When I looked out of the window (our bedroom is situated at the back of the house), I found out that the sound that I had been assuming was rain on the roof, had actually been the crackling of hay on fire.
There was quite a bit of fire behind the house.
As I said, this was at the other side of the footpath, which is separated by a wide swath of grass that had been kept short, and our back yard -- so there was no imminent danger to ourselves or our property. Which alleviated the primal panic upon seeing a bona fide fire around your house somewhat.
This part of the grass had been cut last sunday, and the grass had been lying there ever since -- apparently they (whoever they might be) had not gotten around to collecting the hay. And it is quite a bit of hay too: the grass was over 50cm tall, and it runs all the way from the footpath to the highway a few hundred meters on. It has been quite warm, and it had spontaneously combusted.
It gave off quite a lot of smoke, which drifted towards the back of the houses further down the street. I guess someone over there slept with their window open, who had been awoken by the smoke and had called the fire department.
The compressor that had woken me was the compressor of the fire truck posted a few meters away from the fire, and there were firemen walking to and fro. When they started to use the firehoses (pressurised by the noisy compressor), they made short work of the fire. We went back to sleep.
Later on tonight, it rained. The forecasts predict more rain, so I guess that's the end of the bushfires behind our house.
ETA: klik informs me that the grass had been cut on Saturday, not Sunday.