One of the fastest-growing segments of livestock farming in the United States is aquaculture, according to Roz Naylor, a Stanford professor of environmental Earth system science. And like any other form of livestock, fish generate waste.

But just what happens to the waste produced by coastal aquaculture has largely been a matter of conjecture.

"For many years, people have assumed that because of the ocean's size, because of the energy in its currents, that any substance you introduced into the ocean would quickly be diluted into concentrations that were barely detectable," said Jeff Koseff, professor of civil and environmental engineering.

Now Koseff and Naylor, together with Oliver Fringer, assistant professor of civil and environmental engineering, and a team of colleagues, have developed a computational model that allows researchers to predict where the effluent from a coastal fish farm would go. The answer may not always be appealing to down-current swimmers and surfers.

"We discovered that the state of the natural environment around fish pens can dramatically affect how far waste plumes travel from the source," Koseff said. "This suggests that we should not simply assume 'dilution is the solution' for aquaculture pollution."

The simulation incorporates the influence of variables such as tides, currents, the rotation of the Earth and the physical structure of the pens in calculating the dispersal pattern of the waste.

"These plumes actually remain quite coherent at very long distances from the source and could become a major pollution problem in coastal regions," Koseff said.

Naylor and Koseff said the model should prove valuable in selecting appropriate sites for future fish farms. Knowing the amounts of feces and uneaten food that are generated by pens, researchers will be able to predict how that dissolved waste will travel from a particular location, given local conditions.