Glass Half Full (roughly speaking)

It takes a model to measure subsurface water

The next time you sip a glass of spring water, consider this: Before it got to your lips, that water was soaking through soil, creeping along basalt crevices or flowing through porous volcanic rock. It nurtured microbes, carried dissolved minerals and may have spread the byproducts of human activities. Its pivotal role in the environment has made groundwater a headline topic in human health, waste management and water supplies for growing communities.

One number — 924 million — indicates how vital groundwater is to Oregon. That’s the number of gallons that the U.S. Geological Survey estimates were pumped from Oregon’s aquifers on an average day in 2000. More than 80 percent went to agriculture, most for irrigation.

Large as that number is, it barely begins to tell the story. It is in the subsurface — difficult to see or measure — where the groundwater drama unfolds, and where water availability and purity are subject to the vagaries of geology. Here, uncertainty is a fact of life. And that’s where OSU mathematicians are focusing their efforts to improve the models — equations translated into software code — that help water managers predict the behavior of this unseen resource.

“We really don’t know what’s in the subsurface, and we never will know,” says Malgorzata Peszynska, associate professor in the Department of Mathematics. “You can run seismic waves through it and get a relative idea of how one layer is related to another layer. You can drill observation wells and collect data, but you still don’t know.”

Born and raised in Warsaw, Poland, Peszynska has been working to improve subsurface models for almost two decades. Her love of math goes back to her youth. Undaunted by the teacher who told her there was no future in mathematics for a woman, she received a Ph.D. in the subject at the University of Augsburg in Germany. Her dissertation focused on mathematical techniques for describing liquid flow through porous materials.

In 1994, an invitation to work with one of the field’s leading lights, Jim Douglas Jr. at Purdue, brought her to the United States. Before joining the OSU math department in 2003, she conducted research with Mary F. Wheeler at one of the nation’s leading centers for subsurface modeling, the Institute for Computational Engineering and Science at the University of Texas.

Now, with grants from the U.S. Department of Energy and the National Science Foundation, she is working with students, postdoctoral researcher Son-Young Yi and co-principle investigator and math department chair Ralph Showalter to refine mathematical methods and develop new approaches for simulating groundwater flow.

The researchers are focusing on numerical and computer models. It goes without saying that these sets of equations are complex. They include terms for the velocity of water movement, the porosity and permeability of rock layers and the pressure exerted by water percolating into an aquifer from mountain ridges and other high places.

By simulating water flow through these systems, models can provide insight into how much water is available for human uses and other purposes, but complexity carries a cost. It can add days or weeks to computing time, even on today’s fast computers, such as OSU’s 73-dual-processor SWARM machine in the School of Electrical Engineering and Computer Science.

So the research team’s goal is to develop techniques that can achieve higher accuracy and run in less time. One approach is to simplify details that, in the final analysis, are marginal. That is, they don’t make the model significantly more accurate. The result is what researchers call an “upscaled” model.

“For example,” Peszynska says, “in fractured materials (bedrock), we know there are periodic structures separating blocks of clay (or other impervious materials). Instead of trying to simulate the flow at this scale, we try to come up with an upscaled model of this kind of phenomenon.” The goal is a solution that is close to the original model but does not require as much computational power.

Another goal is to link models that operate at one level — water movement through sand grains, for example — to those that work over a broader scale, such as an entire watershed from mountain ridge to valley floor.

“The use of models that are suitable for laboratory experiments to describe processes on the scale of a watershed will bring any computer to its knees,” says Showalter. “We’re trying to connect information at the microscale to the big picture, and for that we need new mathematical systems that at least give the computers a chance.”

Other OSU faculty members are working on related problems. In the Department of Civil, Construction and Environmental Engineering, Dorthe Wildenschild conducts experiments to understand how fluids behave in the spaces between sand grains. She and Ph.D. student Mark Porter use high-performance X-ray tomography at the Argonne National Laboratory in Illinois to see how air mixes with drops of oil and water in such tight quarters. The speed of these interactions is a critical factor in treating groundwater contaminated by toxic chemicals.

Meanwhile, the speed of model simulation is a factor in the research. “We fly out to Chicago and do the pore-scale experiments in three to four days,” says Wildenschild. “It takes Porter several months to run an equivalent simulation at that small scale on the high-performance computer (SWARM) here on campus.”

In the same department, Brian Wood has worked with Peszynska, Showalter, Enrique Thomann and Ed Waymire in math to characterize groundwater flow in porous materials. Wood focuses on the application of upscaling to the subsurface and to engineered porous systems such as chemical reactors, bioreactors in wastewater plants and sand filters used to clean drinking water. Wildenschild, Wood and other OSU engineers are also collaborating with scientists at the Department of Energy’s Pacific Northwest National Lab in Richland, Washington.

The OSU research couldn’t come at a better time. The need for better models is growing, says Michael Campana, a hydrogeologist and director of OSU’s Institute for Water and Watersheds. Officials who manage water supplies in places such as Oregon’s Klamath, Umatilla and Willamette basins, need to predict availability as demand grows and climate conditions change.

Models are useful approximations of the real world, says Campana, but “uncertainty can stem from the data or from imperfections in the model. It’s a real problem, and it’s getting worse. People are using models to look further into the future. Water managers are increasingly asking what a changing climate will mean for their water resources in 50 years or more. If we give them a number and tell them it could be 30 percent more or less, that’s not good enough.”

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