A STEPWISE PROCEDURE TO DESIGN PLUVIAL DRAINAGE SYSTEMS IN AGRICULTURAL ZONES1

ABSTRACT: This paper describes a procedure to design pluvial drainage systems in such a way as to prevent large excavation volumes and erosive velocities. To this end the storage capacity of the channel system is taken into account. In a preliminary step, the procedure employs an approximate method to determine the channel dimensions. Therefore, the dimensions are adjusted by means of a numerical method of solution of the unsteady flow equations. An example is included.     

COMPUTATION OF STAGE-DISCHARGE RELATIONSHIPS AFFECTED BY UNSTEADY FLOW1

ABSTRACT: The dynamic relationship between stage and discharge which is unique to a particular flood for a selected station along the river can be determined via a mathematical model based on the complete one-dimensional equations of unsteady flow, i.e., the equations for the conservation of mass and momentum of the flood wave, and the Manning equation which accounts for energy losses. By assuming the bulk of the flood wave moves as a kinematic wave, the need for spatial resolution of the flood can be eliminated, and only the time variation of either the discharge or stage at the selected station is necessary for the computation of the other. The mathematical model can be used in river forecasting to convert the forecast discharge hydrograph into a stage hydrograph which properly reflects the unique dynamic stage-discharge relationship produced by the variable energy slope of the flood discharge. The model can be used also in stream gaging to convert a recorded stage hydrograph into a discharge hydrograph which properly accounts for the effects of unsteady flow. The model is applied to several observed floods at selected stations along the Lower Mississippi, Red, and Atchafalaya Rivers. The root mean square errors between observed and computed discharges are in the range of 3 to 7 percent, values well within the accuracy of the observations. A simple, easily-applied graphical procedure is also provided for estimating the magnitude of the effect of the unsteady flow on stage-discharge ratings. As a general rule, the dynamic effect may be significant if the channel bottom slope is less than 0.001 ft/ft (about 5 ft/mi) when the rate of change of stage is greater than about 0.10 ft/hr.     

EFFECTS OF LOMA PRIETA EARTHQUAKE ON SURFACE WATERS IN WADDELL VALLEY1

ABSTRACT: Waddell Creek is a perennial stream near Santa Cruz, California, which discharges into the Pacific Ocean about 38 km from the epicenter of the Loma Prieta earthquake (October 17, 1989, M 7.1). The earthquake caused no significant changes or damage to structures or surface features in the area, but was followed by an order of magnitude transient increase in discharge of Waddell Creek and nearby springs. The transients approximate a step rise followed by an exponential recession with time constants of from 37 to 59 days. The flow recession pattern of Waddell Creek was obscured by heavy rains after about 50 days; however, the springs maintained an exponential recession with minimal rain interference for periods of several time constants, then abruptly ceased flowing. A comparison of the pre-quake and post-quake chemical signature of one of the springs shows only minor changes in water chemistry indicating a common source for pre- and post-quake waters. Increased permeability of the subsurface ground material appears to be the most probable cause of the hydrologic changes. Post-seismic reduction of permeability has not been observed or inferred.     

A DISTRIBUTED DYNAMIC WATERSHED MODEL1

ABSTRACT: A distributed watershed model was developed to mathematically simulate overland and channel flow for a single-event storm. The modeled watersheds in the study were subdivided into rectangular grid elements. All hydrologically significant parameters, such as land slope, rainfall and precipitation excess, were assumed to be uniform within each element. The Green-Ampt method was adopted to generate precipitation excess for each element during the simulation period. A two-dimensional diffusion wave model was used for overland flow routing and an iterative Alternative Direction Implicit scheme was used to solve the simultaneous overland flow equations. Once the overland flow became inflow to the channel, a one-dimensional dynamic wave flood routing technique, based on a four-point, implicit, non-linear finite difference solution of the St. Venant equation of unsteady flow, was applied. A limited number of comparisons were made between simulated and observed hydrographs for areas of about one square mile. Given the appropriate parameters, the model was able to accurately simulate runoff for single-event storms. This paper describes a distributed watershed model developed to simulate overland and channel flow. Comparisons were made between simulated and observed hydrographs for three watersheds. The model was able to accurately simulate the runoff for single-event storms using 61-m by 61-m (200 ft by 200 ft) watershed grid elements.     

LABORATORY AND NUMERICAL INVESTIGATION OF LONGITUDINAL DISPERSION IN OPEN CHANNELS1

ABSTRACT: The non-Fickian nature of the longitudinal dispersion in natural channels during low flow has been investigated using both laboratory experiments and the numerical solution of the proposed mathematical model which is based on a set of mass balance equations describing the dispersion and mass exchange mechanisms. Laboratory experiments, which involved collection of channel geometry, hydraulic, and dye dispersion test data, were conducted to obtain sets of experimental data on a model of four pool and riffle sequences in a 161-ft long tilting flume in the Hydrosystems Laboratory at the University of Illinois at Urbana-Champaign. The experimental results indicate that flow over the model pool-riffle sequences is highly nonuniform. Concentration-time curves are significantly skewed with long tails. The mixing and dispersion in the laboratory channel was simulated using a numerical solution of the mathematical model in which the finite difference method developed by Stone and Brian (1963) was used as a solution technique. The comparison between measured and predicted concentration-time curves shows that there is a good level of agreement in the general shape, peak concentration, and time to peak. The proposed model shows significant improvement over the conventional Fickian model in predicting dispersion processes in natural channels under low flow conditions.     

MODIFICATION OF NEILL'S EQUATION FOR STORM‐TIDE DESIGN FLOW ANALYSIS1

ABSTRACT: Design of bridges spanning tidal estuaries or bays requires an estimate of peak tidal flow. One common approach to estimating these flows (Neill's method) uses a first‐order approximation of uniform water surface rise in the water body. For larger water bodies, the assumptions of this method are decreasingly valid. This study develops a simple modification that accounts for the spatial variability in the response of tidal waterways to storm surge flows. The peak tidal flow predicted by Neill's equation is compared to the peak flow determined by numerical simulation of estuaries with simple geometries, ranging from 1 to 25 km in length, using the U.S. Army Corps of Engineers one‐dimensional unsteady flow model, UNET. Results indicate that, under certain conditions, it may be appropriate to apply a correction factor to the peak discharge and peak velocity predicted by Neill's method. An algorithm, developed by nonlinear regression, is presented for computing correction factors based on estuary length, shape, mean depth, and storm‐tide characteristics. The results should permit the design of more reliable, cost‐effective structures by providing more realistic estimates of the potential for bridge scour in tidal waterways, especially when a full solution of the unsteady flow equations is impractical.     

A PARAMETRIC MODEL CALIBRATED WITH A PHYSICALLY BASED MODEL FOR RUNOFF PREDICTION FROM UNGAGED STREAMS1

ABSTRACT: Recent developments in the numerical solution of the governing partial differential equations for overland and channel flow should make possible physically based models which predict runoff from ungaged streams. However, these models, which represent the watershed by sets of intersecting planes, are complex and require much computer time. Parametric models exist that have the advantage of being relatively simple, and once calibrated are inexpensive to use and require limited data input. In this study, a procedure was developed for calibrating a parametric model against a physically based model, utilizing base areas of one acre and one square mile, with the expectation that base areas can be combined to model real watersheds. Simulation experiments with the physically based model showed that, for the one-acre base area, the dominant parameter (cell storage ratio, K) related to the slope and friction of the planes, whereas for one square-mile areas, the dominant parameters (K plus a lag factor, L) relate to channel properties. These parameters decreased exponentially as rainfall intensity increased.     

UNSATURATED FLOW THROUGH SOLID WASTE LANDFILLS: MODEL AND SENSITIVITY ANALYSIS1

ABSTRACT: The movement of precipitation water infiltrating through the material (refuse) of solid waste landfills is examined via numerical solution of the equations of continuity, and motion (Darcy's Law). The solution of the equations is obtained by a fully implicit, finite-difference scheme. Both unsaturated and saturated surface conditions are considered, making the scheme suitable for real-time simulation of net precipitation and moisture redistribution events. A sensitivity analysis showed that for unsaturated surface conditions the solution is primarily affected by hydraulic conductivity and capillary diffusivity, and is relatively independent of the space and time steps. In addition, the precipitation averaging process is shown to be critical in the correct computation of moisture transport during the time period where the transition from unsaturated to saturated conditions occurs. The model presented herein is suitable for analysis of water movement through landfills, and the design of bottom collection systems.     

EFFECT OF FLOW VELOCITY ON SEDIMENT OXYGEN DEMAND: COMPARISON OF THEORY AND EXPERIMENTS1

ABSTRACT: Theoretical equations that establish the relationship between sediment oxygen demand (SOD) in a lake and the flow velocity and dissolved oxygen concentration in the bulk water already exist. These theoretical equations for oxygen consumption in the sediment express biological consumption with Michaelis-Menten kinetics, and chemical consumption by a first order reaction. Data from laboratory experiments that were conducted to validate the theoretical equations also exist. These experiments were performed in a laboratory channel with well defined flow characteristics for three types of sediments. Herein, the theoretical equations are used to model the experimental data for the three types of sediments. The values used for the parameters in the theoretical equations are determined by iteration until a best fit is obtained for the relationship of SOD to flow velocity from both the theoretical model and experimental data. The goodness of fit is measured by the standard error of prediction and the regression coefficient.     

DEBRIS FLOWS THROUGH DIFFERENT FOREST AGE CLASSES IN THE CENTRAL OREGON COAST RANGE1

ABSTRACT: Debris flows in the Pacific Northwest can play a major role in routing sediment and wood stored on hillslopes and in first‐through third‐order channels and delivering it to higher‐order channels. Field surveys following a large regional storm event investigated 53 debris flows in the central Oregon Coast Range to determine relationships among debris flow characteristics and the age class of the surrounding forest. The volume of sediment and wood delivered by debris flows was strongly correlated with runout length. Debris flows that initiated at roads were significantly longer than nonroad related failures, and road related landslides were an order of magnitude larger than nonroad related landslides. Clearcuts and roads tended to have more numerous contributing landslides relative to second growth and mature forests. No statistically significant difference in the average debris flow runout length was detected among the forest age classes, although debris flows initiating in clearcuts and mixed forest and at roads occasionally supported extremely long runout lengths that were outside the range of variability observed in completely forested basins. The size of wood in deposits was not correlated with the size of trees on the adjacent slopes, suggesting that the majority of wood in debris flow deposits was from remobilization of wood previously stored in low order channels.     

APPLICATION OF AN ACOUSTIC STREAMFLOW-MEASURING SYSTEM ON THE COLUMBIA RIVER AT THE DALLES,OREGON1

ABSTRACT. The need for accurate, independent records of flow on the Columbia River at The Dalles, Oregon, has been met by the installation of an acoustic streamflow-measuring system. This device provides an index of the velocity of flow by measuring the difference in traveltimes of acoustic pulses transmitted through the water in each direction along a diagonal path across the river. The flow of water along the path increases the speed of one signal and retards the speed of the other. The difference in time of travel is related linearly to the water velocity along the path. Installation of the system, which is the first application of an acoustic flowmeter in a large natural channel, was completed in April 1969. It has been in continuous operation since that date. The velocity index and water-surface elevation are used as a two-variable index in the computation of flow. These variables, correlated against current-meter measurements made by use of specialized boat equipment, provide a reliable basis for computations of instantaneous and daily mean discharges.     

DETECTABILITY OF STEP TRENDS IN THE RATE OF ATMOSPHERIC DEPOSITION OF SULFATE1

A method is presented to assist policy makers in determining the combination of number of sampling stations and number of years of sampling necessary to state with a given probability that a step reduction in atmospheric deposition rates of a given magnitude has occurred at a pre-specified time. This pre-specified time would typically be the time at which a sulfate emission control program took effect, and the given magnitude of reduction is some percentage change in deposition rate one might expect to occur as a result of the emission control. In order to determine this probability of detection, a stochastic model of sulfate deposition rates is developed, based on New York State bulk collection network data. The model considers the effect of variation in precipitation, seasonal variations, serial correlation, and site-to-site (cross) correlation. A nonparametric statistical test which is well suited to detection of step changes in such multi-site data sets is developed. It is related to the Mann-Whitney Rank-Sum test. The test is used in Monte Carlo simulations along with the stochastic model to derive statistical power functions. These power functions describe the probability of detecting (α=0.05) a step trend in deposition rate as a function of the size of the step-trend, record length before and after the step-trend, and the number of stations sampled. The results show that, for an area the size of New York State, very little power is gained by increasing the number of stations beyond about eight. The results allow policy makers to determine the tradeoff between the cost of monitoring and time required to detect a step-trend of a given magnitude with a given probability.     

MEASURED AND PREDICTED VELOCITY AND LONGITUDINAL DISPERSION AT STEAI)Y AND UNSTEADY FLOW,COLORADO RIVER,GLEN CANYON DAM TO LAKE MEAD1

ABSTRACT: The effect of unsteadiness of dam releases on velocity and longitudinal dispersion of flow was evaluated by injecting a fluorescent dye into the Colorado River below Glen Canyon Dam and sampling for dye concentration at selected sites downstream. Measurements of a 26-kilometer reach of Glen Canyon, just below Glen Canyon Dam, were made at nearly steady dam releases of 139, 425, and 651 cubic meters per second. Measurements of a 380-kilometer reach of Grand Canyon were made at steady releases of 425 cubic meters per second and at unsteady releases with a daily mean of about 425 cubic meters per second. In Glen Canyon, average flow velocity through the study reach increased directly with discharge, but dispersion was greatest at the lowest of the three flows measured. In Grand Canyon, average flow velocity varied slightly from subreach to subreach at both steady and unsteady flow but was not significantly different at steady and unsteady flow over the entire study reach. Also, longitudinal dispersion was not significantly different during steady and unsteady flow. Long tails on the time-concentration curves at a site, characteristic of most rivers but not predicted by the one-dimensional theory, were not found in this study. Absence of tails on the curves shows that, at the measured flows, the eddies that are characteristic of the Grand Canyon reach do not trap water for a significant length of time. Data from the measurements were used to calibrate a one-dimensional flow model and a solute-transport model. The combined set of calibrated flow and solute-transport models was then used to predict velocity and dispersion at potential dam-release patterns.     

Impact of Temporal Resolution of Flow‐Duration Curve on Sediment Load Estimation1

Chen, Li, Rina Schumer, Anna Knust, and William Forsee, 2011. Impact of Temporal Resolution of Flow‐Duration Curve on Sediment Load Estimation. Journal of the American Water Resources Association (JAWRA) 48(1): 145‐155. DOI: 10.1111/j.1752‐1688.2011.00602.x Abstract: Estimates of a channel’s annual sediment transport capacity typically incorporate annualized flow‐duration curves. Average daily flow data, commonly used to develop flow‐duration curves, may not adequately describe sediment‐transporting flows in arid and semiarid ephemeral streams. In this study, we examined impacts of varied temporal resolution flow data on annual sediment load estimation. We derived flow‐duration curves for eight sites in the Southwestern United States based on both 15‐min and daily‐averaged flow data. We then estimated sediment loads for both flow‐duration curves using the Sediment Impact Analysis Method, implemented in HEC‐RAS. When average daily flow is used to generate flow‐duration curves, sediment load estimation is lower by up to an order of magnitude. This trend is generally unaffected by uncertainty associated with sediment particle size or hydraulic roughness. The ratio of sediment loads estimated by 15‐min versus daily‐averaged flow‐duration curves is strongly correlated with channel slope, being greater on steep‐slope channels. Sediment loads estimated by the two types of flow‐duration curves are closely correlated, suggesting possible relationships for improving predictions when high‐temporal resolution data are unavailable. Results also suggest that the largest flow contributes significantly to total sediment load, and thus will greatly impact ephemeral stream geomorphology in arid and semiarid regions.     

ALTERNATIVE APPROACH TO THE FORMULATION OF BASIN HYDRAULIC GEOMETRY EQUATIONS1

ABSTRACT: Along a drainage network, there is a systematic variation of average flow parameters (width, depth, and velocity) at flows having the same flow duration. Hydraulic geometry equations mathematically express this interdependent relationship of stream-flow characteristics for a basin for annual flow durations varying from 10 to 90 percent. However, the equations proposed so far have had rather poor predictive performance for low flows. An independent investigation of the variation of discharge with drainage area and annual flow duration demonstrates a consistent relationship between these parameters. The relationship for the high to median-flow range differs, however, from that for the median— to low-flow range. The proposed equations provide a better predictive performance for low flows than previous formulations and a versatile means of estimating flow parameters for streams throughout a basin. The improved basin hydraulic geometry equations have a wide range of applications in areas such as stream habitat assessment, water quality modeling, channel design, and stream restoration projects.     

MODELING MULTIPLE CRITICAL DEPTHS1

ABSTRACT: This paper explores the occurrence of multiple critical depths in one-dimensional computational models of open channel systems. The mathematical formulation is reviewed, including examination of the number of possible roots by Descartes' Rule. Governing equations and dependent variables are scrutinized using two compound cross sections. Occurrence tendencies are reviewed for singular channels. Critical flow is introduced as a tool to determine the existence and location of computationally based multiple critical depths. A strategy to manage multiple critical depths in existing one-dimensional steady or unsteady models is proposed.     

OPTIMIZATION OF TRANSPORTATION NETWORKS DURING URBAN FLOODING1

ABSTRACT: In this paper a numerical model for flood propagation in urban areas is proposed. It has been applied to evaluate flooding hydraulic characteristics in terms of potential flood elevations, depths, and inundated areas. Furthermore, the algorithm efficiency and the consequent reduced computation time allow the use of the hydraulic model as a part of a more complex system for civil protection actions, planning, and management. During flood events, the transportation network plays a main role both in rescuing people when they are more vulnerable and in moving people and materials from and toward affected areas. The reduced efficiency of this transportation network is evaluated based on a least‐flood‐risk path‐finding algorithm. The results of a case study concerning the northern part of the city of Rome, show that the numerical model for unsteady flow in open channel networks achieves the proposed aims. It has proven to be able to describe the flood hydraulic characteristics and to be suitable for real‐time flood emergency management in urban areas.     

FLOOD ROUTING THROUGH A FLAT,COMPLEX FLOODPLAIN USING A ONE-DIMENSIONAL UNSTEADY FLOW COMPUTER PROGRAM1

ABSTRACT: The routing of flood waves through the Central Basin of the Passaic River in New Jersey is complex because of flat gradients and flow reversals. The one-dimensional unsteady flow program DWOPER, developed by the National Weather Service, was used to simulate flood wave movement through the Basin. A historical event was used for calibration and two synthetic events were simulated. Boundary conditions consisted of discharge hydrographs at inflow points to the study area, local flow hydrographs at interior points, and a stage discharge relation for flow over the crest of a diversion dam at the basin outlet. Manning's n values were adjusted based on stage and discharge data for the historical event; however, verification data were not available for events comparable in magnitude to the synthetic events. Aspects of the investigation reported include techniques for characterizing the flow system, model calibration, techniques for representing a tunnel diversion, and simulation results.     

Simulation studies of ammonia removal from water in a membrane contactor under liquid–liquid extraction mode

Simulation studies were carried out, in an unsteady state, for the removal of ammonia from water via a membrane contactor. The contactor had an aqueous solution of NH₃ in the lumen and sulphuric acid in the shell side. The model equations were developed considering radial and axial diffusion and convection in the lumen. The partial differential equations were converted by the finite difference technique into a series of stiff ordinary differential equations w.r.t. time and solved using MATLAB. Excellent agreement was observed between the simulation results and experimental data (from the literature) for a contactor of 75 fibres. Excellent agreement was also observed between the simulation results and laboratory-generated data from a contactor containing 10,200 fibres. Our model is more suitable than the plug-flow model for designing the operation of the membrane contactor. The plug-flow model over-predicts the fractional removal of ammonia and was observed to be limited when designing longer contactors.