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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 PMO6VA, the operational radiometer (see also the VIRGO URL and Fröhlich 2006,2003). So, we start with determining the early increase correction for PMO6VA 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 UVdose at each point in time. With the data available at this stage, it is difficult to determine the corresponding coefficients for PMO6VB mainly because its exposure was important and varied during the first two years of operation. The same functions as determined for PMO6VA were therefore used, but with the corresponding exposure time and dose of PMO6VB. This is an approximation, and although further analysis showed that it is not really adequate, it has not been changed. With the corrected PMO6VB, 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 nonexposure 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 nonexposure 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 switchoff and on again, for which we have no explanation but need correction. We do not know the cause of these nonexposure changes, although the HF radiometer on NIMBUS 7 exhibits a similar behaviour (Fröhlich 2006).
Figure A.1: Daily ratios of the VIRGO radiometers to ACRIMII during two years centered on the SOHO vacations. The asterisk with the error bars indicate the mean and standard deviation for each comparison period of 72 days for both VIRGO radiometers. The lines are linear fits to the ratios of DIARAD and PMO6V over the time of the six comparison periods. The results as difference from the adjacent means and the ones determined from the slope are listed in the SoHO gap. Also listed is the standard deviation of the six 72day means which is used as an estimate for the uncertainty of the SoHOvacation bridging. 

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Figure A.2: Daily ratios of ACRIM (of 0811) and TIM (V9 of 0904) to VIRGO (V6.1 of 0812). The uncertainties of the slopes are formal statistical errors. The difference between ACRIM and VIRGO from minimum to minimum of cycle 23 (12.1 years apart) can be obtained by multiplying the slope given in ppm/decade by 1.21 and amounts to A/V1 =  39.8 ppm. 

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Figure A.3: Daily ratios of ACRIM (of 0811) and TIM (V9 of 0904) to VIRGO (V6.2 of 0904). The uncertainties of the slopes are formal statistical errors. The difference between ACRIM and VIRGO from minimum to minimum of cycle 23 (12.1 years apart) can be obtained by multiplying the slope given in ppm/decade by 1.21 and amounts to A/V  1 = 58.1 ppm. 

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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 PMO6VA for PMO6VB 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 PMO6VB, 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 81day 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 25day 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 timeseries. This assignment of the correction influences the final VIRGO TSI at most on time scales of 130460 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.