A supplementary approach for estimating reaeration rate coefficients

Different commonly used predictive equations for the reaeration rate coefficient (K₂) have been evaluated using 231 data sets obtained from the literature and 576 data sets measured at different reaches of the River Kali in western Uttar Pradesh, India. The data sets include stream/channel velocity, bed slope, flow depth, cross‐sectional area and reaeration rate coefficient (K₂), obtained from the literature and generated during the field survey of River Kali, and were used to test the applicability of the predictive equations. The K₂ values computed from the predictive equations have been compared with the corresponding K₂ values measured in streams/channels. The performance of the predictive equations has been evaluated using different error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and coefficient of determination (r²). The results show that the reaeration rate equation developed by Parkhurst and Pomeroy yielded the best agreement, with the values of SE, NME, MME and r² as 33·387, 4·62, 3·58 and 0·95, respectively, for literature data sets (case 1) and 37·567, 3·57, 2·6 and 0·95, respectively, for all the data sets (literature data sets and River Kali data sets) (case 2). Further, to minimize error estimates and improve correlation between measured and computed reaeration rate coefficients, supplementary predictive equations have been developed based on Froude number criteria and a least‐squares algorithm. The supplementary predictive equations have been verified using different error estimates and by comparing measured and computed reaeration rate coefficients for data sets not used in the development of the equations. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluation of various relationships of reaeration rate coefficient for modeling dissolved oxygen in a river with extreme flow variations in Pakistan

Mathematical relationships have been developed for reaeration rate coefficient (K_a) by various researchers. These relationships have a number of variables such as depth, velocity, width, slope, Froud number, molecular diffusion coefficient, kinematic viscosity and the gas‐transfer Reynolds number. From these variables, 29 relations have been developed and divided into four groups. To evaluate their predictive capability for highly variable flow rivers receiving high pollution loads form large cities, these relationships have been used to model dissolved oxygen (DO) in the River Ravi. Such rivers are either saturated with DO during high flows or anaerobic during critical low‐flow conditions. The evaluation is based on the agreement between model DO values calculated using K_a obtained from the available equations and the measured DO concentrations in the river samples in terms of sum of square of residuals (SSR) and coefficient of determination (R²). It has been found that in general, the group of equations containing depth and velocity as the only two variables affecting K_a performed better than the equations in other groups as reflected by lower SSR and higher R² values. The study results also reveal that the turbulence‐based reaeration rate coefficient equation containing additional variables also resulted in close agreement between DO model results and the measured values. The study results identify the most important parameters affecting the reaeration rate coefficient and the suitability of various K_a relationships as well for rivers with highly variable flows. Copyright © 2012 John Wiley & Sons, Ltd.     

Non‐point source pollution estimation using a modified approach

Non‐point source (NPS) pollution from agricultural land is increasing exponentially in many countries of the world, including India. A modified approach based on the conservation of mass and reaction kinetics has been derived to estimate the inflow of non‐point source pollutants from a river reach. Two water quality variables, namely, nitrate (NO₃) and ortho‐phosphate (o‐PO₄), which are main contributors as non‐point source pollution, were monitored at four locations of River Kali, western Uttar Pradesh, India, and used for calibration and validation of the model. Extensive water quality sampling was done with a total of 576 field data sets collected during the period from March 1999 to February 2000. Remote sensing and geographical information system (GIS) techniques were used to obtain land use/land cover of the region, digital elevation model (DEM), delineation of basin area contributing to non‐point source pollution at each sampling location and drainage map. The results obtained from a modified approach were compared with the existing mass‐balance equations and distributed modelling, and the performances of different equations were evaluated using error estimation viz. standard error, normal mean error, mean multiplicative error and correlation statistics. The developed model for the River Kali minimizes error estimates and improves correlation between observed and computed NPS loads. Copyright © 2007 John Wiley & Sons, Ltd.     

PUBLICATIONS OF THE INTERNATIONAL ASSOCIATION OF HYDROLOGICAL SCIENCES

Abstract

Most commonly used biochemical oxygen demand (BOD) and dissolved oxygen (DO) models have been tested for their applicability in the River Kali, which is one of the most polluted rivers in India. A total of 732 field data sets were generated during field survey from March 1999 to February 2000. The modelling of BOD and DO in the River Kali involves derivation and solution of the governing equations that describe concentration change with time and space brought on by advective, decay, settling and loading functions. However, due to continuous discharges (e.g. from wastewater treatment plants) and steady-state flow conditions in the River Kali, the dispersion effects are found to be insignificant. In the analysis, the model parameters used in BOD-DO models were optimized using the Newton-Raphson technique and the performance of different models was evaluated using correlation statistics (r ²) and error estimation, viz. standard error (SE) and mean multiplicative error (MME). The results indicate that the BOD-DO models developed after Camp (1963) yielded the best agreement with the observed values as compared with several other approaches.     

Comparing the stream re-aeration coefficient estimated from ANN and empirical models / Comparaison d'estimations par un RNA et par des modèles empiriques du coefficient de réaération en cours d'eau

Abstract

Dissolved oxygen (DO) is one of the most useful indices of river's health and the stream re-aeration coefficient is an important input to computations related to DO. Normally, this coefficient is expressed as a function of several variables, such as mean stream velocity, shear stress velocity, bed slope, flow depth, and Froude number. However, in free surface flows, some of these variables are interrelated, and it is possible to obtain simplified stream re-aeration equations. In recent years, different functional forms have been advanced to represent the re-aeration coefficient for different data sets. In the present study, the artificial neural network (ANN) technique has been applied to estimate the re-aeration coefficient (K ₂) using data sets measured at different reaches of the Kali River in India and values obtained from the literature. Observed stream/channel velocity, bed slope, flow depth, cross-sectional area and re-aeration coefficient data were used for the analysis. Different combinations of variables were tested to obtain the re-aeration coefficient using an ANN. The performance of the ANN was compared with other estimation methods. It was found that the re-aeration coefficient estimated by using an ANN was much closer to the observed values as compared with the other techniques.     

Uncertainty analysis of flow velocity estimation by a simplified entropy model

The velocity field in a river flow cross‐sectional area can be determined by applying entropy as done in 1978 by Chiu, who developed a two‐dimensional model of flow velocity based on the knowledge of maximum velocity, u_max, and the dimensionless entropic parameter, characteristic of the river site. This is appealing in the context of discharge monitoring, particularly for high floods, considering that u_max occurs in the upper portion of flow area and can be easily sampled, unlike velocity in the lower portion of flow area. The simplified form of Chiu's entropy‐based velocity model, proposed in 2004 by Moramarco et al., has been found to be reasonably accurate for determining mean flow velocity along each vertical sampled in the flow area, but no uncertainty analysis has been reported for this simplified entropy‐based velocity model. This study, therefore, performed uncertainty analysis of the simplified model following a procedure proposed by Misirli et al. in 2003. The flow velocity measurements at the Rosciano River section along the Chiascio River, central Italy, carried out for a period spanning 20 years were used for this purpose. Results showed that the simplified entropy velocity model was able to provide satisfactory estimates of velocity profiles in the whole flow area and the 95% confidence bands for the computed estimated mean vertical velocity were quite representative of observed values. In addition, using these 95% confidence bands, it was possible to have an indication of the uncertainty in the determination of mean cross‐sectional flow velocity as well. Copyright © 2012 John Wiley & Sons, Ltd.     

Determination of reaeration‐rate coefficient by modified tracer gas technique

The modified tracer gas technique is used to determine the reaeration coefficient in six different water bodies of the Itajaí River basin, three with rural land use and three in urban areas. Propane was used as the tracer gas and Rhodamine WT as the conservative tracer, providing information on dilution, mixing and dispersion. Liquefied petroleum gas was used instead of high purity propane, aimed at reducing the costs associated with the field trials. Reaeration‐rate coefficients observed in the field ranged from 25.8 to 367.7 d^?1. Two data sets could be observed where smaller streams had substantially larger coefficients of between 133.1 and 367.7 d^?1, while the larger streams had values ??ranging from 25.8 to 54.5 d^?1. Five empirical equations were evaluated by comparing the values ??obtained in the field. The equations proposed by Tsivolgou and Wallace and Tsivoglou and Neal showed greater adherence to the values ??determined in the tests. Reaeration‐rate coefficients obtained in the field were correlated with the hydrodynamic characteristics of the watercourses, thus establishing a mathematical function through which to obtain estimates for future evaluations. The R² value obtained using this equation was 0.959, indicating a high correlation between the calculated values ??and those estimated in the field. Copyright © 2012 John Wiley & Sons, Ltd.     

Geostatistical analysis and conditional simulation for estimating the spatial variability of hydraulic conductivity in the Choushui River alluvial fan,Taiwan

This work evaluated the spatial variability and distribution of heterogeneous hydraulic conductivity (K) in the Choushui River alluvial fan in Taiwan, using ordinary kriging (OK) and mean and individual sequential Gaussian simulations (SGS). A baseline flow model constructed by upscaling parameters was inversely calibrated to determine the pumping and recharge rates. Simulated heads using different K realizations were then compared with historically measured heads. A global/local simulated error between simulated and measured heads was analysed to assess the different spatial variabilities of various estimated K distributions. The results of a MODFLOW simulation indicate that the OK realization had the smallest sum of absolute mean simulation errors (SAMSE) and the SGS realizations preserved the spatial variability of the measured K fields. Moreover, the SAMSE increases as the spatial variability of the K field increases. The OK realization yields small local simulation errors in the measured K field of moderate magnitude, whereas the SGS realizations have small local simulation errors in the measured K fields, with high and low values. The OK realization of K can be applied to perform a deterministic inverse calibration. The mean SGS method is suggested for constructing a K field when the application focuses on extreme values of estimated parameters and small calibration errors, such as in a simulation of contaminant transport in heterogeneous aquifers. The individual SGS realization is useful in stochastically assessing the spatial uncertainty of highly heterogeneous aquifers. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison of Hydraulic Tomography with Traditional Methods at a Highly Heterogeneous Site

Over the past several decades, different groundwater modeling approaches of various complexities and data use have been developed. A recently developed approach for mapping hydraulic conductivity (K) and specific storage (S_s) heterogeneity is hydraulic tomography, the performance of which has not been compared to other more “traditional” methods that have been utilized over the past several decades. In this study, we compare seven methods of modeling heterogeneity which are (1) kriging, (2) effective parameter models, (3) transition probability/Markov Chain geostatistics models, (4) geological models, (5) stochastic inverse models conditioned to local K data, (6) hydraulic tomography, and (7) hydraulic tomography conditioned to local K data using data collected in five boreholes at a field site on the University of Waterloo (UW) campus, in Waterloo, Ontario, Canada. The performance of each heterogeneity model is first assessed during model calibration. In particular, the correspondence between simulated and observed drawdowns is assessed using the mean absolute error norm, (L₁), mean square error norm (L₂), and correlation coefficient (R) as well as through scatterplots. We also assess the various models on their ability to predict drawdown data not used in the calibration effort from nine pumping tests. Results reveal that hydraulic tomography is best able to reproduce these tests in terms of the smallest discrepancy and highest correlation between simulated and observed drawdowns. However, conditioning of hydraulic tomography results with permeameter K data caused a slight deterioration in accuracy of drawdown predictions which suggests that data integration may need to be conducted carefully.     

Planetary structures in general relativity

Summary For a static single-zone planet assuming that 1) the pressure and density are connected by the equationP =K _Q ^1+1/n–s, 2) a complete spherical symmetry is preserved and the system is in hydrostatic equilibrium; in section II, the expressions for the field equations have been obtained in suitable dimensionless forms. In section III the solution of the field equations forn=0 (which represents a homogeneous liquid) has been given in explicit form; for other prescribed value ofn=2/5 it has been pointed out that solutions must be performed by numerical integrations. Expressions for the mass-radius relation, the ratio of central to average density, the total energy, the proper energy and gravitational potential energy, which give some informations about the internal structure of the planet, have also been given in this section. Section IV discusses the velocity of sound at the centre of the planet. A few concluding remarks regarding the structure of the planet have been given in section V.     

Reedbed evapotranspiration rates in England

Measurements of evapotranspiration from contrasting stands of Phragmites australis [ET(Reed)] were obtained over several years at three sites within England between 1994 and 1998. A comparison with published ET(Reed) values showed the UK rates to be considerably lower than those measured in continental Europe. From the ET(Reed) data monthly crop coefficients [K_c(Reed)] have been developed, which when used with Reference Crop Evapotranspiration will enable reedbed water use to be determined. Due to the differences in study site characteristics, values for K_c varied widely, and it was not considered appropriate to combine results to produce a single set of monthly mean values. However, suggestions are made regarding the application of the K_c(Reed) values to wetland design. Copyright © 2001 John Wiley & Sons, Ltd.     

Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 1: NUMERICAL methodology and semi-analytical solutions

Flow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K ₀. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity contrast =K/K ₀ and by the volume fraction n. The flow is uniform in the mean, of velocity U=const. The derivation of the velocity field is achieved by a numerical method of high accuracy, based on analytical elements. Approximate analytical solutions are derived by a few methods: composite elements, effective medium, dilute systems and first-order approximation in logconductivity variance. The latter was employed by Rubin (1995), while the dilute system approximation was used by Eames and Bush (1999) and Dagan and Lessoff (2001). Transport is solved in a Lagrangean framework, with trajectories determined numerically from the velocity field, by particle tracking. Results for the velocity variance and for the longitudinal macrodispersivity, for a few values of and n, are presented in Part 2.     

Monitoring and modeling dissolved oxygen dynamics through continuous longitudinal sampling: a case study in Wen‐Rui Tang River,Wenzhou, China

Synoptic water sampling at a fixed site monitoring station provides only limited ‘snap‐shots’ of the complex water quality dynamics within a surface water system. However, water quality often changes rapidly in both spatial and temporal dimensions, especially in highly polluted urban rivers. In this study, we designed and applied a continuous longitudinal sampling technique to monitor the fine‐scale spatial changes of water quality conditions, assess water pollutant sources, and determine the assimilative capacity for biochemical oxygen demand (BOD) in an urban segment of the hypoxic Wen‐Rui Tang River in eastern China. The continuous longitudinal sampling was capable of collecting dissolved oxygen (DO) data every 5 s yielding a ~11 m sampling interval with a precision of ±0.1 mg L^?1. The Streeter and Phelps BOD‐DO model was used to calculate: (1) the oxygen consumption coefficient (K₁) required for calibration of water quality models, (2) BOD assimilative capacity, and (3) BOD source and load identification. In the 2014 m river segment sampled, the oxygen consumption coefficient (K₁) was 0.428 d^?1 (20°C), the total BOD discharge was 916 kg d^?1, and the BOD assimilative capacity was 382 kg d^?1 when the minimum DO level was set to 2 mg L^?1. In addition, the longitudinal analysis identified eight major drainage outlets (BOD point sources), which were verified by field observations. This new approach provides a simple, cost‐effective method of evaluating BOD‐DO dynamics over large spatial areas with rapidly changing water quality conditions, such as urban environments. It represents a major breakthrough in the development and application of water quality sampling techniques to obtain spatially distributed DO and BOD in real time. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical modelling-based comparison of longitudinal dispersion coefficient formulas for solute transport in rivers

River water quality models usually apply the Fischer equation to determine the longitudinal dispersion coefficient (D_x) in solving the advection–dispersion equation (ADE). Recently, more accurate formulas have been introduced to determine D_x in rivers, which could strongly affect the accuracy of the ADE results. A numerical modelling-based approach is presented to evaluate the performance of various D_x formulas using the ADE. This approach consists of a finite difference approximation of the ADE, a MATLAB code and a MS Excel interface; it was tested against the analytical ADE solution and demonstrated using eight well-known D_x formulas and tracer study data for the Chattahoochee River (USA), the Severn (UK) and the Athabasca (Canada). The results show that D_x has an important effect on tracer concentrations simulated with the ADE. Comparison between the simulated and measured concentrations confirms the appropriate performance of Zeng and Huai’s formula for D_x estimation. Use of the newly proposed equations for D_x estimation could enhance the accuracy of solving the ADE.     

Eddy covariance‐based evapotranspiration for a subtropical wetland

The eddy covariance (EC) method was used in a 30‐month study to quantify evapotranspiration (ET) and vegetation coefficient (K_CW) for a wetland on a ranch in subtropical south Florida. To evaluate the errors in ET estimates, the EC‐based ET (ET_C‐EC) and the Food and Agricultural Organization (FAO) Penman–Monteith (PM) based ET (ET_C‐PM) estimates (with literature crop coefficient, K_C) were compared with each other. The ET_C‐EC and FAO‐PM reference ET were used to develop K_CW. Regression models were developed to estimate K_CW using climatic and hydrologic variables. Annual and daily ET_C‐EC values were 1152 and 3.27 mm, respectively. The FAO‐PM model underestimated ET by 25% with ET_C‐EC being statistically higher than ET_C‐PM. The K_CW varied from 0.79 (December) to 1.06 (November). The mean K_CW for the dry (November–April) season (0.95) was much higher than values reported for wetlands in literature; whereas for the wet (May–October) season, K_CW (0.97) was closer to literature values. Higher than expected K_CW values during the dry season were due to higher temperature, lower humidity and perennial wetland vegetation. Regression analyses showed that factors affecting the K_CW were different during the dry (soil moisture, temperature and relative humidity) and wet (net radiation, inundation and wind speed) seasons. Separate regression models for the dry and wet seasons were developed. Evapotranspiration and K_CW from this study, one of the first for the agricultural wetlands in subtropical environment, will help improve the ET estimates for similar wetlands. Copyright © 2013 John Wiley & Sons, Ltd.     

Runoff modelling at two field slopes: use of in situ measurements of air permeability to characterize spatial variability of saturated hydraulic conductivity

The time required at a field site to obtain a few measurements of saturated hydraulic conductivity (K_s) will allow for many measurements of soil air permeability (k_a). This study investigates if k_a measured in situ (k_{a, in situ}) can be a substitute for measurement of K_s in relation to infiltration and surface runoff modelling. Measurements of k_{a, in situ} were carried out in two small agricultural catchments. A spatial correlation of the log‐transformed values existed having a range of approximately 100 m. A predictive relationship between K_s and k_a measured on 100‐cm³ soil samples in the laboratory was derived for one of the field slopes and showed good agreement with an earlier suggested predictive K_s–k_a relationship. In situ measurements of K_s and k_a suggested that the predictive relationships also could be used at larger scale. The K_s–k_a relationships together with the k_{a, in situ} data were applied in a distributed surface runoff (DSR) model, simulating a high‐intensity rainfall event. The DSR simulation results were highly dependent on whether the geometric average of k_{a, in situ} or kriged values of k_{a, in situ} was used as model input. When increasing the resolution of K_s in the DSR model, a limit of 30–40 m was found for both field slopes. Below this limit, the simulated runoff and hydrograph peaks were independent of resolution scale. If only a few randomly chosen values of K_s were used to represent the spatial variation within the field slope, very large deviations in repeated DSR simulation results were obtained, both with respect to peak height and hydrograph shape. In contrast, when using many predicted K_s values based on a K_s–k_a relationship and measured k_{a, in situ} data, the DSR model generally captured the correct hydrograph shape although simulations were sensitive to the chosen K_s–k_a relationship. As massive measurement efforts normally will be required to obtain a satisfactory representation of the spatial variability in K_s, the use of k_{a, in situ} to assess spatial variability in K_s appears a promising alternative. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimation of flow resistance in gravel-bedded rivers: A physical explanation of the multiplier of roughness length

The need to estimate velocity and discharge indirectly in gravel-bedded rivers is a commonly-encountered problem. Semilogarithmic friction equations are used to estimate mean velocity using a friction factor obtained from depth and grain size information. Although such equations have a semi-theoretical basis, in natural gravel-bed channels, an empirical constant (6.8 or 3.5) has to be introduced to scale-up the characteristic grain size (D₅₀ or D₈₄) to represent the effective roughness length. In this paper, two contrasting approaches are used to suggest that the multiplier of characteristic grain size is attributable to the effect of small-scale form resistance, reflecting the occurrence of microtopographic bedforms in gravel-bedded environments. First, spatial elevation dependence in short, detailed bed profiles from a single gravel-bedded river is investigated using semivariogram and zero-crossing analyses. This leads to objective identification of two discrete scales of bed roughness, associated with grain and microtopographic roughness elements. Second, the autocorrelation structure of the three-dimensional near-bed velocity field is examined to identify regularities associated with eddy shedding and energy losses from larger grains and microtopographic bedforms. Apart from improving the capacity to determine friction factors for velocity and discharge estimation, the findings have implications in general for the initial motion of gravelly bed material.     

基于Landsat 8 OLI影像反演的湖北大冶湖水体光学衰减特性

水体光学衰减特性直接影响湖泊的清澈程度和沉水植被的生存,利用遥感技术获取湖泊光学衰减分布特性能极大提高效率.基于2017-2019年的原位调查数据,利用Landsat 8 OLI影像开发了大冶湖水体光学衰减系数(Kd)的遥感反演模型,并分析大冶湖水体Kd的多年时空分布特性与驱动机制,以期为大冶湖流域的修复与管理提供参考...     

Variations of crop coefficient and its influencing factors in an arid advective cropland of northwest China

Understanding the variation and magnitude of crop coefficient (K_c) is important for accurate determination of crop evapotranspiration and water use. In this study, we calculated K_c in an irrigated maize field with ground mulching by eddy covariance evapotranspiration measurements during the whole growing periods in 2009 and 2010 in an arid region of northwest China. A semi‐empirical practical approach for estimating K_c was proposed by introducing the dynamic fraction of canopy cover and incorporating the effect of leaf senescence as a function of days after sowing. The contribution of arid advection of sensible heat resulting from irrigation to K_c and the response of K_c to canopy conductance (G_c) were investigated. The averaged values of daily K_c were lower than typical values obtained previously without mulching due to decreasing effect of mulching on K_c, with 0.82 and 0.80 for the 2 years, respectively. The maximum average K_c occurred at the heading stage, with 1.21 and 1.04 for the 2 years, respectively. The difference of K_c was attributed to the difference of leaf area index. The semi‐empirical practical approach could well estimate the variations of K_c, thus could be a robust and useful tool for the practical users and water managers. The contributions to daily K_c from the arid advection were 4.4–28.0% of the measured K_c. The G_c had stronger control on daily K_c at the early and later stages than at the middle stage. When G_c, leaf area index and relative soil extractable water were lower than the respective threshold values of 20 mm s^?1, 3.0 m² m^?2 and 0.5, the daily K_c increased significantly with the increase of the three factors, and almost remained constant when the three factors were beyond the threshold values. These results are helpful for quantifying contributions of individual factors to K_c, and subsequently improving water management practices according to K_c. Copyright © 2014 John Wiley & Sons, Ltd.