Book•
The hydraulic geometry of stream channels and some physiographic implications
01 Jan 1953-
TL;DR: In this paper, the hydraulic characteristics of stream channels are measured quantitatively and vary with discharge as simple power functions at a given river cross section, and similar variations in relation to discharge exist among the cross sections along the length of a river under the condition that discharge at all points is equal in frequency of occurrence.
Abstract: Some hydraulic characteristics of stream channels — depth, width, velocity, and suspended load — are measured quantitatively and vary with discharge as simple power functions at a given river cross section. Similar variations in relation to discharge exist among the cross sections along the length of a river under the condition that discharge at all points is equal in frequency of occurrence. The functions derived for a given cross section and among various cross sections along the river differ only in numerical values of coefficients and exponents. These functions are:
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TL;DR: It is hypothesized that producer and consumer communities characteristic of a given river reach become established in harmony with the dynamic physical conditions of the channel.
Abstract: From headwaters to mouth, the physical variables within a river system present a continuous gradient of physical conditions. This gradient should elicit a series of responses within the constituent...
9,145 citations
Cites background from "The hydraulic geometry of stream ch..."
...…of the physical stream network system and the distribution of watersheds as open systems in dynamic (“quasi”) equilibrium was first proposed by Leopold and Maddock ( 1953) to describe consistent patterns, or adjustments, in the relationships of stream width, depth, velocity, and sediment…...
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.../ fie patterns of organic matter use may be analogous b those of physical energy expenditure proposed by Pomorphologists (Leopold and Maddock 1953; Leo- i Wld and Langbein 1962; Langbein and Leopold 1966; 1 Curry 1972)....
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Book•
01 Jun 2008
TL;DR: The Intergovernmental Panel on Climate Change (IPCC) Technical Paper Climate Change and Water draws together and evaluates the information in IPCC Assessment and Special Reports concerning the impacts of climate change on hydrological processes and regimes, and on freshwater resources.
Abstract: The Intergovernmental Panel on Climate Change (IPCC) Technical Paper Climate Change and Water draws together and evaluates the information in IPCC Assessment and Special Reports concerning the impacts of climate change on hydrological processes and regimes, and on freshwater resources – their availability, quality, use and management. It takes into account current and projected regional key vulnerabilities, prospects for adaptation, and the relationships between climate change mitigation and water. Its objectives are:
3,108 citations
TL;DR: A global model of plastic inputs from rivers into oceans based on waste management, population density and hydrological information is presented to provide baseline data for ocean plastic mass balance exercises, and assist in prioritizing future plastic debris monitoring and mitigation strategies.
Abstract: Plastics in the marine environment have become a major concern because of their persistence at sea, and adverse consequences to marine life and potentially human health. Implementing mitigation strategies requires an understanding and quantification of marine plastic sources, taking spatial and temporal variability into account. Here we present a global model of plastic inputs from rivers into oceans based on waste management, population density and hydrological information. Our model is calibrated against measurements available in the literature. We estimate that between 1.15 and 2.41 million tonnes of plastic waste currently enters the ocean every year from rivers, with over 74% of emissions occurring between May and October. The top 20 polluting rivers, mostly located in Asia, account for 67% of the global total. The findings of this study provide baseline data for ocean plastic mass balance exercises, and assist in prioritizing future plastic debris monitoring and mitigation strategies. Rivers provide a major pathway for ocean plastic waste, but effective mitigation is dependent on a quantification of active sources. Here, the authors present a global model of riverine plastic inputs, and estimate annual plastic waste of almost 2.5 million tonnes, with 86% sourced from Asia.
2,083 citations
TL;DR: The relative importance in geomorphic processes of extreme or catastrophic events and more frequent events of smaller magnitude can be measured in terms of the relative amounts of "work" done on the landscape and the formation of specific features of the landscape as discussed by the authors.
Abstract: The relative importance in geomorphic processes of extreme or catastrophic events and more frequent events of smaller magnitude can be measured in terms of (1) the relative amounts of "work" done on the landscape and (2) in terms of the formation of specific features of the landscape. For many processes, above the level of competence, the rate of movement of material can be expressed as a power function of some stress, as for example, shear stress. Because the frequency distributions of the magnitudes of many natural events, such as floods, rainfall, and wind speeds, approximate log-normal distributions, the product of frequency and rate, a measure of the work performed by events having different frequencies and magnitudes will attain a maximum. The frequency at which this maximum occurs provides a measure of the level at which the largest portion of the total work is accomplished. Analysis of records of sediment transported by rivers indicates that the largest portion of the total load is carried by flow...
1,850 citations
TL;DR: In this article, the authors explore the stream power erosion model in an effort to elucidate its consequences in terms of large-scale topographic (fluvial) relief and its sensitivity to tectonic and climatic forcing.
Abstract: The longitudinal profiles of bedrock channels are a major component of the relief structure of mountainous drainage basins and therefore limit the elevation of peaks and ridges. Further, bedrock channels communicate tectonic and climatic signals across the landscape, thus dictating, to first order, the dynamic response of mountainous landscapes to external forcings. We review and explore the stream-power erosion model in an effort to (1) elucidate its consequences in terms of large-scale topographic (fluvial) relief and its sensitivity to tectonic and climatic forcing, (2) derive a relationship for system response time to tectonic perturbations, (3) determine the sensitivity of model behavior to various model parameters, and (4) integrate the above to suggest useful guidelines for further study of bedrock channel systems and for future refinement of the streampower erosion law. Dimensional analysis reveals that the dynamic behavior of the stream-power erosion model is governed by a single nondimensional group that we term the uplift-erosion number, greatly reducing the number of variables that need to be considered in the sensitivity analysis. The degree of nonlinearity in the relationship between stream incision rate and channel gradient (slope exponent n) emerges as a fundamental unknown. The physics of the active erosion processes directly influence this nonlinearity, which is shown to dictate the relationship between the uplift-erosion number, the equilibrium stream channel gradient, and the total fluvial relief of mountain ranges. Similarly, the predicted response time to changes in rock uplift rate is shown to depend on climate, rock strength, and the magnitude of tectonic perturbation, with the slope exponent n controlling the degree of dependence on these various factors. For typical drainage basin geometries the response time is relatively insensitive to the size of the system. Work on the physics of bedrock erosion processes, their sensitivity to extreme floods, their transient responses to sudden changes in climate or uplift rate, and the scaling of local rock erosion studies to reach-scale modeling studies are most sorely needed.
1,805 citations
References
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TL;DR: The most important single factor involved in erosion phenomena and, in particular in connection with the development of stream systems and their drainage basins by aqueous erosion is called crossgrading.
Abstract: The composition of the stream system of a drainage basin can be expressed quantitatively in terms of stream order, drainage density, bifurcation ratio, and stream-length ratio.
Stream orders are so chosen that the fingertip or unbranched tributaries are of the 1st order; streams which receive 1st order tributaries, but these only, are of the 2d order; third order streams receive 2d or 1st and 2d order tributaries, and so on, until, finally, the main stream is of the highest order and characterizes the order of the drainage basin.
Two fundamental laws connect the numbers and lengths of streams of different orders in a drainage basin:
The infiltration theory of surface runoff is based on two fundamental concepts:
For a given terrain there is a minimum length x c of overland flow required to produce sufficient runoff volume to initiate erosion. The critical length x c depends on surface slope, runoff intensity, infiltration-capacity, and resistivity of the soil to erosion. This is the most important single factor involved in erosion phenomena and, in particular, in connection with the development of stream systems and their drainage basins by aqueous erosion.
The erosive force and the rate at which erosion can take place at a distance x from the watershed line is directly proportional to the runoff intensity, in inches per hour, the distance x , a function of the slope angle, and a proportionality factor K e , which represents the quantity of material which can be torn loose and eroded per unit of time and surface area, with unit runoff intensity, slope, and terrain.
The rate of erosion is the quantity of material actually removed from the soil surface per unit of time and area, and this may be governed by either the transporting power of overland flow or the actual rate of erosion, whichever is smaller. If the quantity of material torn loose and carried in suspension in overland flow exceeds the quantity which can be transported, deposition or sedimentation on the soil surface will take place.
On newly exposed terrain, resulting, for example, from the recession of a coast line, sheet erosion occurs first where the distance from the watershed line to the coast line first exceeds the critical length x c and sheet erosion spreads laterally as the width of the exposed terrain increases. Erosion of such a newly exposed plane surface initially develops a series of shallow, close-spaced, shoestring gullies or rill channels. The rills flow parallel with or are consequent on the original slope. As a result of various causes, the divides between adjacent rill channels are broken down locally, and the flow in the shallower rill channels more remote from the initial rill is diverted into deeper rills more closely adjacent thereto, and a new system of rill channels is developed having a direction of flow at an angle to the initial rill channels and producing a resultant slope toward the initial rill. This is called cross-grading.
With progressive exposure of new terrain, streams develop first at points where the length of overland flow first exceeds the critical length x c , and streams starting at these points generally become the primary or highest-order streams of the ultimate drainage basins. The development of a rilled surface on each side of the main stream, followed by cross-grading, creates lateral slopes toward the main stream, and on these slopes tributary streams develop, usually one on either side, at points where the length of overland flow in the new resultant slope direction first exceeds the critical length x c .
Cross-grading and recross-grading of a given portion of the area will continue, accompanied in each case by the development of a new order of tributary streams, until finally the length of overland flow within the remaining areas is everywhere less than the critical length x c . These processes fully account for the geometric-series laws of stream numbers and stream lengths.
A belt of no erosion exists around the margin of each drainage basin and interior subarea while the development of the stream system is in progress, and this belt of no erosion finally covers the entire area when the stream development becomes complete.
The development of interior divides between subordinate streams takes place as the result of competitive erosion, and such divides, as well as the exterior divide surrounding the drainage basin, are generally sinuous in plan and profile as a result of competitive erosion on the two sides of the divide, with the general result that isolated hills commonly occur along divides, particularly on cross divides, at their junctions with longitudinal divides. These interfluve hills are not uneroded areas, as their summits had been subjected to more or less repeated cross-grading previous to the development of the divide on which they are located.
With increased exposure of terrain weaker streams may be absorbed by the stronger, larger streams by competitive erosion, and the drainage basin grows in width at the same time that it increases in length. There is, however, always a triangular area of direct drainage to the coast line intermediate between any two major streams, with the result that the final form of a drainage basin is usually ovoid or pear-shaped.
The drainage basins of the first-order tributaries are the last developed on a given area, and such streams often have steep-sided, V-shaped, incised channels adjoined by belts of no erosion.
The end point of stream development occurs when the tributary subareas have been so completely subdivided by successive orders of stream development that there nowhere remains a length of overland flow exceeding the critical length x c . Stream channels may, however, continue to develop to some extent through headward erosion, but stream channels do not, in general, extend to the watershed line.
Valley and stream development occur together and are closely related. At a given cross section the valley cannot grade below the stream, and the valley supplies the runoff and sediment which together determine the valley and stream profiles. As a result of cross-grading antecedent to the development of new tributaries, the tributaries and their valleys are concordant with the parent stream and valley at the time the new streams are formed and remain concordant thereafter.
Valley cross sections, when grading is complete, and except for first-order tributaries, are generally S-shaped on each side of the stream, with a point of contraflexure on the upper portion of the slope, and downslope from this point the final form is determined by a combination of factors, including erosion rate, transporting power, and the relative frequencies of occurrence of storms and runoff of different intensities. The longitudinal profile of a valley along the stream bank and the cross section of the valley are closely related, and both are related to the resultant slope at a given location.
Many areas on which meager stream development has taken place, and which are commonly classified as youthful, are really mature, because the end point of stream development and erosion for existing conditions has already been reached.
When the end point of stream and valley gradation has arrived in a given drainage basin, the remaining surface is usually concave upward, more or less remembling a segment of a parabaloid, ribbed by cross and longitudinal divides and containing interfluve hills and plateaus. This is called a “graded” surface, and it is suggested that the term “peneplain” is not appropriate, since this surface is neither a plane nor nearly a plane, nor does it approach a plane as an ultimate limiting form.
The hydrophysical concepts applied to stream and valley development account for observed phenomena from the time of exposure of the terrain. Details of these phenomena of stream and valley development on a given area may be modified by geologic structures and subsequent geologic changes, as well as local variations of infiltration-capacity and resistance to erosion.
In this paper stream development and drainage-basin topography are considered wholly from the viewpoint of the operation of hydrophysical processes. In connection with the Davis erosion cycle the same subject is treated largely with reference to the effects of antecedent geologic conditions and subsequent geologic changes. The two views bear much the same relation as two pictures of the same object taken in different lights, and one supplements the other. The Davis erosion cycle is, in effect, usually assumed to begin after the development of at least a partial stream system; the hydrophysical concept carries stream development back to the original newly exposed surface.
5,348 citations
DOI•
01 Sep 1950
Abstract: CONTENTS Page Introduction. 1 Approach to the problem. _ 3 Limitation of the bed-load function _ _ _ 4 The undetermined function 4 The alluvial stream. 5 The sediment mixture 6 Hydraulics of the alluvial channel. 7 The friction formula 7 The friction factor 8 Resistance of the bars 9 The laminar sublayer 10 The transition between hydraulically rough and smooth beds_ 12 The velocity fluctuations 13 Suspension 14 The transportation rate of suspended load 17 Integration of the suspended load. _ 17 Numerical integration of suspended load 19 Limit of suspension. 24 The bed layer 24 Practical calculation of suspended load___ ____ 25 Numerical example 26 Page Bed-load concept 29 Some constants entering the laws of bed-load motion: 31 The bed-load equation 32 The exchange time 33 The exchange probability 34 Determination of the probability V 35 Transition between bed load and. suspended load 38 The necessary graphs 40 Flume tests with sediment mixtures.. 42 Sample calculation of a river reachl 44 Choice of a river reach 45 Description of a river reach_____ 45 Application of procedure to Big Sand Creek, Miss 46 Discussion of calculations 60 Limitations of the method____ 65 Summary. 67 Literature cited 68 Appendix 69 List of symbols. 69 Work charts _ 71
1,677 citations
TL;DR: In this paper, the authors modify and extend the theory of grade originally set forth by Gilbert and Davis, which is indispensable in any genetic study of fluvial erosional features and deposits.
Abstract: Grade is a condition of equilibrium in streams as agents of transportation. The validity of the concept has been questioned, but it is indispensable in any genetic study of fluvial erosional features and deposits. This paper modifies and extends the theory of grade originally set forth by Gilbert and Davis. A graded stream is one in which, over a period of years, slope is delicately adjusted to provide, with available discharge and the prevailing channel characteristics, just the velocity required for transportation of all of the load supplied from above. Slope usually decreases in a downvalley direction, but because discharge, channel characteristics, and load do not vary systematically along the stream, the graded profile is not a simple mathematical curve. Corrasive power and bed rock resistance to corrasion determine the slope of the ungraded profile, but have no direct influence on the graded profile. Chiefly because of a difference in rate of downvalley decrease in caliber of load, the aggrading profile differs in form from the graded profile; the aggrading profile is, and the graded profile is not, asymptotic with respect to a horizontal line passing through base level. It is critical in any analysis of stream profiles to recognize the difference in slope-controlling factors in parts of the overall profile that are (1) graded, (2) ungraded, and (3) aggrading. A graded stream responds to a change in conditions in accordance with Le Chatelier9s general law:—“if a stress is brought to bear on a system in equilibrium, a reaction occurs, displacing the equilibrium in a direction that tends to absorb the effect of the stress.” Readjustment is effected primarily by appropriate modification of slope by upbuilding or downcutting, and only to a minor extent or not at all by concomitant changes in channel characteristics. Paired examples illustrate (1) the almost telegraphic rapidity with which the first phases of the reaction of a graded stream to a number of artificial changes are propagated upvalley and downvalley and, (2) the more or less complete readjustment that is effected over a period of thousands of years to analogous natural changes. The engineer is necessarily concerned chiefly with short-term and quantitative aspects of the reaction of a graded stream to changes in control, while the attention of the geologist is usually focused on the long-term and genetic aspects of the stream9s response to changes. But the basic problems are the same, and a pooling of ideas and data may enable the engineer to improve his long range planning of river control measures and permit the geologist to interpret, in quantitative terms, the deposits of ancient streams.
927 citations
TL;DR: Time is the most frequent application and of a most practical value in geographical description as mentioned in this paper, and is, of all the three variables, the one of the most frequently used in geographical descriptions.
Abstract: All the varied forms of the lands are dependent on—or, as the mathematician would say, are functions of—three variable quantities, which may be called structure, process, and time. In the beginning, when the forces of deformation and uplift determine the structure and attitude of a region, the form of its surface is in sympathy with its internal arrangement, and its height depends on the amount of uplift that it has suffered. If its rocks were unchangeable under the attack of external processes, its surface would remain unaltered until the forces of deformation and uplift acted again; and in this case structure would be alone in control of form. But no rocks are unchangeable; even the most resistant yield under the attack of the atmosphere, and their waste creeps and washes downhill as long as any hills remain; hence all forms, however high and however resistant, must be laid low, and thus destructive process gains rank equal to that of structure in determining the shape of a land mass. Process cannot, however, complete its work instantly, and the amount of change from initial form is therefore a function of time. Time thus completes the trio of geographical controls, and is, of the three, the one of the most frequent application and of a most practical value in geographical description.
703 citations
TL;DR: In this paper, measurements of sediment and velocity distributions in a laboratory flume were made for various values of rate of flow, slope of channel, and size and amount of suspended load.
Abstract: Measurements of the sediment and velocity distributions in a laboratory flume were made for various values of rate of flow, slope of channel, and size and amount of suspended load. The experimental...
420 citations