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If position unchanged at S13°00.0 - W 163°00.0 , then get refracted distance between Alnair and Peacock at 1,105.3' (vs: 1,107') with a scaling factor at 0.2613° / mm (vs. 0.2617° / mm).

Then the Alnair height becomes 34°03' (vs. 34.06') yielding UT (Alnair) = 05:53:44 (vs 05:53:00), and

The Peacock height becomes 16°43' (vs. 16°45') yielding UT (Peacock) = 05:54:31 (vs. 05:53:54).

Here, in addition to the reduced updated scaling factor decreasing both heights, the most significant effect here seems to be the "introduction" of DIP, since it significantly decreases both unrefracted heights, then delaying UT by about 40 seconds.

Hence with no change in position, (13°S - 163°W) , fine tuning our environmental conditions adds up about another 40 seconds to our initial UT determination which now becomes : approximate UT at 05h54m with the same uncertainty of +/- 6 minutes of time.

Only remains the effect of a change in position if any...

For Longitude, it will vary by 240 s of time / 1° of longitude . Given the atoll dimensions, any Longitude correction would imply an extra correction under one minute of time. To be on the safe side, let's say the same for Latitude, hence any position update is likely to give an overall correction under 1m20s of UT time. This is well under our estimated uncertainty, but might be worth taking in account so as to modify our UT mean value accordingly.

Kermit