A method is presented which enables the computation of the suspended load as the depth-integration of the product of the local concentration and flow velocity. The method is based on the computation of the reference concentration from the bed-load transport. Measured concentration profiles have been used for calibration. New relationships are proposed to represent the size gradation of the bed material and the damping of the turbulence by the sediment particles. A verification analysis using about 800 data shows that about 76% of the predicted values are within 0.5 and 2 times the measured values.

Sediment Transport, Part II: Suspended Load Transport

A framework is provided for scaling and scale issues in hydrology. The first section gives some basic definitions. This is important as researchers do not seem to have agreed on the meaning of concepts such as scale or upscaling. ‘Process scale’, ‘observation scale’ and ‘modelling (working) scale’ require different definitions. The second section discusses heterogeneity and variability in catchments and touches on the implications of randomness and organization for scaling. The third section addresses the linkages across scales from a modelling point of view. It is argued that upscaling typically consists of two steps: distributing and aggregating. Conversely, downscaling involves disaggregation and singling out. Different approaches are discussed for linking state variables, parameters, inputs and conceptualizations across scales. This section also deals with distributed parameter models, which are one way of linking conceptualizations across scales. The fourth section addresses the linkages across scales from a more holistic perspective dealing with dimensional analysis and similarity concepts. The main difference to the modelling point of view is that dimensional analysis and similarity concepts deal with complex processes in a much simpler fashion. Examples of dimensional analysis, similarity analysis and functional normalization in catchment hydrology are given. This section also briefly discusses fractals, which are a popular tool for quantifying variability across scales. The fifth section focuses on one particular aspect of this holistic view, discussing stream network analysis. The paper concludes with identifying key issues and gives some directions for future research.

/pdf/scale-issues-in-hydrological-modelling-a-review-1x61lpwqjr.pdf

Scale issues in hydrological modelling: A review

The sediment delivery problem

Channel networks with artibtrary drainage density or resolution can be extracted from digital elevation data. However, for digital elevation data derived networks to be useful they have to be extracted at the correct length scale or drainage density. Here we suggest a criterion for determining the appropriate drainage density at which to extract networks from digital elevation data. The criterion is basically to extract the highest resolution (highest drainage density) network that satisfies scaling laws that have traditionally been found to hold for channel networks. Procedures that use this criterion are presented and tested on 21 digital elevation data sets well distributed throughout the U.S.

On the extraction of channel networks from digital elevation data

We analyze geomorphic evidence of recent crustal deformation in the sub-Himalaya of central Nepal, south of the Kathmandu Basin. The Main Frontal Thrust fault (MFT), which marks the southern edge of the sub-Himalayan fold belt, is the only active structure in that area. Active fault bend folding at the MFT is quantified from structural geology and fluvial terraces along the Bagmati and Bakeya Rivers. Two major and two minor strath terraces are recognized and dated to be 9.2, 2.2, and 6.2, 3.7 calibrated (cal) kyr old, respectively. Rock uplift of up to 1.5 cm/yr is derived from river incision, accounting for sedimentation in the Gangetic plain and channel geometry changes. Rock uplift profiles are found to correlate with bedding dip angles, as expected in fault bend folding. It implies that thrusting along the MFT has absorbed 21 ± 1.5 mm/yr of N-S shortening on average over the Holocene period. The ±1.5 mm/yr defines the 68% confidence interval and accounts for uncertainties in age, elevation measurements, initial geometry of the deformed terraces, and seismic cycle. At the longitude of Kathmandu, localized thrusting along the Main Frontal Thrust fault must absorb most of the shortening across the Himalaya. By contrast, microseismicity and geodetic monitoring over the last decade suggest that interseismic strain is accumulating beneath the High Himalaya, 50–100 km north of the active fold zone, where the Main Himalayan Thrust (MHT) fault roots into a ductile decollement beneath southern Tibet. In the interseismic period the MHT is locked, and elastic deformation accumulates until being released by large (M_w > 8) earthquakes. These earthquakes break the MHT up to the near surface at the front of the Himalayan foothills and result in incremental activation of the MFT.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JB900292

Active folding of fluvial terraces across the Siwaliks Hills, Himalayas of central Nepal

A review of existing literature reveals some disadvantages of using Shields diagram as the criterion for incipient motion of sediment particles on an alluvial bed. A new criterion based on average flow velocity, fall velocity, and shear velocity Reynolds number is proposed herein with the supporting data collected by different investigators. This new criterion is used to calculate the dimensionless critical unit stream power in a dimensionless unit stream power equation for sediment transport. The dimensionless unit stream power is the ratio of the time rate of potential energy expenditure per unit weight of water and the terminal fall velocity of the sediment. More than 1,000 sets of data from both laboratory flumes and natural streams published by different authors are used to support this dimensionless equation for sediment transport.

Incipient Motion and Sediment Transport

Sediment Transport Theory and Practice is based on the author's many years of research, teaching, engineering, and consulting experience. The book presents a balanced and in-depth treatment of the sediment transport theory and its applications to solving river engineering and environmental problems. The author provides a systematic analysis and comparison of transport theories based on the force and power approaches, blending detailed historical developments with the latest progress and application techniques in research and engineering. It includes numerous examples to enhance readers' comprehension and applications of critical information on river sedimentation. The book can be used as a textbook for students, a reference book for researchers, and an application manual for practitioners. A PC diskette containing commonly used sediment transport formulas is included. A solutions manual is available for professors.

Sediment Transport: Theory and Practice

A thorough study of the existing applicable data reveals the basic reason that previous equations often provide misleading predictions of the sediment transport rates. The error stems from the unrealistic assumptions made in their derivations. Unit stream power, defined as the time rate of potential energy expenditure per unit weight of water in an alluvial channel, is shown to dominate the total sediment concentration. Statistical analyses of 1,225 sets of laboratory flume data and 50 sets of field data indicate the existence and the generality of the linear relationship between the logarithm of total sediment concentration and the logarithm of the effective unit stream power. The coefficients in the proposed equation are shown to be related to particle size and water depth, or particle size and width-depth ratio. An equation generalized from Gilbert's data can be applied to natural streams for the prediction of total sediment discharge with good accuracy.

Unit Stream Power and Sediment Transport

The basic assumptions used in the derivation of bedload or gravel transport equations are reviewed and examined to determine their validities. Laboratory data indicate that unit stream power is mor...

Unit Stream Power Equation for Gravel

Use of the analogy of entropy in thermodynamics reveals two basic laws which govern the formation of all stream systems. The first law is the law of average stream fall, which states that under the dynamic equilibrium condition the ratio of average fall between any two different order streams in the same river basin is unity. The second law is the law of least rate of energy expenditure, which states that during the evolution toward its equilibrium condition a natural stream chooses its course of flow in such a manner that the rate of potential energy expenditure per unit mass of water along this course is a minimum. This minimum value depends on the external constraints applied to the stream. The concavity of a river basin is shown to be the determinative factor in the formation of a stream system. On the basis of Horton's law and the law of average stream fall, longitudinal stream profiles can be calculated. The agreement between observed data and the theories found in this study is excellent.

Chih Ted Yang

Papers

Incipient Motion and Sediment Transport

Sediment Transport: Theory and Practice

Unit Stream Power and Sediment Transport

Unit Stream Power Equation for Gravel

Potential Energy and Stream Morphology