From the book that started off my career as a "Lunarist", something badly written early in the 20th century: …
This is a quote about the part the moon doesn't play in the weather:
Meteorology: Weather and methods of forecasting
Thomas Russell US Assistant Engineer.
MacMillan & Co New York 1895
Originally posted by Thomas Russell:
Weather records ..show that there is a somewhat greater tendency to rain in the quarter after full moon than at other times; there is a greater probability of rain with the moon in perigee than apogee.
There is no doubt in this relation of the moon and rain but the difference is not known even approximately and it varies for the different parts of the earth.
It is of no practical value for weather prediction. Attempts have been made to show that there is less cloudiness at full moon than at other times. The results are contradictory for different places.
The effect is either so small that the longest series of records does not show it, or it does not exist.
The affect of the moon on the frequency of thunder storms is inappreciable.
With regard to the change of the weather and the change of the moon in 5,000 cases examined, 1,800 showed a change of weather and change 3,200 no change.
The effect of the moon on the pressure of the atmosphere is very slight. There is an ebb and flow that is only perceptible near the equator by the most refined instrumental means of observation.
The difference between the least and the greatest pressure due to the effect of the moon is only 0.004 of an inch (of mercury in a barometer. These days we use millibar which is the pressure in millimeters.)
The pressure of the air is probably greater with the moon farthest from the earth and greater at quadriture than syzygies.
No predictions of any value can be based on pressure variations due to the moon.