Online Material

Appendix A: VIRGO radiometry: Comments on the difference between versions 6.1 and 6.2 and related issues of the analysis.

ACRIM, VIRGO, and TIM experiments all have at least one backup or reference radiometer per type which are less exposed and used as degradation reference for the operational one. The starting point of the evaluation are level 1 data, which are corrected for all known effects: e.g. temperature, electrical calibration, and distance (an example are the level 1 data in Fig. 1 of the VIRGO URL). The first step to level 2 is to adjust the operational to the backup, which is straightforward for DIARAD (left channel (L) is the operational, and the right channel (R) is the backup) by simply using the ratio L/R as measured and some adequate interpolation between the values of R once a month. The values in this way corrected are now called level 1.8. For PMO6V, this is more complicated because the backup was used at the beginning quite often and therefore also shows an early increase, which needs to be corrected before it can be used to correct PMO6V-A, the operational radiometer (see also the VIRGO URL and Fröhlich 2006,2003). So, we start with determining the early increase correction for PMO6V-A by comparing it with DIARAD, and the coefficients of the hyperbolic functions describing this early increase. All this is achieved in exposure time and the corresponding UV-dose at each point in time. With the data available at this stage, it is difficult to determine the corresponding coefficients for PMO6V-B mainly because its exposure was important and varied during the first two years of operation. The same functions as determined for PMO6V-A were therefore used, but with the corresponding exposure time and dose of PMO6V-B. This is an approximation, and although further analysis showed that it is not really adequate, it has not been changed. With the corrected PMO6V-B, we can determine the level 1.8 for PMO6V and we have two time series that can be compared. From this comparison, it became obvious that DIARAD has some non-exposure dependent change, which obviously cannot be corrected internally, but needs an independent time series, which is PMO6V. It was already stated in the original proposal that two different types of radiometer are incorporated to enable a clearer understanding of the behaviour in space, and indeed we have detected the unexpected non-exposure dependent change in DIARAD. An exponential function with a step over the unknown change during SOHO vacations, explains the difference very well; the presently used fit was finalized for V6.0 in November 2003 and the coefficients have not been changed since. Obviously it could also be that PMO6V is responsible for this difference, but comparison with e.g. ERBE confirms that it is caused by DIARAD (see e.g. Fig. 3 at the PMOD composite URL). There are also changes in DIARAD after switch-off and -on again, for which we have no explanation but need correction. We do not know the cause of these non-exposure changes, although the HF radiometer on NIMBUS 7 exhibits a similar behaviour (Fröhlich 2006).

Until now no external results have been used to evaluate the VIRGO radiometers. Only changes over the period during which SoHO was lost (25 June to 8 Oct. 1998), called SOHO vacations, need external help, since we can only determine the difference between the corrected DIARAD and PMO6V, but not its absolute value. To determine this correction, we use ACRIM-II for comparison during 122 days before the SoHO vacations and 131 days after the data gap, as a compromise between having enough data points and avoiding sudden changes in the ACRIM record. The normal operation immediately after the recovery lasted only 72 days, when the spacecraft was placed in spinning mode. This still provided accurate solar pointing, but no science data transmission until 3 Feb. 1999. Transmission of science data was not possible in this mode of operation because only the low gain antenna, but not the high gain antenna could be used with a very limited data rate. Although we have no data, the instruments were operated normally, which means that this period does not need to be bridged with ACRIM data. In order to have an independent assessment of the uncertainty we use six periods of 72 days for the comparison, three before the summer vacations and one just after, and two after the data gap as shown in Fig. A.1. The results are listed on the plot in the SoHO gap period. From the linear fit we derive a change of about 15 ppm which may be used as a first estimate of the uncertainty. This can be compared to the differences between the 72-day mean just before and after the gap, which show for PMO6V a change of similar magnitude, but for DIARAD a much smaller one. DIARAD has this strange behaviour after a switch-off and -on, and since this interruption is much longer than the three 1-2 days interruptions used to develop the correction (see e.g. Fröhlich 2003), the effect seems to be underestimated, and thus the applied correction is inadequate. Still another way to estimate the uncertainty is to use the standard deviation of the six averages before and after of 38.9 ppm. This rather high value is mainly due to the last point, which lies outside the distribution represented by the five remaining points, covering the period of about 280 days before and after the SoHO vacations. Although, the standard deviation of the five points is around 15 ppm, we use the larger value of 38.9 ppm for the uncertainty of the change over the SoHO vacation, which is an upper limit.

Shortly after introducing V6.0, it was realized that a slight trend (presently 0.025 ppm/day) in the ratio of the corrected (level 1.8) PMO6V and DIARAD values after the SOHO gap has to be added in the evaluation. At that time, it was attributed to DIARAD because the determination of the exponential function may have needed some adaptation to the data since the original determination. Independently, I started in early 2006 a reanalysis of the whole PMO6V radiometry, which was never completed, but showed that using the early increase coefficients of PMO6V-A for PMO6V-B made its correction too important, especially also since the cycle amplitude and the reanalysis decreased the trend between VIRGO and TIM by about 60 ppm/dec. Although the linear trend is only an approximation to the problem of PMO6V-B, it seems quite reasonable to apply the trend to PMO6V and not to DIARAD. This attribution of the trend represents the change from V6.1 to V6.2, which was applied following the discussions after the presentation of preliminary results at the AGU Fall Meeting 2008 (Fröhlich 2008) and its influence is shown in Figs. A.2 and A.3. The 81-day average centered around the minimum value in 2008 amounts to 1364.899 and 1364.014 for versions 6.1 and 6.2 respectively, with a difference of 83.7 ppm, which is close to the difference determined from the A/V slopes of Figs. A.2 and A.3. The directly determined value is, however, more relevant to the uncertainty in the stability of the VIRGO radiometry, if the version change can indeed be regarded as representative of this uncertainty.

The results of the correlation of TSI with do not change significantly from 6.1 to 6.2 and the results are well within the corresponding uncertainties. Thus, the version change does not influence this correlation and the final result with all points lying on or very close to the fitted line may indeed indicate that the estimated uncertainties may well be upper limits.

There is still another issue that has added to the confusion about the independency of VIRGO TSI, namely the use of ACRIM and TIM in the analysis of the difference between corrected level 1.8 data of PMO6V and DIARAD to provide a reasonable average for the final VIRGO data product. The absolute difference between the two VIRGO radiometers is about 700 ppm, but varies with time within about 80 ppm. The question is, whether a simple average is adequate or whether we can use another TSI record as a reference to decide which radiometer may be responsible for a given difference. As described in Fröhlich (2003), we compare the filtered differences (filter with 3 db points at periods of 130 and 460 days) of PMO6V and DIARAD to the reference, which is now a combination of ACRIM II, ACRIM III and TIM data, the latter since March 2003. From the daily difference and a threshold related to the standard deviation of the differences , a distribution function is defined as for or for or as , if none of the conditions apply. The time series  is then smoothed with a 25-day boxcar and applied to the residual r with  to PMO6V and with to DIARAD. The final VIRGO TSI is the average of the two -corrected time-series. This assignment of the correction influences the final VIRGO TSI at most on time scales of 130-460 days, but does not change the trend. Although this method reduces the noise of comparisons with other TSI, it may be better to remove it from the analysis and determine VIRGO TSI by means, which would definitively avoid confusion.