THE DISCRETE WAVELET TRANSFORM AND THE SCALE ANALYSIS OF THE SURFACE-PROPERTIES OF SEA-ICE

The formalism of the one-dimensional discrete wavelet transform (DWT) based on Daubechies wavelet filters is outlined in terms of finite vec tors and matrices. Both the scale-dependent wavelet variance and wavel et covariance are considered and confidence intervals for each are det ermined. The variance estimates are more accurately determined with a maximal-overlap version of the wavelet transform. The properties of se veral Daubechies wavelet filters and the associated basis vectors are discussed. Both the Mallat orthogonal-pyramid algorithm for determinin g the DWT and a pyramid algorithm for determining the maximal-overlap version of the transform are presented in terms of finite vectors. As an example, we investigate the scales of variability of the surface te mperature and albedo of spring pack ice in the Beaufort Sea. The data analyzed are from individual lines of a Landsat TM image (25-m sample interval) and include both reflective (channel 3, 30-m resolution) and thermal (channel 6, 120-m resolution) data. The wavelet variance and covariance estimates are presented and more than half of the variance is accounted for by scales of less than 800 m. A wavelet-based techniq ue for enhancing the lower-resolution thermal data using the reflected data is introduced. The simulated effects of poor instrument resoluti on on the estimated lead number density and the mean lead width are in vestigated using a wavelet-based smooth of the observations.