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Due to its simplicity, the kinematic wave is commonly applied to open-channel routing in watershed hydrologic modeling. However, these applications must fulfill certain conditions, such as ...

The kinematic wave theory has been a widely accepted technique for modeling overland flow. Although it is recognized that overland flow is nonlinear, linear approximations have nonetheless ...

In this study, the complete governing equations for unsteady open channel flow in fractional time-space are developed from the fractional continuity equation combined with the fractional motion equation, which is based on Newton’s second law of motion, by accounting for the acceleration terms in order to render physically interpretable hydraulic terms. Then the kinematic wave and diffusion wave approximations to unsteady open channel flow with physically interpretable terms in fractional time-space are developed from the fractional continuity and motion equations. Because the powers of all of the derivatives in the conventional governing equations of unsteady open channel flow in integer time-space are one, these conventional equations are derived as special cases of the fractional governing equations when the fractional powers in the fractional equations approach unity.

Applying a lumped runoff model in ungauged basins requires the relationships between the parameter characteristics of a model with watershed characteristics. The authors of this study designed various methods to evaluate the parameter characteristics of the storage function model using the kinematic wave model. They applied genetic algorithms to 101 observed events at 17 dam basins in Korea. The results confirmed that there is a limit to developing an empirical equation for parameter estimation on the basis of observed data. As part of the measures taken to overcome the limit, a runoff simulation was implemented that considered 35,000 various conditions by configuring virtual basins, and the parameter of the storage function model was evaluated based on the results. Hence, the authors discovered that a lag time of the storage function method is primarily determined to be closely connected with the characteristics of the longest stream, and the storage coefficient has high relevancy with the basic ...

This paper presents a set of generalized charts that can be used as an aid for quick hydrologic evaluation of vegetative filter strips to determine the runoff residence time and reductions in storm runoff volume and peak discharge. These charts are developed by using the predetermined numerical solutions to the governing equations for the overland flow and infiltration processes. Kinematic wave equations are used for overland flow and the Green and Ampt equations are employed for infiltration calculations. An explicit finite-difference scheme is employed to couple and solve these equations. The basic mathematical model is verified by using a set of published experimental data. The model is extended to incorporate a design inflow and the governing equations are written and solved numerically in terms of a set of dimensionless variables. The solutions thus obtained are generalized by using the principle of hydrologic similarity and presented in chart form.

An analytical solution for overland flow under (upstream and downstream) moving storms that uses Laplace transformation to solve the one-dimensional (1D) linear kinematic wave equation is presented. This solution, which corresponds to a single continuous function for the total space-time domain of the overland hydrograph, enables evaluation of the discharge over time for the total drainage plane surface. The result was compared with another analytical solution, a numerical simulation, and experimental runs using a laboratory flume. The comparison showed very good fit, and the proposed analytical solution was thus regarded as validated. By applying the model to hypothetical catchments and storm patterns, distinct hydrologic responses for upstream and downstream moving storms were identified.

In comparison with a kinematic wave–based equation for estimation of the time of concentration, three methods, Ben-Zvi’s method, the modified Ben-Zvi method, and Izzard’s method, were applied to determine the time of concentration from the experimental hydrographs reaching an equilibrium flow state. The experiments were performed for stationary rainstorms on a V-shaped aluminum watershed in the watershed experimentation system (WES) at the University of Illinois in Urbana-Champaign, Illinois. The times of concentration determined by these three methods were compared to mathematical equations in the existing literature. It is found that the time corresponding to 89% of the maximum discharge as per the modified Ben-Zvi method yielded a generally agreeable time of concentration for the WES experimental hydrographs, while the criterion of 97% of the peak discharge as per Izzard’s method overestimates the time of concentration. It is found that Woolhiser and Liggett’s and Wong’s equations can predict t...

Derivation of spatial distribution of travel time is required in some conceptual rainfall-runoff transformation models. Application of a kinematic wave (KW) solution to delineate isochrones of travel time may be straightforward, particularly in an overland flow regime. In this article, a new analytical approach based on the diffusive wave (DW) solution is developed for calculation of travel time. The discharge hydrograph over a rectangular plane will be calculated based on the developed analytical DW method through the application of the time-area method. Differences between calculated maximum travel time (i.e., equilibrium time), isochrone locations, and outflow discharge between the KW and DW solutions are compared with those of the numerical dynamic wave (DYW) solution. It is shown that analytical DW results are closer to those of the DYW in comparison with those of the KW. The effect of the K0F02 number on the solution accuracy is investigated, where K0 is the kinematic wave number and F0 is t...

The propagation of flood waves in rivers is governed by the Saint Venant equations. Under certain simplifying assumptions, these nonlinear equations have been solved numerically via computationally intensive, specialized software. There is a cogent need for simple analytical solutions for preliminary analyses. In this paper, new approximate analytical solutions to the nonlinear kinematic wave equation and the nonlinear dynamic wave equations in rivers are presented. The solutions have been derived by combining Adomian’s decomposition method (ADM), the method of characteristics, the concept of double decomposition, and successive approximation. The new solutions compare favorably with independent simulations using the modified finite-element method and field data at the Schuylkill River near Philadelphia. The time to peak calculated by the analytical and numerical methods is in excellent agreement. There appears to be some minor differences in the peak magnitude and recession limb, possibly because...

39 Pags. The definitive version, with figures, is available at: http://ascelibrary.org/toc//17/10, In this paper, a distributed numerical model is proposed on the basis of (1) a hydrologic model for the water exchange laws; (2) a surface runoff model based on a hybrid two-dimensional (2D) diffusive/kinematic wave approximation able to calculate flow over all kinds of wet/dry ground surface slopes; (3) a groundwater flow model based on the 2D Darcy law for both saturated and partly saturated zones; (4) a 2D hillslope erosion model for the sediment transport; and (5) a explicit finite-volume discretization with specific schemes according to the characteristics of the flow equations, upwind for the hyperbolic equations and centered for the parabolic equations. The resulting model offers a variable time step, ensuring numerical stability with the time step size sensitive to the grid cell size in the diffusive wave case and an entropy correction of the upwind fluxes to ensure conservative solutions near local maxima in the slopes controlling the water movement. The validation and practical application of the model is presented in Paper II, in which the potential usefulness of the proposed model is demonstrated., This research has been funded by the D.G.A. (Aragon General Deputation) under research projects no PM088/2006, PI032/08 and budget application 17030 G/5423/480072/91001

Conversion of a natural watershed into its equivalent kinematic wave rectangular plane has long been a concern in the practice of storm water numerical simulations. Based on the principles of mass and energy, the actual watershed and its virtual kinematic wave plane can be related by the watershed shape factor that involves the waterway length and slope and watershed area. In this study, two dimensionless watershed shape functions are derived to use parabolic function and trigonometric sine curve for watershed conversion. These two watershed shape functions produce good agreements with the maximum overland flow length method for hypothetical square watersheds. Also, these two watershed shape functions are able to reproduce similar kinematic wave plane widths as reported in a calibrated model. Furthermore, in this study, these two watershed shape functions are tested by nine observed rainfall events and three levels of modeling details. These 54 case studies reveal that the parabolic shape function...

A stochastic kinematic wave model for open-channel flow under uncertain channel properties is developed. The Fokker-Planck equation (FPE) of the kinematic open-channel flow process under uncertain channel properties is developed by using the method of characteristics. Every stochastic partial differential equation has a one-to-one relationship with a nonlocal Lagrangian-Eulerian FPE (LEFPE). As such, one can develop an LEFPE for the governing equation of any hydrologic or hydraulic process as the physically based stochastic model of the particular process. A linear, deterministic, differential equation in Eulerian-Lagrangian form, LEFPE provides a quantitative description of the evolution of the probability density functions of the state variables of the process at one shot to describe the ensemble behavior of the process instead of the commonly used many Monte Carlo simulations to quantify the same ensemble behavior. Under certain assumptions, the nonlocal LEFPE reduces to the classical local FPE, which ...

Derivation of travel time based on Saint-Venant equations may substantially improve rainfall-runoff routing, particularly in the Clark approach and GIS-based hydrological routing models. Kinematic wave (KW) and diffusive wave (DW) approximations are often applied in lieu of the dynamic wave (DYW) solution to study overland flow regime. In this study, for the first time, travel-time relationships are presented based on DWapproximation. In terms of equilibrium time, the DWapproximation improved results from 5% up to 15% over the KW approximation. After obtaining the semianalytical solution of the DW travel time, discharge hydrographs over a rectangular plane through the well-known time-area method were derived. Considering the DYW solution as the benchmark, it was found that the time-area approach by adopting the proposed DW wave travel time formulation, provided satisfactory results for 2:5 0:1. Using the travel time based on KW approach, the time-area method was found fairly accurate for K0F 2 > 25 and F0 > 0:1. K0 and F0 are the well-known kinematic wave number and Froude number, respectively. Therefore, it is perceived that as K0F 2 decreases, the difference between KW and DW approximations becomes greater. DOI: 10.1061/(ASCE)HE.1943-5584.0000399. © 2012 American Society of Civil Engineers. CE Database subject headings: Hydrographs; Simulation; Travel time; Equilibrium; Kinematic wave theory. Author keywords: Diffusion wave; Travel time; Equilibrium time; Time-area method; Hydrograph; Kinematic wave; Isochrones.

The kinematic wave system of shallow-water equations is posed as an initial value problem, or Cauchy problem, to investigate error analysis using the square-grid finite-element method. The consistent, lumped, and upwind models of the square finite-element method are analyzed using the Fourier (or von Neumann) stability method as separate initial value problems for two-dimensional shallow-water equations. The small difference between the Cauchy solution and integer (or half) multiples of the eigenvalue solution of amplification factors using the eigenvalue method indicates that the Cauchy solution is a possible stable numerical solution of the kinematic wave shallow-water equations within the reasonable limits of solution accuracy. The nodal amplification factors are less than or equal to unity for implicit finite-element schemes for all of the three formulations—consistent, lumped, and upwind for all of the wave numbers, implying unconditional stability. For explicit and semi-implicit finite-eleme...

The influence of moving rainstorms on overland flow is studied by a semianalytical solution and experiments. The effect of the velocity of the moving rainstorms on water depth changes is approximately presented by the kinematic wave method. The effect is also compared with the experimental result and the numerical computation and found to be satisfactory. The semianalytical and experimental results indicate that the changes of peak discharge are dependent on the velocity and direction of the moving rainstorms. The difference of the water depths between the downstream and upstream moving rainstorms with the velocity at the downstream end is proportional to the velocity of the moving rainstorm when the velocity is small. The semianalytical solution indicates that the maximum water depth appears when the velocity of moving rainstorms is equal to that of the flood movement. The effect of the velocity of the moving rainstorm is larger in the watershed of milder bottom slope or larger Manning’s roughness coeffi...

An analytical solution of the nonlinear kinematic wave model of overland flow with time-varying rainfall on a sloping plane is presented by the characteristic equation. To obtain it in the closed form, we approximate discharge of Manning’s formula per unit width by a parabolic curve. It is compared with experimental data of rainfall and runoff process, and their agreement is satisfactory. It is also compared with the numerical result of the finite difference method, and their agreement is found to be good. When the rainfall is time-varying, the method of this study can derive the analytical solution. The analytical solution of the kinematic wave model with time-varying rainfalls is found to be suitable for estimating design flood from rainfall in a simple watershed. Floods in urban areas can be predicted by the kinematic wave model with given time-varying rainfalls when the urban areas consist of several simple watersheds.

Flood wave routing is a common problem in water resources engineering, for example, when a hydrograph enters a stream channel and passes downstream to an observation station. In the past, the problem has been approached by making the best possible estimate of the inflow hydrograph. The channel properties such as geometry and roughness are also estimated, along with any lateral inflow. The best estimates are used with a flood wave routing model to predict the hydrograph at the downstream observation station. Making a prediction by this procedure is full of challenges. It is impossible to exactly know the precise form of the hydrograph that will enter the channel. It is also difficult to select the channel properties from the range of values that may be appropriate. Lateral inflow is notoriously difficult to quantify. Making predictions under these circumstances is full of uncertainties. One approach to analyzing uncertainties is to use Monte Carlo modeling to make quantitative estimates of the uncertainty ...

In this study, the principle of maximum entropy concept is used to estimate the soil moisture profile to a depth of near 50 cm. The procedure involves the use of the surface observation as the principle constraint in physical space, and only requires that a water balance be kept at the surface so that the mean water content of the soil can be computed at each time step. Comparison to experimental data for the wet and dry phases of the infiltration cycle showed that the theoretical profile gave reasonable simulations as measured by the Nash Sutcliffe Efficiency Statistic. It was also demonstrated that the entropy principle, combined with the kinematic wave approximation, is capable of simulating the dynamic phase of the infiltration process if the unsaturated hydraulic conductivity is treated as a calibration parameter of the model.

The time of concentration equation used in Pima County, Arizona, includes a hydrologic parameter representing the impedance to flow for peak discharge estimation on small [typically less than 2.59 km2 ( 1 mi2 ) ] semiarid watersheds. The impedance-to-flow parameter is similar in function to the hydraulic Manning’s n roughness coefficient in the kinematic wave time of concentration equation; however, the impedance to flow is a hydrologic parameter representing all portions of a watershed rather than a hydraulic parameter representing friction loss during uniform flow. To relate the impedance-to-flow parameter to physical watershed characteristics, impedance-to-flow values were calculated for return period and observed events on five undeveloped rangeland watersheds and correlated with Manning’s n roughness coefficients determined from particle size analysis and simulated flow conditions. Impedance to flow displayed a positive trend with observed peak discharge on each watershed. The results indicate th...

The area of a looped rating curve for a channel cross section is indicative of the dynamic effects of a flood wave. These effects may be used as a criterion to decide the suitability of a simplifying approximation, such as dynamic, kinematic or diffusive wave modeling, for the analysis of dam-break flow. Two approximate models to calculate the area of the nondimensional loop for dam-break flow are developed herein based on the computed results for several hypothetical dam failure cases. A comparison of the results obtained from the approximate models and those by simulations shows that approximate models can be used to predict the nondimensional loop area for short distances from the dam. As expected, the area of the nondimensional loop decreases as the flood wave moves downstream, it increases as the breach width increases and it decreases for increased breach time and/or flood-plain width.

Selecting an appropriate digital elevation model (DEM) resolution is an essential part of distributed rainfall-runoff modeling since the resolution affects parameter values and, in turn, leads to predictive uncertainty. Moreover, the DEM resolution directly determines the computational workload required for model simulation. This study conducted several experiments to clarify the interaction between topographic and process parameters due to the spatial resolution of DEMs in distributed rainfall-runoff modeling. First, five different spatial resolutions (from 50 m to 1 km) were used to analyze the effects of DEM resolution on the topographic and process parameters of a distributed rainfall-runoff model [kinematic wave method for subsurface and surface runoff (KWMSS)]. Second, parameter compatibility was tested with regard to the sensitivity of model performance to optimal parameter values for each DEM, by applying the best-performing parameter combinations for each resolution to the models based on differi...

The momentum equation in the kinematic wave model is a power law equation and involves two kinematic wave parameters. It is a common practice to use Manning’s equation to calculate the kinematic wave parameters. One can obtain a kinematic wave equation by inserting the momentum equation into the continuity equation. The kinematic wave equation becomes a partial differential equation with kinematic wave parameters that depend on the flow depth. However, working with the kinematic wave equation comprised of kinematic wave parameters that are independent of the flow depth, is a lot more convenient. Here, regression methods were used to calculate the kinematic wave parameters that are independent of the flow depth for a trapezoidal channel cross-section, which is a common cross-section shape. The developed expressions for the kinematic wave parameters provided very good approximation for the momentum equation of the kinematic wave model. The relationships among the geometry parameters of natural channel cross...

Storm water management models using the kinematic wave (KW) approach require the conversion of a natural watershed to its equivalent rectangular cascading plane. AKW cascading plane is specified by the plane’s area, width, and slope. Without on-site calibration, there is no guidance on how to translate the irregularity of a natural watershed into a rectangular shape that has an equivalent hydrologic response. As a result, the reliability of a KW model depends on an engineer’s experience. Often the use of a computer model to simulate stormwater runoff is the only option because there are not field data at the project site to use statistical methods. The need for calibration at each site defeats the purpose for using computer simulations. This long existing problem has been documented in the EPA SWMM4 User Manual, which continued into the EPA SWMM5 user guidance. In this study, the continuity and energy principles are creatively interpreted as the preservations of watershed area and vertical fall over the r...

A new ensemble-averaged kinematic wave equation is derived for the flow routing problem in channel networks. This derivation is performed by ensemble averaging the second-order Taylor series expansion of the point scale kinematic wave equation around the mean value of the equation’s parameters. Utilizing this ensemble-averaged kinematic wave equation, the ensemble-averaged solution for the same ordered channels (according to the Strahler–Horton ordering) are obtained. Instead of solving the flow at each channel one by one, the ensemble-averaged solution is computed for the ensemble of channels that are of the same order within the channel network. Ensemble averaging is only applied to the channel orders that include a sufficient number of channels to form an ensemble of adequate size. Using this methodology, the computational load, parameter data requirements, and time/effort required to set up the model are reduced substantially. Besides the obtained economy in computations, data requirements and effort ...

Time of concentration of overland flow is an important parameter in many hydrologic design methods. This technical note traces the evolution of the kinematic wave time of concentration formulas for overland flow only. It commenced with Henderson and Wooding’s 1964 formula for a single plane. This formula, however, cannot be easily applied in practice because the parameters were not related to the physical characteristics of an overland plane. Nearly four decades later, in 2002, Wong developed a powerful formula, which can be applied to a series of planes which are of different lengths, different slopes, different roughnesses, different flow regimes, different soil types and infiltration rates resulting in different net rainfall intensities, and for planes subject to different net rainfall intensities, and a combination of all these variables. Finally, a comparison of Wong’s 1996 formula with Overton’s 1971 formula shows that Overton’s formula for a series of planes is incorrect.

In this paper, the variability of simulated flood discharges is evaluated using two methods for estimating impervious surfaces and common design methods in the Mission Creek watershed 31 km 2 located in Santa Barbara, Calif. The two impervious estimation methods are characterized as high resolution from manually digitizing aerial photographs and medium resolution from automated inter- pretation of satellite data. In all cases, the high resolution fraction of impervious area is greater than the medium resolution. The difference between methods is greatest in urban regions having either small or large fractions of imperviousness low- or high-intensity develop- ment. The largest difference observed at the modeling unit scale 3.4 km 2 was 19 percentage points 26 versus 45%. To quantify discharge variability, four events 2- and 100-year for 6- and 24-h durations and three models were used. The models used combinations of Green-Ampt and curve number CN losses and kinematic wave and unit hydrograph routing. The Green-Ampt model tended to overpredict peak discharge relative to the CN model, and kinematic wave routing and unit hydrograph agreed well except for the largest events, where the efficiency of the routing decreased travel time sufficiently to increase the peak discharge. The CN model was more sensitive to the impervious surface estimation method relative to the Green-Ampt model due to the mechanisms for incorporating imperviousness into the models. At the scale of the watershed used in this study, the effects of imperviousness estimation method on simulated peak discharge ranges from 16% for the 2-year event to 9% for the 100-year event. While the effects are present, they are not sufficient to shift the recurrence interval of the design discharges. At the model unit scale, the difference in peak discharge between impervious estimation methods exceeded 41 and 21% for the 2- and 100-year events, respectively. Overall, the two impervious surface estimation methods result in different peak discharges but neither method consistently results in discharges less than flood frequency- based discharges. In terms of design risk, the results suggest that the design methods are sufficient to absorb the imperviousness variability from the two methods used here. For applications where a model is calibrated to a specific event, variability resulting from differences in estimation methods is likely to be further muted by adjusting model parameters in the calibration process.

The applicability of the kinematic wave (KW) and diffusive wave (DW) approximations was investigated for steady flow in prismatic channels by using a second-order two-step Lax-Wendroff numerical scheme coupled with the characteristic method at the boundaries. Two types of downstream boundary conditions, critical-flow depth and zero-flow depth gradient, were considered together with the condition of discharge hydrograph reaching the steady state at the upstream end. The role of inertial, pressure, friction, and gravity forces was investigated for 16 test cases defined through the kinematic wave number K and the Froude number F0 , whose range was assumed to be (3–30) and (0.1–1), respectively. Errors were computed by comparing the steady dimensionless profiles of the flow depth with those estimated by the dynamic wave solution. The accuracy of the two approximations was assessed through the mean value e of the magnitudes of errors computed for the channel region where the solution was not significantly infl...

The applicability of the kinematic wave (KW) approximation was investigated for unsteady flow in prismatic channels. Each of the 16 cases analyzed under steady flow conditions by Moramarco et al. (2008) was now perturbed such that synthetic discharge hydrographs varying around the steady value Q0 and characterized by different values of the wave period T and steady wave travel times, T0′ , were obtained. Therefore, based on the kinematic wave number K and steady Froude number F0 , a set of 224 experimental tests were carried out and the KW accuracy was investigated by routing synthetic discharge hydrographs. In this case, the dynamic wave solution DYW was also considered as a benchmark and adopting the critical-flow depth at the downstream end. The performance of KW was assessed using different accuracy measures: (a) errors in dimensionless maximum flow depth along the channel emax ; (b) explained variance NSQ on discharge hydrographs at the outlet section; and (c) errors in peak discharge e Qp and water ...

Assuming quasi-steady flow, the characteristic velocity of stream bed movement and the relation between the depth of the moving gravel layer and the water depth are derived for both diffusion wave and kinematic wave approximations. The characteristic velocity relation is verified using field data and is compared with the relation derived by Weir in 1983.

This study deals with the estimation of sediment yields and sedimentographs of small watersheds. The proposed mathematical model is based on simultaneous solution of flow dynamics followed by dynamic erosions. The flow dynamics is based on the well accepted kinematic wave theory. As the storm rainfall proceeds, the process of generation of overland depth is a dependent function of the infiltration rates. This has been taken care of by the use of Phillip’s infiltration approach. Recent research has revealed that the flow resistance coefficients greatly influence the overland water depths. Therefore, the concept of depth dependent overland resistance coefficients has been incorporated in the overland flow computations to minimize the errors. The components of the soil erosion model have been modified for better prediction of sediment flow rates and sediment yields. The rainfall-runoff-sediment model as developed was applied to 34 storm events registered over six small watersheds located in different climati...

This technical note presents a combination of isohyetal map, kinematic wave, and rational methods for estimating flash flood synthetic hydrographs in arid regions. They are combined in a logical sequence for the calculations of time of concentration and synthetic flood hydrograph. This empirical approach relates flood peaks to the average temporal and areal intensities of storm rainfalls. The application of the methodology is presented for two arid region wadis in the central western part of the Arabian Peninsula. Hydrograph peaks yield practically reliable estimations of the observed flood magnitudes from individual storms.

In this study the fractional governing equations for diffusion wave and kinematic wave approximations to unsteady open-channel flow in prismatic channels in fractional time-space were developed. The governing fractional equations were developed from the mass and motion conservation equations in order to provide a physical basis to these equations. A fractional form of the resistance formula for open-channel flow was also developed. Detailed dimensional analyses of the derived equations were then performed in order to ensure dimensional consistency of the derivations. It is shown that these fractional equations of unsteady open-channel flow are fundamentally nonlocal in terms of nonlocal fluxes. The derived fractional governing equations of diffusion wave and kinematic wave open-channel flow can accommodate both the long-memory nonlocal behavior of open-channel flow as well as its local, finite memory behavior, as is numerically demonstrated in the accompanying paper by the authors.

In this study, finite difference numerical methods, first order accurate in time and second order accurate in space, are proposed to solve the governing equations of the one-dimensional unsteady kinematic and diffusion wave open-channel flow processes in fractional time and fractional space, which were derived in the accompanying paper. Advantages of modeling open-channel flow in a fractional time-space framework over integer time-space framework are threefold. First, the nonlocal phenomena in the open-channel flow process in either space or time can be considered by taking the global correlations into consideration. Second, the proposed governing equations of the open-channel flow process in the fractional order differentiation framework are generalization of the governing equations in the integer order differentiation framework. Third, the physics of the observed heavy tailed distributions of particle displacements in transport processes, as reported in the literature, may be explained by a flow...

A one-dimensional (1D) hydrologic-hydraulic model for simulating dual drainage in urban areas is presented. It consists of four modules: (1) rainfall-runoff transformation, (2) 1D flow routing on a street network, (3) flow interception at street inlets, and (4) flow interaction between surface water on the streets and the underground storm-water system by interfacing with the EPA-SWMM5 engine (U.S. Environmental Protection Agency-Storm Water Management Model). The hydrologic model (first module) transforms rainfall to runoff using the kinematic wave approximation and simulates the infiltration process with the Green-Ampt method. The street network model (second module) is based on a finite-volume shock-capturing scheme that solves the fully conservative Saint-Venant equations and can be used to model both subcritical and supercritical flows. The inlet model (third module) computes the amount of water intercepted by inlets. The formulation of boundary conditions at the street crossings is generaliz...

An analytical solution of the nonlinear kinematic wave model of overland flow on a sloping plane for time-varying excess rainfalls of sinusoidal functions is presented by the method of characteristics. To obtain the closed form of the analytical solution, discharge per unit width in the expression of Manning’s formula is approximated by a parabolic curve. The analytical solution is also compared with the numerical one and their agreement is found to be good. The analytical solution is applied to rainfall and runoff processes with given hyetograph using Fourier series analysis. The computational results of the analytical solution are compared with the observed data. It explains the observation on an impermeable slope very well. It is found that the analytical solution is suitable for estimating design flood from excess rainfall in a simple watershed.

A new approximate analytical solution to the nonlinear kinematic wave equation is proposed. The solution has been derived by combining an implicit solution obtained with the method of characteristics with analytical decomposition and successive approximation. The new solution was verified favorably with a finite-difference approximation. A field verification via a comparison with observed storm hydrographs from the Schuylkill River near Philadelphia indicated that with constant lateral flow the nonlinear model reasonably predicted the observed flow rates, except during periods of intense rainfall. An improved nonlinear model that accounts for variable lateral flow due to changing effective precipitation is proposed. Numerical measures of accuracy indicated that the new variable-rate nonlinear model performs better than the constant lateral flow and the linear kinematic wave model. The linear kinematic wave model produced poor forecasts, especially in the flow time and flood-peak time. The new solution is ...

Essential to the application of the kinematic wave theory to open channel flow is the kinematic wave parameters which relate the discharge to the flow area in the channel. Earlier works have developed the kinematic wave parameters for a variety of channel shapes, but none for the trapezoidal channel. This paper unveils the kinematic wave parameters for four channel types: (1) trapezoidal channel with unequal side slopes; (2) trapezoidal channel with equal side slopes; (3) trapezoidal channel with one side vertical; and (4) rectangular channel. However, in the application of these parameters, all of them require the determination of flow area which is quite troublesome as the expression is not explicit. For the purpose of developing explicit analytical solutions, for channel types (2) and (3), it is shown that they can be approximated by a wide and a deep trapezoidal channels. For channel type (4), it can be approximated by a wide rectangular, a square and a deep rectangular channel. Further, for cases whe...

The linkage of surface runoff in urban areas to water quantity and quality has been studied extensively in the literature. Many computer models based on different routing theories have been developed to simulate the rainfall-runoff process in urban areas. Those computer models are classified into two categories: hydrologic models and hydraulic models. Hydrologic models are based on a hypoth- esized relation between outflow and water storage in the watershed, which is often modeled as a conceptual reservoir. The nonlinear reservoir method is a typical hydrologic routing method applied in models such as the Stormwater Management Model (SWMM). Hydraulic models are based on approximations of the real physical rainfall-runoff process. Kinematic-wave theory, utilized by many models including the Dynamic Watershed Simulation Model, is a commonly used hydraulic routing method. Previously unpublished experimental data obtained from the Watershed Experimentation System at the University of Illinois at Urbana-Champaign, Ill. were used to test the accuracy of these two routing methods. The nonlinear reservoir routing method as applied in SWMM may provide acceptable results for storms with durations longer than the watershed time of concentration (42 experiments )( average model fit efficiencyE = 0.88), but for storms with durations less than or equal to the time of concentration (26 experiments), poor results were obtained (average E= 0.07). More accurate results generally were obtained using kinematic-wave routing (average E= 0.928 and 0.807 for storm durations exceeding and not exceeding the watershed time of concentration, respectively). These results fit with the theoretical basis of the kinematic-wave theory that considers the actual physical processes in surface flow generation, while the nonlinear reservoir method does not consider the impact from the time lag needed for the flow depth to grow so that runoff can commence.

Overland flow on a hillslope is significantly influenced by its microtopography, slope length and gradient, and vegetative cover. A 1D kinematic wave model in conjunction with a revised form of the Green-Ampt infiltration equation was employed to evaluate the effect of these surface conditions. The effect of these conditions was treated through the resistance parameter in the kinematic wave model. The resistance in this paper was considered to be made up of grain resistance, form resistance, and wave resistance. It was found that irregular slopes with microtopography eroded more easily than did regular slopes. The effect of the slope gradient on flow velocity and flow shear stress could be negative or positive. With increasing slope gradient, the flow velocity and shear stress first increased to a peak value, then decreased again, suggesting that there exists a critical slope gradient for flow velocity and shear stress. The vegetative cover was found to protect soil from erosion primarily by enhancing erosion-resisting capacity rather than by decreasing the eroding capability of overland flow.

During the storm duration, the effects of surface resistance on the developing and receding overland flow depths (hj) on different flow parameters like the overland flow resistance coefficient (Nj), flow velocities (vj), Reynolds number (Rj), and Froude number (Fj) have been studied for the six natural catchments (0.012–92.5 km2) located in different agroclimatic regions of India. The kinematic wave (KW) equations are used for simulation of overland and channel flows using explicit methods for developing numerical solutions for the estimation of flow parameters at short durations. For the complete storm duration hj-Nj relationships have been found to form hysteresis loops. To predict resistance coefficients, simple hj-Nj relationships have been worked out separately for the rising and depleting overland flow conditions. Computed hydrographs simulated by incorporating these equations in the KW model agree well with the observed ones. The overall applicability of the suggested approach is successfully demon...

Time of travel in channel is an important parameter in drainage design. By means of the kinematic wave theory, it is possible to obtain an analytical time of travel formula for certain idealized channel conditions. Hitherto, the kinematic wave theory has been applied to the rectangular channel of special cases only, such as the wide rectangular channel, the square channel, and the deep rectangular channel. In this paper, the discharge-flow area parameters are derived for a rectangular channel of any flow depth, namely, the general rectangular channel. If these parameters are incorporated into the existing computer programs, it will enable these programs to model the general rectangular channel. Further, based on the kinematic wave theory, a generalized time of travel formula for a rectangular channel is developed. It is applicable to the general rectangular channel subject to a uniform lateral inflow and a constant upstream inflow. For the case of zero upstream inflow, the general formula is compared with...