Wavelets are a relatively new - but increasingly popular - mathematical tool for analyzing data in the geosciences. Wavelets reexpress 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 geosystems with interacting scales. In this project, the investigators develop wavelet-based statistical methodology to address three multiscale geophysical problems. The first is to characterize scale-specific variances/covariances of atmospheric pressure time series from NOAA's Tropical Atmosphere Ocean buoy array. Because these series have gaps in them, the investigators construct special wavelets for computing statistically tractable wavelet coefficients. The second problem is to analyze atmospheric turbulence measurements collected by an aircraft. The investigators use statistical methodology 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. Here the investigators use wavelets to extract spatial gradients, to assess variations in area-mean precipitation, and to determine the variability in the estimated quantities using wavelet-based bootstrapping.
The motivation behind this project is to further a scientific understanding of how the atmosphere changes over time, over heights and over different areas. A better understanding of the atmosphere is important for mankind because of the key role that the atmosphere plays as part of the climate of the earth. Federal agencies such as NOAA and NASA (in cooperation with its Japanese counterpart NASDA) are actively collecting sets of data that directly measure how the atmosphere changes. These data sets, along with others collected under NSF sponsorship, are inherently complex to interpret. In this project, the investigators study these data sets using wavelets, which are a mathematical microscope for interpreting changes in complex data sets. The investigators develop new methods for using wavelets to study atmospheric changes. In the future, other investigators can apply these new methods to data sets collected in other areas of science such as oceanography, astronomy, agriculture and forestry.
