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.     

Development of an empirical equation for the transverse dispersion coefficient in natural streams

In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the hydraulic and geometric parameters in natural streams using a regression technique. First, a total of 32 data sets in 16 streams were collected. Among those sets, 16 sets were used for deriving the new equation, and the other 16 sets were used for verifying the equation. Then, through dimensional analysis, it was found that the normalized transverse dispersion coefficient is associated with several parameters such as sinuosity, aspect ratio, and a friction term. The robust least square method was applied to estimate regression coefficients. The newly proposed equation was proven to be superior in explaining the dispersion characteristics of natural streams more precisely compared to the existing equations.     

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.     

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.     

External drift kriging of NOx concentrations with dispersion model output in a reduced air quality monitoring network

In the mid nineteen eighties the Dutch NO_x air quality monitoring network was reduced from 73 to 32 rural and city background stations, leading to higher spatial uncertainties. In this study, several other sources of information are being used to help reduce uncertainties in parameter estimation and spatial mapping. For parameter estimation, we used Bayesian inference. For mapping, we used kriging with external drift (KED) including secondary information from a dispersion model. The methods were applied to atmospheric NO_x concentrations on rural and urban scales. We compared Bayesian estimation with restricted maximum likelihood estimation and KED with universal kriging. As a reference we also included ordinary least squares (OLS). Comparison of several parameter estimation and spatial interpolation methods was done by cross-validation. Bayesian analysis resulted in an error reduction of 10 to 20% as compared to restricted maximum likelihood, whereas KED resulted in an error reduction of 50% as compared to universal kriging. Where observations were sparse, the predictions were substantially improved by inclusion of the dispersion model output and by using available prior information. No major improvement was observed as compared to OLS, the cause presumably being that much good information is contained in the dispersion model output, so that no additional spatial residual random field is required to explain the data. In all, we conclude that reduction in the monitoring network could be compensated by modern geostatistical methods, and that a traditional simple statistical model is of an almost equal quality.

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is presented.     

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.     

Closed population estimation models and their extensions in Program MARK

Program MARK provides > 65 data types in a common configuration for the estimation of population parameters from mark-encounter data. Encounter information from live captures, live resightings, and dead recoveries can be incorporated to estimate demographic parameters. Available estimates include survival (S or ϕ), rate of population change (λ), transition rates between strata (Ψ), emigration and immigration rates, and population size (N). Although N is the parameter most often desired by biologists, N is one of the most difficult parameters to estimate precisely without bias for a geographically and demographically closed population. The set of closed population estimation models available in Program MARK incorporate time (t) and behavioral (b) variation, and individual heterogeneity (h) in the estimation of capture and recapture probabilities in a likelihood framework. The full range of models from M ₀ (null model with all capture and recapture probabilities equal) to M _tbh are possible, including the ability to include temporal, group, and individual covariates to model capture and recapture probabilities. Both the full likelihood formulation of Otis et al. (1978) and the conditional model formulation of Huggins (1989, 1991) and Alho (1990) are provided in Program MARK, and all of these models are incorporated into the robust design (Kendall et al. 1995, 1997; Kendall and Nichols 1995) and robust-design multistrata (Hestbeck et al. 1991, Brownie et al. 1993) data types. Model selection is performed with AICc (Burnham and Anderson 2002) and model averaging (Burnham and Anderson 2002) is available in Program MARK to provide estimates of N with standard error that reflect model selection uncertainty.     

北京河流大型底栖动物空间格局及其环境响应研究

大型底栖动物群落结构及多样性对于区域河流环境状况具有重要的指示意义。基于2014年5月—2015年8月间北京市河流大型底栖动物群落结构调查数据,分析底栖动物的生物多样性特征和空间格局。调查共发现大型底栖动物151种(或分类单元),隶属于5门9纲67科127属,水生昆虫占绝对优势。聚类分析表明76个采样点可被分为4组,组1主要包含北部山区的潮白河水系,具有较为典型的山溪型河流底栖动物特征,组2主要包含永定河山峡段和北运河水系的清河,组3主要包含大清河水系和北运河水系的温榆河、北沙河、南沙河等,二者具有城市河流兼有山溪型河流底栖动物的特征,组4主要包含北运河水系,具有典型的城市河流底栖动物特征。优势种分析表明:组1的优势种为热水四节蜉(Baetis thermicus)、秀丽白虾(Exopalaemon modestus)和网栖石蛾(Cheumatopsyche sp.),组2为直突摇蚊(Orthocladius sp.)、钩虾(Gammarus sp.)和长足摇蚊(Tanypus sp.),组3为摇蚊科幼虫(larvae of Chironomidae)和寡毛类(Oligochaeta),组4是以中华摇蚊(Chironomus sinicus)为代表的摇蚊幼虫。功能摄食类群研究表明:组1以收集者和滤食者占绝对优势,相对丰度分别为60%和29.6%;组2、组3、组4均以收集者占绝对优势,相对丰度分别为97.7%、90%、97.5%。物种数、Shannon-Wiener多样性指数、Pielou均匀度指数和Margalef丰富度指数的组间差异性显著(P0.05)。研究表明,北京河流大型底栖动物受河流自然环境变化的影响显著,形成了典型的山区-城市底栖动物空间格局,山区河流中保持了较高的生物多样性,城市河流及其过渡区的大型底栖动物退化明显,大型底栖动物能够明显指示环境状况的变化并可指导河流环境的保护与恢复。     

Application of an evolutionary algorithm to the inverse parameter estimation of an individual-based model

Inverse parameter estimation of individual-based models (IBMs) is a research area which is still in its infancy, in a context where conventional statistical methods are not well suited to confront this type of models with data. In this paper, we propose an original evolutionary algorithm which is designed for the calibration of complex IBMs, i.e. characterized by high stochasticity, parameter uncertainty and numerous non-linear interactions between parameters and model output. Our algorithm corresponds to a variant of the population-based incremental learning (PBIL) genetic algorithm, with a specific “optimal individual” operator. The method is presented in detail and applied to the individual-based model OSMOSE. The performance of the algorithm is evaluated and estimated parameters are compared with an independent manual calibration. The results show that automated and convergent methods for inverse parameter estimation are a significant improvement to existing ad hoc methods for the calibration of IBMs.     

A non-motorized dye ejector for visualization of flow in situ and its use with coral reef crinoids

We describe a portable, non-motorized device for delivering a tracer dye into seawater under field conditions. Dye is ejected at a constant flow rate over a period of tens of minutes. The ejector works in a wide range of ambient pressures without external energy requirements. The flow rate is adjusted simply by varying the length of the delivery tube. The dye streams permitted observations of the upcurrent and downcurrent flow regimes for a filter-feeding crinoid (Comanthus bennetti) living at a depth of 8 m on a coral reef. The results indicate that the crinoid may enhance the rate of particle capture by changing the scale of turbulence in the water passing through the mesh of the filtration fan.     

Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

● A hydrodynamic-Bayesian inference model was developed for water pollution tracking. ● Model is not stuck in local optimal solutions for high-dimensional problem. ● Model can estimate source parameters accurately with known river water levels. ● Both sudden spill incident and normal sewage inputs into the river can be tracked. ● Model is superior to the traditional approaches based on the test cases. Water quality restoration in rivers requires identification of the locations and discharges of pollution sources, and a reliable mathematical model to accomplish this identification is essential. In this paper, an innovative framework is presented to inversely estimate pollution sources for both accident preparedness and normal management of the allowable pollutant discharge. The proposed model integrates the concepts of the hydrodynamic diffusion wave equation and an improved Bayesian-Markov chain Monte Carlo method (MCMC). The methodological framework is tested using a designed case of a sudden wastewater spill incident (i.e., source location, flow rate, and starting and ending times of the discharge) and a real case of multiple sewage inputs into a river (i.e., locations and daily flows of sewage sources). The proposed modeling based on the improved Bayesian-MCMC method can effectively solve high-dimensional search and optimization problems according to known river water levels at pre-set monitoring sites. It can adequately provide accurate source estimation parameters using only one simulation through exploration of the full parameter space. In comparison, the inverse models based on the popular random walk Metropolis (RWM) algorithm and microbial genetic algorithm (MGA) do not produce reliable estimates for the two scenarios even after multiple simulation runs, and they fall into locally optimal solutions. Since much more water level data are available than water quality data, the proposed approach also provides a cost-effective solution for identifying pollution sources in rivers with the support of high-frequency water level data, especially for rivers receiving significant sewage discharges.     

Modeling and interpreting the accuracy assessment error matrix for a doubly classified map

This paper considers two maps having the same spatial extent and the same mapping categories but where each map is subject to classification error. An overlay of the maps yields a (dis)similarity matrix whose (i, j)-entry is the areal proportion placed into category i by the first map and into category j by the second map. A parametric model, called the latent truth model, is proposed which specifies the dissimilarity matrix in terms of the true (but unknown) proportions for the mapping categories as well as the unknown error rates for the two maps. The number of parameters in the model exceeds the degrees of freedom in the dissimilarity matrix. However, a method of regularization is applied to effectively reduce the dimension of the parameter space and to permit model fitting. From the fitted model, one obtains estimates for the true mapping proportions as well as estimated error matrices for each of the maps. Accuracy assessment characteristics for each map (such as user's accuracy, producer's accuracy, overall accuracy, and the kappa coefficient) can be computed from the estimated error matrices. Methods are illustrated with two landcover maps of Wicomico County, Maryland.     

Evaluation of variance approximation techniques for non-linear photosynthesis—irradiance models

Parameters derived from photosynthesis-irradiance (P-I) models, although often empirical in nature, are useful indicators of the photoadaptive state of phytoplankton in culture and in situ. However objective criteria for determining significant changes in P-I curves are rarely provided, because confidence intervals for parameters of non-linear models are not estimated easily. Examination of least-squares residuals in parameter space and Monte Carlo approaches have been used to estimate confidence regions around parameter values, but the computationally intensive nature of these methods has prevented their routine application. We present an alternative method of estimating confidence intervals for parameters of P-I curves that runs quickly on a microcomputer and is easily combined with common parameter-estimation routines. This algorithm was tested using a 3-parameter P-I model and curves describing a wide range of photoadaptive states, with different numbers of observations and different amounts of inherent variability. The method produced results comparable to the Monte Carlo technique. This analysis makes it possible to specify the sample size required to define parameters with acceptable confidence as a function of data variance and photoadaptive state. In most reasonable situations, 25 observations are sufficient.     

An integrated modeling framework for performing environmental assessments: Application to ecosystem services in the Albemarle-Pamlico basins (NC and VA, USA)

The U.S. Environmental Protection Agency uses environmental models to inform rulemaking and policy decisions at multiple spatial and temporal scales. As decision-making has moved towards integrated thinking and assessment (e.g. media, site, region, services), the increasing complexity and interdisciplinary nature of modern environmental problems has necessitated a new generation of integrated modeling technologies. Environmental modelers are now faced with the challenge of determining how data from manifold sources, types of process-based and empirical models, and hardware/software computing infrastructure can be reliably integrated and applied to protect human health and the environment.In this study, we demonstrate an Integrated Modeling Framework that allows us to predict the state of freshwater ecosystem services within and across the Albemarle-Pamlico Watershed, North Carolina and Virginia (USA). The Framework consists of three facilitating technologies: Data for Environmental Modeling automates the collection and standardization of input data; the Framework for Risk Assessment of Multimedia Environmental Systems manages the flow of information between linked models; and the Supercomputer for Model Uncertainty and Sensitivity Evaluation is a hardware and software parallel-computing interface with pre/post-processing analysis tools, including parameter estimation, uncertainty and sensitivity analysis. In this application, five environmental models are linked within the Framework to provide multimedia simulation capabilities: the Soil Water Assessment Tool predicts watershed runoff; the Watershed Mercury Model simulates mercury runoff and loading to streams; the Water quality Analysis and Simulation Program predicts water quality within the stream channel; the Habitat Suitability Index model predicts physicochemical habitat quality for individual fish species; and the Bioaccumulation and Aquatic System Simulator predicts fish growth and production, as well as exposure and bioaccumulation of toxic substances (e.g., mercury).Using this Framework, we present a baseline assessment of two freshwater ecosystem services-water quality and fisheries resources-in headwater streams throughout the Albemarle-Pamlico. A stratified random sample of 50 headwater streams is used to draw inferences about the target population of headwater streams across the region. Input data is developed for a twenty-year baseline simulation in each sampled stream using current land use and climate conditions. Monte Carlo sampling (n = 100 iterations per stream) is also used to demonstrate some of the Framework's experimental design and data analysis features. To evaluate model performance and accuracy, we compare initial (i.e., uncalibrated) model predictions (water temperature, dissolved oxygen, fish density, and methylmercury concentration within fish tissue) against empirical field data. Finally, we ‘roll-up’ the results from individual streams, to assess freshwater ecosystem services at the regional scale.     

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.     

Design parameters for coastal dikes

This paper presents results of the assessment of the design parameters leading to the definition of the crest level of a coastal dike along the German North Sea. Procedures to estimate the design water level have been proposed, distinguishing between comparative and single value procedures. The transformation of the wave characteristics from deep water towards the shallow foreshore was achieved through the application of a spectral wave model. To improve the wave parameter estimations, the existing model was nested to a grid with a higher resolution closer to the coast. The estimation of the wave run-up followed the Dutch procedure with some adjustments to the local wave characteristics and dike geometry. The computed maximum crest level of 8.4 m is below the crest height of the existing dike, which is 8.8 m. However a proposal for a more economical design should be carefully evaluated, paying attention to the uncertainties encountered in this research. The general recommendation is to enhance the reliability of the hindcasted wave parameters through calibration and validation of the wave model and to include in the design process an investigation of the effect of the medium term morphological developments.     

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。