Comments on “Development of an empirical equation for the transverse dispersion coefficient in natural streams” by Tae Myoung Jeon,Kyong Oh Baek and Il Won Seo

In a recent paper published in this journal, Jeon et al. ((2007), Environ Fluid Mech 7(4): 317–329) have presented a new empirical equation for the transverse dispersion coefficient in natural streams that was developed based on the hydraulic and geometric parameters using a regression technique. A total of 32 data sets collected in 32 streams was used. Among them, 16 data sets were used for deriving the new equation, and the other 16 were used for verifying the equation. Starting from dimensional analysis the authors found that transverse dispersion coefficient depends on three parameters, such as sinuosity, aspect ratio and a friction term. The robust least square method was applied to estimate regression coefficients resulting in an equation which allows better prediction of transverse dispersion coefficient than previous literature equations. The discussers would like to highlight some points raised in the paper.     

Empirical equation for transverse dispersion coefficient based on theoretical background in river bends

There are different approaches to estimating the transverse dispersion coefficient in river mixing. Theoretical approaches have derived the dispersion coefficient from the concept of shear flow, which has dominant effects on the transverse mixing. Empirical approaches have developed an equation using the hydraulic and geometric data of rivers through dimensional analysis and regression techniques. These two equations interact closely with each other. For example, the complicated theoretical equation can be simplified by empirical approaches, and the functional relationships of the empirical equation can be derived from theoretical bases. In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the theoretical background in river bends. As a regression method, the least-square iterative method was used because the equation was a nonlinear model. The estimated dispersion coefficients derived by the new equation were compared with observed transverse dispersion coefficients acquired from natural rivers and coefficients calculated by the other existing empirical equations. From a comparison of the existing transverse dispersion equations and the proposed equation, it appears that the behavior of the existing formula in a relative sense is very much dependent on the flow condition and the river geometry. Moreover, the proposed equation does not vary widely according to variation of flow conditions. Also, it was revealed that the equation proposed in this study becomes an asymptotic curve as the curvature effect increases.     

Parameter estimation for fractional dispersion model for rivers

The fractional dispersion model for natural rivers, extended by including a first order reaction term, contains four parameters. In order to estimate these parameters a fractional Laplace transform-based method is developed in this paper. Based on 76 dye test data measured in natural streams, the new parameter estimation method shows that the fractional dispersion operator parameter F is the controlling parameter causing the non-Fickian dispersion and F does not take on an integer constant of 2 but instead varies in the range of 1.4–2.0. The adequacy of the fractional Laplace transform-based parameter estimation method is determined by computing dispersion characteristics of the extended fractional dispersion model and these characteristics are compared with those observed from 12 dye tests conducted on the US rivers, including Mississippi, Red, and Monocacy. The agreement between computed and observed dispersion characteristics is found to be good. When combined with the fractional Laplace transform-based parameter estimation method, the extended fractional dispersion model is capable of accurately simulating the non-Fickian dispersion process in natural streams.     

北京东南郊大气中多环芳烃的相分配及其致癌毒性表征

采用索氏提取法提取2005年3月至2006年1月间北京市东南郊3个采样点大气总悬浮颗粒物(TSP)样品和气相样品中的多环芳烃(PAHs),利用GC/MS分析其质量浓度,对PAHs在颗粒相和气相间的分配行为进行研究。结果表明,2环组分在气相PAHs中占优势地位,全年平均在95%左右;4环组分在颗粒相PAHs中全年平均占56%左右;5~6环组分几乎全部分布在颗粒相中。引入苯并[a]芘等当量毒性因子(TEFs),探讨致癌毒性组分在2相间的分配行为,研究发现低毒高质量浓度的低环组分与高毒低质量浓度的高环组分对致癌性贡献相当;利用苯并[a]芘等效质量浓度与16种PAHs组分质量浓度进行多元线性回归,得到的回归方程用于粗略计算大气中PAHs致癌性组分的等效质量浓度;在分析PAHs分配行为的季节变化规律基础上,结合气象参数和空气污染指数分析PAHs在大气气相和颗粒相中分配系数的影响因素,并提出了分配系数与气象参数和API指数的回归方程,并利用回归方程来计算PAHs组分在大气中的分配系数。     

Prediction of longitudinal dispersion coefficients in natural rivers using artificial neural network

An artificial neural network (ANN) model is developed for predicting the longitudinal dispersion coefficient in natural rivers. The model uses few rivers’ hydraulic and geometric characteristics, that are readily available, as the model input, and the target output is the longitudinal dispersion coefficient (K). For performance evaluation of the model, using published field data, predictions by the developed ANN model are compared with those of other reported important models. Based on various performance indices, it is concluded that the new model predicts the longitudinal dispersion coefficient more accurately. Sensitive analysis performed on input parameters indicates stream width, flow depth, stream sinuosity, flow velocity, and shear velocity to be the most influencing parameters for accurate prediction of the longitudinal dispersion coefficient.     

Natural cyanide degradation and impact on Ili River drainage areas from a Goldmine in Xinjiang autonomous region,China

The Ili River is a very important river to the northwest of China and Kazakhstan. The Axi Goldmine is located in the upstream of a branch of the Ili River. The cyanide from the goldmine effluent is a threat to the downstream areas. According to our study, the natural degradation of cyanide conforms to a negative exponential equation in the tailings impoundment, second wastewater pond and even in the receiving streams if the dilution action from other streams were deducted. In the combined action of dilution and natural decomposing, the cyanide from the goldmine effluent does not pose a hazard to the trunk of the Ili River in the normal producing states. The equations of cyanide degradation in the streams and the hydrology parameters could be used to assess the environmental impact on the downstream areas if accidental discharges of cyanide occurred. The available way of decreasing the cyanide impact on the streams is to increase the rate of recycled water so that the lower the wastewater level in the tailing impoundment and the second wastewater pond, the lower is the amount of leakage of wastewater to the streams.     

Analytical solution of two-dimensional advection–dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method

In the present study analytical solutions of a two-dimensional advection–dispersion equation (ADE) with spatially and temporally dependent longitudinal and lateral components of the dispersion coefficient and velocity are obtained using Green’s Function Method (GFM). These solutions describe solute transport in infinite horizontal groundwater flow, assimilating the spatio-temporal dependence of transport properties, dependence of dispersion coefficient on velocity, and the particulate heterogeneity of the aquifer. The solution is obtained in the general form of temporal dependence and the source term, from which solutions for instantaneous and continuous point sources are derived. The spatial dependence of groundwater velocity is considered non-homogeneous linear, whereas the dispersion coefficient is considered proportional to the square of spatial dependence of velocity. An asymptotically increasing temporal function is considered to illustrate the proposed solutions. The solutions are validated with the existing solutions derived from the proposed solutions in three special cases. The effect of spatially/temporally dependent heterogeneity on the solute transport is also demonstrated. To use the GFM, the ADE with spatio-temporally dependent coefficients is reduced to a dispersion equation with constant coefficients in terms of new position variables introduced through properly developed coordinate transformation equations. Also, a new time variable is introduced through a known transformation.     

Transport of Pollutant in Open Channel with Short Waves

This study examines the effect of short period water waves on the longitudinal mixing of pollutants in open channel flow. These waves create orbital motions and therefore increase the magnitude of the dispersion coefficient. Experiments are conducted for non-wavy and wavy flow. The values of the longitudinal dispersion coefficients are determined by applying the method of least squares to the measured solute concentrations at various time intervals. For non-wavy flow, the measured values of longitudinal dispersion coefficient match closely with those computed from the empirical equation given by Seo [1]. For wavy flow, a new factor called the wave parameter (a/TU _*, a=wave amplitude, T=wave period, U _*=shear velocity) is found important and a nonlinear multiple regression analysis is used to derive a new expression for the wave induced longitudinal dispersion coefficient (WILDC). An uncertainty analysis is conducted as per IS Code 5168 and the confidence interval is determined. Linear water wave theory is applied to modify the existing expression of the longitudinal dispersion coefficient of Seo [1] by including the effect of short waves. A mathematical model for WILDC is then developed. Comparative study between wavy and non-wavy flow cases has been conducted. The results clearly show an increase in the magnitude of longitudinal dispersion coefficient in the presence of waves.     

Enhancing transverse mixing in streams with submerged vanes

In order to maintain the water quality of moving streams, it is essential to know the process of pollutant mixing. The transverse mixing is very important which is needed to be modeled to understand mixing phenomenon. It was observed that transverse mixing is a strong function of secondary currents, thus, submerged vanes, which are aerofoil skewed at angle of 10°–40° with respect to flow, generate transverse circulations that can be utilized to induce secondary currents in the flow to enhance transverse mixing. Present study is an attempt to utilize submerged vanes as an instrument to enhance the transverse mixing by incorporating various vane configurations. In order to study the effect of vane generated circulations on transverse mixing, experimentations were conducted on three vane sizes and for various row arrangements of vanes attached to bed. An attempt is made to investigate the effect of submerged vane size and rows on transverse velocity, concentration profile and transverse mixing coefficient. It was observed by measurement of concentration profile that transverse mixing was more enhanced for submerged vanes of higher height. It was also observed that as the number of rows is proportional to the transverse mixing. By measuring the transverse velocity profile, it was observed that more and more fluid was advected in transverse direction for higher rows of vanes. By utilizing the observed transverse mixing coefficients, number of vane rows and relative height of vane, a predictor was derived to predict transverse mixing coefficient in the presence of submerged vane rows. It was observed that the derived predictor shows a fair amount of agreement in the result predicted.     

多环芳烃活性参数与色谱保留指数相关性分析

为了简化多环芳烃(PAHs)的Koc、Kow和BCF等活性参数的测定和预测工作,通过对PAHs的活性参数与气相色谱保留指数(I)、苯环个数(N)的相关关系分析,分别建立了I与lgKoc、lgKow和lgBCF,N与lgKoc、lgKow和lgBCF间的2类一元线性回归预测方程,以及I、N与lgKoc、lgKow和lgBCF间的二元线性回归预测方程。结果表明,PAHs类化合物的I值或N值分别与lgKoc、lgKow和lgBCF存在明显的线性相关性,均能对上述3种活性参数进行准确预测,其中,用I值建立的一元回归方程的预测精度更好;而利用I值和N值共同建立的二元预测方程经t检验发现,方程中变量N的偏回归系数的统计检验没有显著意义。本研究利用I值建立的一元线性预测模型能较好地预测PAHs类化合物的Koc、Kow和BCF等活性参数,从而为PAHs的活性参数预测提供了一种简便易行的方法。     

Improved formulae of velocity distributions along the vertical and transverse directions in natural rivers with the sidewall effect

The distribution of flow velocity is a basis for the research into the transport of flow and sediment in natural rivers. Characteristics of velocity distribution in narrow-deep natural rivers are different from those in wide-shallow open channels, and the effect of sidewalls on the distribution of flow velocity is considerable, which leads to a large transverse gradient of the depth-averaged velocity, with the maximum velocity occurring below the water surface. Based on the Reynolds equation of turbulence flow and the analysis of the features of velocity distribution in natural rivers, improved formulae with two empirical parameters α and β have been proposed for the velocity distributions along the vertical and transverse directions, with the effect of sidewalls being considered, through solving the definite solution problem by the method of variable separation. The proposed formulae were validated fully through comparisons between the calculated and measured velocity profiles and depth-averaged velocities at several sections in the Yangtze and Baitarani Rivers, with close agreement between them being obtained. The formula of velocity distribution along the transverse direction in natural rivers with the sidewall effect was also compared with previous studies, and the calculation accuracy of this formula at a section with a narrow-deep geometry was higher than the accuracy of the previous equations. It is confirmed that the proposed formulae can reproduce well the distribution characteristics of flow velocity along the vertical and transverse directions in narrow-deep natural rivers, with a more wide application in practice.     

Calibration and predictive ability analysis of longitudinal solute transport models in mountain streams

The first step in developing travel time and water quality models in streams is to correctly model solute transport mechanisms. In this paper a comparison between two solute transport models is performed. The parameters of the Transient Storage model (TS) and the Aggregated Dead Zone model (ADZ) are estimated using data of thirty seven tracer experiments carried out under different discharges in five mountain streams of Colombian Los Andes. Calibration is performed with the generalized uncertainty estimation method (GLUE) based on Monte-Carlo simulations. Aspects of model parameters identifiability and model parsimony are analyzed and discussed. The TS model with four parameters shows excellent results during calibration but the model parameters present high interaction and poor identifiability. The ADZ model with two independent and clearly identifiable parameters gives sufficiently precise calibration results. As a conclusion, it is stated that the ADZ model with only two parameters is a parsimonious model that is able to represent solute transport mechanisms of advection and longitudinal dispersion in the studied mountain streams. A simple model parameter estimation methodology as a function of discharge is proposed in this work to be used in prediction mode of travel time and solute transport applications along mountain streams.     

RANS-based simulation of transverse turbulent mixing in a 2D geometry

Although transverse mixing is a significant process in river engineering when dealing with the discharge of pollutants from point sources or the mixing of tributary inflows, no theoretical basis exists for the prediction of its rate, which is indeed based upon the results of experimental works carried on in laboratory channels or in streams and rivers. The paper presents the preliminary results of a numerical study undertaken to simulate the transverse mixing of a steady-state point source of a tracer in a two-dimensional rectangular geometry, which is expected to reproduce a shallow flow. This geometry is that of Lau and Krishnappan (J Hydraul Div 13(HY10):1173–1189, 1977), who collected turbulent mixing data for a shallow flow. In the numerical study an approach based on the Reynolds Averaged Navier–Stokes (RANS) equations was applied, where the closure problem was solved by using turbulent viscosity concept. Particularly, the classical two-equations k–? model was used. Two methods were applied to the model results to evaluate the turbulent transverse mixing coefficient. The effect on transverse mixing of a grid located upstream the tracer source was also studied. Numerical results were generally higher than the experimental data. This overestimation could be explained considering the hypothesis of isotropic turbulence underlying the k–? model, which can lead to large turbulent viscosities and rate of mixing. However, RANS-based results may still be considered acceptable also providing the large uncertainties associated with literature predictive equations.     

Metabolic rates of epipelagic marine copepods as a function of body mass and temperature

Metabolic rates (oxygen consumption, ammonia excretion, phosphate excretion) have been calculated as a function of body mass (dry, carbon, nitrogen and phosphorus weights) and habitat temperature, using multiple regression. The metabolic data used for this analysis were species structured, collected from Arctic to Antarctic seas (temperature range: -1.7°C to 29.0°C). The data were further divided into geographical and/or seasonal groups (35 species and 43 data sets for oxygen consumption; 38 species and 58 data sets for ammonia excretion; 22 species and 31 data sets for phosphate excretion). The results revealed that the variance attributed to body mass and temperature was highest (93-96%) for oxygen consumption rates, followed by ammonia excretion rates (74-80%) and phosphate excretion rates (46-56%). Among the various body mass units, the best correlation was provided by the nitrogen unit, followed by the dry weight unit. The calculated Q₁₀ values varied slightly according to the choice of body mass units; overall ranges were 1.8-2.1 for oxygen consumption rates, 1.8-2.0 for ammonia excretion rates and 1.6-1.9 for phosphate excretion rates. The effects of body mass and temperature on the metabolic quotients (O:N, N:P, O:P) were insignificant in most cases. Although the copepod metabolic data used in the present analysis were for adult and pre-adult stages, possible applications of the resultant regression equations to predict the metabolic rates of naupliar and early copepodite stages are discussed. Finally, global patterns of net growth efficiency [growth (growth+metabolism)^-1] of copepods were deduced by combining the present metabolic equation with Hirst and Lampitt's global growth equation for epipelagic marine copepods.     

Population growth in snow geese: a modeling approach integrating demographic and survey information

There are few analytic tools available to formally integrate information coming from population surveys and demographic studies. The Kalman filter is a procedure that facilitates such integration. Based on a state-space model, we can obtain a likelihood function for the survey data using a Kalman filter, which we may then combine with a likelihood for the demographic data. In this paper, we used this combined approach to analyze the population dynamics of a hunted species, the Greater Snow Goose (Chen caerulescens atlantica), and to examine the extent to which it can improve previous demographic population models. The state equation of the state-space model was a matrix population model with fecundity and regression parameters relating adult survival and harvest rate estimated in a previous capture-recapture study. The observation equation combined the output from this model with estimates from an annual spring photographic survey of the population. The maximum likelihood estimates of the regression parameters from the combined analysis differed little from the values of the original capture-recapture analysis, though their precision improved. The model output was found to be insensitive to a wide range of coefficient of variation (CV) in fecundity parameters. We found a close match between the surveyed and smoothed population size estimates generated by the Kalman filter over an 18-year period, and the estimated CV of the survey (0.078-0.150) was quite compatible with its assumed value (approximately 0.10). When we used the updated parameter values to predict future population size, the model underestimated the surveyed population size by 18% over a three-year period. However, this could be explained by a concurrent change in the survey method. We conclude that the Kalman filter is a promising approach to forecast population change because it incorporates survey information in a formal way compared with ad hoc approaches that either neglect this information or require some parameter or model tuning.     

Analytical solutions of nonlinear and variable-parameter transport equations for verification of numerical solvers

All numerical codes developed to solve the advection–diffusion-reaction (ADR) equation need to be verified before they are moved to the operational phase. In this paper, we initially provide four new one-dimensional analytical solutions designed to help code verification; these solutions are able to handle the challenges of the scalar transport equation including nonlinearity and spatiotemporal variability of the velocity and dispersion coefficient, and of the source term. Then, we present a solution of Burgers’ equation in a novel setup. Proposed solutions satisfy the continuity of mass for the ambient flow, which is a crucial factor for coupled hydrodynamics-transport solvers. By the end of the paper, we solve hypothetical test problems for each of the solutions numerically, and we use the derived analytical solutions for code verification. Finally, we provide assessments of results accuracy based on well-known model skill metrics.     

除草剂苯噻草胺在土壤中的吸附

对除草剂苯噻草胺在6种不同土壤中的吸附行为进行了研究。结果表明,土壤对苯噻草胺有较强的吸附性。在试验浓度范围内,苯噻草胺的土壤吸附行为可用线性吸附模型表征。土壤有机质是影响苯噻草胺吸附行为的重要因素,其吸附系数有随土壤有机质含量增高而增大的趋势。通过在线性吸附系数（Kd)和土壤有机质含量（OM％）之间构建的回归方程：Kd=2.6120 OM% 1.0746,可以预测苯噻草胺的Kd值,其预测的可靠性通过蒙特卡洛模拟得以检验。     

酚类化合物结构与醇/水分配系数(logK_(ow))关系研究

将不同非氢原子自身及非氢原子之间的关系参数化并构建出新的结构描述符,对部分酚类化合物分子结构进行了参数化表达。采用逐步回归(SMR)与多元线性回归(MLR)相结合的方法建立了化合物结构与醇/水分配系数(log Kow)之间的关系模型,模型的建模相关系数(r)为0.988,标准偏差(SD)为0.121;"留一法"交互检验的相关系数(Q2)为0.966,标准偏差(SDCV)为0.148。结果表明结构描述符能较好地表征化合物分子结构特征,所建模型稳定性好,预测能力强,对于酚类化合物QSPR研究具有一定的参考价值。     

QUAL2E模型在大沽河干流青岛段水质模拟中的应用

采用QUAL2E模型对大沽河干流青岛段的水质进行了模拟和预测。针对大沽河的具体情况,选用BOD5、COD和氮作为模拟预测指标,用实验模拟方法、模型率定法并参考相关文献确定了BOD耗氧系数k1、BOD复氧系数k2、BOD沉降系数k3、COD耗氧系数和弥散系数等水质参数,并对模拟结果进行了验证,表明预测值和实测值的相关性较好;对BOD5、k1、k2和Q(流量)进行了灵敏度分析,结果表明对大沽河DO浓度影响敏感的参数依次是:Q、k2、BOD、k1,即流量Q是模型最敏感的参数,说明河流的水力学参数对DO影响较大。     

Twenty years of stream restoration in Finland: little response by benthic macroinvertebrate communities

The primary focus of many in-stream restoration projects is to enhance habitat diversity for salmonid fishes, yet the lack of properly designed monitoring studies, particularly ones with pre-restoration data, limits any attempts to assess whether restoration has succeeded in improving salmonid habitat. Even less is known about the impacts of fisheries-related restoration on other, non-target biota. We examined how restoration aiming at the enhancement of juvenile brown trout (Salmo trutta L.) affects benthic macroinvertebrates, using two separate data sets: (1) a before-after-control-impact (BACI) design with three years before and three after restoration in differently restored and control reaches of six streams; and (2) a space-time substitution design including channelized, restored, and near-natural streams with an almost 20-year perspective on the recovery of invertebrate communities. In the BACI design, total macroinvertebrate density differed significantly from before to after restoration. Following restoration, densities decreased in all treatments, but less so in the controls than in restored sections. Taxonomic richness also decreased from before to after restoration, but this happened similarly in all treatments. In the long-term comparative study, macroinvertebrate species richness showed no difference between the channel types. Community composition differed significantly between the restored and natural streams, but not between restored and channelized streams. Overall, the in-stream restoration measures used increased stream habitat diversity but did not enhance benthic biodiversity. While many macroinvertebrates may be dispersal limited, our study sites should not have been too distant to reach within almost two decades. A key explanation for the weak responses by macroinvertebrate communities may have been historical. When Fennoscandian streams were channelized for log floating, the loss of habitat heterogeneity was only partial. Therefore, habitat may not have been limiting the macroinvertebrate communities to begin with. Stream restoration to support trout fisheries has strong public acceptance in Finland and will likely continue to increase in the near future. Therefore, more effort should be placed on assessing restoration success from a biodiversity perspective using multiple organism groups in both stream and riparian ecosystems.