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.     

A kinematic‐wave‐based distributed watershed model using FEM,GIS and remotely sensed data

For the appropriate management of water resources in a watershed, it is essential to calculate the time distribution of runoff for the given rainfall event. In this paper, a kinematic‐wave‐based distributed watershed model using finite element method (FEM), geographical information systems (GIS) and remote‐sensing‐based approach is presented for the runoff simulation of small watersheds. The kinematic wave equations are solved using FEM for overland and channel flow to generate runoff at the outlet of the watershed concerned. The interception loss is calculated by an empirical model based on leaf area index (LAI). The Green‐Ampt Mein Larson (GAML) model is used for the estimation of infiltration. Remotely sensed data has been used to extract land use (LU)/land cover (LC). GIS have been used to prepare finite element grid and input files such as Manning's roughness and slope. The developed overland flow model has been checked with an analytical solution for a hypothetical watershed. The model has been applied to a gauged watershed and an ungauged watershed. From the results, it is seen that the model is able to simulate the hydrographs reasonably well. A sensitivity analysis of the model is carried out with the calibrated infiltration parameters, overland flow Manning's roughness, channel flow Manning's roughness, time step and grid size. The present model is useful in predicting the hydrograph in small, ungauged watersheds. Copyright © 2007 John Wiley & Sons, Ltd.     

Geospatially based distributed rainfall‐runoff modelling for simulation of internal and outlet responses in a semi‐forested lower Himalayan watershed

This study presents a Geographic Information System (GIS)‐based distributed rainfall‐runoff model for simulating surface flows in small to large watersheds during isolated storm events. The model takes into account the amount of interception storage to be filled using a modified Merriam ( 1960 ) approach before estimating infiltration by the Smith and Parlange ( 1978 ) method. The mechanics of overland and channel flow are modelled by the kinematic wave approximation of the Saint Venant equations which are then numerically solved by the weighted four‐point implicit finite difference method. In this modelling the watershed was discretized into overland planes and channels using the algorithms proposed by Garbrecht and Martz ( 1999 ). The model code was first validated by comparing the model output with an analytical solution for a hypothetical plane. Then the model was tested in a medium‐sized semi‐forested watershed of Pathri Rao located in the Shivalik ranges of the Garhwal Himalayas, India. Initially, a local sensitivity analysis was performed to identify the parameters to which the model outputs like runoff volume, peak flow and time to peak flow are sensitive. Before going for model validation, calibration was performed using the Ordered‐Physics‐based Parameter Adjustment (OPPA) method. The proposed Physically Based Distributed (PBD) model was then evaluated both at the watershed outlet as well as at the internal gauging station, making this study a first of its kind in Indian watersheds. The results of performance evaluation indicate that the model has simulated the runoff hydrographs reasonably well within the watershed as well as at the watershed outlet with the same set of calibrated parameters. The model also simulates, realistically, the temporal variation of the spatial distribution of runoff over the watershed and the same has been illustrated graphically. Copyright © 2011 John Wiley & Sons, Ltd.     

Diverging overland flow

This study investigates divering overland flow utilizing kinematic wave theory, which does not appear to have been dealt with previously. Explicit analytical solutions are derived in dimensionless form for space-time invariant rainfall. Analytical solutions do not seem to be tractable for time-varying rainfall. Depending upon the duration of rainfall, equilibrium and partial equilibrium cases are distinguished explicitly. The effect of divergence parameter on the hydrograph shape is shown. The adequacy of kinematic approximation for characterization of diverging overland flow is tested against laboratory watershed results. The diverging overland flow model is found to yield results which compare well with observations and with those of a plane model.     

Multi‐site calibration using a grid‐based event rainfall–runoff model: a case study of the upstream areas of the Nakdong River basin in Korea

Most runoff analyses using a grid‐based distributed model use one parameter group calibrated at the outlet of a watershed, instead of dividing the watershed into subwatersheds. Significant differences between the observed value and the simulation result of the subwatersheds can occur if just one parameter group is used in all subwatersheds that have different hydrological characteristics from each other. Therefore, to improve the simulation results of the subwatersheds within a watershed, a model calibrated at every subwatershed needs to be used to reflect the characteristics of each subwatershed. In this study, different parameter groups were set up for one or two sites using a distributed model, the GRM (Grid based Rainfall‐runoff Model), and the evaluations were based on the results of rainfall–runoff analysis, which uses a multi‐site calibration (MSC) technique to calibrate the model at the outlet of each site. The Hyangseok watershed in Naeseong River, which is a tributary of Nakdong River in Korea, was chosen as the study area. The watershed was divided into five subwatersheds each with a subwatershed outlet that was applied to the calibration sites . The MSC was applied for five cases. When a site was added for calibration in a watershed, the runoff simulation showed better results than the calibration of only one site at the most downstream area of the watershed. The MSC approach could improve the simulation results on the calibrated sites and even on the non‐calibrated sites, and the effect of MSC was improved when the calibrated site was closer to the runoff site. Copyright © 2014 John Wiley & Sons, Ltd.     

Development and application of a spatially‐distributed Arctic hydrological and thermal process model (ARHYTHM)

A process‐based, spatially distributed hydrological model was developed to quantitatively simulate the energy and mass transfer processes and their interactions within arctic regions (arctic hydrological and thermal model, ARHYTHM). The model first determines the flow direction in each element, the channel drainage network and the drainage area based upon the digital elevation data. Then it simulates various physical processes: including snow ablation, subsurface flow, overland flow and channel flow routing, soil thawing and evapotranspiration. The kinematic wave method is used for conducting overland flow and channel flow routing. The subsurface flow is simulated using the Darcian approach. The energy balance scheme was the primary approach used in energy‐related process simulations (snowmelt and evapotranspiration), although there are options to model snowmelt by the degree‐day method and evapotranspiration by the Priestley–Taylor equation. This hydrological model simulates the dynamic interactions of each of these processes and can predict spatially distributed snowmelt, soil moisture and evapotranspiration over a watershed at each time step as well as discharge in any specified channel(s). The model was applied to Imnavait watershed (about 2·2 km²) and the Upper Kuparuk River basin (about 146 km²) in northern Alaska. Simulated results of spatially distributed soil moisture content, discharge at gauging stations, snowpack ablations curves and other results yield reasonable agreement, both spatially and temporally, with available data sets such as SAR imagery‐generated soil moisture data and field measurements of snowpack ablation, and discharge data at selected points. The initial timing of simulated discharge does not compare well with the measured data during snowmelt periods mainly because the effect of snow damming on runoff was not considered in the model. Results from the application of this model demonstrate that spatially distributed models have the potential for improving our understanding of hydrology for certain settings. Finally, a critical component that led to the performance of this modelling is the coupling of the mass and energy processes. Copyright © 2000 John Wiley & Sons, Ltd.     

Refinement of the channel response system by considering time-varying parameters for flood prediction

Impulse response functions derived from different types of flood wave equations (simplified shallow water equations) are continuously developed to conduct the linear channel routing (LCR), which is based on the linearized Saint Venant equation and has been widely applied to avoid any possibility of numerical instability. The impulse response function proposed by Dooge, Napiórkowski, and Strupczewski (1987) and derived from the dynamic wave equation with complete force terms has been acknowledged as a classic work to establish a good physical interpretation for the LCR model; however, the flexibility of altering the shape of impulse response still needs to be improved. Based on the concept of this work, this study intends to introduce the time-varying parameters in the model, so the values of parameters can be adjusted according to the inflow condition, flood stage, and the cross-sectional shape. Moreover, an integrated routing procedure is proposed to formulate the impulse response function for lateral-flow inputs and then to connect multiple inputs from subwatersheds or alongside the main channel with the impulse response function of each channel segment to reflect the spatial variation of hydraulic characteristics among different segments. In the discussion of this article, the impulse response function is analysed to show its sensitivity to hydraulic variables with spatial and temporary variations. Flood-event simulations of a studied watershed are also provided to verify the applicability of the proposed channel routing system.     

Improvement of surface run‐off in the hydrological model ParFlow by a scale‐consistent river parameterization

We propose an improvement of the overland‐flow parameterization in a distributed hydrological model, which uses a constant horizontal grid resolution and employs the kinematic wave approximation for both hillslope and river channel flow. The standard parameterization lacks any channel flow characteristics for rivers, which results in reduced river flow velocities for streams narrower than the horizontal grid resolution. Moreover, the surface areas, through which these wider model rivers may exchange water with the subsurface, are larger than the real river channels potentially leading to unrealistic vertical flows. We propose an approximation of the subscale channel flow by scaling Manning's roughness in the kinematic wave formulation via a relationship between river width and grid cell size, following a simplified version of the Barré de Saint‐Venant equations (Manning–Strickler equations). The too large exchange areas between model rivers and the subsurface are compensated by a grid resolution‐dependent scaling of the infiltration/exfiltration rate across river beds. We test both scaling approaches in the integrated hydrological model ParFlow. An empirical relation is used for estimating the true river width from the mean annual discharge. Our simulations show that the scaling of the roughness coefficient and the hydraulic conductivity effectively corrects overland flow velocities calculated on the coarse grid leading to a better representation of flood waves in the river channels.     

Determination of equilibrium detention storage for a series of planes

Abstract

The detention storage in a drainage basin under the equilibrium condition is an important parameter in rainfall-runoff modelling. As this parameter is an efficient measure of the basin response to rainfall, it is commonly used as a basis of approximation of a complex basin by a simpler one. For flows on an overland plane, the equilibrium storage has also been used as a basis of determining the resistance coefficient of the overland surface. A formula is derived, based on the kinematic wave theory, for the equilibrium detention storage for a series of planes. For practical applications, the formula is further developed in terms of the Manning resistance coefficient. The derived formulae are all consistent with the published formulae for a single plane.     

Development of a SWAT extension module to simulate riparian wetland hydrologic processes at a watershed scale

Using a mass balance algorithm, this study develops an extension module that can be embedded in the commonly used Soil and Water Assessment Tool (SWAT). This module makes it possible to assess effects of riparian wetlands on runoff and sediment yields at a watershed scale, which is very important for aquatic ecosystem management but rarely documented in the literature. In addition to delineating boundaries of a watershed and its subwatersheds, the module groups riparian wetlands within a subwatershed into an equivalent wetland for modelling purposes. Further, the module has functions to compute upland drainage area and other parameters (e.g. maximum volume) for the equivalent wetland based on digital elevation model, stream network, land use, soil and wetland distribution GIS datasets. SWAT is used to estimate and route runoff and sediment generated from upland drainage area. The lateral exchange processes between riparian wetlands and their hydraulically connected streams are simulated by the extension module. The developed module is empirically applied to the 53 km² Upper Canagagigue Creek watershed located in Southern Ontario of Canada. The simulation results indicate that the module can make SWAT more reasonably predict flow and sediment loads at the outlet of the watershed and better represent the hydrologic processes within it. The simulation is sensitive to errors of wetland parameters and channel geometry. The approach of embedding the module into SWAT enables simulation of hydrologic processes in riparian wetlands, evaluation of wetland effects on regulating stream flow and sediment loading and assessment of various wetland restoration scenarios. Copyright © 2008 John Wiley & Sons, Ltd.     

The role of land surface versus drainage network characteristics in controlling water quality and quantity in a small urban watershed

The processes that control run‐off quantity and quality in urban watersheds are complex and not well understood. Although impervious surface coverage has traditionally been used to examine altered hydrologic response in urban watersheds, several studies suggest that other elements of the urban landscape, particularly those associated with urban infrastructure and the drainage system, play an equally important role. The relative importance of impervious surfaces, stormwater ponds, expansion of the drainage network, and drainage network structures in controlling hydrologic response was examined in the subwatersheds of the Kromma Kill, an urban watershed located in Albany County, NY. In this study, geographic information systems was used to compute geospatial land surface and drainage network properties of 5 Kromma Kill subwatersheds. In these same subwatersheds, water quantity (rainfall and run‐off) and quality (macroinvertebrates, nitrate, total nitrogen, dissolved oxygen, total dissolved solids, and nonpurgable organic carbon) parameters were measured. Strong and significant correlations were identified between land surface and drainage network properties and field observations. Causal relationships were then tested using the Environmental Protection Agency's Stormwater Management Model. Field and model analyses suggest that whereas percent imperviousness is a dominant control on water quality, drainage density and slope are equally important. However, for water quantity, whereas imperviousness is positively correlated with increased run‐off volumes, drainage network properties and slope are the dominant controls on run‐off volumes. Results have important implications for stormwater management plans, especially those aimed at reducing the effective impervious surface coverage of urban watersheds. Reducing the percentage of effective imperviousness in a watershed is not a “one size fits all” solution and can help to meet some management objectives, such as reducing nitrogen concentrations and improving water quality, but may not serve as the most effective, and therefore economical, solution for every management objective including reducing run‐off volumes.     

A unifying framework for watershed thermodynamics: balance equations for mass,momentum, energy and entropy,and the second law of thermodynamics

The basic aim of this paper is to formulate rigorous conservation equations for mass, momentum, energy and entropy for a watershed organized around the channel network. The approach adopted is based on the subdivision of the whole watershed into smaller discrete units, called representative elementary watersheds (REW), and the formulation of conservation equations for these REWs. The REW as a spatial domain is divided into five different subregions: (1) unsaturated zone; (2) saturated zone; (3) concentrated overland flow; (4) saturated overland flow; and (5) channel reach. These subregions all occupy separate volumina. Within the REW, the subregions interact with each other, with the atmosphere on top and with the groundwater or impermeable strata at the bottom, and are characterized by typical flow time scales.The balance equations are derived for water, solid and air phases in the unsaturated zone, water and solid phases in the saturated zone and only the water phase in the two overland flow zones and the channel. In this way REW-scale balance equations, and respective exchange terms for mass, momentum, energy and entropy between neighbouring subregions and phases, are obtained. Averaging of the balance equations over time allows to keep the theory general such that the hydrologic system can be studied over a range of time scales. Finally, the entropy inequality for the entire watershed as an ensemble of subregions is derived as constraint-type relationship for the development of constitutive relationships, which are necessary for the closure of the problem. The exploitation of the second law and the derivation of constitutive equations for specific types of watersheds will be the subject of a subsequent paper.     

A MATHEMATICAL QUASI-2D OVERLAND FLOW MODEL

1 INTRODUCTIONThe prediction of future impacts on terrestrial ecosystems by atmospheric, climatic and land-usechanges is the aim of watershed management. Meeting these requirements scientists, managers and policymakers try to achieve the sustainable management of the vitally important resources of watersheds due toan integrated ecosystem approach at the catchment scale. As composite landscapes often have a highdegree of contingency between its elements, the transport over these landscape s…     

Stochastic overland flows Part 1: Physics-based evolutionary probability distributions

A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.     

OPTIMAL MODE OF SEDIMENT TRANSPORT BY SHALLOW FLOWS IN UPLAND AREAS

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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.     

Stochastic overland flows

A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.     

An experimental study of the application of kinematic-wave theory to overland flow

An experimental test to evaluate the accuracy of kinematic-wave theory as applied to overland flow over a rough, uneven surface is described. The depression storage, and the hydraulic roughness for flows without rain were measured in separate tests; the hydraulic roughness for flows under rain was calculated from the rising limbs of the runoff hydrographs from a series of simulated storms. Recession curves were calculated using kinematic wave theory. The close agreement between experimental and calculated recessions showed the accuracy of this theory in predicting the behaviour of flows over the rough uneven surface. Hysteresis was observed in the storage-discharge curves; this was also explained in terms of kinematic wave theory.     

Influences of spatially heterogeneous roughness on flow hydrographs

Spatially uniform roughness, which although may not be adequate in all cases, is often conveniently adopted for rainfall-runoff simulations in conventional watershed hydrology. In this study, effects of spatially heterogeneous roughness on hydrological response were investigated systematically. Three types of surface roughness scenarios, including: roughness decreasing in a downstream direction (Scenario 1), roughness increasing in a downstream direction (Scenario 2) and roughness distributed at random (Scenario 3), were assigned to an overland plane. A non-inertia wave model was developed to generate hydrographs at the end of the overland plane for certain rainstorms. The hydrographs in the three scenarios showed that when rainfall duration was less than the time of concentration of the overland plane, peak discharges generated from the spatially heterogeneous roughness scenarios significantly exceeded those from the spatially uniform roughness condition. The temporal equilibrium discharge which was usually observed on an overland plane under the spatially uniform roughness condition was not found in the present study. The flow peak in Scenario 1 occurred before that in Scenario 2. Nevertheless, the runoff peak could occur at the preceding, the middle or the later part of the hydrograph in Scenario 3, and this depended on the spatial distribution of the roughness. Reasons for the variation of peak discharge and the time to peak discharge were analyzed in detail based on water depth and flow velocity. Spatially heterogeneous roughness had an obviously influence on runoff generation, which ought to be handled with care in hydrological simulations.