Reduced‐complexity flow routing models for sinuous single‐thread channels: intercomparison with a physically‐based shallow‐water equation model

Reduced‐complexity models of fluvial processes use simple rules that neglect much of the underlying governing physics. This approach is justified by the potential to use these models to investigate long‐term and/or fundamental river behaviour. However, little attention has been given to the validity or realism of reduced‐complexity process parameterizations, despite the fact that the assumptions inherent in these approaches may limit the potential for elucidating the behaviour of natural rivers. This study presents two new reduced‐complexity flow routing schemes developed specifically for application in single‐thread rivers. Output from both schemes is compared with that from a more sophisticated model that solves the depth‐averaged shallow water equations. This comparison provides the first demonstration of the potential for deriving realistic predictions of in‐channel flow depth, unit discharge, energy slope and unit stream power using simple flow routing schemes. It also highlights the inadequacy of modelling unit stream power, shear stress or sediment transport capacity as a function of local bed slope, as has been common practice in a number of previous reduced‐complexity models. Copyright © 2009 John Wiley & Sons, Ltd.     

MODELING SEDIMENT PROCESSES ON SMALL WATERSHEDS: A CONCEPTUAL FRAMEWORK Ⅱ. CONCENTRATED FLOW PROCESSES

L INTRODUCTIONThe purpose of this paper is to present a general modeling framework that can serveas a conceptual basis for developing sediment process models by concentrated flow systems on small watersheds. A survey of fundamental principles for developing sedimentprocess models is made with particular emphasis on the effects of space and time averaging on the governing equations. Starting from the most general one--dimensional,unsteady model of sediment processes, simpler model structur…     

Two‐dimensional continuous simulation of spatiotemporally varied hydrological processes using the time‐area method

Distributed, continuous hydrologic models promote better understanding of hydrology and enable integrated hydrologic analyses by providing a more detailed picture of water transport processes across the varying landscape. However, such models are not widely used in routine modelling practices, due in part to the extensive data input requirements, computational demands, and complexity of routing algorithms. We developed a two‐dimensional continuous hydrologic model, HYSTAR, using a time‐area method within a grid‐based spatial data model with the goal of providing an alternative way to simulate spatiotemporally varied watershed‐scale hydrologic processes. The model calculates the direct runoff hydrograph by coupling a time‐area routing scheme with a dynamic rainfall excess sub‐model implemented here using a modified curve number method with an hourly time step, explicitly considering downstream ‘reinfiltration’ of routed surface runoff. Soil moisture content is determined at each time interval based on a water balance equation, and overland and channel runoff is routed on time‐area maps, representing spatial variation in hydraulic characteristics for each time interval in a storm event. Simulating runoff hydrographs does not depend on unit hydrograph theory or on solution of the Saint Venant equation, yet retains the simplicity of a unit hydrograph approach and the capability of explicitly simulating two‐dimensional flow routing. The model provided acceptable performance in predicting daily and monthly runoff for a 6‐year period for a watershed in Virginia (USA) using readily available geographic information about the watershed landscape. Spatial and temporal variability in simulated effective runoff depth and time area maps dynamically show the areas of the watershed contributing to the direct runoff hydrograph at the outlet over time, consistent with the variable source area overland flow generation mechanism. The model offers a way to simulate watershed processes and runoff hydrographs using the time‐area method, providing a simple, efficient, and sound framework that explicitly represents mechanisms of spatially and temporally varied hydrologic processes. Copyright © 2015 John Wiley & Sons, Ltd.     

MODELING SEDIMENT PROCESSES ON SMALL WATERSHEDS:A CONCEPTUAL FRAMEWORK Ⅰ. BROAD SHALLOW FLOW PROCESSE

A conceptual modeling framework for developing process-based mathematical models of sediment generation, transport, and deposition on broad shallow flow areas is presented. The governing equations relevant to process-based modeling of broad shallow flow sediment processes on small watersheds are presented and the effects of space and time averaging on the predictive equations are described. Starting from the most general one-dimensional, unsteady model of sediment processes, simpler model structures are obtained and the successive simplifications made on the governing equations in order to obtain simpler and less detailed formulations are described. Specific model formulations are given for illustrative purposes and applications of these models to erosion and sediment yield prediction from broad shallow flow areas are shown using sediment data from rainfall simulator plots. In spite of some progress made in the development of process-based erosion and sediment yield models from broad shallow flow areas, further developmental modeling efforts must be based on a clear separation between hydrologic and hydraulic processes, and the soil properties which are significant for each.     

Development of a grid‐based version of the SWAT landscape model

Integrated river basin models should provide a spatially distributed representation of basin hydrology and transport processes to allow for spatially implementing specific management and conservation measures. To accomplish this, the Soil and Water Assessment Tool (SWAT) was modified by integrating a landscape routing model to simulate water flow across discretized routing units. This paper presents a grid‐based version of the SWAT landscape model that has been developed to enhance the spatial representation of hydrology and transport processes. The modified model uses a new flow separation index that considers topographic features and soil properties to capture channel and landscape flow processes related to specific landscape positions. The resulting model is spatially fully distributed and includes surface, lateral and groundwater fluxes in each grid cell of the watershed. Furthermore, it more closely represents the spatially heterogeneous distributed flow and transport processes in a watershed. The model was calibrated and validated for the Little River Watershed (LRW) near Tifton, Georgia (USA). Water balance simulations as well as the spatial distribution of surface runoff, subsurface flow and evapotranspiration are examined. Model results indicate that groundwater flow is the dominant landscape process in the LRW. Results are promising, and satisfactory output was obtained with the presented grid‐based SWAT landscape model. Nash–Sutcliffe model efficiencies for daily stream flow were 0.59 and 0.63 for calibration and validation periods, and the model reasonably simulates the impact of the landscape position on surface runoff, subsurface flow and evapotranspiration. Additional revision of the model will likely be necessary to adequately represent temporal variations of transport and flow processes in a watershed. Copyright © 2014 John Wiley & Sons, Ltd.     

An automated routing methodology to enable direct rainfall in high resolution shallow water models

Recent high profile flood events have highlighted the need for hydraulic models capable of simulating pluvial flooding in urban areas. This paper presents a constant velocity rainfall routing scheme that provides this ability within the LISFLOOD‐FP hydraulic modelling code. The scheme operates in place of the shallow water equations within cells where the water depth is below a user‐defined threshold, enabling rainfall‐derived water to be moved from elevated features such as buildings or curbstones without causing instabilities in the solution whilst also yielding a reduction in the overall computational cost of the simulation. Benchmarking against commercial modelling packages using a pluvial and point‐source test case demonstrates that the scheme does not impede the ability of LISFLOOD‐FP to match both predicted depths and velocities of full shallow water models. The stability of the scheme in conditions unsuitable for traditional two‐dimensional hydraulic models is then demonstrated using a pluvial test case over a complex urban digital elevation model containing buildings. Deterministic single‐parameter sensitivity analyses undertaken using this test case show limited sensitivity of predicted water depths to both the chosen routing speed within a physically plausible range and values of the depth threshold parameter below 10 mm. Local instabilities can occur in the solution if the depth threshold is >10 mm, but such values are not required even when simulating extreme rainfall rates. The scheme yields a reduction in model runtime of ~25% due to the reduced number of cells for which the hydrodynamic equations have to be solved. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluating explicit and implicit routing for watershed hydro‐ecological models of forest hydrology at the small catchment scale

This paper explores the behaviour and sensitivity of a watershed model used for simulating lateral soil water redistribution and runoff production. In applications such as modelling the effects of land‐use change in small headwater catchments, interactions between soil moisture, runoff and ecological processes are important. Because climate, soil and canopy characteristics are spatially variable, both the pattern of soil moisture and the associated outflow must be represented in modelling these processes. This study compares implicit and explicit routing approaches to modelling the evolution of soil moisture pattern and spatially variable runoff production. It also addresses the implications of using different landscape partitioning strategies. This study presents the results of calibration and application of these different routing and landscape partitioning approaches on a 60 ha forested watershed in Western Oregon. For comparison, the different approaches are incorporated into a physically based hydro‐ecological model, RHESSys, and the resulting simulated soil moisture, runoff production and sensitivity to unbiased error are examined. Results illustrate that both routing approaches can be calibrated to achieve a reasonable fit between observed and modelled outflow. Calibrated values for effective watershed hydraulic conductivity are higher for the explicit routing approach, which illustrates differences between the two routing approaches in their representation of internal watershed dynamics. The explicit approach illustrates a seasonal shift in drainage organization from watershed to more local control as climate goes from a winter wet to a summer dry period. Assumptions used in the implicit approach maintain the same pattern of drainage organization throughout the season. The implicit approach is also more sensitive to random error in soil and topographic input information, particularly during wetter periods. Comparison between the two routing approaches illustrates the advantage of the explicit routing approach, although the loss of computational efficiency associated with the explicit routing approach is noted. To compare different strategies for partitioning the landscape, the use of a non‐grid‐based method of partitioning is introduced and shown to be comparable to grid‐based partitioning in terms of simulated soil moisture and runoff production. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessing effects of model complexity and structure on predictions of hydrological responses using serial and parallel model design

By utilizing functional relationships based on observations at plot or field scales, water quality models first compute surface runoff and then use it as the primary governing variable to estimate sediment and nutrient transport. When these models are applied at watershed scales, this serial model structure, coupling a surface runoff sub-model with a water quality sub-model, may be inappropriate because dominant hydrological processes differ among scales. A parallel modeling approach is proposed to evaluate how best to combine dominant hydrological processes for predicting water quality at watershed scales. In the parallel scheme, dominant variables of water quality models are identified based entirely on their statistical significance using time series analysis. Four surface runoff models of different model complexity were assessed using both the serial and parallel approaches to quantify the uncertainty on forcing variables used to predict water quality. The eight alternative model structures were tested against a 25-year high-resolution data set of streamflow, suspended sediment discharge, and phosphorous discharge at weekly time steps. Models using the parallel approach consistently performed better than serial-based models, by having less error in predictions of watershed scale streamflow, sediment and phosphorus, which suggests model structures of water quantity and quality models at watershed scales should be reformulated by incorporating the dominant variables. The implication is that hydrological models should be constructed in a way that avoids stacking one sub-model with one set of scale assumptions onto the front end of another sub-model with a different set of scale assumptions.     

A process-based,distributed hydrologic model based on a large-scale method for surface–subsurface coupling

Process-based watershed models are useful tools for understanding the impacts of natural and anthropogenic influences on water resources and for predicting water and solute fluxes exported from watersheds to receiving water bodies. The applicability of process-based hydrologic models has been previously limited to small catchments and short time frames. Computational demands, especially the solution to the three-dimensional subsurface flow domain, continue to pose significant constraints. This paper documents the mathematical development, numerical testing and the initial application of a new distributed hydrologic model PAWS (Process-based Adaptive Watershed Simulator). The model solves the governing equations for the major hydrologic processes efficiently so that large scale applications become relevant. PAWS evaluates the integrated hydrologic response of the surface–subsurface system using a novel non-iterative method that couples runoff and groundwater flow to vadose zone processes approximating the 3D Richards equation. The method is computationally efficient and produces physically consistent solutions. All flow components have been independently verified using analytical solutions and experimental data where applicable. The model is applied to a medium-sized watershed in Michigan (1169 km²) achieving high performance metrics in terms of streamflow prediction at two gages during the calibration and verification periods. PAWS uses public databases as input and possesses full capability to interact with GIS datasets. Future papers will describe applications to other watersheds and the development and application of fate and transport modules.     

A comparison of hillslope drainage area estimation methods using high-resolution DEMs with implications for topographic studies of gullies

Topographic models provide a useful tool for understanding gully occurrence in the landscape but require reliable estimates of gully head drainage areas. Modern high-resolution topography data (collected using structure from motion photogrammetry or light detection and ranging) is increasingly used for topographic studies of gullies, but little work has been done to assess the variability of gully head drainage area estimates using different methods. This study evaluated alternative approaches to using high-resolution digital elevation models (DEMs) so that gully topographic models can be more readily applied to any area with suitably high-resolution data. Specifically, we investigated the impact of single- or multiple-direction flow routing algorithms, DEM hydrologic-enforcement procedures and spatial resolution on gully head drainage area estimation. We tested these methods on a 40 km² site centred on Weany Creek, a low-relief semi-arid landscape draining towards the Great Barrier Reef, Australia. Using a subroutine to separate gully heads into those with divergent or convergent flow patterns upslope, we found that divergent flow conditions occurred at half of 484 studied gullies. Drainage areas estimated by different flow routing algorithms were more variable in these divergent cases than for convergent cases. This variation caused a significant difference between topographic threshold parameters (slope b and intercept k) derived from single- or multiple-direction flow routing algorithms, respectively. Different methods of hydrologic enforcement (filling or breaching) also affected threshold analysis, resulting in estimates of the exponent b being ~188% higher if the DEM was filled than if breached. The testing of the methods to date indicates that a finer resolution (≤2 m) DEM and a multiple-direction flow routing algorithm achieve the most realistic drainage area estimates in low-relief landscapes. For Weany Creek we estimated threshold parameters k = 0.033 and b = 0.189, indicating that it is highly susceptible to gully erosion.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow

This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the limiting case of connected two-fluid-phase flow is considered. A constrained entropy inequality is developed based upon a set of primary restrictions. Formal approximations are introduced to deduce a general simplified entropy inequality (SEI). The SEI is used along with secondary restrictions and closure approximations consistent with the SEI to produce a general functional form of a two-phase-flow model. The general model is in turn simplified to yield a hierarchy of models by neglecting common curves and by neglecting both common curves and interfaces. The simplest case considered corresponds to a traditional two-phase-flow model. The more sophisticated models including interfaces and common curves are more physically realistic than traditional models. All models in the hierarchy are posed in terms of precisely defined variables that allow for a rigorous connection with the microscale. The explicit nature of the restrictions and approximations used in developing this hierarchy of models provides a clear means to both understand the limitations of traditional models and to build upon this work to produce more realistic models.     

ACCURACY AND STABILITY OF FINITE DIFFERENCE EQUATIONS FOR SHALLOW WATER FLOWS IN ORTHOGOPNAL COORDINATES

IINTRODUCTIONNumericalmethodsasatooltosimulateflowsandpollutanttransportareincreasinglyimportantinhydraulicandenvironmentalengineering.AveryusefulapplicationofthenumericalmethodologyinengineeringproblemswouldbetosolvethesystemofZDdepth-integratedshallowwaterequations.ManysolutionsofthegoverningequationsarederivedusingtraditionalfinitedifferencemethodonCartesianregulargrids.ThedisadvantageofthismethodseemstobetheinflexibilityofCartesiangridstocomplywithirregularorcurvedperimeterswhichsur…     

The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

Scaling aspects of river flow routing

Scaling aspects of river flow routing are studied by comparing two flow routing schemes, one designed for use in coupled general circulation models (GCMs) and operated at large spatial scales (～350 km), and the other designed for use in typical hydrological applications at small spatial scales (～25 km). The same runoff data are used as input into the two routing schemes, and comparisons are made between mean annual, mean monthly and daily streamflow simulated at four locations within the Mackenzie River Basin. The results suggest that for the purpose of realistically modelling monthly streamflow at the mouth of the rivers in GCMs, flow routing at large spatial scales gives similar results. However, the amplitude of the annual streamflow cycle is slightly but characteristically larger, when routing is performed at large spatial scales. Flow routing at large spatial scales also results in overestimation of high flows, while low flows are underestimated. Copyright © 2001 John Wiley & Sons, Ltd.     

The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

Embedding isochronous cells overland flow module into MODFLOW

This study integrates a simple overland flow module (isochronous cells model) with the river module of MODFLOW such that temporal and spatial interactions between stream flow and groundwater can be simulated using net rainfall data of a watershed. The isochronous cells model is an efficient travel time runoff approach based on geographic information system (GIS) that considers both spatial and temporal variations of net rainfall through hill slope of the watershed. This overland module is easily coupled with MODFLOW river routing module. Specifically, the stream flow from the isochronous cells model is directly assigned to both sides of river cells of the MODFLOW model. Such an integration of MODFLOW and isochronous cells model is especially useful in watersheds where river flow data are limited. The feasibility of this integrated model was demonstrated using a case study in the middle and downstream regions of the Yitong River watershed, China. Copyright © 2012 John Wiley & Sons, Ltd.     

How much complexity is needed to simulate watershed streamflow and water quality? A test combining time series and hydrological models

Modelled hydrologic processes are represented in a set of numerical equations; the complexity of which can be measured by the total number of variables needed. A single dominant hydrologic process could control the hydrologic response of a watershed, and so the identification of the corresponding dominant variable(s) would aid in identifying a parsimonious model and in collecting more reliable data. By accounting for both model complexity and serial correlation in the variables, a model is used to identify the dominant variables for representing watershed scale streamflow, sediment transport and phosphorus yields. Long‐term water quantity and quality data were used to show that rainfall and non‐linear soil water storage were the dominant variables for weekly streamflow, suspended sediment and particulate phosphorus. Model accuracy did not consistently improve when other statistically significant variables were included. The results suggest that improved model performance may not justify the added model complexity. As such, identification of dominant variables would be the priority for developing parsimonious hydrologic models, especially at watershed scales. Copyright © 2013 John Wiley & Sons, Ltd.     

A gis-based distributed parameter hydrologic model for urban areas

A hydrologic model for urban areas has been developed which incorporates distributed parameter modelling concepts and functions in the context of a geographic information system. In the proposed model, the watershed is represented as a cascade of grid cells, whose size can be specified by the user. Preliminary processing includes the determination of overland flow directions for each cell. An automated procedure is used to establish the cell-to-cell connectivity scheme, which is used to order the computations within each time step. Infiltration is computed using the Green-Ampt equation, while runoff rates are computed using a coupling of the continuity equation and Manning's equation for turbulent flow. Storm sewer flows are routed using time-shift routing. The model is capable of simulating flow through streets and offers the possibility of predicting the downstream movement of sewer system overflows. In preliminary testing on a small residential watershed, the model was able to reproduce measured hydrographs.     

Comparison of the performance of flow‐routing algorithms used in GIS‐based hydrologic analysis

Flow direction and specific catchment area were calculated for different flow‐routing algorithms using TAPES‐G and TauDEM. A fuzzy classification was used along with eight topo–climatic attributes to delineate six landscape classes from a 10‐m USGS DEM. A series of maps and tabular outputs were produced to compare flow‐routing predictions in different parts of the study area in the Santa Monica Mountains of southern California. The matched pair t‐test was used to compare the performance of pairs of specific catchment area grids across six user‐defined fuzzy landscape classes. The results show that (1) the ‘source’ cells predicted with the D∞, DEMON, and FD8 algorithms were confined to hilltops; (2) two single flow‐routing algorithms (Rho8, D8) produced poor results; and (3) the choice of flow‐routing algorithm has potentially important consequences for the calculation of upslope contributing areas, sediment transport capacity, topographic wetness, and several other topographic indices. Copyright © 2007 John Wiley & Sons, Ltd.     

Streamflow routing in the indian arid zone

A lumped model for streamflow routing in arid ephemeral channels has been developed. The governing equations for movement of flood waves subjected to transmission losses are simplified through a time averaging process to develop an ordinary differential equation describing transmission losses as a function of distance, inflow, channel width, time parameters of flow and effective hydraulic conductivity. The resulting equation has an analytical solution and simulates runoff volume and peak discharge rates for individual storm events. The outflow hydrograph is fairly well approximated with a triangular approximation. The model is simplified and constructed to require a minimum of observed data for calibration. It can also be used for ungauged basins in arid regions through parameterization.