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Astron. Astrophys. 330, 1136-1144 (1998)

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3. Data reduction

Even though the solar granulation is directly visible on the sun's surface, the detection of the mesocell flows requires indirect methods such as the Local Correlation Technique (LCT) (cf. November, 1989). The use of such a method implies the careful adjustement of certain space and time parameters. Different LCT and feature tracking codes have been developed (Strous 1994, November 1988, Shine in Simon et al. 1988) in several institutes, and have recently been compared on the same data set (Simon at al. 1995). Particular care has to be applied to the selection of the pixel sizes with respect to the derived displacement between successive frames (Shine, Private communication 1997). An oversampling of the original data makes it possible to obtain reliable results, depending of the LCT method used, either an underestimate of flow velocities or excessive noise (Shine, private communication 1997). In our case, we used the LCT developed by L. November (1988), which is one of the methods suspected to underestimate flow velocities. The data pixel size of [FORMULA] seems to be a reasonable compromise for a time step of 45 seconds between successive frames, leading to shifts from one frame to the next of less than one pixel. In this case, the flows obtained by November's LCT are quite good (Simon, private communication 1997).

Horizontal flows have been computed by both LCT algorithms (November and Shine), on the same data set provided by our present observation. The same LCT parameters were selected in order to compare the flows: a time delay of 45 s., a spatial window of [FORMULA] and a temporal window of 40 min. Fig. 1 shows [FORMULA], [FORMULA] and the divergence amplitudes of the flows as computed by both LCT algorithms from November (Fig. 1, top) and Shine (Fig. 1, bottom). In what follows, [FORMULA], [FORMULA] and divn represent the [FORMULA] and [FORMULA] components and the divergences calculated from November's LCT while [FORMULA], [FORMULA] and divs represent the same components as calculated by Shine's LCT. Fig. 1 shows clearly that November's LCT algorithm tends to smooth flows when compared to the Shine's LCT algorithm although the same parameters have been used in the flow calculation.

[FIGURE] Fig. 1. Velocity components [FORMULA], [FORMULA] and divergence maps (from right to left) calculated by the LCT algorithms of November (top) and Shine (bottom) with a temporal window of 40 min, a spatial window of [FORMULA] and a time delay of 45 s. White pixels in the [FORMULA] and [FORMULA] maps represent for positive velocities, while black pixels represent negative velocities. In the divergence maps (Fig. 1, right side, top and bottom), the positive divergence flows are white and the converging flows are dark. The field of view for [FORMULA], [FORMULA] and the divergence maps is [FORMULA]. The tick marks are [FORMULA] apart.

Over the entire field of view, the correlation coefficients are found to be equal to: [FORMULA] - [FORMULA]: 65%, [FORMULA] - [FORMULA]: 56%, divs-divn: 63%. These correlation values increase up to 95% in well defined flows such as the divergence or convergence areas. A detailed inspection reveals smaller correlation in low velocity amplitude zones which are associated with the less well defined convergence area (Fig. 2a-d).

[FIGURE] Fig. 2a-d. Plot of the moduli and the relative orientations of the flows vectors, as calculated by the two LCT algorithms (November and Shine), using the same reduction parameters: temporal window: 40 min., spatial window: [FORMULA]. a  in the diverging flow region: relative tilt angle between flow vectors (November and Shine) versus the modulus of the velocity vectors as computed by Shine's LCT algorithm. b  in the converging flow region: relative tilt angle between flow vectors (November and Shine) versus the modulus of velocity vectors as computed from Shine's LCT algorithm. c  in diverging the flow region: modulus of the flow vectors as calculated by November's LCT algorithm versus the modulus of the flow vectors as calculated by Shine's LCT. d  in converging flows region: modulus of the flow vectors as calculated by November's LCT algorithm versus the modulus of the flow vectors as calculated by Shine's LCT.

Fig. 2a shows the relative tilt angle between velocity vectors resulting from the two LCT algorithms (November and Shine), in diverging areas. These relative tilt angles are plotted with respect to the velocity modulus (taken as reference) calculated by Shine's LCT. The mean tilt angle is found to be [FORMULA] while the dispersion of the values is [FORMULA] [FORMULA] around this mean regardless of whatever the velocity modulus.

Fig. 2b shows the relative tilt angle, as in Fig. 2a, but this time in converging flows. The degree of relative tilt angle dispersion is very high for velocities with amplitudes lower than 400 m/s. This tends to reduce the correlation coefficient on [FORMULA] and [FORMULA] components, as calculated by both LCT algorithms (November and Shine), over the entire field of view.

A comparison of the velocity vector moduli as calculated by the two LCT algorithms shows a linear correlation (slope = 0.3) of these moduli up to 700 m/s (Fig. 2c). Beyond this value, we detect an underestimation of the high velocity vector moduli in Fig. 2d (saturation effect) as computed by November's LCT with respect to the velocity vectors computed by Shine's LCT.

This underestimation is confirmed by a comparison of the histograms of [FORMULA], [FORMULA] and [FORMULA], [FORMULA] components:

[EQUATION]

The divergence maps deduced from the flow calculated by both LCT algorithms (November and Shine) are quite similar in Fig. 1 (right side) as indicated by the correlation coefficient above. The differences between these two divergence maps are mainly the reinforced divergences in the Shine algorithm flows and the existence of one new small divergence in the Shine algorithm map (left corner) which is not present in the November algorithm map. These noise effects are due to both the saturation of the velocity amplitude in the November's LCT algorithm, and to the relative tilt angle between the flows as calculated by November and Shine's algorithms.

From our detailed comparison of the flow as calculated by the two different LCT algorithms (November and Shine), we conclude that the flows are highly reliable except in regions where the flows have very small amplitudes and the vector orientations are determined with a large error. This tends more or less to reinforce some existent positive divergences and, in our case, to generate one small positive divergence which represents a difference of 5% in the number of the structures detected between these two approaches.

A quantitative determination of cell flow lifetime is commonly obtained by standard methods (temporal correlation, enumeration, etc...) which have been extensively discussed by Alisandrakis et al. (1987) and Title et al. (1989). For mesoscale flows, as in the case of granulation, cells split and suffer premature death when they collide with the supergranule boundaries,so that their intrinsic lifetimes may be somewhat longer (Muller et al. 1992). Nevertheless, the individual tracking and identification of divergence cells (mesoscales) are much easier than for granules. The divergence cells are well defined and few of them mix together or split. It has been estimated that 2 to 3% of the mesocells split during our sequence analysis. Unlike the case of solar granules, cell divergence does not develop from existing cell fragments, which make it easier to measure the lifetime of individual features by visual identification and in turn makes the results quite reliable.

The LCT method requires in particular the adjustment of two parameters, the temporal and spatial window sizes (L. November, 1988). The choice of temporal window depends on the phenomena, on which we would like to concentrate in our study (meso, super cells flow see Darwann 1991), and also on the oscillation, noise, and seeing filtering that we require. Early attempts used temporal window sizes of 20, 40 and 80 minutes to study the mesoscale properties in order to reduce the effect of the 5 min oscillations and seeing (L. November 1988, Darvann 1991, Muller et al. 1992). In the present study, we performed flow computation with 20, 40 and 60 minutes temporal window sizes. An FWHM applied to [FORMULA] and [FORMULA] gaussian window was used for the tracking.

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© European Southern Observatory (ESO) 1998

Online publication: January 27, 1998
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