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3. Data reduction and analysis

Figure 1 (click here) shows two days observed with filter set# 4, where a) corresponds to a clear day and b) to a dusty day. The typical shape of the curves are due to the well known effect of atmospheric extinction. The observed intensity I is given by:
where I0 is the intensity above the terrestrial atmosphere, M(Z) the airmass to be traversed by sunlight before reaching the photometer (normalized to unity at zenith), and Ktex2html_wrap_inline1295 the atmospheric extinction coefficient at tex2html_wrap_inline1297. Representing the photometric measurements by its instrumental magnitude defined in the standard astronomical way, m = tex2html_wrap_inline1301I, we find the well known Bouguer law:

Figure 1: Examples of two days observed corresponding to filter set # 4 (see Table 1 (click here)), a) corresponds to a clear day and b) to a dusty day

A linear fit to m-M(Z) gives the extinction coefficient tex2html_wrap_inline1307 during the time span used.

Before any fitting procedure was applied, data were selected to avoid days where strong transparency changes occurred, i.e. when dust appeared during the day making it partially clear and partially dusty, or vice versa when dust moved away from the observatory during the day. These days yield a variable extinction coefficient which is the result of mixed atmospheric conditions. In addition, days with early shutdown or late startup, power failure or other technical problems, uncompleted days or days with a large fraction of data gaps, have also been discarded. Because to this stringent selection, only 650 days approximately of the 1730 days of the whole campaign were selected for this work. For this reason, any percentage of clear or dusty days obtained with the data used here have no statistical significance.

In the analysis, each day is divided taking 4.5 hours before and after local noon. Points at the beginning and at the end of the day are rejected because the airmass computation is less accurate. After logarithmic transformation, the magnitude as a function of airmass (Bemporad formula, Golay 1974) for the two halves of the day are fitted to straight lines using a least-squares fitting procedure. This yields two extinction coefficients per day per channel together with the standard deviation of the fit which provides information about the dispersion of the points. In this way we separate the effect of the extinction coefficients during the afternoon that usually are 7% lower (Andersen et al. 1988b) than in the morning. This difference is believe to be caused by the influence of the African continent or by local convection effects. The extinction coefficients may also vary as a function of time during the morning and afternoon hours, this effect will be discuss at the end of Sect. 4.

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Up: Diurnal atmospheric extinction

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