Time average of standard deviation (solid red), rms (dash-dot magenta), skewness (long dash blue) and kurtosis (long dash-dot black) of the temperature fluctuations for the models indicated in the panels. The convective boundary corresponding to the Schwarzschild boundary from the 1D initial model is indicated by the vertical solid line. The two vertical dotted lines in each panel indicate the extension of the penetration layer l_max based on f_k and f_δT, respectively. Similarly, the two vertical dashed lines correspond to l_bulk.