First of all, why is your calcium rising? You don't seem to be adding anything that would increase calcium (such cal hypo for chlorine -- you are using bleach).

As for the other parameters, I can reproduce what is going on in your pool by assuming the following (converted to the equivalent as if it were done every day):
ACID: You add 8 ounces of muriatic acid per day PLUS there is an additional equivalent of 10.5 ounces of muriatic acid that is probably coming from the rain.
BUFFER: You add 14.6 ounces (weight) of sodium bicarbonate every day. This is equivalent to the amount needed to raise alkalinity by 20 ppm over 3 days.
OUTGAS: You are outgassing about 5.5 moles (about 8.9%) of your total carbonate in your pool).
CHLORINE: You are adding enough chlorine equivalent of 2 ppm per day. I also assume that this same amount is used up through normal processes each day.

It makes sense that your alkalinity drops faster with rain since the raindrops probably churn up the water and increase the rate of outgassing and you have a lot of that due to the wind anyway. When you say that during rains the acidity rises faster, did you mean the pH rises faster (which is actually more basic, not acidic)? If so, then that doesn't make as much sense since there appears to be more acid getting added to your pool from some source beyond what you add because your pH is not rising as much as it should just from the outgassing (alkalinity change).

If you are getting lots or rain, then I would expect all of your parameters, including calcium and alkalinity, to drop from dilution. Again, the rising calcium is a strange thing.

Anyway, there doesn't seem anything terribly wrong with your situation. When you have a pool exposed to the environment, you're going to be at the mercy of that environment. Only a pool cover that would keep the rain out would help.

That's my two cents.

Richard