My purpose in presenting this data here is to validate the method, ensure I am explaining it clearly, and explore wider scientific ramifications. I greatly appreciate your assistance, including those questions which show my exposition was not understood.

The binomial function shows the probability of a randomly selected group of days receiving a specific amount of rain. I have checked the binomial distribution using excel with the following results.

Total Rainfall in Period (10003 days): 33132 millimetres
Average rain in random 345 days (1/29 or ~3.5% of total): 1142.5 mm

Probability (assuming random distribution) that a random group of 345 days will have
>1142.5mm: 50%
>1150mm: 40%
>1185mm: 10%
>1246mm: 0.1%
>1407mm: 2.2 x ten to the minus 15
>1787mm: ~0%

1787mm of rain fell on the 345 days when the moon was ten days before its Uranus conjunction. This result is way off the binomial scale, which gives results up to 1407mm. Even despite the non-random distribution of rainfall it proves the result is highly significant.

For reference, there were 23 days with more than 100mm rain. The top seven days had a total of 1515mm, of which only the first (326.7mm) and sixth (163.8mm) were in the anomalous Moon-Uranus ten day group. Next highest in this group was the 26th rainiest day (93.6mm) followed by the 50th rainiest (69mm). (Just for interest, I am not sure how to calculate the probability that the six rainiest days will be in a random group of 345 days).

The Sun-Moon cycle may well be more anomalous than the Uranus finding. Over the study period of 27 years, at the first quarter of the moon, a total of 1541mm fell on day 6 and 1620mm fell on day 7, having two days in a row with more than a foot (399mm & 478mm) above the average rain of 1142mm. These Sun-Moon results are separate from the Uranus effect.