Stream Parameters
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 the surface and is slowest along the stream bed and banks due to friction.
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).
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 measured by estimating the cross sectional area of a stream at a given point, for example by measuring its width and estimating its average depth, and velocity can be estimated by timing how long it takes for a floating object to move a measured distance down stream (velocity = distance / time). This is rather crude, especially since the near surface velocity is the maximum velocity in the stream and not the average. A more accurate method is to measure the depth of the stream at 20 points across the stream and measure the velocity at each point at a depth of 0.6 of the way to the bottom, where the average velocity is found. The velocity may be measured with a simple propeller anemometer. After the 20 depth and velocity measurements are made, the average depth is multiplied by the stream width. This area is multiplied by the average velocity determined from the 20 velocity measurements. The most accurate method is with the construction of a concret weir at apoint 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. These records can be found on a USGS web site (check Geolinks).
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.
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 higer 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.
Stream Dynamics
Perennial and Ephemeral Streams
Gaining (effluent) streams receive water from the groundwater. In other words, a gaining stream discharges water from the water table. 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. Gaining streams are perennial streams: they flow year around. Losing streams are typically ephemeral streams: they do not flow year round. They only flow when there is sufficient runoff from recent rains or spring snowmelt. 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 for inputs from tributary streams. The rainwater that infiltrates the ground spreads out the peak flow following a rain event.
Flood Erosion and Deposition: As flood waters rise, the slope of the stream as it flows to its base level (e.g., the ocean or a lake) increases. Also, as stream depth increases, the hydraulic radius increases thereby making the stream more free flowing. Both of these factors lead to an increase in stream velocity. 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.
Land Use, Geology, and Flooding
Runoff
Recall the hydrologic cycle (Precipitation = Runoff + Infiltration + EvapoTranspiration). 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.
Floods
About 5% of U.S. land is in a flood plain.
Many streams reach the bankful stage on average once in 1.5 years and overtop their bank every 2 to 3 years.
Recurrence intervals, or the expected time interval between floods of a given size (discharge, depth, etc.) can be estimated from historic records. Recurrence intervals can be estimated from a record of annual peak discharges on a stream with records for a sufficiently long number of years. From recurrence interval plots, geologists can predict the average time interval between floods of a given size. For example, "100 year floods" are simply floods of a size that are expected (based on historic records) to recur on average once every 100 years. The probability of equaling or exceeding the peak discharge of a "100 year flood" in any given year is 1 percent. A 100 year flood could happen in any given year. They are not spread evenly in time. Because of the short time span of most stream gage records (several decades) it is difficult to predict precisely the probability or frequency of very large floods ("100 year floods" and "500 year floods").
Following are two plots for data recorded over about a 100 year time span at the Flint River gaging station between Montezuma and Oglethorpe, Georgia. Data are from the US Geological Survey. The first plot is the record of the annual maximum flood discharge. The second is a recurrence interval plot. Note that the largest flood recorded at the gaging station was the 1994 flood with a maximum discharge of 136,000 cubic feet per second. Note how this point stands head and shoulders above the other floods for the previous century.
A line fit through the data points on the recurrence interval plot allows for estimates of the annual peak discharges to be expected at various frequencies. For example, a 10 year flood should be expected to have a peak discharge of 60,000 cfs or so, a 100 year flood might be expect to have a discharge of nearly 120,000 cfs, and a 500 year flood a dischare of around 153,000 cfs.
*Note however that the 1994 flood falls off the line on the recurrence interval plot. It was the largest flood recorded at this location on the Flint River during the century. But that doesn't mean that it is necessarily a "100 year flood." If a much longer record were available for this gaging station, and a number of very large floods were recorded, the recurrence interval of large floods would be better defined by actual data. The 1994 flood would then either lie on the "straight" line or a curving line might be found to fit the data better for large floods. Assuming that a longer record showed the straight line below to be the correct predictor for the recurrence of large floods, then the recurrence interval for the 136,000 cfs peak flood discharge of 1994 should be about 250 years. Likewise, the recurrence interval can be predicted forl peak discharges of various sizes. For example, reading off the recurrence interval plot and assuming the line fit is correct for large floods, annual peak discharges of 40,000 cfs and 160,000 cfs should be expectedto recur on average once in 4 years and 700 years respectively.
data from US Geological Survey
recurrence interval (T) = (N + 1) / M
Land Conversion - Urbanization
Conversion of land from forest to rangeland, plowed fields and especially developed urban land:
decreases infiltration
increases runoff
which in turn:
increases land erosion
increases stream discharge
increases storm peak discharge
increases sediment load (stream turbidity)
Urbanization, in particular,
decreases infiltration
decreases water table levelsincreases runoff
increases flood frequencypeak discharges occur more quickly after a rain event
Sediment load in streams and deposition in marine and terrestrial basins has increased by about 70% due to human influence.
A common method for decreasing the runoff associated with urban development and for increasing infiltration is the construction of artificial recharge basins.
Geologic Controls
Streams that flow across crystalline rocks (e.g., granite, gneiss) with low porosity and therefore low infiltration are prone to flash floods ("flashy") and flood events with high peak discharges. Low infiltration means little base flow. Floods are short and sudden and severe. This is a similar situation to heavily paved urban areas.
Streams that flow across porous sedimentary rocks with a high degree of infiltration and a large baseflow are buffered from floods. Peak discharges are spread out.
Meandering Streams: At a bend in a stream the water's momentum carries the mass of the water against the outer bank. Water piles up on the outer bank making it a little deeper and the inner bank a little shallower. The greater depth on the outer side of the bend also leads to higher velocity at the outer bank. The greater velocity combined with the greater inertial force on the outer bank erodes a deepr channel. The deeper channel reinforces the velocity increase. The inner bank remains shallower, increasing friction, thereby reducing the velocity.
Where the depth and velocity of the water on the outer bank increase so do the competence and capacity. Erosion occurs on the outer bank or cut bank. Where velocity of the water on the inner bank decreases so do the competence and capacity. Deposition occurs, leading to the formation of a point bar. 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 leaving an oxbow lake.
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.
Graded Streams: Considering the longitudinal (downstream) profile of a stream:
Where a stream flows down a steep slope velocity will increase which will result in increased erosion. Where that stream then flows onto a gentler slope velocity decreases and deposition will result. This process will reduce the slope of steep stretches and increase the slope of flatter stretches resulting in a more even slope through the course of the stream.
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. 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. 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 on average, on the large scale from the steep headlands to the flat plains, from the dashing moutain 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 somwhat.
Braided Stream patterns are found where there is a very large bed load where there is either a high sediment supply or the stream lies on a loose, unconsolidated bed of sand and gravel. In braided streams the stream does not occupy a single channel but the flow is diverted into many separate ribbons of water with sand bars between.