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   Yanling Yu  
      Oceanographer IV  
      Polar Science Center  
      Applied Physics Laboratory  
      University of Washington  

   Don Percival  
      Principal Mathematician  
      EIS Department  
      Applied Physics Laboratory  
      University of Washington  

   National Science Foundation  

This project is to develop the statistical theory needed to assess changes in ice thickness distributions and to apply wavelet methods to analyze ice draft measurements from submarine cruises spanning the years 1976 to 1997. This effort will advance the knowledge and understanding of Arctic sea ice and how its distribution varies both spatially and temporally. Because ice thickness data are significantly autocorrelated and have distributions that differ markedly from the Gaussian (normal) distribution, standard statistical tests for assessing changes in distributions cannot be used.

The proposed effort simplifies the nature of the non-Gaussianity by partitioning the ice measurements into different types according to thickness. This partitioning leads to series that are binary-valued, thus yielding a simple non-Gaussian distribution to deal with.

The binary-valued series are still highly autocorrelated, but the nature of this autocorrelation can be quantified in an interpretable manner using the Haar wavelet variance. The wavelet variance decomposes the sample variance into components, each of which is associated with a different scale. This decomposition provides a characterization of how Arctic sea ice varies, which is complementary to variations captured by ice type distributions. The proposed effort will also establish a rigorous statistical theory for evaluating changes in characteristic scales.