Ground Water Canada

Features Mapping Research
A groundwater modelling breakthrough

July 3, 2015  By Ground Water Canada

July 3, 2015, Laramie, WY — A University of Wyoming professor has made a discovery that answers a nearly 100-year-old question about water movement, with implications for agriculture, hydrology, climate science and other fields.

After decades of effort, Fred Ogden, UW’s Cline Chair of
Engineering, Environment and Natural Resources in the department of
civil and architectural engineering and Haub School of Environment and
Natural Resources, and a team of collaborators published their findings
in the journal Water Resources Research this spring. The paper, titled
“A new general 1-D vadose zone flow solution method,” presents an
equation to replace a difficult and unreliable formula that’s stymied
hydrologic modellers since 1931.

“I honestly never thought I would be involved in a discovery in my field,” Ogden said.


anticipates this finding will greatly improve the reliability and
functionality for hundreds of important water models used by everyone
from irrigators and city planners to climate scientists and botanists
around the country and the world, as well as trigger a new surge in data

In 1931, Lorenzo Richards developed a beautiful, if
numerically complex, equation to calculate how much water makes it into
soil over time as rainfall hits the ground surface and filters down
toward the water table. That equation, known as the Richards equation
and often shortened to RE, has been the only rigorous way to calculate
the movement of water in the vadose zone – that is, the unsaturated soil
between the water table and the ground surface where most plant roots

Calculating the movement of water in the vadose zone is
critical to everything from estimating return flows and aquifer recharge
to better managing irrigation and predicting floods. But RE is
extremely difficult to solve, and occasionally unsolvable. So, while
some high-powered computer models can handle it over small geographic
areas, simpler models or those covering large regions must use
approximations that compromise accuracy.

For decades,
hydrologists and other scientists have pursued a better way to estimate
vadose zone water. Cornell University Environment and Ecology Professor
Jean-Yves Parlange and Australian soil physicist John Robert Philip
battled one another in the literature, proposing new equations and
disproving each other — from the 1950s until Philip’s untimely death in
a traffic accident in 1999. Princeton’s environmental engineering and
water resources director Michael Celia published a partial solution in
1990 that is not reliable in all circumstances.

Ogden first
worked on the problem in 1994 as a postdoctoral researcher. He teamed
with Iranian hydrology engineer Bahram Saghafian, who was finishing a
Ph.D. at Colorado State University, to publish an equation that
estimates water “suction” in the vadose zone. In the early 2000s, Ogden
advised a Ph.D. candidate named Cary Talbot, a researcher with the U.S.
Army Corps of Engineers, on a project seeking a solution to the RE. The
two developed a new way to represent vadose zone water.

In more
recent years, the search continued, and a major National Science
Foundation research grant in 2011 enabled Ogden to bring additional
experts to the quest and use UW’s supercomputing power to test
prospective solutions.

Then, late last fall, just before the
large American Geophysical Union annual meeting, Ogden and his research
team discovered a novel solution, an elegant new equation that he
thought would equal the RE in accuracy while greatly reducing the
computing power needed to run it. He tested this solution with
precipitation data from his field site in Panama.

“We ran eight months of Panama data with 263 centimeters of rain through our equation and Hydrus,” Ogden said.

is an existing supercomputer model that uses RE. The results his model
generated had only 7 millimeters difference (two-tenths of one per cent)
from the results of the Hydrus model that employs Celia’s solution of
the RE.

“They were almost identical. That’s when I knew,” he
said. “I felt like the guy who discovered the gold nugget in the
American River in California.”

What’s next for the new equation?
First, it is the centerpiece of Ogden’s ADHydro model, a massive,
supercomputer-powered model that’s first simulating the water supply
effects of different climate and management scenarios throughout the
entire upper Colorado River Basin. From there, Ogden hopes other models
will incorporate it, too.

“I think, for rigorous models, it’s
going to become the standard,” he said. “With help from mathematicians
and computer scientists, it will just get faster and better.”

new pushes for data collection often follow technological advances,
Ogden explained. He hopes this discovery will bring soil science back
into relevance for water managers and lead to new soil data collection.

now have a reliable way to couple groundwater to surface through the
soil that people have been looking for since 1931,” Ogden said.

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