Can scientists keep the lake that no one has ever seen from disappearing?

That question may sound like a riddle. But it holds the key to the economic well-being of the Texas Panhandle -- a semiarid region that has been transformed into a cornucopia of cotton, grain sorghum, wheat and corn by irrigation.

The Panhandle draws its irrigation water from the world's largest underground lake, or aquifer, the Ogallala. Formed millions of years ago by runoff from the Rocky Mountains, the Ogallala stretches from the Texas Panhandle to South Dakota, underlies parts of eight states, covers an area about the size of California, contains about as much water as Lake Ontario and provides 30 percent of water used for irrigation in this country.

It also is drying up.

Not much rain falls on the Panhandle, and all but a tiny fraction of what does fall evaporates before it can make its way through the claylike soil of the region and replenish the aquifer.

In Texas alone, 70,000 water wells have been dug into the aquifer since broad-scale irrigation was introduced after the Dust Bowl era of the 1930s. (In the entire Ogallala, there are 170,000 such wells.)

"If you had a big bucket of water with 70,000 straws in it, there's only one thing that can happen over time to your water table: It's going to drop," said William Lyle, professor of agricultural engineering at Texas A&M University.

The water in the Ogallala does not flow freely; it is mixed with sand and gravel. As a result, the areas most heavily drilled are the ones where the depletion problem is greatest. Fully 70 percent of the water depletion in the Ogallala has occurred under Texas.

Parts of the Panhandle have used up more than half the water in the portion of the aquifer beneath them, and an Economic Development Administration report two years ago estimated that by the year 2020 two-thirds of the water stored as of 1977 in the aquifer beneath Texas will be gone.

"We know we're losing our water," said Jim Bell, who manages a 20,000-acre farm just west of here and who each year plugs up a few more of his irrigation wells that have gone dry. "We've just got to learn to use it less -- and better."

Irrigation water, in short, is treated here as a nonrenewable resource -- like coal or oil or anything taken from the ground.

Conservation, until recently, has been considered the region's only hope of maintaining the productivity of its multibillion-dollar agricultural industry. And with energy costs having driven up the price of drilling fourfold in the past decade, farmers here are born-again conservationists. As a result of improvements in irrigation efficiency and a slow reversion to dryland farming, net water depletion in the region from 1979 to 1984 was half that of the preceding five years.

But conservation does not create water; it only slows its depletion. Scientists now are experimenting with two approaches, both disarmingly simple, that may prolong the life of the aquifer beyond what conservation alone could accomplish.

One is the secondary recovery of water. It involves placing the aquifer's wet sand under enough air pressure to break the water's surface tension on each grain of sand. Surface tension is estimated to keep half of the aquifer's water from being withdrawn by normal drilling.

The second approach involves the artificial recharging of the Ogallala by drilling wells to channel rainwater back into it. This technique, tried numerous times, has always failed because the rainwater carries silt that clogs wells. However, experiments with low-cost filtration systems show promise.

"If these two techniques are fully realized, I am confident we can extend the life of the aquifer by at least 100 years," said Robert Sweazy, director of the Water Resources Center at Texas Tech University here.

A. Wayne Wyatt came up with the idea of secondary water recovery. His story sounds like something from a biography of Thomas Edison or Eli Whitney.

Wyatt is manager of the High Plains Underground Water District, a water authority that represents farmers in 15 Panhandle counties. At home, he is a gardener and putterer. In a backyard experiment, he filled a bucket with sand, soaked it with water, covered it, punched some holes in the bottom and measured how much water flowed out by the force of gravity. Then, using the valve stem of a tire and a small pump, he forced air into the bucket. More water dripped out.

"I took my dumb little test to the scientists at Texas Tech, and they thought I was crazy and pretty much told me so," Wyatt said.

"Ground-water recovery is a billion-dollar business," explained Sweazy. "We figured if something as simple as that would work, someone would have done it long ago."

But Wyatt persisted and eventually got a $250,000 state grant to replicate his experiment in the field. The results have been encouraging.

"Basically, we're finding that if you pump air in for about a week, the water table around the injection well rises significantly. What you're doing is forcing the water that remains in the unsaturated area of the aquifer down . . . , where a regular, existing well can pull it out," said Sweazy, now Wyatt's biggest fan.

The artificial-recharge experiments involve taking the storm water that accumulates in the 16,000 natural playas of the Panhandle, filtering it and channeling it underground into recharge wells created alongside water wells.

Playas are shallow, clay-bottomed depressions, two or three feet deep and perhaps 30 acres in surface area, that collect rainwater. The problem with getting the water down into the aquifer before it evaporates has always been the clogging from silt, but Sweazy says he thinks he is conquering it with advances in filtration.

Skeptics, and there are plenty, doubt that either technique will prove inexpensive enough for widespread use. Farmers now pay an average of $50 an acre-foot (the quantity of water, 43,560 cubic feet, that would cover one acre to a depth of one foot) for irrigation water. Both systems would cost almost that much to get the water into the aquifer, much less to pump it out. "If artificial recharge slows the depletion rate by just 10 percent, that would be an optimistic estimate," said Lyle of Texas A&M.

Lyle finds the advances in irrigation efficiency more promising. In the old days of cheap energy, cotton farmers might have used 16 or 20 inches of irrigation water; now the norm is roughly half that.

Everything from the size of the drip in irrigation water to the timing of the application has been modified to improve efficiency. Irrigation efficiency, on the average, has increased to 80 percent from 60 percent in the past five years.

There has also been a slow, steady reversion here to dryland farming, the method used by the fathers and grandfathers of today's farmers. Irrigation peaked here in 1982, said Sweazy, and it has begun what is projected to be a slow decline. Typical dryland yields for cotton are half what they are for irrigation farming -- but the cost per acre also is halved.

The problem is that dryland farming is risky; a drought year can wipe out an entire crop and put a farmer under. Farmers have cut the risk by furrow-diking their fields -- creating dirt mounds every few feet between the cotton rows to capture whatever rain that falls.

All of these approaches have brought some unaccustomed optimism to the Panhandle. "People keep coming out here wanting to write that we are in a crisis over water," Wyatt said. "Well, the truth of the matter is, we aren't."

Sweazy added, "Conservation, recharge, secondary recovery, irrigation efficiency -- a little here, a little there, it all adds up."