Perspectives: Mapping Turbulence

By Rex J. Fleming | July 1, 2009
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Let’s stop flying into turbulence to find it! Let’s avoid beverage spills in our laps and flight attendants bouncing around the cabin. There exists a unique form of GPS processing with subsequent mathematical procedures to produce a national map of turbulence. Introduced at the AEEC Symposium in Minneapolis in early April, the method and its impact on aviation are summarized below.

Science has learned the traits of turbulence, if not its ultimate causality. Turbulence draws energy from the mean flow at large spatial scales and dissipates the same amount by viscous forces at very small scales — when it exists, it is continuous.

Turbulence causes $200 million in losses per year for U.S. airlines. This number pales to the impact of turbulent disruptions in the new operational procedures planned for the Next Generation Air Transportation System (NextGen).

IATA CEO Giovanni Bisignani has said that saving one minute of each commercial flight would save 5 million metric tons of CO2 emissions and $3.8 billion in fuel costs per year. Such savings are possible with future activities of "flow corridors" (interstate highways in the sky) and "choreographed ascent/descent" (enhanced continuous descent approaches). However, turbulence would have a dramatic impact on these applications, significantly reducing fuel efficiencies and compromising safety.

The method for detecting turbulence processes rays from GPS satellites to a greater depth than currently performed for location purposes. Consider a single ray from a satellite to a GPS receiver in your hand. The signal travels at the speed of light through a vacuum, but is slowed (delta time delay introduced) by the effects of temperature and water vapor in the atmosphere. A variety of processes remove other error sources in time delays. One knows when turbulence occurs somewhere between your receiver and the satellite by calculating the time variance of the signal, though this cannot tell you where that turbulence exists along that path.

In smooth (laminar flow) conditions of the atmosphere, the mean signal of the time delay is a slowly varying function of temperature and water vapor changes. When turbulence occurs, the laminar conditions are disturbed and high frequency variability occurs (variance of the GPS signal delay about the mean).

Consider a grid over North America with N points (100 x 100 horizontal points by 25 vertical levels to 40,000 feet = 250,000 points). The spatial distribution and intensity of the turbulence can be computed if there are more rays (R) than points N. Simulations suggest the ratio of R/N = 1.2. GPS receivers at 7,500 surface sites (chosen from more than 14,000 airports in the United States) and on 1,000 active commercial aircraft would provide approximately 300,000 rays in a typical example, with five rays, each a few seconds apart, from multiple satellites.

The concept of using variance information from radar, infrared and lasers to quantify turbulence intensity has already been demonstrated, but such aircraft sensors have failed to see far enough in advance to issue timely warnings. This passive GPS turbulence approach (with sufficient rays) provides a complete 3-D picture over a region with new maps every 10 to 15 minutes.

The main elements of the turbulence approach are already patent protected. GPS receivers uniquely process the variance information. Aircraft avionics and ground equipment communicate the variance data in special formats to a Turbulence Processing Center (TPC), which then computes the geometry of the GPS rays. The TPC has the computer power to produce national maps and tailored products to users with a need to know — including a coded bit stream allowing cockpit displays to show turbulence areas along intended routes.

The data processing is not a walk in the park. There are several mathematical nuances employed (found necessary through numerous simulations) that make it work. And while these are difficult financial times to begin such a major effort, the need is great to bring order to our turbulent airspace.

Rex J. Fleming, Ph.D., has degrees in mathematics and atmospheric science from the University of Michigan. He is an elected fellow in the American Association for the Advancement of Science. He can be reached at (303) 494-0837.

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