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Stream Power and Flood Events

This post is about physics but I will try to keep it interesting. To start on our journey, there are two types of energy - potential and kinetic energy. Potential energy is stored energy and kinetic energy is the energy of movement. Water behind a dam is potential energy, water moving through a dam and turning a turbine is kinetic energy which can be used to create electricity which can be stored as potential energy in a battery or used as kinetic energy through an outlet. Stream power is a measure of the kinetic energy of a stream as it moves substrates which give streams their course.

Small debris flow
Sediment being delivered from what is normally a dry channel - that event had a lot of power.

Stream power is a pretty simple calculation that measures the amount of pressure that streams exert on their channels. Stream power is a function of the density of water (about 1000 kg per cubic meter), gravity (9.8 meters per second squared), discharge (cubic meters per second), and the slope of the stream. The first two parameters are constants - or nearly so as density changes with more particles in the water and gravity differences with elevation changes are negligible for streams. Discharge, a measure of the amount of water that moves down the stream per unit time is typically measured in cubic feet or meters per second (1 cms = 35.3 cfs). Discharge changes over time and is how we measure the magnitude of a flood event. And the slope of the channel changes throughout the stream's course. Slope tends be be higher in headwaters and flatten out as the stream nears its receiving waters (see post of the River Continuum Concept for more about predictable changes in stream channels as streams move downstream). Slope is also greater in riffles than it is in runs or pools. Of all the parts of the calculation, discharge is the most significant as it the most easily changed and it varies the most. During flood events, other parameters may vary but their changes are insignificant relative to how much discharge changes during a flood event.

How discharge is measured
How stream discharge is measured - in the stream power equation, discharge is the variable that varies the most in a flood.

Source: USGS How Streamflow is Measured


More importantly, stream power is a useful measure of stream competence - the maximum particle that a stream can move. This is what engineers care about - they want the infrastructure that they design to stay in place! For the angler, it is what causes changes and damage to streams. Increase the power of a flood and you increase the damage that it can cause. In the last few years, we have all see the power of streams (for example, see Thoughts on Floods - 2021 edition) and how they ruin infrastructure and alter streams. Similarly, stream capacity is how much sediment can be moved by a particular flood event - essentially a cumulative measure of a flood event's power.

Squirrel Rock, Cheat River, WV
Squirrel Rock in the Cheat River in West Virginia. This rock moved a couple of feet during a flood when I lived in WV.

Source: West Virginia History on View, Squirrel Rock


In graduate school at West Virginia University, I took a class in fluvial geomorphology, essentially a study of how water moves sediments and forms channels. It was a fascinating class with a field trip down the famed Gauley River during "Gauley season", the six weekends in the fall when Summersville Lake is lowered over 100 feet. Gauley season is federally mandated for the purpose of whitewater recreation and it is one of the best whitewater experiences anywhere. I will never forget hitting a rock - named "Dildo" because if you hit it, you're screwed - and watching people fly out of the raft, including our professor who threatened us all with F's if he had to swim. But I digress...

Rock climbers on Squirrel Rock, Cheat River, WV.
Another view of Squirrel Rock with rock climbers for perspective.

Source: West Virginia History on View, Rock Climbers on Squirrel Rock in Cheat River


In West Virginia, the "big one" was the 1985 "Election Day Flood" which occurred when the remnants of Hurricane Juan stalled over Virginia and West Virginia. It was the most damaging flood on the Cheat River, the watershed in which I did my dissertation research, in the river's history and one of the most damaging floods in the history of the United States at that point in time. Morgantown is less than six miles from the Cheat River so geologists / geomorphologists in Morgantown have studied the flood extensively. It has been too long for me to remember the details but Squirrel Rock is a behemoth of a monolith, something like 100 million tons in weight. The 1985 flood moved this rock; slide it downstream a few feet, as best I remember. It was chilling to think of the power of that flood.


Stream Power, Competency, and Sediment Transport


It is not just during flood events where water is moving sediments. In fact, many streams do as much "rearranging" during baseflow to bankfull levels as they do in flood events. Anyone that has fished a sandbed stream - like those of Wisconsin's Central Sands region, the Driftless north of Interstate 90 and southwest of Interstate 94, the Lower Wisconsin River, and many other streams in the Midwest - has experienced how often and quickly these streams change. Even in the gravel/cobble streams of much of the Midwest, smaller sediments are being rearranged.


The Hjulström curve explains the relationship between particle size (grain size on the X-axis), current velocity (flow speed on the Y-axis), and whether particles are eroded, transported, or deposited. To put grain size - the X-axis - in perspective, clay particles are less than 0.0039 mm, silt ranges from 0.004 mm to 0.0624 mm, sand is from 0.0625 mm to 2.0 mm, gravel is from 2.0 to 64 mm, cobble from 64 to 256 mm, and boulders short axis is greater than 256 mm (10 inches).

Source: By Hjulströms_diagram_sv.PNG: Karrockderivative work: Karrock (talk) - Hjulströms_diagram_sv.PNG, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=8258823


To walk through the Hjulström curve, we can think of flow speed (note that the axes are both logarithmic) as a measure of stream power and grain size as a measure of how difficult it is to begin moving a particle (erosion) and keep it moving (transport). Once current velocity drops to a critical velocity, a particle of a particular size will no longer be transported and will be deposited. One rather interesting phenomenon is that smaller particles take more energy (flow velocity) to start moving due to the cohesion among particles (think clay). But once a small particle begins to move, it takes very little current velocity to keep it moving. Only later did I figure out that this explained the chronic brown-water state of the Crawfish River and its aptly named tributary Mud Creek, the home waters of my youth. And the larger the larger the rock, the harder it is to move and keep moving. Pretty straightforward and intuitive.

Upper Peninsula (I think) river
A northern river that mostly flows over bedrock is going to move less sediment as the particles are so large.

We, of course, have made it more precise - you may say more complicated - than what I presented above as we further studied the relationship between current velocity, particle size, and transport (see Shields formula and diagram). For example, flat rocks like pieces of shale or slate are more easily moved than are rounder rocks. This might also be applicable to the "face rocks" of LUNKER structures which seem to be moved fairly commonly in flood events.

Post-flood Timber Coulee Creek
Upper Timber Coulee after the stream had receded from a flood event - the smaller particles are still in suspension whereas at baseflow, the stream is crystal clear.

The Hjulström curve is a good starting point and it is mostly correct. Larger floods with greater current velocities move larger "particles" - like Squirrel Rock. And larger floods have a greater stream competency and move more and larger substrates.


Flood Events


As I am writing this, we are less than a week past the floods of the northern part of Yellowstone National Park and the surrounding area, so floods, again, are on our minds (I often write these well ahead of time so they can be edited later). (Edit - and more recently a huge swath of the central US, most notably, Kentucky had massive floods that has killed over two dozen people.)

While we have experienced no shortage of floods around Wisconsin and the Driftless, for me, 2018 is "the big one". The intense rains of late-August followed by early-September rains over saturated ground meant that not only were the floods intense, they were long-lived. The first round of rain broke several dams, including Jersey Valley, the largest impoundment in the area.

LUNKER structures after a flood
LUNKER structure left high and dry by a flood event which means the heavy face rocks on them also were moved.

We can think about floods in two ways - there are those that happen quickly and tend to pass quickly (flash floods) and those that more slowly accumulate from upriver precipitation. Flash floods tend to be more common in small, steep streams whereas areal floods are less common but occur more frequently in larger rivers. In this case, "the big one" was the Great Flood of 1993 that inundated much of the Mississippi and Missouri Rivers. As for flood power, the peak of the 1993 flood was 541,000 cfs (15,300 cms) which crushes anything we can experience in smaller tributaries. By comparison, the peak discharge at La Farge on the Kickapoo River in 2018 was a little less than 20,000 cfs (566 cms) but the river is much steeper than is the Mississippi River which added to the Kickapoo's flood power.

Isolated pool after flood moved the stream
Bohemian Valley Creek's old channel after the stream was re-arranged in August and September of 2018.

While stream power is a function of discharge, slope, and some basic physics - gravity and the density of water are the other parts of the the equation - stream competence is a measure of stream power and what is available to be moved by water. On a larger river - like the Mississippi - there are few large substrates to be moved whereas in headwater streams which are closer to a source of substrates, they can have large competencies due to the amount of material available to be moved.

West Fork Sports Club, Avalanche, WI
Previous floods removed "face rock" - large dolomite rocks - from the LUNKER structures on the West Fork - a measure of the 2018 flood's power.

Why this all matters and why we care is that floods alter that landscape. Ultimately, the measure of a flood is how much "rearranging" it does. 2018 was significant because of how much material it moved and how much it impacted people - the other true measure of a flood event. Streams get rearranged and maybe the stream work that money and effort was put into changes but that all pales in comparison to people's houses, livelihoods, and lives being taken away.

Knick-point waterfall
A number of these small knick-point waterfall were created followin the 2018 flood event. It is bascially the stream finding its new elevation.

The August 2021 flood peaked on the Kickapoo River at La Farge at about 3,000 cfs (85.0 cms). The 2018 flood - the largest in recorded history on the Kickapoo at La Farge - peaked at about 17,000 cfs (481.4 cms). Assuming that the slope and density of water did not change (that is both floods carried similar amounts of suspended sediments), the stream power was 5.7 times greater in the 2018 flood.


Stream Competency


I find the idea of stream competency - how much material a stream moves - quite interesting. Take one of my favorite places, the Lower Wisconsin River, with its shifting sands and ever changing nature. While each grain of sand is small and light; I would assume the Lower Wisconsin River has a huge annual competency as the sand at the boundary layer between the sand bottom and the water is always moving.

Lower Wisconsin River sandbar
A large sandbar on the Lower Wisconsin River - with a bit more water, this is underwater and the sands are shifting.

I have no idea how the annual competency of the Lower Wisconsin compares to that of your average Driftless Trout stream that had a decent flood event. It certainly takes an amazing amount of sand grains to equal the mass of Squirrel Rock but the Lower Wisconsin Riverway is basically a sea of sand particles.


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