Pi me a river: A meandering tale of pi, rivers, and water quality

Article: Dwivedi, D., C.I. Steefel, B. Arora, M. Newcomer, J.D. Moulton, B. Dafflon, B. Faybishenko, P. Fox, P. Nico, N. Spycher, R. Carroll, and K.H. Williams (2018), Geochemical Exports to River from the Intra-Meander Hyporheic Zone under Transient Hydrologic Conditions: East River Mountainous Watershed, Colorado, Water Resources Research, 10.1029/2018WR023377.

 

It’s Pi Day, Pi Day, gotta get down on Pi Day

Every year on March 14th, scientists, engineers, and mathematicians dig into their favorite type of pie. While I’m a firm believer that you never need a special occasion to do so, on this particular day it is in celebration of one of the most famous numbers: pi (π). Pi is a number that goes on and on (check out a million digits here), but just taking the first few digits it is roughly equal to 3.14. It is the number that you get when you divide the distance around a circle (circumference) by the distance across the circle (diameter). While this is important if you are ever trying to find the area of a circle, pi also pops up in several other places, including instances where the shape of things in the environment have an impact on how they function. A recent study led by Dipankar Dwivedi showed how this can be the case for rivers, which is where pi can actually help us to understand what is happening.

Figure 1. The Yellowstone River meandering across a valley CC BY-NC-SA 2.0 (Source: jjjj56cp)
Real rivers have curves

If you’ve ever been around a river, you’ve probably noticed the fact that they are not straight. Rather, they have twists and turns as they flow from one point to another. It’s in these curves that pi appears. In 1996, a scientist named Hans-Henrik Stølum came up with a theory about the curvy paths that rivers take. He was interested in the sinuosity of rivers, which is measured by taking the actual length of a river channel between two points and dividing it by the most direct distance between those two points (Figure 2).

Figure 2. The calculation of sinuosity for a river (Source: JV Wilkening)

Based on a lot of math and simulations about how water flows (you can find out more in this video, which also served as the inspiration for this post’s title), he proposed that the average sinuosity of all rivers across the globe should be equal to pi. It’s still up for debate whether this is actually the case, especially since humans have done a lot to change the course that rivers actually take (check out a previous envirobite here). You can see data for a number of rivers across the globe here. Nevertheless, understanding the curvy courses that rivers take is still important, even if the sinuosity is not always equal to pi.

Some water chemistry with a side of pi

A recent study led by Dipankar Dwivedi revealed one way in which curves in rivers can play a role in the water quality of the river. While we often focus upon the water that is actually flowing in a river channel, that’s not the only water in the area. There is also water in the ground right next to the river, which can interact with the river water and the deeper groundwater. This middle zone is what scientists refer to as the hyporheic zone (Figure 3).

Figure 3. Cross-section of river showing the hyporheic zone between the river channel and the groundwater (Source: JV Wilkening)

In this study, the scientists were particularly interested in the curvy sections of rivers, and how they could impact how nutrients and metals are moving between the river and the hyporheic zone. This can affect the quality of the river water, which is important for the plants and animals that live in around the river. They also wanted to know how this might change when there are different amounts of water flowing in the river, since this can change a lot between really rainy and really dry periods. In order to find out, they took measurements of a curvy section of a river in Colorado and also used a computer model to test various scenarios. They found that these areas within the river curves can act as either sources of nutrients and other compounds or, conversely, as sinks that take these in from the river flowing around them. They act as sinks during times that the flow in the river is high, and as sources when the flow in the river is low (Figure 4).

Figure 4. The hyporheic zone within the river curve can act as a sink during times of high flow (left) and as a source during times of low flow (right) (Source: JV Wilkening)

 

A meandering path from pi to water quality

Dwivedi’s study showed how the shape of a river can play a role in the water quality of the river, but the exact role will change depending on other conditions such as how much water is flowing in the river. It is these sorts of changes that make environmental research both challenging and really important. As humans continue to change the environment around them, we need to know how the environment will respond. While Pi Day can be a great excuse to eat a lot of pie, it’s also an excellent time to celebrate the ways in which pi is used to help understand the shape of the world around us which can also tell us something about how it is functioning. So while you enjoy that slice of pie this March 14th, be sure to take a moment to celebrate all the science and math using one of our favorite numbers!

References:

Dwivedi, D., C.I. Steefel, B. Arora, M. Newcomer, J.D. Moulton, B. Dafflon, B. Faybishenko, P. Fox, P. Nico, N. Spycher, R. Carroll, and K.H. Williams (2018), Geochemical Exports to River from the Intra-Meander Hyporheic Zone under Transient Hydrologic Conditions: East River Mountainous Watershed, Colorado, Water Resources Research, 10.1029/2018WR023377.

Stølum, H. H. (1996). River meandering as a self-organization process. Science271(5256), 1710-1713.

 

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Jeannie Wilkening

Jeannie Wilkening

I am currently a PhD student in Environmental Engineering at UC Berkeley where my research focuses on ecohydrology, which means I look at interactions between ecosystems and the water cycle. Before coming to Berkeley, I did my undergraduate in Chemical Engineering at University of Arizona and an MPhil in Earth Sciences at University of Cambridge, where my research focused on biogeochemical cycling in salt marshes. When I'm not in the lab, I enjoy knitting, hiking, watching too much Netflix, and asking strangers if I can pet their dog. Twitter: @jvwilkening

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