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Accuracy in groundwater research improves with Ogden’s new data model
Written by Natasha Wheeler Details

Published: 22 August 2015
Laramie – Studying how water flows through soil can help scientists forecast floods, estimate groundwater recharge, discover the affect of water table levels on plant growth, examine return water flow from an irrigation area back to the stream and more.
“There are a whole host of different kinds of problems in which people will need to solve for flows of water through soils,” explains Fred Ogden, Cline Chair of Engineering, Environmental and Natural Resources at the University of Wyoming (UW).
Looking at some of these challenges, Ogden and his team developed an equation to calculate water flows based on their physical understanding of the process. To validate their findings, they performed a lab study with a clear plexiglass pipe that was carefully packed with sand.
“We installed sensors to measure water content at different heights in the pipe and then connected it to a controlled system that mimicked the water table going up and down at different speeds,” he comments.
Ogden presented his research the project at the American Geophysical Union annual meeting in December.
Richards Equation
“The results were just amazing. Compared to the USDA solver for Richards Equation, which is called the Hydrus 1D, we did just as well,” Ogden notes.
Richards Equation, published in 1931, is a mathematical formula that was developed by Lorenzo Richards to calculate how much water seeps into the soil as rainfall hits the surface and moves toward the water table.
“It’s accurate, but it’s really hard to solve, and it’s not reliable. For any given instance of Richards Equation, there is no guarantee that we are going to get an answer,” Ogden comments.
But when it does provide an answer, Richards Equation is one of the most comprehensive methods that can be used in groundwater research. Ogden’s colleague at New Mexico Tech, John Wilson, suggested investigating similarities between his formula and Richards Equation.
“He said, ‘Your equation must be some form of Richards Equation because nothing else does that,’” Ogden says.
Sitting down with a blank piece of paper, Ogden worked through the math.
“It was a jawdropping moment because, I thought that maybe we had more than just an approximate solution. I dismissed that as a fancy or too good to be true, but it turned out to be true,” he remarks.
More reliability
Previously, Ogden had been among the scientists who had never taken Richards Equation seriously as a solution.
“Someone has to be really serious to write a model that solves the equation and then have no guarantee that they will get an answer, so people just kind of ignored it,” he comments.
Instead, researchers used approximate methods to find acceptable solutions for their work.
“Those methods are not as rigorous or robust. They don’t give us the right answer for the right reason, but they work,” he continues.
Now, with the discovery of a simpler model of the equation, Ogden hopes that scientists will quit ignoring it.
“Now that we have this robust, reliable method, hopefully people can take that collection of hydrologic properties data more seriously,” states Ogden. “Hopefully, it will start a discussion at USDA or in other places to reinvigorate some soil property data collection activities.”
Practical application
Armed with his latest discovery, Ogden will be traveling to Tuscaloosa, Ala. in the fall to work with the National Weather Service National Water Center, assisting them in using some of the hydrological model techniques that Ogden and his team developed at UW.
“We are thinking about flood predictions primarily, at high resolutions,” he explains.
Such information could allow scientists to predict when an individual creek will flood over the top of a road, for example.
“We could set it up so that we have a way to close that road. That’s our goal,” Ogden remarks.
Agricultural engineers may also benefit from the new information.
“They are interested particularly, in the fate of salts in the root zones,” he comments, hoping that his findings will hold the key to further discoveries.
New technology
Ogden expressed his amazement that another scientist had not yet discovered the new equation.
“It was a surprise when it happened, because of all of the other people that have worked on the problem,” he explains.
The next solution that is considered to be accurate, though still not always reliable, wasn’t published until 1990.
“That’s how hard it is to solve Richards Equation,” he notes.
But Ogden’s brother, a farmer in Colorado, was less shocked by his discovery.
“He said that he wasn’t surprised that it was me, because I am of the first generation of people doing this kind of stuff, really conditioned to think about using computers to solve these problems,” Ogden notes.
Older generations are more prone to pull out a piece of paper and a pencil to derive the equation by hand.
“We knew we couldn’t solve this equation by hand, and we had to use a computer to solve it all along,” he adds.
Improved method
Using the traditional equation and an appropriately large number of samples, there is a good chance that one or more of the samples will fail to produce a solution and the model, as a whole, will not be able to complete the simulation.
“Our method is guaranteed to give us an answer. It removes the penalty of using Richards Equation. We get the same accuracy, we get it much faster and it’s guaranteed to give us an answer,” says Ogden.
Natasha Wheeler is editor of the Wyoming Livestock Roundup and can be contacted at This email address is being protected from spambots. You need JavaScript enabled to view it..