Kinematic Wave Overland Flow Research Articles

Addition of overland runoff and flow routing methods to SWMM-model application to Hyderabad, India.

Hydrological models apply different methods to estimate runoff and route flows. Suitability of these methods is not unique, but varies with catchment conditions. This study aims to find the suitable overland runoff and flow routing methods for a catchment in Hyderabad, India, using customised Storm Water Management Model (SWMM-C). Currently, SWMM adapts only non-linear reservoir (NLR) method to estimate overland runoff. Linear reservoir (LR) and kinematic wave overland flow (KWO) have been incorporated as additional overland runoff methods. For flow routing, SWMM currently has kinematic wave (KW) and dynamic wave (DW) methods. Muskingum, Muskingum Cunge (MC) and lag methods have been included as additional methods in this customised version. SWMM-C was calibrated with four event rainfalls and tested with six event rainfalls using all possible combinations of overland runoff and flow routing methods. Efficiency of SWMM-C in simulating runoff was evaluated using performance indices. Results showed that for low magnitude event rainfalls, NLR, LR and KWO simulated runoff with a maximum deviation of 50%, 60% and 40% from observed runoff, respectively. In high magnitude event rainfalls, NLR, LR and KWO simulated runoff with maximum deviations of 20%, 40% and 20%, respectively, from the observed runoff. It was inferred from model outputs that NLR method could simulate runoff reasonably well for rainfalls that have duration greater than the time of concentration of catchment. LR method could simulate peak runoff better. KWO method was found to be suitable for chosen catchment for all rainfall durations. Flow routing methods KW, DW and MC are found to have minor influences on the runoff.

Nonmonotonic and spatial‐temporal dynamic slope effects on soil erosion during rainfall‐runoff processes

AbstractThe slope effect on flow erosivity and soil erosion still remains a controversial issue. This theoretical framework explained and quantified the direct slope effect by coupling the modified Green‐Ampt equation accounting for slope effect on infiltration, 1‐D kinematic wave overland flow routing model, and WEPP soil erosion model. The flow velocity, runoff rate, shear stress, interrill, and rill erosion were calculated on 0°–60° isotropic slopes with equal horizontal projective length. The results show that, for short‐duration rainfall events, the flow erosivity and erosion amounts exhibit a bell‐shaped trend which first increase with slope gradient, and then decrease after a critical slope angle. The critical slope angles increase significantly or even vanish with increasing rainfall duration but are nearly independent of the slope projective length. The soil critical shear stress, rainfall intensity, and temporal patterns have great influences on the slope effect trend, while the other soil erosion parameters, soil type, hydraulic conductivity, and antecedent soil moisture have minor impacts. Neglecting the slope effect on infiltration would generate smaller erosion and reduce critical slope angles. The relative slope effect on soil erosion in physically based model WEPP was compared to those in the empirical models USLE and RUSLE. The trends of relative slope effect were found quite different, but the difference may diminish with increasing rainfall duration. Finally, relatively smaller critical slope angles could be obtained with the equal slope length and the range of variation provides a possible explanation for the different critical slope angles reported in previous studies.

Sub‐grid scale parameterization of hillslope runoff and erosion processes for catchment‐scale models of semi‐arid landscapes

AbstractThe processes of hillslope runoff and erosion are typically represented at coarse spatial resolution in catchment‐scale models due to computational limitations. Such representation typically fails to incorporate the important effects of topographic heterogeneity on runoff generation, overland flow, and soil erosion. These limitations currently undermine the application of distributed catchment models to understand the importance of thresholds and connectivity on hillslope and catchment‐scale runoff and erosion, particularly in semi‐arid environments. This paper presents a method for incorporating high‐resolution topographic data to improve sub‐grid scale parameterization of hillslope overland flow and erosion models. Results derived from simulations conducted using a kinematic wave overland flow model at 0.5 m spatial resolution are used to parameterize the depth–discharge relationship in the overland flow model when applied at 16 m resolution. The high‐resolution simulations are also used to derive a more realistic parameterization of excess flow shear stress for use in the 16 m resolution erosion model. Incorporating the sub‐grid scale parameterization in the coarse‐resolution model (16 m) leads to improved predictions of overland flow and erosion when evaluated using results derived from high‐resolution (0.5 m) model simulations. The improvement in performance is observed for a range of event magnitudes and is most notable for erosion estimates due to the non‐linear dependency between the rates of erosion and overland flow. Copyright © 2013 John Wiley & Sons, Ltd.

Scale invariance and self‐similarity in kinematic wave overland flow in space and time

AbstractFractals are famous for their self‐similar nature at different spatial scales. Similar to fractals, solutions of scale invariant processes are self‐similar at different space–time scales. This unique property of scale‐invariant processes can be utilized to translate the solution of the processes at a much larger or smaller space–time scale (domain) based on the solution calculated on the original space–time scale. This study investigates scale invariance conditions of kinematic wave overland flow process in one‐parameter Lie group of point transformations framework. Scaling (stretching) transformation is one of the one‐parameter Lie group of point transformations and it has a unique importance among the other transformations, as it leads to the scale invariance or scale dependence of a process. Scale invariance of a process yields a self‐similar solution at different space–time scales. However, the conditions for the process to be scale invariant usually dictate various relationships between the scaling coefficients of the dependent and independent variables of the process. Therefore, the scale invariance of a process does not assure a self‐similar solution at any arbitrary space and time scale. The kinematic wave overland flow process is modelled mathematically as initial‐boundary value problem. The conditions to be satisfied by the system of governing equations as well as the initial and boundary conditions of the kinematic wave overland flow process are established in order for the process to be scale invariant. Also, self‐similarity of the solution of the kinematic wave overland flow under the established invariance conditions is demonstrated by various numerical example problems. Copyright © 2011 John Wiley & Sons, Ltd.

Uncertainty Evaluation of Coliform Bacteria Removal from Vegetated Filter Strip under Overland Flow Condition

Vegetated filter strips (VFS) have become an important component of water quality improvement by reducing sediment and nutrients transport to surface water. This management practice is also beneficial for controlling manure-borne pathogen transport to surface water. The objective of this work was to assess the VFS efficiency and evaluate the uncertainty in predicting the microbial pollutant removal from overland flow in VFS. We used the kinematic wave overland flow model as implemented in KINEROS2 coupled with the convective-dispersive overland transport model which accounts for the reversible attachment-detachment and surface straining of infiltrating bacteria. The model was successfully calibrated with experimental data obtained from a series of simulated rainfall experiments at vegetated and bare sandy loam and clay loam plots, where fecal coliforms were released from manure slurry applied on the top of the plots. The calibrated model was then used to assess the sensitivity of the VFS efficiency to the model parameters, rainfall duration, and intensity for a case study with a 6-m VFS placed at the edge of 200-m long field. The Monte Carlo simulations were also performed to evaluate the uncertainty associated with the VFS efficiency given the uncertainty in the model parameters and key inputs. The VFS efficiency was found to be <95% in 25%, <75% in 23%, and <25% in 20% of cases. Relatively long high-intensity rainfalls, low hydraulic conductivities, low net capillary drives of soil, and high soil moisture contents before rainfalls caused the partial failure of VFS to retain coliforms from the infiltration excess runoff.

Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods

Abstract. Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thoré basin and used as a relatively simple (synthetic observations) but didactic application case. It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting.

Stability and accuracy of two-dimensional kinematic wave overland flow modeling

A two-dimensional finite element based overland flow model was developed and used to study the accuracy and stability of three numerical schemes and watershed parameter aggregation error. The conventional consistent finite element scheme results in oscillations for certain time step ranges. The lumped and the upwind finite element schemes are tested as alternatives to the consistent scheme. The upwind scheme did not improve on the stability or the accuracy of the solution, while the lumped scheme provided stable and accurate solutions for time steps twice the size of time steps needed for the consistent scheme. A new accuracy based dynamic time step estimate for the two-dimensional overland flow kinematic wave solution is developed for the lumped scheme. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the watershed hydrograph. Due to lack of analytical solutions, the time step was developed by comparing numerical solutions of various levels of discretization to a reference solution using a very fine mesh and a very small time step. The time step criteria were tested on a different set of problems and proved to be adequate for accurate and stable solutions. A sensitivity analysis for the watershed slope, Manning’s roughness coefficient and excess rainfall rate was conducted in order to test the effect of parameter aggregation on the stability and accuracy of the solution. The results of this analysis show that aggregation of the slope data resulted in the highest error. The roughness coefficient had a smaller effect on the solution while the rainfall intensity did not show any significant effect on the flow rate solution for the range of rainfall intensity used. This work pioneers the challenge of providing guidelines for accurate and stable numerical solutions of the two-dimensional kinematic wave equations for overland flow.

Scale effects of Hortonian overland flow and rainfall‐runoff dynamics: laboratory validation of a process‐based model

AbstractHortonian runoff was measured in the laboratory from uniform slopes of lengths of 1·5, 3·0, and 6·0 m for steady, high‐intensity rainstorms with durations of 1·0 to 7·5 min. A clear reduction in runoff per unit slope length was found as slope lengths were increased. This effect becomes more pronounced with decreasing storm duration. The runoff data were used to validate a simple process‐based model that combines the Philip‐two‐term infiltration equation with the kinematic wave overland flow principle. The predicted and experimental results agreed well. Laboratory findings were extrapolated with the aid of the model to slopes and rainfall durations similar to those found under West African conditions. The calculated reduction of runoff per unit length is similar to reported observations. Thus, this process‐based model can largely explain the phenomenon of runoff reduction with increasing slope length. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Dynamic Time Step for One-Dimensional Overland Flow Kinematic Wave Solution

Kinematic wave theory is widely used in modeling a variety of hydrologic processes. Results of applying the kinematic wave overland flow solution using different time steps showed that the conventionally used stability criterion known as the Courant condition fails to give a time step estimate that ensures stable and accurate numerical solutions. Accordingly, a new accuracy-based dynamic time step estimate for the one dimensional overland flow kinematic wave solution is developed. The newly developed dynamic time step estimates are functions of the mesh size, watershed slope, roughness, excess rainfall, and time of concentration. The new criteria were developed by comparing the consistent formulation of the Galerkin-Crank Nicholson numerical solution of the kinematic wave equation to the characteristic method-based analytical solution, using different time steps and meshes. For each simulation, characterized by boundary and initial conditions and mesh size, an optimal time step that integrates the problem within 5% error was determined. The series of mesh sizes and corresponding optimal time steps were used to develop the dynamic time step. The time step criteria were tested on a variety of problems, including a steady state and time varying rainfall scenarios, and proved to be adequate for accurate and stable results within an efficient computational time. The criteria can be easily integrated in flow routing models to select the optimal time step with minimal user input.

Distributed modeling of storm flow generation in an Amazonian rain forest catchment: Effects of model parameterization

We describe a process‐based storm flow generation model, Topog_SBM consisting of a simple bucket model for soil water accounting, a one‐dimensional kinematic wave overland flow scheme, and a contour‐based element network for routing surface and subsurface flows. Aside from topographic data and rainfall the model has only six input parameters: soil depth (z), saturated hydraulic conductivity at the soil surface (K0), the rate of decay in K0 with depth (m), the Manning surface roughness parameter (n), the maximum (saturated) soil water content (θs), and the minimum (residual) soil water content (θr). However, the model is fully distributed, so these values can vary in magnitude across space. The model was applied to La Cuenca, a very small rainforest catchment in western Amazonia that has been well characterized in several hydrometric and hydrochemical investigations. Total runoff, peak runoff, time of rise, and lag time were predicted for 34 events of varying magnitudes and antecedent moisture conditions. We compared results for eight different model parameterizations or “sets”; four of these were freely calibrated to yield the best possible model fit to runoff data, whereas the other four were constrained (in various ways) by the use of actual K0 data gathered for the catchment. The eight sets were calibrated on either one of three events or on the three events jointly to illustrate the importance of calibration event selection on model performance. Model performance was evaluated by comparing observed and predicted (1) storm flow hydrograph attributes and (2) spatiotemporal patterns of overland flow occurrence across the catchment. The model generally predicted the right amount of runoff but usually underpredicted the peak runoff rate and overpredicted the time of rise. The “best” parameterization could credibly predict hydrographs for only about half of the events. Significant, and sometimes gross, errors were encountered for about one fourth of the events modeled, raising concerns in our minds about the a priori simulation of events that diverge too far from the conditions that the model was calibrated for. For the best parameterization we were able to predict an overland flow frequency distribution that accorded with field observations, though the model almost always overpredicted the spatial extent of overland flow. We concluded that model performance for the La Cuenca conditions could be enhanced by adding a “fast” subsurface flow pathway and/or by modifying the K0 versus depth decay function.

Modeling hydrology and sediment transport in vegetative filter strips

The performance of vegetative filter strips is governed by complex mechanisms. Models can help simulate the field conditions and predict the buffer effectiveness. A single event model for simulating the hydrology and sediment filtration in buffer strips is developed and field tested. Input parameters, sensitivity analysis, calibration and field testing of the model are presented. The model was developed by linking three submodels to describe the principal mechanisms found in natural buffers: a Petrov–Galerkin finite element kinematic wave overland flow submodel, a modified Green–Ampt infiltration submodel and the University of Kentucky sediment filtration model for grass areas. The new formulation effectively handles complex sets of inputs similar to those found in natural events. Major outputs of the model are water outflow and sediment trapping on the strip. The strength of the model is a good description of the hydrology within the filter area, which is essential for achieving good sediment outflow predictions or trapping efficiency. The sensitivity analysis indicates that the most sensitive parameters for the hydrology component are initial soil water content and vertical saturated hydraulic conductivity, and sediment characteristics (particle size, fall velocity and sediment density) and grass spacing for the sediment component. A set of 27 natural runoff events (rainfall amounts from 0.003 to 0.03 m) from a North Carolina Piedmont site was used to test the hydrology component, and a subset of nine events for the sediment component. Good predictions are obtained with the model if shallow uniform sheet flow (no channelization) occurs within the filter.

VALIDATING A VEGETATIVE FILTER STRIP PERFORMANCE MODEL

Vegetative filter strips (VFS) reduce losses of nutrients, solids, and other materials from land area treated with fertilizers and manures. A number of models are available that simulate nutrient and sediment transport in VFS. While VFS effectiveness is considered to depend on lengths of pollutant source area and VFS areas, few published studies have tried to validate these models using variable pollutant source area and VFS area. The objective of this study was to validate an event-based nutrient transport model (Chaubey et al., 1995) that simulates soluble nutrient transport in VFS. This model links three sub-models: modified Green-Ampt infiltration, non-linear kinematic wave overland flow routing, and a nutrient transport component. The nutrient transport component considers infiltration as the only mechanism of pollutant removal from runoff. Data from a field plot experiment were used to validate the model. The model was executed using an uncalibrated runoff component, a calibrated runoff component, and measured runoff. The concentrations of parameters entering the VFS from three different poultry litter application lengths (6.1, 12.2, and 18.3 m) were not significantly different. However, predicted concentrations at subsequent lengths were different for all the three poultrylitter application lengths. This finding was consistent with the observed data. Model execution with the uncalibrated runoff component, calibrated runoff component, and measured runoff underpredicted concentrations and mass transport at various locations along the length of the VFS. Underprediction of concentration was judged to be the reason for underprediction of mass transport. The agreement between the observed and predicted concentrations and mass transport, however, improved when runoff predictions from the calibrated runoff component and measured runoff were used. This suggests that accurate prediction of infiltration and runoff is critical for accurate prediction of concentration mass transport. Furthermore, since concentration was underpredicted even when measured runoff was used, this study suggests that the nutrient transport component might be improved, possibly by including nutrient removal mechanisms other than infiltration.

A quadratic Petrov‐Galerkin Solution for kinematic wave overland flow

A Petrov‐Galerkin (PG) finite element method was developed to solve the kinematic wave formulation of the overland flow equations. The resultant model uses quadratic basis functions and test functions that are modified by polynomials of cubic and quartic order, yielding a formulation that includes four PH parameters. The PG model was found to reduce the mean sum of square error of the solution compared to a conventional Bubnov‐Galerkin finite element solution by about a factor of 3 as the Courant number (Cr) approached one. Good results were also achieved with the PG method for problems that resulted in shock formation, which are typical of many applied problems of concern. PG parameters were found to depend strongly upon the Courant number and weakly upon the number of nodes in the system. Polynomial expressions were derived to approximate the PG parameters over the range 0 &lt; Cr &lt; 1. As the number of nodes in the system increased, a single‐parameter version of the model yielded solutions approaching the accuracy of the four‐parameter model.

Modification of the Kinematic Wave‐Philip Infiltration Overland Flow Model

In previous work a solution was developed for the kinematic wave overland flow equation with rainfall excess given by Philip's infiltration equation. Subsequent application of this solution to field data from small plots revealed the need for an improved model. The principal requirement is the incorporation of depression storage into the rising limb calculation. A second requirement is a more precise approximation of the water surface profile at the end of rainfall. This improves the falling limb calculations. This paper shows the solutions obtained by incorporating these improvements and demonstrates their effects on predicted hydrographs and water surface profiles.

Converging Flow Model Applied to Urban Catchment

A converging kinematic wave overland flow model was applied to an urban catchment, Rock Creek Watershed in Maryland. The 2-parameter model was easily calibrated and gave reasonable predictions for hydrograph shape as well as peak flow. Two methods for estimating abstractions from gross precipitation were applied. The first was a generalization of a standard infiltration equation and the second used a linear regression between direct runoff and gross precipitation. The fairly accurate results suggest that the converging flow model is ideal for a variety of uses in urban hydrology.