Longitudinal Dispersion Coefficient in Single-Channel Streams

Using a new channel shape equation for straight channels and a more versatile channel shape or local flow depth equation for natural streams a method is developed for prediction of the longitudinal dispersion coefficient in single-channel natural streams, including straight and meandering ones. The method involves derivation of a new triple integral expression for the longitudinal dispersion coefficient and development of an analytical method for prediction of this coefficient in natural streams. The proposed method is verified using 70 sets of field data collected from 30 streams in the United States ranging from straight manmade canals to sinuous natural rivers. The new method predicts the longitudinal dispersion coefficient, where more than 90% calculated values range from 0.5 to 2 times the observed values. The advantage of the new method is that it is capable of accurately predicting the longitudinal dispersion coefficient in single-channel natural streams without using detailed dye concentration test data. A comparison between the new method and the existing methods shows that the new method significantly improves the prediction of the longitudinal dispersion coefficient.     

Predicting Longitudinal Dispersion Coefficient in Natural Streams by Artificial Neural Network

An artificial neural network (ANN) model was developed to predict the longitudinal dispersion coefficient in natural streams and rivers. The hydraulic variables [flow discharge (Q), flow depth (H), flow velocity (U), shear velocity (u*), and relative shear velocity (U/u*)] and geometric characteristics [channel width (B), channel sinuosity (σ), and channel shape parameter (β)] constituted inputs to the ANN model, whereas the dispersion coefficient (Kx) was the target model output. The model was trained and tested using 71 data sets of hydraulic and geometric parameters and dispersion coefficients measured on 29 streams and rivers in the United States. The training of the ANN model was accomplished with an explained variance of 90% of the dispersion coefficient. The dispersion coefficient values predicted by the ANN model satisfactorily compared with the measured values corresponding to different hydraulic and geometric characteristics. The predicted values were also compared with those predicted using several equations that have been suggested in the literature and it was found that the ANN model was superior in predicting the dispersion coefficient. The results of sensitivity analysis indicated that the Q data alone would be sufficient for predicting more frequently occurring low values of the dispersion coefficient (Kx<100?m2/s). For narrower channels (B/H<50) using only U/u* data would be sufficient to predict the coefficient. If β and σ were used along with the flow variables, the prediction capability of the ANN model would be significantly improved.     

Estimation of the Longitudinal Dispersion Coefficient Using the Velocity Profile in Natural Streams

In this study, a theoretical method for predicting the longitudinal dispersion coefficient is developed based on the transverse velocity distribution in natural streams. Equations of the transverse velocity profile for irregular cross sections of the natural streams are analyzed. Among the velocity profile equations tested in this study, the beta distribution equation, which is a probability density function, is considered to be the most appropriate model for explaining the complex behavior of the transverse velocity structure of irregular natural streams. The new equation for the longitudinal dispersion coefficient that is based on the beta function for the transverse velocity profile is developed. A comparison of the proposed equation with existing equations and the observed longitudinal dispersion coefficient reveals that the proposed equation shows better agreement with the observed data compared to other existing equations.     

Longitudinal Dispersion in Ice-Covered Rivers

Longitudinal dispersion is the spreading of suspended or dissolved substances caused by the combined action of differential advection and lateral mixing. Tracer tests in many rivers under open-water conditions have indicated that the temporal spread first increases linearly with downstream distance (linear range). It may ultimately grow in proportion to the square root of distance (Fickian range), very far below the point of release. Test data have been obtained in ice-covered rivers, starting in 1975. They show linear-range behavior even though the test reaches were as long as hundreds of kilometers. As in the case of open-water conditions, the rates of spread under an ice cover are related to the friction factor of the flow, being generally higher than the open-water values for equal friction factors. Based on early results in pipe flow, many water quality models assume Fickian dispersion, contrary to the field evidence. A more correct quantification of the dispersion process is outlined and implications to the method of computation are discussed.     

Longitudinal Dispersion Coefficient in Straight Rivers

An analytical method is developed to determine the longitudinal dispersion coefficient in Fischer's triple integral expression for natural rivers. The method is based on the hydraulic geometry relationship for stable rivers and on the assumption that the uniform-flow formula is valid for local depth-averaged variables. For straight alluvial rivers, a new transverse profile equation for channel shape and local flow depth is derived and then the lateral distribution of the deviation of the local velocity from the cross-sectionally averaged value is determined. The suggested expression for the transverse mixing coefficient equation and the direct integration of Fischer's triple integral are employed to determine a new theoretical equation for the longitudinal dispersion coefficient. By comparing with 73 sets of field data and the equations proposed by other investigators, it is shown that the derived equation containing the improved transverse mixing coefficient predicts the longitudinal dispersion coefficient of natural rivers more accurately.     

Dispersion Coefficient of Streams from Tracer Experiment Data

The paper deals with a method for optimal identification of the dispersion coefficient for streams from observed concentration profiles at downstream sections (at least two sections are required) following injection of an environmentally safe tracer at an upstream section. The method makes use of the exact solution of the one-dimensional advection-dispersion equation. A reliable and accurate procedure is proposed for routing an arbitrary concentration variation further downstream using the convolution equation and pulse kernels. The new method does not require the frozen cloud approximation and avoids the error due to numerical integration of the convolution integral used for routing the concentration. It employs the objective criterion of minimum integral squared errors between observed and computed concentrations. Application of the method to field data sets shows that reliably accurate estimates of the dispersion coefficient are obtained.     

Stage–Discharge Relations for Low-Gradient Tidal Streams Using Data-Driven Models

Development of stage–discharge relationships for coastal low-gradient streams is a challenging task. Such relationships are highly nonlinear, nonunique, and often exhibit multiple loops. Conventional parametric regression methods usually fail to model these relationships. Therefore, this study examines the utility of two data-driven computationally intensive modeling techniques namely, artificial neural networks and local nonparametric regression, to model such complex relationships. The results show an overall good performance of both modeling techniques. Both neural network and local regression models are able to predict and reproduce the stage–discharge multiple loops that are observed at the outlet of a 28.5?km2 low-gradient subcatchment in southwestern Louisiana. However, the neural network model is characterized with higher prediction ability for most of the tested runoff events. In agreement with the physical characteristics of low-gradient streams, the results indicate the importance of including information about downstream and upstream water levels, in addition to water level at the prediction site.     

Longitudinal Dispersion due to Surcharged Manhole

New data describing the longitudinal dispersion of a solute tracer due to a surcharged manhole structure are presented. The increase in both travel time and dispersion caused by this structure is quantified over ranges of discharge and surcharge. Discharge variations exhibit clear trends, whereas surcharge variations are less evident. The results are presented as both Taylor dispersion coefficients and values of parameters used in aggregated dead zone modeling. The limitations of using surcharged averaged parameters with each technique for describing mixing due to a surcharged manhole structure are illustrated. The study shows that the presence of manhole structures within urban drainage schemes has a significant effect on both the travel time and mixing processes of a solute. It is suggested that these processes should be included for the accurate modeling of urban drainage schemes.     

Eulerian-Lagrangian Numerical Scheme for Simulating Advection, Dispersion, and Transient Storage in Streams and a Comparison of Numerical Methods

Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme’s limitations.     

Persistence of Skewness in Longitudinal Dispersion Data: Can the Dead Zone Model Explain It After All?

Field studies reporting coefficients of temporal skewness that do not decrease in the main flow direction have cast doubt on the transient storage (TS) or dead zone model of longitudinal dispersion in rivers and streams. In this study, the conditions under which the TS model predicts persistent or growing skewness coefficients are investigated. The findings clearly show that, though not outright impossible, an instantaneous slug release into a uniform channel reach is, indeed, extremely unlikely to result in persistent or growing skewness coefficients. In contrast, the passage of a tracer or pollutant along a sequence of (hydraulically) different subreaches may easily give rise to nondecaying skewness coefficients, the occurrence of which is governed by the parameter sets of the subreaches concerned. Thus, the TS model does show a certain potential to explain the persistence of skewness. The findings reported here are expected to be useful in guiding future field studies on the subject. An application of the newly derived criterion to stream tracer data has been successful.     

The Longitudinal Relations of Regulation and Emotionality to Quality of Indonesian Children's Socioemotional Functioning.

Data regarding individual differences in children's regulation, emotionality, quality of socioemotional functioning, and shyness were obtained from teachers and peers for 112 Indonesian 6th graders. Similar data (plus parents' reports) also were collected when these children were in 3rd grade. For boys, regulation and low negative emotionality generally predicted positive socioemotional functioning (e.g., social skills, adjustment, prosocial tendencies and peer liking, sympathy) within and across time and across reporters, even at the follow-up when initial levels of regulation or negative emotionality were controlled. For girls, relations were obtained primarily for concurrent teacher reports, probably because girls tended to be fairly well regulated and socially competent and variability in their scores was relatively low. Shyness for both sexes tended to be associated with concurrent measures of low regulation, high negative emotionality, and low quality of social competence. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Empirical and Conceptual Problems With Longitudinal Trait-State Models: Introducing a Trait-State-Occasion Model.

The latent trait-state-error model (TSE) and the latent state-trait model with autoregression (LST-AR) represent creative structural equation methods for examining the longitudinal structure of psychological constructs. Application of these models has been somewhat limited by empirical or conceptual problems. In the present study, Monte Carlo analysis revealed that TSE models tend to generate improper solutions when N is too small, when waves are too few, and when occasion factor stability is either too large or too small. Mathematical analysis of the LST-AR model revealed its limitation to constructs that become more highly auto-correlated over time. The trait-state-occasion model has fewer empirical problems than does the TSE model and is more broadly applicable than is the LST-AR model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Dispersion Model for Tidal Wetlands

Tidal wetlands in California are mostly estuarine salt marshes characterized by tidal channels and mudflats that are flooded and drained on a semidiurnal basis. Depths are rarely greater than 2 or 3 m, except where dredging occurs for harbor operations, and lengths from head to mouth are usually in the range of 1–10 km. This paper presents a coupled set of models for prediction of flow, solute transport, and particle transport in these systems. The flow and solute transport models are based upon depth-integrated conservation equations while the particle transport model is quasi-three-dimensional. Common to these models is an assumption that a turbulent boundary layer extends vertically from the bed and can be described by the law of the wall. This feature of the model accounts for: (1) momentum transfer to the bed, (2) longitudinal dispersion of dissolved material based on the work of Elder (1959), and (3) advection and turbulent diffusion of particles in three dimensions. A total variation diminishing finite volume scheme is used to solve the depth-integrated equations. Using this model, we show that dispersion can be accurately modeled using physically meaningful mixing coefficients. Calibration is therefore directed at modifying bed roughness, which scales both the rate of advection and dispersion.     

A Longitudinal Latent Variable Analysis of Reciprocal Relations Between Depressive Symptoms and Delinquency During Adolescence.

In this longitudinal study, reciprocal relations between depressive symptoms and delinquent behavior were examined for a sample of 1,218 male and female adolescents (mean age, 15.51 years at Time 1). Associations were examined within a latent variable approach, controlling for indicator-specific tendencies, students' age and parental education, time-specific 3rd-variable influences, level of prior problem behavior, and measurement error. Findings thus provided relatively unbiased estimates of existing plausible causal relations. Analyses revealed a relatively small unidirectional effect of delinquency on depression for boys (at 1 of 3 time points), and bidirectional effects of comparable size for girls. The circular process for the girls was explained drawing on gender socialization theory and theories of offending behavior. Implications for preventive interventions are also discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)