Researchers determined what Yellowstone's famous hot springs would look like if coin-throwing tourists had not contaminated them.

The researchers used a mathematical model based on optical measurements that assess what causes the brilliant colors seen in the hot springs, The Optical Society reported. In the past no mathematical model existed that showed the physical and chemical variables of the iconic pools.

"What we were able to show is that you really don't have to get terribly complex - you can explain some very beautiful things with relatively simple models," said Joseph Shaw, a professor at Montana State University and director of the university's Optical Technology Center. Shaw, along with his Ph.D. student Paul Nugent and German colleague Michael Vollmer, co-authored the new paper.

Through a one-dimensional model for light propagation the team was able to reproduce the colors and characteristics of Yellowstone National Park's hot springs.

The researchers took measurements in the pools using "handheld spectrometers, digital SLR cameras for visible images and long wave infrared thermal imaging cameras for non-contact measurement of the water temperatures," the society reported.

In the case of the yellowed Morning Glory Pool, the researchers were able to simulate what it looked like between the years of 1880 and 1940, when it was significantly warmer. During this time the water was a deep blue, before a collection of trash, coins and rocks turned it yellow-orange and green. The colors are believed to be linked to a change in microbial mats caused by resulting lower water temperatures.

The study confirmed the relationship between shallow water temperatures and observed color.

"There are people at my university who are world experts in the biological side of what's going on in the pools," Shaw said. "They're looking for ways to monitor changes in the biology - when the biology changes, that causes color changes - so we're actually looking at possibilities of collaborating in the future."

The findings were published in a recent edition of the journal Applied Optics.