In actual practice, we usually just call it a drought when surface and groundwater levels, and soil moisture contents, decrease significantly over a large region. How do we define significant is not obvious, and there is not a line in the sand where one side is drought and the other is fine and dandy. There are different levels of wetness/dryness which exist, as a spectrum of conditions, so a true drought has to see dry conditions which are extraordinarily unusual for the region (like 5% of less of the time will see such dryness). Kind of the opposite idea of the ten-year and hundred-year flood events (water levels that would be expected about once every ten years or every hundred years, statistically).
To declare a true drought, you have to have a very long history of conditions so you can say, with good statistical support, that this level of dryness is really unusual for the region.
There is a second, more practical, definition of drought which says that water replenishment rates (from natural precipitation) are inadequate to maintain the extraction needs for the region, and this lasts for many months. The weather is not providing for the water needs of the region, and this inadequate provision lasts for many months or more. Natural vegetation suffers as a consequence.
Clearly, you can see that some rain will not be good enough to stop a drought. You need precipitation rates to get back toward normal over time, so the water in the system can return back to normal levels and stay there.
Not that even a bit of rainfall won’t help at all. It will help, but it won’t end the problem on its own. It takes time to dry out the lakes and rivers and ground, and it takes time to provide enough water that the lakes and river and ground become as wet as it usually is.
A rainshower during a drought is like having a tiny sip of water when you are parched from the heat. It helps, a bit, but you will still be thirsty and you will still need more water, a lot more water, if you are to survive.
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