Kinematic Wave Model Research Articles

Analysis of Kinematic Waves Arising in Diverging Traffic Flow Models

Diverging junctions are important network bottlenecks, and a better understanding of diverging traffic dynamics has both theoretical and practical implications. In this paper, we present a new framework for constructing kinematic wave solutions to the Riemann problem of kinematic wave models of diverging traffic with jump initial conditions. Within this framework, the function space of weak solutions is enlarged to include interior states that occur with stationary discontinuities, and various discrete flux functions in cell transmission models of diverging traffic are used as entropy conditions to pick out unique physical solutions. Then in demand-supply space, we prove that the Riemann problem can be uniquely solved for existing discrete flux functions, in the sense that stationary states and, therefore, shock or rarefaction waves on all links, can be uniquely determined under given initial conditions. We show that the two diverge models by Lebacque and Daganzo are asymptotically equivalent. We also prove that the supply proportional and priority-based diverge models are locally optimal evacuation strategies. With numerical examples, we demonstrate the validity of the analytical solutions of interior states, stationary states, and corresponding kinematic waves. This study presents a unified framework for analyzing traffic dynamics arising at diverging junctions and could be helpful for developing emergency evacuation strategies.

Discussion of “Diverging Kinematic Wave Flow” by James C. Y. Guo and Eric S. C. Hsu

The authors of the original paper used data of a laboratory diverging flow model with S0 1⁄4 0.2079, R 1⁄4 0.91 m, n 1⁄4 0.01, and apex angle θ 1⁄4 1.34 rad. For the research reported in the original paper, using Manning’s equation for a wide channel, the kinematic wave parameters will be m 1⁄4 5=3 and k 1⁄4 45.6 (in SI units). For rainfall intensities of ie 1⁄4 78 and 115 mm=h, the rising limb of the hydrograph (Q 1⁄4 kRθym) is computed by the discusser, and shown in Fig. 1(a). Fig. 1(b) shows the corresponding timedependent flow depth. The peak discharge and flow depth under the equilibrium condition are also shown on Fig. 1. The equilibrium flow depths are very small. For these small flow depths (y < 0.14 mm), the Manning equation is not valid as a rating curve. The verification of proposed model needs suitable data for which the Manning equation (or a rating curve) is valid. It seems, for the considered data in the original paper (very small flow depth), that the kinematic wave modeling reported in the original paper is not valid. Concentration time is a key parameter in modeling and analysis of hydrological systems. This parameter depends directly on considered the rating curve. Thus, selection of a valid rating curve is of considerable importance to hydrological modeling with the aid of kinematic wave theory.

Reliable Solution in Dynamic River Flow System Computations

Reliable Solution in Dynamic River Flow System Computations Application and limitation of various computational methods handling hydrologic runoff and varied unsteady river flow equations was studied here. Investigations were focused on many numerical aspects linear, non-linear solution of continuity and dynamic equations. A river catchment was examined, hydrometric stations, water control measures at upstream and hydrodynamic systems of river- reservoir at downstream were modeled provided evaluation and performance of water conveyance systems proposed for water resources planning and management. Application of modeling flow discharge in rivers was reviewed through a number of flow routing techniques. These classical computational methods have been widely used in water resources engineering and are subject of front line research by hydrologic and hydraulic modelers. Application of conventional and practical methods such as Muskingum-Cunge which are classified under hydrologic and hydraulic routing categories was examined for nonlinear variation of hydrodynamic parameters. Several methods including various numerical schemes were used and compared for modeling accurate unsteady flows computations. Analysis were ranked based on four criterions (consistency, stability, convergence and accuracy) examined with field observations and recorded data. Result of analysis verified that with careful description of constant and variable parameters involved in the Muskingum-Cunge model, the nonlinear terms and physical behavior of the problem was best fitted as compared by developed numerical solutions. The kinematic wave model and Hydrologic Engineering Centre (HEC) and Danish Hydraulic Institute (DHI) Mike series software were employed to verify developed fully dynamic wave model. A 42 kilometer reach length (a location between two hydrometric stations) was modeled with hydrologic and hydro-informatics parameters in Kor River were used. Comparing performances of two constant and variable Muskingum-Cunge methods, nonlinear model with variable parameters had highest reliability and accurately was used for dynamic water wave routing in water conveyance systems (especially for rivers without measuring gage stations).

Surface irrigation simulation models: a review

This paper reviews the literature and results of more than one hundred published articles in scientific journals with respect to simulation of surface irrigation. The results showed that 53.4% of the simulations belong to furrow systems. It is 35.9% for border systems and 10.7% for basin irrigation. However, satisfactory simulations were 70.3%, 63.6%, and 54.5% for border, basin, and furrow systems, respectively. The priority of irrigation methods to simulate using hydrodynamic (HD) and other models is border, basin, and furrow irrigation. It is border, furrow, and basin for kinematic wave (KW) and volume balance (VB) models. Finally, this priority is basin, border, and furrow for zero inertia (ZI) model. Meanwhile, the models estimated advance and infiltration phases better than recession and runoff phases during an irrigation event.

Vehicle Specific Behaviour in Macroscopic Traffic Modelling through Stochastic Advection Invariant

In this contribution a new model to include stochastic vehicle specific behaviour and interaction in traffic flow modelling is presented. The First Order Model with Stochastic Advection (FOMSA) is presented as a first order macroscopic kinematic wave model in a platoon-based Lagrangian coordinate system. The use of Lagrangian coordinates allows characteristics of specific vehicles or vehicle-groups to propagate along with the traffic flow using a vehicle specific invariant. The invariant reflects how vehicle or platoon specific characteristics propagate with the vehicles and influence the local behaviour of a vehicle or platoon on a macroscopic level and in interaction with other surrounding vehicles. It represents a local vehicle specific adjustment to the critical density and makes use of two parameters: a stochastic boundary parameter and a transition parameter. These parameters indicate the extent of differences between vehicles or platoons. A case study is also presented in which a demonstration of the model is given and the face validity and sensitivity of the parameters are shown. Previously, similar approaches have made use of second order model descriptions. The formulation of this model as a first order model makes use of the advantages of first order models and also applies the improved accuracy of Lagrangian coordinates over the Eulerian coordinate system in time-stepping.

River discharge assessment under a changing climate in the Chao Phraya River, Thailand by using MRI-AGCM3.2S

In recent years, General Circulation Model (GCM) has been widely used in climate change impact studies. It is an effective tool for well understanding of a change in climate behavior in a long term. Nowadays, more than twenty GCMs have been developed in many research institutes around the world. We selected the latest version of GCM developed by Meteorological Research Institute (MRI), Japan Meteorology Agency, MRI-AGCM3.2S. The model has a horizontal resolution of triangular truncation 959 (TL959), and the transform grid uses 1920 x 960 grid cells, corresponding to approximately a 20-km grid interval with 64 vertical layers (top at 0.01 hPa).We used a regional distributed hydrologic model based on the concept of the variable infiltration capacity to generate runoff intensity and a kinematic wave model including effects of dam operation and inundation to simulate river discharge. The C.2 gauging station at Nakhon Sawan was selected to monitor changes in the river discharge. Input data of the distributed hydrological model, GCM precipitation and evapotranspiration, were corrected to remove biases using the quantile-quantile bias-correction method for precipitation and the different factor bias- correction method for evapotranspiration. The results of the experiment in projecting discharge of the Chao Phraya River under the near future climate (2015-2043) and the future climate (2075-2103) by using the bias- corrected GCM data set showed that 1) the mean annual discharge tends to increase in both near future and future projection periods, 2) During a dry season the tendency of low flow in the near future period tends to decrease. However, the flood frequency analysis using Generalized Extreme Value distribution (GEV) indicates that flood risk in the future will have more severities and damages to the country as the result of the analysis shows that, in the near future the magnitude of 80-year return period flood is greater than the devastating 2011 Thai flood. .

Impact of Urbanization on Stormwater Runoff from a Small Urban Catchment: Gdańsk Małomiejska Basin Case Study

Abstract This paper deals with the impact of different forms of urbanization on the basin outflow. The influence of changes in land cover/use, drainage system development, reservoirs, and alternative ways of stormwater management (green roofs, permeable pavements) on basin runoff was presented in the case of a small urban basin in Gdansk (Poland). Seven variants of area development (in the period of 2000-2012) - three historical and four hypothetical - were analyzed. In each case, runoff calculations for three rainfall scenarios were carried out by means of the Hydrologic Modeling System designed by Hydrologic Engineering Center of the U.S. Army Corps of Engineers (HEC-HMS). The Soil Conservation Service (SCS) Curve Number (CN) method was used for calculations of effective rainfall, the kinematic wave model for those of overland flow, and the Muskingum-Cunge model for those of channel routing. The calculations indicated that urban development had resulted in increased peak discharge and runoff volume and in decreased peak time. On the other hand, a significant reduction in peak values was observed for a relatively small decrease in the normal storage level (NSL) in reservoirs or when green roofs on commercial centers were present. The study confirmed a significant increase in runoff as a result of urbanization and a considerable runoff reduction by simple alternative ways of stormwater management.

The kinematic wave model with finite decelerations: A social force car-following model approximation

This paper derives a five-parameter social force car-following model that converges to the kinematic wave model with triangular fundamental diagram. Analytical solutions for vehicle trajectories are found for the lead-vehicle problem, which exhibit clockwise and counter-clockwise hysteresis depending on the model’s parameters and the lead vehicle trajectory. When coupled with a stochastic vehicle dynamics module, the model is able to reproduce periods and amplitudes of stop-and-go waves, as reported in the field. The model’s stability conditions are analysed and its trajectories are compared to real data.

Simulation of open- and closed-end border irrigation systems using SIRMOD

In many regions in the world, more than 90% of areas equipped for irrigation apply surface methods. The major problem of the surface irrigation system is low performance due to poor design, operation, and maintenance. Use of the mathematical models for simulation of surface irrigation is necessary for reducing costs and decrease of time in analysis of indexes including application efficiency and distribution uniformity. This study aims to simulate border irrigation systems using the SIRMOD (surface irrigation simulation, evaluation and design, developed by Utah State University, Logan, UT, USA) software package under open- and closed-end conditions. For this purpose, 22 sets of data including four no-cultivated open-end borders, nine no-cultivated closed-end borders, and nine cultivated closed-end borders were used. The results showed that the models predicted open-end conditions better than closed-end for recession time. In addition, the hydrodynamic (HD) and the zero inertia (ZI) models estimated volume of infiltrated water, equal or less than volume of observed water in all the borders. Although the HD model uses the Saint-Venant equations without simplification, during numerical solution of them by the software, uncertainty is raised due to further calculations than the ZI and kinematic wave models. This leads to further error of the HD model than the other models in some cases.

Simplified wave models applicability to shallow mud flows modeled as power-law fluids

Simplified wave models — such as kinematic, diffusion and quasi-steady — are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows, and especially for flood routing. While their use may guarantee a significant reduction of the computational effort, it is mandatory to define the conditions in which they may be confidently applied. The present paper investigates the applicability conditions of the kinematic, diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids. The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress, such as clay or kaolin suspensions, which are frequently encountered in Chinese rivers. In the framework of a linear analysis, the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one. Based on this comparison, applicability criteria for the different wave approximations for mud flood of power-law fluids are derived. The presented results provide guidelines for selecting the appropriate approximation for a given flow problem, and therefore they may represent a useful tool for engineering predictions.

A parsimonious model for the formation of oscillations in car-following models

This paper shows that the formation and propagation of traffic oscillations in the absence of lane changes can be explained by the stochastic nature of drivers’ acceleration processes. By adding a white noise to drivers’ desired acceleration in free-flow, oscillations are produced that accord well with observation. This theory suggests that driver error is a function of roadway geometry, that it determines the average speed at the bottleneck, as well as oscillation period and amplitude. The model has been implemented with a single additional parameter compared to the kinematic wave model with bounded accelerations.

DTALite: A queue-based mesoscopic traffic simulator for fast model evaluation and calibration

AbstractA number of emerging dynamic traffic analysis applications, such as regional or statewide traffic assignment, require a theoretically rigorous and computationally efficient model to describe the propagation and dissipation of system congestion with bottleneck capacity constraints. An open-source light-weight dynamic traffic assignment (DTA) package, namely DTALite, has been developed to allow a rapid utilization of advanced dynamic traffic analysis capabilities. This paper describes its three major modeling components: (1) a light-weight dynamic network loading simulator that embeds Newell’s simplified kinematic wave model; (2) a mesoscopic agent-based DTA procedure to incorporate driver’s heterogeneity; and (3) an integrated traffic assignment and origin–destination demand calibration system that can iteratively adjust path flow volume and distribution to match the observed traffic counts. A number of real-world test cases are described to demonstrate the effectiveness and performance of the prop...

Impacts of urbanization on flooding of a coastal urban catchment: a case study of Mumbai City, India

Land use–land cover (LULC) change in space and time is the main cause behind the changing hydrological processes, ecosystem and environment in urban catchments. In the present study, the main focus was on evaluation of spatial and temporal variation of land use and land cover change in a major coastal urban catchment of Mumbai City, India, called Mithi River catchment. The LULC is derived from the topographic map surveyed in the year 1966 and satellite image for the year 2009. The analysis from toposheet and remote sensing data showed that there is a rise in the built-up area of Mithi River catchment, Mumbai by 59.66 % between 1966 and 2009. It also showed adverse human-induced influences on the Mithi River course and its catchment. Flood hydrographs for different land use conditions were derived by using Soil Conservation Service-Curve Number hydrological model and kinematic wave model, for routing available within the HEC-HMS software. Flood plain maps as well as flood hazard maps for the different land use scenarios have been developed by integrating the models HEC-HMS and HEC-RAS with HEC-GeoHMS and HEC-GeoRAS as well as with GIS and remote sensing. Results obtained from the present study revealed marginal increases in the runoff peak discharges and volumes within the catchment. Even though the runoff change is marginal, combined with tidal influence, it may cause major flooding problem. The integrated modeling approach has been found to be very effective for flood estimation, flood plain and flood hazard mapping. The flood plain and flood hazard maps derived can be used as effective tool to minimize the damages within the flood-prone areas of the river basin for the Mumbai City.

Impact of Climate Change on River Flows in the Black Volta River

This paper assesses the impact of climate change in the Black Volta River by using data output from the atmospheric general circulation model with a 20-km resolution (AGCM20) through the Japanese Meteorological Agency (JMA) and the Meteorological Research Institute (MRI). The Black Volta, which flows mainly in Burkina Faso and Ghana in West Africa, is a major tributary of the Volta River. The basin covers 142,056 km2 and has a semi-arid tropical climate. Before applying AGCM20 output to a rainfall–runoff model, the performance of the AGCM20 rainfall data is investigated by comparing it with the observed rainfall in the Black Volta Basin. To assess the possible impact of rainfall change on river flow, a kinematic wave model, which takes into consideration saturated and unsaturated subsurface soil zones, was performed. The rainfall analysis shows that, the correlation coefficient of the monthly rainfall between the observed rainfall and AGCM20 for the present climate (1979–2004) is 0.977. In addition, the analysis shows that AGCM20 overestimates precipitation during the rainy season and underestimates the dry season for the present climate. The analysis of the AGCM20 output shows the precipitation pattern change in the future (2075–2099). In the future, precipitation is expected to increase by 3%, whereas evaporation and transpiration are expected to increase by 5% and by 8%, respectively. Also, daily maximum rainfall is expected to be 20 mm, or 60%, higher. Thus, the future climate in this region is expected to be more severe. The rainfall–runoff simulation is successfully calibrated at the Bamboi discharge gauging station in the Black Volta fromJune 2000 to December 2000 with 0.72 of the Nash–Sutcliffe model efficiency index. The model is applied with AGCM20 outputs for the present climate (1979–2004) and future climate (2075–2099). The results indicate that future discharge will decrease from January to July at the rate of the maximum of 50% and increase fromAugust to December at the rate of the maximumof 20% in the future. Therefore, comprehensive planning for both floods and droughts are urgently needed in this region.

The Distribution of Congestion on a Class of Stochastic Kinematic Wave Models

This paper shows that a wide range of stochastic extensions of the kinematic wave model tend to the same parameter-free expression for the probability of congestion at a given time-space point. This is shown for white noise initial density with deterministic and stochastic fundamental diagram in the case of Riemann problems and the bottleneck problem. It is also found that the stochastic solution (i) preserves the structure of the deterministic solution and (ii) tends to the deterministic solution with time at a given location.

Self-Adaptive Tolling Strategy for Enhanced High-Occupancy Toll Lane Operations

In this paper, a self-adaptive tolling strategy (SATS) is developed for dynamically and systematically enhancing highoccupancy toll (HOT) lane system operations. This strategy enhances the overall system performance of both the HOT and general purpose (GP) lanes by better utilizing the HOT lane capacity while maintaining high speed and/or high travel-time reliability for HOT lane traffic when GP lanes are congested. To formulate SATS, the Lighthill-Whitham-Richards kinematic wave model is used to characterize HOT lane traffic flow evolution, and the unilateral Laplace transform is used to convert the system representation from the time domain to the frequency domain. Then, an adaptive tolling controller is designed with both the proportional and integral control components. Real-time traffic measurements, including lane occupancy, average speed, and flow rate, are utilized for toll rate calculations. Following a dual-phase control scheme, the appropriate flow rate for HOT lane utilization is computed, and the corresponding toll is estimated backward. To examine the effectiveness of the proposed tolling strategy, microscopic traffic simulation experiments are conducted using VISSIM. The experiment results demonstrate that the proposed tolling strategy performs reasonably well in improving the overall operations of HOT lane systems under various traffic conditions.

Physically-Based One-Dimensional Distributed Rainfall-Runoff Model Using the Finite Volume Method and Grid Network Flow Analysis

This work develops a grid based rainfall-runoff model (GRM), which is a physically based and spatially distributed model. Surface flow was analyzed using a kinematic wave model with the governing equations discretized using the finite volume method (FVM). This paper suggests a grid network flow analysis technique using variable rainfall intensity according to the flow directions to analyze one-dimensional flows between the grids. The model was evaluated by applying it to the Wuicheon watershed, a tributary of the Nakdonggang (Riv.), in Korea. The results showed that the grid-based, one-dimensional kinematic wave model adopted the FVM and the grid network flow analysis technique well. The simulation results showed good agreement with the observed hydrographs and the initial soil saturation ratio was most sensitive to the modeling results.

Clustering Approach for Assessing the Travel Time Variability of Arterials

Travel time variability may significantly influence a driver's route choice. Urban infrastructure managers are interested in reliable estimation of travel time, which could provide better information to drivers, encourage reassignment on the network, and optimize use of the network. This study addresses arterials in undersaturated conditions with known fixed-time traffic signals. The kinematic wave model was chosen to represent traffic dynamics simply. A semianalytical (grid-free) method is applied to determine the separation between vehicle groups at each signal of the arterial. The main contribution of this paper is an aggregated diagram that describes the functioning of this arterial. The aggregated diagram graphically provides a direct assessment of vehicle travel times with respect to their departure and traffic flow. This tool depends only on signal settings and is cyclic and invariant for fixed-time signals. The diagram can be used to generate probabilistic travel time distributions when some input parameters are uncertain. The diagram appears to offer insight when traffic flow is not accurately known.

Cross-correlation velocity measurement of horizontal oil–water two-phase flow by using parallel–wire capacitance probe

Horizontal oil–water two-phase flow widely exists in petroleum industry. The flow measurement in oil well, which is one of key production logging technologies, is becoming more and more important for horizontal well production management. The complicated flow structures happened in horizontal oil–water two-phase flow bring a great challenge to flow measurement. We employ a parallel–wire capacitance probe (PWCP) to compose the cross-correlation velocity measurement. Firstly, we investigate the distribution of sensitivity field of PWCP by using finite element method (FEM). Then, we carry out the flow loop test to figure out the cross-correlation velocity from the voltage fluctuation signals measured from upstream and downstream probes. The results indicate that the cross-correlation characteristic of PWCPs depends on the oil–water flow structures. Finally, we use the kinematic wave model to predict the homogeneous velocity for six different horizontal oil–water two-phase flow patterns.

A kinematic wave approach to traffic statics and dynamics in a double-ring network

Recently there has been much interest in understanding macroscopic fundamental diagrams of stationary road networks. However, there lacks a systematic method to define and solve stationary states in a road network with complex junctions. In this study we propose a kinematic wave approach to defining, analyzing, and simulating static and dynamic traffic characteristics in a network of two ring roads connected by a 2×2 junction, which can be either an uninterrupted interchange or a signalized intersection. This study is enabled by recently developed macroscopic junction models of general junctions. With a junction model based on fair merging and first-in-first-out diverging rules, we first define and solve stationary states and then derive the macroscopic fundamental diagram (MFD) of a stationary uninterrupted network. We conclude that the flow-density relationship of the uninterrupted double-ring network is not unique for high average network densities (i.e., when one ring becomes congested) and unveil the existence of infinitely many stationary states that can arise with a zero-speed shockwave. From simulation results with a corresponding Cell Transmission Model, we verify that all stationary states in the MFD are stable and can be reached, but show that randomness in the retaining ratio of each ring drives the network to more symmetric traffic patterns and higher flow-rates. Furthermore we model a signalized intersection as two alternate diverge junctions and demonstrate that the signalized double-ring network can reach asymptotically periodic traffic patterns, which are therefore defined as “stationary” states in signalized networks. With simulations we show that the flow-density relation is well defined in such “stationary” states, and asymptotic traffic patterns can be impacted by signal cycle lengths and retaining ratios. But compared with uninterrupted interchanges, signalized intersections lead to more asymmetric traffic patterns, lower flow-rates, and even gridlocks when the average density is higher than half of the jam density. The results are consistent between this study and existing studies, but the network kinematic wave model, with appropriate junction models, is mathematically tractable and physically meaningful. It has offered a more complete picture regarding the number and type of stationary states, their stability, and MFD in freeway and signalized networks.