In the hydrologic cycle
Precipitation = Runoff + Infiltration + Evapotranspiration
Surface water runoff is the water that flows at the Earth's surface. Infiltration is the water that soaks into the ground to become part of the groundwater system. Infiltration accounts, by far, for the smallest proportion of precipitation. Evapotranspiration (ET) refers to the water that is directly evaporated or transpired by plants (evaporated from leaves) back into the atmosphere. ET generally accounts for the largest proportion of precipitation.
Stream Networks - Stream Drainage Basins The water from precipitation is drained from the land via networks of connected streams. Each stream network lies in its own drainage basin separated from adjacent stream networks by drainage divides.
The average annual runoff is that portion of the annual precipitation in a drainage basin that flows out of the basin as surface water. It is calculated as:
Runoff = Total Annual Discharge / Basin Size
Runoff increases with increasing precipitation, steepness of the land, imperviousness of the land, and use by man.
Stream velocity is the speed of the water in the stream. Units are distance per time (e.g., meters per second or feet per second). Stream velocity is greatest in midstream near (just below) the surface and is slowest along the stream bed and banks due to friction.
Stream velocity depends on the slope of the stream bed, the degree of roughness of the stream bed, and the hydraulic radius (see next).
If velocity increases because of a local increase in slope, then the depth must decrease to maintain a constant discharge (the water in the steeper stretch can't get ahead of the water behind it). One consequence of this is that the shear (velocity gradient from the stream bed to the surface) will increase.
Hydraulic radius (HR or just R) is the ratio of the cross-sectional area divided by the wetted perimeter. For a hypothetical stream with a rectangular cross sectional shape (a stream with a flat bottom and vertical sides) the cross-sectional area is simply the width multiplied by the depth (W * D). For the same hypothetical stream the wetted perimeter would be the depth plus the width plus the depth (W + 2D). The greater the cross-sectional area in comparison to the wetted perimeter, the more freely flowing will the stream be because less of the water in the stream is in proximity to the frictional bed. So as hydraulic radius increases so will velocity (all other factors being equal). As streams get deeper, for example during a flood, the hydraulic radius increases. There is a greater mass of water per frictional wetted perimeter. The stream flows more efficiently.
Stream discharge is the quantity (volume) of water passing by a given point in a certain amount of time. It is calculated as Q = V * A, where V is the stream velocity and A is the stream's cross-sectional area. Units of discharge are volume per time (e.g., m3/sec or million gallons per day, mgpd).
Stream Gaging: Stream discharge can be calculated by determining the cross sectional area of a stream at a given point and the velocity at that point. The most accurate method is with the construction of a concrete weir at a point across the stream. The weir creates bottom and sides with a known shape, so as the stream level increases and decreases the cross sectional area can easily be determined. The U.S. Geological Survey maintains a network of approximately 10,000 stream gaging stations throughout the United States where water depth and stream velocity are continuously monitored. Discharge is calculated from these.
At low velocity, especially if the stream bed is smooth, streams may exhibit laminar flow in which all of the water molecules flow in parallel paths. At higher velocities turbulence is introduced into the flow (turbulent flow). The water molecules don't follow parallel paths.
Perennial and Ephemeral Streams
Gaining (effluent) streams receive water from the groundwater. In other words, a gaining stream discharges water from the water table. Gaining streams are perennial streams: they typically flow year around.
On the other hand losing (influent) streams lie above the water table (e.g., in an arid climate) and water seeps through the stream bed to recharge the water table below. Losing streams may be intermittent (flow part of the year) or ephemeral (only flow briefly following precipitation events). They only flow when there is sufficient runoff from recent rains or spring snow melt.
Some streams are gaining part of the year and losing part of the year or just in particular years, as the water table drops during an extended dry season.
Streams have two sources of water: storm charge, from overland flow after rain events, and baseflow, supplied by groundwater.
Stream hydrographs show a stream's discharge over time. Peak discharges follow rain events. There is a lag time between the rain event and the peak stream discharge due to the time required for rain water to collect as overland flow and for inputs from tributary streams. The rainwater that infiltrates the ground spreads out the peak flow following a rain event.
Streams carry dissolved ions as dissolved load, fine clay and silt particles as suspended load, and coarse sands and gravels as bed load. Fine particles will only remain suspended if flow is turbulent. In laminar flow, suspended particles will slowly settle to the bed.
Hjulstrom's Diagram plots two curves representing 1) the minimum stream velocity required to erode sediments of varying sizes from the stream bed, and 2) the minimum velocity required to continue to transport sediments of varying sizes. Notice that for coarser sediments (sand and gravel) it takes just a little higher velocity to initially erode particles than it takes to continue to transport them. For small particles (clay and silt) considerably higher velocities are required for erosion than for transportation because these finer particles have cohesion resulting from electrostatic attractions. Think of how sticky wet mud is.
Stream competence refers to the heaviest particles a stream can erode and thus transport. Caliber referst to the diameter of the largest particle that can be eroded. Stream competence depends on stream velocity (as shown on the Hjulstrom diagram above). The faster the current, the heavier the particle that can be eroded and transported. Note however that the finest particles (clays) are cohesive and require particularly high velocities to erode them from the stream bed.
Competence also depends on the magnitude of shear at the stream bed. Since stream velocity is lowest (approaching zero) along the stream bed and increases toward the surface, the greater the rate of change of velocity near the stream bed the greater the shear stress applied to sedimentary particles lying on the stream bed. Given two streams with different depths, flowing at the same velocity, the shallower stream will exert a greater shear on the sediments of the stream bed.
Stream capacity is the maximum amount of solid load (bed and suspended) a stream can carry. It depends on both the discharge and the velocity (since velocity affects the competence and therefore the range of particle sizes that may be transported).
As stream velocity and discharge increase so do competence and capacity. But it is not a linear relationship (e.g., doubling velocity does not simply double the competence). Competence (weight of the heaviest particle) varies as approximately the sixth power of velocity:
Δ competence (weight) ∝ Δ velocity6
or since weight is proportional to particle diameter cubed (or volume), the caliber, maximum particle diameter varies as the velocity squared:
Δ caliber (diameter) ∝ Δ velocity2
For example, doubling the velocity results in a 64 times (26) increase in the weight or 4 times (22) increase in the diameter of the largest particles being transported .
Capacity varies as the discharge squared or cubed.
Δ capacity ∝ Δ discharge2 to Δ discharge3
For example, tripling the discharge results in a 9 to 27 times (32 to 33) increase in the capacity.
Therefore, most of the work of streams is accomplished during floods when stream velocity and discharge (and therefore competence and capacity) are many times their level during low flow regimes. This work is in the form of bed scouring (erosion), sediment transport (bed and suspended loads), and sediment deposition.
Flood Erosion and Deposition: As flood waters rise and the stream gets deeper the hydraulic radius increases thereby making the stream more free flowing. The stream flows faster. The increased velocity and the increased cross-sectional area mean that discharge increases. As discharge and velocity increase so do the stream's competence and capacity. In the rising stages of a flood much sediment is dumped into streams by overland flow and gully wash. This can result in some aggradation or building up of sediments on the stream bed. However, after the flood peaks less sediment is carried and a great deal of bed scouring (erosion) occurs. As the flood subsides and competence and capacity decline sediments are deposited and the stream bed aggrades again. Even though the stream bed may return to somewhat like its pre-flood state, huge quantities of sediments have been transported downstream. Much fine sediment has probably been deposited on the flood plain.
The load supplied to a stream from the surrounding land is dependent on:
Stream channels may be straight, meandering, or braided. Streams are seldom straight for any significant distance. Turbulence in the stream and inhomogeneity in the bank materials lead to small deviations from a perfectly straight course. These deviations are amplified as discussed below.
At a bend in a stream the channel is deeper near the outer bank than it is near the inner bank. The greater depth on the outer side of the bend results in there being a higher velocity at the outer bank because of the greater mass of water compared to the friction from the bottom and sides. Also at the bend, the water's momentum carries the mass of the water against the outer bank. The greater velocity combined with the greater inertial force on the outer bank increase the competence and capacity. Erosion occurs on the outer bank or cut bank. The cut bank is steep and frequently undermined by stream erosion.
Meanwhile, the part of the stream channel near the inner bank is shallower. This shallowing results in less mass of water to over come the friction of the stream bed and thus a reduction in velocity. The velocity reduction results in a decrease in the competence and capacity. Deposition of the coarser fraction of the stream load occurs, leading to the formation of a point bar. Point bar deposition gradually produces flat, low-lying sheets of sand.
Over time, the position of the stream changes as the bend migrates in the direction of the cut bank. As oxbow bends accentuate and migrate two bends can erode together forming a cutoff and eventually leaving an oxbow lake.
The size of meanders has long been of interest to geomorphologists. Meanders come in many sizes. One obvious relationship is that big streams have big meanders and small streams have small meanders. Measures of the size of meanders include the meander wavelength (distance from the center of one meander to the next) and the radius of curvature of a meander (like the radius of a circle). Meander wavelength is proportional to streams width. More importantly, the wavelength is proportional to discharge. The greater the discharge the larger the meander, or, the greater the mass of water flowing down a stream the harder it is for the stream banks to turn back the mass of water. Meander wavelength is also inversely proportional to the clay and silt content. Since clay and silt are cohesive it is easier for banks rich in clay and silt to withstand the inertia-driven erosion on the outer bank. The stream is more readily turned by the cohesive bank. Smaller tighter meanders are produced where streams flow through clay and silt rich valleys.
Another characteristic measure of a stream's meandering nature is its sinuosity.
A stream's sinuosity, S = channel length / valley length
The sinuosity of a stream is a way the stream maintains a constant slope. The more sinuous a stream, the more gentle the slope. If tectonic uplift or subsidence occurs along the course of a stream, the stream can readjust its slope by changing its sinuosity.
A stream's width to depth ratio is also inversely proportional to clay and silt content. Streams flowing between banks rich in clay and silt are deeper and narrower while streams flowing between banks poor in clay and silt are broad and shallow.
At the extreme, where streams flow through beds of sand and gravel, they erode very wide and shallow channels, and take on a braided pattern. The water in a braided stream does not occupy a single channel but the flow is diverted into many separate ribbons of water with sand bars between. The separate ribbons continually diverge and re-merge downstream. The sand bars and channel positions frequently change during floods.
Braided streams (and broad, shallow single channel streams) have a lower hydraulic radius than single channel meandering streams of similar discharge. They also have a very large supply of coarse-grained bed load. In order to overcome friction and continue to transport their sediment load, the slope must increase (to increase the velocity and therefore competence). Braided streams flow on steeper slopes than single channel streams of similar discharge.
Considering the longitudinal (downstream) profile of a stream:
Local Grading: Where a stream flows from a gentler to a steeper slope, velocity will suddenly increase. At the point where the velocity increases (and the depth decreases and shear increases) competence and capacity increase resulting in increased erosion. Where that stream then flows from a steeper slope onto a gentler slope, the velocity decreases (competence and capacity decrease) and deposition will result. This process will erode away and fill in abrupt changes in slope resulting in a more even slope through the course of the stream. Young streams have many changes of slope resulting in rapids and falls. As streams mature, these gradually wear away.
The Big Picture:
The ideal graded profile of a stream is concave upward: steeper near the head or beginning and flatter near the bottom or mouth of the stream. The reason for this is that in the upper reaches of a stream its discharge is smaller. As streams merge with other streams their discharge increases, their cross-sectional area increases, and their hydraulic radius increases. As one goes downstream and the stream grows in size, the waters flow more freely (less friction). Less slope is required to maintain velocity (and competence). In the upper reaches, a small stream must be steeper to transport its sediments. The extra gravitational energy on the steeper slope is needed to overcome the frictional forces in the shallow stream.
Maintenance of Grade: If the slope is too gentle and velocity is too slow to transport the sediments being supplied by weathering and erosion, the sediments will pile up. This increases the gradient which causes the water to flow faster, which increases erosion and transport, which then reduces the gradient. In the lower reaches of a stream, where the discharge is greater, since friction is less, the stream need not be so steep to transport the load. If it were steeper than needed to transport the sediments, erosion would result. But this would decrease the gradient leading to a decrease in erosion.
It seems counter-intuitive but stream velocity generally doesn't decrease from the steep headlands to the flat plains, from the dashing mountain brook to the broad peaceful river. The broad lowland rivers have much greater discharge and hydraulic radius. They flow much more freely (e.g., the water doesn't have to dash around boulders in the stream). The net result is that velocity actually increases somewhat.
Equilibrium: When a stream has attained a graded profile, it neither erodes downward (degrades) nor builds its bed upward (aggrades). Rather it transports sediments from the source areas (headwaters and hills surrounding valley) to its end.
However, the ideal graded profile and equilibrium are seldom achieved, or not for extended periods of time, because conditions are constantly changing requiring streams to constantly change their grade. Changing climate can change stream discharge or sediment supply necessitating changes in slope. Uplift of headlands or lowering of sea level can cause slopes to increase, streams to flow faster and valleys to be eroded downward. Rising sea level or building of dams elevates streams' base levels and cause sediment to gradually aggrade upstream.
Meandering streams produce sheets of sand that are built laterally across the flood plain as a bend and its point bar migrates across the valley. Periodically, when the stream floods, sheets of mud (silt and clay) are spread across the flood plain. As flood waters spill out of the stream channel onto the adjacent land, the velocity suddenly decreases because of the sudden decrease in depth and increase in friction. The courser sediments (sand and course silt) are therefore deposited adjacent to the stream. Through many floods, natural levees are built along the banks of streams. They are highest near the river and gradually taper away from the river.
In some large river valleys, the flood plain may develop into a convex shape as levee deposits grow on the central portion of the valley. Streams that formerly fed as tributaries into the river may be cut off from the river by the broad levees. These yazoo streams then flow down the valley, parallel to the river, until they eventually meet with it farther downstream. The lower, poorly-drained margins of these convex stream valleys may also contain backswamps.
Stream Valley Evolution
Youthful Stream Valleys have steep-sloping, V-shaped valleys and little or no flat land next to the stream channel in the valley bottom.
Mature Stream Valleys have gentle slopes and a flood plain; the meander belt width equals the flood plain width.
Old Age Stream Valleys have very subdued topography and very broad flood plains; the flood plain width is greater than the meander belt width.
Rejuvenated Streams: At any stage in the development of a stream valley, if the gradient increases, for example due to tectonic uplift or drop in sea level, the stream will flow faster. This will result in a new period of vertical downcutting and development of a steep-sided V-shaped valley profile. The stream cuts into its former flood plain leaving incised meanders. Gradually the stream will erode the sides of its new valley and eventually develop a new flood plain lying at a lower level than the original flood plain. The original flood plain remains as a stream terrace.