The primary component of your water's total alkalinity are substances called dissolved inorganic carbon (DIC) of which there are three species - dissolved CO2 gas, bicarbonate ion (HCO3-) and carbonate ion (CO3--). At normal pool pH, the bicarbonate ion is the most abundant species. When you add acid to a pool, the bicarbonate ion reacts with the acid and forms lots of carbonic acid (H2CO3), the same substance in an unopened can of pop. However, carbonic acid is not stable in water at normal pool pH and standard atmospheric pressure so, like a bottle of pop, it breaks down into water (H2O) and dissolved (CO2). Since the pool water is over carbonated relative to atmospheric carbon dioxide levels the natural driving force is for CO2 to want to leave the water (much like how bubbles of CO2 want to leave pop). Stagnant water and still water surfaces are not very good at transferring CO2 to the atmosphere so anything that can mix up the water and break up the surface increases the rate at which CO2 leaves the water. That is the process we call aeration.
Now, when CO2 does leave the water there's a second reaction that occurs which we call an equilibrium reaction. The rest of the bicarbonate ions sitting in the water are now in a new state of equilibrium with the higher levels of dissolved CO2. When that CO2 now tries to leave the water, the bicarbonate ion says -
So the bicarbonate ion wants to stay in equilibrium and it does so by consuming a proton (H+) and forming more carbonic acid which then dissociates into water and dissolved CO2. The process of consuming a proton causes the pH to increase.
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