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Distribution of Supergranular Sizes

A gradient-based method of tessellation was applied to SOHO Dopplergrams and to Ca II K filtergrams in order to study the cellular pattern of the solar surface, in specific the geometric relationship between the tessellation and the chromospheric network/supergranulation. We found that for zero spatial smoothing and low temporal averaging the above data sets yield mean tessellation scales of 8-10 Mm for the SOHO Dopplergrams of 2'' pixel resolution and 14-18 Mm for K line filtergrams of 3.″2 pixel resolution. This difference is attributed to the dependence of the tessellation on the resolution of the images. The distribution of the tessellating tiles shows a broad, right-skewed spectrum, tending to greater broadness, symmetry, and larger scales when the image is smoothed. The skewness and kurtosis curves of the distribution of the tiles as a function of the smoothing show local peaks when the mode of the distribution approaches the traditional supergranular scale of 25 Mm. The values of skewness and kurtosis in this limit, 1.1 and 4.6, respectively, are close to the corresponding parameters for supergranular distribution derived independently, implying that supergranulation may be geometrically identified with the tessellation at the corresponding resolution. Time averaging also leads to an increase in length scale when averaged for up to 30 hr. In the case of Dopplergrams the size increases from 9 to 16 Mm and for the K line filtergrams from 18 to 23 Mm. This feature can be attributed to the suppression of short-lived, small-scale features. The effects of both spatial smoothing and temporal averaging can be explained in terms of enhancement of the supergranular signal.