Showing papers in "Advances in Water Resources in 2003"

Incompressible sph method for simulating newtonian and non-newtonian flows with a free surface

Abstract: An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier–Stokes equations. The method uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.

Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives

Abstract: A consistent framework for parameter estimation in distributed hydrological catchment modelling using automatic calibration is formulated. The framework focuses on the different steps in the estimation process from model parameterisation and selection of calibration parameters, formulation of calibration criteria, and choice of optimisation algorithm. The calibration problem is formulated in a general multi-objective context in which different objective functions that measure individual process descriptions can be optimised simultaneously. Within this framework it is possible to tailor the model calibration to the specific objectives of the model application being considered. A test example is presented that illustrates the use of the calibration framework for parameter estimation in the MIKE SHE integrated and distributed hydrological modelling system. A significant trade-off between the performance of the groundwater level simulations and the catchment runoff is observed in this case, defining a Pareto front with a very sharp structure. The Pareto optimum solution corresponding to a proposed balanced aggregated objective function is seen to provide a proper balance between the two objectives. Compared to a manual expert calibration, the balanced Pareto optimum solution provides generally better simulation of the runoff, whereas virtually similar performance is obtained for the groundwater level simulations.

The assimilation of remotely sensed soil brightness temperature imagery into a land surface model using Ensemble Kalman filtering: a case study based on ESTAR measurements during SGP97

Abstract: An Ensemble Kalman filter (EnKF) is used to assimilate airborne measurements of 1.4 GHz surface brightness temperature ðTBÞ acquired during the 1997 Southern Great Plains Hydrology Experiment (SGP97) into the TOPMODEL-based Land–Atmosphere Transfer Scheme (TOPLATS). In this way, the potential of using EnKF-assimilated remote measurements of TB to compensate land surface model predictions for errors arising from a climatological description of rainfall is assessed. The use of a real remotely sensed data source allows for a more complete examination of the challenges faced in implementing assimilation strategies than previous studies where observations were synthetically generated. Results demonstrate that the EnKF is an effective and computationally competitive strategy for the assimilation of remotely sensed TB measurements into land surface models. The EnKF is capable of extracting spatial and temporal trends in root-zone (40 cm) soil water content from TB measurements based solely on surface (5 cm) conditions. The accuracy of surface state and flux predictions made with the EnKF, ESTAR TB measurements, and climatological rainfall data within the Central Facility site during SGP97 are shown to be superior to predictions derived from open loop modeling driven by sparse temporal sampling of rainfall at frequencies consistent with expectations of future missions designed to measure rainfall from space (6–10 observations per day). Specific assimilation challenges posed by inadequacies in land surface model physics and spatial support contrasts between model predictions and sensor retrievals are discussed. 2002 Elsevier Science Ltd. All rights reserved.

A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations

Abstract: A new technique for generating coarse scale models of highly heterogeneous subsurface formations is developed and applied. The method uses generic global coarse scale simulations to determine the boundary conditions for the local calculation of upscaled properties (permeability or transmissibility). An iteration procedure assures consistency between the local and global calculations. Transport processes are simulated using a subgrid velocity reconstruction technique applied in conjunction with the local-global upscaling procedure. For highly heterogeneous (e.g., channelized) systems, the new method is shown to provide considerably more accurate coarse scale models for flow and transport, relative to reference fine scale results, than do existing local (and extended local) upscaling techniques. The applicability of the upscaled models for dierent global boundary conditions is also considered.

Pipe system diagnosis and leak detection by unsteady-state tests. 1. Harmonic analysis

Abstract: As shown in Part 1, the analysis of a pressure signal in the frequency domain can give items of information for leak detection even though, moving from time to frequency domain, interesting information about the arrival time of pressure waves are lost. To overcome this limitation and to widen the applicability of transient-test based methodologies for leak detection, the wavelet transform of laboratory experimental data is used. Such data consist of pressure time histories acquired at one measurement section during transients in a single pipe system. The wavelet transform is used to detect local singularities in the pressure time history due to the presence of a leak. The discontinuity occurrence in time reveals the arrival time of the leak reflected pressure wave and is the basis for leak location.

Hydrologic controls on soil carbon and nitrogen cycles. I. Modeling scheme

Abstract: The influence of soil moisture dynamics on soil carbon and nitrogen cycles is analyzed by coupling an existing stochastic soil moisture model [Adv. Water. Resour. 24 (7) (2001) 707; Proc. R. Soc. Lond. A 455 (1999) 3789] to a system of eight nonlinear differential equations that describe the temporal evolution of the organic matter and the mineral nitrogen in the soil at the daily to seasonal time scales. Special attention is devoted to the modeling of the soil moisture control on mineralization and immobilization fluxes, leaching losses, and plant nitrogen uptake, as well as to the role played by the soil organic matter carbon-to-nitrogen ratio in determining mineralization and immobilization. The model allows a detailed analysis of the soil nitrogen cycle as driven by fluctuations in soil moisture at the daily time scale resulting from the stochastic rainfall variability. The complex ensuing dynamics are studied in detail in a companion paper [Adv. Water Resour. 26 (1) (2003) 59], which presents an application to the Nylsvley savanna in South Africa. The model accounts for the soil moisture control on different components of the nitrogen cycle on a wide range of time scales: from the high frequency variability of leaching and uptake due to the nitrate flushes after persistent rainfall following a period of drought, to the low frequency temporal dynamics of the soil organic matter pools. All the fluctuations in the various pools are statistically characterized in relation to their dependence on climate, soil, and vegetation characteristics.

Species differences in stomatal control of water loss at the canopy scale in a mature bottomland deciduous forest

Abstract: In order to evaluate factors controlling transpiration of six common eastern deciduous species in North America, a model describing responses of canopy stomatal conductance (GS) to net radiation (RN), vapor pressure deficit (D) and relative extractable soil water (REW) was parameterized from sap flux data. Sap flux was measured in 24 mature trees consisting of the species Carya tomentosa, Quercus alba, Q. rubra, Fraxinus americana, Liriodendron tulipifera, and Liquidambar styraciflua in a bottomland oakhickory forest in the Duke Forest, NC. Species differences in model coefficients were found during the 1997 growing season. All species showed a reduction in GS with increasing D. RN influenced GS in the overstory shade intolerant L. styraciflua to a larger extent than the other species measured. In addition, despite a severe drought during the study period, only L. tulipifera showed a decline in GS with decreasing REW. The primary effect of the drought for the other species appeared to be early autumn leaf senescence and abscission. As a result, despite the drought in this bottomland forest accustomed to ample water supply, maximum daily transpiration (1.6 mm) and growing season transpiration (264 mm) were similar to a nearby upland forest measured during a year of above average precipitation. These results may aid in assessing differences in water use and the ability of bottomland deciduous species to tolerate alterations in the frequency or amount of precipitation. Results also suggest little variation in water use among forests of similar composition and structure growing in different positions in the landscape and subjected to large interannual variation in water supply. � 2003 Elsevier Ltd. All rights reserved.

Comparing transient storage modeling and residence time distribution (RTD) analysis in geomorphically varied reaches in the Lookout Creek basin, Oregon, USA

Abstract: The stream tracer technique has been widely used as a method of characterizing hyporheic exchange in stream-catchment studies, commonly incorporating the use of the numerical, transient storage model OTIS, which assumes an exponential residence time distribution. In this study, we compare OTIS and, a model that admits a general residence time distribution (RTD), called solute transport and multirate mass transfer-linear coordinates (STAMMT-L). Models were compared using slug-tracer injections of rhodamine WT (RWT) in three geomorphically distinct stream reaches in the Lookout Creek basin, Oregon USA: a second-order reach of a stream in Watershed 3 which is characterized by pool-step morphology; and two fourth-order reaches of Lookout Creek, one characterized by a single-thread, pool-step morphology, the other a morphologically complex reach with braided channels. OTIS modeling results tended to match short time scale concentrations well, including the advective peak, but the simulated late-time RTD of stream RWT concentrations was in error. The STAMMT-L model allowed for more accurate characterization of late-time stream RWT concentrations, and so characterized a larger portion of the entire RTD. Although both models are sensitive to morphologic differences among the studied stream reaches, they are also clearly different in the relative importance placed on short vs. long residence time distributions. Consequently the two models will result in different views of the hyporheic zone and its role in stream ecosystem processes.

Hydrologic controls on soil carbon and nitrogen cycles. II. A case study

Abstract: The nitrogen and carbon cycles in the broad-leafed savanna at Nylsvley (S. Africa) are modeled using the stochastic approach presented by Porporato et al. [Adv Water Res (this issue)]. An accurate representation of the hydrological mechanisms that control the nitrogen cycle at the daily time scale is shown to be necessary to capture the impact of the high-frequency variability of the soil moisture on the nitrogen and carbon dynamics. The fluctuations of the random precipitation forcing propagate to soil moisture, carbon, and nitrogen dynamics, giving rise to a gamut of fluctuations at different time scales. Long simulations are carried out to achieve a probabilistic characterization of the dynamics of the state variables under different rainfall regimes.

Theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models

Abstract: Computer models must be tested to ensure that the mathematical statements and solution schemes accurately represent the physical processes of interest. Because the availability of benchmark problems for testing density-dependent groundwater models is limited, one should be careful in using these problems appropriately. Details of a Galerkin finite-element model for the simulation of density-dependent, variably saturated flow processes are presented here. The model is tested using the Henry salt-water intrusion problem and Elder salt convection problem. The quality of these benchmark problems is then evaluated by solving the problems in the standard density-coupled mode and in a new density-uncoupled mode. The differences between the solutions indicate that the Henry salt-water intrusion problem has limited usefulness in benchmarking density-dependent flow models because the internal flow dynamics are largely determined by the boundary forcing. Alternatively, the Elder salt-convection problem is more suited to the model testing process because the flow patterns are completely determined by the internal balance of pressure and gravity forces.

Assimilation of remotely sensed latent heat flux in a distributed hydrological model

Abstract: This paper addresses the question of whether remotely sensed latent heat flux estimates over a catchment can be used to improve distributed hydrological model water balance computations by the process of data assimilation. The data used is a series of noaa-avhrr satellite images for the Drentse Aa catchment in the Netherlands for the year 1995. These 1×1 km resolution images are converted into latent heat flux estimates using sebal ( s urface e nergy b alance a lgorithm for l and [J Hydrol 2000;229:87]). The physically-based distributed model simgro ( sim ulation of gro undwater flow and surface water levels [J Hydrol 1997;192:158]) is used to compute the water balance of the Drentse Aa catchment for that same year. Comparison between model-derived and remotely sensed area-averaged evapotranspiration estimates show good agreement, but spatial analysis of the model latent heat flux estimates indicate systematic underestimation in areas with higher elevation. A constant gain Kalman filter data assimilation algorithm is used to correct the internal state variables of the distributed model whenever remotely sensed latent heat flux estimates are available. It was found that the spatial distribution of model latent heat flux estimates in areas with higher elevation were improved through data assimilation.

Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems

Abstract: Numerical solutions to nonlinear reactive solute transport problems are often computed using split-operator (SO) approaches, which separate the transport and reaction processes. This uncoupling introduces an additional source of numerical error, known as the splitting error. The iterative split-operator (ISO) algorithm removes the splitting error through iteration. Although the ISO algorithm is often used, there has been very little analysis of its convergence behavior. This work uses theoretical analysis and numerical experiments to investigate the convergence rate of the iterative split-operator approach for solving nonlinear reactive transport problems.

A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

Abstract: The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.

Predicting changes in hydrologic retention in an evolving semi-arid alluvial stream

Abstract: Hydrologic retention of solutes in hyporheic zones or other slowly moving waters of natural channels is thought to be a significant control on biogeochemical cycling and ecology of streams. To learn more about factors affecting hydrologic retention, we repeated stream-tracer injections for 5 years in a semi-arid alluvial stream (Pinal Creek, Ariz.) during a period when streamflow was decreasing, channel width increasing, and coverage of aquatic macrophytes expanding. Average stream velocity at Pinal Creek decreased from 0.8 to 0.2 m/s, average stream depth decreased from 0.09 to 0.04 m, and average channel width expanded from 3 to 13 m. Modeling of tracer experiments indicated that the hydrologic retention factor (Rh), a measure of the average time that solute spends in storage per unit length of downstream transport, increased from 0.02 to 8 s/m. At the same time the ratio of cross-sectional area of storage zones to main channel cross-sectional area (As/A) increased from 0.2 to 0.8 m2/m2, and average water residence time in storage zones (ts) increased from 5 to 24 min. Compared with published data from four other streams in the US, Pinal Creek experienced the greatest change in hydrologic retention for a given change in streamflow. The other streams differed from Pinal Creek in that they experienced a change in streamflow between tracer experiments without substantial geomorphic or vegetative adjustments. As a result, a regression of hydrologic retention on streamflow developed for the other streams underpredicted the measured increases in hydrologic retention at Pinal Creek. The increase in hydrologic retention at Pinal Creek was more accurately predicted when measurements of the Darcy–Weisbach friction factor were used (either alone or in addition to streamflow) as a predictor variable. We conclude that relatively simple measurements of channel friction are useful for predicting the response of hydrologic retention in streams to major adjustments in channel morphology as well as changes in streamflow.

Fuzzy logic algorithm for runoff-induced sediment transport from bare soil surfaces

Abstract: Utilizing the rainfall intensity, and slope data, a fuzzy logic algorithm was developed to estimate sediment loads from bare soil surfaces. Considering slope and rainfall as input variables, the variables were fuzzified into fuzzy subsets. The fuzzy subsets of the variables were considered to have triangular membership functions. The relations among rainfall intensity, slope, and sediment transport were represented by a set of fuzzy rules. The fuzzy rules relating input variables to the output variable of sediment discharge were laid out in the IF-THEN format. The commonly used weighted average method was employed for the defuzzification procedure. The sediment load predicted by the fuzzy model was in satisfactory agreement with the measured sediment load data. Predicting the mean sediment loads from experimental runs, the performance of the fuzzy model was compared with that of the artificial neural networks (ANNs) and the physics-based models. The results of showed revealed that the fuzzy model performed better under very high rainfall intensities over different slopes and over very steep slopes under different rainfall intensities. This is closely related to the selection of the shape and frequency of the fuzzy membership functions in the fuzzy model.

The relative roles of climate, soil, vegetation and topography in determining seasonal and long-term catchment dynamics

Abstract: This paper develops and demonstrates a preliminary set of coupled analytical models for the seasonality and annual water balance of catchments. We include the effects of temporal variability of atmospheric forcing and the interaction of nonlinear catchment processes, while assuming that climate, soil and vegetation are effectively uniform over the catchment. The models make predictions for the water balance of the canopy, root zone, saturated zone and catchment system, as functions of 6 dimensionless similarity parameters. These parameters quantify: (i) climate dryness; (ii) interception capacity relative to rainfall; (iii) combined climate seasonality and rootzone storage; (iv) subsurface flow responsiveness; (v) saturated subsurface flow capacity, relative to mean annual rainfall rate; and (vi) a geomorphological exponent controlling the expansion of saturated area fraction. The model can provide estimates of throughfall, evaporation, drainage, subsurface flow, saturated area and catchment yield. Testing of these estimates is in progress. The coupled models can be used to predict hydrological differences between catchments using differences in the dimensionless parameters. The sensitivity of water balance to each of the similarity parameters can be presented graphically or analytically, so that dominant controls on water balance can be identified as functions of climate and catchment properties. The principal application we envisage is as a simple method to transfer measurements to ungauged catchments.

Numerical modeling of coupled nitrification-denitrification in sediment perfusion cores from the hyporheic zone of the Shingobee River, MN

Abstract: Nitrification and denitrification kinetics in sediment perfusion cores were numerically modeled and compared to experiments on cores from the Shingobee River MN, USA. The experimental design incorporated mixing groundwater discharge with stream water penetration into the cores, which provided a well-defined, one-dimensional simulation of in situ hydrologic conditions. Ammonium (NH 4 + ) and nitrate (NO 3 − ) concentration gradients suggested the upper region of the cores supported coupled nitrification–denitrification, where groundwater-derived NH 4 + was first oxidized to NO 3 − then subsequently reduced via denitrification to N 2 . Nitrification and denitrification were modeled using a Crank–Nicolson finite difference approximation to a one-dimensional advection–dispersion equation. Both processes were modeled using first-order reaction kinetics because substrate concentrations (NH 4 + and NO 3 − ) were much smaller than published Michaelis constants. Rate coefficients for nitrification and denitrification ranged from 0.2 to 15.8 h −1 and 0.02 to 8.0 h −1 , respectively. The rate constants followed an Arrhenius relationship between 7.5 and 22 °C. Activation energies for nitrification and denitrification were 162 and 97.3 kJ/mol, respectively. Seasonal NH 4 + concentration patterns in the Shingobee River were accurately simulated from the relationship between perfusion core temperature and NH 4 + flux to the overlying water. The simulations suggest that NH 4 + in groundwater discharge is controlled by sediment nitrification that, consistent with its activation energy, is strongly temperature dependent.

Modeling hyporheic zone processes

Abstract: Stream biogeochemistry is influenced by the physical and chemical processes that occur in the surrounding watershed. These processes include the mass loading of solutes from terrestrial and atmospheric sources, the physical transport of solutes within the watershed, and the transformation of solutes due to biogeochemical reactions. Research over the last two decades has identified the hyporheic zone as an important part of the stream system in which these processes occur. The hyporheic zone may be loosely defined as the porous areas of the stream bed and stream bank in which stream water mixes with shallow groundwater. Exchange of water and solutes between the stream proper and the hyporheic zone has many biogeochemical implications, due to differences in the chemical composition of surface and groundwater. For example, surface waters are typically oxidized environments with relatively high dissolved oxygen concentrations. In contrast, reducing conditions are often present in groundwater systems leading to low dissolved oxygen concentrations. Further, microbial oxidation of organic materials in groundwater leads to supersaturated concentrations of dissolved carbon dioxide relative to the atmosphere. Differences in surface and groundwater pH and temperature are also common. The hyporheic zone is therefore a mixing zone in which there are gradients in the concentrations of dissolved gasses, the concentrations of oxidized and reduced species, pH, and temperature. These gradients lead to biogeochemical reactions that ultimately affect stream water quality. Due to the complexity of these natural systems, modeling techniques are frequently employed to quantify process dynamics. This special issue of Advances in Water Resources presents recent research on the modeling of hyporheic zone processes. To begin this preface, a brief history on modeling hyporheic zone processes is presented. This background information is by no means complete; additional information may be found in Streams and Groundwaters [17] and the references therein. The preface concludes with an overview of current re-

Measuring and simulating moisture uptake in a fractured porous medium

Abstract: Water uptake in fractured brick samples is monitored with X-ray radiography. This technique can measure both the moisture profiles in the matrix and the height of the waterfront in the fracture during the experiment. It was found that the waterfront in the fracture could quickly reach the opposite side of the specimen, resulting in an extra water source for the surrounding matrix over the total height of the sample. For smaller fracture apertures, however, the waterfront in the fracture stagnates and moisture profiles in the matrix run ahead of the waterfront in the fracture. To simulate the experiments, a numerical model for unsaturated moisture transport in fractured porous media is developed. The model combines a discrete fracture model for moisture flow in a variable aperture fracture with a finite element model for unsaturated flow in the porous matrix. To achieve a stable numerical solution, movable nodes, following the moisture front in the fracture, are introduced on the boundary of the finite element mesh. The numerical results of height of rise in the fracture as well as of moisture profiles in the matrix show to be in good agreement with the measurements. The paper ends with a parameter analysis, investigating the effects of fracture aperture and matrix properties on the unsaturated moisture flow in fractured porous media. 2002 Elsevier Science Ltd. All rights reserved.

Comparison of transient storage in vegetated and unvegetated reaches of a small agricultural stream in Sweden: seasonal variation and anthropogenic manipulation

Abstract: In this work, we compare solute transport and hyporheic exchange in vegetated and unvegetated reaches of Sava Brook, an agricultural stream in Sweden subject to extreme variations in channel vegetation and morphology due to both natural seasonal effects and anthropogenic manipulation. A solute injection experiment was conducted in September, 2001 (late summer), at which time there was extensive in-channel vegetation in upstream reaches but none in downstream reaches due to channel excavation by farmers. Experimental results are interpreted using both the advective storage path model and the transient storage model. Results from the vegetated and excavated reaches of the stream are compared both with each other and with the results of a previous experiment conducted in April, 1998 (early spring), when the stream was not excavated but there was only minimal vegetation present in the area due to natural seasonal effects. Results from the two injection experiments are compared by using scaled parameters that appropriately include the effects of stream velocity and depth on hyporheic exchange. This analysis indicates that the variation of solute storage time in all non-excavated agricultural reaches is attributable to differences in stream flow depth, velocity, and the hydraulic conductivity of the streambed sediments. Mixing in vegetated reaches is characterized by rapid exchange and considerable lag of the mean solute peak relative to the mean channel velocity. In addition, excavation altered the stream channel geometry so as to increase the storage time of solutes and reduce the effective exchange rate. This work indicates the need to consider the effect of specific processes when analyzing hyporheic exchange using tracer-injection methods, and supports the use of model frameworks with the potential to explicitly include different formulations for various hyporheic and dead zone transport processes.

Hydrologic modeling of extreme floods using radar rainfall estimates

Abstract: High resolution radar rainfall fields and a distributed hydrologic model are combined for analysis and monitoring of extreme floods. Hydrologic modeling is based on a Hortonian infiltration model and a network-based representation of hillslope and channel flow. Model analyses are used to examine the hydrology and hydrometeorology of the 27 June 1995 Rapidan River flood which produced a measured peak discharge of 3000 m 3 s −1 at a drainage area of 295 km 2 . The unit discharge of 10.2 m 3 s −1 km −2 is the largest for the US east of the Mississippi River for basins larger than 100 km 2 . Rainfall estimates at 1 km horizontal scale and 5 min time scale are used to reconstruct flood response to the Rapidan storm at basin scales ranging from 1 to 295 km 2 . Peak storm total rainfall accumulations for the 27 June 1995 storm exceeded 600 mm in a time period of approximately 6 h. Scale dependent flood response is related to the structure and motion of the Rapidan storm and the drainage network structure of the Rapidan River basin. The envelope curve of peak discharge for the Rapidan flood at basin scales less than 295 km 2 , derived from model analyses, is compared with envelope curves, based on extensive indirect discharge measurements, from the 19 July 1942 Smethport, Pennsylvania flood and the 18–19 August 1969 Nelson County, Virginia flood. These three events largely define the envelope curve of flood peaks for the US east of the Mississippi River at basin scales less than 1000 km 2 . Analyses illustrate how radar rainfall estimates can be combined with conventional stream gaging and indirect discharge measurements to enhance monitoring of extreme floods.

Finite-volume component-wise TVD schemes for 2D shallow water equations

Abstract: Four finite-volume component-wise total variation diminishing (TVD) schemes are proposed for solving the two-dimensional shallow water equations. In the framework of the finite volume method, a proposed algorithm using the flux-splitting technique is established by modifying the MacCormack scheme to preserve second-order accuracy in both space and time. Based on this algorithm, four component-wise TVD schemes, including the Liou–Steffen splitting (LSS), van Leer splitting, Steger–Warming splitting and local Lax–Friedrichs splitting schemes, are developed. These schemes are verified through the simulations of the 1D dam-break, the oblique hydraulic jump, the partial dam-break and circular dam-break problems. It is demonstrated that the proposed schemes are accurate, efficient and robust to capture the discontinuous shock waves without any spurious oscillations in the complex flow domains with dry-bed situation, bottom slope or friction. The simulated results also show that the LSS scheme has the best numerical accuracy among the schemes tested.

Newtonian nudging for a Richards equation-based distributed hydrological model

Abstract: The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model’s behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation techniques in a Richards equation-based hydrological model.

The hydraulic characteristics and geochemistry of hyporheic and parafluvial zones in Arctic tundra streams, north slope, Alaska

Abstract: Sodium bromide and Rhodamine WT were used as conservative tracers to examine the hydrologic characteristics of seven tundra streams in Arctic Alaska, during the summers of 1994–1996. Continuous tracer additions were conducted in seven rivers ranging from 1st to 5th order with samples collected from instream, hyporheic, and parafluvial locations. Tracer data was used as input for a computer model to estimate hydrologic characteristics of each study reach. While solute concentrations during the tracer additions indicated that steady-state or ‘‘plateau’’ conditions had been reached, interstitial samples indicated that there were additional hyporheic and parafluvial zones that had not been fully labeled at the time of apparent steady state in the stream channel (plateau). Exchange between channel and hyporheic water was a function of location within a pool–riffle sequence, with rapid downwelling at the head of riffles and delayed upwelling in riffle tails. The extent of exchange between channel and hyporheic water was positively correlated with apparent streambed hydraulic conductivity. Tracer additions indicated interstitial velocities ranging from 0.030 to 0.075 cm s � 1 and hydraulic conductivities from 2.4 to 12.2 cm s � 1 . Hyporheic and in-channel samples were collected for N, P, DO, and CO2 analyses in conjunction with conservative tracer additions in four of the stream reaches for which the interstitial velocities were also determined. Transformation rates based on these data indicated that there was rapid nitrification of mineralized organic N and production of ammonium, phosphate, and carbon dioxide in the interstitial zones of all four reaches. Dissolved oxygen did not appear to be limiting in the reaches studied. The hyporheic zone of all four reaches was a source of nitrate, carbon dioxide, and ammonium to the channel water based on the average concentration of upwelling waters. Increased contact time with hyporheic and parafluvial zones was related to decreased temperature and increased conductivity. Net nitrogen flux from the hyporheic zone was equivalent to 14–162% of benthic N uptake requirements for the Kuparuk River. These observations are important because we expected that the presence of continuous permafrost in this Arctic environment would limit the importance of hyporheic processes, either physically (i.e., through the presence of a restricting thaw bulb in the permafrost) or biogeochemically (i.e., through low temperatures). Instead, we found that biogeochemical processes in the hyporheic zone of these Arctic streams are at least as important as it is in similar temperate stream ecosystems. 2003 Elsevier Ltd. All rights reserved.

Unsaturated hyporheic zone flow in stream/aquifer conjunctive systems

Abstract: Saturated flow is typically assumed for seepage from a stream underlain by an alluvial aquifer. However, if the water table falls a sufficient distance below a semipervious streambed, the head losses in this less conductive layer will cause the region beneath the stream, or hyporheic zone, to become unsaturated. Hyporheic zone flow is defined loosely in this research as the flow that occurs underneath the streambed. Unsaturated flow transforms streams from constant head boundaries to constant flux boundaries, impacting the biogeochemistry in the hyporheic zone. The objective of this paper is to discuss the development and implications of unsaturated flow beneath the streambed. Conditions under which saturated or unsaturated flow occurs and the characteristics of each flow regime are discussed. Next, the effect of unsaturated flow is illustrated for the case of stream leakage induced by a well pumping from an aquifer that is hydraulically interacting with a partially penetrating stream. Prior analytical solutions for alluvial well depletions fail to model unsaturated flow between the streambed and water table. An approximating solution is proposed to estimate aquifer drawdown and stream depletion under saturated/unsaturated hyporheic zone flow conditions.

A regression approach to estimating reactive solute uptake in advective and transient storage zones of stream ecosystems

Abstract: A method is developed, the Regression Partitioning Method (RPM), for estimating the proportion of reactive solute uptake occurring within transient storage zones of streams. The RPM is a technique for analyzing solute addition data in which whole stream uptake (mg m � 2 d � 1 ) is determined from the longitudinal pattern in plateau tracer concentrations. At one location, a time series of samples are collected that define the rising limb of the solute breakthrough curve. The y-intercept estimated by regressing a measure of reactive tracer availability (e.g. NO3– 15 N:Cl ratio) and the percentage of tracer that has resided within, and returned from, the transient storage zone (i.e. hyporheic zone) was used to predict channel-specific NO3 uptake rates. Uptake within the transient storage zone of stream-derived material is calculated by difference. Several numerical steps are developed that link uptake rate estimates to first-order reaction rate constants (kC and kS, min � 1 ) more commonly used to describe solute behavior in onedimensional transport models. The RPM was used to analyze the results of 2 stable isotope additions performed in Snake Den Branch, a small headwater stream in western North Carolina, USA. Channel-specific uptake rates (UC) ranged from 10.6 to 23.0 mg NO3–N m � 2 d � 1 and slightly exceeded uptake in the transient storage zone (US), which varied from 10.1 to 18.2 mg NO3–N m � 2 d � 1 . Uptake within the transient storage zone accounted for 44–49% of the total uptake. kC and kS estimates ranged from 0.023 to 0.034 min � 1 and 0.011 to 0.024 min � 1 , respectively. These processing rates correspond to solute residence times of 30–44 min and 41–90 min in the channel and storage zones, respectively. Finally, we assess the sensitivity of our approach to variation in the subsurface uptake coefficient and differing proportions of uptake occurring within the hyporheic zone. � 2003 Elsevier Ltd. All rights reserved.

Catchment-scale hydrological modeling and data assimilation

Abstract: This special issue of Advances in Water Resources presents recent progress in the application of DA (data assimilation) for distributed hydrological modeling and in the use of in situ and remote sensing datasets for hydrological analysis and parameter estimation. The papers were presented at the De Wageningse Berg conference center, september 2001

Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow

Abstract: Richards’ equation (RE) is commonly used to model flow in variably saturated porous media. However, its solution continues to be difficult for many conditions of practical interest. Among the various time discretizations applied to RE, the method of lines (MOL) has been used successfully to introduce robust, accurate, and efficient temporal approximations. At the same time, a mixed-hybrid finite element method combined with an adaptive, higher order time discretization has shown benefits over traditional, lower order temporal approximations for modeling single-phase groundwater flow in heterogeneous porous media. Here, we extend earlier work for single-phase flow and consider two mixed finite element methods that have been used previously to solve RE using lower order time discretizations with either fixed time steps or empirically based adaption. We formulate the two spatial discretizations within a MOL context for the pressure head form of RE as well as a fully mass-conservative version. We conduct several numerical experiments for both spatial discretizations with each formulation, and we compare the higher order, adaptive time discretization to a first-order approximation with formal error control and adaptive time step selection. Based on the numerical results, we evaluate the performance of the methods for robustness and efficiency.

Physiological tradeoffs in the parameterization of a model of canopy transpiration

Abstract: We examined physiological parameter tradeoffs in modeling stomatal control of transpiration from a number of forest species. Measurements of sapflux, micrometeorology, and leaf area index were made in stands representing 85% of the forest ecosystems around the WLEF eddy flux tower in northern Wisconsin. A Jarvis-based canopy conductance model was used to simulate canopy transpiration (EC) for five tree species from these stands. They consisted of conifers and deciduous species in both upland and wetland locations. Parameter estimation was used to assess the tradeoffs between physiological parameters used in the calculation of stomatal conductance. These tradeoffs were then evaluated against current theory on stomatal regulation of leaf water potential. The results showthat the best simulations of EC were obtained with values of maximum stomatal conductance (gSmax) and stomatal sensitivity to vapor pressure deficit (d) that closely followed this hydraulic theory. The model predictions reveal a large variation in the strategies used to regulate water potential among species. Aspen showed the greatest tendency towards efficiency, indicating that it has high EC under lowvapor pressure deficit ( D) conditions, but is susceptible to rapid EC decline at moderate to high D. Other species showed more conservative water use. The results indicate that inter-specific differences in dynamic response to D can produce large spatial variation in EC under typical environmental conditions. 2002 Elsevier Science Ltd. All rights reserved.

Attenuating reaches and the regional flood response of an urbanizing drainage basin

Abstract: The Charlotte, North Carolina metropolitan area has experienced extensive urban and suburban growth and sharply increasing trends in the magnitude and frequency of flooding. The hydraulics and hydrology of flood response in the region are examined through a combination of numerical modeling studies and diagnostic analyses of paired discharge observations from upstream–downstream gaging stations. The regional flood response is shown to strongly reflect urbanization effects, which increase flood peaks and decrease response times, and geologically controlled attenuating reaches, which decrease flood peaks and increase lag times. Attenuating reaches are characterized by systematic changes in valley bottom geometry and longitudinal profile. The morphology of the fluvial system is controlled by the bedrock geology, with pronounced changes occurring at or near contacts between intrusive igneous and metamorphic rocks. Analyses of wave celerity and flood peak attenuation over a range of discharge values for an 8.3 km valley bottom section of Little Sugar Creek are consistent with Knight and Shiono’s characterization of the variation of flood wave velocity from in-channel conditions to valley bottom full conditions. The cumulative effect of variation in longitudinal profile, expansions and contractions of the valley bottom, floodplain roughness and sub-basin flood response is investigated using a two-dimensional, depth-averaged, finite element hydrodynamic model coupled with a distributed hydrologic model. For a 10.1 km stream reach of Briar Creek, with drainage area ranging from 13 km2 at the upstream end of the reach to 49 km2 at the downstream end, it is shown that flood response reflects a complex interplay of hydrologic and hydraulic processes on hillslopes and valley bottoms.