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The Power of Statistics in Flood Prediction

Posted on December 9th, 2013
Tibebu Ayalew hopes his graduate degree in engineering will allow him to contribute to society.

Tibebu Ayalew hopes his graduate degree in engineering will allow him to contribute to society.

IIHR graduate student Tibebu Ayalew has a dream — to develop a statistical method of flood prediction that works across multiples scales of time and space. The beauty of this approach, Ayalew says, is that unlike simulation models, it requires no calibration, and it can work anywhere, even in ungauged basins and in the face of changing climate.

Researchers have a long way to go to make this dream a reality, however.

Two major schools of thought compete in the area of flood prediction, Ayalew explains. The first, rainfall-runoff simulation, uses a numerical model to predict the magnitude of peak floods. The second is the statistical analysis method — there are several statistical approaches for flood prediction. The approach Ayalew is pursuing is based on the statistical self-similarity of peak floods, or scaling theory. This method is also known as nonlinear geophysical flood theory. The theory assumes that a special mathematical relationship called power law exists between peak floods and drainage areas. Ayalew, who is a PhD student working with Witold Krajewski, is working to link the parameters of the power law formula to the physics of runoff generation in drainage basins of various sizes. In his study, he analyzes data within a basin, including runoff; flow velocity; the shape of the landscape; rainfall characteristics such as intensity, duration, and direction and speed of movement; and the dry periods between storms.

If we get the physics behind the power law parameters right, Ayalew says, researchers can use data to predict peak floods anywhere in the basin. After gaining significant insights through numerical simulation of the small Clear Creek basin, Ayalew is now analyzing observational data from the much larger Iowa River basin, to see if the theory will hold up. “It’s a big leap,” he says.

Flooding near Dubuque Street and City Park in Iowa City, 2013.

Flooding near Dubuque Street and City Park in Iowa City, 2013.

Although Ayalew hopes someday to use the statistics-only approach to flood prediction, he’s currently limited by the amount of observational data available to further advance the theory. So, he uses the CUENCAS model to further establish and test the theory with systematic numerical experiments. Whenever Ayalew notes a peculiar trend in the observational data that he can’t explain physically, he uses systematic simulation experiments to understand what is going on.

“The beauty of using simulation as a diagnostic framework is that we can set up different scenarios of rainfall and catchment physical variables (e.g., river network, wetness, land use, slope) and see how the peak-discharge scaling parameters change,” Ayalew explains. Thus, the investigation goes both ways: researchers study the observational data to determine if the predictions of the simulation model make sense, and they also use the model when they don’t clearly understand the physical meaning behind certain features of the data.

The statistical approach to flood prediction could make a real difference in developing parts of the world where most streams are ungauged. Satellite data can complement the approach and makes flood prediction possible in these areas, Ayalew says.

Power law exists in many natural systems, Ayalew says, but not all researchers agree that it can be successfully applied to flood prediction at the event scale. Ayalew will be presenting his research at the upcoming AGU Fall Meeting, and he says he expects some pushback from the audience. He believes the effort will ultimately be successful. “I think we are making a significant contribution,” he says.

After two years of work, one published paper, and one more in press, Ayalew says he’s grateful to have found a research area that he finds so fascinating. His adviser, Professor Witold Krajewski, gave him the leeway to explore several areas before focusing on one. It’s just one of the reasons Ayalew says Krajewski is an excellent mentor.

“I consider myself lucky to be given the chance to work with Witek,” Ayalew says.

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