UCAR > Communications > Staff Notes > January 1995 Search

Statistics Initiative:
A New Look At Old Problems

How can the rigor and power of modern statistical techniques be used to improve global climate models and the conclusions drawn from them? A small group of crosscutting researchers at NCAR is trying to address this and other questions. With support from NSF's Division of Mathematical Sciences, the NCAR statistics project is bringing statisticians to collaborate with in-house scientists during both short- and long-term visits to Boulder.

Photo of Rick Katz and Rol Madden
Rick Katz and Rol Madden. (Photo by Carlye Calvin.)

Coordinators of the project, tentatively funded for $3.6 million over five years, are Rick Katz, deputy head of the Environmental and Societal Impacts Group (ESIG), and Rol Madden, deputy head of the Climate and Global Dynamics Division (CGD) Climate Analysis Section. The two senior scientists embody the collaboration sought out by the project: Rick is a statistician, Rol an atmospheric scientist. "There's not a lot of collaboration today between the two disciplines," says Rick.

It's acknowledged that some types of statistical practices are firmly embedded in the routine practice of meteorology. For instance, high and low temperature forecasts and precipitation probabilities are produced twice daily by a computer at the National Meteorological Center through a statistical program that compares the latest computer model output to similar situations in the past. This output then guides forecasters at local offices before they issue the [eventual] public outlook.

However, Rick says, up to now the appropriation of statistical techniques to atmospheric science has been fairly haphazard, occurring largely after such techniques have been applied in other areas such as biomedical and geological sciences. "Because there isn't a close collaboration, often atmospheric scientists aren't up to date on research innovations in the statistical sciences." He foresees the NCAR initiative helping lead to a "knowledge-based" pool of techniques, as opposed to the traditional "sequential" approach. "Statistics can help in designing experiments to search for phenomena predicted by theory or to compare fields that vary in all four dimensions. But until we get the communication going [between scientists and statisticians], we won't know all of the areas where we might make specific headway." In early 1993, NSF's Directorate for Mathematical and Physical Sciences solicited proposals in the geophysical sciences for large projects that would encourage multidisciplinary collaboration. NCAR's statistics project is one of the first recipients of these awards. "I think NSF feels that a lot of difficult problems don't get solved if all funding is on a narrow, disciplinary basis. There already had been some university- oriented programs supporting collaboration between mathematics and the geosciences," says Rick. However, he adds, these were fairly small and focused on collaboration between individual investigators rather than groups.

Coinvestigators on the initiative from NCAR, including Linda Mearns, Kevin Trenberth, Joe Tribbia, and Dave Williamson (all of CGD), serve along with Jack Herring (Mesoscale and Microscale Meteorology Division) as members of the internal steering committee. An advisory panel with eight members, mostly statisticians or mathematicians affiliated with universities, is chaired by Dick Jones, a former NCAR visitor and expert in statistical applications now at the University of Colorado Health Sciences Center in Denver.

While coordinating day-to-day details of the initiative, Rick and Rol have undertaken an extended search for a senior statistician with interests in atmospheric science to serve as a resident manager throughout the five-year project term. Jones and Harvard statistician Arthur Dempster have provided statistical expertise during the search for this long-term leader, which is now in progress.

Other staff have come on board through the initiative as well. Associate scientist Tim Hoar and postdoctoral statistician Steve Cherry joined the project last year. Two other postdoctoral researchers working closely with the project are Luning Li, a statistician supported by the Advanced Study Program, and Mike Chin, an electrical engineer with interests in oceanography who is being supported by both ASP and the statistics project. Two more postdocs are expected to arrive later this year. A number of university-based researchers have visited Rol and Rick for varying lengths of time through the initiative.

Over 30 participants, including graduate students and recent Ph.D.s, came to Boulder 6–19 July for the initiative-sponsored colloquium "Applications of Statistics of Modeling the Earth's Climate System." (A summary of the colloquium lectures has just been released as NCAR Technical Note TN-409+PROC.) Along with tutorials on climate, objective analysis, scaling, and spatial ARMA (autoregressive moving average) processes, there were more specialized lectures on a wide variety of statistical problems in the atmospheric and oceanic sciences. "The colloquium was meant to act as a catalyst in generating interest for these kinds of activities," says Rick, "and we feel it was a major success." Even the difficulties were instructive: "There was evidence that we indeed had different disciplines talking to each other. We had terminology barriers, but we confronted them head on."

Rick cites one example hinting at the distance between the two disciplines. The Yule-Walker recursion technique is a popular statistical method for modeling time series. Cocreator Walker happens to be Sir Gilbert Walker, the British mathematician sent to India in 1904 to work on prediction of the Asian monsoon. Walker named the now-famous Southern Oscillation and, later, Jakob Bjerknes gave Walker's name to the zonally aligned circulation cells in this region. According to Rick, "Some people have heard of both the Walker circulation and the Yule-Walker recursion but have no idea that they refer to the same person."

Although most of the personnel and projects with the statistics initiative thus far have come from within CGD, the coordinators are eager to involve other divisions. Any interested NCAR researchers are invited to contact Rick or Rol. "We hope that the statisticians we bring on board will be not simply consultants but active participants in research," says Rick. "We are especially interested in applying some recent developments in statistical science dealing with the theory of random fields and with inferential techniques for nonlinear, chaotic time series."

Initiative organizers believe there could hardly be a better way to address some of the problems remaining in global climate modeling than through statistical technique. According to Rick, "It is often said that ‘mathematics is the language of science.' In a similar vein, it could be said that ‘statistics is the language of uncertainty,' and every aspect of climate modeling involves uncertainty." --BH


Says Rick Katz: "In all areas of life, including scientific research, ‘chance' agreements are not as surprising as we might suppose." As an example drawn from elementary probability theory, Rick offers the following riddle: "How many people would have to be present at a cocktail party so that there is a better than 50-50 chance that at least two of them have the same birthday?" Explains Rick, "Most people would guess the answer to be 183, disregarding 29 February, but actually only 23 people would be needed." Case in point: there have been 42 U.S. presidents to date, and two of them--James Polk, the 11th president, and Warren Harding, the 29th--share the same birthday, 2 October. The probability of at least one pair of matched birthdays among n people, disregarding leap-year birthdays, is:

1 - (365/365) (364/365) . . . ((365 - n + 1)/365)

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Edited by Bob Henson, bhenson@ucar.edu
Last revised: Wed Mar 29 12:32:53 MST 2000