water models with depth-dependent integral porosity

Abstract A two-dimensional shallow water model with depth-dependent porosity is presented. The purpose is the coarse grid simulation of shallow flows over complex topographies and geometries. Two flux closures are examined: the Integral Porosity (IP) and Dual Integral Porosity (DIP) closures. Energy losses are described using a subgrid scale model that accounts for bottom and wall friction, transient momentum dissipation and energy losses induced by obstacle submersion. A complete wave propagation property analysis is provided for the IP and DIP closures, yielding more accurate numerical stability constraints than published previously. Five computational examples are presented, including transients in compound and meandering channels, urban dambreak problems with building submersion and runoff over variable microtopography. The ability of the model to deal with subgrid-scale features is confirmed. The DIP flux is shown to be superior to the IP closure. The transient dissipation term is essential in reproducing the effect of obstacles and microtopography. Distinguishing between the building wall- and building roof-induced friction is seen to be essential. The model is validated successfully against a scale model experimental dataset for the submersion of a coastal urban area by a tsunami wave.

Application of the 2D Depth-Averaged Model, FLATModel, to Pumiceous Debris Flows in the Amalfi Coast

Few studies about modelling pumice debris flows are available in literature. An integrated approach based on field surveys and numerical modelling is here proposed. A pumiceous debris flow, which occurred in the Amalfi Coast (Italy), is reconstructed by the numerical code, FLATModel, consisting of a two-dimensional shallow-water model written in curvilinear coordinates. The morphological evolution of the gully and of the alluvial fan was monitored by terrestrial laser scanner and photo-modelling aerial surveys, providing, in a cost-effective way, data otherwise unavailable, for the implementation, calibration and validation of the model. The most suitable resistance law is identified to be the Voellmy model, which is found capable of correctly describing the friction-collisional resistance mechanisms of pumiceous debris flows. The initial conditions of the numerical simulations are assumed to be of dam-break type: i.e., they are given by the sudden release of masses of pumice, whose shape and depths are obtained by reconstruction of the pre-event slopes. The predicted depths and shape of deposits are compared with the measured ones, where a good agreement (average error smaller than 10 cm) is observed for several dam-break scenarios. The proposed cost-effective integrated approach can be straightforwardly employed for the description of other debris flows of the same kind and for better designing risk mitigation measures.

Fast Simulation of Large-Scale Floods Based on GPU Parallel Computing

Computing speed is a significant issue of large-scale flood simulations for real-time response to disaster prevention and mitigation. Even today, most of the large-scale flood simulations are generally run on supercomputers due to the massive amounts of data and computations necessary. In this work, a two-dimensional shallow water model based on an unstructured Godunov-type finite volume scheme was proposed for flood simulation. To realize a fast simulation of large-scale floods on a personal computer, a Graphics Processing Unit (GPU)-based, high-performance computing method using the OpenACC application was adopted to parallelize the shallow water model. An unstructured data management method was presented to control the data transportation between the GPU and CPU (Central Processing Unit) with minimum overhead, and then both computation and data were offloaded from the CPU to the GPU, which exploited the computational capability of the GPU as much as possible. The parallel model was validated using various benchmarks and real-world case studies. The results demonstrate that speed-ups of up to one order of magnitude can be achieved in comparison with the serial model. The proposed parallel model provides a fast and reliable tool with which to quickly assess flood hazards in large-scale areas and, thus, has a bright application prospect for dynamic inundation risk identification and disaster assessment.

Preliminary Numerical Analysis of the Efficiency of a Central Lake Reservoir in Enhancing the Flood and Drought Resistance of Dongting Lake

During the past few decades, the ecosystems of lakes have been reshaped greatly by global climate change and expanding human activities. As the second largest freshwater lake in China, Dongting Lake is the most important regulating lake in the Yangtze River Basin because it has extensive flood storage capacity. The dynamic characteristics of its circulation and sediment transport are significantly affected by the scheduling and interception of control reservoirs at the upper reaches of the Yangtze River. In this paper, a central lake reservoir is proposed to improve the flood and drought resistance of Dongting Lake. The efficiency of the central lake reservoir is investigated numerically by developing a two-dimensional shallow water model. We demonstrate that current velocity and water elevation during flood and drought events can be influenced significantly by the construction of the central lake reservoir. The flood storage capacity of the central lake reservoir can reduce the peak flood elevation significantly in West Dongting Lake, which would enhance its flood resistance. The water replenishment of the central lake reservoir in the dry season can also efficiently increase the lake water elevation to enhance the drought resistance in the area surrounding the lake. Our findings have important implications for policy makers and their management of Dongting Lake.