"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.
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.