Colorado State Researcher Hopes Mathematicians Can Help Solve Problems that Water Causes in Mathematical Models of Atmosphere

The problem with mathematical models that attempt to mimic global water circulation is water itself, and a professor of atmospheric science at Colorado State University is seeking help with the challenge.

Water vapor and clouds play a crucial part in the atmospheric branch of the earth’s hydrological cycle, but they also play havoc with attempts to describe that process through computer-based mathematical models. David Randall of Colorado State joined a Feb. 20 symposium at the American Association for the Advancement of Science annual meeting in Washington, D.C., to talk about the problems and to seek solutions.

In a presentation from 3-6 p.m. with four other geophysical scientists, Randall presented no new, research-based information to an audience made up primarily of applied mathematicians. Rather, he provided some simple information on water vapor and clouds in the atmosphere and outlined some of the difficulties so-called Global Atmospheric Models have encountered.

His remarks, and questions he hoped the audience would raise, may spark a new approach to the modeling difficulties, he said. Randall likened the event to bringing together the great mathematician John von Neumann and popular television weatherman Willard Scot to discuss water vapor, clouds and how to represent them in numerical form.

"It’s a very, very messy problem for a number of reasons," Randall said. "For example, water tends to be very lumpy. You have a wet spot (in the atmosphere) a few kilometers across, then a dry spot, then another wet spot, and so on.

"The motion of air in the vicinity of clouds is especially complicated," he said. "As soon as air enters a cloud its motion becomes turbulent, and that, too, is a real problem-causer for mathematical modeling."

Scientists know that water evaporates from oceans and land and may change phase (e.g., turn from water to vapor to water to ice) several times during the average eight to nine days it remains airborne before precipitating out as rain or snow. Water is crucial in energy absorption and transfer. Evaporating a kilogram of water takes about the same amount of energy as burning 25,000 100-watt light bulbs for one second.

Meanwhile, water condenses into clouds, warming up the atmosphere. Thunderstorms in particular, Randall said, move water and energy around in the troposphere, the five to 10 miles of air above the earth’s surface in which weather takes place.

"Thunderstorms can carry air to the top of the troposphere in 30 minutes," he said. "A thunderstorm is like an express elevator, and thunderstorms have a tremendous effect on the flow of energy through the atmosphere."

Meanwhile, radiation–sunshine and infrared wavelengths reflected from earth–interact with clouds and water vapor. Clouds reflect sunshine back to space, cooling the planet off, but by trapping infrared, clouds can heat the planet.

These relatively simple atmospheric phenomena make modeling difficult, so much so that certain important mathematical methods used in Global Atmospheric Models have been scrapped. Randall, who enjoys the mathematics of his work, hopes the atmospheric scientists-applied mathematicians’ interchange will spur new, fruitful ideas on both sides.

"Water’s a nightmare," he said. "Within the atmospheric science community, there are some of us who are mathematically inclined and some who are not, and even most who are inclined to deal with modeling flee from the complications of water. It’s a dirty mess, mathematically speaking, but some of us like it because it makes the problem of understanding the atmosphere much more interesting."