Kinematic Wave Research Articles

Monitoring and Modelling Fluxes of Water and Nutrients to Surface Drainage Network From Irrigated Agricultural Fields in a Hydraulically Reclaimed Coastal Area

ABSTRACTThis paper describes the application of a physically based agrohydrological model (named FLOWS), coupled with a kinematic wave approach model (named KWV) for water and solute runoff routing, for interpreting the fate of water and nutrients coming from cultivated fields to surface drainage network located in ‘Piana del Sassu’ in the Arborea plain, a hydraulically reclaimed area with shallow groundwater. Modelling was supported by a large complex database on soil, groundwater and surface drainage water, which was used for establishing the boundary conditions for simulations, as well as for calibrating and validating the model. The model FLOWS provided the water and nutrient fluxes to the surface water, which were passed to the KWV model for their routing along the elementary fields in the experimental area and from these to the ditches and finally to the drainage channel. The modelling approach effectively predicted the water and solute distribution along the soil profile, as well as the losses of water and nutrients to the surface water. The results showed a significant amount of water and dissolved nutrients to flow quickly from the soil uppermost layer to the surface drainage network during both the irrigation season and during rainfall events. During irrigation applications, losses were mostly due to rainfall intensity exceeding the maximum infiltration velocity of the shallow soil layer in the case of sprinkler irrigation and to subsurface lateral drainage in the case of exceeding irrigation water provided by drip irrigation. This makes the Sassu plain a significant contributor of nutrients (nitrate and phosphorus) to the surface water. Consequently, even though the agricultural activities might not be an important issue for the groundwater vulnerability, the management of water and nutrients should be significantly improved to avoid ecohydrological threats to the important coastal water bodies present in the area.

Random fractional kinematic wave equations of overland flow: The HPM solutions and applications

This paper presents new findings from analyses of a random fractional kinematic wave equation (rfKWE) for overland flow. The rfKWE is featured with orders of temporal and spatial fractional derivatives and with the roughness parameter, the effective rainfall intensity and infiltration rate as random variables. The new solutions are derived with the aid of a numerical method named the homotopy perturbation method (HPM) and approximate solutions are presented for different situations. The solutions are evaluated with data from overland flow flumes with simulated rainfall in the laboratory. The results suggest that on an infiltrating surface the temporal nonlocality of overland flow represented by the temporal order of fractional derivatives diminishes over time while the spatial nonlocality manifested by the spatial order of fractional derivatives continue if there is overland flow. It shows that the widely used unit discharge-height relationship is a special case of the solution of the rfKWE. Procedures are demonstrated for determining the fractional roughness coefficient, nf, the order of spatial fractional derivative, ρ, and the steady-state infiltration rate during the overland flow, As. The analyses of the data show that the mean spatial order of fractional derivative is ρ=1.25, the mean flow pattern parameter m=1.50, and the mean fractional roughness coefficient is nf=0.002 which is smaller than the conventional roughness coefficient, n=0.108. With these average values of the parameters and their standard deviations, simulations were performed to demonstrate the use of the methods, which is also a comparison of the classic KWE and rfKWE models.

A Lagrangian approach for variable speed limit implementation in C-ITS framework

With the development of Cooperative-Intelligent Transport System (C-ITS) technologies, new strategies based on embedded technologies have emerged to manage road networks. This paper focuses on adapting to this connectivity context a Variable Speed Limit (VSL) system to detect shockwaves and anticipate their propagation based on the kinematic wave theory to dampen them. We provide an alternative framework to adapt the VSL strategy, well-suited for Eulerian approaches, into a Lagrangian context. While the Eulerian approach is based on Loop Detector (LD) and macroscopic traffic indicators (e.g. flow, density), our Lagrangian approach relies on Road Side Units (RSUs) that record the GPS traces shared by Connected Vehicles (CVs). Based on the combination of CV trajectories, Fundamental and Space-Time Diagrams theory, shockwave estimation and prediction processes directly operate on congestion waves, which release the estimation issue for traffic density. The simulation-based analysis reveals that the performance of the Lagrangian approach is comparable to the Eulerian configurations.

Car-following model based on spatial expectation effect in connected vehicle environment: modeling, stability analysis and identification

In driving situations, if drivers have advanced access to downstream traffic conditions ahead of time, they may modify their driving behavior accordingly. This proactive approach can help reduce frequent acceleration and deceleration of vehicles and minimize traffic congestion. This paper considers the average headway of downstream vehicles to predict the traffic conditions of downstream roads. Based on the full velocity difference (FVD) model, we propose a car-following model that incorporates spatial expectation effect (SEFVD). Firstly, a linear stability analysis is performed on the SEFVD model, and the results indicate that the critical value of the SEFVD model is relatively small, and the stabilization region increases gradually with the number of vehicles downstream. Secondly, employing perturbation amplitudes on a virtual circular road, a numerical simulation of the SEFVD model is carried out and compared with the FVD model. The results demonstrate that the SEFVD model has the ability to suppress the formation of traffic oscillations and stabilize vehicle formation more quickly. Simulation results for the 11 cars starting from a traffic signal indicate that the delay time and kinematic wave speed of the SEFVD model are within reasonable limits. To evaluate the changes in energy use, we also carried out energy consumption experiments. The experimental findings show that the SEFVD model uses less energy compared to the FVD model. Finally, the parameters of the models are calibrated and verified by using NGSIM data. The total calibration error of the SEFVD model (m = 2) decreases by 42.97% compared to the FVD model, and the total validation error decreases by 29.3%. The results show that the proposed model can fit the actual data well, and the fitting error is smaller.

The impact of pulsating parameters on particle dynamics in vertical pipe during hydraulic conveying with pulsating inlet flow

This paper presents a numerical investigation of the hydraulic conveying performance of coarse particles with the inlet pulsating fluid velocity in a vertical pipe. The influence of pulsating parameters, in terms of pulsating amplitudes and frequencies, on hydraulic conveying is mainly considered. The pulsations of particle and slip velocity are as periodic and regular as the inlet pulsating velocity. The variation of the normalized force in one pulsating time cycle is also analyzed. Then the laws of particle group distribution with transient time and vertical distance are obtained: the plug phenomenon is more obvious at the larger pulsating amplitude, further leading to pipe blockage, while a larger pulsating frequency is beneficial to the weakening of the plugs. Particle relaxation time is introduced to explain the changes in particle group distribution. Additionally, the temporal variations of flow fields are also used to illustrate the propagation of kinematic waves.

Physics-informed neural network for solution of forward and inverse kinematic wave problems

The one-dimensional kinematic wave (KW) model (KWM) is widely used in surface water and water quality hydrology as well as for modeling the movement of traffic on long highways. The KW model involves a first-order nonlinear partial differential equation which is solved numerically for realistic geometric representation, input, and initial and boundary conditions. This paper developed a method to solve the partial differential equation using a neural network structure, called the physics-informed neural network (PINN). The PINN was applied to solve the one-dimensional nonlinear KWM for forward and inverse problems. To enhance the accuracy and convergence and to suppress the spurious oscillation at the steep front, a technique with redistributed collocation points as an improved algorithm of PINN was employed. To deal with the fractional order of the nonlinear advection term, a stop-gradient technique was proposed. For validation, the KWM for steady and unsteady overland flow, and open channel flow without lateral inflow was analyzed for the forward problem. For the inverse problem, the unknown Manning coefficient was correctly computed, demonstrating the capability of the proposed algorithm for the identification of KWM parameters.

A new kinematic wave model that describes lateral subsurface flow and percolation in hillslopes

Kinematic wave (KW) models are commonly used for flood forecasting in large river basins, but have limitations in their ability to simulate percolation effects. Here, we suggest an extended KW model wherein the vertical pressure head is under non-hydrostatic conditions. The proposed model uses the Brooks Corey and Mualem models to estimate the water retention curve and unsaturated hydraulic conductivity and adopts the pressure head gradient as a new variable to calculate runoff based on changing water content distributions over time due to percolation. The increase in the pressure head gradient with rainfall infiltration is determined from the relationship between water storage and pressure head distribution, while the decrease in pressure head gradient due to percolation is modeled as exponential decay with time. A comparison of the proposed KW model and a numerical solution of the Richards equation shows that the proposed KW model can reproduce the storage effect caused by percolation, delaying runoff and reducing peak discharge. The agreement between the proposed KW model and the Richards equation is high for soils with high water retention. Conversely, the agreement becomes lower for soil with low water retention or deep soil layer thickness, where the complexity of water content distribution requires further refinement. The proposed model can easily be incorporated into distributed models while low computational cost with keeping the important percolation effects.

Simulating event-based pesticide transport with runoff and erosion; OpenLISEM-pesticide v.1

This study presents a novel pesticide transport module for the OpenLISEM runoff and erosion model. During water erosion events, high amounts of pesticides can be transported alongside the runoff. Simulating this process helps to mitigate adverse effects of pesticides in the environment. We conceptualized pesticide uptake during runoff with a mixing-layer, including mass transfer of dissolved pesticides into the runoff water and detachment in combination with enrichment of sorbed pesticides. Lateral transport of pesticides is modelled with a kinematic wave based on the overland flow of water. The model simulations were in line with observations for two events in a small agricultural catchment in South-Limburg, the Netherlands. A sensitivity analysis showed that pesticide transport was mainly influenced by the mass transfer rate, the soil-water partitioning and the exponent for the enrichment ratio. The accurate simulation of runoff and erosion by OpenLISEM, enables OpenLISEM-pesticide to simulate transport and redistribution adequately.

Macropore flow in relation to the geometry and topology of soil macropore networks: Re-visiting the kinematic wave equation

The rapid flow of water through soil macropores significantly affects the partitioning of precipitation between surface runoff and infiltration and also the rate of solute transport in soil, both of which have an impact on the risk of contamination of surface water and groundwater. The kinematic wave equation is often employed as a model of gravity-driven water flow through soil macropores. The exponent in this simple model influences the pore water velocity attained in the macropores at any given input rate and is usually estimated by inverse modelling against measured flow rates or water contents. In theory, the exponent in the kinematic wave equation should depend on the geometry and topology of the conducting macropore networks, although these relationships have not so far been investigated. In this study, we related metrics of soil structure derived from X-ray images to values of the kinematic exponent estimated from drainage experiments on twenty-two columns sampled at three different field sites under two contrasting land uses and at three different depths.We found that smaller values of the exponent in the kinematic wave equation, which would equate to more rapid flow of water through soil macropores, were found in plough pan and subsoil columns of smaller macroporosity, for which biopores comprised a significant fraction. The macroporosity in these columns was more vertically oriented and poorly inter-connected, though still continuous across the sample. In contrast, topsoil columns from both arable land and grassland had better connected, denser and more isotropically-distributed macropore networks and larger values of the kinematic exponent. Our results suggest that for predictive modelling at large scales, it may be feasible to estimate the kinematic exponent using class pedotransfer functions based on pedological information such as land use and horizon type.

Element Free Galerkin (EFG) Formulation in Solving Kinematic Wave Equation for Hydrological Modelling

Meshfree methods such as Element Free Galerkin Method (EFG) are the cutting edge of numerical methods as it does not require user to perform meshing which often is time consuming and tedious. The method being "meshfree" for the user can theoretically generate more accurate models which follow more complex boundary conditions such as natural rivers etc. The time saving and potential of higher accuracy in modelling makes EFG formulation an interesting research topic. EFG formulation is used to solve kinematic wave equations which is detailed in this paper. Galerkin weighted residual method using EFG’s shape function parameters is used to discretize the partial differential equation (PDE) of kinematic wave equations. To discretize the equations, a forward difference scheme is used for temporal discretization and Picard direct substitution method is employed to solve the nonlinear system at each time step. The formulations are validated by making a comparison between well-established numerical techniques against actual recorded datasets. After which it is found that EFG method agrees with conventional established techniques, thus validating the formulations as useful. To further investigate the usefulness of this formulation, an optimal performance study was also conducted to determine the most optimal shape function parameters. The optimal shape function values improved the performance to where it was found that established methods such as FDM were surpassed and on par with FEM. This shows that EFG is a good alternative for hydrological modelling.

Flood Routing in Rivers by Numerical Modeling Preissmann Scheme, Saint-venant Equation and Muskingum’s Method Based on Kinematic Wave Model

Flood Routing in Rivers by Numerical Modeling Preissmann Scheme, Saint-venant Equation and Muskingum’s Method Based on Kinematic Wave Model

Parameter Estimation Using the Inverse Problem Method for Simulating Lateral Inflow and Runoff Depth in a small catchment of Amazon.

The inverse problem method can be applied to determine the properties of hydrological phenomena and estimate the parameters, which cannot be measured directly. This type of inverse focus can facilitate the implementation of the kinematic wave model (direct model-DM), to fill gaps for lateral inflow rate and runoff depth in watersheds. Thus, the goal of the study was the application of the inverse problem method (IP). The lateral inflow rate was generally obtained as a Fourier transform to represent any watersheds. The study was developed using a small catchment in the Amazon where intense rainfall events occur, producing runoff and sediments, which affect rural populations. Lateral inflow rate and runoff depth were derived using precipitation data and parameters estimated through the KINEROS2 (K2)/direct model (DM) model and the ensuing solution methods with MCMC (Markov chains Monte Carlo)/Fourier transform. The developed method was applied to four rainfall-runoff events, leading to a good fit between the observed and predicted data (Nash-Sutcliffe coefficients between 0.76 and 0.85 and RMSE values between 1.80 mm and 6.72 mm).

Three-dimensional X-ray imaging of macropore flow

Macropores are known to be important pathways for the rapid transport of water, solutes and colloids in soil. Nevertheless, we still know very little about how the topology and geometry of macropore networks govern water flow configurations and velocities in natural soil. In this study, we aimed at gaining more insight into macropore flow by using X-ray tomography to quantify air–water distributions in the macropore networks of undisturbed topsoil and subsoil columns of a clay soil at varying steady-state flow rates. We observed that while large fractions of the macropore network remained air-filled, the air phase only became entrapped when the irrigation rate was very close to the saturated hydraulic conductivity of the soil. The data enabled us to parameterize a kinematic wave model for water flow following the approach proposed in Jarvis et al. (2017a). Follow-up experiments would be required to evaluate whether these kinematic wave parameters derived by X-ray imaging match with those obtained from outflow measurements. We found that quantitative X-ray imaging of macropore flow through soils still remains a challenging task. We recommend that future experiments are conducted on smaller soil samples to improve image resolution and minimize experimental time spans as well as X-ray image noise and illumination bias. Such experiments could also include 3-D tracer imaging to identify the imaged macropore networks transporting most of the water (i.e. the backbone) at varying steady irrigation rates.

Coupling water, solute, and sediment transport into a new computationally efficient hydrologic model

While surface–subsurface interactions strongly impact water quality and quantity in ecosystems, only relatively little attention has been given to solute mass transfers at this boundary. The KINEROS2 (K2) model solves the 1D kinematic wave equation for water flow and the advection–dispersion equation for non-absorbing solute (or sediment) transport at the surface, whereas the HYDRUS-1D (H1D) model solves the Richards equation for flow and the advection–dispersion equation for solute transport in the subsurface. We previously coupled water flow in the surface and subsurface environments using the K2 and H1D models (H1D-K2). Herein, an innovative framework was developed to additionally couple solute transport at the surface–subsurface boundary in the simple, accurate, and computationally efficient H1D-K2 model. To test the H1D-K2 model’s accuracy and robustness, simulation results are compared to analytical solutions, experimental data, and results from the two-dimensional HYDRUS-2D (H2D) code. The relative differences in water and solute balance components between the H2D and H1D-K2 models are less than 1% for homogeneous cases and 4% for heterogeneous cases. The simulated hydrograph and chemograph are almost identical for the two models. Furthermore, simulated Bromide (Br) concentration in runoff is in good agreement with observations. The proposed model also accurately reproduces soil erosion under different rainfall patterns and intensities.

Analytical Solution of Kinematic Wave Equation for Overland Flow due to Storms Moving at a Velocity Lower than Flow Velocity

Analytical Solution of Kinematic Wave Equation for Overland Flow due to Storms Moving at a Velocity Lower than Flow Velocity

Kinematic analyses of wave–packet structures in non-isothermal jet flows: Effects of length scales

A kinematic wave–packet sound-source model is developed for non-isothermal jets based on large eddy simulation results of subsonic jets at temperature ratios 0.86, 1.0, and 2.7. To find the suitable variable for the sound-source model, coherent structures in these jets are extracted by leading modes of the proper orthogonal decomposition (POD), and they are classified according to spatial–temporal features. To extend the model, an approach is proposed to represent the growth and decay length scales separately by a single continuous function. Applying such function, the acoustic affections are discussed for the variable length scales of amplitude envelope, L, and coherence, Lc. The results show that the jet temperature desynchronizes the leading POD modes of radial velocity, pressure, and density, and the jet temperature changes the density mode from radial puffs into stripes or ridges. The axisymmetric component of the pressure clearly presents a train of radiant waves, as captured by its leading spectral-POD mode at the peak radiation frequency. Therefore, this pressure component is employed for modeling. In the wave-number domain, the elongation of L stretches the cross-spectral density (CSD) of the source signal, denoted by CSD(k1, k2), along the k1- and k2-axes; the decay of Lc stretches the CSD along the diagonal of the axes. Both of them tend to spread the CSD into a radiant region near the origin point, so as to enhance the radiation. The radiation seems insensitive to the variation of the L, as it only slightly distorts the CSD in the radiant region.

Kinematic waves and collision effects in dense fluid–particle flow during hydraulic conveying

The effects of fluid–particle and particle–particle interactions on the kinematic waves and particle dynamics in a vertical pipe with continuous upward fluid flow are investigated. The unresolved computational fluid dynamics-discrete element method, in which fluid flow field is modeled using large eddy simulation with dynamic Smagorinsky model for the eddy viscosity, is used to simulate the conveying process for particle Reynolds numbers within 8000 and 40000. The results imply that it can show kinematic waves and determine wave velocity based on the wave frequency and wave number relationships, which is also found to closely agree with the theory of kinematic waves based on the Richardson-Zaki relation. One feature is that the kinematic wave velocity in hydraulic conveying manifests itself in relation to the upward fluid velocity. In addition, two different flow regimes are found in the simulation. For relative low particle Reynolds numbers (8000<Rep<16000), the collision and hydrodynamic effects are equally important (regime 1). As the particle Reynolds number increases, the relative significance of collision effects increases. At Rep=16000, the collision effects go beyond the hydrodynamic effects, leading to the flow regime transition (regime 2). The increase of the collision effects also makes the particles uniformly distributed.

Propagation characteristics of the flow and suspended sediment peaks in the three gorges reservoir, China: Insight from numerical simulations and measured data

AbstractEffective management of reservoir sedimentation necessitates the characterization of flood events, especially in relation to the propagation of the flow peak (Qpeak) and the suspended sediment concentration peak (SSCpeak). This study, based on a one‐dimensional river network hydro‐sediment model together with field data, presents an exploration of the flood events in the Three Gorges Reservoir (TGR) with focus on the propagating characteristics of Qpeak and SSCpeak. The findings reveal that the main flood season (from July to September) contributed over 80% of the annual sediment load into the TGR, with the mainstream Yangtze and its tributary, the Jialing River, being the primary sediment sources. After the impoundment of the TGR, the propagation time of Qpeak decreases with the raise of the water level in front of dam (WLdam). The increases in Qpeak discharge extends the range of river reach dominated by kinematic wave, resulting in an increase trend in Qpeak propagation time. The propagating speed of SSCpeak is closely related to the ratio of sediment concentration to flow discharge and WLdam. Finally, the propagating durations of Qpeak and SSCpeak in the TGR are compared, and empirical formulas are proposed for quantifying their difference.

Experimental Study on Hydrodynamic Performance of the Integrated Floating Breakwater-Wind Turbine Device

This study presents the design of an integrated floating breakwater-wind turbine device. The hydrodynamic performance was evaluated in a two-dimensional water tank under typical operating conditions to investigate its kinematic response and wave dissipation effect, while the original design was improved and optimized to enhance the overall performance of the integrated device. The improved integrated device had lower heave and sway motion amplitudes, better wave resistance, and better wave dissipation performance than the prototype. The improved integrated device can effectively reduce costs and optimize the allocation of resources by using a floating breakwater as a carrier for wind power generation and has broad application prospects.

Estimation of traffic energy consumption based on macro-micro modelling with sparse data from Connected and Automated Vehicles

Traffic energy consumption estimation is significant for the sustainable transportation. However, it is difficult to directly employ macro traffic flow data to accurately estimate the traffic energy consumption due to many traffic energy consumption models need second-by-second vehicle trajectory. To solve this problem, this paper proposes a traffic energy consumption model based on the macro-micro data, which the macro data derived from the fixed-location sensors and sparse micro data derived from the Connected and Automated Vehicles (CAVs). The completed vehicle trajectories are constructed by the nonparametric kernel smoothing algorithm and variational theory. To test the performance of the proposed method, the Next Generation Simulation micro (NGSIM) dataset and Caltrans Performance Measurement System macro dataset obtained from the same road and time are used. The results indicate that the proposed method not only can reflect the characteristics of traffic kinematic waves caused by traffic congestion, but also minimize the errors generated by the macro-micro transformation. In addition, it can significantly improve the accuracy of energy consumption estimation.