Drainage density
First described by Robert E. Horton, drainage density is defined as the total length of channel in a drainage basin divided by the total area, represented by the following equation: [1] The quantity represents the average length of channel per unit area of catchment and has units
Horton (1945) used the following equation to describe the average length of overland flow as a function of drainage density:[2] Where
Conversely, if the right-hand side of the equation is less than zero, Bras et al.[5] determine the hillslope to be unstable, and small erosive structures, such as rills, will tend to grow and form a channel and increase the drainage density of a basin.
In this sense, "unstable" is not used in the sense of the gradient of the hillslope being greater than the angle of repose and therefore susceptible to mass wasting, but rather fluvial erosive processes such as sheet flow or channel flow tend to incise and erode to form a singular channel.
Water is carried through channels much faster than over hillslopes, as saturated overland flow is slower due to being thinned out and obstructed by vegetation or pores in the ground.
[7] Because of the more extensive drainage system in a higher density basin, precipitation entering the basement will, on average, travel a shorter distance over the slower hillslopes before reaching the faster-flowing channels and exit the basin through the channels in less time.
[8] More of the water entering the drainage basin during a precipitation immediately following a rainfall event exits quickly through streams and does not become infiltration to contribute to baseflow discharge.
[7] In a relatively low drainage density environment, the lower average discharge results predicted by this relation would be the result of the surface runoff spending more time travelling over hillslope and having a larger time for infiltration to occur.
The increased infiltration results in a decreased surface runoff according to the water balance equation.
[7][10] The falling limb occurs after the peak of the hydrograph curve and is when overland flow is decreasing back to ambient levels.
In higher drainage systems, the overland flow reaches the channels quicker resulting in a narrower spread in the falling limb.
[10] According to the proportionality put forth by Gregory and Walling,[9] as drainage density increases, the contribution of baseflow to the falling limb of the hydrograph diminishes.
Montgomery and Dietrich (1989)[3] determined the following equation for drainage density by observing drainage basins in the Tennessee Valley, California: [3] Where ws is the mean source width, ρw is the density of water, R0 is the average precipitation rate, W* is the width of the channel head, ρs is the saturated bulk density of the soil, Kz is the vertical saturated hydraulic conductivity, θ is the slope at the channel head, and φ is the soil angle of internal friction.
Materials with a low hydraulic conductivities, such as clay or solid rock,[6] would result in a higher-drainage density system.
In a basin with a higher vertical hydraulic conductivity, water more effectively infiltrates into the ground and does not contribute to saturated overland flow erosion, resulting in a less developed channel system and therefore lower drainage density.
Vegetation prevents landslides[11] in the source area of a basin that would result in channel formation as well as decrease the range of drainage density values regardless of soil composition.
[11] While there is significant variation between species, plant roots grow in underground networks that holds the soil in place.
The increased soil strength also protects against surface runoff erosion, which hinders channel evolution once it has begun.
This effect imposes an upper limit to the total reduction in drainage density that vegetation can result in.
Coarse-grained sediment like sand would have a higher hydraulic conductivity and are predicted by the equation to form a relatively higher drainage density system than a system formed by finer silt with a lower hydraulic conductivity.
Forest fires, both natural and unnatural, destroy some or all of the existing vegetation, which removes the stability that the plants and their roots provide.
Computer simulation experiments have validated that drainage density will be higher in regions that have more frequent forest fires.
[7][10] The falling limb occurs after the peak of the hydrograph curve and is when overland flow is decreasing back to ambient levels.
In higher drainage systems, the overland flow reaches the channels quicker resulting in a narrower spread in the falling limb.
At effective rainfalls of greater than 10-14 inches, the decrease in sediment yield is interpreted to be the result of increasing vegetation cover.
[12] Increasing precipitation supports denser vegetation coverage and prevents overland flow and other methods of physical erosion.
The region features steep slopes, high relief, an arid climate, and a complete absence of vegetation.
[13][7] Because the slopes of hillslopes are often greater than the angle of repose, the dominant erosional process in the Caineville badlands is mass wasting.
[13] This is interpreted by Howard to be a result of the critical source area needed to support a channel increasing.
The Caineville Badlands are located in an arid environment, receiving an average of 125mm of precipitation per year.
