Amanda Brown
ID: 300291567
Geog 319: Essay
1)Discuss the major controls on stream power for bedrock and alluvial rivers with particular focus on the roles of the exponentsmandnin the stream power law.
Introduction
Fluvial erosion has a primary role in altering the environment around us and as a result of its significance, it is not surprising that Tucker and Whipple (2002) argue that understanding the dynamics of river erosionis essential to constructing models of landscape evolution over long time scales. The rate that channels incise establishes the rate at which the surface landscape evolves and hence channel incision is the essential link between landscape and tectonics (Hancock, Anderson and Whipple, 1998).
It is gravitational potential energy that is the driver of the fluvial system, that gravitational energy is converted into another form and it is this transformed energy which has the power to erode. Stream power is the transformed energy and is often thought of as ability of flowing water to carryout geomorphic work. The main controls on stream power are slope, discharge and bed lithology.
Many equations have been developed in order to calculate the stream power and it is argued that the most applicable for bedrock incision is the stream power erosion law due to it being directly related to the physics of erosion (Howard and Kerby, 1983). For alluvial rivers Seidl and Dietrich (1993) suggest it is the sediment transport law that is appropriate. As is typical with any equation the stream power law is generalized. Unfortunately in order to simplify it some of the complexities of the process mechanics are obscured (Skylar and Dietrich, 2001). As a result a wide range of complex processes are characterised together under a single coefficient.
What is stream power?
Stream power is commonly described as the capacity for flowing water to carry out geomorphic work, as Bizzi and Lerner (2015) simplified,it offers a measure of the driving forces within a channel. It is gravitational potential energy that acts as the driver for the fluvial system. The gravitational potential energy is converted into kinetic form through the downslope flow of water, where due to the conservation of energy, any energy lost due to falling must be converted in to another form (Anderson and Anderson 2010).This transformed energy is what has the potential to erode channel beds or transport sediments.
As it is stream power that details fluvial erosion, it is therefore unsurprising that it has a significant effect on the fluvial system with Knighton (1999) arguing that stream power influences channel characteristics like that ofbedform type, channel pattern and processes like the migration of the channel or the bedload transport rate.
Stream power law
The development of the stream power equation is necessary because of the impossibility and expense of collecting all the data needed. By generalizing equations and using variables that can be interpreted remotely such as drainage area and slope gradient, calculations can be made for areas where it is either inaccessible or too expensive to collect data.
The main variables controlling channel erosion and sediment transport rate are that of slope, discharge and bed lithology. Calculating channel erosion or transport rates at large spatial and temporal scales, especially due to the variation of discharge over significant periods of time, can be difficult due to limited data. Howard and Kerby (1983) suggested thatupslope drainage area can be used as a proxy for that of dominant discharge, Howard, Dietrich and Seidl (1994)state the surrogate is possible due to the average long term incision
rate being proportional to the sheer stress exerted by the dominant discharge within the channel.
Many equations have been developed to help predict channel incision of a river into its bed. It is argued by Howard and Kerby (1983) that it is the Stream Power Law (1), of all that have been proposed, is the most applicable due to it relating to the physics of erosion. It is also relevant to a wide variety of studies due to its generality, however as Wipple and Tucker (1999) state, with such a generalization there are some poorly understood parameters.
The generalized and most frequently used stream power erosion law (1) is useful because there are fewvariables and can be measured against topographical data. (Howard & Kerby, 1983; Skylar & Dietrich, 2001).
E=KAmSn(1)
This model can also be used to calculate the sediment transport rate (2) which asSeidl and Dietrich (1993) state is the appropriate form for alluvial channels.The fundamental parts of the stream power erosion law and the transport law are quite similar in each equation, with incision being replaces by sediment transport rate.
qs = KQmSn(2)
Geomorphic parts of the equation
E=KAmSn
With E representing the erosion or incision rate, the variable K is as Whipple (2001) describes a dimensional coefficient of erosion that considers many factors such as the rock strength and the erosional capabilities of the fluvial system. A is defined as upstream drainage area which acts as a substitute for discharge and S represents the slope or stream gradient.
qs = KQmSn
Where qs represents the sediment transport rate and K is once again the dimensional coefficient. Q is the water discharge and S represents the stream slope.
Stock and Montgomery (1999) identify the exponent m as the representation of the discharge drainage area interaction which is weighted by the importance of discharge on incision and could vary between river basins due to variations in hydrological processes.Little information is available on the slope exponent n, perhaps due to the process involved not being completely understood. Although Whipple (2001) suggests it depends on the dominant erosion process. The n exponent is said to be directly associated to the degree of nonlinearity in the link between erosion rate and stream power (Whipple and Tucker, 1999). The exponentis also said to be important in determining the landscape response time.
Very few studies have reported the values for the exponents m and n. Howard and Kirby (1983) conducted a study in the anthropogenic Virginian Badlands to determine that m=≈1/3 and n=≈2/3 (assuming erosion rates are linearly proportional to bed shear stress).
The ratio m/n has been called the concavity index as it influences the speed with which the gradient changes as area increases (Anderson and Anderson, 2011).This reflects the shape a rivers longitudinal profile takes. Whipple and Tucker (1999) argued that the ratio is independent of the dominant erosion process and dependant on only the relative rates of increase of discharge. It is thought by many studies that the ratio has been shown to significantly influence the shape of stream profiles.
Whipple (2001) states that the m/n ratio is geometric term as a result of it being influenced by the downstream rates of increase in discharge and channel width and thereby does not change considerably in response to tectonic or climatic disturbances. This means that the ratio is predicted to fall between 0.35 and 0.6 which conforms to values calculated from field data. Larger values of m/n typically mean the river profile has greater concavity.
However Stock and Montgomery (1999) conducted a study in order to calibrate the equation (1), their results showed that there was no individual set of results for m and n that could be applied universally to all channels studied and that boundary conditions had a significant influence on the parameters.
Stream Power Law Assumptions
Skylar and Dietrich (2001) state the simplicity of the stream power equation comes at the expense of obscuring the complexities of the process mechanics. This means that a wide range of complex processes are put together under the same coefficient.Individually these processes would not usually be characterised together by a common stream power parameter (Howard et at., 1994). As a result the equation carries quite a few assumptions, the most significant being that parameters are kept constant over time and space.This is especially the case with K, which assumes that lithology and precipitation are unvarying and implies that slope is the only variable that may adjust in response to change in boundary conditions (Whipple and Tucker 1999). As a result the simple act of changing the channel from bed rock to that of alluvial cover would violate these assumptions.
In fact Seidl and Dietrich (1992) state that the exponent m and the coefficient K are particularly sensitive to climate variations.For example changes in the temperature, distribution and amount of precipitation affect the drainage-discharge area relationship which influences m.
The presence or absence of alluvium cover on a bed is mostly determined by the gradient (Howard and Kerby, 1983). Alluvial rivers traditionally have a lesser gradient and have an inverse dependence upon drainage area. Bedrock rivers however, are usually steeper lacking a sediment cover. It is not surprising that there is a difference in stream power between the two channel types when slope or gradient is a large control upon the equation. With a steeper gradient the stream power is likely increased. A channel bed with no alluvial cover, where sediment supply is limited, stream power is likely to concentrate on incision. However for an alluvial channel with an excess supply of sediment, a transport limited channel, stream power is instead likely to be used for transport.
Conclusion
Fluvial erosion and therefore stream power plays an important role in the evolution of the landscape. Many authors have developed equations in order to calculate stream power and the one argued to be the most applicable to bedrock incision is the Stream Power Erosion model (1) due to it relating to the physics of erosion. For alluvial channels it is the sediment transport equation (2) that is the most applicable.
The major controls on the equation are that of slope, discharge/upstream area and erodibility of the rock. The parameters m and n are not understood comprehensively, although m is thought to represent the drainage discharge area interaction and n is said to be directly associated to the nonlinear link between the erosion rate and stream power. N is also thought to be significant in determining the landscape response time. Howard and Kirby’s (1983) study of the Virginian Badlands determined that m=≈1/3 and n=≈2/3, although no single set of numbers can be applied universally to all rivers.
The ratio of m/n defines the longitudinal profile of a channel and is often called the concavity index. The ratio is thought to be particularly robust when facing climate variations and is predicted to fall between 0.35 and 0.6 which conforms to values calculated from field data.Often the larger the m/n ratio number is the more concave a channels profile is.
Due to the simplified nature of the stream power equations many complex processes are grouped together under a single parameter. This means that there some significant assumptions in order for the equation to hold true. An example is the assumption that the parameters such as dimensional coefficient is held spatially constant over time. It simply takes the widening of the channel or the addition of alluvial cover to void this assumption. The parameters K and m seem to particularly vulnerable to climate and simply takes a change in precipitation or temperature for the discharge area relationship to be influenced.
The stream power law is a powerful tool in order to understand the processes behind fluvial interaction with the landscape and provides a cheaper alternative to the labour intensive gathering of field data. However further study into understanding the constants K, m and n is needed due to assumptions being easily violated.
References
Book
Anderson, R. S., & Anderson, S. P. (2010) Geomorphology: The mechanics and chemistry of landscapes. Cambridge, New York: Cambridge University Press.
Howard, A. D. (1980) Thresholds in river regimes. In D. R. Coates & J. D. Vitek (Eds.), Thresholds in Geomorphology (pp. 227-258). Boston, London: Allen and Unwin.
Journal
Bizzi, S., & Lerner, D. N. (2015). The use of stream power as an indicator of channel sensitivity to erosion and deposition processes. River Research and Applications, 31(1), 16-27.
Hancock, G. S., Anderson, R. S., & Whipple, K. X. (1998). Beyond power: Bedrock river incision process and form.Rivers over rock: Fluvial processes in bedrock channels, 35-60.
Howard, A. D. (1980). Thresholds in river regimes. Thresholds in geomorphology, 227-258.
Howard, A. D., & Kerby, G. (1983). Channel changes in badlands. GSA Bulletin, 94(6), 739.
Howard, A. D., Dietrich, W. E., & Seidl, M. A. (1994). Modeling fluvial erosion on regional to continental scales. Journal of Geophysical Research - Solid Earth, 99(B7), 13971. doi:10.1029/94JB00744
Seidl, M. A., & Dietrich, W. E. (1993). The problem of channel erosion into bedrock.Catena supplement,23, 101-101.
Stock, J. D., & Montgomery, D. R. (1999). Geologic constraints on bedrock river incision using the stream power law.Journal of Geophysical Research: Solid Earth (1978–2012),104(B3), 4983-4993.
Tucker, G. E., andK. X. Whipple,Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison,J. Geophys. Res.,107(B9), 2179, doi:10.1029/2001JB000162,2002.
Whipple, K. X. (2001). Fluvial landscape response time: how plausible is steady-state denudation?.American Journal of Science,301(4-5), 313-325.
Whipple, K. X., & Tucker, G. E. (1999). Dynamics of the stream‐power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs.Journal of Geophysical Research: Solid Earth (1978–2012),104(B8), 17661-17674.