The Swamp Stomp

Volume 15, Issue 29

In 1931, Lorenzo Richards created an extremely complex equation to calculate how much water is absorbed into soil over time as rainfall hits the ground surface and filters down toward the water table. Until now, the Richards equation (RE), has been the only rigorous way to calculate the movement of water in the vadose zone, the unsaturated soil between the water table and the ground surface where most plant roots grow. Now, however, Fred Ogden, a University of Wyoming professor (UW), has developed a new equation to replace the unreliable RE.

After spending decades devoted to the task, 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 his team of collaborators published their paper, titled “A new general 1-D vadose zone flow solution method,” and introduced the world to his new equation.

Ogden and his team anticipate that their findings will greatly improve both the reliability and functionality of hundreds of important water models used by everyone from irrigators and city planners to climate scientists and botanists, as well as trigger a new flood in data collection.

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

RE has been so important over the last 64 years because calculating the movement of water in the vadose zone is critical for estimating return flows, aquifer recharge, managing irrigation, and predicting floods. The problem with RE, though, is that it is so complex that it is extremely difficult to solve, and in some cases even unsolvable. Therefore, while some high-powered computer models can handle the equation over small areas, simpler models or those covering much larger areas can only use approximations.

It is clear then why alternative methods have been pursued. It wasn’t until late last fall, however, that a new solution was found. Ogden then tested his solution with precipitation data from his field site in Panama.

Ogden said, “We ran eight months of Panama data with 263 centimeters of rain through our equation and Hydrus.” Hydrus is an existing supercomputer model that uses RE. The results of Ogden’s model only generated a 7 millimeter, or two tenths of 1 percent, difference from the Hydrus model.

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

The equation is now the centerpiece for Ogden’s ADHydro model, a massive supercomputer model that’s first simulating the water supply effects of different climate and management scenarios throughout the entire upper Colorado River Basin. After that simulation is complete, Ogden hopes that other models will adopt his equation as well.

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

The equation could prove even more important as technological advances call for new data collections. Ogden hopes that his discovery will bring soil science back into relevance for water managers and ultimately lead to new soil data collection.

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