Kinematic Overland Flow Research Articles

DEVELOPMENT OF FLOOD ROUTING MODELS FOR WANG RIVER BASIN

Nowadays, severe flooding frequently occurs in various parts of Thailand resulted from changes in climatic condition and land use patterns. The flooding has caused great damages to properties and lives and affects country economy. Experience from the most severe flooding in the northern and central regions of Thailand in the year 2011 reveals that reliable flood warning system is still lagging. For flood warning purpose, it is necessary to have an accurate flood routing system. This study is aimed at developing mathematical models for flood routing so as to provide data for flood warning. Two different models are developed, i.e., kinematic overland flow model and kinematic stream flow model. The finite element method with Galerkin’s weighted residual technique is used in model development. The second-order Runge-Kutta method is applied to solve the set of differential equations obtained from finite element formulation. The developed models are applied to simulate flows in the Wang river basin in the northern region of Thailand during July 1 – October 31, 2011 when severe flooding occurred in this region. Model calibration is made by adjusting some parameters in the models and comparing the obtained results with measured data recorded by RID at 5 stream flow gauge stations along the Wang river. For correlation analysis, three statistical indices are determined, these include coefficient of determination, R2 , Nash–Sutcliffe model efficiency coefficient, NSE, and coefficient of variation of the root mean square error, CV(RMSE). It is found that the model results at the upstream portion of the river satisfactorily agree with the observed data, with the values of R2 greater than 0.55 and CV(RMSE) less than 0.57. For the downstream portion of the river, there are remarkable differences between the model results and the observed data. The values of R2 are less than 0.35, CV(RMSE) greater than 0.76, and the NSE values are less than 0.16. This might be due to some errors in the input data, including rainfall pattern, topography, land use, river cross-sectional area, and water seepage along the river. More detailed field investigation and model calibration are still needed.

Analytical Closed-Form Solution for 1D Linear Kinematic Overland Flow under Moving Rainstorms

AbstractAn 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.

KINEROS2/AGWA: Model Use, Calibration, and Validation

KINEROS (KINematic runoff and EROSion) originated in the 1960s as a distributed event-based model that conceptualizes a watershed as a cascade of overland flow model elements that flow into trapezoidal channel model elements. KINEROS was one of the first widely available watershed models that interactively coupled a finite difference approximation of the kinematic overland flow equations to a physically based infiltration model. Development and improvement of KINEROS continued from the 1960s on a variety of projects for a range of purposes, which has resulted in a suite of KINEROS-based modeling tools. This article focuses on KINEROS2 (K2), a spatially distributed, event-based watershed rainfall-runoff and erosion model, and the companion ArcGIS-based Automated Geospatial Watershed Assessment (AGWA) tool. AGWA automates the time-consuming tasks of watershed delineation into distributed model elements and initial parameterization of these elements using commonly available, national GIS data layers. A variety of approaches have been used to calibrate and validate K2 successfully across a relatively broad range of applications (e.g., urbanization, pre- and post-fire, hillslope erosion, erosion from roads, runoff and recharge, and manure transport). The case studies presented in this article (1) compare lumped to stepwise calibration and validation of runoff and sediment at plot, hillslope, and small watershed scales; and (2) demonstrate an uncalibrated application to address relative change in watershed response to wildfire.

Kinematic wave modeling of overland flow using characteristics method with cubic-spline interpolation

Use of characteristics method integrated with cubic-spline interpolation technique (CSMOC scheme) for computation of one-dimensional and two-dimensional kinematic overland flow has been examined in this study. The characteristic trajectory is allowed to fall on space line and time line for interpolating the corresponding values at the foot of trajectory in terms of neighboring grid points. The effects of different endpoint constraints on use of cubic-spline interpolation are investigated. As far as accuracy and simplicity are concerned, the not-a-knot constraint could be a better choice. Three hypothetical examples are used to examine the capabilities of CSMOC scheme through the comparison with the analytical solution and the well-known Preissmann scheme. Some degrees of numerical diffusion and numerical oscillation, attenuating and overestimating the peak discharge, are induced by the Preissmann scheme. In contrast, the CSMOC scheme gives convincing results for the kinematic overland flow computations.

A kinematic overland flow model to determine depression storage tilled surfaces

A method of predicting a spatial average value for depression storage of tilled surfaces is proposed. The method is based on the kinematic flow approximation to overland flow on a plane. In the laboratory, only the aspects of tillage, rainfall intensity and slope were investigated. The following impermeable models, simulating various tillage techniques, were used: plastic corrugations; concrete ridges; contrete mounds; concrete plane surface as reference. The experiments were repeated for each tillage model with different slopes (varying from 0.5 to 4%), and for each slope with different rainfall intensities (varying from 0.009 to 0.109 mm s −1). The method was verified by comparing predicted depression storage with depression storage obtained from water-balance consideration based on the experimental data. It is believed that the model can be used to estimate spatial average depression storag if infiltration is known.

Overland Flow on Pervious, Converging Surface

A desk-top method based on kinematic overland flow and Green-and-Ampt infiltration models is developed to determine the time of concentration of and the peak runoff rate from a converging basin. The governing equations of the rainfall-infiltration-overland flow process are written in terms of various dimensionless parameters. Common values of these parameters indicate hydrologic similarity of an infinite number of different converging basins, and therefore the results obtained in terms of these physically-based parameters can be generalized. Using this similarity concept, two charts have been developed to determine the time of concentration of a basin and the peak runoff rate. As illustrated by a sample application, these charts can be used for quick estimates of the design discharge for storm drainage facilities.

The Rational Formula Interpreted Using a Physically-Based Mathematical Model

A new interpretation is given for the rational formula in view of a mathematical model founded on the kinematic overland flow and Green and Ampt infiltration equations. The potential variability of the runoff coefficient with various rainfall and basin characteristics is demonstrated. However, using the concept of hydrologic similarity, it is possible to predict the runoff coefficient in terms of several physically-based non dimensional parameters for homogeneous planar, rectangular basins.

Pollutant Washoff by Overland Flow

A physically based mathematical model is presented for the process of pollutant washoff by overland flow on impervious surfaces. The model is based on the kinematic overland flow and convective pollutant transport equations. The pollutant detachment rate at any point along a surface is assumed to be proportional to the overland flow bottom shear stress and the amount of the pollutant on the surface. The constant of proportionality depends only on the pollutant characteristics, and therefore it can be treated as a calibration parameter insensitive to changes in the hydrologic conditions of the basin. The governing equations are written in dimensionless form, and are solved using an implicit finite difference scheme. The mathematical model is verified with a set of published experimental data. Based on the concept of hydraulic similarity, the results of the model are generalized and presented in chart form.

Kinematic overland flow — Generalization of Rose's approximate solution, Part II

The approximate kinematic overland flow equation derived by Rose et al. and generalized by Moore includes a water surface profile shape factor C. Rose et al. assumed a constant C = 0.625. The variation of C as a function of normalized discharge q∗ is examined during various phases of the overland flow hydrograph rise and recession under constant and time-varying rainfall excess. The possible range of C values is bounded by rising and falling limb boundary curves. These vary linearly from C = 1, q∗ = 0 to C = 0.625, q∗ = 1 (steady state or equilibrium) during the hydrograph rise and linearly from C = 0.625, q∗ = 1 to C = 0.4, q∗ = 0 during the recession. At any time during an event the value of C depends on both the value of q∗ and its previous pattern of variation or history. Analytical equations are presented that allow C to be estimated during a runoff event, thus permitting improved predictions of overland flow on plane surfaces using the approximate theory without any increase in computational complexity.

Time of Concentration of Overland Flow

A mathematical model based on kinematic overland flow and Green-Ampt infiltration is developed to calculate the time of concentration of overland flow on a rectangular plane surface. The governing equations of the rainfall-infiltration-overland flow process are written in terms of various dimensionless parameters. The relative time of concentration, defined as the ratio of the time of concentration of an infiltrating plane to that of a geometrically identical impervious surface, can be expressed in terms of only two other dimensionless parameters. These parameters are physically based and they account for the subsurface soil properties and the antecedent moisture content. The results, presented in chart form, can be used for predicting the time of concentration of a rectangular plot under constant-intensity rainfall.

Kinematic overland flow: Generalization of Rose's approximate solution

The approximate kinematic overland flow equation for parallel-sided planar surfaces proposed by Rose et al. has been generalized to a form that includes a water surface profile shape factor. Rose's equation assumes that transient water surface profiles can be approximated by the shape of the steady-state water surface profile using the steady-state shape factor (= 0.625). As a further development of his approach shape factors have been derived for rectangular, triangular and parabolic profiles. The rectangular profile approximates the actual profile during the early part of the overland flow hydrograph rise, while the steady-state profile approximates the profile near the hydrograph peak (or steady-state runoff). The water surface profile approaches a triangular or parabolic shape during the latter stages of the hydrograph recession. Use of the appropriate shape factor during the relevant portion of the hydrograph rise and fall allows improved predictions with Rose's approximate theory. Rose's theory has also been generalized for application to converging and diverging planar surfaces. This complete theory incorporates a brink depth convergence factor and a water surface profile factor that allows the predictions from an equivalent parallel-sided planar surface to be corrected to account for the effects of convergence or divergence on the overland flow hydrograph. These factors can be calculated directly from the physical characteristics of the overland flow plane.