Don Percival         Principal Mathematician         EIS Department         Applied Physics Laboratory         University of Washington	In recent years, wavelets have become increasingly popular for analyzing data in the geosciences. Wavelets re-express data collected over a time span or spatial region such that variations over temporal/spatial scales are summarized in wavelet coefficients.Individual coefficients depend upon both a scale and a temporal/spatial location, so wavelets are ideal for analyzing geo-systems with interacting scales. While mathematical wavelet theory is mature, use of wavelets in the geosciences has, to date, met with mixed success, mainly because of the largely descriptive nature of their usage, with little attention paid to sampling variability. The full potential of wavelets cannot be realized without advances in statistical theory. In this project, wavelet-based statistical methodology is being developed to address three multiscale geophysical problems. The first is to characterize scaled-specific variances/covariances of atmospheric pressure time series from NOAA's Tropical Atmosphere Ocean buoy array. Because these series are `gappy,' special wavelets are being constructed for computing statistically tractable wavelet coefficients. The second problem is to analyze atmospheric turbulence measurements collected by an aircraft. Statistical methodology is used to combine wavelet coefficients with aircraft heights to determine scale/height variations of winds. The third problem is to assess spatial/temporal variations in ground-based radar rainfall measurements. Wavelets are used to extract spatial gradients and to assess variations in area-mean precipitation. The variability in the estimated quantities will be assessed using wavelet-based bootstrapping. For all three problems, the proposed wavelet-based methods promise a clear improvement and should broadly impact the analysis of other multiscale geophysical data.