Distribution of supergranular sizes

A gradient-based method of tessellation was applied to SOHO Dopplergrams an d to Ca II K filtergrams in order to study the cellular pattern of the sola r surface, in specific the geometric relationship between the tessellation and the chromospheric network/supergranulation. We found that for zero spat ial smoothing and low temporal averaging the above data sets yield mean tes sellation scales of 8-10 Mm for the SOHO Dopplergrams of 2" pixel resolutio n and 14-18 Mm for K line filtergrams of 3 ".2 pixel resolution. This diffe rence is attributed to the dependence of the tessellation on the resolution of the images. The distribution of the tessellating tiles shows a broad, r ight-skewed spectrum, tending to greater broadness, symmetry, and larger sc ales when the image is smoothed. The skewness and kurtosis curves of the di stribution of the tiles as a function of the smoothing show local peaks whe n the mode of the distribution approaches the traditional supergranular sca le 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 resolut ion. 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 eff ects of both spatial smoothing and temporal averaging can be explained in t erms of enhancement of the supergranular signal.