2 Data gathering and data validation

We evaluated the sunspot drawings of the KSO from January 1975 to December 2000. Within this period, 6900 observation days were available, which represents a data coverage of $\sim$73%. (Missing sunspot drawings are due to bad seeing conditions at the location of the KSO.) From this data set we derived daily, monthly mean and smoothed monthly mean hemispheric Sunspot Numbers.

Figure 1: Scatter plots of the daily (top panels), monthly mean (middle panels) and smoothed monthly mean (bottom panels) hemispheric Sunspot Numbers for the northern (left panels) and the southern (right panels) hemisphere. Calculated hemispheric Sunspot Numbers from KSO, $R_{{\rm n} {\rm , KSO}}$ and $R_{{\rm s} {\rm , KSO}}$, are plotted against the International hemispheric Sunspot Numbers provided by the SIDC, $R_{{\rm n} {\rm , SIDC}}$ and $R_{{\rm s} {\rm , SIDC}}$, for the period 1992-2000.

For each observation day, the Sunspot Number was counted separately for the northern and the southern hemisphere, respectively. From this "raw" hemispheric Sunspot Numbers we determined the relative fraction of the northern and southern component, "n'' and "s''. The final hemispheric Sunspot Number, $R_{{\rm n} {\rm , KSO}}$ and $R_{{\rm s} {\rm , KSO}}$, was obtained by multiplying the northern and southern fractions with the definitive International Sunspot Number, $R_{\rm i}$, of the day. With this procedure we ensure that the derived hemispheric Sunspot Numbers are normalized with respect to the International Sunspot Numbers, fulfilling the relation

$$n \times R_{\rm i} + s \times R_{\rm i} = R_{{\rm n} {\rm , KSO}} + R_{{\rm s}{\rm , KSO}} = R_{\rm i} .$$ (2)

Figure 2: Smoothed monthly mean Sunspot Numbers derived from KSO data (solid line) and reported from SIDC (dashed line), for the northern (top panel) and the southern (bottom panel) hemisphere.

To validate this procedure, we compared the derived hemispheric Sunspot Numbers, $R_{{\rm n} {\rm , KSO}}$ and $R_{{\rm s} {\rm , KSO}}$, with the International hemispheric Sunspot Numbers, $R_{{\rm n} {\rm , SIDC}}$ and $R_{{\rm s} {\rm , SIDC}}$, for the overlapping period 1992-2000. For comparison, we utilized the daily, the monthly mean and the smoothed monthly mean values of the International hemispheric Sunspot Numbers provided by the SIDC, online available at http://sidc.oma.be/. A detailed description of the SIDC data sets and the methods that are used for its determination is given in Cugnon (1997).

The top panels in Fig. 1 show the scatter plots of the derived daily Sunspot Numbers, $R_{{\rm n} {\rm , KSO}}$ and $R_{{\rm s} {\rm , KSO}}$, versus the corresponding International Sunspot Numbers provided by the SIDC, $R_{{\rm n} {\rm , SIDC}}$ and $R_{{\rm s} {\rm , SIDC}}$, for the period 1992-2000. The scatter plots clearly reveal that no systematic difference exists between the derived and the International daily hemispheric Sunspot Numbers. Moreover, the scatter turns out to be rather small. In Table 1 the results of the regression analysis are summarized. The slope derived from a linear least-squares fit to the data as well as the cross-correlation coefficients are very close to 1. For the standard error between the fitted and the original data we obtain $\sim$3.7, given in units of the SIDC Sunspot Numbers. Thus, it can be inferred that the derived daily hemispheric Sunspot Numbers very well render the International ones.

On the basis of the daily $R_{{\rm n} {\rm , KSO}}$ and $R_{{\rm s} {\rm , KSO}}$ we derived also the monthly mean hemispheric Sunspot Numbers for the period 1975-2000. In this regard, it has to be stressed that the KSO data set does not steadily cover the overall period; rather, 27% of the daily values are missing. Thus, to reconstruct those missing data we performed a linear interpolation on the daily values, separately for the northern and southern hemisphere, respectively. The middle panels in Fig. 1 show the scatter plots of the derived monthly mean northern (southern) Sunspot Numbers against the corresponding International northern (southern) Sunspot Numbers provided by the SIDC for the overlapping period 1992-2000. In general, the derived monthly data clearly follow the SIDC data, which is also reflected in the high cross-correlation coefficients and the parameters of the regression line (cf. Table 1). However, for the northern Sunspot Numbers one outlier shows up (May 2000), in which the observed daily data are obviously non-representative of the monthly mean. This case can easily be explained by the exceptional low number of observation days (5). It has to be noted that during the considered period of 26 years only for three months was the data coverage less than 11 days.

 

 

Table 1: Summary of the regression analysis of the KSO and SIDC hemispheric Sunspot Numbers 1992-2000. The analysis was performed for the daily, the monthly mean and the smoothed monthly mean northern and southern Sunspot Numbers. We list the cross-correlation coefficients (Corr.), the parameters obtained from the linear least-squares fit (const., slope), and the standard error between the fitted and original data (StE).

	Corr.	Linear Fit		StE
		const.	slope
daily N	0.991	$+0.009\pm0.103$	$0.993\pm0.003$	3.662
daily S	0.991	$+0.127\pm0.104$	$1.002\pm0.003$	3.668
monthly N	0.992	$+0.336\pm0.428$	$0.996\pm0.012$	2.792
monthly S	0.998	$-0.026\pm0.218$	$1.003\pm0.006$	1.414
sm.mon. N	0.999	$+0.150\pm0.088$	$0.975\pm0.003$	0.508
sm.mon. S	0.999	$-0.014\pm0.054$	$1.003\pm0.002$	0.303

To circumvent the problem that possible outliers of the monthly mean data also influence the preceding and succeeding months when calculating the smoothed monthly mean hemispheric Sunspot Numbers, we reversed the sequence of averaging and smoothing the data. First we smoothed the daily (interpolated values included) hemispheric Sunspot Numbers with a 365 days running average. Subsequently we calculated the monthly means of this annually-smoothed daily data. The bottom panels in Fig. 1 show the scatter plots of the derived smoothed monthly Sunspot Numbers for the northern and southern hemisphere versus the smoothed monthly mean hemispheric Sunspot Numbers from the SIDC. Both panels clearly reveal that the derived smoothed data closely match the SIDC data (see also the outcome of the regression analysis summarized in Table 1). In particular, the influence of the outlier of the northern monthly mean Sunspot Numbers is almost eliminated. In Fig. 2 we plot the time evolution of the derived smoothed monthly mean hemispheric Sunspot Numbers (solid line) for the period 1992-2000, which closely resemble the corresponding data from the SIDC (dashed line).

Figure 3: Smoothed monthly mean hemispheric Sunspot Numbers for the time span 1975-2000. The thick line indicates the northern, the thin line the southern Sunspot Numbers derived from the KSO data.