Predicting longitudinal dispersion coefficient in natural streams by artificial intelligence methods

In this study, three artificial neural network methods, i.e. feed forward back propagation, the radial basis function neural network, and the generalized regression neural network are employed to compute the longitudinal dispersion coefficient in order to evaluate its behaviour in predicting dispersion characteristics in natural streams. These methods, which use hydraulic and geometrical data to predict dispersion coefficients, can easily be applied to natural streams and are proven to be superior in explaining their dispersion characteristics more precisely than existing equations. This method of predicting the longitudinal dispersion coefficient in river flows was tested on 65 data sets, obtained by researchers from 30 rivers in the USA. Results using the models are compared with results obtained in many other studies, and are shown to be more accurate than the other methods considered. Copyright © 2008 John Wiley & Sons, Ltd.     

The problem of underpowered rivers

This study has hypothesized that for many rivers the trade-off between flow accumulation and the decrease in slope along channel length means that stream power increases downstream and, moreover, that given the low slope angles in headwater and low-order streams, they would have insufficient stream power to erode let alone transport sediment. The study considered the stream power profile, the particle travel distances and the application of the Hjulström curve based on the velocity profile of nine, large UK catchments. The study showed that:

1. Some rivers never showed a maximum in their longitudinal stream power profile, implying that some rivers never develop a deposition zone before they discharge at the tidal limit.
2. Particle travel distances during a bankfull discharge event showed that for some rivers 91% of the upper main channel would not be cleared of sediment. Furthermore, while some rivers could transport a 2 mm particle their entire length in one bankfull event, for another river it would take 89 such events.
3. The Hjulström curve shows that for three of the study rivers the upper 20 km of the river was not capable of eroding a 2 μm particle.
4. The study has shown that for all rivers studied, erosion is focused downstream and deposition upstream. Many UK rivers have a dead zone where, on time scales of the order of centuries, no erosion or transport occurs and erosion only occurs in the lower courses of the channel where discharge rather than slope dominates – we propose these as underpowered rivers.

© 2020 The Authors. Earth Surface Processes and Landforms published by 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.     

Daily discharge estimation at ungauged river sites using remote sensing

A methodology is developed to estimate daily river discharge at an ungauged site using remote sensing data. Use is made of ERS‐2 and ENVISAT satellite altimetry to provide a time series of river channel stage levels and longitudinal channel slope and Landsat satellite imagery to provide a range of channel widths over a 50 km reach of river. The data are substituted into the Bjerklie et al. ( 2003 ) equation, which is based on the Manning's resistance equation and has been developed using a global database of channel hydraulic information and discharge measurements. Our methodology has been applied at three locations on the Mekong and Ob Rivers and validated against daily in situ discharge measurements. The results show Nash–Sutcliffe efficiency values of 0.90 at Nakhon Phanom and 0.86 at Vientiane on the Mekong, and 0.86 at Kalpashevo on the Ob. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

SNOW CLASSIFICATION OF THE INTERNATIONAL ASSOCIATION OF SCIENTIFIC HYDROLOGY (IASH) AND CLASSIFICATION OF SOLID HYDROMETEORS OF THE INTERNATIONAL CLOUD ATLAS OF THE WORLD METEOROLOGICAL ORGANISATION (WMO)

Abstract

This study of longitudinal stream profiles of rivers of the Midcontinent (rivers tributary to the Mississippi) and Atlantic and East Gulf Slopes has revealed five types of longitudinal profiles: (1) Overall concave-upward profiles with or without long constant slope segments; (2) convex upward, for example, the Missouri River has a profile that has a constant slope for its lower 560 miles and then is convex upward with constant slope segments to a point beyond the Yellowstone River junction; (3) concave-upward irregular, ungraded, low-gradient profiles (Ohio and Tennessee Rivers); (4) irregular unsegmented and steep profiles, such as shown by the Delaware and Savannah-Tugaloo Rivers; and (5) irregular ungraded, steep-gradient profiles that are concave-upward in the upstream reaches and downstream convex-upward, for example, on most of the Atlantic Slope and East Gulf Slope Rivers above the Fall Line. Constant slope profiles occur where the last type of rivers flow across relatively weak Coastal Plain sediments and also inland on the Coosa and Oostanaula-Conasauga Rivers. The profile characteristics of the Atlantic and East Gulf streams lend support to the hypothesis of multiple erosion cycles in the Appalachians.     

Refinement of predictive reaeration equations for a typical Indian river

Dissolved oxygen mass balance has been computed for different reaches of River Kali in western Uttar Pradesh (India) to obtain the reaeration coefficient (K₂). A total of 270 field data sets have been collected during the period from March 1999 to February 2000. Eleven most popular predictive equations, used for reaeration prediction and utilizing mean stream velocity, bed slope, flow depth, friction velocity and Froude number, have been tested for their applicability in the River Kali using data generated during field survey. The K₂ values computed from these predictive equations have been compared with the K₂ values observed from dissolved oxygen balance measurements in the field. The performance of predictive equations have been evaluated using error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and correlation statistics. The equations developed by Smoot and by Cadwallader and McDonnell showed comparatively better results. Moreover, a refined predictive equation has been developed using a least‐squares algorithm for the River Kali that minimizes error estimates and improves correlation between observed and computed reaeration coefficients. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of channel size on solute residence time distributions in rivers

The effect of channel size on residence time distributions (RTDs) of solute in rivers is investigated in this paper using tracer test data and the variable residence time (VART) model. Specifically, the investigation focuses on the influence of shear dispersion and hyporheic exchange on the shape of solute RTD, and how these two transport processes prevail in larger and smaller streams, respectively, leading to distinct tails of RTD. Simulation results show that (1) RTDs are dispersion-dependent and thereby channel-size (scale) dependent. RTDs increasing longitudinal dispersion coefficient. Small streams with negligible dispersion coefficient may display various types of RTD from upward curving patterns to a straight line (power-law distributions) and further to downward curving lognormal distributions when plotted in log–log coordinates. Moderate-sized rivers are transitional in terms of RTDs and commonly exhibit lognormal and power-law RTDs; (2) the incorporation of water and solute losses/gains in the VART model can improve simulation results and make parameter values more reasonable; (3) the ratio of time to peak concentration to the minimum mean residence time is equal to the recovery ratio of tracer. The relation provides a simple method for determining the minimum mean residence time; and (4) the VART model is able to reproduce various RTDs observed in rivers with 3–4 fitting parameters while no user-specified RTD functions are needed.     

LONGITUDINAL DISPERSION IN OPEN-CHANNEL FLOW

Laboratory experiments on longitudinal dispersion in clear-water and sedimentladen flows are reported. These experiments indicate that the presence of suspended sediment does not have a significant effect on the dispersion process other than its possible effect on the friction factor. Analysis of the writers' and other's data collected in laboratory flumes and natural streams Shows that Taylor's model of longitudinal dispersion based on one-dimensional Fickian diffusion equation with a constant dispersion coefficient, DL, is not suitable for describing the dispersion process in natural streams as DL tends to increase in the downstream direction. Therefore, a similarity analysis of the concentration distributions, on the lines of Day and Wood, has been carried out. Based on dimensional analysis an improved empirical method has been obtained for predicting the concentration-time relation without the use of DL     

Estimating longitudinal dispersion in rivers using Acoustic Doppler Current Profilers

The longitudinal dispersion coefficient (D) is an important parameter needed to describe the transport of solutes in rivers and streams. The dispersion coefficient is generally estimated from tracer studies but the method can be expensive and time consuming, especially for large rivers. A number of empirical relations are available to estimate the dispersion coefficient; however, these relations are known to produce estimates within an order of magnitude of the tracer value. The focus of this paper is on using the shear-flow dispersion theory to directly estimate the dispersion coefficient from velocity measurements obtained using an Acoustic Doppler Current Profiler (ADCP). Using tracer and hydrodynamic data collected within the same river reaches, we examined conditions under which the ADCP and tracer methods produced similar results. Since dead zones / transient storage (TS) are known to influence the dispersion coefficient, we assessed the relative importance of dead zones in different stream reaches using two tracer-based approaches: (1) TS modeling which explicitly accounts for dead zones and (2) the advection–dispersion equation (ADE) which does not have separate terms for dead zones. Dispersion coefficients based on the ADE tend to be relatively high as they describe some of the effects of dead zones as well. Results based on the ADCP method were found to be in good agreement with the ADE estimates indicating that storage zones play an important role in the estimated dispersion coefficients, especially at high flows. For the river sites examined in this paper, the tracer estimates of dispersion were close to the median values of the ADCP estimates obtained from multiple datasets within a reach. The ADCP method appears to be an excellent alternative to the traditional tracer-based method if care is taken to avoid spurious data and multiple datasets are used to compute a distance-weighted average or other appropriate measure that represents reach-averaged conditions.     

Solute transport routing in a small stream

Abstract

The impact of pollution incidents on rivers and streams may be predicted using mathematical models of solute transport. Practical applications require an analytical or numerical solution to a governing solute mass balance equation together with appropriate values of relevant transport coefficients under the flow conditions of interest. This paper considers two such models, namely those proposed by Fischer and by Singh and Beck, and compares their performances using tracer data from a small stream in Edinburgh, UK. In calibrating the models, information on the magnitudes and the flow rate dependencies of the velocity and the dispersion coefficients was generated. The dispersion coefficient in the stream ranged between 0.1 and 0.9 m²/s for a flow rate range of 13–437 L/s. During calibration it was found that the Singh and Beck model fitted the tracer data a little better than the Fischer model in the majority of cases. In a validation exercise, however, both models gave similarly good predictions of solute transport at three different flow rates.     

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.     

Analysis of rill step–pool morphology and its comparison with stream case

In this paper, the morphology of step–pool features is analysed using rill measurements and literature data for streams. Close-range photogrammetry was used to carry out ground measurements on rills with step–pool units, shaped on a plot having slope equal to 14, 15, 22, 24 and 26%. Data were used to compare the relationships between H/L, in which H is the step height and L is the step length, and the mean gradient of the step–pool sequence, S_m, for streams or the slope of the step–pool unit, S, for rills. The relationship of H/L against S_m is widely used to test the occurrence of the maximum flow resistance condition in streams, which is associated with the range 1 ≤ (H/L)/S_m ≤ 2. Further analyses were carried out to compare both the formation process and the profile of the pool in rills with those related to streams. Moreover, for a single rill channel, an analysis of flow characteristics expressed in terms of Darcy–Weisbach friction factor and Froude number was developed. The results allowed us to state: (i) the relationships of H/L versus S_m and S are quite similar and the steepness ratio for streams, (H/L)/S_m, and for rills, (H/L)/S, generally ranges from 1 to 2; (ii) the formation process and the profile of the pool in rills are not consistent with those occurring in streams; (iii) in the rills, the longitudinal size of the pool is dominant with respect to the maximum scour depth; (iv) the presence of a sequence of step–pool units within a rill segment noticeably increases flow resistance compared to segments with a flat bed; (v) the Froude number of the flow over the sequence of step–pool units in rills is slightly below the range of 0.8–1 corresponding to the maximum flow resistance in step–pool units.     

The form and function of headwater streams based on field and modeling investigations in the southern Appalachian Mountains

Headwater streams drain the majority of most landscapes, yet less is known about their morphology and sediment transport processes than for lowland rivers. We have studied headwater channel form, discharge and erosive power in the humid, moderate‐relief Valley and Ridge and Blue Ridge provinces of the Appalachian Mountains. Field observations from nine headwater (<2 km² drainage area), mixed bedrock–alluvial channels in a variety of boundary conditions demonstrate variation with respect to slope‐area channel initiation, basic morphology, slope distribution, hydraulic geometry, substrate grain size and role of woody debris. These channels display only some of the typical downstream trends expected of larger, lowland rivers. Variations are controlled mainly by differences in bedrock resistance, from the formation level down to short‐wavelength, outcrop‐scale variations. Hydrologic modeling on these ungauged channels estimates the recurrence of channel‐filling discharge and its ability to erode the channel bed. Two‐year recurrence discharge is generally larger and closer to bankfull height in the Valley and Ridge, due to low soil infiltration capacity. Discharge that fills the channel to its surveyed bankfull form is variable, generally exceeding two‐year flows at small drainage areas (<0·5 km²) and being exceeded by them at greater drainage areas. This suggests bankfull is not controlled by the same recurrence storm throughout a channel or physiographic region. Stream power and relative competence are also variable. These heterogeneities contrast relations observed in larger streams and illustrate the sensitivity of headwater channels to local knickpoints of resistant bedrock and armoring of channels by influx of coarse debris from hillslopes. The general lack of predictable trends or functional relationships among hydraulic variables and the close coupling of channel form and function with local boundary conditions indicate that headwater streams pose a significant challenge to landscape evolution modeling. Copyright © 2005 John Wiley & Sons, Ltd.     

The effect of riparian land use on transport hydraulics in agricultural headwater streams located in northeast Ohio,USA

This study examined if riparian land use (forested vs agricultural) affects hydraulic transport in headwater streams located in an agriculturally fragmented watershed. We identified paired 50‐m reaches (one reach in agricultural land use and the other in forested land use) along three headwater streams in the Upper Sugar Creek Watershed in northeast Ohio, USA (40° 51′42″N, 81° 50′29″W). Using breakthrough curves obtained by Rhodamine WT slug injections and the one‐dimensional transport with inflow and storage model (OTIS), hydraulic transport parameters were obtained for each reach on six different occasions (n = 36). Relative transient storage (A_S:A) was similar between both reach types (As: A = 0·3 ± 0·1 for both agricultural and forested reaches). Comparing values of F_med²⁰⁰ to those in the literature indicates that the effect of transient storage was moderately high in the study streams in the Upper Sugar Creek Watershed. Examining travel times revealed that overall residence time (HRT) and residence time in transient storage (T_STO) were both longer in forested reaches (forested HRT = 19·1 ± 11·5 min and T_STO = 4·0 ± 3·8 min; agricultural HRT = 9·3 ± 5·3 min and T_STO = 1·7 ± 1·4 min). We concluded that the effect of transient storage on solute transport was similar between the forested and agricultural reaches but the forested reaches had a greater potential to retain solutes as a result of longer travel times. Copyright © 2009 John Wiley & Sons, Ltd.     

Alluvial architecture in headwater streams with special emphasis on step–pool topography

Alluvial mountain streams exhibit a range of channel forms: pool–riffle, plane bed, step–pool and cascades. Previous work suggested that these forms exist within discrete, and progressively steeper slope classes. Measurements conducted at over 100 sites in west‐central and central Idaho confirm that slope steepens progressively as one moves from pool–riffle, to plane bed, to step–pool, and finally to cascades. Median slope for pool–riffle topography is 0·0060, for plane beds 0·013, for step–pools 0·044, and for cascades 0·068. There is substantial overlap in the slopes associated with these channel forms. Pool–riffle topography was found at slopes between 0·0010 and 0·015, plane beds between 0·0010 and 0·035, step–pools between 0·015 and 0·134, and cascades between 0·050 and 0·12. Step–pools are particularly striking features in headwater streams. They are characterized by alternating steep and gentle channel segments. The steep segments (step risers) are transverse accumulations of boulder and cobbles, while the gentle segments (pools) contain finer material. Step wavelength is best correlated to step height which is in turn best correlated to the median particle size found on step risers. This result differs from past studies that have reported channel slope to be the dominant control on step wavelength. The presumed geometry and Froude number associated with the features under formative conditions are consistent with the existence field for antidunes and by extension with the hypothesis that step–pools are formed by antidunes. Copyright © 2000 John Wiley & Sons, Ltd.     

Developing a Lagrangian sediment transport model for open channel flows

A three-dimensional stochastic Lagrangian particle tracking sediment transport model is developed to solve the discrete advection-dispersion equation using a combination of empirical dispersion equations.The performance of three widely-used longitudinal dispersion coefficient equations was examined to select one of them as the primary dispersion equation term in the developed model. Also, a conditional empirical equation was used to consider the effect of vertical dispersion term in top layers n...     

Adjustments in channel form,sediment calibre and vegetation around check‐dams in the headwater reaches of mountain torrents,Calabria, Italy

The structure and dynamics of vegetation in valley bottoms are both strongly associated with fluvial processes and landform dynamics. All of these associations are disrupted by the installation of engineering control works. We use survey and analysis methods developed previously to investigate the impact of the installation of check‐dams within the confined headwaters of steep seasonally‐flowing streams (fiumaras) in Calabria, southern Italy, on active channel form, sediment calibre, and the richness, cover and development of riparian vegetation. Based on detailed field measurements along transects across the active channel, estimates of indices of vegetation extent (GCC), development (WCH) and their cross‐sectional variability (coefficients of variation of both indices at each survey site CV_GCC, CV_WCH), the number of species present (Ns), channel shape (w/d – the width/depth ratio), cross‐sectional area (CSA), downstream gradient (slope), surface bed sediment calibre (D₅₀) and subsurface fine sediment content (percentage less than 250 µm by weight) were obtained for 60 transects located immediately upstream (U), downstream (D) and at intermediate sites (I) around 20 check‐dams located in four different headwater catchments. Analysis of this data set suggests that statistically significant changes in channel form and sediment calibre upstream of check‐dams are associated with more consistent vegetation development across the active channel, including an increase in species richness relative to other transects, but notable increases in vegetation cover and development only arise where the physical characteristics of the channel are notably different from intermediate and downstream channels. Because of the naturally steep profile of the study torrents, intermediate sections between check‐dams tend to be more similar in form to channels located immediately downstream of check‐dams than those located upstream, leading to similar structural properties in the riparian vegetation. The intermediate transects support considerably more species than downstream reaches, but the conditions upstream of the check‐dams appear to be so favourable for riparian vegetation development that species richness exceeds that found in intermediate reaches. Despite the confined headwater locations, these contrasts in form, sediment and vegetation development around check‐dams are strong and consistent across the study catchments, over‐riding more subtle contrasts in species richness and sediment calibre between catchments. Copyright © 2009 John Wiley & Sons, Ltd.     

Total load transport in gravel bed and sand bed rivers case study:Chelichay watershed

Field experiments were conducted on total load transport in the Chelichay River Basin,a mountainous catchment (1,400 km~2) located in north eastern of Iran,to evaluate total load formulas including four gravel bed rivers and a sand bed river(Qaresoo River).Gravel bed rivers in Chelichay River Basin can be grouped into two types;steep slope rivers with high shear values(Chehelchay River and Khormaloo River) and mild slope rivers with low shear values(Narmab River and Soosara River).Two depth integrating suspended load samplers(DH-48 and D-49),and two bed load samplers(Helley-Smith and BLSH) were used to measure total load.The performance is tested of 8 total load transport formulae including 4 macroscopic and 4 microscopic methods.A systematic and thorough analysis of 59 sets of data collected from sand bed river indicate that Yang and Engelund and Hansen reach to the better results, and from four gravel bed rivers confirmed that the methods of Karim and Kennedy and Engelund and Hansen yields the best results for steep slope rivers,and the methods of Einstein and Bijker are ranked highest in gradual slope rivers.     

Are artificial neural network techniques relevant for the estimation of longitudinal dispersion coefficient in rivers? / Les techniques de réseaux de neurones artificiels sont-elles pertinentes pour estimer le coefficient de dispersion longitudinale en rivières?

Abstract

Abstract Accurate application of the longitudinal dispersion model requires that specially designed experimental studies are performed in the river reach under consideration. Such studies are usually very expensive, so in order to quantify the longitudinal dispersion coefficient, as an alternative approach, various researchers have proposed numerous empirical formulae based on hydraulic and morphometric characteristics. The results are presented of the application of artificial neural networks as a parameter estimation technique. Five different cases were considered with the network trained for different arrangements of input nodes, such as channel depth, channel width, cross-sectionally averaged water velocity, shear velocity and sinuosity index. In the case where the sinuosity index is included as an input node, the results turned out to be better than those presented by other authors.