features in these maps are outflows due to supergranules, surrounded by inflows. Figure \[figDataExamples\] also shows histograms of the maps. Both LCT and TD histograms are asymmetric about zero and have a nonzero skewness, which is well known [e.g., @Duvall2000]. The skewness of the $i$th map $X^{{(i)}}(\bx)$ is $$\begin{aligned}
\skewMap^{{(i)}} &= \frac{\langle X^{{(i)}}(\bx)^3 \rangle}{\sigma_{X^{{(i)}}}^3},\end{aligned}$$ where the variance is $$\begin{aligned}
\sigma_{X^{{(i)}}}^2 = \langle X^{{(i)}}(\bx)^2 \rangle= h_k^4 \sum_{\bk} |X^{{(i)}}(\bk)|^2.\end{aligned}$$ Here, $\bx=(x,y)$ denotes the horizontal location, $\langle \cdot \rangle$ is a horizontal average, $\langle X^{{(i)}}(\bx)\rangle = 0$ by construction, $X^{{(i)}}(\bk)$ denotes the horizontal Fourier transform of $X^{{(i)}}(\bx)$ – see Appendix \[appFourier\] –, and $h_k$ is the resolution in Fourier space. We use the same symbol for a function and its Fourier transform. We use $\skewData$ for the (mean) skewness computed from the entire dataset.

![image](fig1){width="\linewidth"}

The skewness depends slightly on disk position. In the following, we therefore only use the 11 locations that are closest to disk center for each segment, ranging from about $23\degr$ east to $23\degr$ west, where the skewness is approximately constant. For the entire datasets, this results in a skewness of $\hatmudata=0.277\pm0.001$ for the LCT maps, $\hatmudata=0.421\pm0.002$ for the TD maps, and $\hatmudata=0.512\pm0.003$ for the smoothed TD maps. @Duvall2000 