The discovery that the recorded values of T_HOT and T_COLD were in error has implications for narrowband data taken before the upgrades. The skydip reduction will be different with the revised values, and as we have shown, the CSO Tau relations change once this error is taken into account.
Unfortunately, it is very difficult to quantify the extent to which data (in terms of measured signal in mJy) will have been affected. It depends very much on the individual case. The error will be greater for sources observed at high airmass, and for those observed in wet and/or variable conditions. This error is minimal for 850-µm data, but can be significant at 450µm depending on how Tau450 was estimated. If the original CSO Tau relations were used, the error in the data is likely to be acceptable, however, observers are still encouraged to investigate their own case. On the other hand, if 450-µm skydips were relied upon, the error in the data could be very large indeed, especially in poor weather conditions as the skydip fits were increasingly poor with increasing Tau. The error also depends on the calibration source; if it was observed at a similar Tau and airmass to the target source, the effect of measuring an incorrect Tau is mitigated somewhat.
A preliminary investigation of a few sample cases indicates that some of the data may not have been that badly affected - at most a few percent at 850µm, and maybe 10-15% at 450µm. However, these numbers represent the `best-case scenario'. Under less favourable conditions, we have seen the error in the flux be as much as 10% at 850µm and over 50% at 450µm. In some extreme cases, the situation could be worse than this.
As mentioned above, quantifying this error is very difficult given the number of factors it depends on. Observers are encouraged to re-reduce observations, especially those taken at 450µm, using the new relations or skydip values, to see how badly their individual situation is affected.
A theoretical calculation can also be made to determine the extent to which an individual observation will have been affected. Consider observations of a source and a calibrator, reduced with two different methods of determining Tau. The difference in the source flux estimated by the two methods is:
Js1 / Js2 = eAs(Taus1-Taus2)-Ac(Tauc1-Tauc2)
where J is the above-atmosphere flux, A is the airmass, Tau is the zenith sky opacity, the subscript `s' refers to the source, the subscript `c' refers to the calibrator, the superscript `1' refers to the first method of estimating Tau, and the superscript `2' refers to the second method of estimating Tau.
Observers are further encouraged to use this equation, given the airmasses and Taus at which their data was taken, to get a feel for how large or small the errors are.