Kinematic Wave Approximation Research Articles

Regional analysis using the Geomorphoclimatic Instantaneous Unit Hydrograph

Abstract. The construction of design flood hydrographs for ungauged drainage areas has traditionally been approached by regionalisation, i.e. the transfer of information from the gauged to the ungauged catchments in a region. Such approaches invariably depend upon the use of multiple linear regression analysis to relate unit hydrograph parameters to catchment characteristics and generalised rainfall statistics. The concept of the geomorphological instantaneous unit hydrograph (GIUH), in relating the shape and scale of the catchment transfer function to stream network topology and channel characteristics, offers an alternative methodology. GIUH derivation depends upon a series of assumptions, including that of estimating a "characteristic velocity"; these continue to attract attention and debate. However, if this velocity is expressed in terms of the kinematic wave approximation, the peak and time-to-peak of the IUH may be expressed in terms of a group of catchment and channel characteristics and the intensity of rainfall excess, giving the so-called geomorphoclimatic IUH (GCIUH). Previous studies involving the GCIUH have developed a single IUH relating to the total duration of rainfall excess. In this study, the rainfall excess duration was divided into several (equal) time increments, with separate IUHs being generated for each interval. This quasi-linear approach was applied to 105 storm events from nine catchments in the south-west of England, ranging in size from 6 to 420 (km)2 . The results showed that, providing the time interval chosen is fine enough to capture the shape of the runoff hydrographs, a comparable level of goodness-of-fit can be obtained for catchments covering a range of about 1:75 in area. The modified GCIUH approach as described is therefore recommended for further investigation and intercomparison with regression-based regionalisation methods. Keywords: floods; geomorphology; rainfall-runoff modelling

Validation of a vegetated filter strip model (VFSMOD)

AbstractVegetated filter strips (VFS) are designed to reduce sediment load and other pollutants into water bodies. However, adaptation of VFS in the field has been limited owing to lack of data about their efficiency and performance under natural field conditions. A number of models are available that simulate sediment transport and trapping in VFS, but there is a general lack of confidence in VFS models owing to limited validation studies and model limitations that prevent correct application of these models under field conditions. The objective of this study is to test and validate a process‐based model (VFSMOD) that simulates sediment trapping in VFS. This model links three submodels: modified Green–Ampt's infiltration, Quadratic overland flow submodel based on kinematic wave approximation and University of Kentucky sediment filtration model. A total of 20 VFS, 2, 5, 10 and 15 m long and with various vegetation covers, were tested under simulated sediment and runoff conditions. The results of these field experiments were used to validate the VFS model. The model requires 25 input parameters distributed over five input files. All input parameters were either measured or calculated using experimental data. The observed sediment trapping efficiencies varied from 65% in the 2‐m long VFS to 92% in the 10‐m long filters. No increase in sediment removal efficiency was observed at higher VFS length. Application of the VFS model to experimental data was satisfactory under the condition that actual flow widths are used in the model instead of the total filter width. Predicted and observed sediment trapping efficiencies and infiltration volume fitted very well, with a coefficient of determination (R2) of 0·9 and 0·95, respectively. Regression analyses revealed that the slope and intercept of the regression lines between predicted versus observed infiltration volume and trapping efficiency were not significantly different than the line of perfect agreement with a slope of 1·0 and intercept of 0·0. Copyright © 2001 John Wiley & Sons, Ltd.

Predicting floodplain inundation: raster‐based modelling versus the finite‐element approach

AbstractWe compare two approaches to modelling floodplain inundation: a raster‐based approach, which uses a relatively simple process representation, with channel flows being resolved separately from the floodplain using either a kinematic or diffusive wave approximation, and a finite‐element hydraulic model aiming to solve the full two‐dimensional shallow‐water equations. A flood event on a short (c. 4 km) reach of the upper River Thames in the UK is simulated, the models being validated against inundation extent as determined from satellite synthetic aperture radar (SAR) imagery. The unconstrained friction parameters are found through a calibration procedure, where a measure of fit between predicted and observed shorelines is maximized. The raster and finite‐element models offer similar levels of performance, both classifying approximately 84% of the model domain correctly, compared with 65% for a simple planar prediction of water surface elevation. Further discrimination between models is not possible given the errors in the validation data. The simple raster‐based model is shown to have considerable advantages in terms of producing a straightforward calibration process, and being robust with respect to channel specification. Copyright © 2001 John Wiley & Sons, Ltd.

Flood Runoff Analysis in the Upper Chang Jiang Basin

Channel network with 1km mesh is developed for the Upper Chang Jiang Basin of 760, 000km2 by using DEM and GLOBE. Arrangement of the network to one dimensional array enables runoff computation for the large area with the small mesh. The runoff analysis with kinematic wave approximation and input data from ISLSCP on rainfall and evapotranspiration gives appropriate discharge hydrograph at Yichang.

Two-dimensional simulation of two viscous debris flows in Austria

Risk mitigation and hazard assessment in steep torrent catchments requires a high level of information about possible runout distances, depth, velocities and resulting impact forces of mass movement processes and its consequences to endangered areas. Two well documented debris flow events at Wartschenbach/Eastern Tyrol and Moschergraben/Styria enable to investigate possible applications of the FLO-2D computer model. The FLO-2D computer model was developed at the Colorado State University and is a grid-based physical process model which routes precipitation-runoff and flood hydrographs over unconfined surfaces and channels using either a kinematic, diffusive or dynamic wave approximation to the momentum equation. All transitions between water floods and fully developed debris flows can be simulated using topographic data files to build the grid elements, information about surface roughness and properties of the sediment water mixture. A quadratic rheological model is used to describe flow behaviour of viscous debris flows. The rheological properties of deposited debris flow material are determined using a rotational viscometer and a new developed conveyor-channel.The simulation results and the gained experience are of great promise to the future of debris flow modelling.

A simple raster-based model for flood inundation simulation

In this paper the development of a new model for simulating flood inundation is outlined. The model is designed to operate with high-resolution raster Digital Elevation Models, which are becoming increasingly available for many lowland floodplain rivers and is based on what we hypothesise to be the simplest possible process representation capable of simulating dynamic flood inundation. This consists of a one-dimensional kinematic wave approximation for channel flow solved using an explicit finite difference scheme and a two-dimensional diffusion wave representation of floodplain flow. The model is applied to a 35 km reach of the River Meuse in The Netherlands using only published data sources and used to simulate a large flood event that occurred in January 1995. This event was chosen as air photo and Synthetic Aperture Radar (SAR) data for flood inundation extent are available to enable rigorous validation of the developed model. 100, 50 and 25 m resolution models were constructed and compared to two other inundation prediction techniques: a planar approximation to the free surface and a relatively coarse resolution two-dimensional finite element scheme. The model developed in this paper outperforms both the simpler and more complex process representations, with the best fit simulation correctly predicting 81.9% of inundated and non-inundated areas. This compares with 69.5% for the best fit planar surface and 63.8% for the best fit finite element code. However, when applied solely to the 7 km of river below the upstream gauging station at Borgharen the planar model performs almost as well (83.7% correct) as the raster model (85.5% correct). This is due to the proximity of the gauge, which acts as a control point for construction of the planar surface and the fact that here low-lying areas of the floodplain are hydraulically connected to the channel. Importantly though it is impossible to generalise such application rules and thus we cannot specify a priori where the planar approximation will work. Simulations also indicate that, for this event at least, dynamic effects are relatively unimportant for prediction of peak inundation. Lastly, consideration of errors in typically available gauging station and inundation extent data shows the raster-based model to be close to the current prediction limit for this class of problem.

Physically based river basin modelling within a GIS: the LISFLOOD model

Although many geographical information systems (GISs) are very advanced in data processing and display, current GIS are not capable of physically based modelling. Especially, simulating transport of water and pollutants through landscapes is a problem in a GIS environment. A number of specific routing methods are needed in a GIS for hydrologic modelling, amongst these are the numerical solutions of the Saint-Venant equations, such as the kinematic wave approximation for transport of surface water in a landscape. The PCRaster Spatial Modelling language is a GIS capable of dynamic modelling. It has been extended recently with a kinematic wave approximation simulation tool to allow for physically based water flow modelling. The LISFLOOD model is an example of a physically based model written using the PCRaster GIS environment. The LISFLOOD model simulates river discharge in a drainage basin as a function of spatial data on topography, soils and land cover. Although hydrological modelling capabilities have largely increased, there is still a need for development of other routing methods, such as a diffusion wave. Copyright © 2000 John Wiley & Sons, Ltd.

Kinematic wave approximations to hillslope hydrological processes in tills

Kinematic wave approximations to hillslope hydrological processes in tills

Kinematic wave approximations to hillslope hydrological processes in tills

This work has been carried out within the framework of NOPEX - a NOrthern hemisphere climate Processes land surface EXperiment. Its purpose is to describe the spatial variability of groundwater lev ...

Physically based river basin modelling within a GIS: the LISFLOOD model

Although many geographical information systems (GISs) are very advanced in data processing and display, current GIS are not capable of physically based modelling. Especially, simulating transport of water and pollutants through landscapes is a problem in a GIS environment. A number of specific routing methods are needed in a GIS for hydrologic modelling, amongst these are the numerical solutions of the Saint-Venant equations, such as the kinematic wave approximation for transport of surface water in a landscape. The PCRaster Spatial Modelling language is a GIS capable of dynamic modelling. It has been extended recently with a kinematic wave approximation simulation tool to allow for physically based water flow modelling. The LISFLOOD model is an example of a physically based model written using the PCRaster GIS environment. The LISFLOOD model simulates river discharge in a drainage basin as a function of spatial data on topography, soils and land cover. Although hydrological modelling capabilities have largely increased, there is still a need for development of other routing methods, such as a diffusion wave. Copyright © 2000 John Wiley & Sons, Ltd.

Solute transport under steady and transient conditions in biodegraded municipal solid waste

The transport of a conservative tracer (lithium) in a large (3.5 m3) undisturbed municipal solid waste sample has been investigated under steady and fully transient conditions using a simple model. The model comprises a kinematic wave approximation for water movement, presented in a previous paper, and a strict convective solute flux law. The waste medium is conceptualized as a three‐domain system consisting of a mobile domain (channels), an immobile fast domain, and an immobile slow domain. The mobile domain constitutes only a minor fraction of the medium, and the access to the major part of medium is constrained by diffusive transport. Thus the system is in a state of physical nonequilibrium. The fast immobile domain is the part of the matrix which surrounds the channels and forms the boundary between the channels and the matrix. Owing to its exposure to mobile water, which enhances the biodegradation process, this domain is assumed to be more porous and loose in its structure and therefore to respond faster to a change in solute concentration in the mobile domain compared to the regions deep inside the matrix. The diffusive mass exchange between the domains is modeled with two first‐order mass transfer expressions coupled in series. Under transient conditions the system will also be in a state of hydraulic nonequilibrium. Hydraulic gradients build up between the channel domain and the matrix in response to the water input events. The gradients will govern a reversible flow and convective transport between the domains, here represented as a source/sink term in the governing equation. The model has been used to interpret and compare the results from a steady state experiment and an unsteady state experiment. By solely adjusting the size of the fraction of the immobile fast domain that is active in transferring solute, the model is capable of accurately reproducing the measured outflow breakthrough curves for both the steady and unsteady state experiments. During transient conditions the fraction of the immobile fast domain that is active in transferring solute is found to be about 65% larger than that under steady state conditions. It is therefore concluded that the water input pattern governs the size of the fraction of the immobile fast domain which, in turn, governs the solute residence time in the solid waste. It can be concluded that the contaminant transport process in landfills is likely to be in a state of both physical, hydraulic, and chemical nonequilibrium. The transport process for a conservative solute is here shown to be dominated by convective transport in the channels and a fast diffusive mass exchange with the surrounding matrix. This may imply that the observed leachate quality from landfills mainly reflects the biochemical conditions in these regions. The water input pattern is of great importance for the transport process since it governs the size of the fraction of the immobile fast domain which is active in transferring solute. This may be the reason for leachate quality to be seasonally or water flux dependent, which has been observed in several investigations. The result also has a significant practical implication for efforts to enhance the biodegradation process in landfills by recycling of the leachate.

RUNOFF ANALYSIS IN THE ABUKUMA RIVER UPSTREAM BASIN FOR THE FLOOD AT THE END OF AUGUST, 1998

Heavy rain that began to fall from the beginning of August 26, 1998 wasespecially intense in the boundary region of Fukushima and Tochigi Prefectures. The total rainfall in six days reached more than 1200mm. This paper deals with the runoff analysis in the Abukuma River basin for this rain. The model based on the channel network with the mesh size of 500m and the kinematic wave approximation for the dircct runoff component was applied. The comparison between analysis and observation in the discharge gives the runoff rate of 0.73 which is about twice for the usual floods in the basin. The long duration of the previous rain is supposed to affect the high efficiency of the runoff.

Kinematic wave model for water movement in municipal solid waste

The movement of water in a large (3.5 m3) undisturbed sample of 22‐year‐old municipal solid waste has been modeled using a kinematic wave approximation for unsaturated infiltration and internal drainage. The model employs a two‐parameter power expression as macroscopic flux law. The model parameters were determined and interpreted in terms of the internal geometry of the waste medium by fitting the model to one set of infiltration and drainage data. The model was validated using another set of data from a sequence of water input events. The results of the validation show that the model performs satisfactorily, but further development of the model to incorporate spatial variability would increase its capability.

Accuracy of the kinematic wave and diffusion wave approximations for time-independent flows with infiltration included

Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with infiltration were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1·4% for KF20≥7·5, and up to 14% for KF20≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF20 (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. © 1998 John Wiley & Sons, Ltd.

Simulation of the direct runoff hydrograph at basin outlet

A simple model describing the transformation of effective rainfall to direct runoff through the overland flow mechanism is presented. The model is based on the classical representation of a watershed by a combination of planes and channels. The dynamics of overland flow in each plane is simulated by the non-linear kinematic wave, but the outflow from a given plane is concentrated in the middle of the corresponding drainage channel. The water routing in the channels is carried out by a piece-wise linearized formulation in space of the kinematic wave approximation. Using synthetic events on 10 watersheds, the model was tested by comparing it with results obtained by applying the non-linear kinematic wave to all the elements of the watershed. The model was found to be adequate, even in a form that simplifies the geometric features of the planes through an averaging procedure based on the Horton–Strahler ordering scheme of the watershed. © 1998 John Wiley & Sons, Ltd.

On the interaction between infiltration and Hortonian runoff

Abstract A model which couples the kinematic wave approximation for Hortonian overland flow and the conceptual approach developed by Corradini et al. (1997) [J. Hydrol., 192, 104–124] for local infiltration was used to investigate the effects of random spatial variability of saturated hydraulic conductivity, K s , on the outflow hydrograph at hillslope scale. The model incorporates a representation of infiltration of overland flow running over pervious downstream areas (“run-on” process). Single rainfall pulses and complex storms over two soils, representative of a silty loam and a sandy loam soil, were considered. Our results suggest that for realistic values of the coefficient of variation of K s the run-on process cannot be disregarded, because it produces a significant decrease of overland flow during both the rising and the recession limb of the hydrograph. Furthermore, the role of the level of spatial correlation of K s was found to be typically minor and the run-on process concurred to this result. The possibility of simplifying the stochastic problem by a deterministic approach based on the use of a uniform lumped value of K s was also examined and rainfall patterns adequate for this simplification were deduced in terms of scaled storm intensity and storm duration.

ACCURACY OF KINEMATIC WAVE AND DIFFUSION WAVE APPROXIMATIONS FOR TIME-INDEPENDENT FLOW WITH MOMENTUM EXCHANGE INCLUDED

Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with momentum exchange included were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1% for KF20≥7·5 and up to 12% for KF20≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF20 (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary condition both in terms of the error magnitude and the segment of the channel reach for which these approximations would be applicable. © 1997 by John Wiley & Sons, Ltd.

A spatially distributed hydrologic model utilizing raster data structures

A distributed hydrologic model, known as the Terrestrial Hydrologic Model or THM was developed for use with rasterized databases to simulate surface runoff. Computations are performed on a pixel-by-pixel basis and all physical drainage basin properties including area, slope, stream length, and stream order are obtained or estimated from a digital elevation model (DEM). Other data sets, such as curve numbers or infiltration rates, are required for estimating the hydrologic abstractions. Precipitation is supplied in the form of gage input, uniform distributions, or raster data. At the present time, hydrologic abstractions can be estimated by any of three methods: a constant infiltration rate, the Soil Conservation Service curve number method, or solution of the more physically based Green-Ampt equation. Overland flow is computed by a kinematic wave approximation and channel routing is performed using the Muskingum-Cunge method.

Application of Two Direct Runoff Prediction Methods in Puerto Rico

Two methods for predicting direct runoff from rainfall data were applied to several basins and the resulting hydrographs compared to measured values. The first method uses a geomorphology-based unit hydrograph to predict direct runoff through its convolution with the excess rainfall hyetograph. The second method shows how the resulting hydraulic routing flow equation from a kinematic wave approximation is solved using a spectral method based on the matrix representation of the spatial derivative with Chebyshev collocation and a fourth-order Runge-Kutta time discretization scheme. The calibrated Green-Ampt (GA) infiltration parameters are obtained by minimizing the sum, over several rainfall events, of absolute differences between the total excess rainfall volume computed from the GA equations and the total direct runoff volume computed from a hydrograph separation technique. The improvement made in predicting direct runoff using a geomorphology-based unit hydrograph with the ephemeral and perennial stream network instead of the strictly perennial stream network is negligible. The hydraulic routing scheme presented here is highly accurate in predicting the magnitude and time of the hydrograph peak although the much faster unit hydrograph method also yields reasonable results.

Analytical Integration of the Kinematic Equation for Runoff on a Plane Under Constant Rainfall Rate and Smith and Parlange Infiltration

An analytical solution to the kinematic wave approximation of the Saint‐Venant equations describing surface water flow with infiltration is presented. Adopting the Smith and Parlange formulation for the ponding time and the postponding infiltration rate, a change of variable among time and infiltration rate allow the analytical integration of the characteristic equations when the flow rate is expressed as the second power of the water depth. In the case of any other real exponent a simple numerical integration method may be used for the computation of the characteristic curves. An illustration is made to compare the solutions for different values of the exponent, as well as to assess the accuracy of some numerical schemes.