## 4. Temporal behavior of the mesocellsThe temporal properties of the mesocale flows were investigated using two different approaches: 1) temporal correlation coefficients applied to the and flow components. 2) identification and tracking of individual features in the divergence pattern. ## 4.1. Temporal correlationFollowing the method used by Brandt et al. (1994), we characterize the mesoscale persistence by the temporal correlation coefficient, applied to the measured and flow components as obtained with the windows 40 min. , and 60 min. , . As in Darvann (1991) and Brandt et al. (1994), we used the exponential form C(t)= C0 exp(-t/T) to get an 1/e decay estimation. Figs. 3a and b show, for each temporal window, the correlation coefficient "r" measured from various combinations of average flow maps as a function of the time difference between the maps. For example, the point at time difference = 10 min. in the Fig. 3 represents "r" measured between average flow maps no. 1 and 2, 2 and 3, 3 and 4, etc, and this for all the different time lags; the three plots in Fig. 3 represent the extrema (minima and maxima) and the average of the correlation coefficient values derived by this method.
In this correlation coefficient estimation, we selected the 40 and 60 minute temporal windows. This choice is a good compromise between the reduction of the seeing and granulation noise and the need to preserve of the intrinsic evolution of the flow pattern (see Brandt et al, 1994). Taking, like Brandt et al. (1994), the highest values to represent the correlations which are less affected by residual seeing, we find a characteristic lifetime for between 86-185 min and for between 111-144 min. which is from 3 times to 40% less than the values previously obtained by the author cited above. The high scattering of the correlation coefficient values, as noted in Darvann (1991) and Brandt et al. (1994), is the major uncertainty in the estimation of mesogranulation lifetime by this method.
However, the means for and are found around 40 min. and 60 min. respectively, which indicates that the correlation technique is sensitive to the temporal window used in the LCT. This method is a global statistical approach in which the correlation coefficient is directly computed from frame to frame so that (, ) are located at exactly the same (x,y) coordinates of the correlated sequence. Thus, it is natural that this method, computed over the entire field of view, should be affected by the temporal window. As will be shown below, directly tracking positive divergence by following the non negligible motions of the mesocell (in a small field) reduces influence of the temporal window (shape of the lifetime distribution) because of the cells' displacements. The and components which are indirectly correlated via the divergence values, are found at different locations (x0,y0),(x1,y1)....(xn,yn) during the mesocells' evolution, which tends to reduce the temporal window effects. The local proper evolution of the mesocells also reduces also these effects. Thus, the correlation coefficient is representative of both the cells' lifetime and their proper motions. ## 4.2. Direct trackingTo study the temporal characteristics of the mesogranules, we computed the divergence from the horizontal flows. We define mesocells as the positive diverging flows. The temporal and spatial windows used in the present study help to prevent the generation of "artificial" divergence cells (with a scale of mesogranules), produced by strong gradients in the flows. The animated sequence of divergence maps when superposed on the granulation pattern, reveals granular explosion in the positive divergence corresponding to the existence of mesogranules. This increases our confidence in the use of the previous mesocell definition when studying their temporal properties. In order to monitor the persistence of the divergence cells as accurately as possible, a time step of 10 minutes between two consecutive divergence maps was selected. There is some flow pattern overlapping between successive divergence maps, but the experiment revealed that some features evolve independently of the temporal window sizes. The divergence maps of the flow field are made up of cells with a - diameter, whose divergences values are found to be around:
The divergence values resulting from the 40 and 60 min temporal
windows are commensurate with the previous results published by G.
Simon et al. (1994). In the case of the 20 min temporal window, the
divergence value appears sensitive to the granulation expansion.
Darvann (1991) has demonstrated that granular evolution is the
dominant noise source in the measurement of large scale flows. A rough
estimation of the divergence for a symmetrical expansion
-. - with a horizontal
velocity of 1 km/s gives, in our case, a value of 6.2 10 Direct tracking of the cells during their evolution seems more suitable for our study. In order to track the cells during their life as accurately as possible, we focused our analysis on the three pairs of temporal and spatial windows given above. The divergence cell lifetime histograms are shown in Fig. 4 for two time sequences, 6 h 40 min and 3 h 00 min (Muller et al. observation 1992), resulting from flow computations with 20 min and (FWHM) windows. The two graphs are quite similar in shape peaking around 30 min with a distribution reaching up to 2 h 20 min. This reveals the existence of a predominent component, probably due to the exploding granules (68% of cells with lifetime 50 min.), and of a flat component due to the mesoscale in the long lifetimes. Fig. 5 displays the cell lifetime histograms, for the 40 min , , 60 min , and 40 min , windows. These distributions peak at around 30 to 40 min, with a respective maximum lifetime of 2 h20 min and 2 h 40 min. These graphs (and the associated integrated histograms), reveal that 70% of the cells have a lifetime . The highest local maximun of the histogram ( 60 min , pair) is probably a result of the convolution of the larger temporal window. In Fig. 5, the comparison between the cell lifetime histograms for the window pairs 40 min , and 40 min , shows that, contrary to our expectation, an increase of the spatial window from to shifts the lifetime histograms to the smaller values on the abcissa. It seems that the larger size of the spatial window tends to smooth the effect of a greater number of granules with their proper motions. Thus, the combination of the granule evolutions and motions with a large window seems to reduce the measured cell lifetime.
We observe that, regardless of the spatial and temporal window sizes the positive divergences represent half of the field with a high stability (49% ( = 1.5)%) during the entire time sequence (6 h 40 min). A surprising result concerns the change in the number of new positive divergence cells over time during our sequence. Indeed, this number varies with a period of 90 to 100 minutes, regardless of the spatial and temporal window sizes (Fig. 6). This variation is less marked for the 40 min. , pair. A verification of our data reduction process (alignment, filtering, LCT) revealed that it does not seem to produce a variation on such a time scale. It is thus like that this variation has probably a solar origin, but it has to be confirmed by another long time sequence.
The direct tracking method allows us to follow divergence cell motions with quite a high accuracy. Fig. 7 shows the measured displacements of the barycentre of cells with a lifetime , over the solar surface. We observe more random mesocell motions in the supergranule than were observed by Muller et al. 1992. These motions do not seem to tend in any particular direction with respect to supergranule boundaries, which have been delineated by NPBs present in our observation and by the flow field averaged over 6 h 40 min (Fig. 8). The horizontal velocities deduced from these proper motions are represented in the histogram (Fig. 9). The values of horizontal mesocell velocity lie between 0.1 to 0.9 km/sec, with a peaked distribution at 0.5 km/sec, which is consistent with previous determinations (Muller et al. 1992, Brandt et al. 1988, Simon et al. 1994). The distance covered by cells during their lifetime is between 1 to (mean = ) which corresponds to 25 to 50% of the cells' size.
© European Southern Observatory (ESO) 1998 Online publication: January 27, 1998 |