The fractal dimension is examined as a descriptor of ice roughness for more than 3000 km of under-ice draft submarine sonar data. The data can be considered to constitute a fractal set within a limited range of scales, as defined by the Hurst parameter H. It was found that 0.55<H<0.78 for scales of 3--15 m and 0.15<H<0.45 for scales of 15--75 m, beyond which H is near unity. From this it is seen quantitatively that sea ice on the large scale is smooth. The fractal dimension, D=2-H, at the smaller scales is similar to that measured by other investigators for individual ice features such as keels. The fractal dimension did not show any changing spatial pattern across ice regions, indicating that the scaling relationship is similar even when first-order measures such as the mean and variance of ice draft change. Therefore, D does not appear to be useful for partitioning the transect into homogeneous ice areas in the draft data examined. ¿ American Geophysical Union 1991