During a dry day in April 2010, scientists trying to trace the source of pollution in Silver Springs dropped 30 pounds of fluorescent dye into several wells and sinkholes a few miles away.

What happened next did more than show the pollution woes facing the state's springs are more serious than anticipated.

It also highlighted a flaw in how water pumping permits are routinely issued throughout much of Florida, suggesting the state has issued thousands of permits while underestimating their impact. It may also explain why some of the state's springs have lost some or all of their flow.

State officials base all their permitting decisions on computer models that use a false assumption. The models assume that the aquifer flows at a steady rate through layers of sand and gravel.

Actually, what's beneath our feet is called karst — a landscape made of limestone that's full of holes both big and small, where water sometimes shoots through as if sprayed by a firehose.

The dye test gave a vivid illustration of the difference. The scientists running the test picked their drop sites with help from one of the state's models. The model predicted how fast a liquid would trickle along underground toward the spring. Different zones would give the dye a 2-year trip, a 10-year trip and even a 100-year trip.

But when they dropped the dye in, the stuff rocketed through the aquifer. It zoomed across half the predicted 100-year distance in just six months.

"It was going a mile a month," said Pete Butt, the scientist who oversaw the test. The dye would have traveled even faster had the test been conducted during the rainy season, he noted.

Current and former state officials acknowledge that there's a false assumption behind all their modeling. They accept it as something they have to live with and work around.

But critics argue the computer models are as full of holes as the karst itself. They are so far off-base "they shouldn't be used to make decisions," said David Still, former executive director of the Suwannee River Water Management District.

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Much of Florida's water for drinking and sprinkling comes from its aquifer. Because it lies deep in the earth, the state's water districts rely on modeling in making decisions about how much can be pumped out without harming nearby springs, lakes and wetlands, not to mention other water users.

"It's the primary tool that's used for looking at what the impacts of groundwater withdrawals will be," said Ken Weber, who until last year oversaw permitting for the Southwest Florida Water Management District, commonly known as Swiftmud. The agency approved more than 1,000 permits for its 16-county area last year and rejected only two.

The computer models — a series of mathematical equations based on data from wells and other sources — have also been crucial to the state's effort to track nitrate pollution from fertilizer, sewage and animal waste that have fouled the springs and fueled the growth of toxic algae blooms.

Florida's water districts have been relying on computer models since the late 1970s, Weber said, and the models have gotten better over the years. But they all suffer from the flaw exposed by the Silver Springs dye test. They all assume the aquifer is filtered through layers of sand and gravel.

"It assumes the aquifer is a sandbox," said Todd Kincaid, a geohydrologist critical of the state's computer models. "The water flows through the porous spaces between the grains."

But what lies underground around the state's approximately 1,000 springs is karst. The holes in karst function as speedways for flowing water as well as pollution.

"Things travel a lot faster than was previously thought," Weber said. That means that when pollution spills into the ground, "that stuff can get into the water supply much faster."

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Darrin Herbst, now in charge of Swiftmud's permit program, contended that his staff can tweak the models to fit what they see pumping doing to the aquifer, so there should be no problem.

However, he acknowledges their model tweaking did not foresee what happened three years ago in Plant City: Farmers trying to protect their crops during a freeze pumped so much water that the aquifer dropped 60 feet in just days. As a result, 140 sinkholes opened up throughout the region. "The magnitude caught us off-guard," he said.

The models still do all right when they are focused on projecting the aquifer's flows on a regional scale — say, covering from Central Florida to the coast — because "you can be off by quite a bit but it doesn't matter," Weber said. But looking at a smaller area for individual permits is "a lot trickier.''

A lack of information about what's underground is the big problem, studies show.

"Very little has been done as far as travel time and flow path mapping at springs in Florida," a 2008 geological study of the springs along the Santa Fe River noted in criticizing the inaccurate models. Dye tests in that area showed "travel times in this system were … up to one mile per day," far faster than what the models predicted.

Harold "Hal" Wilkening, who heads up the division of water resources at the St. Johns River Water Management District, conceded that the sand-and-gravel model "is not going to be as precise or reliable for a karst landscape."

But creating a more accurate one is nearly impossible given all the fissures and cracks, he said.

"There really isn't any way around it unless you have a lot of money to spend to find all those conduits underground," agreed Weber.

Not true, said Kincaid. He developed a karst-based computer model — at the behest of Coca-Cola.

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Coca-Cola was operating a bottled water plant near High Springs and became concerned pollution from nearby farms might contaminate its source of water.

According to Kincaid and Coca-Cola vice president Jonathan Radtke, the company hired Kincaid to put together a more accurate model. It took four years and $400,000.

When it was done in 2007, Kincaid said, they presented it to officials from the state Department of Environmental Protection, three water management districts and the U.S. Geological Survey.

"Coca-Cola said (to the state officials), 'We'll give it to you for free, give you the software to run it, send your guys to the courses and show them how to run it.' They said no," Kincaid recalled. "Because it was built by a corporation, they couldn't touch it."

Still, who was the head of the Suwannee River water district at the time, said his staff never told him about the alternate model. If they had, he said, "I would've taken it."

Coca-Cola gave up on the idea and no longer owns the bottling plant, Kincaid said. But state officials continue to resist changing their model even though they know it's wrong, he said. "They don't want to have any impediment to permit issuance," he said. The current computer models let them continue cranking out water-use permits, so "why would they want to mess with that?"

But as the springs sputter and dry up, Kincaid said, it exposes what's wrong as surely as that dye test: "Either we saw all this stuff coming and we're happy with it, or the models are wrong."

Craig Pittman can be reached at craig@tampabay.com.