# Science Briefing

The beauty of fractals may have real-world benefits in the field of aerosol dispersion. **RAP's Alexander Praskovsky and Eleanor Praskovskaya (RAP/ATD), along with NCAR associate director Walt Dabberdt, have used fractal geometry to examine the surfaces of smoke plumes and follow their dispersion in a wind tunnel.** The results appeared on 1 January in the *Journal of the Atmospheric Sciences*.

##### Walt Dabberdt (left) with Alexander Praskovsky and Eleanor Praskovskaya. (Photo by Bob Bumpas.)

The authors focused on fully developed turbulence, where large eddies are breaking into smaller ones that resemble the former but on a smaller scale. High-resolution video imagery was obtained for three cross-sections of a turbulent smoke plume in a wind tunnel at New York's Environmental Science and Services Corporation. NCAR Graphics software was used to analyze the imagery. The scientists confirmed fractal behavior for surfaces of constant aerosol concentration. This finding could help air pollution modelers represent diffusion more accurately.
"In many applications," they note, "it is necessary to know the effective area of the contact surface between contaminant and ambient air to estimate the rate of entrainment, diffusion, chemical reactions, wave reflection, and so on. This area, measured at an appropriate scale, is related to the fractal dimension of the interface." The authors' next step, now in progress, is to study concentration fields from the experiment more closely to see if they might be multifractal in character (fractals of different dimensions sharing the same space).

For many years, simple statistical models of daily precipitation have been unable to account for all of the longer-term variation over months or seasons. **This recurring problem, called "overdispersion" by statisticians, was addressed by senior scientist Rick Katz (ESIG) in a paper presented at the 13th Conference on Probability and Statistics in Atmospheric Sciences,** reporting on research partially funded by the Geophysical Statistics Project. The meeting was hosted last month in San Francisco by the American Meteorological Society. Rick and coauthor Marc Parlange (University of California, Davis) found that overdispersion may be treatable if regional-scale atmospheric circulation can be factored into the model.

##### Rick Katz. (Photo by Carlye Calvin.)

In their paper, Rick and Parlange examined a particular type of statistical model known as a chain-dependent process. It divides precipitation into two components, one for occurrence (for instance, rain vs. no rain) and the other for intensity (how much rain falls, given its occurrence). They used the model to represent time series of daily precipitation at Chico, California, and several other locations, then to compare the results with actual reports over a 78-year period. A simple chain-dependent model was "upscaled" (extended to longer time scales) to produce a standard deviation for January precipitation totals that is about 22% below the actual, interannual standard deviation. Even if more complex statistical models for daily precipitation are considered, the deviation is still underestimated by at least 16%.
When the original model is linked to a regional-scale circulation index, the estimated standard deviation rises to virtually match the observed value. "Perhaps this result, in which the overdispersion has apparently been eliminated, could be viewed as reflecting some degree of actual predictability," write Rick and Parlange. Though it involves upscaling, this research has implications for the reverse operation, popularly termed statistical downscaling. This technique can be employed, for instance, to translate the National Weather Service long-lead outlooks for monthly or seasonal precipitation into statistical information on a daily time scale. Likewise, downscaling could be used to convert the output of general circulation models into scenarios of climate change on the shorter time and finer spatial scales required in impact assessments.

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UCAR |
NCAR |
UOP**

**Edited by Bob Henson,
bhenson@ucar.edu**

Prepared for the Web by Jacque Marshall

Last revised: Thu Mar 30 11:46:20 MST 2000