I have a deep water well, with a length of 1/4" drip tubing, open at the bottom, taped to the pump 180' down. The other end of the tubing is connected to a gauge pressure sensor in the cabinet of my home control computer, about 10' above the top of the well. The computer periodically releases a bit of compressed air into the tubing to make sure the air-to-water interface is at the bottom of the tube, waits a bit, and records a reading. Seems to work great.
My neighbor has an online weather station that records rainfall rate and volume, and barometric pressure. Matches my local barometers. So I'm looking at his charts alongside mine, and it looks like rainfall makes the well level rise immediately... If that is true I have a serious contamination risk! But then I notice the well stops rising before the rain stops falling.
Long story short, it is the decreasing barometric pressure as the rain begins that correlates with the well appearing to rise. And it stops rising and actually drops as higher pressure fair weather begins to arrive. Measured in PSI, the changes are pretty much equal and opposite:
But why? More atmospheric pressure should affect the top of the well and the outside of the pressure gauge similarly, right? Yes it measures gauge pressure, not absolute pressure. If it was measuring absolute pressure, then it seems the barometer rising should make the well gauge rise. What could provide the opposite effect?
Could there be an effect from the water-to-air interface at the top of the water column in the well casing being about 170' below the air-to-air interface in the gauge at the other end of the tube? But it seems having heavier, more compressed air in that well column would increase the apparent pressure on that end, not decrease it.
I'm utterly stumped!
I guess this should be a comment to the answer by @Bob Jacobsen, but I wanted to add another chart...
So "rock porosity pressure" is due to gravity acting on water, plus barometric pressure acting on the water-to-air interface - outside the well casing. The same forces as inside the casing. (I guess there would be some additional capillary action outside the casing in the rock, but that would remain constant with barometric pressure?) The water inside can respond quickly to barometric changes, but the water outside the casing has to force its way through the "weathered sandstone" to slowly equalize its level. Makes sense!
The little chart segment shows the effect of water use, in summer when none is ever added and barometric pressure is constant in this part of California. (That spike is 1.7 PSI, huge compared to the barometric changes in the first chart.) Heavy use (~500 gal) takes days to equalize, while a daily ~50 gallons refills relatively quickly. I never thought to consider the same thing happens on a tiny scale as the barometer moves...