Dynamique des rivières res 1
Rivers are enormously diverse size: varies by many orders of magnitude geometry: highly variable substrate: bedrock or sediment sediment type: sediment size ranges from mud to gravel stage of development: young, with rugged topography and rapid change, to old, with gentle topography and slow change climate: ephemeral and flashy to very steady 2
Morphology of rivers wetted perimeters cross sectional area hydraulic radius = wetted perimeter 3
Morphology of rivers 4
Morphology of rivers The base level of a river is the elevation of the water surface of the water body, either the world ocean or a lake along the river course, into which the river flows. 5
Morphology of rivers Northern Tian Shan, China 6 Poisson, 2002
Morphology of rivers The river has some equilibrium longitudinal profile, in the sense that if conditions of tectonic, precipitation, sediment supply, and 7 base level remain constant the longitudinal profile stays the same.
Classifying rivers Rivers can be classified in several ways: by the nature of their substrate by the percentage of time they flow by their relationship to the groundwater table by their morphology by the kind of sediment load they carry by the dominant particle size of the bed sediment 8
Classifying rivers Nature of substrate detachment limited rivers transport limited rivers 9
Classifying rivers Nature of substrate Taiwan, bedrock river Tibet, Alluvial river 10
Classifying rivers Percentage of time river flows 11
Classifying rivers Percentage of time river flows Runoff cycle At the end of the first dry spell the river level lies below the ground water table in the river banks. After a heavy rainfall the river stage rises rapidly to lie well above the level of the ground water table in the banks. Ground water is stored in the river banks, in the sense that the ground water table is locally and temporarily higher there than in the surroundings. At the end of the rainy period both the river stage and the ground water level are of about the same height and are about at their highest. Then both the river stage and the ground water table fall back to the dry 12 spell situation shown.
Classifying rivers Relationship to ground water table (unsaturated zone) (Ground Water Table) (LOSING RIVER) (GAINING RIVER) 13
Classifying rivers Morphology 14
Classifying rivers Morphology l sinuosity = l L L sinuosity 1 15
Classifying rivers Morphology Straight Braided Minnesota, USA Meandered Sunwapta River, Alberta, Canada Anastomosed Yukon, Canada 16 Columbia River in British Columbia, Canada
Classifying rivers Morphology wavelength 17 amplitude radius of curvature
Classifying rivers Morphology 18
Classifying rivers Morphology 2003 McGraw-Hill Higher Education 19
Classifying rivers Morphology meander scrolls point bar 20 Laonong river, Taiwan
Classifying rivers Morphology narrow neck cutoff oxbow lake sealing channel realignment 21
Classifying rivers Morphology Tortous meanders 22 Confined meander scrolls
Classifying rivers Morphology ~100 m Torrent St Pierre, Ecrins, France Meunier, 2004 23
Classifying rivers Morphology Meunier, 2004 24
Classifying rivers Morphology 1.5<sinus.<1.8 sinus.>1.8 Burbank & Anderson, 2001 25
Classifying rivers Morphology 26 Church, 2006
Measurements of stream flow The stage of a river is the height of the water surface of the stream above an arbitrary datum, usually either sea level or an elevation slightly below the channel bed. Stage is related to depth, but the two are not the same. 27
Measurements of stream flow The stage of a river is fairly easy to measure. Various kinds of stream gauges are in use. 28
Measurements of stream flow The discharge of a river is the volume rate of flow past a given cross section, measured in cubic meters per second, m 3 /s. Most measurement of river discharge makes use of a simple equation that relates discharge Q past a cross section to the area A of the crosssection and the mean velocity U of flow past that cross section. Q = UA u 29
Measurements of stream flow Torrent St Pierre, Ecrins, France 30
Measurements of stream flow Hydrographs 31
Measurements of stream flow Stage-discharge diagram or rating curve 32
Measurements of stream flow 33
Measurements of stream flow AB: end of spell without rainfall; all surface runoff has ceased, and groundwater runoff is gradually decreasing. B: surface runoff from a rainstorm reaches the channel. BC: this is the rising limb of the hydrograph; surface runoff increases sharply. 34
Measurements of stream flow C: this is the peak or crest of the hydrograph; surface runoff peaks. CD: this is the falling limb or recession limb of the hydrograph. Groundwater runoff peaks here somewhere, then tails off slowly; surface runoff decreases to zero. D: by this time there s no more surface runoff, only decreasing groundwater runoff. 35
Measurements of stream flow C A B D 36
Measurements of stream flow Isochrons of equal travel times of surface runoff 37
The resistance equation for open channel flow 38
The resistance equation for open channel flow α α 39
The resistance equation for open channel flow α 40
The resistance equation for open channel flow α α Hydrostatic fluid pressure on both upstream and downstream are the same and they act opposite to each other. 41
The resistance equation for open channel flow W α Frictional force α = τ.( 1).( W o ) Basal shear stress 42
The resistance equation for open channel flow A α α Downstream component of the weigth = ρ.(1).( A). g. sinα w 43
The resistance equation for open channel flow τ.(1). W o τ o = ρ.(1).( A). g.sinα w ρw. A. g.sinα = W d W A = W. d τ o = ρ. d. g. sinα w 44
Stream power river bed Δx Δh From Burbank & Anderson, 2001 Stream power = rate of change of potential energy Stream power Ω = unit length ΔE p = Δt. Δx Recall that change of potential energy Δ E p = m. g. Δh Ω = m. g. Δh Δt. Δx Discharge Q = Vw Δt = m ρ. Δt w m Δt = Q. ρ w Ω = Q. ρw. g. Δh Δx Slope S = Δh Δx Ω = Q.ρ w. g. S 45
W Stream power d river bed Δx Δh From Burbank & Anderson, 2001 Specific Stream power = power available per unit area of the bed Ω ω = = W ρ w gqs W But Q = W ( d cosα )( Δx / cosα ) Δt ω = ρ g( d cosα ) S w Δx / cosα Δt Δx / cosα Recall that U =,and that S = tanα Δt ρ w ω =τ U So, ω = dg sinα U o 46
Drainage networks divide Drainage basins, watersheds, catchments 47
Drainage networks 48
Drainage networks Putorana Plateau, Russia 49
Drainage networks Canadian shield 50
Drainage networks 51 Wyoming, USA
Drainage networks Cantal, France 52
Drainage networks Central Tibet 53
Drainage networks Arthur Newell Strahler, 1918-2002 Strahler Stream Order 54
Drainage networks 3 Order Number of Segments Bifurcati on Ratio 2 1 14 2 4 3 1 3.5 4 1 55
Drainage networks Rb = 3.58 1 2 3 4 5 Order Ra = 4.65 Rl = 1.91 1 2 3 4 5 Order Rs = 1.7 1 2 3 4 5 Order 1.0 1.5 2.0 2.5 3.0 3.5 56 4.0 Order Mean Stream Area 10^6 5*10^6 5*10^7 Number of Streams 1 5 10 50 Mean Stream Slope Mean Stream Length 0.05 0.10 900 2000 4000
Drainage networks Link Slope 0.005 0.050 0.500 S = k. A θ avec 0.3 < θ < S ~ A^-0.35 0.6 Flint s Law 5*10^4 5*10^5 5*10^6 5*10^7 Link Contributing Area Data from Reynolds Creek 30 m DEM, 50 grid cell threshold, points, individual links, big dots, bins of size 100 57
Drainage networks Montgomery et al., 1996 58
Drainage networks Longest Upstream Length 500 5000 50000 Lα C l h. A avec 0.5 < h < L = 1.7 A^0.51 0.6 Hack s Law 10^3 10^5 10^7 10^9 Link Contributing Area 59